close

Вход

Log in using OpenID

embedDownload
CENTRAL BOARD OF IRRIGATION AND PO
ER
NEWOEI.HI
.Proceedings
Forty-Thi,
Annual Research Session
Dehra Dun, U.P.
19·21 June 1973
Volume IV .. B-Power
Technical Papers on
bcll·5
C·B·\· P
TRANSMISSION
COMMERCIAL ASPECTS/GENERATION
Publication No. 121
New Deihl
Mny 1973
PROCEEDINGS
FORTY-THIRD ANNUAL RESEARCH SESSION
Dehra Dun, U.P.
19·22 June 1973
,
.. (
.,
\
(
I
,
Volume IV-B-Power
Technical Papers on
TRANSM ISSION
COMMERCIAL ASPECTS/GENERATIO~
Publicat ion No . 121
CENTRAL BOARD OF IRRIGATION AND POWER
New Delhi
May 1973
U. A. . BANGALORE
UNIVERSITY LIBRARY
, 18 MAk ,-",
ACC.
r
"0.-.!Jj~;:~
___
.04••• •
.i
CL. NO.....~ ___ •. _.......... .
NOTE: The statements and opinions expressed in this publication are not necessarll)
those of the Central Board of Irrigation and Power.
FOREWORD
An important function of the Central Board of lrrigation and Power
is tbe coordination of research on Jrrigation, Power and allied subjects and
the dissemination of the re ult of such research . The Board provides a
forum where infonnation on various activities in the country relating t
Irrigation and Power can be presented and discussed. The Board annually organi es a Research Session at which represen tatives f all the
research, design and construction organisations in the country u well a
representatives from educational in t.itution . meet to con ider and dis u s
the activities in the field of Irrigation and Power. Papers are invited on
all topics related to the Irrigation and Power sector to channelise the
discussions.
The Forty-third
at Dehra Dun, U.P.
will be discussed at thi
pre-session proceedi ng
Annual Research Sessi on is scheduled to be held
from 19 to 22 June 1973. The 74 papers which
Session have been compiled in five volume
f the
on various topics as Ii ted below:
Volume [
Hydraulics
(a) Design, Construction and Performance of
Irrigatjon and Power Structures
(b) Hydraulics of Open Channel Flow
(a) Model J nvestigations for Hydraulic Struct-
Volume JJ
Hydraulics
ures
(b ) Ground Water Hydraulics and Hydrology
(c) Coastal Engineering and Tidal Hydraulics
Volume III
Concrete and
Soil
(a) Concrete, Ma sonry and Pozzolana
(b) Soils and R ck Mechanics
Volume IV (A )
Power
(a) Protection
(b) Distribution
(c) Radio Interference and Corona
Volume IV (B )
Power
(a) Transmission
(b) Commercial Aspects/Generation
(i)
(iiJ
The General Reports on these papers will be issued separately before
the Research Session . The post-session Proceedings will be issued subsequently. Written discussions received by 30 September 1973 will also be
included.
We hope that these pre-session volumes will be of immense benefit
to our Researchers, Designers, Construction and Maintenance Engineers
to prepare for fruitful discussions and to participate actively during the
Session.
C. V. J. Varma
New Delhi
May 1973
Secretary
Centra] Board of Irrigation and Power
CONTENT
PAG
(i)
FOREWORD
TRANSMI
ION
Step and Mesh Potentials at High Voltage
Non-uniform Soil
(2)
Efficacy of Dampers and Improved Techniques of
Vibration Control in Transmission Lines
Nagin Singh Grewal, S.L . Goyal
and Klrpal Singh
II
(3)
Stability for Developing 400 kV E.H .V. System
O.D. Tllllpar
22
(4)
Performance of 110 and 220 k V Lines
£.S. Narayallall
31
(5)
Preventio n of Flashover in Polluted Insulators by
Conducting Bands
P. K. Mukllrrjel'
39
(6)
Switching Surge Flashover or Polluted Insulators
J.R. Bi.rwos
42
(7)
Optimal Load-Flow Analysis
R.N. Dhllr alld P.X. MIIJ...herjec
48
( 8)
Sparse Matrix Technique for Solution of Load
Problem by Newton·Raphson Method
P.K. Chattopadhyay, R.N. Dhar
alld G.P. PurkyaJtha
53
(9)
tations in
B. Tllapar and J.K A rllra
(I)
Flow
Transmi5sioll Line Towers of Tubular Sections
(10) Power Network Planning by Computer Simulation
(11J Transient Analysis of Power Systems Using Fourier
and Fast Fourier Tran formers
T. V. Gopalall alld
T.D. Mohan Babu
64
B.N.N. Iyengar
and D.K. Subramanian
75
B.N.N. Iyengar,
K. Partha,farallzy. B.S. Ashok
Kumar alld G.C. Kothari
79
COMMERCIAL ASPECTS /GENERATION
(12) Tariff Principles for Intercbarge/Exchange of power
between States under Integrated operation
G.R. Ramachandran
(13) Cracking of Hydro-Turbine Runner Blades
L.R . Malik and M .L. Chaw/a
107
(14) Micromachine Modelling uf Generators
S.M. Peeran and Sunil Kumar
121
(jjj) - (iv)
93
TRANSMISSION
•
Step and Mesh Potent ials at H igh Voltage Stations in
NonMun iform Soil
B. THAPAR
J. K . ARORA
ProfeS50r and Head
Departmcnt of Elcctrical Englncering. Punj .. b
AS~O';'Rtc Prorcssor
nglllccnna
olk~c,
handignrh .
Y~op 1
Horizontally huried condUClOrs form the basic groundinl1 sptt·'" ill hi/ih
voltage stations. A method is rll'l'elopl!d to dl'lermine th e maximum .Itep and mesh
potell/ials produced by a groulldi,~g grit! cOll1pri.I'jnK IOlll{ paral/('I cOllductors
buried neor the swface of the "arth III 'lOn-till/form .\oil. A two . laYl'r .flrarijiclllioll
ofofe S"O/ i'ls- assumccr, lI'rlrcr! rlllr n"pn?sl:1I {mos{ oJ {fie sort ('olllffttol/," tfiat 1I0f/IIally occur in practice. The motflt'ma,ical expressions ohtainC'cJ/or the m{[):i",rUlr
step and mesh potentials arc evaluateq lVith the 1m' of (I digital c(llI/puter for
l'arious ralues of the parameters usuaf/;. ellcountered ill prartice Ulul the oppar(.'lIt
resistivities of the soil to he used to determifle step ali(I 1I1('.I' fI po/elltials an'
ohtained.
1.
I nt roductioD
1.1 Under fault cClnd itions , th~ flow of cu rrent to
earth results in potentia l gradients within and arOllnd
a su b-station . The maximum potenlial gradients alon8,
the gfClund surface may be ~.o high as to ~n~anger th e
life of a per on in the sub·statlOn area It ,IS Imrortant
to investigate the step and mes~ P?tentlals and keeA
their values below the tolerable limIts through proper,
design of the grounding system . In th e stud ie~
devoted to the pre-determination of the potentiul gradi ·.
ents in high voltage sub-stations. it is assumed that the:
resistivity of the soil is uniform(l)(2). Under cerlail'\
conditions. where oil i non-uniform, this assumptlol'\
can be misleading. To obtain correct re ults analYlica'l
expressions are developed in thi!. paper to d~termll:tC:
the potential gradients in high-voltage stall~ns ITI
non-uniform soil. The mesh and step potentIal s are:
evaluated for different values of the variable parameteri
usually encountered in practice.
2.
Grounding y tem
2.1 In most high-voltage s\\ ilchyards basic ground_
ing system is formed by a grid of conductors
buried horizontalJy near the surface of the earth,
Methods for determining grounding resistance of SUc}l
n grid in non-uniform soil are available( n)(l). but the
determination of the rotential gradient~ involve
math ematica l dimculti e~ and has nOI yel been inves ti·
gated .
ror mathematical exrediem'y the type of grid
for analy~i s co n6ish of" co nductors of radius
',buried in parallel lines with horizontal ~ p8cing D ,
at a der1h " , helow the flat grou nd I>urface. The
co nductors are assumed to eXIt:nd 1>0 far that the end
effects can be negle ted at place. where potential
gradient are determined . The lengt h L of the grid
2.2
~elec t ed
is D(n
I) .
2.3 Experimental le~ts have proved that in uniform !>oil" omitting Ihe crosll-connection~ in the
grounding grid and neglecting the end effects of the
remaining parallel co nductors usually inlroduce an
error of Ie s than 10 percent in the mesh pOlentialli(Z)
It is , therefore, expected that the type of the grid
elected will give results which are quite c10lte to tho e
for the practical grid .
3.
Re i tlvity of the Soli
3.1 The resistivity of the earth varies within
extremely wide limits between one and 10,000 ohm-
2
THAPAR AND ARORA
k::
~ v~ v......
,,~ ...
~
200
(:..-0' ~
SO
20
I
~V
~
~~
....
~
ztw_
a:>
<o..t-
2
t- r--
0'5
~~
-
\'-
~"
0..",
<-
'"
w
~
a:
0·5
0·2
0'1
0'05
~
0·02
2
'·0
10
5
0 '0 1
50
20
100
4.2 If both air and the bottom soil strata have
infinite resi tance, each of the images di charges into a
uniform medium of resistivity PI, a current equal to the
actual ground current of the wire onductor. The
potential gradient in this image system is equal to its
true potential gradient in the upper layer of the soil.
If P2 IS not equal to infinity, a modification of thi
method is possible. In this process, whenever an image
is taken on the boundary between the top and the
bottom strata of the soil, the currents of the images
change by the ratio
u= P2- P.
1000
. .. (1)
P2+Pl
0 ·2
t'-....
I'-..
0-1
o
5
~ ~ I-.... >-
100
Thus, the images are not carrying equal currents now.
The whole space of the image system is still of resistivity equal to PI and the potential gradient for this
idealized condition still yields its true value in the
upper layer of the soil for the actual conditions(B).
5. Analysis
S/h
FJGURE J
I
Valucs of apparcnt resistivity measured
witb the lour-electrode method.
meters. It depends on the type of soil, chemical
conlents, moisture and temperature, and varies with
distance as well as with depth. The variation of the
resistivity with depth is more prominent because of
the non-uniformity of the sub-soil strata. A convenient
method of representing the variations of the soil resistivity with depth, that can be adopted in many cases, is
the two layer representation(6). The earth is assumed
to consist of a surface layer of certain depth It and
resistivity PI' and a lower layer of infinite depth and
resistivity p~.
3.2 PI> P2 and It at a particular site can be evaluated by making measurements of apparent resistivity by
the four-ele trode method. The electrode spacing S is
varied from about 2 111 t a large spacing in convenient
steps. The tc ts are conducted along various direction s
in the propo ed sub tation area and repeated over a
long period of time. From the average test data a
curve showing apparent resi tivity ver us probe spacing
is plotted on log-log graph paper. Pi is then obtained
by extrapolating the curve to where it cuts the ordinate
of zero probe spacing. The apparent resistivity curve
drawn on proper scale is matched with the curves
shown in Figure I and P2/pl and S/" are determined.
4. Method of Image
4.1 The method of images is used for determination of the potential gradients in the upper layer of the
soil(6). There are three materials involved, viz.• air
with resistivity equal to infinity. top soil layer of re isti.
vity Ph and the bottom soil layer of resistivity PI'
Since both boundary planes between the three materials
produce images, there results a two-way infinite
sequence of image .
5. 1 Four of the II conductors of the grid and a
few of the infinite images are shown in Figure 2. The
conductors are designated ai' a~, as, etc. Double sub·
cripts indicate the images of the conductors. The
di stance of the images from the surface of the ground
and the current they di charge per uni t length into the
uniform medium of resistivity PI are indicated in the
figure.
5.2 The potential drop within the grid is assumed
to be negligible, as compared to that within the soil
and it is assumed that D and h are much greater
than r .
5.3 Consider a point p (x, O), where the x-axis is
perpendicular to the conductor and is on the snrface of
the ground and the y-axis passes through the
conductor.
Let
j".,Current flowing into the ground per unit
length of the conductor.
o= Current per unit area at any point due to
the current discharged by the conductor
or its images.
x= Unit vector in the direction of x.
5.4 The current density at P due to the current
discharged by conductor a 1 and all its images is :
." (2)
STEP AND MESH POTE TlALS AT HIGH VOLTAG8 TATIO
o
o
ON-U I
o
o d,.
RM
OIL
3
f
I
21'1 2
o
o
o
od"
21'1 ,
o
o
o
?
~
d,.
I
Zh z
\
d
~
d,
P2
U1
d
j.d
cl~'l 0
5
,o
.- .-- •
d,.
d)
dl
•
0
0
0
o ci"
0
0
0
o d o)
o
o
o
o
o
o
FIGURE 2:
._
8 = _!_[~ ~
"
7t
L. L.
I
£ " ,,,
L. L.
1G. dx
... (4)
o
m
u [(k -::l)D -:_x] .
[(k-1)D ;- xp + (2mh + hl)~
+
"
00
= ~ ~~
27t [
k
~
k - Im
11
11'1
In
[(k- l )D t- l]a-l (2mh h l )1
.
[(k- I)DF t (2m" -t 111)2
0
00
00
~ ~
od"
is given by :
k=lm = O
n
d,
Grounding grid In two-layer ellrth .
5.5 Similarly, current density at P due to conductors a2 , a3 , a•• etc. , and all their images can be found.
The total current density at P due to the n conductors
and their images is in the direction of x . and is given
by:
n
02
tim [(k - I )D + x]
]
[(k - l )D -l- xF + (2mh - /h r
+
k=l m= 1
..
(3)
The potential gradient at x is :
The maximum potential gradient will be in the direction of x. Taking the distance between 0.6 m (2 ft)
of a person as one meter. the maximum step potential
2:" 2:
k- I m
[(k - I)D IF + (2mh- hl)2 ]
[(k - I )DJ ~ (2mh - IrJ)l
I
.. . (5)
5.6 Maximum me, h potential is the potential drop
from the condu ctor to a poinl (- D/2,O) on the surface
of the earth .
(6)
where, E., = Potenlial drop between (0,0) and ( - D/2.0)
4
THAPAR AND ARORA
and
E,, = Potential drop between (0,0) and (O, - h)
-t
r)
The maximum step and mesh potentials in uniform
soil can be expressed as :
(12)
m ( (kD - 1.5D)2 + (2mh+hl.j2
u n (kD- DY -t (2mli ;- hl)~
00
~ ""
+L L
um I (kD- 1.5Df+ (2 mh - h 1)2 ]
n (kD- D)~+ (2mll-hlY
k -lm= O
.. . (7)
5.7 Since 171 is much less than D, the componeDt
of current density due to conductors other than al and
their images in the y direction, vertically between
conductor a l and the surface of the ground, is negligible. Therefore, while evaluating the value of Ell the
contribution of only al and its images is considered.
5.8 The current den ~ ity at a point Q(O, - y), vertically above the conductor 01 due to a l and all its
images is given by
m
u
}
- -=2-m--;-h-:'
+";'I-+-)-'
'2:
00
m
{ - 2mh u hl+y -
2m}:~hl-y
m
1]
+
.. (l3)
where, K. u and K",u are the factors calculated considering the soil to be of apparent uniform re istivity Pal and
Pam respectively. K." and Kmu can be determined from
the expressions for the step and mesh potentials by
substituting Pl = P1' Pal and P..", can then be obtained
by comparing Equation (10) to (13).
P".= ptK./K.u
(14)
(15)
5.10 The variables in volved in the expressio ns fo r
determining 1\. an d K", are D, r, h, hI, P2, PI and n.
For several values of these va riables the calculations
were carried out on the digital compu ter IBM \ 620(7).
The radius of the conductor. r, was taken as I 0 em
and the depth of burial of the grid , hI , was chosen to
be 0.3 m. The values of the other variables were
taken as given below:
Separation of the grid conductors, D, 1.3, 6, 10 m.
Height of the tipper layer, h. 2, 5, 10, 15 m.
... (8)
m= l
Number of the grid conductors, n, 2, 3, 5, 9.
p ~/ P1,
0.01,0.1,10.100.
Therefore,
o
f
£,, = (>1
~" d)'
- 111 + '
i~ [i
=
m= O
00
2:
lll
u
III
.. . (9)
5.1 J The values of Pn. and Pam are given in Tables 1
& 11 respectively. From Tables I & II, the charts
shown in Figures 3 & 4 for Pas and Pam respectively are
developed , with the use of which Paa and P.. ", at a
certain site may be determined. To use the chart
select L /(h v' D) of the grounding grid on the Jeft hand
ordinate and follow along a horizontal line where it
intersects the required line for the ratio P2/p1 . Proceed
vertically to the intersection with the curve representing
the number of conductors in parallel, then proceed
horizontally to the left ordinate axis and read the ratio
Pa./P1 or Pam/PI as the case may be.
m:::: l
Hence E", •• /o is determined from Equations (6), (7)
& (9).
5.9 The expres ions for step and mesh potentials
can also be written as
(l0)
(11 )
5.12 The range of the different variabJes given on
the chart is adequate to cover the dimensions of parameters of grounding grids for high voltage stations and
most of the soils normally encountered in practice.
5.13 The value of apparent resistivity, p... to predetermine the resistance of a grounding grid is found
to be quite different from the values of p... and (>.. '" for
the grounding grid in non-uniform soil. The presence
of a lower strata of soil of lesser conductivity tends
to increase the maximum step potential and decrease
5
TEP AND fESH POTENlIALS AT HIGH VOLT GE TATIO
I
I
/
1
[V
1
1
3.0
5
VV
/V
1.8
~/
II ; y
V
V
/
7
/
V
I
/
;~ ~
1,.4
1,0
~
V
/~I
~ t
0.. 6
1\
~ ...
:"
r'
•
,
- I.E.
fl
II
10
001 0 , 1
I
V
L
h,ff
4
~
/
~~
2
o
[7
II
/
\
/.
V
/_.......V
'/
./
V
100......
v
v
:/
:/
~~
\ IT
FIGURE 3; Apparent reslstl Ity for maximum .ttll potmtial.
/
V
7
6
THAPAR AND ARORA
[/9
•
I.
1. 6
~
J~:m
~.;,__;:_
I~
1.2
V
/5
V
n
V
/
h
v
3
. ~V
YI
2
1.0
31--
. /~
0· 8
5/
0· 6
V
V
~
'/
2
V
9/
0. 4
r' 100
8
L
h.JO
6
...
10
0 .1
\\
\ \
\"
\
\
\' 1\
)
j
/
'0
"""
~
o
FIGURE 4:
~
~
: ~ P'"
~
V
~
V
/
/ /
V
Apparent resistivity for maximum m b potential.
VJ
v
0 .01 J2
II
r'
-y,- -
STEP A
o
MESH POTBNTlALS AT HIGH
o
OLTAGE STATION IN
TABt.
-U IFOR.M
7
IL
1
Apparent resi tivlty for Itep potential.
No. of conductors
n
Distance between
conductors
D
(m)
2
Height of
upper layer
p., fp l
Pt/Pl
11
(m)
10
100
3
4
5
0. 1
6
0.01
7
2
2
2
2
1.0
1.0
1.0
1.0
2.0
5.0
10.0
15.0
1.130
1.019
1.003
0.999
1.219
1.057
1.032
1.029
0.Q15
0981
0992
0.994
0.903
0.979
0.992
0.994
2
2
2
2
3.0
3.0
3.0
3.0
2.0
5.0
10.0
15.0
1.250
1.057
0.993
0.985
1.362
1.077
1.022
1.010
0 .870
0.965
0.990
0.995
0 .84
0.96J
0.989
0.995
2
2
2
2
6.0
6.0
10.0
10.0
10.0
15.0
10.0
15.0
1.028
1.011
1.037
1.018
1.036
1.018
1.051
1.023
0 .985
0.992
0.977
0.987
0.945
O.9R5
0.974
0.987
3
3
3
3
1.0
1.0
1.0
1.0
2.0
5.0
10.0
15.0
1.221
1.035
1.004
0.999
UI4
1.050
1.009
1.001
0.1l63
0.968
0.987
0.991
0.840
0 .965
0.91\5
0 .990
3
3
3
3
3.0
3.0
3.0
3.0
2.0
5.0
10.0
15.0
1.430
1.112
1.030
1.012
1.663
1.160
1.042
1.018
0.806
0 .Q32
0.976
0.988
Q.771l
0.922
0.975
0 .987
3
3
3
3
6.0
60
10.0
10.0
10.0
15.0
10.0
15.0
1.060
1.030
1.080
1.040
1.085
1.041
1.120
1.060
0.964
0.982
0.954
0.973
0.961
0 .980
0.950
0.973
5
5
5
5
1.0
1.0
1.0
1.0
2.0
5.0
10.0
15.0
1.410
1.082
1.018
1.005
1.605
1. 120
1.027
1.006
0.771l
0.940
0 .978
0.987
0.745
0 .930
0.975
0.985
5
5
5
5
3.0
3.0
3.0
3.0
2.0
5.0
10.0
15.0
1.738
1.246
1.083
1.042
2.240
1.362
1.118
1.057
0 .740
0.953
0.978
0.706
0.860
0.947
0.975
5
5
6.0
6.0
10.0
10.0
10.0
15.0
10.0
15.0
1.142
1.078
1.173
1.104
1.207
1.108
1.270
1.153
0.932
0.961
0.925
0.949
0.920
0.954
0.915
0.938
5
5
0.~78
8
THAPAR AND ARORA
TABLE] (Confd.)
2
3
4
5
7
6
9
9
9
9
1.0
1.0
(,0
(,0
2.0
5.0
10.0
15.0
1.742
1.197
1.052
1.020
2.160
1.287
1.076
1.067
0.674
0.878
0.956
0.975
0.628
0.858
0.959
0.973
9
9
9
9
3.0
3.0
3.0
3.0
2.0
5.0
10.0
15.0
2.172
1.487
1.200
1.108
3.252
1.771
1.292
1.152
0.678
0.808
0.900
0.943
0.637
0.781
0.884
0.932
9
9
9
9
6.0
6.0
10.0
10.0
10.0
15.0
10.0
15.0
1.296
1. 182
1.329
1.217
1.470
1.272
1.572
1.350
0.883
0.917
0.892
0.914
0.868
0.906
0.878
0.902
TABLE lJ
Apparent resistivity for mesb potentiul.
No. of conduc.
tors
n
Distance between
conductors
Height of
_~m I PI
upper layer
P ~i
Ii
Pi
D
(m)
(m)
2
3
2
2
2
2
1.0
1.0
1.0
3.0
5.0
10.0
15.0
2.0
0.993
0.993
0.993
1.005
0.993
0.993
0.992
1.007
0.995
0.994
0.994
1.060
0.996
0.994
0.994
1.065
2
2
2
2
3.0
3.0
3.0
6.0
5.0
10.0
15.0
10.0
0.998
0.998
0.999
1.000
1.001
1.000
1.000
1.000
1.007
1.003
1.000
1.010
1.017
1.003
1.013
1.011
2
2
2
3
6.0
10.0
10.0
1.0
15.0
1.000
1.000
10.0
0.990
0.994
15.0
5.0
0.990
0.982
0.992
0.952
1.002
1.020
1.000
1.002
1.005
1.015
1.007
1.004
3
3
3
3
1.0
1.0
3.0
3.0
10.0
15.0
2.0
5.0
0.985
0.986
0.930
0.975
0.985
0.986
0.932
0.972
0.992
0.988
1.185
1.062
0.994
0 .990
J .212
1.072
3
3
3
3
3.0
3.0
6.0
6.0
10.0
15.0
10.0
15.0
0.995
1.000
0.980
0.990
0.995
1.000
0.978
0.990
1.020
1.011
1.044
1.022
1.026
1.012
1.052
1.026
10
4
100
0.1
5
0.01
7
STEP AND MESH POTE TIALS AT HIGH
OlTAGE ST TIO
-u
9
IPOR t . It
TABLE II (Con/d.)
1
2
3
3
3
5
5
10.0
10.0
1.0
).0
10.0
15.0
5.0
10.0
0.900
0.967
0.936
0.965
0.955
0.9Mi
0.930
0964
0.993
1.077
1.040
1.056
0 .996
5
5
5
5
1.0
3.0
3.0
3.0
15.0
2.0
5.0
10.0
0.969
0780
Ot<:W
0 .961
O.96X
0.756
O.X74
0.953
0.9H3
1.396
I. 188
1.070
0.984
1.444
1.218
1.080
5
5
5
5
3.0
6.0
6.0
10.0
150
10.0
15.0
100
(l . 9~(l
0 .926
o 95!S
0.892
0976
() 912
0949
O.H77
1.031
1.137
1.0110
1.173
1.038
1. 159
1.092
1.200
5
9
9
9
10.0
1.0
1.0
).0
15.0
5.0
10.0
15.0
0 .923
0739
0.888
0 .922
0.911
0698
0.875
0.915
1.11 K
1.308
1.061
1.002
1.137
1.368
9
3.0
3.0
3.0
3.0
2.0
5.0
10.0
15.0
0 .545
0.723
0.469
0638
0 .834
O.90b
1.732
1.460
1.232
1.131
1.808
1.523
1.270
1.154
6.0
6.0
10.0
10.0
10.0
J 5.0
10.0
15.0
0778
0.849
O.74!<
0.800
1.310
1.21 !!
1.324
1.254
1.354
1.251
1.460
1.290
9
9
9
9
9
<)
9
6
4
(un I
0.932
0813
O.H78
O.7tO
O.~30
1.067
J .034
1.04~
7
I.mm
1.010
the maximum mesh potential. On the other hand a
higher conductivity lower strata tends to decrea e the
maximum step potential and increase the maximum
mesh potential.
6.4 The values of apparent resistivity u!tcd to calculate the grounding re~i~tance of grids cannot bc used
to pre-determine the maximum !ttep and mesh potentiab .
6.
6.5 Soil ~tratil do:.e to the gr(}undillg grid have
mMe LlTcet on potentiul gradient th n the boil btrutu
at great dept h.
Conel o ion
6.1 Grid formed of conductors buried in parallel
lines. 0 3 m below the fiat surface of the ground i~
conside~d .
For the study of maximum potential
gradients it represents closely the actual grounding
grids in high-voltage stations.
6.2 A non-uniform soil may be represented by two
horizontal layers configuration, where a uniform surface
layer of a certain depth having the resistivity PI overlays a lower uniform layer of infinite depth and of
resistivity P2.
6.6 For grids in soils with lel>b conducting lower
layer the step potential i., L!reater and the me h potential is smaller thnn that ol->tained by no; liming a uni.
form soil haVing the resistivity of the upper layer.
Similarly for grids in soils of a comparatively more
conducting lower layer the me .. h potelltiul is greater
and the step potential i'l smaller than that obwined hy
a~,>umjng a uniform soil having the re i tivity of the
upper layer.
6.3 The maximum potential gradients of grounding
grids in non-uniform soil can be evaluated by assuming
the soil to be uniform and u)ing the proper value of
P... and Pom . po. and P~m depend not only on the soil
conditions but also on the ize of the grid.
6.7 An increa~e in the number of parallel conductors beyond 9 will give' practically no change in p", Or
Po",. Therefore.
prJ and Pau, given for 9 parallel
conductor may be u ed even when the number of
condllctor i ~reater than 9.
10
TIlAPAR AND ARORA
6.8 If LI(tz -iD) is less than 0.5 the assumption of
a uniform soi l having resistivity same as that of the
upper layer w ill not cause an error of more than 10
percent.
6.9 In tht.) absence of any method available for
the pre-determination of the potential gradients produced by the grounding grids in non-uniform soil. most
electric supply companies have depended on previous
experience and non-scientifk methods for the design of
the grounding systems. With the usc of tlie method
presented, it should now be possible to pre-determine
the maximum step and mesh potentials quite closely
and to design the grounding system -to provide the
required safety on truly scientific basis.
7.
References
( 1) "Guide
for Safety in Alternating Current Substation
Grounding . " AlEE Publicafion No. 80. 1961.
(2) THAPAR, B. and PURl. K.K. : "Mesh Potentials in High
Voltage Grounding Grids ." IEEE Transactions on Power
Apparatus and Systems, Vol. 86, 1967, pp . 249-254 .
(3) THAPAR, B. and GROSS, E.T.B. : "Grounding Grids for
High Voltage Stations-IV Resistance of Grounding Grids in
Non-uniform Soil." IEEE Transactions on Power Apparatus and Systems, Vol. 82, 1963, pp. 782-788.
J. : "Soil R~istivity Testing Guide and the
Evaluation of Tests for Station Grounding Design Purposes." Research Division Report No. 62-81, The HydroElectric Power Commission of Ontario. Tronto. Onteario,
Canada, 1962.
(5) SUNDE, E .D . : "Earth Conduction Effects in Transmission
Systems (Book) ." D. Van Nostrand Company, Inc., New
York, N .Y ., 1949, p . 47.
(4 ) ENDRENYl,
(6 \ ZABORSZKY, J. : "Efficiency of Grounding Grids with
Non-uniform Soil." ALEE Transactions, PI. III B, Power
Apparatus and Systems, Vol. 73,1954, pp. 1011-1016.
(7) ARORA. J. K . : "Grounding
Electrodes in Non-uniform
Soil." M.Sc. Electrical Engineering Thesis, Panjab University, India, March 1967.
Efficacy of Dampers and Improved Techn iques of
Vibration Control in Transmission Li nes
NAGIN SINGH
GR
W AL
Superintending Engineer
Punjab State Electricity Board, Paoala .
. L. GOYAL
KTRPAL IN 11
Deputy Director
A. istnnt Director
Resear h Unil, Pun.lob State "lectru;JI) Board, h nOllllllh
Y OP I
Aeolian vibration is a major source of damage 10 ol'erlread transmission lint's .
Existing I'ibration conlrO/lllethods "al'e proved qllite useful to a reasonable de/(ree
in reducillg the Vibration, particu/arly stockbridge damper, but its pel!ormance has
not bem lip to the mark because of its inherent resonant characteristics. As such
there is a need for radically lIew vibratioll cOlltro/ techniques. To hall(' a hroader
outlook on this concept, general prinCiples of I,,./lrotion control \l'ith rcgard to
ellergy equilibrium considerations have been Olltlined, The frequellcy (lnd magni.
tude of tlte vibratory forces are derived and energy input from the wind has bct'll
calculated, Efficacy of cOllventional dampers, i.e .. stockbricl1(e, armollr rod and
spiral vibratioll damper has heell illl'estigated under actual fi eld conditions with thc'
help of Ontario Hydro Vibration Live Line Vihration Recorders, Nr'1V illlprovrd
techniques of vibratioll control ill transmissioll lines, viz., velocity proportional
damper and self-clamping conductor havt' been introduced in this paper,
1.
lntroduction
1.1 Conductor Vibration is a complex phenomenon invohing large number of controlled and uncontrolled
parameters. Investigations carried out so far and critical
appraisal for sometime past of dynamic behaviour of
overhead transmission lines ha\'e led to better and
clearer understanding of the problem of dynamic in·
stability of suspended conductor system, thereby making the evolution and development of new type of protective equipment such as vibration dampers, antigalloping devices and other fittings of the line conductors, all keeping to mitigate the trouble of vibration
and reducing the magnitude of dynamic instability,
thus minimi ing the damage to the conductor and
fitt ings,
1.3 Since aeolian vibrations are more pronounced
In this count ry , as I>uch th i~ type of dynum ie insulbility
i~ the main concern of thi~ paper. This type of vibration i, caused by the regular ~hcdding of vortices from
the cylindrica l or nearly cylindrical surfaces whieh
give ri,e tel a small alternating force ot ril!ht angle to
both the wind direction and the axis of the cylinder.
If the frequency of the force IS close to 0 natural frequency of the conductor, a Vibration is exited whose
amplitude increases until the energy input i~ balanced
by the rapidly rising losses,
1.4
Vibrations futlgue damallc
the co nductor,
aod towers and generall y it is characterised by
means of glos!>y fracture and broken strands in the
outer layers of the conductor near the entry of the
conductor into the dead end clamp. Becuuse of clamping stresses, the damage has bee n ob erved quile evere
near the mouth of the clamp than anywhere el e,
filting~
1.2 There are various types of vibrations which
damage the overhead tran mission line conductors.
To name some of them are aeolian vibration , galloping, sub-conductor 0 cillation in the ca e of bundle
conductors and floating, etc. The nature and characteristics of these vibrations, are given in reference( I).
1.5 In developing countrie like lndia, generating
stations are not located near the load centres which has
given rise to long transmi sion line ystem, Als the
IJ
12
GREWAL, GOYAL AND KIRPAL SINGH
~roblem of vibrations i now a.:quiring larger dimensions as huge blocks of power are to be transmitted
economically over lon g distances wh ich has necessitated
the adoption of ex tra high voltages, which in turn
require taller structures a nd larger ~ izes of co nductor.
from eO I1 <; ideratioll of corona :.lnd r::dio interference.
Line practices have continued to evolve in direction
which makc vibration, more likely to oc.. ur and more
difficult to co ntrol. Cable diameters have grown, increasing the aerodynamic driving force. Spans are
larger, so th at more energy is received at the anchor
s upport ~.
I ncreased tension ha eo nccntra ted the
strain in Ihe co ndu l..tor l o~e to the clamps. Economically des igned towers accommodate Je s additional
forces. All these developments no doubt bring great
benefit 'i and bring abotl! potential sa vings in the co nstru ction of tran mi ss ion lin e~ by reducin g the number
of towers and thcir heights but incn:ased susce ptibility
to aeolian vibrati on is a maj or threat inhibiting any
further progress in thi S direction .
1.6 Under the circumstanccs the effective vibration
control is a must for all th e transmiss ion lines and the
method s employed for damping the vibratiom can influen ce the design and the cost of the line. To make
a critical study of the dampin g devices to combat the
evil of vibrations, it is ne ces~a ry that the fundamental
princi ples ~elating to the .conductor vibratio~ s and
their damping and the vunous factors responsible for
vibrations and characteristics of the damping devices
need to be studied and cMrelated. In this paper, fundamental principles of damping and energy equilibrium
considerations have been outlined. Apart from thi s
efficacy of t he conventional type of da mper being used
at present ha s been investigated in the field with the
help of Ontario . J:Iydro Live Line Vibr~tion Recorder
under Held conditions. Improved techniques for damping the vibrations in the tran smi ion lines have also
been di scus ·cd .
2.
where, T is the ten sion, g is the acceleration due to
gravity, wand m are the weight and mass of per unit
length of the conductor.
The veloci ty of propagation v is given by :
I'= J~
.. (3)
2.2 By uitable choice of the wave amplitudes, the
deflection of the cable during ·teady \ ibrations may be
written in the form of standing wave equation:
y=A sin (2,,/1) sin (27CX/"'A)
According to the concept of vortex shedding
introdu ced by Karman , alt ernating transver e forc.:e is
cau~ed by th e aeolian vibratiom.
To calculate the
energy input from the wind to a vibrating conductor,
we must consider the frequency and amplitude of thi s
force .
2.3
2.4
Frequency
2.4.1 The frequen cy of the force is given by the
formul a introduced by Relf and Ower as :
f
KV
d
2.1 The analogy of tran mis ion line conductor
vibration can be fairly well undtrstood by the theory
of single frequency vibrations of a heavy ~tring u.pended freely between supp rts and struck near one of
the supports . The single frequency vibration of.an
ideal heavy string may be represented by the travelling
wave equation :
where, V is the wind velocity and d the diameter of the
co nductor. K is the Strouhal number, itself a function
of
Vd
"1)
2.5
Magnitude of the Force
2.5.1 The magnitude of the transverse force acting on
an elemental length of conductor is proportional to the
length dx, the square of the wind speed and the diameter. Treating the instantaneous value of the force
dF as a sinusoidal function of the time t, we may
write :
dF= K o dV2 cos (21t/t)dx
where, y is the amplitude, 1 the ti~1e ~nd x the distance
along the line. The wave length IS given by :
1\ -
f
r Tg
\j
... (6)
where, Ko is a constant of proportionality and its value
for all practical purposes may be taken as
Ko= 4.35 x 10-- kg wt sec2 /m4 (1.11 X 10- 3 Ib
wt sec'{ftJ)
~
=} J:
... (5)
where, "1) is the kinematic visco ity of the air and the
value of which may be taken as 0.185.
Vi bration of a Hcavy String
"\ __1_
... (4)
... (2)
EFfICACY OF DAMP8RS A D IMPROVl:D TECH . IQU
2.6
Work done by tlte Wind Foras
3.2
2.6.1 Travelling wave Equation ( I). without los of
generality may be written as :
y = A , sin (2... f ' + 2...
x/,,)
~ BI
sin (2-::/f- 2-::x A)
. .. (7)
which may further be written a
'"l' Energy Input/rom ,lie Wind
Increased rarural DUlllfling
.. (8)
3,3, I Thc sel' ond way (If maintuining equilihrium
bctween ellergy input from the WlIld and the energy
dissipated in thc l'()nductClr. i~ by in ' rcnsing the ~clfdamping of the c nductOr, ~ec Figllre 1 (c).
nerg
di ipatiol1 IS n) doubt reduced hy I w t n ~ d e ~ tresses
of Ihe conductors but It 'annot be uttempted he ullse
of economical reu~ons. i c.. low temil ' strcsse of
t~ conductor~ mny mean lower optimal span lengths,
higher towcrs and higher cost of th e line con~tructi()n ,
where,
and
The work done on a line of length L can be obtained
by integrating the product of velocity and force over
the cycle and then o\er L a l>uming that L is a whole
member of half wave lengths and by making sUitable
substitution~ and reasonable a~sumptjons, we get work
done by the vibrating condUCIN as :
.. (9)
W = 2q cJ3PL A
where,
3.4
Prol'ision of Damping Del'/'res
3.4, I If the amplitude of vihration f an undamped
line i, larger thrln the safe value Au, II follow\ thllt the
di sipation of energy in the cn nductor is less thun the
e~ergy input from the \\ inu. When u dumper is proVIded to reduce the amplitude of vibruliom, Ih' effect
of natural dis ~i patlon or energv hy (he condllctM may
be neglected. From the field experiments It can be
determined over which frequcncy runge tltc amplitude
of the undamped lines exceeds the su fe valliI' A" Dnd
then th e damper to be efTective in that fr quency raoge
mu st absorb energy per cycle at lettSl equal to
W 2 q d" f2 L A"
and
= 127 / 10 -1 kg wt secZ/ml
(0.0322 Ib wt secz/ ft i
3.
Reducing
~.2 , I B. ' redu ing the energy input from th wind
the amplitude of the ,ibrnti n clln be br \l~hl 10 A G•
i.e., arc value. M:C Figure l (hl. Tlu cun he I hicved
by providmg spe ial condu tor sections \\ hi h r uu e
the aerod\ nami ' forces, This type of llndu t r has
be n di u. sed in a laler ,ccti n,
3.3
J'= A(x) sin (2-:: f r+ ¢ )
13
OF "I BRAT!
Principles of Damping
)
onlrol
3.1 For a particular conductor ten sio n the vibration in the conductor i~ proportional Ie the possible
rate of energy input from the wind . Once the conductor tarts vibrating, the amplitude of vibration will
begin to increase till the energy input from the wind
as described by Equation (9) were not balanced in
someway. The amplitude at first increases but eventually the energy input from the wind which is proportional to the first power of the amplitude A, is overtaken by the natural loss or energy dissipation which
increase as A1 as shown in Figure I (a) , Now with
this if the vibrations reach orne amplitude A whereas
the afe value is only AD' then to bring down the
amplitude to the safe value three alternatives are a va ilable; firstly, to reduce the energy input from the wind,
secondly. to increase the energy 10 s or di sipation in
the conductor and thirdly to attach a damper which
will absorb the excess energy and bring down tbe
amplitude to the desired level.
.. (10)
obtained from quatiol1 (9) by sub5tit uting A A., In
this regard se~ Figure I (d), From quation (10) it is
very much eVident a to wby the vibration intensity is
greater with the increa~e of conductor diameter llnd
longer spans.
4.
Field Jove ligation Regarding Efficacy of Dampers
4. J As already di ellS ed above the fundamental
aim of vibration control is that thc amplitude of vibration hould be maintained Dt or below the value
train con~ideration or
determined by dynamic
other sa fe value based on field
experience,
ntario Hydro Power Commission ha not obllerved
any fatigue damage with their lines in service
for the po t about 30 years having a vibration ampli .
tude of the order of 5 mil , The e ~ential requirement
for an efficient damping is that the energy dissipated
by tbe conductor and damper should be at lea t equal
to the energy input from the wind and the amplitude
of vibration should not increase lhe . are value. urther
it i preferable that energy dissipation in the conductor
and damper houJd ri e more rapidly with increase of
amplitude than the possible rate of energy input from
..
14
GREWAL, GOYAL AND KJRPAL SINOH
ClI
DISSIpatIon
u
>...
u
>.
0'
L
ClI
C
W
A
(0)
t
~
u
>.
u
~
u
>.
u
......
>.
0'
L
......
>.
ClI
L
0'
C
W
ClI
C
W
(C)
(d)
FIGURE 1.
the wind. A damping device which does not perform
this function well would accelerate the damage to the
conductor and the device itself rather than acting a
damping device.
4.2 The efficacy of some of the conventional type
of damping devices which are generally used on the
transmission line in the field were tested by the
Research Unit of Punjab State Electricity Board with
tbe help of Ontario Hydro Live Line Vibration Recorders. These vi bration recorders work on the method
of measurement of bending amplitude which ha got
a linear relation \ ith bending strain which is closely
related to the fatigue of the conductors. Bending
amplitude has been defined as total peak to peak
• displacement of the conductor measured relative to the
suspension clamp at a distance of 8.9 cm (3i in.) out
from the last point of contact between the clamp and
the conductor. Ontario Hydro Vibration Recorder
are very ophi Ii ated in trument and ar capable of
measuring both
amplitude.
4.3
vibration
frequency and
bending
Stockbridge Type oj Dampers
4.3.1 To study the effect of two types of stockbridge damper of different makes, field tests were performed by the Research Unit of Punjab State Electricity Board on a span of 132 kV Single Circuit 132 kV
Jullundur-Bhogpur line (under construction) be tween
tower Nos. 16 and 17 in the month of Septe mberl
October. 1970. The line was provided with 30/7 13 mm
ACSR conductor upported on steel towers . The test
span was 305 m long located in flat terrain in th e open
fields . Figure 2 shows the state of accumulated vibrations experienced by the two conductors fitted with two
types of dampers under similar conditions. It is clear
from the figure that damper 'B' is more effective than
'A'.
EFFICACY OF DAMPI!RS AND IMPROVED TECH IQUES OF \"fBR TlO
Per io d of tests
064 !
'\
056
\
\
\
i
o
048
.c
\
\
\
,~
\
III
.2
~0· 40
E
\
Line
--
~
\
'0
\
~ 032
\
.D
\
\
\
0.
0·16
\\
\.
CII
u
15
132KV. s;ngle circuit
.Jullundul" -Bhogpu r
.
,.
1
damp r A
t1
\
\
III
LIN
1
\
...
10
\
\
c:
,
>,
......
u
o
C1>
-----
~
.......
III
~ 0 ·08
o
I'll
'\
\
C1>
VI
1970
_ _ Wilh S-Brldg
\
o
-oct
Sep
CONTROL I , TRA
2·4
0-8
~
--~
-
~
40
J
48
Bendll"O ampillude In mils peoK 10 peaK
FlGURE 2
4.4
I
Accumulative vibration-damper comparl.lon .
4.5
Tapered Armoured Rods
4.5.1 To make a comparative study of the efficacy
of the spiral type of dampers manufactured indigenously by some firm in India with respect to stockbridge type of damper. the investigations were made
on 66 kV Jamalpur-Ludhiaoa Radial line in the month
of November 1972. Stale of accumulated vibration
experienced by the conductor without aoy damper, by
the conductor fitted with piral vibration dampers and
4.4.1 Similarly a field investigation was made to
study the effect of tapered armoured rods in reducing
the vibrations. These experiments were conducted in
January-February 1972 on Double Circuit 220 kV
Indraprastha-Delhi-Balabhgarh line under Bhakra
Management Board. The re ults of these investigations
with respect to the accumulated vibrations are shown in
Figure 3.
tstrJ
Spiral Vibration Dampers (S. V.D.)
tr
I
"·I~' !~: ~ SClU«U \!> '" ~ 8
16
GREWAL, GOYAL AND KfRPAL SfNGH
Lon. 220KV double c.rcuo'
Perood of 'uh -Jon - Feb 1972
I P BOllobgorh
c
J
,
'5 0
o
..
\
.t:.
~
::, 25
"Eo
'"c
-0
; 10 0
SJ
'"c
..
.
....
-0
:;:0 75
o
.
'0
~O
...
--Wf1 h OrMOur rOdS
~\
- - - WtlhOui
\..
'\
1\\
u....
u
o
..
00
~O
.
z
\
o
4.5. 2 The spiral vibration dampers so far developed are suitable up to a diameter of ] 9.3 mm. The
material of S. Y.D. is a high impact rigid PVC. The
design of S.V.D. is hased on the principles of dissipation of energy through impact unlike that in the stockbridge damper where the energy is dissipated by the
interstrand friction of the cable holding the weights.
For spans of 244 to 305 m S.Y.D. of either extra length
or two of standard length at each end are required.
The gripping section of the S.V.D. was put about 12.7
to J 5.2 cm away from the support clamp. The gripping
section of the second S.V.D. was put at a di tance of
about f 5.2 em from the end of the fir t S. V.D .
5.
\\,
t
..
II
by the conductor fitted with stockbridge dampers are
shown in Figure 4.
10
Conventional Methods of Vibration Damping
5. J The following some of damping devices either
in single or in conjection with the other are generally
employed at present to deaden the vibrations:
'"
K'
20
...
30
-- -- -40
(i) Armour rods (Plain or tapered) .
(ii) Pre-formed armour rods.
-
(iii) Bates type parallel wire dampers.
Sending amplitude- In mds peak 10 peok
FIGURE 3
I
(iv)
Accumulative vibrlllion-Effect of armour
rods.
Bates dampers in combination with armour
rod.
(v) Stockbridge dampers.
( vi)
Spiral vibration dampers.
Period of tests-No v -Dec 1972
c
0 ·8
~
II>
Q)
"0
; 0 ·6
'l5.
01
c
Q)
0-4
\
u
J(
.8
'-
~ 0·2
\.
u
a
Q)
0
_ .-
Wdh slock-bridge domper
~
, .\ ~ ._._._
II>
">.
l:
\
I
U
0
ony dompe r
____ W ith spirol-type domper
,
, ,,
\
I
\. ,
\
,
•\
Q)
01
_ _ without
,'. ~
E
a
~
Line 66KV. double cirCUit
radiol line Ludhiono
\
o
.J::
.•
"
\... "'..........
4
8
12
16
Bend ing amplitude in mils peak to peak
20
24
LI
EFFICACY OF DAMPERS A. 0 IMPROVED TE H . IQU£l. 01 \I R 110
Tit
17
LI
Dompel'" clomp
Domper coble
Oomper weight
01'"0" 1'1 hole
Topered sleeve (ollumil'\ium 0110)')
Cross sec:',onol view of a do mper we i;'"
F IGURE 5:
(vii)
(viii)
lockbridge damper mountl'd on
conductor.
A the stc I cable i
ubje led to hending
prolonged and high amplitud ihrution can
lead 10 fatigue damage 10 its trands in 1I similar
manner t thm in u live onduct r. Further, if the
natural frequency (If the C( ndu tor c in ides with one
f th e re~onnnce fr qucneies (If th dampcr C'x c:ssive
010 ement of th' \\ ight, could t k
plal'c ond lh
damper might fHil in 1I compnrlltively hurl time.
5.3.3
~train.
Specially adopted u pension clamps.
Clamp with neoprene padding.
5.2 These damping devices have proved quite u. cfuI to a reasonable degree in preventing the vibrations
from reaching the line anchorage where it cau es the
maximum damage. Out of these, ~Iockbridge damper
is enjoying a greater popularity at pre enl . the enice
experience of Ihis type of dumper is reported to be
good. so it may be of intere t ro examine the perfor·
mance of a stockbridge damper (Figure 5) .
5.3
5.4 The most of the conventional damping de jl,:e!.
have fuiled 1('1 provide ad quote prole ·tion a~lIin t the
c('ntinued and high amplitud' vibrlliioll. Thl~ i quile
c\ldcnt from thc Held iO\ stigtltiolls reporled curlier
whercln 01 I of the l:ascs Ihe umplitude of the vibru·
t ion~ has exceeded Ihe safe IImils. The ~Iockhridge
damper. f r exomple. has feature, whi h set on inherent
limit t it~ ef~ ctivencs~ 10 spite of the refinement. which
more recent versi(lll have al'quired.
No re nont
damper, however I:omp)ex. cun nlirel over om Ihe e
diml· llltie~.
) I ~cems de. irable. th 'ref reo 10 se k orne
more direct methods of obtaining the m()othly rising
ener),t UOl-ol'plion chilruc l eri~tJl'l> whi h it. requlf(:d for
effective damplnll. A~ stich new improved I chniques
f I vibration ol1trol I1re nece. sary to ~Ilfeguurd the
tr~nsmission lin e conductor .. agllinst fntllW damage
due to vlhrati()l1~
Stockbridge Damper
5.3.1 This is a very simple device CODSIStlllg of a
piece of . tranded tee I cable which ha weight. attached
to its ends. The centre of this steel cable i clamped on
the conductor. The damper is a re"onant devil:e with
uneven frequency respon e characteri tics which include
two pronounced resonance peaks-an upper and a
lower, as shown in Figure 6. The lower COl re ponds app,
roximately to the oscillation of the weight about the
t40
....
I
120
V
.
II)
.D
80
I
v
-
\mill
,r 25 mils
\\ ;
('5 mila
60
~tOlmilS
0
~
40
II)
~
Q)
ex:
20
o
10.11
50 mils
Q)
c
o
I
I.
25 ~"~,5 mit.
~ 100
Q)
I
50 m'il'
,\
~, ~
10
I md: 0 ·001 inch
\
i\
\~ \ \
~ ~ _II Jj
::-/
r:::::::
...........
~
20
30
'"
~
40
:50
i--
60
70
Frequency-C.P. S.
FIGURE 6:
Mecb:uticaJ r
nee or a tJindllld JG-pouod tockbrld
double amplitude ohlbration of damptr clamp 10 mil .
d mper (II:'? • ar for Con tant
18
GREWAL. GOYAL AND KlRPAL SINGH
e
FIGURE 7 I
6.
V.P. Damper.
Neff lDevelopment of Damping Device
6.t Two n ~ w u e velopment have been introduced for
the vibrali n co ntrol during recent years and it i a big
step forward in the direction of vibration control.
6.2 The first one is velocity proportional (v.p .)
damper (Figllre 7) developed by Burndy Co rporat io n
in the United States. Accelerated life tests on the
damper by the Corporation over a long period under
severe conditions of vibrations and temperature have
The
shown no deterioration of any component.
dampers have undergone sati factory field trial on two
lines in Canada where severity of vibrations wa quite
high. The econd development is the self-damping
(s.d.) conductor developed jointly by Ontario Hydro
and Aluminium Laboratorie Ltd.
6.3
URNOV
Velocity Proportional Damper
6.3.1 When an efficient damper is u edt elf-damping
property of the conductor may be neglected, it being
insignificant as compared to the damper. Neglecting
self· damping. it can be shown that :
WI =
q d3A of L {T
TC /
'\} m
... (J I)
where.
W,=Energy input in tbe conductor due to
wind.
Ao=Critical conductor amplitude which
has a fixed value for a particular
conductor.
r= Vibration frequency.
l = Distance of the damper from
clamp.
the
6.3.2 The vibrating velocity of the conductor is equal
to 2TtAof Since A. is fixed for a particular conductor
and clamp combination, W, is, therefore, proportional
to ~he conductor velocity. For ideal matching. it is
deslfable that the energy loss in the damper should also
be velocity dependent.
IlFFICACY OF DAMP itS A 0 IMPR
I'D TE H IQ ES
m \ IORATIO
NTR L 1
11 '1'
IR
ndu t r
The
m(1)
u
>.
6.4 The () I of a \ . p. damper i
pe ted 1 e m r
than a 10 kbridge type f damper for the same c ndu tor izc. HO~levcr , a only on . p. dumper per
pan would be r quired as ugnin t tw
ilh a lOckbridge t pe. the 0 rull mt of .p. dnmper~ m y c
equal or les thun that of providing the to khridge
type of dumper '.
(.)
>.
0'1
L.
(1)
C
W
Self-dampil/g
6.5
Frequency - FIG RE 8:
Frequency characteristic of 11
.P . Dal1lper.
6.3.3 Most dampers in use have pronounced re onant
characteristics and although these might be etTecti e
at some frequencies, at others they will absorb too
little energy and thus exert so much retarding force
that the conductor might become severely trained at
the damper clamp. These difficulties arc eliminated in
a fluid dash pot damper. in which the expres. ion for
energy dis sipation is given by :
7.5.1 A SR o nduct r generull us d for overh ad
transmi ion lines ha inherent) u ~clf-domping pr pert y. If the elf-dumpi ng prop 'rty is quite adequ te
at all ve loci tie. and ten~ion such that th e amplitude
of vibrali n d es not e cecd the safe vulue , n additional damping is necessary . If. however, self-damp in
is inadequate whi h is the ell e in m()~t of the line.
additiona l damping will be a must t
ombn t th e evil
of vibrationb .
6.5.2 The amplitude of a vibrating conductor at res nance i given by :
.. (12)
where,
WcI=Energy di ssipated in the damper.
R=- Dashpot constant.
6.3 .4 As both th e energy input in the conductor and
the e~ergy di s ipated in the damper are frequen cy (i.e.,
velocIty) dependent , a smooth transfer of energy i
~ssured and a Don-resonant frequ ency characteri tic
JS obtained as given in Figure 8.
6.3.5
I
A= 21t
-I
F
Z,
'" (13)
o that f r a parlicular frequency I and
nstant excitin g force F, th e amplitude A is inversely proportiona l
to the self-damping force Z,. If the damping force
c uld be increased. it is evident that the amplitude
A could be reduced.
6.5 .3 In the self-damping (s.d.) conductor igure 10
concentrically self-suppor ting layer are stranded fr m
trapezoida l shaped alumin ium wires. Al last Il minimum of two alumini um layer!> arc laid around the
Damper Construc(ion
6.3.5.1 A fluid das~pol is used in the Burndy
Damper, the constructIon of which is shown in Figure
6. A eo~crete J?ass is supported internally by a helica l
compressIon spnng, the lower end of which rests in the
bottom plunger of the dash pot. The plunger is
~o.nnected ?y a shaft through a guide bearing to a ball
Jotn~. Thl en ' ur~s . tha.t the. damper always hang
vertIcally, thus ehmmatIng Side thurst in tbe bearing
and torque at the clamp. The clamp i of conventional
hook on design, allowing easy live line installation. A
close-fitting metal shroud prevents ingres of water.
6.3.6
COIIc/uC(Or
t
a>
u
>u
.....
>-
0'1
L.
a>
c
W
The unique characteri tics of this damper are:
(i) -Z:he ~0!lcrete ~ass remains almost stationary and
energy IS dIS Ipated In the dasbpot mechanism by the
movement of the plunger. (ii) The energy absorp-
FreQuency ___
FIGUR
9
I
Eaergy absorptIon
rrequency.
II
n runction or
20
GREWAL, GOYAL AND KJRPAL [NGH
FIGURE 10: Self-damping conductor.
ci:ntral t~el c r". Th ~ slrlll "bj Llmi nill ffi I:ly~r; aro!
separated by mlll annular clelran~!~ fr-:>m ea h oth"r
and the central core.
6.5.4 Design of the new conductor i ba ed on two
principle of dis ipation of vibration energy; fri lion
between the aluminium wires in each layer and interference between the conductor core and surrounding
aluminium wire layer. The trapez idal hape of the
wire facilitates the interwire movement neces ary for
propagatiag energy dissipation by fri ction, and each
layer of wire is desigaed to reduce the radial load between layers which has been found to re trict inter-wire
movement. In addition the tropezoidal shape has
resulted in mechanically turdy conductor with predicable performance characteristic . The compact de ign
give the required area for a smaJler diameter than with
conventional conductors which i advantageous in terms
of tower loading and reducing the weight. 1
6.5.5 Vibration control with s.d. conductors can only
be possible with new installations. The t'rice of the
s. d . conductors is not yet available as it is not being
manufactured indigenou Iy.
Because of its special
de ign, the price i expected to be more than that of a
conventional conductor.
7. Condu ion
(I)
The amplitude of vibrations exceeds the safe
value in almost all tbe jines, as such effective
EFFICACY OF IHMPeR
vibration ontrol
mi sion lines.
-\"0 IMPR VCD rECH I US' OF vl81H TI . CONTROL I. TR
a mu·t for all the Iran -
(2) The criterion for an efficient damping is that
the energy di sipated by the conductor and
?amper hould .be at least equal to the energy
Input from the wlDa and the amplitude of vibration should not exc ed the afe value. preferably the enerro' dis ipation in the condu tor
and damper should ri e more rapidly with
increase of amplitude than the po ible rate of
energy input from the wind.
(3) Both velocity proportional damper and elfdamping couductor provide an improved
technique of vibrati n control than hitherto
bas been possible. Y.P. damper, is a more
versatile damping device as it could be u ed 00
aoy line wherea s.d. cooductor could be u ed
on new installations only.
(4) Tncrea e in the every-day tension level should
be po sible on the line equipped with improved
damping devices and potential saving in the
line cost could be effected. Because of nonavailability of prices of the e devices, an accurate estimate of cost reduction is not possible
at thi s stage.
8.
. MIS. 1 !II Lt ,
References
(I ) GOYAL, S.L. and KIRPAL SINGH: "Conductor Vibrations and their Measurements." Proceedings of the Annual
Meet of Institution of Engineers (India), Punjab, Haryana
and Himachal Centre, 1973 (Under Publication ).
21
116. Proceed-
\4) DEY. P : " Improved iC l hoJ~ (r ,erhe. d tnt' ib Ii n
ontr I." leClrl I Revic" No. 4, JUlie 1971, pp. 761-70S.
(S)
0'> RD . \ T . Ilnd 1 INOT
. . . : " elf·dampina ondu tors for the Control of Ibr tlon and Oalloplng
of the Trln mi 5ion Line .. Pre entcd at the I
S mposlUm on onductor Vibrat ion and Galloping In hla 0,
June 1968.
(6) Energy Inlem lional. ..
tor " .
If· damping
lumlnium Conduc-
(7)
PROUL. J.E. and · DWAROS. .T .: "Pro res tow rd
Optimum Dampins of Trammi ~~ian ondu tors. " 1oms.
IEEE, 01. 79. pp. 44·847.
IS)
C\~mCl)\ f 1>0OW RDS, A.T . nnd II YD, l .M .; ·'
du etor Vibration ." CIOR Committee. No. 6, July 1965.
(9) B TE ERNEST: "Vibration of Trammis ion Une onduetors." Trans. of In tltution of nginc:er. Vol. II, 19 O.
pp . 277·80.
(10) MA NAR ERVIK : "Vlbra jon of dcmping nv vlbra jon
pa kraftliner."
Ie trolee TID . 79. ( II J. 1966. pp. 169·76.
(11 ) TOMPKINS; J. S.; MERRILL. L.L Dnd JON • B. L.:
"Quantitative Relationsbips in
onductor Vlbrlltlon
Dampins ." AI
Tran ctions, ctober 1956, pp . 879·96.
. : " toclcbridlle Damper
(12) CLAR N. R . and DIANA
Analysis. " J E Paper 31C. 83·b. 1967.
(2) PULLEN, J. : "The Control of Aeolian Vibration in
Single-Conductor. Transmission Lines- Part I General
Discussion and Theory." Research Report No. 60, Bumdy
Research Divi sion, 1968 .
(13) EDWARDS, A.T . and nOYD, J. M. : "Ontario, Hydro Live
Line Vibration Recorders for Tr n mi ll i n Conductort."
Trans. IEEE, PAS·82, 1963, PI'. 269·273.
(3) SARWAL, S.S.; GOYAL, S.L. and GILL. H .S. : "Effect of
Tension on Conductor Vibration- Theoretical Analysis
(14) Literature on Alcoa elf-damping Conductor l upplied by
ALCOA Conductor Product. Company .
Stability for Developing 400 kV E.H.V. System
0.0. THAPAR
Director (Electrical)
Beas Designs Organization, Nanga).
SYNOPSiS
Dehar Power Plant is to be interconnected with Northern Regional Grid by
400 and 220 k V lines. 400 k V is to be introduced for the first time in tlze region .
Considerations affecting stability of power system, i.e. , generator parameters, fault
clearance time, excitation .rystem, operation and network conditions, auto-reclosing
have been discussed in the context of modem developments ill the equipment and
experience available. Transient and dYllamic stability studies of Dellar E.H. V.
system and interconnected Northern Regional Grid have been detailed. Stability
has been ensured in an economical manner by reducing fault clearance time, emp/oying high gain fast acting static excitatioll system and incorporating suitable
feed back stabilising signal. Further studies for gUiding system operation have
been outlined and stability criteria for stability studies in the region also
enunciated.
1.
IntroducCfon
1.1 1,000 MW Dehar Hydro Power Plant of BeasSutlej Link is proposed to have 4 generators of 0.95
P.F. of 165 MW each in the first stage. Two more
units of equivalent capacity are to be added in the
second stage. The power plant will occupy a significant
position in the Northern Regional Grid and will be
interconnected with this grid, in the first stage by 60
km long double circuit 220 kV line at Gaoguwal and
by a 280 km long single circuit 400 kV E.H.V. line at
Panipat. A second 400 kV line is likely to be added
alongwith two second stage units.
1.2 Introduction of 400 kV and large sized generating
station in the region is likely to change significantly the
stability characteristics of the power system of this
region. In the initial stage of development of E.H. V.
system problem of stability are liable to be critical
because of weak system, lower short circuit level, operation at leading power factor, and need for economy
in providing transmission outlets and fixing the size
and parameters of generating units. Detailed tability
studies carried out for Dehar E.H. V. system to determine optimum characteristics of the control equipment
at Dehar Power Plant have been described. More
exhaustive studies are aloin hand to fix operating
restrictions and con traint 0 as to optimi e operating
conditions of this power house with the equipment
selected. The stability characteristics of the power
system of Northern Region with pecific reference to
Dehar Power Plant have been examined and dis.
cussed in this paper. It is considered that weak
sy terns of different regions may face similar problems
during initial development stage of an E.H.V. system.
2.
General Sy tern De cription
2. 1 Figure 1 shows the main connected transmission
system 220 kV aod above to which Dehar Power Plant
will be connected. Figure 2 shows interconnection of
Dehar Power Plant with the grid. Dehar E.H.V. 400
kV sending end step-up sub-station has a double bus
arrangement as shown in this figure.
2.2 At Panipat receiving end sub-station, bus and
breaker arrangements are tentative.
3.
Co~iderations
affecting Stability of Power Sy tern
3.0 Various factors which have an importanr influence
on the stability of Power System are:
(a)
Generator parameters.
(b) The strength of the system after clearance of a
22
STABILITY lOR DEVELOPI ' G
Bhokro R'ght
00
3
K
Bl'lokro Left
Amr,tsor
ToD
'iystern
jJllu•.:.;:::;........,__.....
22
V
To 132KV.
sys tem
'Tb132KV
s}'Ste m
legend : -
~
o
Bhatindo
Synchronous condenser
Power stotion
--E- Tronsformer
HG RE 1 I Debar E. H .\' . ystrm und inl reonn ct d nortbem r
lonal arId Ingl lin dlaaram
220 I. \' Dnd IIbo\r.
J
Bonk
d3 Pho'.}
" ~ng' e
2'OMIIA 220/..001<11.
tranl former
~
I
•
400KV. llne
lfo"tur.,
III of 41:
,nt'ollollon crt
POntpOI i. t...tot,yw
':""-+
t
.. 00 1(1/.
'onl pa' 2201(\1.
FIGURE 11 lnt rcOftllection f Debar Pow r PJaot 'lflth arid.
24
THAPAR
fault, in relation to size of generators, i.e., the
impedance between the generator and the rest
of the system.
(c)
Fault clearance time.
(d) Excitation system.
(e)
Auto-reclosing of lines.
(I) The operating conditions of the generator.
3.1
Generator Parameters
3.1.1 In the early stage of design of Dehar Power
Plant it was decided that generators with normal characteristics be specified and requirements of stability be
achieved by optimising parameters of other factors
involved. In a recent study of the British System(3)
also, it has been shown that changing generator parameters, i.e .• short circuit ratio, transient reactance and
inertia constant of generator have comparatively much
less effect on the stability margins.
3.1.2 Preliminary transient stability studies on the
A.C. Network Analyser (using constant voltage behind
transient reactance) i'1dicated that only marginal stability would be obtained. It was, therefore, decided
that other aspects as regard minimum fault clearance
time, high speed static excitation equipment and autorecJosing be examined to improve stability margins.
3.2 Strength of the System
stability is critical. shorter fault clearance timl:s are very
helpful. It has been shown(1) that with modern industry practice, a fault clearance time in E.H.V. ystem of
80 m .s. composed of 40 m.s. for circuit breaker operation and 40 m.s. for protection operation is feasible
and is being provided for Dehar E.H.V. system.
3.3.2 Although all transient stability studies were
carried out with a total fault clearance time of 0.1
seconds so as to get swing behaviour of the system. It
is considered that in due course more detailed studies
may be carried out to find critical fault clearance time
for various conditions of operation and excitation
system parameters so a to have more clear idea of
stability margins available.
3.4
Excitation System
3.4. J Conventional excitation sy~tem presently employed on generators in the region consist of shaft
mounted DC. machine. This is a slow speed machine.
These systems even when equipped with direct acting
magnetic amplifier type of voltage regulators can
although provide ceiling to satisfy response req uirement but the time delay to reach ceiling is appreciable,
i.e. of the order of 0.2 seconds . On the other hand the
static excitation system has a time delay of only up to
0.03 econds to reach tbe ceiling. Considerable improvement in stability with the lise of fast acting static
excitation systems u ing tbyristers hu, been reported(S-U). This system can be used for improving stability
of the region by using the same on the future more
important generators as in case of Dehar.
3.5 Stabilising Signals/o r Static EXcitation Systems
3.2.1 It has been shown(D) that strength of the system
after the fault, i.e .. sh rt circuit infeed from the system,
is an important consideration in d~termining the sta?ility
of a power station. In general hIgher the short Circuit
in feed stronger the sy tern and more stable tbe generators.' As a rough gu ide if hort circuit infeeds are
less than three times. the generator rating for all conditions of operation stability may be of concern. In the
first stage of operation of Dehar Power Pla.nt in the
grid when it is connected t the ystem by a stOgie long
400 kV E.H.V. line, strength of the ystem will be quite
weak and as per details given elsewhere(l). these may
be of the order of twice or even less the generator
rating connected on 400 k'-: .btl . of .the .tation: It i '.
therefore evident that stablltty In thIS regIOn \\ III be of
vital con~ern for this power tation and may be required to be frequently reviewed thro~~hout the life C?f ~he
power wtion. Tn general prOVIS!On ?f transmISSIOn
outlet and size of the p wer station IS chosen from
ccon mic con ideration other than system stability. It
wa . there~ re, endeavoured to ensure tabllity within
these constraints .
3.3
Fault Clearance Time
3.3.1 Fault clearan e time has an important bearing
on stability of generators. 1n the situation in which
3.5.1 Previous work( 1- 8) has also indicated that the
use of orne form of stabilising feed back . ignals in a
static high gain automatic voltage regulator is es entia I
to achieve atisfactory damping of system tran ient
oscillations. The high gain and instantaneous response
of static excitation sy terns required to force the field
voltage to its upper limits under fault conditions. thus
as, i ting the maintenance of transient stability, may
give rise to prolonged oscillation in the post-fault
period and auxiliary signals derived from a suitable
sourc may be needed to provide extra damping.
3.6
Alito-recIosure of Lilies
3.6.1 Auto-reclo ure of lines is an important consideration in the tability of a power system. Desirable
method f rectosing, i.e., whether 3-phase or single
phase, whether instantaneous or delayed a well as the
con 'equence of reclosiog into a fault are some of the
relevant consideration in this case which are di cussed
later in this paper.
3.7
3.7.1
Operating Condition 0.( Generators
Di connecti n of generators sImultaneously with
u
TABILlTY FOR DEY LOPI G 400 K"
Ganguwol 220KV
.H. \. S
25
TI! ~
Z " 0{)()575-+)0 ' 0 577
8 =1·538
jO ·05
PonlPot 400KV
-5%
)00286
0 ·OJ23+jO·0C5S4
Pon,pot 220KV
Z= O· 0037 2+JO.OltH,I"
_ 1I'Ie ond transformer Impedances and
susceptonc.es in PU on 100 MVA
transformer tops In per cent
Boxes ore equivalent shunt Impedances
FIGURE 3:
Reduced
Bodorpur group
I Eq ul'lIol.nt moch" .. l
~y
the outage of a line could also aid stability in certain
case .
3.7.2 It bas further been reported(8) that critical fault
clearance time is considerably reduced if generator is
operating at leading power factor. In remotely located
bydro-station connected with grids by E.H.V. lines. it
may be difficult to avoid this condition. It is propo ed
to tudy this particular condition in more detail in due
course and impose operating re triction if considered
necessary. Shunt reactor installation on E.H.V. system
j
primarily for the purpose of voltage control.
In ystems where stability is critical installation of
shunt reactor is also required to be examined with
respect to system stability which is proposed to be done
in due course.
4.
tability Criteria
4.1 It j consjdered tbat all E.H.V. system hould
have as high a standard of security as economically
possible. With this object in view the aim should be
to design a system which bouJd be transiently stable
for a permanent fault on the 400 kV line involving
unsuccessful reclosure on to the fault and dynamically
table for all condition where tile 400 kV line wa
tem u cd for detAiled ludle .
removed . It j desirable that the e aim hould be mot
with tinder three-pha se fault conditions. the probability
of uch fault occurring in practice is small , but i II t
con idered mall enough to be regarded a c eptable
risk. It is furth er con idered that in devel ping .H.V.
ystem in India pole slipping lasting for It very sh rt
time be accepled in the initial 8t ge of de ign of an
E.H.V. system 0 as to reduce co t .
5. Repr
iudl
S.l
ntatlon of Dehar
t m
for
tabU
I,
System Representation
S.l. I It was onsidered that no bus in the ystem
could be considered infinite for any accurate study.
For rhe purpo e of detailed tudy it wa decided to im
at a reduced yst{'m in which the Dehar Macbine were
repre ented in full, and the rest of the sy tern was
concelltrated at e entially two bus-bars - Ganguwal
and Panipal giving a system with four machines group
-two at Dehar. one (equivalent) at Ganguwal and one
(equivalent) at Panipat a shown in igure 3. In this
way the identity of tbe mOllt important element of the
sy tem wa fuJly pre erved. The e element are the
Debar machin , the bu -bar and tran former. the
bu -bar at Ganguwal and Panipat the 400 kV line and
26
THAPAR
Oil
C • Commond 5.."nol
Inormolly . bP 1
1 T" . 004 Me
Trz=O 207,-e
Tw .2· 07 IMIC
Td .IO He
Tn ,,00
bP· 004
bt ,,0 4
T ,o :; PU Output tOrque
01 normal spe.d
("I"!l,n th ••• studieS)
&0
p .U. R otar oce.lerot"",
.... 9;
IP. U SPMdl
Permanent droop
PU.Speed
C honge ( ;:'0-1)
~---------------VT
I(A
.. 400
VR.mOA
VR .... n
Jl
= O·Ow-I·90
11
= 2 '24 to 2·88
=
=
°
tolO
0 '02tol'80
Flour. 5
FIGURE 4
I
Power Prime Mover and Governor.
the 220 kV lines from Dehar to Ganguwal. Reduction
was carried out by MIs. English Electric CO.(2), U.K .
using the A .E.]. network reduction digi(al computer
programme which yields values for all equivalent interconnections between preserved bus-bars. Swing curves
obtained for full system were used for comparison with
similar wing curves obtained for the reduced system
so as to establish the identity of reduced system.
5.2
Representation of Dehar Generators
5.2.1 The four identical first stage Dehar generatorstwo Jeeding 220 kV bus-bars and two 400 kV bus-bars
were cOlilsidered in the groups , i.e., one equivalent
machine on 220 kV and two separate machines on
400 kV so as to study tbe effect of generator di connection on stability as discussed in para 3.7.1. All the
machines of Debar were repre ented in the sys tem
studies by generalised two axes model which includes
the more important damper winding effl cts . The
governor was repesented in accordance with Figure 4.
5.3
Representation of Excitation System
5.3.1 The static excitation system block diagram used
in stability studies is hown in Figure 5. It was c nsi·
dered that two type of stabili ing feed back signals on
the AVR could prove useful in maintaining lability
and provide additional damping in the post-fault
period. The e are derived re pectively from rotor speed
change and ac elerati n. Both the e type were accordingly included in the repre entation for detailed studie
as shown in the block diagram .
FIGURE 5: Dehar excitation system .
6.
Stability
tudies
6.0 Digital computer stability studies for 1st stage
units were carried out with the help of MIs. English
Electric Co.(2) in U.K. so as to fix optimum parameters
of excitation system. For the purpose of these studies
it was considered that the most stringent requirement
for the excitation system of Dehar generators will be
obtained when 400 kV Dehar-Panipat line carried
maximum power. As such the generation scheduled
for conditions of maximum hydro generation in the
month of September were adopted . More detailed
studies are to be carried out so a to fix operating
con traints with equipment parameters actually procured for various generation schedules and will also cover
econd stage operation.
6.1
Transient Stability Studies with Detailed Machine
Representation
6.1.1 A large number of tran ient stability studies
were carried out with a three-fold purpo. e; to determine
accurately the system behaviour under a number of
different fault conditions, to fix values of excitation
re pon e ratio and field voltage limits. and to obtain
some as essment of the effects of stabili ing ignals of
the kind described in para 5.3 applied to the Dehar
excitation system.
6.1.2 The studies were of real time duration ranging
between 4 and 14 seconds in order to fully gauge the
effects in the po t fault period. In all cases 3-phase
fault cleared in 0.1 seconds from both ends were
TABlUT\' FOR DEVElOPl G
_7
400 K\- .11.\. Y. TrM
0."0 ••00 KV
0.
"CIt' zoo KY.
8hQkrQ
......
Bodo~
__,, _ _
- lao
i
QO
:- eo
.4
9 30
•
~
0 r-~~~~~~~-h~~~~~--~
o -)0
120
-IBO .L-_..IIIl!:___...IIC._--'L-._L-.__;III-_ _- - J
3¢ faull ot Panlpat
Cleared in 0.1 sec-No reclo ure.
considered. The studies may be grouped under three
different heading in terms of their swing behaviour
and damping characteristics, viz. ;
No auto-reclos1lre; both Dehar 400 kV
machines in circuit after line clearance.
(ii)
Auto-reclosure; both Dehar 400 kV machines
in circuit after line clearance.
(iii)
Auto-reelo ure; one Dehar 400 kV machine
disconnected when line i cleared.
No Auto-reclosure,
Circuit
bot"
400 k V M achilles ill
Figure 6 & 7 show the rotor angles aDd .speed
change with time up to 6.7 seconds fro~ fault inception for a typical case. Referenc~ to Figure . 7 h~ws
marked rise in speed of all machines over thiS peflod
so that the apparently violent behaviour of rotor. an~le
depicted in Figure 7 is understandable. Examm8tlon
of figure reveals that there is no Joss of sync~ronism of
the machines relative to each other, the sWing curve
following each other consistently with a maximum
angular separation of machines (actually Dehar 400 kV
and Badarpur) of 74° occurring at about 0.5 second.
6.2.1
6.3
Di-
ndition )ne f the h) unit
feedin!! the char 400 k bu ·bn rs Wll~ di. anne ted
from the 400 .k \' along with the line and remnin I disconnected from the s stem ubsequcntly. Rotor angle
for a Iypical en e f r 'a fnult t end of 400 k line is
~hown in Figure 10. Thi. ca. e is with n I wer limit f
~tati c excitnti n 'eiling v huge, i.e.. _ 24 P. U in. teod
of 2.40 P.ll. for n e 6.2 and 2.RR for eu e in 6.1. This
doe indicate thut di connect inn of generation lIid
lability.
6.4. 1 Under this
-I~O
6.2
1aC'''in
T''''.llIcl
:;
'0 ·e o
« -90
(i)
Auro.rt'Closllre, 011 Dellar 400 I.. V
COIlnl'c/etill'lten Line is clrarrd
6.5
(abi/j.faliol1
(obi/i(y
Fred
Bock
igllul (md Transi til
ii.S. 1 An examination of the swing urves and 8peed
again t time I,;urve revealed thnt the machine ontinue
t osclllatc for n long time foil win thr e-phu e flmlt
on the Dehar-Panipnt 400 kV line. The nnturul
frequency of (he~e 0 cillutions is of the order of I cycle
per se ond . It , th refore. appeared desirable to employ
ome additional damping in the form of excitor; n feed
back si nals to ensure that the ystem return t tcady
operati n a quickly as po sible.
tTect of families of such si nat ba ed on vel 6.5.2
city feed back with varying value of ga,in an~ ti~e
constants were tried but wa ' found to be IDetTe live In
providing damping. Another family f signal w~re
found, however, to have ignif1cant effect in damping
out the !.clilatil)n in the sy tem. The e relied n
acceleration feed back only . It was found that th.e
signal in the form of a p ~ilive feed back of per unit
Auto-rec!osure, both Dehar 400 k V Machines in
Circuit throughout
6.3.1 Rotor angle and speed changes with ti~e for a
typical case is shown in F!g~es 8 &~. AgalO I~rge
rotor angle fluctuations are lOdlcated wIth all machmea
swinging e entially together, but by the end of the 8.8
seconds covered by the run all angle have alma t
settled to new value with the arne eparations as in
the steady state. During the wing the maxjmum
angular machine separation (which is again between
Dehar 400 kV and Badarpur) is 71°, occurring at 0.5
second after fault inception. There is, therefore, on
loss of synchroni m between machine.
_
D.hM0600KV
___ D.hQr 200KV
__ aho",o
_ ._
2
FIGUR 7:
3
lowp".
G
7
I
nct ol400 kV lin .
o mJ
r.
28
TJiAPAR
.
:
:
9
~
~
120
::>
QO
~
eo
0
~ 0010
O,hor 220KV ___-:
BhClkro . . • . _ . _
Bodo'pur
. _a_It-
~
r---~~~~~~--~--~--~~~-4
2
:5
e 7 r. .... I ••e I
~-eo
_
0.1\0' 400KV
___ Delio, 220KV
3 - QO
_ _
- 120
15 0
'eo
O,I\or .OOKV _ _
..
30
_ 30
O·O I!l
u
! o ·oo~
X
'"
BI\okro
8000 r Puf
2
J
4
7
8
Tlm,lneJ
k--,!--JI.~c---*""--+--___-~iL,II=-!:""_"........J
FIGURE 9: 3 ¢ fault at Dl'hllr end of 400 kV line.
Line cll'ared in O.t sec - Dead time
to recloure 0.5 sec VR = 2.37 to
- 1.90 (wltbout feed back damping
signal to excitation) .
FIGURE 8 I 3 ¢ fault at Dehar cnd of 400 kV
line. Line cleared In 0.1 sec- Dead
time to reclosure 0.5 sec VR - 2.37
to - l .90 (without feed back damping
signal to excltatlon).
O,hor ,,00 K V ____
Olhor 220 K V
BhOkro .... _..
Bodorpur . ...
_ _ ._
- )<-1<-
::> I 0 I
'!:
.
'"g 1·005
.c.
u
'0
: 1' 00
~
oL_~~~Z--~3--~4--~5--~6~~7~~8--J
T,,,,. ' •• Cl
FIGURE 10 I 3 ¢ fault ot Ponipat end of 400 kV
line. Line cleared and one Debar
400 kV machine dl.sconnected at 0.1
sec- dead time to reclosure VR = 2.88
and O.
rotor acceleration through a lag function (Figure 5).
Per unit rotor acceleration is dd
t
~
wo
where, wand wo
are respectively actual and 50 Hz rotor angular velocities. The gain (flol) of this function may lie between
3 and 7 and the time constant (1'1) should be of the
order of 20 m sec. Damping j most effective with
the higher value of gain while with !J.l=-I there i little
effect. The results with a gain of 5 are shown in
Figure 11. The ere. ults may be compared with Figure
9 where no stabilising signals were employed. The Dew
steady tate conditions in the network would be different from the one that existed before the inception of
the fault. Therefore, the final steady state values sould
be different from the prefault conditions.
7. Dynamic Stability Studie
7.1 The results de cribed in para 6 show that following a major di turbance to the system the machines
at the two ends of the 400 kV line transferring power
from the hydro-generation centre at Dehar to the load
centre around Qelhi (represented by Bad a rpur) eX·
perience oscillations of considerable magnitude for a
FIGURE 11 :
Sp~cd of Debar 400 kV macbincas Figure 9 but with acceleration
feed back !J.l = 5, 't'1 = 0.02 sec.
period of time of the order of ten seconds and more.
These 0 cillations diminish with time, but the decrement is low.
7:2 O sci~l~tions will occur also unde~ s?lall perturbation conditions such as the system IS lIkely to continuously encounter in service and under which it must
be capable of remaining stable. Example of such
conditions are small sudden load fluctuations and Line
switching. The ystem , in other words, must preserve
dynamic stability in normal steady state running.
Dynamic (small signal) stability is a important as
Transien t (large signal) stability in the design of a
system.
7.3 Dynamic stability studies were carried out with
the help of MIs. Engli h Electric Co.e), in order to
check the parameters of stabilising feed back signals.
More exhaustive studie are contemplated in due course
to optimise ettings of control equipment for various
operating conditions.
7.4
7.4.1
Stabilising Feed Back Signal of EXcitation System
and DynamiC Stability
It was found that under
small perturbation
TABIUTY FOR DEVELOPI '0
.\J~
:J04
~I03
r----------------
"
~'02
,10 ,
~IOO
::
~~
geO~~-~Z~~3~~4--~~---O~~---e~~
T . ~. I
,Ie
I
FIGURE 12: Dynamic: stnbillty machine terminal
volta.ge \'ersus time.
conditions the improvement in damping is lcs .significant with the values of gain and time constant of sta·
bilising feed back signal indicated in transient stability
tudies in para 6.5. On the other hand the system is
dvnamically stable even without stabilising feed back
signal. It is considered that recovery from major
disturbances is likely to be of great importance e recially in initial stages of operation and parameters may
have to be varied as sy tern develops. It was accor·
dingly decided to procure A.V.R. with adjustable value
of gain and time constant of feed back signals.
7.4.2 Figure 5 shows the optimum parameter of the
Dehar A VR which is satisfactory for both transient
and dynamic stability. As a check of the stability
calculations, one dynamic stability run was carried out
using the transient stability programme but specifying
a small disturbance in the network. Thjt. was specified
as a step change of - 5 percent in the voltage at Dehar
400 kV machines terminals. Figure J 2 shows the curves
of the above voltage against time. It i5 seen from
this curve that the damping in the system is quite
satisfactory.
8.
Auto-reclosing of 400 kV Line and
deration
lability Consi-
29
400
.2
Sillg/e Pole R closing
8.2: lingle p Je automalic recJosing L emplo ed 10
malnu,in yn hronous , t bility Ii r . inQI ph e to
ground fault . But npolicnti n f thi., type of reel(l io~
iotr duces man. pr blem..
elerminatinn f the
nature and durnli n f eo ndllr. arcs i, imp rIot be·
fore single pole automntit: reclo. ing is adopted. tage
fault te. lseO) have been performed t determine the
acceptable rc 10 ing time and other unkn wn pc t. r
single pole switching at 500 tV v Itllge level. In goneral the longer the tllne the lower (he lability limit is
likely I be and the horter th toler ble (l\lta~e time
n the faulted pha e. However. the I nger the line the
greater i the cnpaciti e coupling hctween phase Dnd u
longer outage lime required to e tingui h the . econdnry
nrc. At orne point these two requirement b come
incompatible nnd succc!lsful rio, ing cannot be
achieved.
8.3
Auro-re('/osillg for DC'ltar E.H. V. }'stem l
or Deh",. 400 kV . y tem, the que tion f fifO .
viding reclosing has not yel been decided although
equipment i being procured which Will be suitable for
single phase or 3· phase reelo ing. Thi n pecl is propo ed to be tudied nfter \he instul\ntiOl' of reactor
and their size htu been finaliseJ ~() that operating
restriction imposed by tranhient ovcrvollagc conditions
can be fully u certaincd. Further, duration of se ondary arcs for single phase lIutomalic reclosing al 0
needs to be established .
S.3. \
9.
onclusions
(I) Transient and Dynamic Stability of Dehar
E.H .V. system and interconnected weak Northern
Regional Grid has heen ensured in an ec nomicnl
manner by reducing fuult clearan e time; employing
high gains fast acting static excitlltlon system nnd incorporating a suitable feed back stsbiJi.ing signal t
A.V.R.
8.1
General Consideratioll
Desirable metbod of reclosing, i.e., whether
3·phase or single pha e, whether instantaneous reclosing or delayed reclosing needs to be carefully investigated. Although instantaneou reclosing is generally
desirable to maintain stability and provide better operation, but may not be applicable to a particular system
as in Keystone(t). In particular the required circuit
dead time for 400 kV is approximately 20 cycle. If
this is a system separation lime, it may be too long to
retain in synchronism when reclosing is affected. Furtber in case of critical stability conditions effect on tbe
system of unsuccessful reclo sure , i.e., reclosing on to
a fault also needs to be ascertained.
8.1.1
8. 1.2 Delayed reclosing provided for necessary dead
time and transient overvoltage conditions do not remain
and is quite frequently applied(·). Tn the Briti h system
vet)' much delayed 3-pbase reclosing is applied.
(2) Developing .11 .V. ~y~tem of Northern Region
demands similar detailed jnveqiglltions of all future:
major power stations so as to reduce osciJIlltion and
eosure stability. For this purro e a rigid criteria of
stability needs to be e In blishcd for the region.
(3) Stability studies 011 continuous basi are
recommended for major stations 80 a to guide operations and ensure security of service.
(4) Special Parameters of generators feediog E H. V.
sy tem like reduced t.ransient reactance bigher ioerlia
constant aod hort circuit ralio has very much reduced
significance.
(5) Overall fault clearance time of 80 m.S.
(4 cycle) i now pos ible due to improvements in circuit breaker and protection performance. Significant
improvement in transient lability with reduced fault
30
THAPAR
clearance times could be adopted in the region.
(6) Fast acting static excitation system improve
stability margins and are recommended for use on
major stations in the region.
(7) Stabilising feed back signals are necessary to
achieve satisfactory damping system transient oscillation if fast acting static excitation system is adopte~.
Signals derived from rotor acceleration were partl.
cularly useful at Dehar and are required to be individually studied for different power stations. Studies on
a continuous basis are recommended to fix adjustable
parameters of gain and time constant of the signal.
(8) Auto-reclosing of E.H.V. lines require detailed
investigations in the region.
10.
References
(I) THAPAR, O.D . and SAKSENA. R.B. : "Relaying for 400
kV EHV System". CBl & P Forty·Second Annual Research
Session, June 1972, Publication No. 116, pp. 102·112.
(2) CORCORAN, J.C.W.; GUPTA, S. and 'PAL, M.K. in
cOllaboration with GARDE, V.D. (HElL) and THAPAR,
O.D. (BEAS) : "System Studies to Determine Excitation
System Characteristics of Dehar and Pong Generators for
Heavy Electricals (India) Limited" , Parts 2 & 3.
(3) HAIL, J.E. and SHANKSHAFT, G. : "Developments in the
Stability Characterist ics of Power System of England and
Wales" . 32·0.5, CIGRE. 1970 Session, 24th August, 2nd
September.
(4) DANDENO. P.L.; KARAS A.N. ; McCylymont, K.R.
~nd WATSON, W. : "Effect of High Speed Rect ifier Excitation Systems on Generator Stability Limits" . lEEE Transactions Power Apparatus and Systems, Vol. PAS·87, January
1968, pp. 190-196.
(5) SCHLIEF, F.R.; HUNKINE, H.D. MARTIN G.E. and
HATTAN, E.E. : "Excitation Control to Imp(ove Power
Line Stability". Ibid, June 1968, pp. 1426.1431.
(6) ELLIS. H.M.; BLYTHE, A.L.; HARDY, J.E. and
SKOOGLUND, J,W. : "Dynamic Stability of the Peace
River Transmission System". A.J.E.E. Transaction Paper
No . 31, pp. 65-813, October 1965.
(7) HANSON, O.W. ; GOODWIN, C.J. and DANDENO. P.L.:
"Influence of Excitation and Speed Control Parameters in
Stabilising Intersystem Oscillations". ] .E E.E. Transactions Power Apparatus and System, Vol. PAS·87. May 1968,
pp. 1306·1313.
(8 ) BYERLY, R ,T. ; KEA Y. F.W. and SKOOGLUND, J.W. :
Damping of Power Oscillations in Salient·Pole Machines
with Static Exciters." Ibid, Vol. PAS-89, July/August 1970,
pp, 1009-1021.
(9) COMMITTEE REPORT: "Relaying the Key Stone 500
kV System". l.E.E.E. Transaction on Power Apparatus and
System, Vol. 87, pp. 1434-1439. June 1968.
(10) LEOEDWARD, J.W.; CHADWICK, H.A. and REISCH,
L.E. SMiTH: "Single Pole Switching on TVA's ParadiseDavidson 500 kV line-Design Concepts and Staged Fault
that results" T.P. l.E.E.E . winter Power Meeting. New
York, January 31, February 5, 1971.
Performance of 110 and 220 kY Lines
E. S. NARAYANAN
Executive Engineering
Tamil Nadu Electricity Board. Madras
YNOPSI
Details of trI]Jouts for a period of 8 years of $el'eral J 10 alld 220 kV lines
in the Tamil Nadu Grid are analyesd and causes identified. Lightning performance of the lines is computed and compared as per AlEE Committee Report. Lil'e
line testing of insulators and replacemenT of low gradient insulators recorded
marked improvement in the performance of the lines. Measurement of footing
resistances coupled with live line testing of insulators are programmed ;11 the
coming months.
1.
Introduction
1.1 A number of EHV Jines (I 10 aod220 kV) have
been in service for several years now in Tamil Nadu
Electricity Board and it was co nsidered useful to obtain
statistical information on their performance. Data
were collected for the eight years. 1961 to 1968 in
respect of 61 lines in the Tamil Nadu Grid (13 Nos.
220 kV and 48 Nos. 110 kV lines) . Though many of
the 110 kV lines were in service before 1961. statistics
relating to the 8 years period 1961-68 have only been
considered in this report.
2.
Details of Tripout
TABLE I
No. of Tripouts
Total length of
line in km
2
3
6
460
1963
4
7
460
3
13
34
39
31
37
640
1074
1120
1400
1400
---171
110 kV Lines
67
96
158
247
267
1968
3250
3250
3650
3900
224
3900
3900
192
189
4500
4500
---Total:
220kV Line
196)
1962
Total:
1961
1962
1963
1964
1965
1966
1967
2.1 A study of the tripouts of the 220 and 110 kV
lines in the Tamil Nadu Grid for the years 1961
through 1968 are indicated in Table J.
Year
1964
1965
1966
1967
1968
2
1440
2.2 The tripouts are further analy cd and given in
Table II.
2.3 The tripouts due to unknown causes are assumed
to be mostly due to Jightning.
600
31
32
NARAYANAN
TABLE II
2
SI.
Details
220 kV Lines
------
Trip ..
outs
No.
2
Percentage
of total
4
3
8
4.65
2
14
16
1.16
8.20
9.4
4
5
6
110 kV Lines
------PerTripouts
centage
of total
6
5
7. Wrong relay
operation
8. Cement pollution
9. Causes unknown
Total
1. Snapping of
conductors
2. Snapping of
earth wire
3. Contact by men
4. Growing trees
5. Failure of terminal equipments
6. Blowing of P.T.
Fuses
3
28
29
24
13.46
4
2.32
91
53.81
142
9.87
1205
83.68
---------------1440 100
171
100
1.95
6
2.00
0.42
7
4.1
5
0.35
5
2.9
25
1.73
2.4 Table III gives tbe list of circuits covered, their
operating voltage and type of construction and Table
IV gives detailed information of the performance of
these circuits.
3. Evaluation
3.1 The product of the length of the circuit in
kilometre and years considered divided by 100 is used
as a basis for determining the lightning performance
and is given in Col. 3 of Table IV.
TABLE III
Name of the Line
SI.
No.
2
Year of
Commissioning
3
Single or
Double
Circuit
Configuration
of Conductors
as per
Figure 2
4
5
220 kV Lines
1.
Kundah P.H. Jl-Salem
1961
S.C.
D
2.
Salem-Korattur up to 1965
Salem -Singarapet thereafter
1961
S.C.
D
1966
S.C.
D
-1963
S.C.
D
5S m/88 km
3.
Singarapet-Korattur
4.
Kundah P.R. II-P.H. III
S.
Kundah P.H. III-P.R. IV
1963
S.C.
D
6.
Rundah P.H. IV-Thudialur
1963
S.C.
D
7.
Thudialur-Madurai
1963
S.C.
D
8.
Madurai-Trichy
1964
S.C.
D
9.
Trichy-Neiveli
1963
S.C.
D
10.
Neiveli-Singarapet
1967
S.C.
D
11.
Mettur-Salem
1963
S.C.
D
12.
13.
Mettur-Singarapet
Singarapet-Bangalore
1966
1965
S.C.
S.C.
D
D
PERfORMANCE OP
110
AND
220
K
U
33
Ii
TABLE m (Conld.)
1
2
3
----
-
4
5
D.
D.
A
- -
llO kV Lines
14.
15.
16.
17.
IS.
19.
20.
21.
22 .
23.
24.
25 .
26.
27.
28 .
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
4S.
49.
50.
51.
Erode-Moyar No . I
Erode-Moyar No . II
Pykara- Moyar No . I
Pykara- Moyar No. II
Erode- Mettur No. I
Erode- Mettur No. II
Mettur- Singarapet No . I
Mettur- Singarapet No . II
Singarapet- Korattur No . 1
Singarapet- Korattur No. II
Erode- Trichy
Erode- Salem
Villupuram-Singarapet
Kundah P.RI- P.R . 5
Kundah P.H. I-P.H. II No . I
Kundah P.H. I- P.H . II No. II
Kundah P.R . II- Thudia1ur No . I
Kundah P.R. II- Thud ialur No . II
Korattur-Villupuram No . I
Korattur- Villupuram No . 11
Pykara - Thudialur No . I
pykara--Thudialur No. II
Pykara- Thudia1ur No. III
Thudialur- Madurai
(a) Thudialur-U dumalpet
(b) Udumalpet-Madurai
Coimbatore-Udumalpet (converted )
UdumaJpet- Madurai (converted)
Udumalpet-Aliyar No. I
Udumalpet- AJiyar No. II
Sarkarpatti- AJiyar
Madurai-Theni No. I
Madurai- Theni No . II
Periyar- Theni No. T
Periyar- Theni No . II
Theni-Trichy No. I
Tbeni- Trichy No . II
Neiveli-Salem No. I
Neiveli-Salem No. It
Madurai-Kayathar No. I
1952
1952
1952
1952
1937
1937
1937
1937
1949
1965
1953
1952
1957
196 5
1960
1960
1960
1960
1958
1963
193 3
1933
1955
1955
196;
1965
1966
1963
1966
1966
1966
1958
1958
1958
1958
1958
1958
1959
1962
1963
D .C.
DC.
D.C.
D.C.
D'
S.
S.C.
S.
S.C.
S.
S.
D .C.
D .C.
D.
D.C.
D .C.
D .C.
D .C.
D.C.
S.C .
S.C.
S.C.
S.C.
S.C.
S.C.
D .C.
D .C.
S.C.
D .C
D .C.
D.C.
D .C.
D.C.
D .C.
D .C.
DC.
A
A
A
A
A
A
A
A
A
A
A
A
A
A
C
A
C
A
A
A
A
A
A
A
A
A
A
34
NARAYANAN
TABLE
m (Con/d.)
2
1963
1963
1958
1963
1959
1962
1963
1963
1964
1963
Madurai- Kayath ar No. II
Thudialur-Erode
Neiveli - Villupuram No. 1
Neiveli-Villupuram No. II
Periyar - Kayathar No . I
Periyar- Kayathar No . II
Villupuram - Kaochee
8alem- Trichy
Link feeder at Singarapet
Link feeder at Trichy
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
4
3
5
D .C.
S.C.
D.C.
D.C.
D.C.
D .C.
S.C.
S.C .
D.C.
D .C.
A
C
A
A
A
A
C
C
A
A
TABLE IV
81. No.
Length
in km
Years
considered
100 km /
year
lx2
100
Total
No . of
faults
--I
2
No . of
Lightning
faults
Lightning
faults per
year
Average
Isoceraunic
level
4x 8
6+ 9
9
10
--
3
4
5
6
7
163
98
190
11.4
5.4
10
202
114.8
134.4
]32.8
40
102.4
160
8
8
3
6
6
6
6
5
6
2
6
3
4
13.05
7.85
5.7
0.684
0.324
0.6
12.12
5.72
8.05
2.65
2.4
3.07
6.40
24
19
17
1
5
6
13
11
23
5
2
4
17
2
3
21
6
14
3
1
1
10
0.75
1.625
3.66
0
0.33
0.5
3.5
1.2
2.33
1.5
0.16
0.33
2.5
45
40
40
45
45
45
50
50
45
45
50
50
45
588
314
228
30.8
14.6
27.0
606
286
262
120
120
154
288
0.0]2
0.041
0.0482
0
0.137
0.111
0.0346
0.021
0.0535
0.025
0.00832
0.0065
0.0347
116.8
) 16.8
13.28
13.28
54.4
54.4
102.4
8
8
8
8
9.32
9.32
1.06
1.06
4.35
4.35
8.2
75
66
12
15
37
26
68
68
61
10
12
27
8
61
8.5
7.625
1.25
1.5
3.375
1.00
7.625
45
45
45
45
45
45
45
420
420
47 .7
47.7
196
126
369
0.162
0.145
0.21
0 .252
0.138
0.048
8
220 kV Lines
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
11
34
9
110 kV Lines
]4.
15.
16.
17.
18.
19.
20.
8
8
8
0_165
PERFORM A CB OF
110
220
AND
35
KV LI
TABLE IV (Con/d.)
1
3
4
5
6
7
102.4
190.4
190.4
126.4
62.4
110.4
8
8
4
8
8
8
8
4
4.8
4.8
40
40
156.8
156.8
68.8
68.8
68.8
204.8
67.2
137.6
80
131.2
40
8
8
8
8
8.2
15.2
7.62
10.10
5.0
8.86
0.320
0.384
0.384
3.2
3.2
12.5
9.4
5.5
5.5
5.5
16.4
2.68
5.5
2.4
7.87
1.2
1.2
0.52
5.77
5.77
4.5
4.5
13.1
13.1
12.2
10.64
7.4
7.4
6.04
2.82
2.11
9.44
8.3
9.2
.44
0.12
0.23
81
79
22
53
55
48
7
5
3
19
10
37
30
44
56
39
15
12
4
22
34
75
69
19
46
51
42
6
3
3
5
I
27
21
40
S3
39
15
10
4
14
31
7
8
8
5
21
13
31
37
24
27
26
14
19
51
44
47
80
1
2
7
8
7
9.36
8.625
4.75
5.75
6.375
5.25
1.5
0.375
0 .375
0.625
0.125
3.375
3.5
5.0
6.625
4.875
1.875
2.5
1.0
4.66
5.16
0.33
0
0
0.875
1.000
0 .875
0.375
2.25
1.25
3.5
4.57
3.83
4.16
2.16
1.625
2.66
6.0
5.57
5.83
9.33
0
0 .33
2
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
(a)
(b)
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
SO.
51.
52.
53.
54.
55.
56.
57 .
58.
59.
60.
61.
40
17.6
72
72
56
56
163.2
163.3
152
152
123.2
123.2
100.8
35.2
35.2
118.4
118.4
158.6
140.8
2.4
3.84
8
6
8
8
8
8
4
4
3.
6
3
3
3
8
8
8
8
8
8
8
7
6
6
6
8
6
8
7
6
6
5
6
3
18
10
28
32
23
25
13
13
16
48
39
35
56
NIL
2
9
50
40
40
50
50
40
45
45
45
45
45
40
40
45
45
45
50
50
50
50
50
50
50
50
45
45
55
55
45
45
45
45
55
55
50
40
40
55
55
40
45
40
40
410
606
305
505
250
355
14.4
17.3
17.3
14.4
14.4
500
376
248
248
248
820
129
275
120
494
60
60
25
260
260
248
248
590
590
550
478
406
406
302
113
84.4
520
456
368
380
4.8
9.2
10
0.1 3
0.114
0.0624
.0912
0.204
0.112
0.416
0. 174
0.174
0.347
0.0694
0.054
0.0558
0.161
0.214
0.1575
0.0183
0.0778
0.0145
0 .1) 65
0.0628
0.0167
0
0
0.027
0.0308
0.0282
0.0121
0.0282
0.017
0.05]
0.0670
0 .0568
0.0615
0.043
0.115
0.190
0 .0924
0.0855
0.095
0.1475
0
0.2]7
36
NARAYANAN
I()O
_"~KV.
90
r
I
~
80
",70
~
:60
0
0
ZSO
CQ)
u40
j
...
V
Q)
c.
30
20
10
I
I v/
.
v
/
v
/
V
/
V
v
./
v
/"
~
/
II()KV.
,L_
.-
//
v
0
. 2 0 04 006 0 ·08 010 0 ·12 0 ·14 0 ·16 0 ·18 020 022 0 .24 O· 26
00
No.ofhghtn.ng faults per IOOkm/yeor per storm day
(Le ss than absclssoe)
FIGURE 1.
3.2 Table IV also gives, in Col. 5, the total number of
faults experienced during the period considered and, in
Col. 6, the number of lightning faults. Col. 7 gives the
lightning faults per year and Col. 8 the average isoceraunic level for the route. Col. 9 gives the storm day
times ] 00 km years. Col. 10 (by dividing Col. 6 by
Col. 9) gives the experienced lightning fa ults per 100
km per storm day per circuit, which figure is used to
indicate the lightning performance.
4.
4.1
Analy i ' of Fault Statistics
General Comme1lts
4.1.1 Among the 61 circuits considered, 4 experienced
no lightning fault during the period under consideration.
4.3
Single and Double Circuit Lillt!s
4.3. 1 All the 220 kV lines considered are si ngle circuit
type. Among the 110 kV lines the average number of
lightning faults per 100 km/year per storm day is 0.088
for single circuit lines and 0.107 for double circuit
lines.
5.
Yardstick as per AlEE Committee Report
5.1 As per the AlEE Committee ReporW) on the
evaluation of lightning perform ance of E.H.V. lines,
the expected trjpouts due to lightning per 100 km line
per year for an isoceraunic level of 40 - 45 tfor the
conditions of design adopted in the Tamil Nadu Grid)
work out as under:
4.1.2 Circuit 7 is the longest (202 km) 220 kV line
and circuits 37, 22 and 23 are the 10Dgest ]}O kV lines
(205, 190, 190 km respectively). Circuits 21 and 59
experienced the greatest number of lightning faults.
4.2
Lightning Performance
4.2.1 Figure 1 shows the percentage number of 220
kV circuits that have experienced number of lightning
faults per 100 km/year per storm day less than
abscissae, e.g., 50 percent of the circuits have e perieDced less than 0.032 faults per 100 km/year per storm
day. Figure 1 also covers the 110 kV lines.
Tower
Footing
20 ohms
(i)
(ij)
220 kV lines
110 kV lines
Resistance
40 ohms
].0
3.1
3.6
9.0
5.2 With 20 ohms footing resistance, the expected
tripouts per ]00 km/year per storm day will be 0.025
and 0.09 for 220 kV aod 110 kV lines.
PERFORMA CE OF
110 A 0 220
0, =2 8'm
0l = 320m
0 )= 32 0 m
H , =H2~ "') =!> 79 m
,LJ
G
, ype-A
It
U
recorded more than the expected lightning rault were
taken up for detailed examinati n. These are circujt
Nos. 14 & 15 and 20 & 21 which are 16 & 31 years old
respectively. About 25 percent r the 110 kV line
covered by this report are more than 15 year Id at
the time of review. One plausible e planation for the
higher indd nce or lightning faults i that the in ulators may ha e developed low gradient. According to
U.S. Nat ional Bureau of Standards(~), n eries f tests
were conducted on insulators with surges of different
rates of rise up to 7000 kV/micr e ond. On one f
these initial trial , did an in. ulator puncture or shu rter
on the first voltage application even with the higher
However, se eral
ra!e of voltage rise obtainable.
faIlures were noted after repeated applications of te t
voltage; in some cases the rate of voltage rise was as
Iowa 3000 kV jl"!"'icrosecond . As the lines 14, 15,20
& 21 are fairly old. it wa. thought thaI the insulator
may have become aged. Live line te ting or in ulators
was carried oul on these lines by means of 'Hipot
Tester' or Mcgraw dison Make. Sixty.three insulator
were found to have developed low gradient in ne
section of lines 14 & 15 and 300 in the enlire reach of
lines 20 & 21. With the replacement of these insulalors, the number or tripouts got reduced onsiderably.
These are indicated in Table V.
G
TABLE V
T
lc===~~==~~~
Line No.
Ho. "21,,,
Overall Tripoul rate p r 100 kmjyear
Before replacement
of iosulator
H,. Hz- 609",
0,= ~· 03m
14
Ty pe-O
15
20
FIGURE 2.
21
6.
37
EO
9 .1
7.3
8.0
10.0
After replacement or
insulator
5.0
2.5
4.4
2.5
Performance Correlated to Yard tick
6.1 Among the 220 kV Jines, circuits 5, 6 and 9 show
more than expected lightning faults.
6.2.2 1n respect of other lines. a phased programme
of live line testing of insulators and measurement of
footing resistances are proposed in the coming months.
6.1.1 The two circuits 5 & 6 are very short (5.4 and)
10 km) and the lightning statistics, based on averages,
are probably not representative. It may also be seen
from Figure 1 that about 40 percent lioes have experienced less than the expected number of lightning faults.
Tower footing
resistance measurements are also
proposed to be undertaken in respect of these circuits
to get a more accurate evaluation and to adopt
counterpoise earthing, if neces ary.
7.
6.2
110 kV Lines
6.2. I It may be seen from Figure J that 50 percent
of the lines have experienced less than the expected
number of lightning faults. A few lines which have
Double ver us
Ingle Circuit Lines
7.1 The lightning performance of double circuit Jioes
will be inferior to that of single circuit Jines. becau se of
the taller towers used in the former . In the case of
110 kV Jines in the Tamil Nadu Grid , the average
number of lightning faulls per 100 km /yea r per storm
day is 0.88 for single circuit and 0.107 for double circuit
Iines.ln respect of aboul 15,000 km lines of over 220
kV covered by a ClGRE Report of 1960(2) the numbers
are 0.04 and 0.06 respectively for a 40 degree earthwire shielding anglo. A significant reduction in double
circuit outages is po sible by either installing a second
skywire or by changing the circuit arrangement to a
double triangular onfiguration with less insulation on
38
NARAYANAN
the lower circuit(4) (Ontario Hydro Research, Second
Quarter 1970). The latter will be tried in certain lines
and the performance watched.
8. Conclusion
(1) Major cause of tripout of 110 and 220 kV lines
is lightning.
(2) Assuming 20 ohm footing resistance, 40 percent
of the lines had experienced less than the expocted
number of lightning faults. With higher footing resistance, this percentage will be more.
{3) Tower footing resistances are to be measured
and counterpoise earthing adopted if necessary to
reduce the number of tripouts due to lightning .
(4) Live line testing of insulators of lines which
have recorded more than the expected number of lightning faults 3nd which are more than 15 years old helps
in detecting low gradient in5ulators and reducing the
number of tripouts.
(5) Double circuit lines have experienced more
number of lightning faults than single circuit lines of
same parameters.
(6) Reduction in double circujt lines outages is to
be considered by changing the circuit arrangemen ts to
a double triangular configuration.
9.
References
(I ) AlEE Committee Report, AlEE Transactions, 1950. Part
pp.1192.
(2) U.S. National Bureau Standards.
(3) ClORE. 1960, Vol. III, Paper 416.
(4) Ontario Hydro Research. Second Quarter 1970 .
n.
Prevention of Flashover in Polluted Insulators
by Conducting Bands
P.K.
MUKHERJEE
Reader in Electrical Engineering
Jadavpur University, Calcutta.
SYNOPSIS
In the first internatiollal symposium on High Voltage Technique held;/I
Munich, West German), ill March 1972, a paper was presented suggesting a Ilollel
method to improve the flasho ver characteristic of polluted insulators. In tMs paper,
the author who attended the Symposium p ersonally, reviews the method alld discusses the similar experiments recently carried out ill the High Tension Laboratory
of Jadavpur University.
1.
Introduction
1.3 Sometimes the lines a re over-in8u lated with
respect to clean conditions to prevent pollution flashover. But this extra expenditure specially in towers,
etc., may Dot be permissible in many cases.
1.1 With feverish industrial activities in modern
times, there is high degree of atmospheric pollution.
The combined action of pollution and moisture causes
flashover of high voltage insulators. For example, the
25 kV traction insulators of the railways in the inaustrial subarbs of Calcutta experiences flashover during
the mornings of winter, when there is considerable fog
in the atmosphere.
1.4 Rumeli has recently suggested putting of conducting rings on high voltage in ulators t top pollution
The paper discus e the method and
flashover(V).
compares the test results of Rumeli with those obtained
in experiments at the High Ten sion Laboratory of
Jadavpur University.
1.2 Several methods are being employed to reduce
flashover, such as hand cleaning of insulators which
is practically feasible only at substations. On line
insulators it is very difficult and requires long outage of
service. Live washing of dirty insulators using mobile
and fixed installations, which does nol require outage,
is being used on high voltage systems(l)(2)(8)(4). The
disadvantages of this method are : (I) the measure is
expensive and has to be done frequently in heavily
polluted regions, (ii) the water of low conductivity is
required, (iii) it may be difficult to reach line insu.
lators in hilly and mountainous areas, (iv) chance of
water infiltration in some equipments such as circuit
breakers exists. The covering of insulators with diffe.
rent types of grease is effective in prevention of flashovers, but is costly and requires considerable outage
time(2)(')(6). Very good results have been obtained
with semi-conducting glaze, but there are difficulties
due to thermal instability and electrolytic corrosion(2){')(5)(')(T)(').
2.
Di charge Propagation and Effect of Conducting
Band
2. 1 A discharge of length x burning on the conducting surface with the application of a d .c. voltage is
shown in Figure 1. The applied voltage V may be
written as :
V=x.E(i>+i. R(x,t)
where, E(/) is the discharge voltage gradient. that is,
voltage per unit length of discharge and R is the pollution resistance in serie with the discharge.
For the discharge length x to increase leading to
flashover, current must also increase. And this is
possible only if additional voltage b.E needed to
2.2
39
MUKHERJEE
40
FIGURE 1:
A polluted model .
increase the discharge length by b,x is negative.
is,
That
Conducting
or,
E- ri < O
where,
r = - 'OR-
oX
FIGURE 2
·
I'
.
per
= e ftiectlve
po IutlOn
resistance
unit length or effective pollution re istivity. Note that r
is positive.
I
A cylindrical suspeo ion
insultator .
with conducting band as compared to without it.
Aquadag paint was used for conducting band .
does not cause any reduction in R, that is, oR = 0. So
3.3 Rumeli has suggested conducting rings for pin
and cylindrical suspension insulators as a practical
outcome of the theoretical and experimental investigation(l°). Figure 2 shows positions of the rings in
the latter type of insulators as suggested by him. In
the test performed here with cylindrical suspension
insulators, aquadag rings in the positions suggested
by Rumeli raised the fia hover potential by 25 percent.
But it has been noted that higher flashover potential
is obtained if the outer rings are shifted inside as shown
by arrows in Figure 2.
the di charge cannot cross the band and flashover is
prevented.
4.
2.3 The voltage gradient in the discharge E has a
positive value for any value of current. Therefore,
if 'OR
ax
is made equal to zero, E- ri> O and the flash-
over is prevented . Let there be a conducting band in
front of the discharge root as in Figure I and discharge
has covered up to this band, then an increa e of x
ax
3.
Experimental Verification
3.1 Rumeli did te ts with artificially polluted disc and
rod model. Artificial pollution was done with 12.5
gm methyl cellulose, 1 gm salt and 25 gm chalk
du t in one litre of water sprayed on the models. The
experiments were done with constant d.c. voltage
The theory and the
uddenly applied to model.
method developed was verified showing that though the
fia nover took place in polluted models, the e are
prevented in similar polluted models with conducting
bands.
3.2 In the High Tension Laboratory of Jadavpur Univer ity thin glass plate ha e been polluted by a olution of Kieselguhr, SiO~ and calcium chloride. The
pollution layer is depo ited over in ulator surface by
spraying and the layer is then moistened by distilled
water. The test specimen was subjected to a.c. 50
cyclesl ec voltage gradually rai ed and about 50
percent increase in flashover voltage was obtained
Conclusion
4.1 As felt by the author and as dl$cussed by the
experts present in Munich Symposium, further investigations should be done for the determination of the
optimum location of the rings and choosing the proper
material for them with due consideration of its economics . Though for experimental purposes, aquadag
may be employed to locate the suitable position of the
rings, this is easily removable and cannot be u ed in
practical insulator. The following points should be
observed in the use of the rings: (J) there should be
good contact between the rings and insulator, (2) the
ring must not have ,barp edges to eliminate corona,
(3) thl!' material of the rings must withstand electrolytic and atmospheric corrosion and spark erosion,
(4) the rings should not deter the cleaning action of
rain .
S.
5.1
Acknowledgement
The author wi hes to thank Mr. Alexander on
Humboldt Foundation We t Germany for one year
PREVE TlON OF FLASHOVliR I . POLLUTED I
post.doctoral fellowship during which he could attend
the above mentioned Symposium in Munich. and Prof.
Hans Prinz of the Technical University, Munich for
allowing him to attend the Symposium . He also
tbanks Sbri N. Chatterjee. his colleague in Jadavpur
University for the various tests performed in H.T.
Laboratory of Jadavpur University.
6.
References
41
UL TORS 8Y CONDUCT! G llANO
(4\ LAMBETH. P.J . : "Pre cntina Pollution
Ele trical Review, 174, PI'. 662-668, 1964 .
Flashover."
( 5) L MBETH. P.J. ; LOOMS. J.. T . ;
TAL WSKl, A . and
TODD. W. .: " urfnce Coating for Hi h Volta e In ulator in Polluted Area ," Proc. lEE . 113, pp. 861-869, 196 .
(6) FORREST. J.S. : "The Performan e of lliah Volt.ae
lnsula.tors in Polluted Atmo pilore."
lectrotechnik . 35;
(19), pp. 448·458, 1957.
(I) NASSER, E.: "Zurn Berechnung des fremd chichtube·
rschlages on isolatoren." E.T.Z., 83A, pp. 356·365, 1962.
(7) FORRE T. J .. : "The Electrical Propcrtic of Seml-c:ondUCling Cerami
IlIlC '. " J. Scien. Inst.. 24. pp. 211-216,
1947.
(2) FORREST, 1.S. ; LAMBETH, P.l . and OAKESHOTT
D.F. : "Research on the Performance of HV Insu lators i~
Polluted Atmospheres ." Proc. lEE, 107, pp . 172·195 and
574·579, ) 960.
(8) LUCAS, D.H.: "The Propenie of
Glazes ." JIE • 3, pr o293-297, 1952.
(3) LAST, F.H.; PEGG, T.H.; SELLERS. N.; STALEWSKI
A. and WHITTAKER, B.B. : "Live Washing of High Volt~
age Insulators in Polluted Areas." Proc. IEEE, J 13. pp. 847·
860,1966 .
emi onductina
(9) RUMELY. A. I "Prcvenling Discharge rowth Over Polluted lnsulating Surfaces ." olleclion of papers pre ented in
International Symposium on High Voltage Te hnology in
Tech. Uoiver ity, Munich, pp. 504·509, 1972.
(10) RUM ELl. A. : "Turkish Patent." Ministry of Industry,
No. 1525 1, 1969.
Switch ing Su rge Flashover of Polluted Insulators
1. R.
I
BISWAS
Electrical Engineering Department
JaJavpur University Calcutta.
YNOPSIS
In extra-higl! .voltage systems, the insulation requirements are primarily
based all switching surges, their probability oj occurrence, amplitudes, and wave
shapes pertaining to system configuration and voltage.
Even in low tension systems, the reliahility oj system operation under switching surges, is oftell called illto question because oj lowering oj withstand capabilities of naturally polluted line insulators in foul and foggy weather. In this
paper the author presents a ver), brief report on the laboraTory investigations 0/1
switching surge flashover oj artificially polluted insulators, carried out by him .
Switchillg surge behaviour of polluted insulators with different grades oj
ortijicial pol/ution severity and pollution sUlface conductivities, with and withollt
a. c. pre-energization, arc discussed.
Lastly, The presence oj conducting bands formed at the narrow section oj the
insulators in counteracting the effect of dry balld/ormaTion at these sections, shows
some improvement in Illithstand capahilities of the polluted insulaTors against these
surges generated in ale laboratory.
t. Introduction
Authorities, Ministry of Railways, Government of India
that in routes of combined (team as well as electric)
traction, the overhead line insulations catch up coal
du t pollution very quickly and in late night and early
morning hours, in heavy fog and mi t in winter months,
the witching urges arising from breaker operations
even in 25 kV a.c. traction system cau e flashover on
these insulators leading to system hazards and outage.
Similar experience i also reported by several State
Electricity Boards, enrouting their lines through
industrial and coa tal terrain where pollution severity
is high.
1.1 With the advent of EHV and UHV transmis ion
ystems at and above 400 kV, the cience f coordinating
insulation in the sy tem requires extensive revi si n ,
based 011 the importance of ' witching surges which
primarily dictate the insulation requirement in the
ystem. The most concerning problem in designing
. y. tem in ulation
at elevated sy tern
voltages
accrues from lowering of with tand capabilities of
pollu ted line insulation against switching impulses in
fou l weather condition . With the rapid growth of
industrie in thi era of mechanisati 0, the everity of
natural pollution on line in u lation, particu larly in
industrial belts and coastal terrains, i n the increase
to cau e seriou system hazard an~ eventual outage
under switching surge. Even in comparatively lowten ion systems the phen mena of flashove r of polluted
li ne insulation under uch surge have endangered the
reliability in sy tern operation to a con iderable extent.
It ha. been experienced by Traction Electrification
1.2 In India, even though the system voltage hardly
exceeds 220 kV there are imminent po ibi lities of having 400 kV systems, oon. To this view investigations
must be undertaken for e tabli hing pollution performance of line in ulation under witching surges,
with simulated pollution everities.
1.3
42
Studies on
witching
urge and inve tigation in
SWITCHING
URGe FLASHOVER
flashover characteristics of polluted in ulstors were
undertaken by the author in the High Tension
Laboratory, .oep~rtme.nt ?f .Electrical Engineering of
Jadavpur Umverslty, as a significant step in this respect
and probably the fir t attempt in lndia to venture
upon investigation on witching surge fla shover of
artificially polluted insulators. The work ha been
submitted by the author in form of thesi for Ph.D.
degree in engineering. The present article is just a very
briefed summary of the abo ve work.
2.
Generation of Switching urge. in the Laboratory
2.1 Switching surges were simulated in the laboratory
by modifying the discharge circuit of the available
standard impul e generator having 1400 k V and 16
kilojoule rating The test surges were of 35/1 60 (J-s.
65/ 180 (J-S and 75/275 IJS wave shapes. The limitati ns
imposed by the available re ouree in the laboratory,
(permitted the author to carry ut investigation on II
kV insulators only with te t surges of pretty low
durations) . For tbe above test surges, wave front and
tail times were measured in accordance with IEC Tech ·
nical Committee recommendation 42 of 1969 but with
test piece having dry pollution and connected across
the output circuit.
3.
Artificial Pollution Technique
3.1 In the investigation, the polluting slurry
ba ically the following compo ition :
Distilled water (30 kiloohm-cm)
Kieselguhr powder (400
mesh size, calcined)
Calcium chloride
had
= 1000 c.c.
= 200 gms
- variable from 15 gm
to 35 gms
3.2 The addition of calcium chloride in variable
quantities is to obtain different pollution everitie on
the test insulators with different degrees of welting.
3.3 The polluting slurry was sprayed on the insulators
by means of spraying of slurry was alternated with
blasts of hot air and the process was repeated till
uniformity and pre-assigned deposit density were
achieved in conformity with tandardization maintained
throughout the investigations.
4.
Wetting of tbe Polluted In ulator
4.1 Before application of witching surge voltages,
the polluted but pre-dried in ulator was subjected to
atomised water pray for a required degree of wetne
in terms of conductivity of the pollution layer. Tbe
degree of wetnes was standardized by measuring total
leakage current flow over the damp pollution layer at
50 V, 50 Hz upply acro the in ulator electrode and
determining the form factor of the insulator. A slow
wetting process with up and down technique wa taken
F POLLUT I) 1
43
AT R
rec~u r e to, ~ r maintaining the c n. tan y of dampne
dUTIng a complete te t erie.
5.
alibration of urg Voltag and
$
orreclloll 'actor
5.1 The cr st magnitudes of the urges ere cnlibrnt d
with 25 crn diamet r tandard . pher ~ us p r indi ntion
in E.T.D . . draft pecifi ntion 19 (121-).
5.2 Th e humidity correction \Va not applied sin e
the te t pie 'e wa s J.. pt m()i~t while f r air den. ity
correction, the ex ponent of air d nsit y wus tnk n
roughl y unity in view of te 'l surges f small duration
and small length of teSI object.
6.
witching urj!c Fin hover of Pollull·d ln ulntor
at Different urface onduct h,lt Ics of J ollllt ion
6. 1 Pollution severity on 11 kV pin and di ~c in s ulator ~
wa. simulated by different sa linity grade and degree
of wetness and wa. expressed in term s of pollution
surface conductivity in microsiemcn .
or a pre-a signed surface conductivity •. cries of
6.2
te t voltage surges were appli ed to determine relative
frequency of Jlashov r ranging from lOt 0 ) 00 percent.
The time to F.O . was also noted on the R . creen.
6.3 Lower and higher percentages f F.O .. viz., 10 to
30 percent and above 70 p rcent
O. va lues were
determined on th e basis of 30 to 50 hot s for fair
accuracy. The critical .0. voltage was determined
with 20 shots. Tebt voltages were referred to standard
condition f temperature (20 0 ) and pre ~s ul'e (760
mm of Hg.) by applying correction factor for relative
air density.
6.4 The distribution of fla shover probabilities wa~
identified as approximately a normal Gaussian distribution again t either polarities of all the specified test
surges on both pin and di sc in ulator .
6.5 The variation of C 0 voltage in kV peak with
surface conductivity of pollution on in sulators are
repre. ented by curves in Figure 1.
6.6 By applying tati stical concepts the standard
deviations (a) of flashover were determined and the
with tand of polluted insulators at different pollution
everitie were asse ed at (CFO - 3a). The effect of
surge front, p "ution alinity and surface conductivity
on critical fla hover voltage. were obtained. The
variations of surface conductivity of pollution as
well as the ratio of time to .O. /time to ere t versus
F.O. voltage, were al so ob erved.
7.
witching urge
Illbhover Te
Energized Polluted Insulator
I
on A. ', Pre-
7. 1 The pollution performance on insulatorRat different
BlSWAS
44
70
681-- -- - -4----:---:--1'-..,.-, Range of poll. ~everitylH 5)
Ronge of rnediurn Rongeofe~rerne
mOdifying surge wove for
POII.severitylfsl polf.seventY'fSl
higher CrO voltoge
66
64
62
Q.
35/ 160 f s
65/180f$
II KV pin i nsulator
75/275f
$
_ _ _ +ve polarity CFO vo l l'o~
curve
-\Ie polari ty CFOvoltoge
C\rve
~60
8, 58
2
~ 56
o
~
U 54
CFO ISO%FOlvoltoge versus
poll. severity in terms af uofoce
conductivi ty in f 5
52
50
Worst case of pol~tion s\rfoce
conduct ivity at 16 micros iemens
48
4OL__~~~~~~~~~~~~~~r---2 3 4 56 8 101
Su rfo ce conductivity of pollution i n f 5 Ilog scolel
62
~
60 Range of me- Range of
I
58
Range of poll. sever ity
modifying surges for
higherCFO voltage
dium poll .
elttr8lTle poll . jA
severi ty 11-'5 I severity I}JSI :
I
,
,,
IlKV standard d isc insuloto,.
I
56
-+ve polar ity C ~ O voltoge
curve
- ve pola ri ty CFOvoltoge
curve
I
,,
,
I
I
,I
I
CFO(SO%FOI voltage versus
poll. sever ity in terms of surface
conduct i vi ty In I-'s
.
I
Worst cose of pollution surface
cOnductivity at IOmicros iemens
42
2 3 4568
2
:3 4 56 8 IOz
Surf ac e conduct ivi ty of pollution in fJs , Log scalel
FJGURE 1 : Varia tion of CFO voltage with incres e of surface conductivity <p.s) of pollution ,
WITCHING SURGE Fl A HO BR OF POLL TEO I
4S
ULATORS
68 ~~----------------------~--68r---------------_____________
l.
POllvilon &010""1
of COC1dl,'r. of Slurr y
Initial poll s udoc.
conductlYlty I at hOI . 18 5 ... I
POllutl()n sol, nlty
15Qt"
64
~\
~,
/
\\ 101 t
I
/
~e-ec
<
\\
/
I
\\
I
~ 56
.0,
\\
\\
/
60
35Qtft of C o C ll~"rtt of " 0.1"1
I ~ , t (II pall surfoce COnduc ' ,Y,I ,
\
~
.;
o
o
~> 52
o
u
~
48
44
P,n Inl ulo fo r
40
Curve (or<t\le 1>Clarlty _
Curve
35
36
(or
- ve polor,t, ___ _
0 : 35 / 160;<1 suroe CFO POnt
• : 75 / 275", su'O' C FO po",t
8
2
3
4
5
o
6
T,me ot A.C Energlzaloon on m,nutel
4
TIme of A C Energizoflon In mln"te.
Ibl
( 0)
FIGURE 1 (b) I Varlallon of S1Irse FO kVp 1I'llb
time of A. . prMnt'rglzal lon (I).
FIGURE 2 (a) : Variation of surge CFO kVp with
time of A.C. prc-energlzation (I).
pollution severities with prior a.c. energiz8tion against
switching surges, is likely to be worse so far as the
reliability of system operation is concerned. This is
due to growth of dry bands at narrow sections of the
insulator during pre-energization by system a.c. prior
to incidence of switching impulse in a line.
switching impulse. likely to occur in a ystem at
critical time of pre-energization , the effect of dry band,
causing lower withstand capabilities, was counteracted
by forming condu ting bands at narrow ection of the
insulators by aquadag paint prior to artificial pollution
(Figure 3).
7.2 The lowering of CFO voltage and statistical withstand of polluted insulators at (CFO- 3a) with time of
a.c. pre-energization, against +ve and -ve polarity test
surges, was determined for both pin and di c insulators
with d ifferen t grades of pollution alinitie. The curves
in Figures 2 (a) & 2 (b) show the variation of surge
CFO (kVp) with time of a.c. pre-energization (at about
50 percent of system voltage over an external circuit
resistance of 6.8 kilo-ohm) for pin insulator.
8.2 The variations of CFO and withstand voltage at
(CFO - 3a) against the test surge , with different preenergization periods, were determined for both pin
and disc insulators with different grades of pollution
severities. The nature of dependence of tandard
deviation (a) on CFO voltage, corre ponding to different
eoergization periods, was al 0 tudied.
7.3 R elationship between standard deviation (a) of
CFO and CFO kV peak at different duration of a.c.
pre-energization, were also established.
8.
Cancellation of Dry Band Effect in Switching Surge
Fla bonr of Polluted Insulator by Fonning
Conducting Band
8.3 The performance of the insulator with conducting
bands, against prescribed standard impulse and power
frequency (both wet and dry) voltage te ts, with and
without pollution, was gtudied in order to a certain
the valid ity of conducting band formed even with a
considerable reduction in effective creepage length in
view of the percent improvement in switching surge
CFO and with tand voltages, achieved by formation
of conducting band .
9.
8.1 In view of the critical situation in pollution
performance of pre-energized line insulators under
9.1
Findiog
Few of the most important finding
from tbe
46
BrSWAS
Conduct. 1'19 bends are shown by broken lines 0101'19 ~"e.pOg.
lengths of insulators
Conducting bendS ocross
creepoge element of pin
Insulotor
PI Pz
= 10mm
= 26mm
= 20mm
Pe = 20mm
P3 ~
P5 Po
P7
" KV pin i nsulotor (creE:poge length 28Smm)
(All dimensions are in mnq
Conducting b8ndsocross~---'-""
creepoge elements of
disC insulator
d, d z 24mm
=
d) d4
=34mm
109
--~~~~~~~
__________~1
II KV disc insulator (cre.po~e
(All dim."siC;na
FIGURE 3
above investigation
follows :(a)
I
or. in
~
I.n(ltk 200mml
"'til)
Conducting bands at narrow region of 11 kV pin and disc insulators across elements
of crcepagcs at the e ectioos .
are summarily
presented
as
The distribution of flashover probabilities of
polluted in ulators under switching surges,
follows clo ely a normal Gaussian di tribution.
(b) The critical situation in pollution performance
corresponding to a particular value of surface
conductivity giving minimum CFO and with-
stand voltages. This is true irrespective
wave hape and polarity.
(c) The positive polarity CFO value. refen
given surge wave shape, are lower thl
for negative polarity under same condi
test.
(d) The nature of vanallon of CFO volt,
surfa e c nducti ity of pollution, are
WITOIING SURGE FLA HOVER OF P LLUT 0 I
similar, irrespective of surge, polarity and type
of insulator.
(e)
(n
(g)
Times to flashover of polluted insulators at
different surface conductivities, comply with an
approximate constancy of the product (time to
FO) X (FO voltage) in lower range of flashover
probability.
(h) With a.c. pre-energization, dry band~ develop
at the narrow sections of the polluted in sulator
and cause further lowering of minimum CFO
and withstand voltages for a critical energization
time depending on the energization voltage
sustained and circuit impedance.
(i)
The lowest CFO voltage attained at critical
energization time, corresponds to surge and
salinity of 75/275 fLS and 35 gms of CaC/2 /
litre of slurry, respectively. The CFO voltage
decreases with increase of alinity of pollution
as well as with the crest of incident surge.
(}) The CFO withstand voltages decrease sharply
with increase of energization period till
corresponding minima are reached. Thereafter,
the pollution performance improve teadily
with longer energization time corresponding to
drying-up of pollution layer.
(k) With a.c. pre-energization, the pollution performance of insulators with conducting bands
improves. The CFO and withstand voltage
minima are higher than those in the corresponding cases without conducting bands.
(I) The critical situation
of pollution flashover
with conducting bands, is reached at shorter
energization time, called the critical time and
this is irrespective of surge wave shape and
polarity.
(m) The formation of conducting band on insulators
lowers impulse and power frequency (dry aod
wet) flashover voltages considerably for an
47
apprel:iuble improvement in pollution b ho\'iour
under wit hing impulse.
The CFO voltages are lower with higher time
to crest of tbe applied surge while tbe effect of
tail time is insignificant.
With high surface conductivity of pollution ,
the incident surges are favourably modified
with appreciably reduced time to peak, front
and tail re ulting in high CFO value. in that,
pollution beha\ iour at extremely high surface
conductivity is similar to a surge attenuating
and diverting device.
UUTOR
(n)
10.
The CFO and withstand oJtage relation with
energization time ar similar. They sh \V n
,harp rise with lime of cnergization bey nd the
critical time alld then . unlike the cases with ut
conducting band , tend t be orne more or Ie
flat beyond a certain energinlti n durati n.
onc!u ion
10.1 Judici u application of ondu ting band. of
narrow section of insulators with omc de. ign modifications , is likely to open up avenues for a more reliuble
pollution performance of ystem insulation again t
switching transients in regions f high utmospheric
pollution severity. The creepage length of line in ulator
should be in rea 'ed and to avoid formation of dry
band the insulator diameter at different ections should
not vary widely.
10.2 The form -factor of in~ulator having little bearing
on pollution performance. a high figure of merit i mo t
desirable for improved withstand abilities against swit hing urges. For string insulator•• u e f deep-ribbed disc
is highly recommended. The conducting bands formed
on disc will improve tring efficiency a (l re ult of
increased disc to di c capacity. To minimise the adverse
effect of dry band formation, conducting bands may
be suitably formed for some improvements in the withstand of polluted insulator against switching surges.
The c nsequent reduction in effective creepage may be
compensated by increasi ng the creepage by a required
minimum for a compromised withstand against prescribed power frequency and impulse tests. The conducting
band techinque may be recommended for line insulation
in industrial belts and coa tal terrains where atmospheric
pollution severity is high.
10.3 Though, the conducting bands were put around
the narrow section of the in. ulators to obtain the
improved swi tching surge performance. It is a matter
of further inveHigation as to the location of the band
to obtain the best surge performance under pollution.
11.
Acknowledgement
The author is indebted to Dr. B. Chaudhuri of
Electrical Engineering Depl:lrtment, Jadavpur UDiversity
for his supervision and guidance in the work carried
out and submitted by the author for a Ph. D. degree
of Jadavpur University. He is al 0 thankful to Dr. P.K.
Mukherjee of Electrical Engineering Department. for
inspiring the author to present thi report of his Ph.D.
work and for giving him valuable sugge tions and
criticism. He IS also thankful to Prof. O.K. Deb,
Head of the Electrical Engineering Department, for his
encouragement for presenting tbis report.
Optimal Load-Flow Analysis
P.K. MUKHERJEE
DHAR
Reader
Reader.
Electrical Engineering Department Jadavpur University, Calcutta.
R.N.
SYNOPSIS
Load-flow and optimal 10ad.Jlow problems of a power system have been
defined. The nature of variables connected with a system bus has been discussed
and they have been classified into three groups-control variables, controlled variables and parameters. Sensitivity matrix relating the changes of the control and
controlled variables has been derived and its application in the optimal load-flow
problem has been shown. Finally, optimalload-jloll' of a 25-bus system has been
solved using digital computer.
List of Symbols
Vt =Vt L8t
= complex voltage of the bus i with
respect to ground.
Yc".-= Yc",L Ocm = complex admittance between the
buses i and m.
= Net active and reactive powers
respectively injected into the
bus i.
= Superscripts indicating maximum
M,m
and minimum values respectively
of a variable.
= Number of system buses.
N
ng
= Number of generating buses including slack bus.
s
= Slack bus.
= Jndicate conjugation of a comp*
lex variable.
1. Introduction
Optimal load -flow envisages a condition in which
the power flow in an electrical power system occurs
optimally. It is one among the many feasible loadflow solutions in which a certain gain is optimised as
well as the operating limitations of the system are satisfied. In the past, this was achieved througb many
load-flow studies in which much judgement and intuition was involved in deciding what Quantities are to
I.]
be adjusted in attaining the optimal condition. During
the past decade, however, many analytical methods(l-U)
have been developed which have turned this formidable
problem into a routine calculation. In this short paper,
the problem bas been discussed in the light of the
modern development and then optimal load-flow of a
25-bus system has been solved using digital computer.
2. Load-flow Equations
From the knowledge of circuit theory, the current
injected into a particular node i of a network is given
by:
N
... (1)
Ic = ~ YcP' 9;"
2.1
m=l
In the terminology of electrical power system, the
nodes are koown as buses and in a system bus powers
are more interested tban bus currents. Converting,
therefore, the above current relation into a power
equation one may write:
N
P,+j Q,= Vc 1.*= V;
~
Y,,,,* v,m*
m=l
If now polar expressions are used,
reduces to
N
P,+iQ,=
above relation
~
m= l
(2)
49
OPTIMAL LOAD-FLOW ANAL SIS
Above equation is a complex power equation which i
non-linear and for a N-bus system, N such equations
These equations are known as load-flow
results.
equations.
(i) Independent or ontrol
generally denoted by II.
(ii) Dependent or ontrolled variable - The
generally denoted by x.
2.2 Separating real and imaginary component of
Equation (2), following 2N equations are obtained :
N
I
N
I
I
I
p.= 1: Vi Y im V", cos (8 j - Om- Bim) I
m=l
I
QI= 1:
V, Y,mVm sin (31- 0",-6-1",)
m= l
J
i = I ,2 ... 2N
...
(3)
Remembering that:
p. = PG.-PD 1
ann
Q.= QG.-QD,
where PG. and QG, are active and reactive generation
respe~tively and P Di. and QD 1 are act!ve and reacti~e
consumption respectIVely of the bus I, we can write
Equation (3) in the form:
Ilriable - The e are
0
nre
.
(iii) Parameters or uncontrollable variable - The e
are generally denoted by p and remain mpletely sp cified.
2.5 U ing the e notation. the S I f load-flow quotion (4) cnn be exprcs ed in a ompnct form o. :
g(X,u,p) - O
... (5)
where. g defines 2N p wer flow equation of the form
(4). For load-flow study with the help of n computer.
only (2N- 2) such equation need to be solved since the
equations corre. ponding ((l the slack bll. are not
required.
3.
Optimal Load-flow Equation
3.1 Tn a particular load-flow analysis, independent or
control variables denoted by II remain pecified and
dependent or controlled variables indicated by x are
determined by solving Equation (5) since the parameter
variables p remain also specificd.
But generally a
Vi Y im Vmcos (1). - Il,,, - e'm)- PG 1 + PD,=O
supply undertaking is intere ted to make a lurge
number of load -flow studies to determine what i
m=l
I
I i= l. known as optimal operating condition and the p wer
12 .. 2N flow corresp nding to this optimal operating condition
N
\
is known as optimal load-flow. An op ruting ondi1: Vi Yim V", sin (Oi- Om - Oi", )- QG,+QD,= O I
tion becomes optimal when the value of some perIn=-]
J
formance index chosen by the utility undertaking
becomes optimal. For instance, if the Objective i to
(4)
operate the ystem in such a way that minimum trans2.3 let us now investigate the nature of variables mission los. occurs then the performanc index, also
involved in tbe above Equation (4). Vi and V,,, are known as objcctive function, be ome. the tran . mi sion
voltage magnitudes of buses, both load and generator, loss. Objectives might be minimi ation of operation
while 0, and 8m are their phase angles with respect to cost. known as optimal dispatch, or the opt imal curtailslack bus. Out of these, the voltage magnitudes, phase ment of load (load shedding) during emergency condiangles of load buses and phase angles of generator lion arising either by generation hortnge or from a
buses are completely dependent on the operating condi- severe faull.
tion determined by such quantities as active and reactive generations, voltage level of generator buses in- 3.2 In achieving the optimum value of the objective
cluding slack and the conSumer demand. The former function . some or all of the control variable . denoted
quantities can therefore be called dependent or by u in Equation (5). are varied in steps following some
controlled variables, while the latter ones can be rule within their respective maximum and minimum
divided into two distinct groups. Power generations, limits and then the values of dependent or controlled
active and reactive, voltage magnitude of the generator variables, indicated by x, are found out by solving the
buses, etc., can be controlled meaning thereby that load-flow Equation (5) . The values of x th\lS found
these quantities can be varied by th.e supply .under- shou ld also remain within their respective range of
takings conforming the statutory regulatIons, eqUIpment maximum and minimum values. Thus the optimal
ratings, etc. These variables a!e therefore kn~wn as load-flow solution will be one among the many feasible
independent or controllable or SImply control vanables. solutions of qualion (5 ) when the objective function
On the other hand, the con umer demands on the or the performance index optimise.
The optimal
system buses are neither controllable by the utilities load-flow problem can therefore be stated as follows:
nor controlled. These variables are, therefore, known
Optimise f (x , u)
(5)
as parameters. Included within this set are s~stem
admittances Yim for a particular system configuratIOn.
subject to g(x, u, p)= O
(6)
2.4 The variables involved in the load-flow equations
xm <;x.;;;;x M
... (7a)
are therefore classified into three groups:
and
~
1
50
DHAR AND MUKHERJEB
... (7b)
3.3 The relations shown in Equations (7a) and (7b)
a.bove are known a inequality constraints on tbe variables and in power system these are of the form;
... (9)
p,m <.,Pi<;.PiM
... (7c)
Q,m <;.Qi<.,QtM
.. . (7d)
where, S=- JIt- 1J.. is the sensitivity matrix. In Equation
(9) , J.,- I indicates inver ion of the matrix Jf1j. J.. and JIt
are commonly known a Jacobian matrices. Needless
to say the elements of the sensitivity matrix provide an
insight of the effect of control variables on controlled
variables .
Vi m <;. Vi <;. vM
i
.. . (7e)
5.
ISj - Sml<..Tim
... (7/)
5. 1 Optimal load-flow of a 25-bus system(5) is solved
using the sensitivity matrix. The matrix is evaluated
connecting the active loadings (controlled variables) of
the generator buses with their phase angles (control
variables). The relation may be expressed by :
where, T i m is the maximum phase angle difference permitted between the two buses.
...
which gives
Sensitivity Analysis
4.1
Once the objective and the related control variables are decided, changes of the dependent variables
with the change of the control variables can be shown
by what is known as sensitivity analysis(4) . Sensitivity
is defined as the ratio of L). Xtl L). u, where both L). Xj and
6 Ut are small and the matrix whose elements are
formed by these quantities is known as sensitivity
matrix . Since g(x , U, p) is a non-linear function , the
elements of the sensitivity matrix depend on the operating values of x, Ii and p, that is, on operating con.dition and hence need to be evaluated at each operatmg
condition. The derivation is as follows.
4.1.l
At any operating condition specified by say
xo, U o and p let the control variables undergo small
changes indicated by 6 u. This will cause changes of
the controlled variables also. Equation (5), therefore,
reduces to
Application of Sensitivity Matrix
ng
I:::,.P,= 1: S i; 1:::,. 8" i= 1,2 .. .ng
j= l
I# s
change ill transmission loss PL is given by :
Ilg
I:::,. P
L
=
... (8)
The higher order terms in L). x and I:::,. ft have been neglected since the changes are kept within small magnitude. Jf1j in Equation (8) is obviously a matrix since
L).x represents changes in controlled variables. Tbi
matrix contains the first derivatives of Equation (5)
with respect to the set of variables x. Similarly, J.. is
a matrix containing the first derivatives of Equation (5)
with respect to the group of variables u. In Equation
(8)
b, Pi
1:
i= 1
Now introducing the Equation (10) :
ng
ng
I:::,. P L = 1:
1: S iil:::,.Sj
i= 1 j = I
j=l=s
from which
I:::,. P
Applying now Taylor's series expansion, the above
relation can be written as :
... (10)
- -L =
b,8J
ng
Sij,j= 1,2 .. .ng
1:
i=
J
... (11)
j=l=s
The phase angle of the slack bus is not cantrollable
since it has been taken as reference.
5.2 The relation (J 0) may be further utilised to find
out the optimal dispatch. If the total fuel cost of the
system is F T then
FT = /(P,), i= I,2 .. .ng
from which ,
g(Xo, Uo• p) = O
since the system was in operating condition before the
changes occur. Hence
where, F, is the fuel cost of the plant i only and
dF,
is its incremental cost.
dP,
OPTIMAL LOAD~FLOW ANALY (
5.3
Using the relation (10), Equation (12) reduces to :
ng dE.
~ FT 1:: - -'
ng
1:: Sij ~ 8;
;= 1 dP, j = l
j ::p s
51
6.3
Optimal load-flow condition j arrived when the
rate of improvement of the obje tive function is found
to be less than a gi en tolcran e.
7.
tudy of a
ample
y tcm
from which
t :.F T
-
l1o
~oJ
ng
dE.
=1::
d'P' Sil, j = I,2 ...ng ...(13)
;= 1
i
j ¥: s
The sensitivity relation (J 0) is thus utilised to find out
the sensitivities of the transmission losses (Equation 11) and fuel cost (Equation 13) respectively with
respect to the phase angles of the generator buses excluding slack. Adjusting the phase angles in step
according to Equation (11), optimalload-f!ow in which
minimum transmission loss Occurs may be obt.ained.
Similarly optimal load-flow minimising the fuel cost
may be obtained by adjusting the phase angles in steps
according to Equation (13). It may be noted here
that the optimal loadings of the generator buses including slack obtained in the above two cases will be generally different. They will be identical if and only if
the incremental fuel cost of all the plants of the system
are same which is a too idealistic proposition.
6.
7.1 The pro edure mentioned abo e hn been utili ed
to find out the optimal load-flow conditi n for a 25bus sy tem(5) baving 4 generating plant.
1I0wing
loading of the plant · (in per unit with respect to 100
MY A base) have been obtained with the help of digital
computer.
Bus No. Net initial Ion ling
Net loudin" for
minImum trunsmis ion 108s
Net londing for
minimum fuel
consumption
I.S5+J 0.71413
1.9S736+J 0.S8313
2
0.679 - j 0.23936 0.50- j 0.17663
0.50- j 0.16863
3
0.89002+J 0.39422 1.14524+JO.30653
0.75+10.44884
4
0.1836 -t J 0 098860.38350 +10.006080 .383 50 tj 0.02198
I (slack ) 1.83828+10.63218
Consideration of Constraint
6.1 Inequality constraints shown in Equations (7c) to
(7 f) are now considered. Inequalities (7d) and (7e)
are interrelated and are mostly independent of Equation (70) which is highly sensitive to changes of phase
angles(6) only. In the case under consideration,
voltage magnitudes of the generating buses including
slack have been beld constant. Inequalities (7d) and
(7e), therefore, need not be considered . Inequality
(7j) is ignored due to the fact that tbe cases of optimal
loading considered are normal operating conditions
and hence Equation (7f) is assumed to be satisfied.
6.2 Inequality constraint (7c) is considered by exchanging the variables in the relation (10.). I n the
iterative procedure, the matrix S is built-up at every
operating point and Equations (II) or (13) is utilised
depencling upon the objectives to find out the sensitivities of the objective function. The phase angle of
the generating buses are then adjusted proportional to
these values and solution of Equation (5) follows to
find out new operating point. During the search if,
however, the active loading Pi of tbe i-th generating
bus exceeds its limit, upper or lower, the matrix S
obtained at this point is nOl utilised as it is but is
modified using Jordan elimination(1) and thereby the
positions of 6 P. and 6 8, are interchanged indicating
that 8, ceases to be a control variable. 6 P. is now
given a value:
6P,=P" l'mU- P,
to calculate ~8i' 8, behaviug as a controlled variable.
Next, the sensitivities are calculated using the modified
matrix excluding the elements of the i-th row.
Transmission losses have been reduced by 1.3 J MW
from its initial value of 12.81 MW to the final vulue f
11 .50 MW in 30 iterations while optimising the tran mission losses. Similarly, while minimising the fuel
consumption. the fuel consumption has been reduced
by 679 x 10' B.T.V. per hour from the initial value of
8461 x 106 B.T.V. per hour to the final value of
7782 x IOn B.T.U. per hour in 15 iterations.
8.
Conclusion
Problem of Optimal load-flow has been defined and
solved with objectives of: (0) minimum transmission
loss, (b) minimum fuel consumption. With pha e
angles of the generating buses taken as control variables and their active loading as controlled variables,
the sensitivity matrices have been calculated from
which the sensitivities of the objective functions have
been evaluated. Optimal load-flow condition has been
found out by adju ting the control variables proportional to these sensitivitie and tben solving the load -flow
equations iteratively.
9. Reference
( I) DOMMEL, H.W. and TINNEY, W.F. : "Optimal Power
Flow Solution ." Trans . I EE, Power Apparatus and
System, Vol. 87, 0 tober 1968, pp . 1866-76.
(2) EL-ABIND, A. H. and JAIMES, F.J. : "A Method for
Optimum Scheduling of PO\l:er and Voltaac Maanitude."
Trans. IEEE, Power Apparutu and System, Vol. 88. April
1969, pp. 413· 22.
(3) SASSON, A.M.: "Nonlinear Proarammina Solution
for
52
DHAR AND MUKHERJEE
Load-flow Minimum Loss and Economic Dispatching Problems." Trans. IEEE, Power Apparatus and System, Vol.
88, April 1969, pp. 399-406.
Operation of an lntegrated Power System." Proceedings
of the 42nd Annual Session of the Central Board of Irrigation and Power, New Delhi, December 1969, pp. 171-202.
(4) PESCHON, J. ; PIERCY, D . S. ; TINNEY, W F . and
TVEIT. O.J . : "Sensitivity in Power Systems. " Trans.
IEEE, Power Apparatus and System, Vol. 87, August 1968,
pp. 1687-1695.
(6) JOLlSSAINT, C.H. et al : "Decomposition of Real and
Reactive Power Flows." Trans. IEEE, Power Apparatus and
System, Vol. 91 , March/April 1972, pp. 661-69.
(5) DRAR, R.N . ; MUKHERJEE, P.K . and PATRA , S.P. :
"A Composite Digital Method for Load-flow and Economic
(7) ZUKHOVITSKIY and AVDEYEVA: "Linear and Convex Programming." (Book ), Kiev Institute, Saunders
Company .
Sparse Matrix Technique for Solution of Load Flow
Problem by Newton-Raphson Method
P.K.
CHAITOPADHYAY
R.N. DHAR
G.P. P UR YA TH
Department of Electrical Engineering, Jad vpur University.
I utta.
SYNOP I
Of the different methods available at present for solution of fhe load flow
problem ill electric power systems, using Digital ompute,., Newton.Raphson
method has been proved to .be ".lOst pow.erjul. Though the method was first proposed by Vanness and Griffin In 1959, II was "Of accepted as a practical method
until about 1968, due to its excessive memory requirements OIl the computer. The
storage problem was solved in 1968 by W.F. Tinney and others by employing
sparse matrix method. In this method only the no,,·zero elements ar caleulat d
and stored, thus the storage requirements are brought down to a minimum. This
has resuited in its turn a complicated computer programme. The allthors hal'e
developed sllch a sparsity oriented programme and te.Hed it for a 14·btls standard
IEEE system.
1.
Introduction
1.1 The mathematical formulation of the load flow
problem lead to a set of no-linear simultaneous equations. Several methods have been established for
solution of these equations. Of these, NewtonRaph on method, though not infallible, has proved to
be the most reliable.
The method has been
found to give correct results even for iIIconditioned systems, where, the conventional met·
hods, for example, GUmn and Stagg' (1) method, fail
to converge. Besides, with minor changes in the ba ic
method, problems like constant area interchange, automatic adjustment of tap settings for on· load tap
changers and phase shifters may be dealt with. Moreover, the method forms a basis for accurate solution
of the optimi ation problem.
1.2 In spite of all these advantages the method did
not become very popular a it required about four
times high speed memory compared to other les reliable methods. The present day poularity of NewtonR aphson method of solution is mainly due to its implementation with sparse matrix technique.
1.3
In Newton-Raphson
method
of
olution, the
original ystem of non-linear equation i fir t tran
formed to a set of linear equations which i then solvedby Gaussian elimination method(~). The coefficients f
the e equation may be arranged in a matrix form
known as Jacobian matrix or variationa l matrix. I~
load flow analy i of practical ystems, thi matrix ha
a highly sparse tructure. Thi fact ugge ts th t a
con iderable aving can be made in memory and a
well as in c mputation, if only the non-zero clement
of the Jacobian matrix are proce d and stored. Th;
is known a spar e matrix method. However, nly thi
alone doe n t help much in saving computer memory.
If the equation are not properly ordered. the par ity
may be largely 10 t during elimination. It is, therefore,
necessary to pre.determine the order of elimination.
Tbi is done by numbering the bu es uitably. The
renumbering procedure is known a optimal ordering.
With thi optimally ordered and spar ity oriented programme, it ha been pos ible to solve 2000 node problem with a computer having only 32 K memory(·).
1.4 Considerable work ha
been done and some
paper ('-6) bave been publi hed in the line. None of
these paper give the details of programming which j
very much complex since only the non-uro element
are tored. The authors bave developed a simple
S3
54
CHAITOPADHYAY, DHAR AND PURKYASTHA
programme to exploit the sparsity of the Jacobian
matrix. The present paper gives a brief description of
the method of solution with some hints towards the
programming technique .
The Load Flow Problem
2.
2.0 In the simplest form, the load flow problem may
be stated as follows :
(i) the schedule of active and reactive loads at load
buses (P-Q buses),
(ii) the schedule of active generation and voltage
magnitude at all the voltage controlled generator buse (P-V buses), except the slack bus
where the voltage is completely specified.
2.2.2 The active and reactive power P t and Qk are
obtained by separating the real and imaginary components in Equation (3); Em is the magnitude and 8.,. is the
angle of the phasor Em measured with respect to the
slack bus. The advantage of the polar formulation lie in
the fact that number of unknown variables reduces to
2 (N- I) -NG, where NG is the number of generator buses, since voltage magnitudes are specified for
the generator buses.
2.2.3 Equations of the form of (3) may be written for
all the buses except the slack, which are then solved for
the unknown variables E and 8.
2.3
Newton-Raphson's Method of Solution
2.3.1 From Equation (3) it is seen that both P and Q
are fun...tions of E and 8, so that PIc and Qk may be
written in the form
The load flow problem consists in solution for
(i) complex voltage at the load buses,
(if) voltage angles at all the generator bu es except
the slack.
(4)
2.1 Once the voltages at all the buses are completely
known, all other variables of the system, for example,
reactive power at generator buses, active and reactive
powers at slack bus, line flQws , line losses, etc., may be
found out easily.
... (5)
Equations (4) & (5) are non-linear and, therefore, are
solved using numerical methods . If in any iteration 1
the estimates for the solution vector be {81(1) , 82(1), ... ,
2.2
Mathematical Formulation of the
Problem
Load
Flow
8 (1), E1(1), E 2(1) ... , E (1) }, and
N
2.2.1 The complex node current 1;, at any bus k in an
'N' node power system may be expressed in terms of
complex voltages Em of all other buses through the
linear relation
],.=
1:
mEk
... (1)
YIo'" £."
where, Y~m = (G.tm +jBk"') are elements of the bus
admittance matrix and the notation mtk emphasizes
that the summation should be taken only for those
buses that are directly connected to bus k.
N
the
required
correction vector be { 681(1),6Ih(1), ... 68N(1),6El(l),
6E2(1), .. ., 6EN(l) }, then Equation (4)
may
be
written in the form:
Pt= Pt(81(l) + 681(1), Ih(l) + 68 2(1) ..... . ,
8 (l) + 6 8 (1), E 1(1) + 6 E 1(1), E~(l)+ 6E2(1)
N
N
(6)
The complex power at bus k is given by
Expanding the right hand side of Equation (6) by
Taylor's theorem,
P,, +J Qk= Ek It.·
=-EII l: (YIc'" Em)·
... (2)
mtk
Using polar co-ordinates for the voltage ariable, Equation (2) may be wrHlen in the form
P,,+J Q"= E,, e 8" .E (~.,,-J B"m) Eme -J 8...
lm:k
j
... (3)
+ ~ ::~
mr.k
68.,.(1)+
~
mr.k
:t
6Em(1) + ¢t(1)
... (7)
SPARSE lATRIX T ECHNIQUE FOR OLUTIO. OF LO 0 FLOW PR BL t BY
BWTO -RAPH
T B
The term ¢I.te) contain
higher degree terms in the
differentials t:. ~",e) and t:. Eme). The e terms may
be neglected for a sufficiently close estimate for the
solution. Under this condition, Equation (7) may be
written as
-r. . E"
Nu = 8P"
(8)
(9)
b,p,,(l) is the difference between the specified quantity
PIt and the calcu'lated va lue P,,(I). Proceeding in a
similar manner Equation (5) may be written to the
form:
mtk
a'/.: ~ 8111(1)+
8
I
Q,t
£:",(1)
6. Qke) = Qk- qk(1)
P,,+ Et : Gu
:~: - Pt-E,.~ G""
Ltt =
:~:
. E,. = Q,, - Et 2
e'l! "-Zo E". cos
I".=E". sin ai m
am e,,, G.",-/.,. B"",
( 11)
bm= e mBk", +
solved for equal
2.3.3 The expressions for the partial derivatives to
Equations (8) & (10) may be derived from Equation (3). The results are shown in T able 1.
B~1t
a'no
(10)
2.3.2 Two Equations of the form (8) & (10) may be
written for each load bus. Since Q is not specified at
the generator buses , only Equation (8) is written for
all generator buses except the slack for which no equation is written. Thus 2(N - 1)-NG linear equations
may be obtained which may be
number of unknown variables.
B ltlll
Ju =
where.
nlt k
Em(I) = 6 Q,.(I)
where,
b,Eno(l) /
I (Colltd.)
- Qt-Et'
8t
I
S5
Diag onl term
H",, = apt
where,
M TH 0
... (12)
1m Gk",
It may be seen that
H kno - Lkm
J..",= - N"m
( 13)
t14)
2.3.4 Since the variable for the slack btl are specified, their differential are zero, and hence, the partial
derivatives are not calculated for the slack bu s.
2.3.5 For the sample sy tem hown in Figure l, the
linearjsed equation involving Jacobian matrix may be
written, considering bus 1 to be the lack, as shown in
Table I (a).
TABLE I
Expre sions for the partIal derlvaU,e .
2.3.6 It may be noted that for each bus two row and
two columns are allotted . This i done io order to
implify the retrieval of the elements 11, J, Nand L
from the common compact storage.
Off· diagonal terms
2.4
The Flow Diagram
2.4.1 The method of oluHon of the load flow problem
by Newton Raphl'on's method may be understood by
means of the simplified flow chart hOWD in Figure I.
3. Programmiol:
Jl m =
b jj
aaQt
8 = -a m el- m t
m
3.0 The success of the method is very much dependent on skillfu1 programming. Only the oon·zero cle·
ments of the J acobian matrix are processed and stored
in compact arrays. Auxiliary tabJe are used for retrievaJ of these elements from the packed storage. Tbe
56
CHATTOPADHYAY, DHAR AND PURKYASTHA
TABLE I (a)
1
2
3
4
3
Hu
Nu
4
h.2
L22
5
7
6
10
8
9
H24
N~,
H 2o
ll3r.
llPz
Ju
Lu
J 26
ll E 2/E 2
ll Q,
H a,
Nu
Ha .
ll a3
2
5
Ha3
6
. Na3
J3d
L33
J3,
Na,
Ja r.
7
Her,
N,r.
H"
N43
Hu
N"
Hu
8
J42
L,2
J'3
L,·,
J"
L"
J'5
9
Ha
NI;~
I-l.;a
NS3
H.u
Nil '
ll Ea/ E3
H 65
_I
-
6.Pa
I
6. Qa
ll a~
6. P,
ll E,/Ec
6. Q,
6. 8.>
6. P 5
10
... (13)
programming logic, as such, is very complex. The
details of programming have been discussed under
following heads:
(i) Optimal ordering
(ii)
Formation of the bus admittance matrix, and
(iii) Load flow solution.
3.1
Optimal Ordering
3. I.) The purpose is to ass.ign code .Durn ber~ to . buses
in such a manner that dUring the tnangulansatJon of
the Jacobian matrix. fewest Jlewelen~ents are ge!1er8~ed.
The determination of absolute optImal ordermg IS a
very labourious job. Approximate solution are usually
preferred . Various schem~s(6) have bee~ developed for
approximate ordering. Of these the simplest, tho~gh
not very efficient, scheme is to code the buses starl~ng
with that having fewest connected branche and endlOg
with that having the largest number of connected
branches .
equivalent parameters, namely, resistance, reactance
and shunt capacitance. 1 he terminal buses of each
line are stored in two integer arrays KB and LB and
the line parameters in three arrays. R, X and Y. One
data card is used for each line. Five quantities are
puncbed on it, two for the counts of the terminal buses
and, three for the line parameters. The line data may
be fed in any order. The programme is so written that
only the Don-zero elements of the bus admittance matrix
are processed and stored in two arrays G and B together with the indexing tables KB and LB.
7t-
3.2.2 For the sample system shown in Figure 2, the
contents of the input and output arrays are shown in
Tables II & IIJ.
TABLE lJ
The Input array.
Location
KB
LB
1
3
2
5
4
3
5
5
R
X
Y
R13
Y1 3
X13
2
5
R52
Xu
Y.\2
3
1
R15
Xlii
Yl&
4
2
3.2 Formation of Bus Admittance Matrix
RiC
Xu
Y2,
4
5
Ru
X'3
Y'3
3.2.1 The only information required for determining
6
3
Y3~
X. 6
Ru
the bus admittance matrix is a table that gives the. cou!lt
R,:;
X,;
4
7
Y's
for the terminal buses of each line together WJth ,:_1l::S_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
1
SPARSB MARTJX TECHNIQUE FOR OLUTIO
OF LOAD FLOw PROBLIiM: B
I Reod
input,optlmol ordering,
estoblishing G,B,P,O,ER.EI
r Bus
l
I
J= J+I
,
count J :1
"
1
I
Yes
( Slack bus? )
I
N WTON-l\APII
.
No
r( Voltage
controlled bus?'
No
Yes
Compute single row of
JacobIan motrix,.4 P ,
eliminate all terms to
the left of the diogonol
term . Normalise and
store I n co mpoct 0 rr ay
Compute both th e rows of
Jacobian matriX 6P and AO,
eliminoteoll the termsto th~
left of the diagonol term In
both t he rows. No rmalls and
store in compact array
,
No
J
=N ?
•
)
Yes
Bock substitution, Compute AG
6E/E Correct 6 ondE, store
ER ond E1.
No
Test for convergence ore 011
6P and AO less thon toleronce
Yes
I
Print- output
E ~, E I, Pond Q
I
FIGURE 1.
FIGURE 2 I A .lmple fi" baI.., t m.
?
57
58
CHATTOPADHYAY. DHAR AND PURKYASTHA
TABLE III
following informations are read in :
The output array.
Location
KB
(a) Number of lines connected to each bus : NL
LB
(b) Nature of the bus, whether a
Gll
Bu
(c) Real part of starting voltage :
G1 3
B13
(d) Imaginary part of starting voltage: EI
Bl;
B22
P-V type bus: NOB
- --J
3
2
P-Q type or a
B
G
ER
3
1
5
4
2
2
G1"G 22
5
2
4
Gu
B~4
6
2
5
B z•
7
3
Gzo
GSl
8
J
3
G33
.833
9
3
4
Ga 4
B',}I
TABLE IV
10
3
5
Gar.
Bar.
Table of Input Quantitie .
11
4
2
G'2
B4~
12
4
3
B~3
13
4
4
G'3
Gu
J4
4
5
G,_
Bu
15
I
2
G&l
G.i 2
Bu
16
5
5
13;'2
17
5
3
G~3
B63
18
5
4
Gu
B54
19
5
5
GGr.
BSG
B31
Bu
(e) Active power:
P, and
(f) Reactive power: Q
for the system shown in Figure I , the input arrays are
shown in Table IV.
Location
NL
NOB·
ER
El
P
Q
E3
E,
E,
0.0
0.0
0.0
0.0
0.0
Pz
Q2
Pa
Qa
E.
E,
0.0
0.0
P,
P5
Q,
0.0
---J
2
1
2
2
3
3
0
0
4
3
0
5
4
where, E , denotes the voltage magnitude specified for
the slack bus
3.3
Load Flow Solution
• NOB (J) = O and I respectively indicates that bus J
3.3.1 The programme for load flow solution is of
considerable length, and can be di cussed under the
following heads :(a) Reading input data
(b) Generation of the Jacobian elements and calcu-
lation of residuals
(c) Triangularisation of the Jacobian matrix
(d) Back-substitution and voltage correction
(e) Checking for convergence, and
(f) Printing output data.
3.3.1.1
R ading Input Data: In addition to Table Ill.
is a load bus or a voltage controlled
bus.
3.3.1.2 Generatioll of Jacobian Elements and Calculation of Residuals: One bus is considered at a time .
The lack bus has no contribution. Depending upon
whether it is a generator bus or load bus, it contributes one or two rows.
3.3.1.2.1 Only tbe non-zero elements are calculated
using relations shown in Table I. For the load bus,
both the rows, corresponding to l::.P and l::. Q are
calculated simultaneou Jy to take advantage of the
equality relations (13) & (14). For the generator bus
only one row corresponding to l:::,.P is calculated. The
elements of the two rows are respectively stored temporarily in two compact arrays A and B together with
their indexing table NA and NB which store the
columns designation of the elements stored in A and B.
wro
SPARSE MATRIX TECHNIQUE FOR. SOLUTtON OF LOAD FLOW PROBL {BY
3.3.1.2.2 The contents of these arrays while generating
elements for bu 2 are shown in Table V. The location
of the diagonal terms of the rows in the packed tables
A and B are stored separately in another table ND.
This table is required during triangularisation proces .
The contents of this table after processing of all the
roWS are shown in Table VI. The active and reactive
powers are also calculated for all the buses using
Equation (3). These are required for calculation of the
residuals b,P and b, Q for the load buses and b,P only
for all generator buses except the slack. The entries
of these arrays after processing all the rows have been
shown in Table VII.
-R.APH 0
t llTHOD
TABL
9
T 8
P01l'fl'
Location of dl onal tum .
ND
Location
VlJ
~
Location
0
1
2
3
4
5
Idll I •
P
Q
0.0
0.0
0
t
2
2
P~
Q,
1
3
Pa
6
2
TABLE V
7
8
5
6
4
Pc
Q.
Q,
Storing of Jacobian elements of bUJ 1 in temporary location.
9
10
7
5
P6
0.0
NA
A
NB
B
3
H22
3
J ~2
2
4
N22
4
LZ2
3
7
Hu
7
J2C
4
8
Nu
8
Lu
5
9
Hz.l
9
J 2.;
Location
0
Since row I, 2 and lOin Table VI have not been
proces ed, these eotrie in location ND are left zero.
3.3.1.3 Trja"glllar{.~atjoll oj the Jacobiall Matr{,, :
The Jacobian matrix is triangularised by the method of
Gaussia n elimination. In the co mmonly adopted
elimination alogrithm. a matrix is trianglliori ed by
eliminating. from all tbe rows, only one column at a
time. This method is not very sui table for sparsity
oriented programme, since all the row are to be
generated and stored before elimination starts.
3.3.1.3.1 The cherne adopted is the same as that u ed
by Tinney and Hart (a). In thi scheme, one row is
considered at II time; all the elements to the left of the
diagonal are eliminated step by step by subtracting from
this row suitable multiples of previou Iy processed rows.
The resid uals b, P or b, Q as the ca. e may be, are
simultaneously modified. All the elements of the row,
including tbe re iduals, are next divided by the diagonal
term and th en the elements to the right of it are transferred to the final compact storage AD and the olumn
de ignate to the indexmg array NAB.
6
7
8
9
It is needless to mention that the dimension of these
arrays should be at least equal to the maximum
number of elements in a row when the elimination is
complete.
TABLE
3.3.1.3 .2
The locations of the first and the last element,
vnr
Entries of the compact storage.
Location
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
8
9
8
9
9
X
x
x x
NAB
4
7
8
9
7
8
9
6
7
8
9
7
AD
X
X
X
X
X
X
X
X
X
X
X
X
X
18
-
19
20
60
CHATTOPADHYAY, DHAR AND PURKYASTHA
corresponding to each row, in the commpact storage
AB are stored in auxiliary tables NS and NF. These
are required during the back substitution .
3.3.1.3.3 The elimination process is the most compli.
cated part of the programme. The elimination is per·
formed on one row at a time in the auxiliary location A
and NA . New elements may be generated during elimination of some co lumns in A. In such cases, some of the
elements in A are shifted to the right to make room for
the new element. The elements in the temporary location
A, NA are always stored in order of their column
designations .
3.3.1. 3.4 For the system shown in Figure 1, Table
shows the contents of the arrays AB and NAB of
all the buses while Table IX shows the entries of the
arrays NS and NF.
vnr
3.3.1.3.5 1t is needless to mention that the dimension
of the variables AB and NAB should be at least equal
to the total number of elements to be stored. In
Table VIn 'x' in the array AB indicates the value of the
element.
3.3.1.4 Back Substitution and Voltage Correction:
The voltage corrections are determined by solving the
triangularised Jacobian matrix . The elements correspond.
ing to any row of the matrix are identified by the use
of tables NS and NF. The correction .6. 8 and £::.E/E
(for generator buses £::.£= 0) are used to update the
previous estimates of voltage variables. For this , the
rectangular components of the voltage variables are first
transformed to polar components, the polar corrections
are added and finally this corrected voltage is stored
again in rectangular form.
FIGURE 3
I
TABLE IX
Entries of the indexing Tables NS and NF.
Location
2
NS
NF
o
o
o
3
o
4
4
5
7
5
8
11
6
12
14
7
15
16
8
17
17
9
o
\0
o
o
o
3.3 . ).5 Checking for Convergence : The residuals
6:,P and .6. Q for all the buses are next compared with
the specified tolerance 'ETA'. If all the residuals are
less than this limit, the problem is solved, if not, the
next iteration is stated. Since the residuals of previous
iterat'on are compared at the end of the present iteration,
the checking is delayed and therefore one extra iteration
A fourt n bus AEP test sy tem.
SPARSE lATRIX TECH IQue FO~ OLUTIO
OF LOAD flOW PRORtB f BY N WTON-RAPH.
is to be performed. The final results are, however,
much more accurate then the specified tolerance.
TAB
61
D
•
Xli
3.3.1.5.1 One iteration may be sa ed by alculating
the residuals at the start of the iteration. This will
however involve extra computation time per iteration.
3.3.1.6 jrincillg OlllPli1 Data: The oJlages and powers
at all the buse are printed out at the end of each itera.
tion. For a vi id idea about the displacement in
different buses, in the output voltage is printed in polar
form.
4.
Numerical Example
4.1 A programme ha been written in Fortran and
tested with IB M·1130 computer. Two systems heve
been tested. The system have been shown in Figures 1&2.
The sy tern data and the cheduled voltages and powers
have been shown in Table X to XIII. The results
have been shown in Tables XIV & XV. The system
shown in Figure 2 is a 14·bus standard IEEE test
system(7). The buses are n t optimally ordered in these
examples.
TABLE X
Impedances and line chargings for system 1·.
Bus code
Impedance
Line charging
---1·3
5-2
loS
2-4
4-3
3-5
4·5
0.08 + } 0.24
0.04 , i 0.12
0.02 +} 0.06
0.08 + i 0.24
0.01 + } 0.03
0 .06 + J 0 .18
0.06 + } 0.18
0.0 +1 0.025
O.O +J 0 .015
O.O+} 0.030
O.O+} 0.025
O.O + } 0.010
O.O T } 0.020
O.O + } 0.020
1·5
0.05403 -+ j 0.22304
2-3
0.046 9+ J 0.19797
j 0.0219
2·4
0.05 II
j 0.01 7
2·5
0 .05695 +J 0.1738
J 0,0170
3-4
0.06101 -+ J 0 .17103
.i 0.0173
4-5
0.01335 + J O. 4211
} 0.00 4
4·7
O.OOOoo- J 0.02912
1 0.0000
4·9
O.oooOO + j 0.5561 II
.I 0.0000
5-6
0.00000 t-j 0.25202
} O. 000
6-11
0.09498 + ) 0.19890
j 0.0000
6-12
0.12291 + J 0.25581
} O. 000
6-13
0.06615 + j 0.13027
j 0.0000
7-8
O.OOOOO + J 0.17615
j 0.0000
1·9
O.OOOOO+ J 0.11001
.10. 000
9-10
0.03131 + J 0.08450
j 0.0000
9-14
0.12711 +1 0.27038
j 0.0000
10- 11
0.08205 + 10.19207
J 0.0000
12-13
0.22092 J 0.19988
+
J 0.0000
13-14
0. 17093 + J 0.34802
) O. 000
JO.116n
--The data are given in P.V. of 100,000 leVA base.
All the transformers are assumed to operate at normal
-The data are given in P.V. of 100,000 kVA base.
setting.
TABLE Xl
Scheduled &eocrallon and load and
Bus code
2
3
4
5
Assumed bus voltage
1.060+ J 0.000
1.000+ J 0.000
1.000 + } 0.000
1.000+i 0.000
1.046+J 0.0
umed bus voltaaell.
Generation
Load
-------------Active
Active
Reactive
Reactive
0.000
0.000
0.000
0.000
0.200
0.000
0.000
0.000
0.000
0 .000
0.000
0.600
0.450
0.400
0.000
0.000
0.100
0.150
0.050
0.000
Remark
Slack bus
P-Q bus
P-Q bus
P-Q bus
P-V bus
62
CHATTOPADHYAY, DHAR AND PURKYASTHA
TABLE Xlll
Scheduled generation and loads and assumed bus voltages.··
Bus code
Assumed bus voltage
Generation
Load
Active
Reactive
Active
Reactive
1.060+ j 0.000
0.000
0.000
0.000
0.000
Slack bus
2
1.045 + j 0.000
0.400
0.000
0.217
0.000
P-V bus
3
1.010 +j 0.000
0.000
0.000
0.942
0.000
P-V bus
4
l.oo0 + j 0.000
0.000
0.000
0.478
-0.039
P-Q bus
5
1.0oo + j 0.000
0.000
0.000
0.076
0.016
P-Q bus
6
1.070+ j 0.000
0.000
0.000
0.112
0.075
p-v
7
1.000 +j 0.000
0.000
0.000
0.000
0.000
P-Q bus
8
1.090 + j 0.000
0.000
0.000
0.000
0.000
P-V bus
9
1.000+j 0.000
0.000
0.000
0.295
0.166
P-Q bus
10
] .000+ j 0.000
0.000
0.000
0.090
0.058
P-Q bus
11
1.000+ j 0.000
0.000
0.000
0.035
0.018
P-Q bus
J2
1.000 + .i 0.000
0.000
0.000
0.061
0.016
P-Q bus
13
1.000+.i 0.000
0.000
0.000
0.135
0.018
P-Q bus
14
1.000 + j 0.000
0.000
0.000
0.149
0.050
P-Q bus
The data are given in P.V. of 100,000 kVA base.
normal setting.
bus
All the transformers are assumed to operate at
*'II
4.2 Results
TABLE XV
TABLE XIV
Results for sample system II
No. of Jacobian clements stored: 136.
Results Cor somple system I
No. of Jacobian elements stored: 17.
-- -- Bus
Voltage
magnitude
Voltage
angle in
degrees
Active
Power
1.06000
0.00000
1.29589
-0.04434
2
1.01653
-6.13499
- 0.60000
-0.10000
3
1.02305
- 4.48315
- 4.45000
-0.15000
4
1.02237
- 5.31478
- 0.40000
5
1.04600
-2.78232
0.2000
Bus
code
Remarks
Reactive
Power
code
Voltage
magnitude
2
- - - - - - - --
Voltage
angle in
degrees
3
Active
Power
4
Reactive
Power
5
1.06000
0.00000
2.32398
-0.23888
2
1.04500
-4.94852
0.18300
0.13526
- 0.05000
3
1.01000 -12.60392
-0.94200
-0.02680
0.17080
4
1.03046 - 10.42814
-0.47800
0.03900
SPARSE MATRIX TECHNIQUE FOR SOLUTIO
OF LOAD FLOW PR08LliM 8Y
TABLE XV {Contd.}
2
3
5
1.03566
-8.96 183
--0.07600
- 0.0 1600
6
1.07000 -14.66860
-0.11200
0.32388
7
1.05630 -13.55747
0.00000
0.00000
8
1.09000 -13.55747
0.00000
0.20849
9
1.05008 -15.17229
- 0.29500
- 0.16600
10
1.04616 - 15.36757
- 0.09000
-0.05800
11
1.05446 - 15.14509
- 0.03500
- 0.01800
12
1.05471
- 15.51274
-0.06100
- 0.01600
13
1.04954 - 15 .57289
- 0.13500
- 0.05800
14
1.03180 - 16.35277
-0. 14900
- 0.05000
5.
4
5
Conclusions
5.1 The programme has been run success~ully for two
systems, one is a 5-bus system and the other IS a. tan~ard
14-bus system. In both the cases only three IteratIOns
were required for convergence with a tolerance of
0.0001 p.u. of active and reactive powers, but the
programme had to run up to four iterations due to the
delay in checking up of convergence. Due to the
increase in complexity of the programme, the storage
requirements for storing the programme it el~ i considerable. Comparing with the programme written by
the authors previou ly using Glimn and Staggs method,
which required about 1600 lo~ations, the ne.w programme
required about 2,200 locatIOns for stonng the programme. The bus codes were not optimal, still only
136 elements of the Jacobian matrix had to be stored.
In a normal programme which is not sparsity oriented,
(26 x 26/2-26) = 312 elements are to be processed and
stored for solution.
-RAPt! 0
IFTH D
63
S. 2 The authors have the e perienre of running the
programme u ing b th polar and rectangular oordin te ,
The polar method of formulati n h
the a vantage
of les storage requirement and Ie numb r of equ ti n
to be solved, but trig nomelric I ca l ulati II C n n t
be avoided. On the other hand, the r tangul r f, rmulation ha the advantage that time
n umin
trigonometrical (,alculati n can be ompl telya ided ,
bUllarger number of equation are t be , olved. The
advantages of both the melh ds may be combined by
u ing the polar coordinates ~ r the variables of voltage
controlled bu es and the rectangular co rdin te for the
load bu variable . The author re at pre ent engaged
in developing a programme using this mi ed formulotion,
6.
Reference
(I) GLlMN, A.F . and STAG ,W. . : "Automati
leu 1 _
tion of Lond Flow ." Tron . AI ,Vol. 76, Pt. Ill, pp. 811828, 1957.
(2) McCRACKEN, D .O . and DORN, W.S. ; "Numerical
Methods and FOrtran Programmina." A book .
(3) TINNEY, W. . and HART, . . : " Power low Solution
by Newton's MethOd" . Trans. [
, Vol. PA -86, No. 11,
pp . 1449-1460, Nov . 1967.
(4) TINNEY, W . . and SATO, N : "Techniques for xploitina
Sparsity of the Network Admittanco Matrix .. , Tran , IE ,
Vol. PAS-82, No. 12, PP. 944-950, Dec. 1963.
(S) TINNEY, W.F. and WALK R, J.W. : "Direct Solution of
of Sparse Network Equation by Optimally Ordered Trianaular Factorisation." Pree . J EE, Vol. 55, No. 11, pp. 18011809, Nov. 1961,
(6) STOrr and HOBSON : "Solution of Large Power System
Network by ordered Elimination". Pree . I
(London),
pp. 125-32, August 1911.
(7) FRERIS, L .L. and SAS ON, A.M .: "Inveali lion on the
Load Flow PrOblem ." Proc. l EE (London ), Vol. 115,
No. 10, pp. 1459-1470. Oct. \968 .
Transmission Line Towers of Tubular Sections
T.V.
GOPALAN
T.D. MOHAN BABU
Assistant Director
A sistant Director
Central Power Research Institute, Bangalore.
SYNOPSIS
Angle sections of mild steel of high tension are generally employed in the
manufacture of towers for the transmission lines ill India. Angles being
unsymmetrical sections have unequal moments of inertia with respect to their
principal axis. The angle section has the least moment of inertia with respect to
its vv-axis and consequently. the area of cross·section to the least radius of
gyration (a/r) , which is a measure of tire effectiveness of the material employed
for the tower, is less in the case of angle sections and more in the case of
tubulars.
The design of lighter towers is. therefore, made possible
employed in place of angle sections.
if tubulars are
Also the tower made up of tubulars has a definite advantage in that the area
exposed to wind is consideraby rpdl/eed. Because the tubulars have cylindrical
surfaces, tlte area exposed to wind is only 2/3 of its projected area whereas the
effective exposed area in the case of angles is the same as the projected
area. The willd load on the tower is, therefore, reduced with a consequent
reduction ill the weight of the tower. This is all the more significallt in case of
towers used for extra High Voltage Direct Current Transmission. The ultimate
reduction in weight of tower is found to be around 25 percent.
The connection of members in a tubular tower of course poses a problem
which can be effectively done by use of gussets and flattening the ends in case of
bracings. The bracing assembly and parts of the cross·arms can be easily welded
and transported. Flanged connections can be adopted for the leg members.
In order to calculate the main dimensions and weight of the tower a set of
empirical formulae has been used. These formulae are derived in the same way
as for towers made up of angular members.
The comparatively higher cost of tubes is offset to a great extent by way of
saving of material effected by reduced weight cheaper transportation and erection
cost.
1. Introduction
least radius of gyration. The angle section has the
least moment of inertia with respect to its vv-axis and
consequently the ratio of the area of cross-section to
the lea t radius of gyration (aIr) which is a measure
of the effectiveness of the material employed for the
tower is les in the case of angles and more in the case
1.1 The members of transmiSSion line towers are
generally made of mild tcel angles. These are designed
applying the strut formulae. The permissible compre~
ssive stre s for any trut increases with increase in its
64
TRANS II
ION U
Ii TOWER OF TUB LAR
of tubulars. By employing tubular sections it is possible to get a higher value of least radius of gyration
than angles of the same sectional area and material.
This in turn reduces the overall weight of the tower.
1.2 By the use of tubular section in the fabrication
of transmission line towers, the wind load on the tower
is found to be reduced considerably. Since the external
load on the tower due to wind on the tower body i of
appreciable magnitude, reduction in wind load brought
about by the use of tubular ection is of advantage.
This is all the more significant in case of towers for
HVDC transmission lines.
1.3 Thi paper covers the various significant Ilspe.:ts
of towers u~jng tubulars in place of angles. Other
relevant details regarding fabrication , erection, etc., are
also discussed. Since 80 percent of the tower used
are tangent towers a typical 220 kV single circuit
tangent tower was chosen for this study. The outline
of the tower is shown in Figure 1 and the external loads
acting on the tower are given in Appendix-].
2.
Material and Minimum Thicknes
2.1 The tubular sections to be employed for fabri·
cation of the tower should conform to IS: 1161-1968.
"Tubes and Tubulars for Structural Purposes". The
properties of these sections are given in the Indian
Standard Specification mentioned above.
2.2 The minimum thickness of tubular section assumed
for the purpose of calculation is 3.25 mm . Experience
with steel tubular poles for distribution lines has shown
that this thickness is adequate.
3.
Calculation of Sizes of Tubular Section
3.1 The strut formulae mentioned in IS : 802 (Part 1).
1967 are used in the calculation. 'These are reproduced
below for convenience :(i)
(ii)
1=1" for
where,
1= (it~l
K ::an! £ / 150
3.3 The redundal1t member nre not on idered in
the calculations sin e the memb rs nrc 110t generlllJ
designed for any calculated load. A redundant member
is de igned to take 3 percent of the load in the member
It is supporting and the maximum permibsible lendernes ratio i limited to 250. Also, the numher f
redundant member present in n tower i minimum .
3.4 Becau.e the tubulars have ylindrical surfaces the
exposed arca 10 wind is only 2/3 of it projected area
whereu the effe tive exposed area in the co e of IIngles
ill the sam as the pr je ted area. The wind I ad on
the tower is. therefore. reduced with a con~equent reduction in the weight of tower. 'But the al ulation of
revised sizes of tuhular section s due to the reduced
wind load on tower is not d ne on account of the fa t
that the effect f wind load on the stru ture by way of
increa ing the member size is negligible.
3.5 The loads in the members of the tower, the size
of M.S. angles, for the members having calculated load
and the size of ubstituted tubular se tion. for the e
angles are given in Table I
Table II gives weights of legs, including ground
wire peak, cross-arm and frames of tower in the
horizontal plane using angles and tubular ection!!. This
enables one to have an idea of the per entage reduction
in weight at a glance.
3.6
4.
Reduction in Weight and
tfective
"po cd Area
The reduction in weight of tower if tubular
sections are used i about 25 percent and corre ponding
reduction in efTective exposed area i 40 percent. When
the tubular sections are substituted for angles except
for lattice the above figures are 14 percent and 21
percent respectively.
4.1
l/r-20 )
for 20<I/r< 150
(iii)
6
of Tower
0 <1/1'< 20
1=111-( I~~: )(
Ii TlON.
S.
for I/r> 150
1=ultimate stress in compre
If/= stress at the yield point
1= unsupported length
r= least radius of gyration
sion
Approximate Formula for
alculatln Ih Wel&Jtt
of the Pori ion of the Tower above Ground LeveJ
5.1 The empirical formula for calculating the weight
of the tower made of angles of M.S. above ground
level is expres ed as W= K h M
v
where, W= weigbt of tower above ground level
h= the height of the tower measured from
ground level.
66
GOPALAN AND MOHAN OABU
1600
0
0
130
IX)
,...
IX)
to-
C"")'
C"")
Peak
I()
co
IX)
01
N
0
0
0
0
390
10
10
It"l
F i '-sf porf
I()
01
I(')
C'\I
,...
'<t
I()
2nd
po,., '<t
10
I()
2'
420
""
If)
01
3rd
Tronsvers.
Q
art~
roc.
0
I(')
C'\I
It) to11"1
Longitudinal face
FIGURE 1.
0
0
TRANSMISSIO
LlNE TOWER OF TUBULAR
M =tbe overturning moment
67
ECTJONS
e pres ed in ton.
re P lively).
feet and 1000 Ib-ft
units
k =a constant.
When W, hand Mare expres ed in kilogram, metres
and kilograms - metres respectively, the value of K is
approximately 0.4535 for suspension towers.
5.2 In the above formula the minimum Ihi kne of
angle u ed ~ r leg member nd br cin
re 6.2 10m
and 4.7 mm respe lively. The entio, of area to r diu.
of gyration of angle (aI r) con~ rmiog t B. . p j-
(The value of K =0.00 16 if W, hand Mare
ncation are 2.41 and 1. 2 re pe thoely. The aJr rntio
for the tubular se lion of nominal diameter f 15 mrn
and of thickness 3 .• 5 mm i 2.8 em .
TABLE I
Member
Size of M .S. angle
Size of M .S. tubular
section
Load in the member in ka
in Iud ina factor of safet
ondition
s
2
3
(in mm)
(inmm)
90 x 90 x 6
16.1 x 3.6S
11215 (C)
WB
2nd "
lOO x IOO x 8
101.6 x 4.0S
11680 (C)
T B
3rd "
110 X IIO x l0
114 .3 'Y 4.5
21960 (C)
T n
4th ..
IIO x llO x lO
-do-
23100 ( )
T B
IIO x ll0 x 8
-do-
24230 (C)
T 0
Legs lst Part
Extension
4
Lattices
(e)
1'1
11&0'
4S x 30 x 5
26.9 x 3.25
1175
b
SO x SO x 5
42.4 x 3.2S
4175 ( )
b'
SO x SO x 6
48 .3 x 3.2S
5000 (C)
nw
BWe
c
60 X 60 x 5
48.3 x 3.2S
4830 ( )
BW
C'
60 x 60 x 5
48 .3 y 3.25
5350 (C)
d
60 x 60 x 5
42.4 x 3.2S
402S (C)
awe
owe
d'
60 x 60 x 5
48.3 x 3.2S
4610 (C)
BW
S5 x 5S x 5
42.4 x 3.25
3445 (C)
60 x 60 x 5
42 .4 x3. 2S
3922 (C)
d2
55 x 55 x 5
42.4 x 3.25
3125 (C)
dt'
60 x 60 x 5
42.4 x 3.2S
3418 (e )
ds"
60 x 60 x 5
42.4 x 3,2S
3123
d3
SS x SS x 5
42.4 x 3.2S
2760 (C)
d,'
60 x 60 x 5
42.4 x 3.2S
2760 (C)
5S x SS x 5
42.4 x 3.25
2A65 (C)
e'
60 x 60 x 5
42.4 x 3.2S
2470 (C)
f
60 x 60 x 5
42.4 x 3.2S
2250 (C)
f'
60 x 60 x 5
42.4x3.2S
2305 (C)
Bwe
awe
Bwe
awe
Bwe
Bwe
Bwe
Bwe
awe
Bwe
Bwe
(e)
68
OOPALAN ANO MOHAN BABU
TABLE 1 (Con/d.)
5
4
3
2
g
60 x 60 x 5
42.4 x 3.25
2975 (C)
BWC
N'
55 x S5 x 5
42.4 x 3.2S
2760 (C)
BWC
11&'"
SS x 5S x 6
42.4 x 3.25
J465 (C)
BWC
j & j'
SO x SO x S
33.1 >< 4.05
2645 (C)
BWC
Ground Wire Peak
55 x S5 X .5
42.4 x 3.25
3720 (C)
BWC
Lower Member
Joo x 100 x 8
101.6 x 3.65
14755 (C)
BWC
Upper Member
80 X 80 x 6
48 .3 X3.25
2955 (T)
NC
Cross Arm
Diamond Diagonals
t2-6)
SO x SO x 5
33 .7 x 3.25
3400 (C)
BWC
(2-3)
65 x 65 >< 5
48 .3 x 4.05
6500 (C)
BWC
Long belts
55 x 55 x 5
42.4 x 3.25
2405 (C)
BWC
Transverse belts
80 x 80 x 6
60.3 x 4.5
8500 (C)
BWC
Note: GWB - Ground Wire Broken
TCB-Top Conductor Broken
NC - Normal Condition
C-Compression
T - Tension .
TABLE II
When M.S. angles
are u ed
When M .S. tubular
sections are used
Reduction in
weight
Percen tage reduction in weight
1.
Weight of Jegs members
and ground wire peak
in kg.
1601.5
1234.5
367.0
23.4
2.
Weight of main bracings
in kg.
1488.7
1115.2
373.5
25.1
468 .0
298.0
170.0
36.4
3. Weight of main Crossarm members in kg.
4.
Weight of horizontal
frames in kg.
185.4
152.7
32.7
17.6
5.
Weight of tower In kg .
3743.6
2800.4
943.2
25.2
TRANS
n
JON L1 E TOWER OF TUBULAJl
(01
CTIO
9
Ibl
FIGURE 2.
5.3 Proceeding in the same way as in the Appx. 7.1
of the article mentioned under Reference (I) and a suming that the minimum thickness of tubular eClion
used for the tower to be 3.25 mm we have the following resul ts :
(i) The formula for the weight of the tower above
ground level becomes :
W = O.OOI26 It V M tons.
(ii) The most economical base width = O.447 V Mft.
6.2 Figure 2(a} shows n gus et plate welded t the
tubular ection. When the izo of weld i such that
the thickne of pipe i in ufTicient, two L-clamp can
be w Ided as shown in Figure 2(b) to make
ne
f angle of tubular ection flatgusset. The lattice
tened at the end. can be connected to gusset plate.
6.2.1 The legs can be joined
by flanged connection .
as iIIu tnlled in
igure 3
6.2.2 Figure 4 hows the tub below ground level.
or providing better bearing urfn c a plate is welded
to the stub.
(iii) The ratio of weight of leg members to the
weight of bracings = I.
(iv) The slope of bracings or the angle that the
bracings make with the horizontal = 41 o .
5.4 The actual percentage saving calculated for the
particular tower under consideration is 25 percent as
against 17.65 percent obtained theoretically by applying
the above formula. This can be accounted for by the
fact that the weight of the eros -arms i not taken into
account in calculating the theoretical weight of tower.
Besides, there are other theoretical factors which cannot be strictly adhered to in the design of towers. The
calculations are given in Appendix-H.
6.
Constructional Detail
FIllet w.'dTng
~~v~,rng,fo,.
JOining pIpes
of Tower u ing Tubular
Section
6.1 Towers of tubular sections have been used in
other countrie and are normally fabricated by welding.
The various parts are fabricated separately and
assembled at site by bolting the .flanges provided on the
legs. This method of fabrication unit by unit i likely
to pre ent difficulties in transportation as they require
a lot of space.
JGURE3.
70
OOPALAN AND MOHAN BABU
p
h
Plate welded on to
the p ipe
~--------------b----
FIGURE 4.
6.3 By adopting the method of connections detailed
in Figures 3, 4 & 5 the tubular member of the tower
can be tran ported to site and erection done as in the
ea e of towers of angle members. The ground wire peale
and cross-arms can be conveniently fabricated at shop
by welding and then transported to site. This is not
likely to create any problem. If any it reduces the
time of assembly to some extent. The connections
between legs and bracing can be done by gusset plates.
The bracings are flattened at the ends wherever necessary. Flanged connections for the bracing are likely
to prove expensive.
6.3.1 If the double-warren bracing pattern poses any
problem. it is suggested that the lattices be of angles
and the re t of the member of the t wer can be of
tubular sections.
______
~
FIGURE 5.
6.3.2 The percentage saving in weight when the lattices
are made of angles and the re t of the members of
tubular sections is found to be 14.2 percent.
7.
Conclusion
7.1 The reduction in weight when M.S. tubular
section are substituted for M.S. angles is considerable.
7.2 Further the wind load on the tower is also reduced appreciably.
7.3 Though the tubular cost more than angle the
ultimate co t of the erected tower using tubulars might
fRA SMISSION LINE roWERS OF TUBULAR
be favourably reduced.
7.4 The theoretical study carried out in C.P.R.I. has
yielded promising re ults. The electricity Boards and
manufacturers of transmission towers may i uali e
the advantages of substituting angle sections by tubular
sections in transmission towers.
8.
Acknowledgement
The authors wish to express their thanks to the
Director, Central Power Research Institute, Bangalore
for his kind permission to carry out this study in
C.P.R. I.
9.
7J
eCTlo
Reference
(I) RYLE, P.J.: "Steel Tower
01. 93, Put 2, 263 .
onomic ." J urn.11. . . ,
(2)
Pamphlet of Monkey H Ie Tower Te tin
tati n.
(3)
PROFESSOR ING. LADIMIR LIST lind IN . KAR
POCHOP : "Meehani I D ign of Overbead Tran mi sion
line". SNTL-Publi hers of Te hni al Inter alia.
(4) CARPENA, A.: .. peei I Li htened e·tion f r H1ah
Voltaac Tronsmis ion Line Siru lures". lORE Repon
No. 22·07, 24 ugu t- 2 September, 1970.
72
GOPALAN AND MOHAN BABU
APPENDIX-I
Extemalloads acting on the tower (design loads) deviation for which the tower i designed 2°
1.
Transverse loads in kg
Ground wire
NC
BWC
Conductor
NC
BWC
Due to wind on wires
266
200
698
542
92
46
182
91
400
400
Due to deviation
Due to wind on tower (taken as equivalent)
Total
2.
Vertical Loads-kg
3.
Longitudinal loads- kg
358
246
1280
1033
450
325
975
700
2626
3911
Note ;-
4.
(1)
BWC- Any one conductor or ground wire broken.
(2)
For tower design unbalanced cond uctor tension is taken as 75 percent of maximum working
tension of 6,2] 5 kg.
Minimum factor of safety
Normal condition
Broken-wire condition
= 2
= 1.5
TRA S flS JO
LINE TOWER OF
run
LAR
7
I!CTIO
APPEND] -IJ
Load per leg =
1000 Ph
2b
(Figure 5)
For a slenderness ratio of J00, the permi sible
stress with a factor of safety of 2
= -
2746 - 12.3
100
2
kg!
m~
= 10,800 lhl q in.
The leg area required
1000 Ph
...
= 10,800 x 2 b In. PIr ...
= 21.66 10 " .
PIr
4h x 21.6 b X J2 inS.
Volume of steel required for 4 legs
=
Weight of legs
= 0.28 x 4 >< lr x 21.6 b Ib
PIr
X
12
= O . 6~ Plr~ Ib
The ratio of area to radius of gyration for a tubular
section of 3.25 mm thick
= 2.83 em or 1.113 in.
PIr
ft
(21.6 x 1.113x 12 x b)
The radius of gyration of leg
At I/r= 100, the unsupported length
==
0.346 Ph
b
(The average value of I/r for legs of any towers
jf found to be 100 by statistical analysis)
ft
igure 5)
Length of one bracing
12 h .
= -In.
cos e
For I;r = 150, the radius of gyration
12 b
ISO '
= cos 9 x
In .
The area of cross-section of bracing
=
1.113 x l2b .•
co 6 X 150- 10 ".
-
0.089 b
cos 6
jn~.
It
The total length of braces per mast face
= -SIO
'0 ft
The weight of all braces
= (4 X 0' 284 x
=
The weight of braces
1.21S bh
~X
510 0
Ib
in 8 cos 8
0.6075 b (a:+ 4b' ) lb
a
0.089 h ) Ib
COS
0
74
GOPALAN AND MOHAN BABU
Substituting for 'a' the weight of braces
-
0 .2 10 Ph 2
b
..L
I
7.025 b 3 Ib
P
The total weight of mast
=( 0.840 P;2+ 7'02) b
Differentiating w.r.t. base width ' b' and equalling to 0,
the economical base width b
= 0.447 v' Ph ft
Substituting the value of 'b' weight of legs
= 1.407 h v' Ph Ib
Total weight
= 0.00112 h
Percentage saving
=
3
)
Ib
Ph tons
(0.00153 - 0.001 J2)h Pbx 100
O.OOJ 53 It v' Ph
= 26.8 percent
Ratio of weight of legs to total weight of tower
=
l.407 II v' Ph
x 100 percent
2.4995 Iz
PI!
v
= 56.3 percent
Tan O= al2b
-
0 .346 Ph
2 x (0.447)~ Ph = 0.8625
= 40 0 48' say 41 0
Note :-These calculations are done for the structure only and do not include the weight of crossarm, etc.
Power Network Planning by Computer Simul ation
B.N.N.
IYENGAR
D .K . DRAMA IAN
Professor
A. sistant Profc or
Department of Electrical Engineering, Indinn Institute of Science, Bllnalllore.
YNOPSI
This paper presents a new methodolog), for the planning of power IIttH'orks.
The planning occurs in two phases . During rhe first phase, ol'erall parametric
analysis is performed resulting in different 1I0itage levels. type of transmiSSIon,
conductor structure and dimensions. network configura/io!l.1' on(/ oIlier pCr/il/ent
details. Math ematical programming technique assist;lI the analysis af optimality
problems ill routing and ne/lvork configuration.f. Normall]' the resultant Olltput
of the first phase is a set of alternate strategies auf of which one is picked by
mealls oj a decision theoretic approach. An importaJlt. .fimple and IIseful cool
which helps in this expedition is computer simulation. Powerful modelling
techniques, queuing algorithms, Monte Carlo techlliques, numerical procedures and
routines for event selectioll, p,.oces.~iflg and r{'port generation exist today to
undertake a guided tOl/r on Ihe power system operatjollS on an hourly basis
absorbing in the proce,~s the effects of actllal or predicted growth, random
variations il1 load, replacement policies and regular outages. At tile end of the
simulation over a period of 5 to 10 years of operation-all performed inside
the computer within a f ell' hours - a weallli of illformatioll regardlllg tlte ystem
performance, throughput and utilizatiol1 will be generated. This gUide.v us in Ihe
selection of an optimal configuratio" for physical implcmentatioll. Tltis paper
briefly explains Ihe t!teory behilld computer simulation and dl'velops (/ model
for power system compatible for simulation.
computer imulation. the performance indice can be
generated which aid the system de igner to evaluate
the relative merits of the different cheme and sieve
them 10 bring out the be t strategy suited to hi
objective.
1. Introduction
1.1 Every utility goes through the activity of network
planning especially when many new generating stations
are under urvey or implementation. Tn order to
achieve a stable, optimal, economically feasible, reliable
de ign of the network, many design automarion
procedures containing mathematical
programming
techniques are available, The output of design automation is a set of alternative network configurations and
network data . The selection of one out of this set of
feasible designs is a decision theoretic problem.
1.3 There exist many operating state in a power
system. Some of the randomly varying conditions
are: (a) each load center can draw power at different
levels at diflerent time of the day, (b) the power factors
can take random walk, (c) a variety of combinations
of generations is pos ible to meet each set f load
requirements. (d) olltagl!s can ceur on a preplanned or
random ba j. Any model de igned to study the
network over a period of years should take c gnizance
of the e variant. A normal design procedure concern
1.2 This paper accepts a it input a set of alternate
design strategies and briefly explains bow through
7S
76
IYBNGAR AND SUBRAMANIAN
itself with worst case and normal averaged working
conditions. What we aim here is a technique which
simulates tbe happenings in the power system at many
instant of time and integrate to obtain the cumulative
performance index for each strategy. True this
methodology consumes computer lime, but it is more
accurate and enhances the visibility on the system
operation under each feasible strategy.
2.
3.
Whenever we plan a network to cater to randomly
variant traffic, the network configurations are drawn
lip and network constants are computed for both worst
case and optimistic/normal conditions. Our objective
in simulating the many configurations and network
constants is to find out that configuration which will
optimize the performance index, which may be :
3.1
Computer Simulation
fa) a total cost of operation,
2. I Simulation of a design problem is different from
solution in so far as the system model is not necessarily
purely mathematical and the output expected being .n
set of repetitive solutions based on so me parametrtc
variations. ]n addition, a real time exposition of the
system is another feature of simulation especially for
discrete system.
2.2 Any computer simulation process starts with
modelling. The model comprises a multitude of entities
of the system. their attributes, cause effect relutioD!.hips,
interlinking and controlling features. The model includes
both mathematical description of the system as well as
events based description. Hence the events that occur in
the system are listed. The next step in simulation involves
the focussi ng of the objectives of the problem. This i
followed by computer runs and report generations.
Finally one arrives at a decision by analysing the
performance indices.
2.3 The computer ~un cr.eate~ the system <;>pera~ion
at each instant of time (tIme IS normally dtscretlzed
into units of 1 hour, t hour; ]/4 hour, or a minute,
etc.) and updates the performance factors acco_rding to
suitable calculations. It also checks for satisfactory
and safe system operation at each instant of time and
produces a system state conditions, i.f warranted. The
time instant is decided by the arrival of events m a
random process. The system state indicates the status
of the various entities and their attributes. Jt is possible
to output the system state-if not in its entirety. the
vulnerable parts at least-at important landmarks of
time. Once the period of simulation-5 years or 10
years as decided earlier-is covered by the computer run.
the run is terminated and the report generation activity
is initiated. This prints out a report on the throughputs.
utilization factors, cost estimates. abnormality conditions, periods f over/under activity ao? other related
featutres. The run is then repeated WIth a dIfferent
trategy.
2.4 The application f event based imulation to power
system ha not been attempted 0 far. In this paper,
a model is devel ped to weld the characteristics of a
continuous system with the features of discretization
like event generation, 'ervicing, parametric counters,
attribute variations,-not governed by well defined
continuous/differentiable functions. The model
ex.plained in the next section.
imulation Model for a Power System
(6) total cost of investment plus operation if the
configuration reacbes obsolescence at the end
of the simulation period,
(C)
total system los es,
(tI) available duration of a minimal generation (this
in vo lve~
a probabilistic model) ,
(c) a suitable blend of the
above factors with
proper weights.
While computing investment cost, it is preferable
to separate it into two segments-c st of imported
components and the remaining cost -and weigh them
with unequal coefficients. 1nflationary trends are to be
imbedded in the depreciation figures.
3.2
3.3 During the computer run, the performance index
is computed at each instant of time and accumulated.
At the end of all runs, we choose that configuration
which produces the optimal value.
The mathematical model for use at each instant
of time j selected from:
3.4
(0 ) Load Flow Equations(l)
... (I)
k = l, 2, ... , N - l.
where.
Y':n = nodal admittance between kth and nth
buse
Vn = voltage at nth bus
St=power at I..'th bus
N= total number of buses.
POWER
i Ii
ed OItC in three
month. During en h quarter, no growth is
all wed. Thi. di retile the I ad urve ver
a year.
(b) Economic Dispatch Modele)
Minimize ¢
L
77
ETWORK PLANNING BY CO U>UTER :1 I LA'lIO
(ii) The load growth
Fi (Pi)
i£Nq
.. , (2)
(iii) The load duration urve i. cli. cretiz d b
assummg onstaol I 3d for ea h h ur. Thi L
nece siHltcd by the as umption f a time unit
ubject to
of one hour for
... (3)
~imulation .
Thi period can be III dined t
different
durati nS-t hour, 1/4 hour. 2 hours.- within
n run whene\er the need i ' felt.
k=I.2 •...• N
vcr a p ri d of 5
years. the numbor of syst m operation to be
studied i 43,800. Instead if WI! simulate the
entire Ihre month by nly OIlC w ck and
proportionately update the results over the
period of three months, we call reduce the
number of operation. (0 3,360.
urther
reductions can be organlled hy obtaining one
week operlltions from the operalions for twol
three day only. A two day' operational
scheme upgraded to a week bring down tho
number of operations uh tllntially low-960.
Normally each hour of peration may demnnd
computer time of the order of 10 econds.
So the total run lime i. about 160 minutes.
(i\') To pel'form the simulation
where,
... (4)
al.
bl ,
Ct
are constants
F, is the output cost of ith generalor
P, = power generated at ith generator
Nu
et of indices referring to the generator
buses.
(c) Load GrOll'Ih Forecasting and Prediction-Daily,
Quarterly and Yearly.
(tl) Energy Loss Minimization Model
3.6 The above imulalion model can be further
improved to incorporate the random nature of variations also. A true ystem imulutioll will always
introduce the probabilistic model. For the £Ike of
simplicity, reduced computer time and efficiency, the
stochastic variational model i not included .
... (5)
subject to Equation (3).
In addition, constraints can be incorporated into the e
models to effect oltage. power and other controls.
Detailed model procedures are available in literature.
For event geDeratjon, the following data are requested
for
(i) Load duration curve for each day of the week
for all load centers.
(ji) Generating capacities and voltage requirements.
(iii) 'Network configurations and constants.
3.5
In activating this model, the assumptions made
are:
4.
imulatlon Procedure
4.1
The procedure is explained in teps below:
(i) As ume
ne network configuration from tbe
given set.
(ii) Pick out one et
of constants.
(iii) Divide the load growth curve for 5 years into
20 egments. Calculate the percent growth
during each quarter.
(ill) loitialize
performance indice
and
ystem
state.
(v) Set the day to the first day of week.
(\1r) Set the timer to the ftrst hour of tbe day.
(i) The
probabilistic nature is replaced by
determini tic load duration patterns for the
simplicity of simulation.
(vii) Obtain tbe estimated load for this particular
bour from tbe daily load duration curves.
78
IYENGAR AND SUBRAMANIAN
(viii) Conduct load Bow and economic dispatch
studies to bring out schedules of generation,
voltage, transmission powers and losses.
(Ix) Modify suitably the system state and per.
formance criteria.
(x) Update the timer by ODe hour.
(xi) Repeat from step (vii) onwards if the day is
not completed.
(xii) Proceed to the next day's activity.
(xiii) Repeat from step (vi) onwards if the week is
not completely covered.
(xiv) Knowing the performance factors over a week.
proportionately increase their values to reflect
a quarter.
(xv) Change the load growth curves to represent
the next quarters operation.
(x vi) Until the last quarter is simulated, repeat from
step (v).
(xvii) Generate pertinent reports to assist in the
system evaluation or assessment policies.
(xviii) Rerun the simulation pattern [from step (iii)
onwards] with a new configuration and constants until all alternatives are exhausted.
S.
5.1
Conclusion
The above mentioned simulation scheme has been
a very helpful tool to blend planning and operation.
It allows the planner and designer to vjew the operational smoothness or roughness or difficulties of their
designs. Thus it bridges the gap between planning
and operation.
5.2 The simulation technique considers the complex
structural and input and control variants in power
system and reproduces the system activity to a desired
depth of details.
5.3 In addition to its utility in the selection of a
physically implementable design, simulation also helps
in reporting idle times for each component of the system,
thereby providing ways and means of scheduling
maintenance activities. A bird 's eye view of the system
operation over a period of years may bring to focus
weak operating points which can be remedied in advance.
The planner need not wait over a period of five years to
learn about problems in operation. A total map of
the system's activities during the span of five years can
guide him in futuristic planning.
6.
References
(1 ) STAGG, G . W. and EL ABIAD, A. H.: "Computer
Methods in Power System Analysis." McGraw-Hili, New
York , 1967.
(2) SASSON, A.M. : " Non-linear Programming Solutions for
the Load Flow, Minimum Loss and Economic Dispatch
Problems." lEEE Trans . on Power ApD. Systems, Vol. 88,
pp . 399-409, 1969.
(3) DOMMEL, H.W. and TINNEY, W.F .: " Optimal Load
Flow Solutions." Jbid, Vol. 87, pp. 1866-1876, 1968.
(4) SUBRAMANIAN. O.K . : " Some Computational MethOdS
for Power System Load Flow and Optimization Problems."
Thesis submitted to 1.1.Sc., Bangalorc 1970.
Transient Analysis of Power Systems Using Fourier
and Fast Fo urier Transforms
B. .N.
IYENGAR
K.
B..
PARTHASARATHY
ASHOK
UM R
nt
Rl
Department of Electrical Engineering, Indian 1n thute of s.:l nee, Dana lore.
y OP I
All accurate estimation of the transiellt voltage alld current waN' simp s ill
complex power systems during switching operations and fault conditions is anr
important design criterion. This paper present the mode of trallsiellt alwlysesfo
('omplex systems usillg Modified Fourier ond Fast Fourier Trallsformotioll. The
tronsformatioll approach presents itself to be a powerful computatiOllal tool
for transiellt analyses and im'oll'es ollly the use of steady state onalytical soltltiem .
This method also allows the consideration of mulual coupling between circuit and
the prefault conditiolls of the system. Typical results are presented for a .\ample
system together with the necessary computer software for tit Fourier inl'ersion
algorithm.
1.
Introduction
1.1 The progre sive development of power sys~ems
and the increasing power demand calls for a hIghly
reliable and fast protective ystem and switchgear.
The design of such systems and their acce sories,
requires an accurate estimation of the power system
transients both dur ing faults and switching operations.
The design and analyses of the present-d~y fa~t operating
static relays demand an accurate estImatIon of fault
current and vo ltage wave shapes. Further, with the
increase in the operating voltage level of long di tance
transmission systems, the insulation problem beco~es
more stringent and requires an accurate predelermlOa.
tion of the switching overvoltages, to keep the overall
insulation co t of the system at the minimum level.
to be fully taken into account. t.M. W depohl and
S.E.T. Mohamed(&) have discussed the problem of
single and simultane u pole losure for energization
by an infinite source. The purp se of the pre ent
paper is to intr duce the method, computer programme
and result
from the Modified
i crete
ourier
Transformation and
a t Fourier Transformation
approach. Thi~ approach i simpler from Ole point of
view of prograDlnllDg and more accurate from the
point of simulation of the power ystem and it
accessorie. The method in general, can be u ed for
the e timation of the switching transient I recovery
voltage and 01 0 the fault tran ient for the analyse
of fast protective equipment. The merit of this method
are:
(I) The method utilize the bus impedance matrix nd
prefault voltage for the fault calculation. Hence
accurate simulation of even a complex y tern,
inclusive of electromagnetic and electrostatic
coupling and initial condition is po sible.
1.2 The theory of wave propagation(lW) has been
applied to the study ,!f transi~nt. overvoltages o~
overhead }jnes, both dUring energlzatlon and de-en.e~gl­
zalion. Arismunand ar et aleS). have developed a dJ~ltal
programme for the determination of switching transIents
using the Lattice technique. The use of Laplace transforms for transient analyses of overhead lines has been
suggested by U ram et al(.). But these methods do not
allow the frequency dependence of the system parameters
(2) Since the impedance matrix is generated a nd
the voltage and current components are
determined for each complex frequency sample,
the derivation and manjpulation of complicate<!
79
80
IYBNGAR, PARTHASARATHY, ASHOK KUMAR AND KOTHARI
expressions of voltage and current in frequency
domain are avoided .
~w
then:
6 w=21t/T
(3) Only the corresponding components of each
frequency sample in the time domain are
calculated and stored in the memory, thereby
eliminating the need for large computer storage.
(4) Accelerated frequency step can also be employed
in the programme to realise faster computation
without loss of accuracy.
(5) Depending on the speed and memory of the
computer, any complex power system can be
considered for its transient analysis.
(6) The frequency dependence of the network
parameters can also be included if so desi red.
(7) The use of the Fast Fourier Transformation
aJgorithm(6)(1) enables the accurate simulation
of pre-insertion resistors and also the nonsimultaneous breaker pole operation. But, the
Fast Fourier Transformation requires a computer of large memory capacity. since the entire
frequency samples have to be stored.
2.
2.1
Modified Fourier
Inversion
Transform and it
Numerical
and
1
(t) = r
2.3 Equation (5) represents the complex form of a
Fourier series with a repetition time T. The series
representation of Equation (5) becomes divergent for
system having transient time constants much longer than
the repetition time. Also, if the poles of the integrand
lie close to the path of integration, the Inver e Fourier
Inte~ral has a tendency to undergo rapid rate of change
at lOtervals along the path of integration. This
!'ecessitates .the . use of. a very small step length
lD the numencal IDtegratton. These two difficulties in
the ordinary Fourier transform can be overcome by
the Modified Fourier Transform. The use of the
Modified Fourier Transform shifts the path of integration by a constant 'a' away from the poles, smoothening the profile of the integrand and enabling the use of
a greater step length. If I (t)=O for 1<0, then the
Modified Fourier Transform is given by
00
F(a +jw)= f I(t) exp (- (a + jw)t) dt
1(/)=
2~
f(t)exp( -jwt)dt
... (1)
I F(a ~..jw)
J
e p [(a+jw)tJ d(Jl
00
1>0
F(w) exp (.iwl) dw
... (7)
... (2)
The function I (I) being the inverse Fourier transform
?f F(w). Th~ Fourier Inver e Integral of Equation (2).
10 all but slmplest case will have to be evaluated
numerically.
Wh!l~ numericaUy evaluating the Fourier Inverse
Integral 11 1S necessary to determine discrete F(n~w) of
2.2
the frequency function F(w), by selecting a finite step
length ~ w. . The integra) of Equation (2) thus changes
to a summatJon as follows:
2~
(6)
+ 00
I(t) = ..!...
2r.
+ 00
- 00
I(t)=
'"
together with its inver e
-
and
. 21t
)
( J Tnt
... (5)
+00
f
+ 00
1: F (n6 w) exp
- 00
o
If F(w) is the Fourier transform of I (t), then
F«(Jl) =
'" (4)
+ 00
J F(n~ w) (jn b. wt) 6w ... (3)
-00
If 'T' is the time period of the angular frequency
2.4 If the integral in Equation (7) is to be evaluated
numerically. it is necessary to truncate the range of integration from (-00 to 00) to (-0 to 0). The appearance
of unwanted oscillation resulting from this truncation
can be removed by inclusion of a standard sigma
factor (8) ,
a = sin (1tw/O)/(1tw/O)
.. , (8)
Hence Equation (7) will be modified as
l(t)= 2~
o
r F(a+iw)
exp [(a+iw)tJ
-0
sin (1tw/O)/(1tw/O) dw ... (9)
TRANSIENT ANALYSIS OF POWER
YSTEM
U ING FO illER AND FAST
Since in a phy ical system ! (1) i real, and F(w) =
P( - w), Equation (9) reduces to :
o
(/) = eX P (al) Re
7t
JF(a ... jw)
o
exp (jWI) sin (7tw/O)/(7tw /O ) dw
... (10)
For numerical integration Equation (10) can be \\fitten
in summation form as :
N
!(t) = exp_;at)
2:
Re[Fta+Jn L. W)
n= O
sin (n7t/N)
(n7t/N)
.
]
exp (jn/).wt) 6 w
.. (II)
where, N is the total number of samples considered .
2.5 The observation time, slep length, truncation
frequency and shift factor should be cho en properly .
Tbe effect of sampling in the frequency domam ~or
numerical inver ion results in interference of successive
stimulii in the time domain, and under certain circumstances can result in considerable error (Appendix.I).
The step length /). w ... 27t/T where •T' is the period of
repetition of the Fourier series, is cho en such that the
system reaches a sleady state before cOlJl:mencement of
the next period . Ideally, the Iruncallon frequency
should be the cut·off' frequency of the frequency function or the highest transient frequency required in the
response . The value of the shift facto~ 'a' is selected by
considering that the system has attained a state of re t
when the response has settled down to about I.~ per~ent
of its initial value at the end of the ob ervatlon time.
This avoid the interference between the succes ive
stimulii and gives the followin~ rel ~tion s hip between
the shift factor and the observation tllne
aT= 9.2
.. (12)
2.6 The use of variable tep size such that it is small
in regions where the profile of th~ freq~ency function
undergoes rapid change and large In regions wher~ the
profile is nearly Hat enables faster calculations.
Appendix-II give the computer. programme for the
numerical inversion of the Founer Tran form , for a
three-phase system. This general programme can be
used together with a sub-routine 'FUNCT' wher.e the
frequency function W is to be calculated. The IOput
data for the programme are the . num.ber of frequency
and time domain samples. the time Interval and the
frequency interval of sampling.
2.7 The numerical inversion of the Modified Fourier
Transform is expensive in computing time. a co.mpared
to other methods. For saving computation time, the
Rl
TRAN F RM
accelerated frequen
computation without
. t m onl the first
transient nanly i of Ie tri nl
few cy les f the resp n e being important. th inver. ion
can be cllTried out ~ r whnt ver p ri d i
, eoti I.
The main ad antage of th~
urier Tran form technique
is that the bn i ub· routines lind pr pertie
f te dy
slate condition. c n be u ed to obtain the fr ueney
domain fun ti n. Anoth r imporl nt
00 ' ideration
whi h favours the u e f Fourier Tran. ~ rm technique
is the enormous aving in th 'mputer tor ge. The
st rage pa ce required for th e PUrpl e of inver i n
can be maue almo t trivial.
3.
Fa t Fourier 1'1".n form
3.1 The digital computation f time re p nse by the
F urier tran formation given by the qua tion (6) show.
that when the numb r of frequen y umple are N, the
total number of multiplication required arc approximately N 2. The time factor involved in such inver ion
pr hibits the use of ourier Transform technique
parti ularly when the number of snmple. nre very large.
The a t ourier transform algorithm ( FT) developed
by Cooley and Tukeye) provides an immediate answer
to thi problem . The FFT is ba ically an efficient
means of computing Lhe Discrete ourier Transform
(OFT) and its inversion . The reduction reali cd in the
numher of computations
is from N1 to
TN
log. N.
The usefulne ~ of OFT is in its effectivene to approximate the
ontinlJous
ourier Tran sform ( F"T>.
Appendix-HI shows the programmed algorithm f the
Fast Fourier Tran formation technique. Let
f( n /).
=
and F(k)
T.!v (n/)./),
~ F",
(13)
(k.6w)
where the subscript 'P' denoteb
Appendix.I.
(14)
alia scd function,
3.2 Then, jf the input to the above algorithm i Flk},
the output obtained is trle time equence! (n) . The
arne routine can al be u ed for the determination of
DFT from the time domain. For thi , the input
10 the algorithm mu t be!(n)/N 10 reali e F(k). urther,
the variou input variable in the programme are,
N - numher of ample.,
M = an integer defined by
N~ 2M,
Xl = array of sample F(k) or! (n)/N,
SIGN = 1.. .. ..... for 10FT
==- 1...... for OFT
T - repetition time.
82
IYENGAR, PARTHASARATHY, ASHOK KUMAR AND KOTHARI
~----------ABCD------------~j
~Id~_
-JXC
I
X
-
1
FIGURE 1 I
chematic for switching surge computation .
The final problem is the recovery off (t) from
(n) = T fp (n6,t). This recovering of the time response
3.3
f
froro its sampled aliassed ver ion can be effected without
introducing error only if.{ (/) = 0 in the range T/2 <I
<: T. If oth.erwise, the recovered function will only be
an approximation of the actual time re ponse. The
error left over due to this reason is called the 'aliassing
error'. The aliassing errors in FFT can be considerably
minimised by adopting the technique of Modified
Fourier Transform. The sampled aliassed complex
sequence F(k) is obtained from the transfer function of
the system after introducing the shift factor a' . Then
finally, the time response is obtained by multiplying the
an 6, t
equence f (n D. t) by a factor e
.
3.4 Th.e FFT algorithm, even though gives a very
fast and efficient method of determining the transients,
its use is restricted by the computer memory requirement. The above routille requires '2N' cozuplex memory
spaces in the computer. However, the same algorithm
can be programmed with only N complex memory
spaces. But on the other hand, it should be remembered
that the memory requirement for the direct numerical
inversion of the Modified Fourier Transform is almost
negligible.
4.
4.2 For each sampling frequency, the posItive and
zero sequence (zero sequence only for unbalanced faults)
impedance matrices are generated taking into account
the mutual coupling, charging of the lines and the
constant impedance loads. Since the impedance matrices
are symmetrical only the upper halves of the matrices
are generated and stored. Using these impedance
matrices and the prefault conditions, the tran ient
voltage and current waveshapes for aoy SWitching
operation can be computed by the general network
equations (10).
5. System Details
5.] Figure I shows the sample power system considered
for transient analysis . The various parameters of the
system are .'
Generator: 3 X 250 MVA. Xl = X1. = 12.5 percent,
Xo= J0 precent,
(on its own base)
Transmission line: R 1 = O.0084 p.u. / IOO km
Xl = O.130S p.u./l00 km
Y1 = 0.0865 p.u./lOO km
Outline of the Method
4.1 The power system in general consist of distributed
constant transmission lines and lumped parameter
equipments. The distributed constant transmission lines
are repre ented by their equivalellt 7t circuits (the equivalent 7t circuits are calculated for each frequency sampJe).
The synchronous machines are represented by constant
voltage sources behind their respective subtransient
reactances. This simplified representation for the
synchronous machine can be adopted since the transient
analysis is done during a very sho rt period preceding
the time at which the machine impedance begin to
change. Prefault voltages are determined by the load
flow analysis of the given power system and loads
are repre euted by constant impedances for the fault
analysis.
R.=O.033
p.u./IOO km
Xo=0.65
p.u./IOO km
Yo = 0.0610 p.u./IOO km
(on 500 kV, 1000 MVA base)
Length of line=800 km
Transformers:
3 x 300 MVA, 151500 xV.
X1=X 2 =10 percent, Xo =8 percent.
5.2 For the above system, transient studies were
conducted to determine the switching surges during
energization, nature of fault transients and the recovery
voltages. The effect of shunt and series compensations
TRANSIENT ANALYSIS OF POWER SY rEM
USING FOURU!R AND FA T
URlBR TRAN. fOR
J
tlme(msec}
(0') Series camp a 0 0 0J0
FIClIRE2.
(b~
FlCURE 3 :
time (m sec)
Series camp c:. 25 °/.
witching ov,,"ollllge at the recelvlna end
on these transients were also taken into account.
6.
(/ ~
800 km).
be written as :
Switching Surges: Energization
6.1 The constants A" B" C. and D, represent the
parameters of the terminal equipments and of the system
preceding the sending end circuit breaker. The constants
A, B, C and D include the parameters of the compen ating units and also of the transmission line.
6.2 Let x be the di tance from the free end of the line
to the point where the transients are to determined.
Then the expression for the voltage at the point 'x' can
IS)
where,
V' G = (..4 '- 1)
and
(.o) =
(.o) p
VG
Z,=. A, - 1 B.
are the Tbevenin's equivalent of the internal sy telll.
84
IYENGAR, PARTHASARATIfY, ASHOK KUMAR AND KOTHARI
time (m .sec)
(<: ) Serie!o comp .• 50
0,.
FIGURE 4.
time(m. sec)
( d) Series compo• 7!5 .,.
FIGURE S,
Slvitching overvoJlages at the receiving end 0 = 800 kDl).
For the three phase-system considered, V' G and V+
are column vector representing the three-pha e oltages
and C, All, Z. and A are all 3 x 3 complex matrices.
Equation (15) was used to obtain the frequency samples
at intervals of b.w= 40 radians/sec and the time
respon e was obtained by FFT inversion .
6.3 Figures 2 through 6 represent some of the typical
waveforms of the switching surges on the transmission
line considered . It is observed. that the series capacitor
has the effect of reducing the switching voltages only
when the degree of compensation is low. For the line
con idered, the switching voltages come down to about
3.4 p .u. for 50 percent compensation from 4.4 p.u. for
the uncompensated line. Beyond 50 percent series
compensation. the magnitude of the switching surges
increases again (Figures 2 through 6). The shunt
compensation bas a more pronounced effect in reducing
the everity of tbe switching surges (Figure 7). On the
50 percent series compensated line. a maximum voltage
of 3.4 p.u. was ob erved. which reduced to about 2.5
p.u . and 1.9 p.u. with 50 and 100 percent hunt
compen ation respectively.
6.4 The Fast Fourier Transform technique bas also
TRANSIE T ANALY IS OF POWER
Y TEM
U INO FOURIER AND FA T l'()URlEll TRA,
l'()Jt i
.....,.
::J
ci
v
B
(5
>
O~--+-~~~~~r---~~~--~--~~~---+----;-~
VI
-20
time (m .s.ec)
(e) Series comp .. 100%
FIGURE 6:
witching ovenoltllilc at the rtcelvlna end (/ 800 km).
2·
::J
ei.
,.
tI
01
B
g
-2·
time (m.!:>ec)
( a ) Se. Comp · 50% Sh. Comp .. 50o/"
-2·
-3·
time (m .sec)
(b) Series comp.=50·'. Sh. COmp.-l00·'.
FIGURE 7, S,,'tchio& ovt"olt. es at tbe reeettllll fIId (1-
Inll).
5
86
IYENGAR, PARTHASAR",THY , ASHOt( KUMAR AND KOTHARI
o
A
FIGURE 8
System for fnult tran ients.
I
v
~
Q
o
...
01
E
u
lcm =2·5ms (0)
SLG-Fault I No Compensation • 800kms Fault at 0
Transients at A .
I
,
:i
ci.
o
1cm =2·5ms (b)
SLG-Fault, Se .Comp .- 50% , Sh Comp .• 500f0 , 800kms, Fault atC,
Transients at A .
:J
ci
q.- ~~---------~~---------~~~~~---~~~~~~-II
~
1cm·2·5ms _
•
{c)
_SLG-Fault, Se Comp=50 , Sh .Comp:o.50Ofo, 800kms, Fault at 0
Transients at B .
%
FIGURE 9.
Er
TRANS IENT ANALYSIS OF POWER
YSTIiM
USI G FOURIER A D fA T fO RJER TRA
f
;:,'
ci
o
1cm . 2,5m (0)
3 - Ph - Fault, No Compensatl~n, 800km
Transients at A
Fault at 0,
:::l
a.
o
"~~---------~~~--------~~--~'-~~~----~~~~
E
.....u
( b)
3-Ph-Foult, Se. Comp ::50 0 /0, Sh, CCl(11) .• 50 0/0,800km FaJltot 0 ,
Transients at A .
II
E
~
1cm·2·5m -
(C)
3 - Ph-Fault Se Comp·50·'. , Sh.Comp.-50·,. , BOOkm
Fault at C, Transients at A
.
FIGURE 10 .
7
88
IYI!NGAR, PARTHASARATHY, ASHOK KUMAR AND
been used for the determination of transient recovery
voltages across the circuit breakers during switching.
The recovery voltage for single phase switching can be
evaluated without any difficulty. However, for threepbase opening, and for sequential pole switchi ng the
transient evaluation involves tluctuation between time
and frequency domains.
7.
Fault Transient
7.1 Figure 8 represents the system considered for the
fault transient analysis. Typical waveforms of fault
currents and voltages are shown in Figures 9 & 10 for
compensated and uncompensated lines. Th~ type of
faults considered were SLG and three-phase and the
transients were computed at various breaker locations.
The pronounced severity of the fault transients in
compensated lines can be realised from these waveforms.
The fault transients also indicate the existence of severe
voltage and current harmonics at the relay locations.
These harmonic voltage and currents can under certain
circumstances be very severe resulting in delayed or
maloperation of the protective equipment.
8. Conclusions
8.1 A powerful tool for the transient and the fault
analysis of a power system has been presented together
with the necessary computer software for an IBM 360,
Model 44, computer (Fortran JV) . The method in general is versatile and is eminently suited for fast computer
application. Attempts are in progress for mathematical
modelling of dynamic relay test bench for the prediction of dynamic response of high speed protective
relays, using the Fourier and Fast Fourier Transform
technique.
9.
Acknowledgement
The authors wish to acknowledge the encouragement given to their work by Prof. Joseph Vithayathil
~OTHARI
of the Department of Electrical Engineering, Indian
Institute of Science, Baogalore.
10. References
(I) WHITE. E.L. and REECE, M.P.: " Switching Surges on a
275/132 kV Auto Transformer." E.R.A. Technical Repon,
Ref. SIT , p. 111 .
(2) McELROY, A.J. and SMITH.
H.M .: "Propagation of
Switching Surge Wavefronts on EHV Transmission Line ."
Trans . AlEE, Vol. PAS-82, Part Ill, 1963, p. 983 .
(3) ARISMUNANDAR, A., et al
: "A Digital Computer
Iterative Method for Simulating Switching Surge Responses
of Power Transmission Networks." Trans. IEEE, Vol. 83,
PAS , 1964, p. 356.
(4) URAM. R ., et al : " Mathematical Analyses and Solution of
Transmission Line Transients." Trans. IEEE. Vol. 83,
PAS, 1964, p. 1123.
(5) WEDEPOHL.
L.M ., et al : "Multiconductor Transmission Lines- Theory of Natural Modes and Fourier
Integral Applied to Transient Analyses." Proc. lEE
(London), Vol. 116, No.9. 1969, p. 1553.
(6) COOLEY, J.M . and TUKEY. J.W. : " An Algorithm for tbe
Machine Calculation of Complex Fourier Series."
Mathematics of Computation, April 1%5, pp. 297-301 .
(7) KRISHNAN . V.. et al : "Introduction to Fast Fourier
Paper presented at the Annual ConTransforms. "
ference of the Computer Society of India, Bombay. March
1972.
(8) MULLlNEUZ, N ., et al : "Developments in obtaining
Transient Response using Fourier Transforms- Gibb's
Phenomena and Fourier Integrals ." lJEEE, Vol. 3, No.4,
1965. p. 501.
(9) MULLINEUZ, N., et al : "Developments in obtaining
Transient Response using Fourier Transfonns- Use of
Modified Fourier Transform." lJEEE, Vol. 4. No. I,
1966. p. 31.
(10) STAGG. G .W.• EL-ABIAD. A.H.: "Computer Methods
in Power System Analysis." (Book ), McGraw-Hill Book
Company. New York. 1968, Chapter 6.
TRANSIENT ANALYSIS Of POWllR SY TBM USING FOURIBR AND P
T FOURlliR TRAN POll.
APPENDl ·1
. F(w) is assumed to be sampled at intervals of (k~w) apart (k = O.
perIod of the angular frequency /'::"w, then we have,
=
T
±
I. ±2 . .... ). nd if T j the time
2r.
/'::"w
.. . (l )
+ 00
and
F(k/'::,,(u)=
J
I(I} . exp
t-
2;;;jk 1IT) dl
... (17)
_ 00
The integral in the above equation can be split as follows:
+00
- TT
J
+ 00
F(k/'::"w)=
f
(/+ J)T
T
()+ f ()+· ..
() 4 ..
.. . (I ~
IT
0
- T
f
(/+ J)T
2:
1=
()t- ...
- (/ + J)T
- 00
or
r
() = .. . +
0
}
I
T
(X)
If a new variable I= t - IT is defined. the above equation
F(k6 W)=I[
... (19)
(I) cxp (- 2-:tjkr IT) dr
reducc~
to :
I~"':(I-IT)J ..P(- 2. ,ikl/T) dl
... (20)
T
F(k /'::" w)=
or
f Ip
(I) exp (- 2rt jkt l T) ell
.. . (21)
I(I- IT) f::,. IF (I)
.. (22)
o
where.
--::
1=- 00
j P (t) is called the 'aliassed' form of the continuous
period T, it can be expres ed as a compl ex
sign' I
r (I)
Slllce
I p (I)
is a periodic
ignal with
ourier series, as,
+ 00
fp (I) =
I
ale.
exp (2r.jkl / T)
... (23)
k=- oo
where
CIt
are the Fourier coefficients, given by.
T
a...=
f
~ Ip (I) exp{-27tjkl/T) I
o
... (241
90
IYENGAk, PARTHASARA1}JY, A HOK KUMAR AND KOTHARI
From Equations (24) and (21), we have
... (25)
or,
substitution in Equation (23) yields,
fp (I)
= ~ l:
F(k 6 w ) exp (27tjkt{T)
.. . (26)
The above equation shows the effect of numerical summation of discrete samples in the frequency domain.
Even the direct numerical summation in the frequency domain results in an aliassed version in the time domain.
Tlle time function thus obtained in tbe interval 0<; 1 ..;; T is hence influenced by the successive periods and a
true representation of time function in the Fegion 0";; t ~ T is possible if the function f (I) is non-zero only In
the interval 0";; I Et; T.
APPENDIX-II
'.
TRANSIENTS IN THREE PHASE CIRCUITS
COMPLEX W, S, D
DIMENSlON A(200, 3), W(3)
999 READ 100, NSAMP, NT, DELT, DELW
998 PRINT 99, NSAMP, NT, DELT, DELW
99 FORMAT (2X,2110, 6FIS .6)
100 FORMAT (2110, 6FI0.0)
NREAD- O
DAMP ... 9.2' DELW/6. 28
OMEGA-=o.o
DO II 1= 1, NSAMP
S- CMPLX (DAMP, OMEGA)
CALL FUNCT (W, S, OMEGA, NREAD)
NREAD - I
S = S- DAMP
DO 13 JI - I, 3
13 W (JJ) - W(JJ)·DELW
DO 12 I ,ad. NT
T = (I - t ) 'DELT
D =- C EXP(S'T)
DO 12 JJ = I, 3
t2 A(I, JJ) - A([, JJ )+ W(JJ )·D
11 OMEGA= OMEGA + DELW
DO 1611 ... 1,3
DO 16 I - I, NT
J6 A(J, IJ )=A(J, JJ )' EXP (DAMP·DELT·(J - I )/3. 14159)
DO 17 JJ1 = I, 3
17 PRINT 102, (A(I, JJJ ), 1= 1, NT)
102 FORMAT (2X ,/( 2X, SFIS, 6»
GOTO 998
STOP
END
APPENDIX-III
SU:BROUT1NE FOR FAST FOURJER TRANSFORM
SUBROUTINE FFT (N, M , XI, SIGN, T)
DIMENSION Xl (600), X2 (600)
COMPLEX Xl , X2, W, X1K3
DO 10J= I, M
12J = 2··J
N2J = N/12 J
N2 = 12J/2
NI = N2J
DO 20 1= 1, N2
IN2J = (I - I )'N2J
Pl2N = 6.2832/N
ARG = P12N·IN2J·SIGN
W= COS(ARG) + (O.O,I .O)·SIN '. ARG)
DO 20 K = l, NI
KI = K+1N2J
K2 = K+IN2J·2
K3 =- K2+n2J
K4 = K1+N/2
XIK3 = W·XI (K3)
X2(KI) = XI (K2)+XIK3
X2(K4 )=XI (K2)-XIK3
20 CONTINUE
DO 10 K ~ I, N
10 XI (K ) = X2 (K)
RETURN
END
COMMERCIAL ASPECTS/GENERATION
Tariff Principles for Inter-change/ Exchange of Power
Between States under Integrated Operation
G,
RAMACHANDRAN
Member (Accounts)
Andhra Prade h StBte lectricity Board , Jiyderabad ,
int~graled operation of the adjoining y tern to II hieve
optimum conomy preferably under a c mm n 10 d
despatch cenlre,
1. The question of tariff principle that may g~ve~n
inter-State exchange of power have been dealt wlthtn
the past by Venugopalan Committee and later by the
Power Economy Committee, The former committee
recommended that pooled (;ost of generation and
transmission of the elling Board should form the basis
for tariff with profit element of 3 percent added in
.respect of long-term supply and without the profit
element in other case, The Power Economy Committee' main approach in this regard was on the
premi e that exchange of power even o~ long-term
basis need arise only when there \\-as carcHy of power
availability in one State or ,region an~ availa~ility of
urplus in others, Proceed 109 on thlli preml e, ~he
Committee proposed that pO,oled cost of generatl~n
cannot form the basis of tariff excbange of power In
the above context and that it was ~etter to base the
inter-State tariff on incremental (mamly fuel) cost of
supply to the selling system and the documental cost of
the buyer system, The abo,":e approach o~ the Power
Economy C:ommittee, ~r~ceedmg on the b~ IS of s~rl?l\ls
or scarcity In the abJotOlng system has indeed !11~l1~ed
application. Exchange of power bet~ee~ adjoJOtng
systems need not be thought of only I,n circumstance
of scarcity or surplus but could be con Idered under all
circumstances so that connected y tern are oper~ted
under a common load despatch centre, to , achieve
maximum economy in costs, A system which l,S already
deficit in meeting it power dema,nd, co~ld stili supply
power during night hours to a nelghbourmg ystem by
working its thermal tations as b,a e load stations to
enable the waters in bydro reservOirs to be conserved
to meet peak demands of botb the systems t~rougbout
the year, A deficit system can al 0 prOVIde p,eak
assistance during its off-peak hours to a neIghbouring ystem . O:ving, to rapid gro~th of power
requirements, the tlme 1 fa~t approacblDg w~en. ~o
State will really be having~apaclty and energy ~vailab~lIty
in excess of its own regulrements. So what. ~s reqUired
is not so much the exchange of power aTlSmg out of
surplus condition as exchanges under day to day
2, Integrated peration must. therefore,
following purpo es :
erve the
(a)
~in e the peak demand of the tw
y tem
!nterconnected ,may fall in different hotlr', there
IS a~vantage III one y tern helping the other
meet 109 the peak load of the other 10 the
extent margin is vailable. Thi will en ure
0.ptirnu~ utili ation <?f in tulled capacity in
either grid. thus saving in fre h inve tment
The re erve c~p,acity in either y tern to meet
emergent conditions could also be reduced .
(b)
Integrated operation with a common load
de patch may re ult in the rno t economic
cheduling of power generation taking all the
connected grids into con ideratlon. Thu the
waters in hydro-re ervoirs c01lld be c nse~ved
by working Thermal Stations a ba e load
tations to supply energy during h ur when
meeting of peak-demand i not a problem.
Co~versel~, the peak a~ i lance from hydr
lations Will become avaJlable to the intearated
ystems to meet peak demand in either
Ybtem .
(c) The . energy in one grid which is urplu to its
reqUirements may be made available to the deficit
grid. and fto:w of thi ener~ will also inevitably
be hoked WIth support a I tance in regard to
demand,
3. The ca e for integrated operation of power y tern
in India derive its ju tification mainly from the point
of view of optimum utilj ation of installed capacitie
and reduction of re erve capacities nd viewing the
country or a region as a whole for the purpose of power
93
94
RAMACHANDRAN
development. Development of thermal stations near
coal pits and scheduling their generation in co-ordination with hydro stations located even in other States
should follow as a natural corollary to integrated operation of the power systems in a region. This rational
approach differs from the concept of limited interchange of power between utilities which enter into
agreement for the purpose of mutual assistance in
regard to exchange of energy on ad hoc basis. Such
arragements are really not in the nature of integrated
operation but merely a pre-arranged scheduling of
exchange of blocks of power. An integrated approach
in development is possible only if the basic principles
regarding the tariffs that should apply for i!1terchange
of power are agreed upon .
4. When integrated operation is taken in hand, the
basic tariff principles should aim at fully recovering
the cost of power (providing also for a profit) of the
supplying system and also take into account the savings
that may accrue to the receiving system. For this
purpose, all the types of exchanges of power under
integrated operation indicated in para 2 have to be
dealt with not merely from the point of quantum
of demand or energy that flows,
but also
having regard to the time at which such power flows
occur. A simplified approach for formulating a tariff
for exchange of power is to go on the basis of pooled
cost of under certain circumstances the incremental
cost of power of the supplying grid or the decremental
cost of power of the receiving grid, but such an
approach does not take into accoullt the prevailing
incidence of power demand in the supplying system
at the hour of supply and the costs that have gone into
creating facilities to meet such demands. The value
of power made available by a system is much more at
a time when there is already a high incidence of demand
on the system than at a time when the system load is
low as during non-peak and night hours. In any
rational appraisal of the value of power, the time at
which supply is made should, therefore, have a significant relation to the cost of power. The main approach
in this paper is to suggest a proper evaluation of tariff
according to the hour of supply so that the technical
responsibility of the consumer in contributing to the
demand at that hour is duly taken into account.
5. Evolving a suitable tariff fol' exchange of power
under integrated operation should provide sufficient
incentive for the supplying and the receiving system to
supply and rec~ive power. C.ost of power is the main
premi e on which such a tariff has to be evolved, but
this cost hould be scientifically evaluated so that the
costing is related to the time ~f supply. Cost of power
comprises both fixed and vanable charges. The fixed
charges viz .• interest on inve tment, depreciation of
the ass~ts. fixed element of operation and maintenance
which do not vary with output or consumption, are in
any case to be incurred by the public lltility and these
fixed charges have relation mainly to tbe peaking
capacity created in the system to meet the sy tern peak
load. At the same time, for power consumed during
non-peak hours there should also be an equitable
levy of fixed charges, but the element of the fixed
charges levied for the non-peak period should logically
be less than that for the peak hours. For this purpose,
the allocation of fixed charges of a system requires to
be carried out scientifically relating it to the changing
incidence of loads on the system according to each
hour of the 24-hour period. Such a scientific allocation
is possible to be made adopting the 'Method of
]ntercepts'-a theoretical exposition of which is found
in the Article on "Allocating Fixed Costs" by H. Christopher, H. Armstead in the 'Energy International',
December 1969.
6. Fixed charges could aJso be stated as maximum
demand costs, because the fixed assets to which these
charges relate have been built up to meet the maximum
demand on the system. Variable charges are, however,
different as these are related to the output of energy
and these charges could be derived on uniform rate
per kWH. In respect of power from hydro station.
the entire expenditure incurred is practically fixed
charges as the expenditure does not vary with output,
while in the case of Thermal Stations, cost of fuel,
lubricants and other consumables has a direct relation
to the output of energy and fall under ' variable charges'.
Cost of power purchased from outside sources also
falls under 'variable charges' unless there is a commitment to purchase a minimum block of power, in which
case co t of that minimum could be treated as 'fixed
charges' . The problem of allocating costs according
to the time of the day arises only in the case of fixed
charges (maximum demand costs).
7. As the exchange of power between two systems
takes place at EHT level fixed charge. relating to
generation and EHT system only need be taken into
account for the purpose of allocating costs according
to the time of incidence of demand. The element of
interest included in the fixed charges may perhaps be
arrived at not with reference to the entire value of
inve tment on the fixed assets in use, but after deducting
therefrom the accumulated depreciation and internal
resources which have gone to build up the e fixed
assets. The abovc net investment value is secured if
the formula for arriving at Capital Base' prescribed
by World Bank to judge the financial returns of State
Electricity Boards is broadly adopted limiting the
'Capital Base' to cover only the generation and EHT
fixed assets.
8. While the approach suggested in para 7 above
give the most favourable premises to the consumers
in the computation of cost of power, it is po sible to
argue that depreciated cost of the assets should not be
the basis of calculating the interest element included in
the co t of power. According to this argument. the
portion of fixed a set built out of accumulated
depreciation or other internal re erve should also
TARIFP PRINClPLB3 FOR lNTBR-CHANOa/aXCHANGB OF POWER 8I!TWBBN STA
earn a return which would have been the ca e,
had these reserves been inve ted outside instead of
being ploughed in busine s. Bu t tben the receipts
from such external investment should be on idered a
extra receipts to be taken into account to give a suitable
rebate to reduce the expenditure compri ing cost of
power. Electricity Supply Act 1948, in its Eighth
Schedule provides for calculation of cost of power ba d
only on interest on tbe depreciated cost of the a et.
9. Under the Method of Intercepts the total fixed
charges of the S~ate EI~ctricity Board .for tl~e whole
year having relatlo~ ~amly to the blllil up Installed
capacity and TransmIssIon System to cater to the peak
demand on the system, have to be divided by the peak
demand reached on the system during that year, 0
that fixed charges of the entire system for th e year
per MW of demand could be arrived at. There are two
ways of determining the peak demand on tllc system
during the year, viz., absolute peak demand reached
during the year and tbe average pe~k demand taking a~1
the days in the year. The first one IS to go by the maXI·
mum peak demand reached on the system at any time
during the year. This peak taking the load curve of the
day on which the peak was reached cannot, however, be
taken as represen tative of the demand on. the. system
throughout the year. To get a representatIve pIcture of
the demand on the system throughout the year, the more
scientific method is to take the demands on the system
at each hour (or half hour) on each day of the year and
at arrive the average demand on the sy tern for the year
each at hour (or half hour~ . The system load cur~e
determined on the above basIs of average demand will
certain1y be more representati ve than the load curve of
the system on the day it touched the _peak. The fixed
charges incurred for the whole year If these are .to be
expres ed ' per MW' should, therefore, be appropriately
divided by the average peak demand reached on the
system and not by the absolute peak _reached at .any
time during the year. If the latter IS taken mto
account, it means that the fixed charges as. allocated
per MW will be understated and the allocation of the
fixed charges according. to the hour o~ supply under the
method of intercepts WIll not result In th7 recovery of
the entire fixed charges. On the ol~er hand, If th~ 4verage
load curve is taken as the basIs for allocatmg fixed
charges, it will result in full recov7ry . of the fixed
charges. This point is further dealt WIth 10 para 14.
10. Having arrived at the fixed c~arges per MW for
the year, these could be expressed 10 terms of char~e
per day hy dividing the annual figure by 365. Taluog
the ca es of Tamil Nadu, Mysore and Kerala State
Electricity Boards, their fixed charges for the year
1970-71 have been worked out in Table I. These fixed
charges provide al 0 for a 3 percent profit o~ the
capital base adopting Venkatraman Comrmttee
recommendations. The average hourly deman~ da~a
for these Boards for the year 1970-71 are also gIven ID
Table n. The average load curves ~or tb~e three Boar~
for ) 970· 71 are al 0 illustrated tn FIgure 1. It wlll
UNO It I
ATl
5
be een that the av r g maximum
du o M t nod
for the year 1910·7 1 in Tamil
Kerala wer re pectively lOS8 MW at 8 A. M.), 678.4
MW (at 19 h urs) nd 305.2 M
t 20 110Urs).
Dividing the total fi ed char e arriv d at per d t of
the abo • a crage ma imum d m nd f the re. p tive
ystcms, it i een that the Ii cd charge per MW Po r d y
for the year 1970·7.1 \ rk out to R . 62 for TamIl Nndu,
R . 60S Ii r My ore and R . 9L for Ketola. Ha in
thus arrived al the fi ed ch rge per day p r MW it j
now pos ible to allocate the e Ii ed cl\Mge according
to each hour of the day depending upon the demand
00 the y tern Ilt thnt pnrticul r hour. T king for
example. the average lond curve f the Tamil Nudu
ystem for the ycar 1970·71 (Fi811r I), it will he , een
that a minimum load of 495 MW wa on th y tern
throughout the 24 hours, (\ load of 532 MW Ii r 20
hours, a load 766 MW for 10 hours ond 0 on till the
maximum load of 1,058 MW wn reached ju. t n hour
between 7 A.M . and 8 A.M . The number of JlOllr for
which a particular demand has b en on the sy, tem i
defined as the 'intercept' and with reference 10 this
'intercept' the fixed charge orc arrived at per MW t
various stages of demand btnining on the sy tern. For
example, the fixed charges per MW when the ystem
load is 1,058 MW will be much more than when the
system load is say 532 MW. This is bec(lu e the time
intercept for the demand of 1,058 MW wa only I hour
while for the demand of 532 MW it was 20 hours.
11 . From the above allocation of fixed charge per
MW charges according to the load on the system, the
flow rate of fixed charges accordin~ 10 sy tem inc id~nce
of demand during the 24·hour period could be nrrtved
at. Taking the case of Tamil Nadu
lectricity
Board the above flow rate of tixed charge .
proce;ding on the basi of the average syst m load
cu rve for 1970-7 1, is given in Table TIL rom
this flow rate of fixed charges (Maximum Demand
Costs), the fixed charge that ought to be charged for
eacb bour of the day per MW of supply taken at tllat
hour can be determined. This, for Tamil Nadu lectricity Board for 1970-71, is arrived at in Table n (CoI7).
II will be seen from Table 11 that the M.D. charge
for the 24-hour period varies hour to hour. Jt is as
low as Rs. 26.18 per MW at 3 A.M . and goe up to
Rs. 114.89 at 7 A.M. when the demand on the ystcf!l
reaches the peak. In re pect or inter: Stat~ upply. If
the neighbouring grid take!; supply dunng nlabt hours,
it will be charged Ie s than J14th of wh~t it will be
charged if it were to take power at the Tamll .N~du p~ak
hour of 7 A.M. Thus there is an automatic JOcenllve
to take supply during njght hour and disincentive to
take supply during the peak hours.
12 Taking the same year) 970-7 J, the average system
lo~d curve for the year, the allocation of fixed charge
according to hour of the day, etc., ha been worked
out for My are and Kerala State Electricity Board a
weJl. Table IV&V how the now rate of M.D. charge
96
RAMACHANDRAN
"00
J
I\M~
,
1\
1000
goo
~
/T omllnodu
x....:
100
f\
.!:
I
'--
""
oj
100
E 600
·1&00
"00
'""""=
V
l/;
- V
- - -./
200
e
2
FIGURE 1:
Myaor.\
_..
~
10
12
H6vrs
''''
V"
~'\
~
~'""-
30~
/Kerolo
v
lL
v-
100
L/
~- .r--
-
300
Ir1\\
16
18
..............
20
'"
22
Annunl hourly avel1lge maximum demand 1970-71 .
for Mysore and Kerala according to varying demands on
the system and Cols. 3 & 5 in Table II show the M.D.
charge according to hour of the day. It will be seen
from Table 11 that flxed charges reach the maximum in
Tamil Nadu Electricity Board at about 8 A.M. when the
system 1 ad i at its p uk, while in the ca e of My ore
and Kerala, the charges are maximum in the evening at
7 P.M . and 8 P .M.
13. Over and above the fixed charges payable under
the Method of Intercepts, the receiving system will
also have to pay to the upplying system varia ble
charge based on the total energy drawn from that
pstem. If the supplying system is wholly hydro-ba ed,
the entire charges incurred by th supplying sy tern get
cIa sified as fixed charges becau e the expenditure on a
hydro- y tern does not vary with output. If the supplying sy tern is partly thermal, there will be a good element
of variable charges that are incurred compri ing mainl
cost of fuel, ,onsumable, et ., incurred in the thermal
p wer
station . Similarly, if a system purchase
from outside, the cost of that purcha e als fall
under varia ble charge. I t is not difficult to arrive
at the varia ble charges incurred per unit of
energy generated or purchased aod transmitted .
Thi s va riable cost per unit could be arrived at either on
month to month basi or for the sake of convenience.
the vari a ble cost per unit as incurred in the earlier year
could pcrhap be applied f r the consumption of
energy in t he next year . The variable costs of the three
Boards for 1970-71 a re al so howo in Table I.
14. The allocation of M.D. cbarges to a chosen consumer (in the case of inter-State upply, the other State
Electricity Board receiving the supply) is totally
independent of the load curves of any other consumer.
The fixed charges ac ording to each bour of upply i
arrived at scientifically, and 0 long a the chosen
consumer is charged a per this rate, be is made to bear
his portion of fixed charge going by his technical
respon ibility of adding to the demand on the system at
his hour of drawal of power. The accurac of the
TARIFF PRINClPLES FOR INTER-CRA OE/EXCHA OE OF POWER IlIITW
TA
orR I T Oft.
OOP RATI
TAB
tatement howlng Fixed
2
hal11
lind Yaril\blc
h:llll
1970-71
My. re tute
lect ricity
Board
K r lu I te
Ie Iri il
Boord
3
4
5
(R . in Inkh )
1. Capital Base
Fixed Assets :
(i) Generatation
14,03 .00
1,112.40
6,647.24
9.20
13.12
2,961. 10
1,21 4.09
5, 49.00
4,082.70
7.t<74 .45
19,087.00
on Generat ion A els
552.04
I,056.2~
1,9 6. 0
on Transmis ion Asse t
430.25
Total (iii)
982.29
1,056.28
3,007. 00
Capital Base
3.100.41
(i,HIM.17
) 6.0 0.00
IB6.02
409.09
964.80
15.50
34.09
0.40
120.45
170.38
400.15
321.97
613.56
1.445.35
93.01
204.55
482.40
960.00
26. 5
Hydro
Steam
Diesel
(ii) Tran mission
Total
Deduct
(iii) Depreciation
2.
Fixed Charge on Capital Base
1nterest
1
61)(,
General Re erve @
!%
Depreciation for the year
Total (2)
3. Profit
I(f
3%on Capital
B8lIe
4.
1,071.00
ADD : Co t of Power
98
RAMACHANDRAN
•
TABtE I (Con/d.)
2
3
5
4
Salaries and Wages to Repairs and Maintenance
(a) Hydro Generati on
83. 76
102.08
}
(b) Steam
(c) Diesel
0.41
(d) Transmission
Total (4)
Total fixed charges for the yea r ( + Profi t)
Annual average Maximum Demand
Fixed charges per MW (Rs.lakhs)
303.69
39.62
70.25
195.06
1,083.79
199.18
498.75
1,498.77
1,017.29
2,426.50
678.4
305.2
2.209
M.D. charges (Fi xed Charges) per day (in rupees)
"1
605.20
3.333
913.20
1,058.0
2.294
628 .35
Variable Costs :
(a) Fuel
(b) Cost of Power
87.62
(c) Water
323.10
1,428.61
6.28
1] .39
(d) Royalty and Others
------- --------------
Total (Rs. in lakhs)
87.62
Units available at the E.H.T. end (MkWh)
4,519
Variable cost of a U nit (paise)
0.19
1,769.38
5770
3.07
------------------------------------determination of the fixed charges depend solely on
the accuracy of the system load curve which forms the
basis for applying the method of intercepts. As
already stated in Para 9, jf th e system load curve on
the day the peak demand was reached in the year is
taken as the basis, it will not be representative of the
demand obtaining n the system throughout the year,
and as such allocation of fixed costs as per the peak-day
curve will result in following anomalies:
(0) The peak demand reached during a day of the year
being much more than the average peak demand
taking all the 365 days into account, the fixed
charges per MW would work out lower. COllsequently, the charge per MW recoverable
from the chosen consumer will be unduly low,
(b) The measurement of intercepts in regard to the
duration of demands at various levels will be
different on the peak-day curve from what it
would be if the average demand curve for the
whole year is taken as the basis. Consequently,
the accuracy in the determination of fixed
charges for each hour gets affected.
It is, therefore, appropriate that for the allocation
of the annual fixed charges, only the average system
load curve for the year should form the basis. The
figures worked out in the tables for Tamil Nadu,
Mysore and Kerala State Electricity Boards have been
arrived at only on the above basis.
1.5 If two systems are inter-connected for integrated operation, the hourly demand registered in either
of the systems for supply received could be recorded
according to each bour of the day for all the days in
a month. By totalling the demand as recorded for
each particular hour for all the days of the month, the
total demand availed of during that particular hour
TARIPP PRINCIPLES POlllNTER-CHA GE/EXCHANGE OF POWER BET"
TAB
Annual lIourly
8\'era
maximum 4emand ond hourly
Mysore
Hour,
of the
day
110'11'
o
R INT., R 1 0
P RATION
11
rate or 1\1.0. charae - M
Kerilla
- -- - -
I't!,
K NIls and Tamil 'lIdli.
T mil
----v rage
du
-----
Avenige
Maximum
Demand
IMW)
Flow late of
M.D. charges
l.
<44 5
25.26
207
38.27
51.
2.
0438
25.23
202
38.09
O:!
2 .20
3.
434
25.22
200
38.05
495
26. 18
4.
445
25.27
200
38.05
50
... 21
5.
0475
25 .60
203
38.09
544
26.60
6.
530
26.57
223
38 .99
665
2 .48
7.
588
28.27
244
40.57
I05K
114.~9
8.
600
29.22
252
4UO
967
66.57
9.
609
30.33
261
44.91
856
37 .24
10.
606
29.79
259
43 .84
865
38.16
11.
591
28 .50
256
42.96
777
31.8
12.
587
28.25
248
41.22
766
31.26
13.
554
27.08
238
39.97
742
30.30
14.
,549
26.96
235
39.73
71O
29.37
15.
573
27 .69
241
40.29
720
2 .63
16.
586
28 . 19
250
41 .54
790
32.57
17.
603
29.45
255
42.69
868
38.57
18.
615
31.53
258
43.6
R70
31:!.97
19.
678
54.62
286
65.53
841
36.04
20.
676
52.26
305
112.83
751
30. 2
21.
638
37.58
290
71.72
701
29.17
22.
563
27.35
271
52.85
641
28.07
23.
492
25.89
242
40.31
573
21.02
24.
468
25.51
219
3 .78
532
26.45
For detail
(Rs. /P)
ee Tabels lTI to V.
A"era~e
Maximum
Demand
(MW)
III w r le of
M.D. charges
(Rs. /P)
Mu imum
DOland
(MW)
2 ....
RAMACHANDRAN
)00
TABLE
m
Tamil Nadu EleclriciCy Board- FlOw rate of M .D. charges 1970-71.
Sl.
No .
M .D.
(MW)
Time
intercept
Rate of M .D. charges
M .D .
charges
Progressive
Flow
rate
M.D.
- - - - - - - - - - - -Rupees- - - -
cbarges
1.
495
24
628.35/24
26.18
12,959.72
12,959.72
26.18
2.
502
23
628.35 /23
27.32
191.23
13,150.96
26.20
3.
503
22
628.35 /22
28.56
28.56
13,179.52
26.21
4.
516
21
628.35/21
29.92
359.05
13,538.57
26.29
5.
532
20
628.35 /20
31.42
534.10
14,072.67
26.45
6.
544
19
628.35/19
33.07
396.85
14,469.52
26.60
7.
573
18
628.35/18
34.91
) 012.34
15,481.86
27.02
8.
641
17
628.35 / 17
36.94
2,513.40
17,995.26
28.07
9.
665
16
628.35/ 16
39.27
942.53
18,937.79
28.48
10.
701
15
628.35 / 15
41.89
1,508.04
20,445.83
29.17
11.
710
14
628.35 / 14
44.88
403.94
20,849.77
29.37
12.
720
13
628.35 / 13
48.33
483.35
21,333.12
29.63
13.
742
12
628 .35/ 12
52 .36
1,151.98
22,485.10
30.30
14.
751
11
628.35 / 11
57.12
514. 10
22,999.20
30.62
15.
766
10
62835 /10
62.84
942.60
23,941.80
31 '26
16.
777
9
628.35 /9
69.82
767.98
24,709.78
31.80
17.
790
8
628.35 /8
78.54
1,021 .07
25,730.85
32.57
18.
841
7
628.35 /7
89.71
4577.98
30,308.83
36.04
19.
856
6
628.35/6
104.72
1,570.80
31,879.63
37.24
20.
865
5
628.35/5
125.67
1,131.03
33,010.66
38.16
21.
868
4
628.35/4
157.09
471.27
33,481.93
38.57
22.
870
3
628.35/3
209.45
418.90
33,900.83
38.97
23.
967
2
628.35/2
314.17
30,474.49
64,375.32
66.57
24.
1058
628.35/ 1
628.35
57, 179.85
1,21,555.17
114.89
TARIFF PRINCIPLES FOR INTER-CHA GI!/ BXCH
Gil OF POWER B6TWIiEN TAT!! UNDBRJ
ORA1l!D OPBltATt
101
TABLE J\'
My ore tate Electricity Board- Frow rat of M.D.
Sl .
No.
M.D.
(MW)
Time
intercept
Rate of M .D . charge
(twa
(916-1(.
M .D.
harge
Progrc ive
low
r te f
MD.
char e
Rupe -
- ----
1.
434.0
24
605.20/24
25.22
10,944.03
10, 44.03
25.22
2.
437.8
23
605.20/23
26.3 1
99.99
11 ,044.02
25.23
3.
444.9
22
605.20/22
27.5 1
195.31
) 1,239.33
25 .26
4.
445.2
21
605.20/21
28.82
.65
11,247.98
25.27
5.
467.8
20
605.20 /20
30.26
683.88
) 1,931.86
25.51
6.
474.7
19
605.20/19
31.85
219.78
12,151.64
25.60
7.
492.4
18
605.20/ 18
33.62
595.11
12.746.75
25.89
8.
529.9
17
605.20/ 17
35.60
1,335.00
14,0 1.75
26.57
9.
548.6
16
605 .20/16
37.83
707 .33
14,789.0
26.96
10.
553 .6
15
605.20/ 15
40.35
101.75
14,990.83
27. 08
11.
563 .0
14
605.20/ 14
43.23
406.35
15,397.18
27.35
12.
573 .2
13
605.20/ 13
46.55
474.85
15,872.03
27.69
13.
586.0
12
605.20/12
50.43
645.55
16,517 .58
28.19
14.
587.4
11
605.20/ 11
55.02
77.02
16,594.60
28.25
15.
587.7
10
605.20/10
60.52
18.16
16,612.76
28.27
16.
591.2
9
605.20/9
67.24
235 .35
16,848. 11
28.50
17.
600.4
8
605.20/8
75.65
695.98
17,544.09
29.22
18.
602.8
7
605.20/7
86.46
207.50
17,751.59
29.45
19.
605.7
6
605.20/6
100.87
292.51
18,044.10
29.79
20.
609.3
5
605.20/5
121.04
435.74
18,479.84
30.33
21.
615.4
4
605.20/4
151.30
922.93
19,402.77
31.53
22.
63f$.1
3
605.20/3
201.73
4,579.27
23,982.04
37.58
23.
675.5
2
605.20/2
302.60
11,317.24
35,299.28
52.26
24.
678.4
1
605 .20/1
605.20
1,755.08
37,054.36
54.62
102
RAMACHANDRAN
TABLE V
Kerals tate Electricity Board Flow rate of M .D. cbs:'gcs 1970-71.
SI.
No.
M .D.
(MW)
Time
intercept
Rate of M.D . char~es
M.D.
charges
Pro~ressive
Flow
rate of
M.D.
charges
- - : - - - - - - - - - - -Rupee - - - - - - - - - - - - ~--
1.
199.8
24
913.20/24
38.05
7,602.39
7,602.39
38 .05
2.
200.2
23
913.20/23
39.70
15.88
7,618.27
38.05
3.
202.4
22
913.20/22
41.51
91.32
7,709.59
38.09
4.
202.5
21
913.20/21
43.48
4.35
7,713.94
38.09
5.
207.3
20
913.20/20
45.66
219.17
7,933.11
'38.27
6.
218 .7
19
913.20/19
48.06
547.92
8,481 .03
38.78
7.
222.7
18
913.20/18
50.73
202.93
8,683.96
38.99
8.
234.5
17
913.20/17
53.72
633.87
9,317.83
39.73
9.
237.8
16
913.20/16
57.07
188.35
9506.18
39.97
10.
241.4
15
913 .20/ 15
60.88
319.17
9,725.35
40.29
11.
241.6
14
913.20/ 14
65.23
13.04
9,738.39
40.31
12.
243 .7
13
913.20/13
70.24
147.51
9,885.90
40.57
13.
248.3
12
913.20/12
76.10
350.06
10,235.96
41.22
14.
250.2
II
913.20/11
83.02
157 .73
10,393.69
41.54
15.
251.5
10
913.20/10
91.32
118.72
10,512.41
41.80
16.
255.3
9
913.20/9
101.46
385.57
10,897.98
42 .69
17.
256.3
8
913.20/8
114.15
114.15
11.012.13
42.96
18.
258.4
7
913.20/7
130.45
273.96
11,286.09
43 .68
19.
258.8
6
9 I 3.20/6
152.20
60.88
11,346.97
43.84
20.
260.8
5
913.20/5
182.64
365.28
11 ,712.25
44.91
21.
271.3
4
913.20/4
228.30
2,625.45
14,337.70
52.85
22.
285.7
3
913.20/3
304.40
4,383.36
18,721.06
65.53
23.
290.3
2
913.20/2
456.60
2,100.36
20,821.42
71.72
2-4.
305.2
913.20/1
~13.20
34,428.10
112.83
13,606.6
TARIff PRINCIPLES FOR INTI!R.CHANGE/ EXCHANG
OF POWI!R '8 TWEEN STAT
can be arrived at and this when multiplied by the
Maximum Demand Cost of the supplying Board for
that hour gives the fixed charge payable by the receiv.
ing Board in respect of supply availed of during that
particular bour throughout tbat month. Like that, the
maximum demand charge payable for power drawn at
each of the 24 hours througbout the month could be
convenientfy added up. As an example, it has been
worked out how under the Method of Intercepts, the
export of power from Kerala State Electricity Board
grid to Tamil Nadu Electricity Bard grid during
March 1972 when the two systems were inter·connected
could be costed . Table VI to this note gives the details
of the above e port of power in terms of MW at each
hour of the day in re pecI of all the 31 days of March
1972, the maximum demand rate applicable for that
hour as per the fi ed charges of Kerala State Electricity
Board for 1970·71. and the total fixed charge payable
by Tamil Nadu Electricity Board to Kerala State
Electricity Board for upply received in March 1972.
16. It will be seen from Table vn that Tamil Nadu
Electricity Board drew a lotal of 66,630 MWs of hourly
instalments during March 1972. The total energy
drawn was 68.69 million kWh. The total fixed charges
payable as per the Method of Intercepts for March
1972 come 10 R . 30.57 Jakhs. The average unit rale
works out to 4.45 P/kWh. It is, however, not appro·
priate to express the fixed charges in terms of an average
unit ratem but this is done just to show that the average
rate does not work out to any abnormal figure). The
above fixed charge have been arrived at on the basis
of depriciated value of fixed as ets and after adding 3
percent profit on the capital base. A suitable policy
decision regarding the profit element to be included has
to be taken. There are no significant variable charges
to be added to the above si nce the entire charges incurred in the Kerala State Electricity Board are practi.
cally in the nature of fixed charge.
17. An attempt has also been made to compute the
fixed charges payable under the Method of Intercepts
in respect of the inter·State upply between Mysore and
Tamil Nadu taking again March 1972 figures a exam·
pIe. Details of the export and import between the two
Boards are given in Table VH. In this ca e, the power
flow has been mutual. While Mysore State Electricity
Board exported 4875 .5 MWs of hourly inslalmen.ts 10
Tamil Nadu Electricity 'Board in March 1972, the
latter al 0 exported 7,082 MWs to My ore State Electri·
city Board during the sallle month . Table VTl brings
out the export of power according to each hour for the
entire month, the M.D. cost of Mysore State Electrj·
city Board at each hour, the total amount payable by
Tamil Nadu Electricity Board to My ore State Electrl'
city Board for the export according to Mysore cost,
UND R INT
T B
RATED
P RATI N
10
"I
Orawal of powu b Tamil Idu
Irk B
K rail tal EJ Irl It Boerd, Much
d fro
1m.
Hour of
drawal
M .D .
drawn
(in MW)
Flow rale
ofM.O .
harg
( t
Amount co
be billed
Ker In
r tes)
1.
2.
3.
2210
2105
2245
4.
5.
6.
7.
8.
9.
10.
II.
261 8
2530
2930
3015
3065
2935
3275
2870
3] 85
3005
2818
3200
3234
3330
2945
2180
2425
2455
2925
2715
2415
]2.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
38.27
4.576.70
80.179.45
5,422.25
99,614.90
96,367.70
114,240.7
122,318.55
128,117.00
131, 10.85
143,576.00
123,295.20
131,285.70
120,109.85
111,959.14
128,928.00
134.340.36
142,157.70
128,637.60
142,855.40
273,6 12.75
176,072.60
154,586.25
109,441.65
93,653.70
3 .09
38.05
38.05
38.09
38.99
40.57
41.80
44.91
43.84
42.96
41.22
39.97
39.73
40.29
41.54
42.69
43.68
65 .53
112.83
71.72
52.85
40.3 1
38.78
3,057,160.00
.....,
Averaae Fixed cost per unit (Paise)
Total Units drawn by Tamil Nadu
Board in MatCh 1972
lectricity
68.69
MkWh
the M.D. cost of Tamil Nadu Electricity Board for
each hour and the total amount payable by Mysore
State Electricity Board to Tamil Nadu Electricity
Board for the export according to Tamil Nadu Electri·
city Board costs.
18. It will be seen that owing to the maximum
demand costs and variable charges of Tamil Nadu
Electricity Board being higher than those of Mysore
State Electricity Board, the amount payable a per
Tamil adu Electricity Board's co ta for supply received
from that Board is higher than the costs for corresponding quantum of power received by Tamil Nadu
Electricity Board from Mysore State Electricity Board
104
RAMACHANDRAN
TABLE VII
Drawal of power by Tamil Nadu Electricity Board from Mysore Stale Electricity Board and from Tamil Nadu
Electricity Board by Mysore tate Electricity Board In March 1972.
From T.N.E. Board to M.S.E. Board
From M.S .E. Board to T.N.E. Board
-Hour of
drawal
1.
2.
3.
4.
5.
6.
7.
8.
9'
10.
]].
12.
13.
]4.
15.
16.
17.
18.
19.
20.
21.
22.
Z3.
24.
M.D.
drawn
(in MW)
74
63
76
60
64
]28
480
54]
618
382
290
340
240
186
244
194
262
186
38
56
104
60
100
90
Flow rate
of M.D.
charges of
M.S.E. Board
Rs./MW
25.26
25.23
25.22
25.27
25.60
26.57
28.27
29.22
30.33
29.79
28.50
28.25
27.08
26.96
27.69
28.19
29.44
31.53
54.62
52.26
37.58
27.35
25.89
25.51
4,876
Add: Variable charge @ 0. 19 P/Unit
M.D .
drawn
(in MW)
1,869.24
1,589.49
1,916.72
1,5 16.20
1,638.40
3,400.96
]3,569.60
15,808 .02
18,743.94
11 ,379.78
8,265.00
9,605.00
6,499.20
5,014.56
6,756.36
5,468.86
7,713.28
5,864.58
2,075.56
2,926.56
3,908.32
1,641.00
2,589.00
2295.90
626
653
653
515
493
188
60
90
] 14
74
84
88
138
J08
128
74
74
60
18
50
114
786
1,203
691
] 42,056.73
7,082
4.806 Million Units
Total Units drawn by T.N.E. Board
Total Charges
Amount to
be billed
by M.S.E.
Board
Rs.P.
R . 1,51,188.13
Flow rate
of M.D.
charges of
T.N.E. Board
Rs./MW
Amount to
be billed by
T.N.E. Board
Rs.P.
16,457.54
17,108.60
17,095.54
13,498.15
13,113.80
5,354.24
6,893.40
5,991.30
4,245.36
2,823.84
2,671.20
2,750.88
4,181.40
3.171.96
3.792.64
2,410.18
2,854.18
2.338.20
648.72
1,531.00
3,325.38
22.063.02
32,505.06
18,276.95
26.29
26.20
26.18
26.21
26.60
28 .48
114.89
66.57
37.24
38.16
31.80
31.26
30.30
29.37
29.63
32.57
38.57
38.97
36.04
30.62
29.17
28.07
27.02
26.45
2,05,102.54
TOlal Units drawn by M.S.E. Board
Add:
. Rs. 9,131.40
-
6.845 Million Unit
ariable charge @ 3.01 PfUnit
Rs .
Total Charges
R.
2,10,145. 0
- 4,15,244.04
- ---
-----
TARiFf PRINCIPLES FOR INTER-CHANGE/ EXCHANGE OF P WEll BETWE
according to the costs of the latter Board. Be id the
fixed costs, Tamil Nadu Electricity Board incur ubstantial variable costs in the shape of variable harge
for thermal power and co t of power paid for power
purchases from other. On the other hand there are
no significant variable charges incurred by My re
State Electricity Board as its entire expenditure fall
under fixed charges. It is, therefore, apparent that the
cost of power supplied by Tamil Nadu Electricit
Board will be higher than the cost of power supplied
by Mysore State Electricity Board . 1n the above
context, it will not be in the interest of the Mv ore
State Electricity Board to import at all any power -from
Tamil Nadu Electricity Board except when Mysore
State Electricity Board require upply during its peak
hours in case it ha a deficit in capacity. This point
is dealt with in para 19 .
If Mysore State Electricity Board is having deficit
in energy over the year, it will certainly not agree to
supply power to Tamil Nadu Electricity Board even
for peak assistance except under the condition that
the same quantum of power should be returned by
Tamil Nadu Electricity Boa'rd to Mysore State Eleclri ·
city Board. In this context, while for the export of
power from Mysore State Electricity Bo ard to Tamil
Nadu Electricity Board (which will be mainly for peak
assistance), Tamil Nadu Electricity Board should pay
according to Mysore State Electricity Boa rd cost.
applicable to the hours of supply, for the p wer
returned by Tamil Nadu Electricity Boord to My, re
State Electricity Board, it will not be proper to expect
Mysore State Electricity Board 10 pay at Tamil N adu
Elecritcity Board's cost. In this unusual situation
when supply of power by Tamil Nadu Electricity Board
to Mysore State Electricity Board is made in the
interest of supplying Board, it is obvious that the
theory of maximum demand costs developing on the
supplying Board dealt with in Ihis paper cannot apply.
For such flow of power, it would be logical if
Mysore State Electricity Board pays according to its
own costs and to keep such cost s to the minimum,
Mysore State Electricity Board could as well specify
that the return of such power by Tamil Nadu Electri·
city Board may be made only during the night hour~
when the costs are minimum .
If for example, Mysore State Electricity Board has
no deficit in meeting its energy requirements over the
year, it can still agree to receive supply from Tamil
Nadu Electricity Board in case Tamil Nadu Electricity
Board wants to store its power with My ore Stale
Electricity Board and wants redraw it for meeting its
peak demands. Similarly , even when Myso.re State
Electricity Board has a deficit when TamJI Nadu
Electricity Board bas to return the power drdwn ~a~k
to Mysore and in addition if Tamil Nadu ElectriCity
Board aJso wants to store some p ower with My)ore
State Electricity Board. Mysore can slill agree to
receive that power for storage purpose. ~n. both the
above situation. when Tamil Nadu ElectncllY Board
o
TA
OP RATION
lOS
want to t
20. To sum up, following pos ibl slluat;
arl e in integrated ope rat; n elween Iw system
whieh a uitable solution in the application f
tariff rrinciples dealt wilh in thi puper h . I
found.
(il Both the ~y tem are . elf·su m ient in energy
but int grated oper tion help . them (0 utili e
exi ting installed capacities t 0 ptimum level.
y~tem' are deficit
in energy and
demand and integrated operat ion give mutual
support.
(ii) Both the
(iii) Both the sys tem
are self-s u fflcient in energy
and demand and inleltrated orerll ti n re ult
in thermal generation in on e
y tern being
saved owing t surplus hyd lo-power beina
available in th e other sy tem.
(ii" Thermal generation b stepped up eonsiderably
in one ~y . lem to supply energy to other yslem
so a to co nserve the wuter, in hydr ·re ervoir
10 meet peak demand in either . y tc.m,
(v) One sys tem is in
demand and
sy tem .
urpl Ul> bo th in energy and
upplies the urplu . to the other
10 regard (0 ituations mentioned at (/) & (II) above,
the billing could be a per the co t of the upplyin&
sy tern according to the hour .of upply. Thai i • the
tariff prinCiple a
ugge led In thl paper may apply
without any modificatto n .
In regard to (iii) above. the yslem of aving ther·
mal power and obtainin 10 lieu hydro -power in urplu
in the otber y tem could pay accMd i"$ t the co IS of
the supplying sy tem a per the tariff principle ,uUe t·
ed in thi paper. but the overall payment may be
106
RAMACHANDRAN
Jimted to a ceiling unit rate equal to the incremental
cost of generation in their least efficient thermal stations
which would have been shut down to conver,e costs.
Such supply of surplus power has been in vogue between Kerala State Electricity Board and Tamil Nadu
Electricity Board vide para 15.
In regard to (iv) , the approach as suggested in paras
18 and 19 may apply. This situation has actually
been obtaining in the exchange of power between
Mysore and Tamil Nadu vide para 17.
21. Conclusion
The method sugge ted in this paper is suited for
adoption under all circumstances of inter·State Supply.
The calculation of costs need be made only on the
basis of annual figures . While the previous years'
In regard to (v). the system of receiving supply costs may be the basis for arriving at the fixed and
should pay as per the costs of the supplying system variable charges for billing purpo es, such billing could
according to hour of supply That is, the tariff principles be provisional and made subject to revision after the
suggested in this paper will apply without modjfication. costs of the actual year of supply could be worked out.
Cracking of Hydro-Turbine Runne r Blades
L.R.
M.L.
MALIK
Chief Generation Supdl.
. e utive
Bhakra Powe r Hou e • Bhakrn Management B
HAWLA
nainccr
rd. Nanaal.
YNOP I
An attempt has been made in this paper to Im'estigate the cal es leading to
the extensive cracking of runner blades on Bltakra Right Bank POlller Piant.
Thickening and strertgthening of the trailing edges of the runner blades could not
help in eliminating the damage to the runner blades. Th oretical anal)' is of
this problem supported byfield observations inti; ales to the fact that til opp aronet
of the cracks on the runner blades can be attributed to the occurrence of vibration
on account of resonance between the frequency of shedding of Von-Karman Vortex
trail and the natural frequency of the blades. Rounding of the blades on tht
trailing edges on one of the unit Irelped ill eliminotl'ng the cracks on Ihe runner
blades QIId also in improving the operational hehaviour of tire WItt . Ac('ordlngly
tire trailing edges of rllnner blades of all the units are being round doff.
1.
Introduction
L.I In this paper, a detailed analysis of the proble'!l
of frequent cracking of the runner blades of th e FranCIS
turbines installed on the Bhakra Right Bank Power
Plant is being made. These Francis turbines w ~re
supplied by Mis Lenjngrad Metal Works, SSR. Braef
particulars of the turbine are:
(i) Rated output of the turbine
(ii) Rated head of the turbine
-
127.00 MW
-
121.92 m
(iii) Maximum head of the turbine -
158 M
(iv) Minimum head of the turbine
-
79.86 m
-
187.5 r.p.m.
-
91.8 perce nt
(v) Speed of rotation
(vi) Maximum efficiency at rated
conditions
(vii) Diameter of the turbine runner
(viii) Geometry of trailing edges
- 4. 1 m
-
Square
(ix) Original trailing edge thickne s
- 8 mm
(x) Modified thicknes of tr iling
- ) 2 mm
1.2 Five units of 120 MW e ch are in tolled on the
Bhakra RighI Bank Power Plant (numb red from 6 to
10). The runners of unit N . 6 and 7 are made of cast
steel (C= O.20 percent, M,J - 1.1 percent, I 0.80 percent) with stai nless steel overlay on areas prone to cavita.
tion . The runn ers o f unit No . 8, 9 and 10 are, however,
made of stainless steel (C "", 0. 12 percent, Cr - 12.5 percent, Ni= 1.3 percent, u - 0.50 precent).
ven the
fi rst inspection of the runners after their com mi iODing
revealed erious throu!!h cracks on the trailing edge f
the blades alongwith numerou surface cracks. Two
photographs of the cracks ob&erved o n the runner
blades are hown in Figures I & 2.
1.3 Init ially the manufacturer
attributed the e
damages to the operation of the unit beyond the
normal peralional constraints. However. this view
could not be ub tantiated on checking the operational
data. Further investigation at their research unil leO
the manufacturer to conclude that the cracking of the
runner blade c uld be on account of their structural
failure and they thus recommended trengthening of
the runner blade of aU the five units .
(0) Blade of unit NOI. 6 and 7 were to be streng-
thened by replacemcn t of the 8 mm thi k ca t
teel trailtng edge by 12 mm thick staiole s steel
edges
r07
108
MALIK A 0 CHAWLA
FIGURE 1:
Photograph sho\\lng through crack on the blade 12 of unit
0.6 .
trailing edges . The strengthening was to be done
on the last 200 mm width of the blade as shown
in Figure 3. The supplier also offered to upply
the stainless plates duly bent to the contour of
the trailing edges.
8, 9 and 10 were less severe as compared to the
damages to the runners of unit Nos. 6 and 7. An
extract(l) of the damages observed on various turbine
runner blades on various dates of inspection of the units
are given in Table I.
(b) Blades of unit Nos. 8,9 and 10 were t be
strengthened by depositing on vacuum side of
trailing edges 4 mm thick stainle s steel weldmetal. The strengthening \Va to be done 00
the la t 150-200 mm width of blade a howo
in Figure 4.
1.5 As the thickening and strengthening of tbe
trailing edges failed to improve the operational
behaviour of the turbines, the matter was referred to
Prof. Govinda Rao (formerly Adviser (lrrig.), CBIP
and Dr. G.T. Wadekar (C.R.O., CWPRS, Poona), They
were of the view that this cracking of runner blades
could be due to resonant vibrations on account of the
hedding of Von·Karman Vortex trail behind the
trailing edges and the natural frequency of thl.: runner
blade. One of their recommendation was to round
the trailing edges on the pre sure side of the runner
blade,
1.4 Re-inspectioll of the runner after carrying out the
above strengthening did not reveal any tangible improvement in the operational behavi ur of the turbine.
Through cracks were still ob erved. However, it was
noticed that tho damages to the runner of unit Nos.
CRACKI G OF HYDRO-TURDI
FIGURE 2:
RU
10
R 8lAD
Photograph showing 15.2 em (6 In .) tbrour:b crack in thl.' middl
or Ih(' bhld
9
or unit
0. 7.
(i) Pressure impulse effect of the parlial tream.
}.6 The Bharkra Management Board, accordingly
decided to round the trailing edge of one of the unit
on experimental basi and further desired to continue
with the investigations to ascertain the causes leading to
tbe cracking of runner blades.
(iii) Periodicity of the hear flow due to cavitation.
2. Po ible Cau e
(iv)
2.1 Since the strengthening of the trailing edges did
not belp in eliminating the damage to the runner blade ,
occurrence of cracks on account of weak tructura)
design could therefore, be ruled oul. The e crack
could thus !>e' caused on account of excessive vibrations
of the runner blades.
2.2 Though a number of ources can be held ~esponsib)e
for the presence of vibration~, yet .t~e followmg fact?r
contribute greatly toward mstabdlty of flow(t) which
ultimately lead to excessive vibrations with consequent
damage to the runner blades.
(iI) Lack of torsional rigidity of the blade.
2.2.1
Formation of Karman V rtex trail behind the
trailing edge of the runner blade.
Pres ure Impulse Effect of the PartIal Streams
2.2.1.1 Pressure impul
are exerted on each turbine
blade by the action of each of p rtial .treams which
are formed by the space between the wicket gate. Prior
to passing the leading edge of the turbine, runner, th e
partial streams are conducted into the moving ring of
water downstream from the wicket gate and lend to
rejoin within this region . As the annular water ring
between the wicket gate and the leading edges of the
runner blades ill cue of Bhakra Runners i qujte
110
MALIK AND CHAWLA
TABLE J
Extract of Damage.
S!.
No.
Date of
inspection
No. of hours
rUD since last
inspection
No. of througb
cracks on trailing edges
Length of
cracks
rom
Remarks
Unit No.6
1.
6.4.67
2.
3.
4.
5.
6.
7.
13.6.68
4.1.69
7.6.69
10.9.71
2.3.72
20.7.72
4433
5154
2030
1335
8953
2067
1882
21
30
32
30
8
75-375
110-800
50-475
60-490
30-105
80
Before thickening
-do-do-doAfter thickening
After rounding
-do-
NIL
Unit No.7
l.
2.
3.
4.
5.
6.
7.
12.9.67
21.2.68
4.7.68
24.1.69
28.2.70
29.11.72
10.7.72
4834
761
2035
1353
5018
3473
2501
20
23
27
24
25
32
3
40-130
60-300
65-315
30-275
40-400
20-700
95-125
Before thickening
-do-do-do-doAfter thickening
-do-
Unit No.8
I.
7.2.68
5563
7
10-175
2.
3.
14.11.69
4448
9
50-400
27.11.70
5057
19.1.72
6248
150-390
225-300
After thickening
4.
2
3
2199
3719
11593
7061
1
3
2
75
40-150
125-185
120
Before thickening
1369
8101
3
4
6
Before thickening
-do-
-do-
Unit No . 9
1.
2.
3.
4.
8.3.68
5.2.69
3.3.71
18.8.72
-do-doAfter thickening
njt No. 10
1.
2.
3.
7.4.69
15.12.70
27.3.72
5153
10-30
130-250
160-250
Before thickening
-doAfter thickening
CRACKJNG OF H) ORO-TURBINE RVl\
StAO
111
SectIon ot A-A
S ectIon ot
B·8
Weld'n9 of runne r b'<\de for moklnt~
'rodln; edge thicker 01 crown
rnIk
~:;v
? u/2222222222222???U
?ie
~---------------150mm
Wel(j,ng of runner blade for ma k ing
1"0.1'''9 edQe thick.,. ot shrOud r ing
~ [ ,(______________________
;u m4
200mm ____________________
>722222222 22222 22 ZZ ( 22
?? ?
iii
II
~
FIGURE 4
I
Modification
sufficient to break the pressure impulse effect of the
partial treams, tbe possibility of any vibration in tbe
runDer on this aCCouDt could easily be ruled out.
2.2.2
lAck of TorsiolUll Rigidity of the Blades
2.2.2.1 For a given position of the runner blade with
respect to the velocity of ftow, a hydro.dynamic force
and a twisting moment are exerted on the face of the
~
or runner No . 8. 9 '" JO.
blade. If the torsional rigidity of tbe blade is Jow, the
blade will twi t appreciably and the twi ting moment
and hydro-dynamic force acting OD the face of the blade
will change, increasing with one direction of motion
and decreasing for the other direction of motion of
the blade, tbus setting the blade into vibration. The
supply of energy is continued from the flow of water
to sustain the vibration of each blade. Thi pos ibility
can also be ruled out since nO crack. appeared at the
junction of tbe blade with the CrOWD where concentra
112
MALIK AND CHAWLA
130
120
110
OIH"92391
1Ql H -105561
MWIH=139861
100
- - - j OIH:79.901
I
...
I
G>
.....
'"
....
E,
160
'"
t
90
/
"0
;:
e
/
.,0>
E
G>
0>
l-
e
80
MWIH=105'0611
.... _,..
.&.
..,
v
0
- '- -I --- ..-
70
I
/
/,,/"
".".",. -
601--- -
120 :;
a.
-
:;;t
_.
0
100
MW,I H=92·341
.,c
.0
....
:;;t
80
f-
MWIH= 79'9_(m _
60
50
40
30
Y;,/i:,/ ~/./
~
I/,~~".~".".
"'l -",/
.,., . . .
.. ~
~
,. -". , ~ ~__:..-:__----,_--~-- __;.----I----'-----I2 0
_.~
20L----3-0k----4~0----~50-----6~0-----7~0----8 ~0----~9~
0----,~00o
Gate openIng - per cen t
Dlschorge m3 / sec __ _________ _ _ __
Turbine outlet megawQtts _ _ ___ ____ _
FIGURJ.1: 5
I
Output discharge CU"~S for turbines, power plant II (Ref. Drg. No. BRB-2-JQ.6).
tion of stress is the max.imum . In spite of tbis fact the
fillet radii at such junctions have been strengthened.
2.2.3 Periodicity of the Shear FlolV due to Cavitalion
2.2.3.1 Whenever the pressure in the reaction zone
drops. owing to the high velocity flow, below evaporation pressure, free bubbles of vapour are formed .
Sometimes it happen that the streams of water cut
short their path, thereby giving ri e to eddies and
vortices which may contain these bubbles. These
bubbles mainly formed on account of low pressure,
are carried by the stream to high pressure zones where
the vapours condense and the bubbles collapse suddenJy.
The collapsing pressure being as high as hundred
atmospheres. This sudden collapsing produces vibrations in the liquid which may be transmitted to
the runner vanes and runner envelope. In certain
circumstances. the blade
of the runner are
excited in this way at the natural frequency and
emit a singing ound. The collapsing bubbles
moreover set up forces which tend to destroy the blade
urface resulting in formation of cavities. Thus it can
be concluded that the periodicity of the shear flow and
magnification of pre sure fluctuations due to cavitation
creates n potentially dangerous forCing function which
cau es hydro-electric vibrations.
CRACKI G Ot! HYDRG-TURBI 'f RUN ER BLAD
2.2.3.2 Although cavitation wa noti ed on the runner
blades but the extent of damage to the blade on thi
account was nominal. This migbt ha e helped in
aggravating the situation to some extent but il could
not be considered as the sole cau e of cracking of the
runner blades.
2.2.4
Formation of Karman V(lrtex Trail behind the
Trailing edges of 'he Runner Blades
113
3.1.2 The armaD orte '
citation requen ' h
been cal uluted f r II operating rellim of the unit for
arious head .
e h 1S b en m d f the utput di charge cune, (Figure ) pertaining I the turbine at
Bhakra Right B nk Power Plant rg. o.BRB-2-10 6.
The re ult f I ulati n (If Karman
Frequency are ummnri.ed in Table
alculati n i added in Appendl 1.
3.2 No/ural F,.('qut!ncy
2.2.4. 1 The most evident cau e of runner vibration
appears to be associated with the shock type pre ure
changes at the trailing edges of the runner vanes due
to presence of vortices which are continuously shed
and arrange them elves in the Von-Karman V rtex
street downstream. These vortices provide periodic
transverse forces on the runner blades and cau e them
to vibrate across the streamlines. When this vibrating
tendency is close to natural frequency of the blades,
resonance occurs causing magnification of oscillation .
Frequency of such a Karman periodic force is governed
by Strouhal number, velocity of water at discharge edge
and the effective vane thickness.
3.
Theoretical Analy i
3.0 The frequency of shedding of Von-Karman Vortex
trail and the natural frequency of the runner blades
have been calculated to check for any possibility of
occurrence of resonance between the two.
3.1
Diffi ulty WIl e perien cd in mell uring/ Iliculaling the natural frequency of the runner blade on
aCC(lunt of lock of fo ilitie /equipment av il ble t
Bhakra. The mailer was di o. cd with hri V. V.
N
• pert on Hydr uli
Barlit. a Ru sian
Machine
(working with Muulana Azud
olleae
of Technology, Bhopal). 10 identully he ~ IU I 0
connected wilh the de ign of Bhakra Runners. He
gave the information that n Model Runner which wa
having the same blade system ns thnt of the runners
for Bhnkra('). wa. te led and the natural frequencic
of the runner blade of the model were found to be
62.5 , 130, 258,452, 730 and 1060 /.
3.2.1
3.2.2 The following formula a developed by onald ·
son(6), gives the relation hip between the natural frequencies of model and prototype runner :
Karman Vorrex Excitation Frequency
3.1.1 Investigations carried out by Strouhal initially
and later on modified by Gongwar for .Iender
objects(3) show that the frequency o~ she~dlng of
Karman Vortex trail is given by the relationship :
where.
fp .... Frequency of protolype in cp .
1m = Frequency of model
in cp .
k ... Ratio of prototype diameter
meter 4100/460- 8.91.
where,
S = Dimensionless
number.
modified
Strouhal
V=Velocity of approach.
Em = Young'
modulu
10
for bronze
model dja-
O.94S x 1()4
kg/cm~.
Ep = Y ung' modulus for cast teel - 2.1 x 10'
kg/cm'.
I=Thicknes of the trailing edges.
dp - Density of prototype- 7. S (stainle
e= Virtual boundry layer Ihick~e s o~ the
liquid on one side of the rotating object.
b= Wake thickness of the trailing edge.
f = Frequcncy of shedding of the vortex
trail .
8
teel)
dm - Density of model = 8.84 (Bronze).
3.2.3 Accordingly the natural frequencies of the proto.
type Bhakra runner blade were calculated and come
to 11.1, 23.1. 45.8, 80.2, J30.0 and t 88 cycle per
condo
MALIK AND CHAWLA
114
~ 120
u
1
>.
u
C
•
.
......
~
a
~60
c
~
~
:.:
~~~~~~
~ L2v'~~~rr""
,"",~""'=tl'.h"'
~~~*:"""'+-+-+-+-+--jl
'I ~I"
30 H--;¥V:,,_'-+-
•'-fp= 4,5,8 ~S
Note :
Curve I to 6 cre for 8 mm thick
trooling edges ot different heodl.
-+- + -+ - + - - - r - - r - - r - i 2 Curve 7 to' I2 ore for 12 m m thick
troollng edQes ot different heods .
Lood in M W
FIGUR ' 6: Loud
3.3
VS ,
CO/llparison
3.3.1 Karman Vortex Excitation Frequencies as calculated above for the original blade of 8 mm thick
square edge as well as the modified 12 mm thick square
edge are shown in Figure 6 agai.nst the load (~W) . as
abscissa. It is ob erved that prior to the modIficatIOn
f the trailing edges from a thickness of 8 mm to 12
mm re onance of the blade were occurring with the
nat~ral frequency of 130 c/ when the discharge was
about 66 m 3 /sec and 80 ma/sec for the maximum ,head
158.82 m and a minimum head of 79.9 m re pectlvely.
The second resonance at 80.2 c/ at low loads can be
discarded becau e the unit s were not operated below
60MW.
3.3.2 With the thickening of the trailing edges to
12 mm the Karman Vortex Excitation Frequencies for
the ru;mer blades came down appreciably to avoid
resonance at the previous natural frequency of 130 cIs
but this modification brought the operating range well
within the next natural frequency of 80.2 cIs a is clear
from Figure 5., The resonance between the Karman
Vortex Excitation Frequency
and the natural
frequency of the runner blade occurred when the di charge was about S6.0 m 3 / ec and 6~.~ rn 3 /sec for a
maximum head of 158.82 m and a mlnlmUm head of
79.9 m re pe tively. The critical di charge for other
heads varied between the above two limit.
Karman Vortex Frequency ,
3.3.3 It may thus be ob erved that the thickening of
the trailing edges, instead of avoiding the resonant
vibrations has only helped to alter the frequency of
resonance ' from 130 cIs to 80.2 cIs. It also shifted
slightly the load range for resonant vibrations .
4.
Field Ob ervation and Analysi
4.1 To investigate the sources of vibrations leading
to the cracking of the runner blades even after thickening and strengthening of the blades, periodical readi~gs
of vibration amplitudes at the spider and at the turblDe
shaft of various units at different heads and loads were
taken. Simultaneously pressure pul ation readings on
the pressure gauges for draft tube, scrol!case. and lab~­
rinth cover were also recorded. The vlbratJon amplitudes observed for various di charges (loads) at diffe·
rent heads for unit No. 7 are shown in Figure 7. Here
it will be observed tbat the vibration amplitude for
different heads is the maximum when the discharge is
between 60 to 72 m 3 /sec. This coincides very closely
with the theoretical analysis that when the discbarge
is 56 to 69 m 3 / ec, there is a probability of resonance
occurring between the frequency of shedding of VonKarman Vortex trail and the natural frequency of the
runner blades.
5.
Remedies
5.1 The incidence of cracking of (UDner blade in case
CRACKING OF
HYD~O'TU RBI
TABLE
11 S
F R N IlR SlAD
n
Result of calculation for Karman
orle Fftqu ney.
--- K rill n Vort e
Gate opening
percent
Head 79.90
In
Output
requen
Discharge
ma, ec
fficienc)
5.834
18.729
33.101
44.746
55.228
64.580
70.475
24.900
40.500
57.000
72.000
85.500
96.540
106.050
0.300
0.590
0 .740
0 .792
0.823
0.848
0.857
39.7
70.0
963
118.5
138 .5
J 55.0
169.0
12. 127.
27.969
26.892
44.388
0.500
0.693
52.0
81.5
45.377
59 .8 47
74.466
85.862
91.650
62.532
78.232
93.960
106.272
115 .506
0.864
0.842
0.878
0.895
0.879
109.0
126.5
155 .0
173.5
187.0
16.18l>
37.38l>
58.262
76.657
94.564
107.641
29.060
47.470
67.940
84.968
101.136
114.380
0.540
0 .764
0.832
0.875
0.907
0.912
58.5
94.0
121.0
145.5
170.5
J 88 .0
102.0
119.S
131 .0
31 .450
92.500
110.075
0. 578
0.778
0.8 48
0.895
0.916
68 .7
105.0
136.0
162.0
187.0
48.2
73.6
95.2
113.S
131.0
33.830
56.715
81.192
0.586
0.767
0.855
74.5
111.2
148.5
52.2
7 .0
103.7
101 .092
0.902
177.5
124.5
36.631
61. 84 5
87.261
0.640
0.761
0.843
85.7
121.0
107.5
60.0
84.5
117.0
t; mm edge
12
mm cd c
(262/t)
20.20
33.67
47 . 14
60.61
74.07
87.54
100.00
Head, 92.341/1 (3/5/t)
20.20
33.67
47.14
60.61
74.07
87.54
100.00
~ .0
49 ..
67.6
3.0
97.~
109.0
IIS.5
36.8
57.2
76.3
8.5
108.S
121 .5
131.5
Head 105.06 m (342/t)
20.20
33.67
47 . 14
60.61
74.07
87.54
41.2
66.0
4 .~
Head J20.69 m (396 / t)
21.432
48.540
74.579
97.637
118 .9 13
20.20
33.67
47.14
60.61
74.07
Head 130.86
20.20
33.67
47.14
60.61
In
52·910
74.510
(458/t )
2.t.857
59.583
94.978
124.893
Head 158.82 m (520/t)
20.20
33.67
47.14
36. 514
73.315
115.264
116
MAliK AND CHAWLA
'7\
0 ' 07
'I
\
/
0 ·06
7
E
E
\
H=510--
41
"0
~ 0 · 05
1/
Q.
E
0
H=400
c:
-.2...
~
0·04
10'
J/ \
7.\H = ~
Iv!
/p ~~~:;
0
.0
>
L//
0·03
-'
f;J ~
>
_,,'
~
T'\
, \
.......
\.
1/
\
I...H=433 \
'I
.......
'"
~
f)- ....\
I
42'45
56·60
70·75
H =470
~
~
"
H=308-W
-.,j
28'30
~
;/~\., V
,.._H:34/ I....H=470
H=2 5
l'i
H=400
~
~H=
370
"
" "---- ~
, ~ ....
84·90
99·05
))3·20
Dischorge ",3/sec
171GURE 7:
Discharl:(' vs. vibration amplitude-unit No. 7.
of Bhakra Runnen due to ~hedding of Von-Karman
Vortices behind the trailing edges is not a new phenomenon. Such incidences are also reported in variou
power houses all over the world. M/s R.M. Donaldson
and F.e. Taylor have reported about 10 such cases of
vibration/cracking of the runner blades in U.S.A. and
that modifications of the geometry of trailing edges of
the runner blades have improved considerably the
operational behaviour of the runner in almost all the
cases. Parmakian(O) and Jacob on have also demonstrated that the detrimental re onallt vibrations in turbine can be eliminated by a modification of Ihe trailing
edge geometry. Mr. D.R. Olbert(') has also reported
that the rounding of the trailing edges at 45° completelyeliminate the incidence of vibrations. Similarly
in a separate independent study by Mr. R.M. Donald son, he has concluded that the rounding of the trailing
adges at an angle of 45° reduces the amplitude of
vibration by 80 percent as compared to that of a square
edge.
5.2 The rounding of the trailing edges was carried out
in October 197 I on unit No.6, ubsequent inspections
after modifications showed that cracking of runner
blades had disappeared virtually on unit No. 6 as
compared to a number of cracks on unit No.7. It
may thus be inferred that the appearance of cracks was
mainly due to the occurrence of resonance between the
Karman Vortex Excitation Frequency and the natural
frequency of the blades and with the rounding of the
trailing edges, the said Karman Vortex Excitation frequency ha been attenuated substantially if not eliminated completely.
5.3 It has been further reported that the rounding of
the trailing edges on suction side was adopted in case
of Canyon Ferry, Whitcey, Norris, Hiwasseo, Denison,
Osage Power House where as reprofiling to trailing
edges on pressure s\de was carried out in case of
Clayton, Grand Coulee, Parkar, Keswick Power Houses
in USA with equal success. Further Mis John Parmakian and Mis R.S. Jacob on have reported that the
modifications on pressure side of the trailing edge of
the runner blades eliminate the periodicity of the tur·
bine blade ibration but this leads to increase in power
output of the unit for all gate positions by about 6.5
percent in the max.imum output of the unit.
5.4 Calculations in case of Bhakra runners indicated
that with the rounding of the trailing edges on the
pressure aide, the area of discharge at the exit of the
runner blade would be increased by about 8 percent.
This would shift the critical load range of resonance
CRACKI G Of HYDRO-TURIll E R
117
BROLAD
Pressure "de
Suction sode
Moteriol to be removed
FIGURE 8 t
Rounding of trailing edges on
from 43-65 MW to 48-72 MW for the two e '!reme
head variations. The Bhakra turbine on the Right
Bank are not operated below 60 MW. Therefore. tbe
effect of rounding on pressure ide would thus increase
the critical operating range from 60-65 MW to 60-72
MW.
5.5 It has now been decided in consultation with the
manufacturers as well as Dr. G.T. Wadekar and other
experts on hydro-turbines to round the trailing edges
of the remaining units on the suction ide as per
Figure 8. Experiments are till continuing to ascertain
the result of rounding.
6.
Conclusion
On the basis of above investigation, it may be concluded that the cause of severe damage to the runner
blades can be attributed to the excessive vibrations due
to resonance of Karman Vortex Excitation Frequency
and th e natural frequency of the runner blades. There
is every possibility that other causes of vibrations enumerated above may also be con tributing towards this
damage to the runner blade but their effect may not be
as predominant as that of Karman Vortices. However,
continued check on the operational behaviour of the
modified runners is being carried out to confirm the
above findings.
7.
tlon Id .
References
( 1)
Bhakra Right Bank Power Plant Re ord .
(2)
HRIVASTAVA.
. K . : " low
Turbines." M .Toch . Thesis.
(3)
GONGWAR, C.A.: "A
tudy of V ne
Inain in
Water." Journal of Applied Mechanic, Vol. 19, Tr n .
A.S. M . . ,1952.
\4)
Leningrad Counc il of Nalion I onomy, Leninlmd Melal
Works, U .S.. R . Explanatory Note No. 1394 .
(5)
DONALDSON, R .M . : "Hydrauli c Turbine RunDer"
Vibrations. Tran . A .S. M . . , July 1956.
(6)
PARMAKIAN, JOHN : H ydraulic Turbine Operation
Difficultie " . Water Power, OctOber 1963.
(7)
HESK STED,
UNNER nnd OLD RTS, D .R . : "Influence of Trailina Edae eomctry on Hydraulic Turbine
Blade Vibrations re uiting from Vortex Exclt tloo".
Journai of EllIineering for Power, April 1960.
(8)
English Electric Research NOle No. 26, Issue A .
(9 )
NECHL BA. M . : "Book-Hydraulic Turbine, Their
Design and Equipment."
In t"bility In Fr neis
118
MAl.lK AND CHAWLA
APPENDIX-I
Calculations for Karntan Vortex Excitation Frequency
For Bhakra Runners, the inlet area of flow of the
blade for the mean stream line is 10.88 m2 whereas
the area of flow at the exit of the runner comes to
13.93 m2 •
From Drawing No. BRB-2-JO-66 showing the output
and di charge curves for 120 MW turbines at Bhakra
Right Bank Power Plant, the output is 44.746 MW
with a discharge of 72.00 rna/sec for a gate opening of
60.61 percent at a minimum head of 79.90 m (262 ft).
The corresponding efficiency is 79.2 percent.
Now, perjpheraJ veJocjty for mean stream jjne at
runner inlet (Figure 9) :
_
V1-
7t
VmJ at inlet
=
Discharge
Area of flow
-
72.0
10.88
At the first instant, it i assumed that Vu, = O. then
H.'fj.= -
or
VUl
Where, 'D' is the mean diameter at the inlet edge and
)
(VU1.Ul)
9.81 x 79.9 x O.792
37.2
= 16.7
n is the speed of rotation of the runner :
3.14 x 3.795 X 187.5
60
/
m sec.
Euler's Energy Equation is
g
Dn
60
= 66
.
m/sec .
The inlet velocity triangle can now be completed
yielding
=37.2 m/sec.
100---- U I - - - - - - i
......_ _ _ VUI _ _ __
Runner
(01 Inlet velocity triongle
\
IIGURE 9:
Inle( and outlet velocity triangle ror runn r .
CRACKING OF H DRQ-TUIlBIN
RUNNER 8LAD
11
Similarly at the ex" edge of the runner
2= 29.4 m/sec and
I
I
/ I
f I
Vm!=5.16 m/sec.
Normally the exit whirl is of the order of 10 percent
of its inlet value and so for the purpose of calculating
Karman Vortex Excitation Frequency, its value is
assumed as such, i.e.,
VU 2 .U2==0.10 (VUl.Ul)
O.IO x 16.7 x 37.2
or
..1--+I
_- /
/ I
I
./
/
I
/
/
I
I\
/
\\
I \
\)
/
29.4
/'
/'
./\
\
\
\
\
= 2. 11 m/sec.
The outlet velocity triangle can now be drawn, and the
value of Vz comes to 5.58 m/sec.
Thlls the average absolute velocity
Vi \-
\
I
/
I
I //
/
V~
2
....
18.0 + 5.58
2
11.79 m/sec .
The ehord length C of the runner blades as measured
from Figure J0 is 119 em.
Reynold number based on this chord length and
average absolute velocity of 11.i9 ml ec is
Rc=
FIGURE 10 I
Runner powcr plllnt.1I
(Rcf. DI1l. No. .20(5997).
(l1.79 x 1OO) x 119
0.01
= 14.05 X 106
As Rc is greater than lOG, the boundary layer thiek.ness
will be
0= 0.154xC '
(Re)! /?
0.J54x I 19
= (14.05 x Joe)!"
=1.745 em
Hence total virtual boundary layer thickness will be
2e = 0.643 x 3D
= 0.643 x O.2J8
= 0.1405 em
Therefore, the wake thickness will be :
b= t+ 2e
= 0.8 + 0.1405
and the displacement thickness will be
aD=O.125x3
-0.125 x }.745
... 0.281 em
= 0.9405
(for original thickness of 8 mm of exit edge and
will be 1.3405 em for the modified tbickness of 12 mm
of exit edge) .
120
MAL~
AND CHAWLA
Frequency of formation of Karman Vortices is given by
/=..§!::_
b
It has been found that the value of S varies between
0.18 and 0.205. Assuming its value(l) to be as 0.20,
the Karman Vortex Excitation Frequency for the
original thickness of 8 mm of exit edge of the runner
blade:
/0
0.20 x 5.58 x 100
0.9405
= 118.5 cIs
and for the modified thickness of 12 mm of exit
edge of the runner blade, the Karman Voltex Excitation
Frequency is
/",=
0.20 x 5.58x 100
1.3405
=8 3.0 cIs
various other results obtained on similar ground have
already been tabulated in Table n.
Micromachine Modell ing of Generators
.M.
PEERAN
UNtL
Electrical Engineering Department.
K
M R
niversit ' f Roorkee. Roorkc:e ( .P. r
YNOP I
Present day digilal simulation of power systems is based all the dynamic
equations of the machine which are derived hy making !'ariOIiS simplifying
assumptions . Detailed representation of machine hehavlour sllch as the C'ffect of
excitation s),stems, governors and tlteir /lolI.linearilies, magnetic SflfurotiOIl ill tltl'
machine, magnetic losses, etc., is usually avoided ill mas/ of the tabllity studies
for tlte sake of simplicity of the computer programmes. Howl.'l'er, for tlte design
and testing of the excitatioll systems governor and otllt'r generator con/rol
mechanism. '1 more detailed simulation of 'he l{enerator Is desired. It is /11 this
field that the scale modellillg of generator alld 'heir cOlltro/s hy microma('hille,~
proves eXlremel)' useJul.
This paper primarily deals lI'ilh differ""t modelling criteria alld survey oj
model swdies conducted ill I'arious pOll'er laboratories in 'he world and describes
briefly the proposed model of a 100 MW water· wheel generator belllg .fet lip at
Uni,'ers;I), oj Roorkee. The work reporled in tlris paper is (I parI 0/ the r('uarclt
work undertaken under the ,~pOtl orship of Ihe Central Dnard of [rriKalio" olld
Power .
1.
Introduction
1.1 Digital computerli are now widely u ed for
investigating transient and steady s late phenom na
in electrical power systems. The repre entation of the
alternator in such studie i ba ed on Park ' equations.
These equations involve severa l simplifying a sumption .
There are, however, still attractions in u ing analogue
models which can give virtually perfect simulation in
both tran ient and steady stale conditions.
1.2 Till some time back the conventional technique
for simulating multimachine power system(1) has been
to establish a direct analogue of the transmission net·
work and the load in which the inductance, re i tance
and capaci tance of the sy tem are repee 'eoted by
inductance, resi tance and capacitance in the analogue.
To the analogue is coupled an equi alent circuit for a
synchronou machine which U',ually con 'ist of alternating voltage, variable in magnitude and phase in
series with re istance nnd inductance, Thi'! c mbination
j usually referred to as an a.c. network nna lyser. The
principal di 'advantage of thi approach ha been the
inadequate representation of the sy nchronous machine
which increase th e difficulty in carrying out tran ient
lability tudie.
1.3 To improve the ynchronou machine repre entation the mo I promisi ng technique i the u e f analogue
computer. However, the difficultie of coupling these
analogue to a conventional a.c. network analy er i
formidable.
un Ie
a con'!iderable number
of
approximation
are made. The iden of an logue
computer is to replace each component of a power
sy tem by an
equivalent
electronic analogue
interconnection. By piecing together the individual
interconnections the complete . ystem i imulalcd.
121
122
PEERAN AND SUNlL KUMAR
1.4 Though analogue computer has distinct advantages
over tile conventional a.c. network analyser, the principal difficulty with it is that it is unlike most dynamic
systems. Power systems require to be thought about
in a reference form ; this distorts the equation into a
form that is sometimes difficult to relate the physical
representation of the system. For this reason instead
of a mathematical model of a power system an actual
dynamic model of the system is preferred in carrying
out stability studies.
1.5 The designe) of a model machine or a micromachine can be broad ly classified in three ~dilTerent
ways. The first is based on design of a model machine
of excessively large dimensions. In this the per unit
values of rotor and stator resistances can be made
equal to those of large machine but the inertia constant
cannot be controlled and value is very high. The
second method is direct use of sma ll mass produced
synchronous machines complete with these existing
rotor and stator stampings. Here al so though the per
unit leakage reactances can be co ntrolled but not the
time co nstants except by using auxiliary devices. The
last method is the complete design of a model machine
with the object of achieving constant by constant
simulation of all important parameters. Thi s method
leads to an over-dimen ioned machine.
existing stator and rotor stampings. The per unit
~eakage reactances c~ n
be. ~odified by ~dding
Inductances to the vanous wlOdlOgs, here agam it is
not possible to obtain the required time constant without the use of auxiliary devices. It is possible to Use
these devices in rotor circuits but not in stator
circuits.
3.3 The third method is the complete design of a
model machine with the object of achieving constant
by .constant simulation of all the important parameters.
ThIS method lead s to an over-dimensioned machine.
4.
4.0 According to the equations by Concordia (which
express the dynamic process in a sy nchronous machine)
to achieve an equality in dynamic response, the fundamental per unit electromagnetic and mechanical machine
constants must be identical in both the machines (the
model as well as the full scale). The important parameters which must be simulated are :
4· 1 Electrical alld Magnetic Quantities
(a) a term by term equality of machine per unit
synchronous transient and sub-transient constants on both the axes;
1.6 Various power system models have been developed
in different countries. These equipments contain many
component to represent various parts of power system.
The most ditlicult part to simulate are the alternators.
The model alternators (often called micromachines)
must have per unit parameters equal to those of a full
scale machine. For this a number of similarity criteria
must be satisfied.
2.
3.
(b) equality of the per unit magnetisation characteristics on both the axes;
(c) equality of the leakage reactance and saturation
characteristics on bOlh the axes;
(d) similarity in per unit core losses.
Modelling Criteria
2.1 A number of imilarity criteria mllst be satisfied
to obtain an acceptable scale model of the full -size
machine. Various scale factors have been outlined in th e
literature to give a fundamental insight into the problem.
These cale factors are then modified to comply with
manufacturing and other constraints which are imposed
on the model system.
De ign Methods
3.1 There are three main methods which ha e been
pursued in designing a model. The first ba e the
design on a machine f exce sive!y large dimensions
although tbe stator and rotor per unit resistances can
be designed to have their correct values, the drawback
in this method is that the rotor dimen ions are such that
the inertia constant of tJle machine i many times the
desired value.
Similarity Criteria
M echanical Quantities
42
(a) equality of the machine's inertia constant;
(b) similarity in per uuil
4.3
Scale Factors(3)
4.3. 1 The simiJarity criteria in model building may be
expressed in various sets of derived units. The basic
approach i by using units of magnetic permeability
electrical conductivity a, electrical permittivity E,
density "A, characteristic length I and time t, as these
are directly as ociated with the properties of the
materials employed.
4.4
3.2 The second method is direct u e of mall mass
produced synchronous machine complete with their
windage and friction
losses.
4.4.1
Power Scale Factor ( K_ )
When an alternator with an output of 100 MW
ueRO ~ACHI E tOO LLI 0
or more i to be modelled. then power cale fa tor
bould be so cho en that the required output of the
model i relatively small (5 kW or Ie ). Taking int
account all the fundamental unit mentioned ab ve the
expression of power scale factor i given by
ERA T
4. .3 Thus to find an c ept
step are cho en :-
Mass Density Factor
ondu t rs with nn eire tive r j t 1\ j ty InU ·It
lower than Ihal of pper at normal temp ruture
mu t be emp1 y d.
4.6
(il') Material
Time Scale Fac/or Kt )
Wilh low
m(l!-:-
den Ilies
h uld
e
u cd .
4.6.1 Time scale factor, in excc of unity, i needed
to give low power scale factor bUlthis leads 10 transienl
time constant in the model exceeding Iho e in the
original machine. A time scale ractor of unity i
elected .
4.9
Efec/rQIIIQI:IIC'tic Scale Factors (Table /)
TABLE 1
Dimensioll Scale Fac/or
-- -
4.7. 1 As the densi ty and time cale factors are cho en
to be unity. The power scale factor i dependent only
on the physical size of the model. Thus to achieve
a power scale factor of 0.25 X 10- 1 to enable a 200 MW
machine to be represented by a 5 kW model, the
dimensions of the model would have
10
be - 8.;25
time those in Ihe original
8.325
Such a cale factor may only be u ed if the conducti vity
and permeability cale factor have the appropriate
values.
COlldUCliJlily and Permeability
ling mu I
melri
ri uit with mu It greater P fine biljtie than th . e pre cnt in the ma hin mu t e
incorporated.
(iii)
4.8
110 ing
(ii) Magneti
4.5.1 From Equation (I) for small power cale factor .
the mass density scale factor hould be low. Generally.
it is chosen a unity.
4.7
~
Ie oluti n the
(i) Deparlur' from perf
be n pte I.
.. (I)
4.5
F G
Scale FaClors Ka , Kr).
The value eho en for Ka, K!). in the model mu~t
apply to all materials in use to en ure that 11m. and
current palhs are correct. The conductivity of iron in
the model hould be increa ed to the appropriate
value. . This occur when the temperature is reduced.
Copper i a suitable winding material for model
alternator, since at -200°C, it has higher conductivity
than at 20 C and is about 8.5. 0 a conductivity eale
factor of 8.5 is obtained.
Quantity
erivntion
KI
Length'
comctric . imiInrily
I l K,
f 1/t
Resj~tnnec R
I/ K/KtJ
R
aA
Reactllnce X
I IK,Krr
..\
R
Inductance L
Power P
Kt/K,Ka
X IVL
K'AK, I K, :'
KJ...K16IK,~
Voltage V
KAI Il.Kl ~/KaI I! K, a I~
P_vz/ R
Frequen y
urrent I
4.8 .1
4.8.2 Permeability s ale factor should be higher in a
model machine. Since the magnetic materials with
higher permeability than in original machine are used
in the model, therefore, permeability of spaces
corresponding to air gaps should be inc.reased This i
achieved by decreasing the air gap length in the inver c
proportion of the permeability cale factor. This
re uJt in departure from geometric imilarity.
. cale fetor
II'
K'A( UK1GKa( "/ Kl nl~ p
I
[ 1R
J(.8)
c.m. f dl
--nIJ- NJ/l
Torque T
T- P/angular
peed
(N- No. of turn ).
4.10 T aviod problems a ociated with negative
r i lance device, a po sibilily exisls of operating the
machine at a temperature ufficiently below the normal
ambient level. This results in ignificant reduction in
124
Pfl!RAN AND SUNIL kUMAR
Fouit It\ston'
/
.. I, clor
FIGURE 1: Schematic diagram of proposed experimental set-up for each machine.
the resistivity of the winding material. A model
machine cooled with liquid nitrogen was developed at
Imperial College, London. To obtain the same ratios
of the resistivities of all the conducting materials in
tl e model to the corresponding ones in full-size
machine; all the model machine windings are cooled
to the same temperature. For small machines this is
achieved by immersing it in a vessel containing
liquefied gas .
4.1 I Micromachines have been constructed for
different models. On e of the test machines was modeUed
at Imperial College(2), London. The following is the
table (Table II). which gives the comparative per unit
values of the different parameters.
s.
Proposed Model of the Power System at University
of Roorkee, Roorkee
5.1 Two motor generator sets simulating the a.c.
generator and prime movers are instaIJed as model
machines. The various electrical, magnetic and
mechanical parameter of the sets will be sca led in order
to Jet them represent machines of larger output. The
various constants of one of the sets have been experimentally determined and computed.
5.2 Figure 1 gives the proposed scheme of the model
to be set up at Univer ity of Roorkee.
5.3
Power Angle (8) Meter(,)(8)
5.3.1 The power angle is measured between the
generator and the tacho ignal. Both the signals are
sinu oida!.
5.3.2 Both the inputs are fed to two similar circllit .
The high input impedance is due to the field effect
of transistor. The signal are then fed to zero cro sing
circuits. Jo one of the circuit, sigoal is fir t inverted
and then fed to the zero crossing circuit. The output
of the zero crossing circuit squares at zero of the ine
TABL, II
Micro
machine
Large
machine
Rated Power
3kW
333 MW
Rated apparent power
3 kVA
333 MVA
d axis magnetising reactance Xma 1.332
1.00
q axis magnetising reactance X lIlq 0.846
0.55
Stator leakage reactance Xu
0.113
0.) ]
Field leakage reactance X,
0.240
0.15
0.098
0.18
0.052
0.09
Stator resi tance Yo
0.0050
0.0015
Field resistance y,
0.000952
0.000233
d axis damper resi tance YKd
0.034
0.054
q axis damper resistance YKq
0.0182
0.020
Inertia Constant H kWs/kVA
4.27
4.5
d axis damper leakage reactance
X](d
q axis damper leakage reactance
X Kq
Stray Losses
00
fuU load
0.019
0
Stray losses saturation factor K.
0.6
1.0
fnitial o.c. generated voltage on
no load
1.000
1.000
fnitial open circuit generated
1.872
voltage on full load
1.000
0.220
0.220
Resistance to infinite bus bar R 0.022
0.005
Reactance to infinite bus bar X
MICROMACHIN~
from
9."e r o 1o r
'"'"
High I "put
i mpedonc.
M OELU G 0
GBNERA TOR
Zero
crossing
CIrCU li
SIOCk dlogrom of power o"gl. "'eler
Input No 2
InpulNol
Output
~(ze,.o
croUlng No ·2
I-- -70utput of the
Iw O dIffer n-
I'otor
OlllplJl of Ihe
Iwo bi"obte
c i rcuill
FIGURE 1.
.126
PEERAN AND SUNIL KUMAR
Three phose"""
IIO{3
Single phose......,
AmplIfIer
BlOCk diagram af autamatic speed control
Three
phose
l...--"">
Armature bridge
convertor
FIGURE 3.
wave. Both the signals ar then differentiated and fed to
a measuring circuit. It is a bistable circuit whose
average output is proportional to the phase difference
of the two input. Figure 2 will explain the working
more clearl . In ca e of zero pha e difference the output
of bi table (which is a square wave) will be zero.
That means both positive and negative square will be
equal. Hence the average output will be zero.
5.4 The other equipment of the power system which
are being simulated are the transmis ion line and the
fault instant selector. The three-pha e transmis ion
line has been divided into eight sections of equal length.
Each section is being repre ellted by equivalent 'rr circuit.
The fault instant elector i being developed. The
elector witt be able to control the duration of fault
and time of isolation of the line. The entire circuitory
is tran i torised.
5.5
For the excitation ystems and the speed control
systems su pplies usin& thyri tor bridge have been
developed. Work on further improvement is being
done, on the same. Figure 3 give the basic circuit
which i being employed for the automatic control of
the d.c. motor.
5.6 For the automatic speed control of the d.c. motor
a closed loop .) tern is formed. A tachogenerator is
coupled to the armature shaft which provides the true
velocity signal. Thi is chosen for it good linearity of
utput voltage to spe d characteristics. The tacho
output is rectified with the help of an ordinary rectifier
bridge and . filtered. The filtered output is then fed
to an error bridge. The output of the error bridge is
the voltage variation linearly proportional to the speed
variation of the d .c. m tor. Thi error is uperimposed
after ampUfication on the 6 a.c. pbase hifted voltage
from a tran former and R.C. pba e hifter and applied
to the trigger circuit to hift the firing angle of the
pulse from the isolating tran former secondary till the
error signal is zero.
MICRO 'ACHI
6.
1 7
fODBLU 0 OF 0 N RA TOR
(7) Mlll,fA • J. and T \JB. H. : "Put e,
wit hin W. form ," M row Hili B
Acknowledgement
The authors wish to expre s their gratitude to Dr. T.S.M .
R ao, Professor and Head of Electrical Engineering
Department for his keen inlere t in the w rk and
valuable sugge lions from time to time.
lallal and
., I
(8) MIT HELL. B,B.: .. emi ndu t r Pul r
Exp riment:' Bool... ~ Ilk 1. ., I 9.
i ' uit
'ilh
7. Reference aod Bibliography
( I) ALDRED, A.S. : "Electroni Analogue ompuler imulalion of Multima hine Power System Net work ," Proc. 1.
Vol. 109, Pl. A. June 1962, p. 195.
A.J . " Design of Mi roAlternator for Power Syslem Stability Investigations." ProC.
I.E.E. , Vol. 118, 0 . 10.0 tober 1971 , p. 1421.
(2) HAMMONS, T.1. and PARSON ,
(3) JEPFERIES, M.J , and WRIGHT, A . ; "New Approach
to Micromachine Con truction ," Proc. I.E, ., Vol. 117, No .
7, July 1970, p, 1309.
(10)
BNIKO and I AN V : "0 velopm lit
lektrich tr
Models for leetri ,I )'51 <.'n1l,"
pp. I 10.
( 11 ) KOTTENKO, M .P.: "EI
tability."
tt U 'naml M del
Elektrich. tro 1951 (9, pp. ~.(I
r
fot
Ph leal
1
(8)
tudylna
( 12) ROBERT, M.R . : "The Mi ronet"ork Oyn mi Model of
Power Transmission Networl..."
1954,38, pp. 67-87.
Uull.,
oc . Frtln c I
I,
(J3) RAMK1N, A.W.: "Per Unit Impedance. of 'ynchronou
Machines," Trans. A.I. . . , 64, 1945, pp. '6 73.
(4) HAMMONS, T.J . a nd WINNING , D.J ,: "Compari on of
Synchronous Machine Model in the Study of Transierlt
Behaviour of Electrical Power System." Proc. I.E,E., Vol.
118 , No, 10, October 1971, p, 1442,
(14) DALTON,
K .F. nd
AMBRON, A.W.: "Implified
Measurement of Sub-tronsient and Neaatlve equcn
Reactances in Sollent Pole ynchronous Machine ." Trani ,
A. I.E. ., 71, 1952, pp 752- S7 .
(5) ADKINS, B . & WIDGER. G,F,T . : " Micromachine Studies
at Imperial College." Electrical Times, 6 August 1971,
p , 29.
( 15 ) ADKINS, n .:
(6) ADKINS, B,R, and
( 16) CORLES ,K.G . aod ALORBO, A.S.: "An
WIDGER, G.F,T,: "Investigating
Generator Stability with Micromachines ," Electrical TimeS,
20 August 1971, p. 39.
"Geoeral Theory of ~ Iectri co l Machine ."
nook, Chapman nd Holl, 1957.
Electronic Power System
1958. pp. 503- 11.
It. A. . I!IANGALORE
UNIVERSITY UBRARY.
j
IBM
J't
~49~S
•........... ", .....
ACC NO......
CL. "'0 .. _ .-............................ ..
perimcnlll
imulator." Proc. 1. . ., lOS A.
REFERENCE
17 JUN 1974
UAS LIBRARY GKVK
111111111 IIIU'lllll 1111
54928
1/--pages
Пожаловаться на содержимое документа