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

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