THE EFFECT OF THE CAP ACITANCES ON THE WAVE PHENOMENA IN POWER TRANSMISSION SUBSTATIONS

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THE EFFECT OF THE CAP ACITANCES ON THE WAVE PHENOMENA IN POWER TRANSMISSION SUBSTATIONS

By

A. DERI and E. VOROS

Institute of Heavy Current Engineering, Technical University Budapest (Received June 1, 1974)

Presented by Prof. Dr. O. P. GESZTI

I. Introduction

The importance of the analysis of the overvoltages due to lightning surges is increasing with the increase of the voltage level of the transmission systems.

These overvoltages cause damages in the apparatuses and thereby they are injurious to the reliability of the network. With the knowledge of the arising overvoltages a proper overvoltage protection can be chosen. The increase of the voltage levels results in an increase of the dimensions of the power transmission substations, therefore from the aspect of the occurring residual voltages, the wave reflections within the substations must not be neglected.

The transient phenomenon going on as superposition of elementary waves can be influenced by the capacitances of the apparatuses in the substations.

The determination of the overvoltages taking into consideration the bus bar branches and the capacitances of the apparatuses needs the application of a computer for the calculations.

In this study, transient phenomena will be analysed by means of digital computer method. The effect of the capacitance of the apparatuses on the shape and magnitude of the overvoltages in substations ,,,ill he shown, numerical results will be given for the case of a 400 k V suhstation. Thc results show that from the point of view of the surge protection it is desirahle to carry out exact calculations for every individual case in consideration of the substation topology and the capacitance of the apparati.

The results are obtained by using a digital computer program based on Bergeron's method. The program was written in ALGOL computer language.

The computations were carried out in the computing Centre of the Research Institute of Electric Energy Industry (VEIKI), on a RAZDAN-3 computer, the diagrams were obtained by using an off-line plotter.

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14 .1. DERI and E. VOROS

2. The calculation method

The digital computer program used in this study for the analysis of wave reflections in suhstations, is applicahle for the calculation of transient phenomena on any looped network of N node. The network treated hy the program is supposed to he huilt up of distrihuted parameter lines ,dth lumped resistive shunt elements in the nodes. The program calculates the instantaneous values of the node voltages and the hranch currents for each time step. The algorithm permits to consider an incident wave of arhitrary time function hy using a current generator simulation.

For choosing the time step of the computation, several aspects have to he taken into account. On the one hand, the time step LIt must he small enough to follo'w the form of the incident waye with a sufficient accuracy, and the length corresponding to the time LIt has to he the larger common quotient of the length of the lines in the network studied ,vith sufficient accuracy as well. On the other hand, hy decreasing the time step LIt hoth the needed computer storage capacity and the computation time increase.

In this study the effect of the capacitance of the apparatuses was taken into consideration. The lumped capacitances were dealt ,vith as distrihuted elements transformed to short lines. The smaller the length of the equivalent line, the higher is the accuracy of this method. The length of the substituting line must be necessarily smaller than that of the adj acent lines. So it is ohvious to take the length of the suhstituting line equal to the length corresponding to the computation time step LIt. The choosing of the time step LIt is influenced hy this circumstance, too. The line suhstituting the lumped capacitance can be characterized by a characteristic impedance

z=-

LIt

_{c .}

To improve the calculation accuracy,

.at

has to be chosen for a small yalue, so this characteristic impedance will he small as well. This fact is in accordance with the theory of the transformation of lines into lumped elements [3].

According to this, a line hehaves in a transient phenomenon as a capacitance if its characteristic impedance is much lower than that of the adjacent lines (proyided that its length is shorter than that of the adjacent lines).

3. Analysis of hasic cases

As a first step of the study of the surge phenomena in suhstations, some simple cases concerning the effect of the capacitances were analysed. An incoming wave of 800 kV crest was applied and was simulated hy a double ex-

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CAPACITASCES LV POWER TRA:VS.\fISSIOS SUBSTATIONS 15

ponential time function. The surge was supposed to arrive from a line of infinite length and of 400 ohms characteristic impedance in the substation busbar of 300 m length having a characteristic impedance of 200 ohms. The overvoltages were calculated \vithout capacitances (Fig. 1), \vith a capacitance in the junction point (Fig. 2) and \vith a capacitance on the end of the busbar (Fig. 3). The capacitance considered was 4000 pF corresponding approximately to the value of a 400 kV voltage transformer capacitance. The computations were made for different front times and different values of time to 1/2 maximum

\lMAX= 1476.940

1 \ w Vl,.--,.- :i a.

i

_ TIME MIKROSEC NODE;;' 1,2

UMAX = 1 505.766

- TIME MIKROSEC NODES' 1,2

la)

TX=10 200 OHM 400 OHM

Ib) 2

20.000

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16 ^{A. VERI}^ami^E.^VGRGS

voltage: 0.1 X 50 ,us, 1 X 50 .us, 1 X 30 ps, 3 X 50 ps wayes were considered. The time step LIt was chosen to be 0.1 ps (Figs 1 to 3) being the travel time of a 30 m long line. It is 1/10 of the length of the busbar analysed. This rate was modified to a rate of Ij20 for having a control over the accuracy (Fig. 4).

In Fig. 1, the superposition of the elementary waves is to be seen. The length of the busbar is 300 m, so 2 [Is is the double traYeI time of this line, and

U1VoAX= 1470.373

_ TIME MIKROSEC NODES' 1. 2

1973. 05. 09. TL=O.1 XL=l

UMAX = ^1558.953

TX=10

4

^I ^{200 OHM}

.4.S7KA t ~oo ^OOM

i

_ TIME MIKROSEC NODES' 1. 2

1973. 05. 09. TL=O.1 XL= i

20.000

le)

20.000

id)

Fig. 1. Overvoltages in substation c,?nsidered by sin:pJified scheme without capacitan.ce with different incoming waves: a) 0.1 X;,O flsec; b) 1 x;,O flsec; c) 1 X 30 flsec; d) 3 x;,O flsec

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CAPACITANCES IN POWER TRANSMISSION SUBSTATIONS 17

the superposition occurs in every 2 fiS according to the reflexion coefficient of

e

⁼ 1 at the open end. In the case of 0.1 X 50 ,lLS wave the reflected wave arriving from node 2 is superposed on the decreasing tail of the incident surge.

The highest value is obtained in the case of a 3 X 50 fiS wave, when the reflected wave was superposed on the front of the incident surge, near to the crest. The peak value of the first step of the resulting wave in node 1 is about 500 kV, which corresponds to the refraction factor (3

=

0.66. The front of the 0.1 X 50 f1S surge is not quite smooth, not because of the character of the physical phenomenon but of the drawing technics of the plotter used.

UMAX = 1513.516

1 TX=l 2 TX=20 3

W

\Jl <!

I a..

k03!IA

CD ~

~ ^{400 OHM}

t

_ TIME MIKROSEC NODES: 1, 2,3

'="

1973. 05. 11. TL=O.05 XL=O.5 0.1150

UMAX = 1419.860

- TIME MIKROSEC NOOES: 1, 2 • 3

1973. 05. 11. TL=O.l XL= 1 1130

2 Periodica Polytechnica El. 19/1.

2a)

2b)

20.000

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18 A. DERI and E. VGRGS

Comparing the curves of Fig. 1 ",ith that in Fig. 2, it is seen that the wave phenomenon is modified by the presence of the capacitances:

oscillations appeared;

i

the overvoltage is lower in the most part of the time interval analysed than that ,vithout capacitance;

the average rate of rise of the resulting wave decreased;

the initial part of the front flattened.

1 iX=l 2 IX=10

r~I--""2"'OO::'::O:.:cli"-M--;:

4.1a KA

(D 0

⁴⁹⁰^OHM

{-

_ liME MIKROSEC

~jODES: 1, 2, 3

1S73. 05 21. TL=O.i XL=l ~!50

2c)

20.000

UMAX " 1506.362

1

1 iX=' 2 TX='O 3

"si ^!lA

~ W 1

⁴⁰⁰^OHM ^.

---+ TIMS MIKROSEC NODES: 1, 2,3

.~

1973. 05. 11. 1L= 0.1 XL= 1 3/50 2d)

20.00-0

Fig. 2. Overvoltages in substation considered by simplified scheme with capacitance at the junction point. Incoming waves: a) 0.1 X 50 f1sec; b) 1 X 50 f1sec; c) 1 X 30 f1sec; d) 3 X 50

f1sec

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CAPACITANCES IN POWER TRANSJHSSION SUBSTATIONS 19 The frequency of the dominant oscillation is equal to 1/4. = 1/4 fLS. In Fig. 2a it is seen that by taking the capacitances into consideration higher peak values may occur than that of the peak value in Fig. 1, in spite of the fact that the average value is lower than that of the case in Fig. la. The amplitude of the oscillations depends:

2*

on the rate of the front time of the incoming wave to the travel time of the line;

on the characteristic impedances of the network.

UMAX " 1390.986

1 ,.X=10 2 ,.X=l 3 I 200 OHM

MJ3KA t

0

⁴⁰⁰^OHM ^{25 OHM}

1 +-

~ TIME t":lKROSEC NODES 1, 2, 3

1973. 05 ;1. ~L=O.i XL= 1 0.H50 3a)

UMAX = 135'5.074

j,

1 IX = 10 2 H=l 3

.-+-~~~--~

1

^I ^{200 OHM} ^{25 OHM}

4.3 KA

CV

~400 ^OHM

- liME MIKROSEC NODES' 1, 2,3

1973. 05. 11. TL=0.1 XL" 1 1130 3b)

20,000

20.000

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20 ^,i.^{DERI and}^E.^VOROS

The statements above are valid for the case of Fig. 3 where the capacitance is on the end of the line, the average value of the overvoltage decreased more than in the previous cases. The maximal values are lower than in the case without capacitance.

The voltages on both ends of the equivalent line (nodes 1 and 2) are coincident in the figures, proving that the length of the equivalent line was chosen for a value low enough (0.1 fls). This was also proved by the control

UMAX = 1423.925

TX=lO 2 iX=1 3

' I -Ti~2~OO~O~H~M--~~

w <f)

« I 0..

4.18 KA

(D 0

^{400 OHM}

. ~ .

- - TIME MIKROSEC NODES 1.2.3

1973. 05. 11. TL=O.l XL= 1 1/50

3c)

IJ"1AX = 1488.249

<f) w :;1 a:

i

_ _ TIME MIKROSEC NODES: 1, 2,3

1973. 05. 11. TL=O.l XL=l 3/50

3d)

2 TX=1 3 rs:==:J

250""\1

20.000

Fig. 3. Overvoltages in substation considered by simplified scheme with capacitance at the end of the busbar. Incoming waves: a) 0.1 X 50 f.lsec; b) 1 X 50 f.lsec; c) 1 X 30 f.lsec; d) 3 X 50

{lSeC

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CAPACITANCES IN POWER TRANS;IIISSION SUBSTATIO,,·S

UW.X = 1518.374

_ TIME MIKROSEC NODES' i, 2, 3

1973. 05. 1i. TL=O.l XL=1 0.1/50 a)

WAX = 1494.568

1 TX=1 2 TX=20 3

~

4.'Ia KA

(D

~ ^{400 OHM}

i

- - TIME MIKROSEC NODES 1, 2.3

1973. 05. 11. 1L=005 XL=O.5 1/50

b)

20.000

Fig. 4. See Fig. 2a and b but calculated with increased accuracy

21

calculation 'with a lower time step (0.05 fiS) shown in Fig. 4a (0.1 X 50 ps) giving an incident surge of identical peak and shape 'with that in Fig. 2a only the curves are smoother. The curve in Fig. 41 (1 X 50 fiS incoming wave) is quite identical 'with that in Fig. 21.

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22 ,i. DERl and E. VOROS

4. Analysis of a given substation

In the folio'wing the analysis results on the overvoltages of the 400 kV substation God "ill be given. The incoming wave was supposed to arrive from a line of infinite length and to be a 1 X 50 p,s wave ,,,ith a crest of 900 kV corresponding to the surge flashover voltage of the overhead line insulators. The topology of the substation analysed is shown in Fig. 5. The characteristic impedance of the overhead line is 347 ohms, that of the busbar is 365 ohms .and that of the connections to the apparatuses is 336 ohms (they are supposed

152m

=-

, '.

Fig. 5. Topology of the substation analysed llMAX : 978.469

i

_ TIME MIKROSEC NODES' 3; 10.9, 7, 15

1973. 05. 21. Tl=O.o2 XL=l 1/50

4.00J

Fig. 6. Node volt ages in the substation of Fig. 5 without the consideration of capacitances

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CAPACITAI'!CES II'! POWER TRAI'!S,UISSION SUBSTATIOI'!S

l,NAX = 820.656

t

- - + - TIME MIKROSEC NODES: 3, 10,9, 7. 15 1973. 05. 28. TL=0.02 XL=l 1/50

23

4.000

Fig. 7. I'Iode voltages in the substation of Fig. 5 with the consideration of the capacitances of apparatuses

UMAX = 779.320

_ TIME MIKROSEC _~.OOQ

NODES 3, 10, 9, 7, 15 1973. 06. 01. TL=0.02 XL=l 1150

Fig. 8. Node voltages in the substation of Fig. 5 with the consideration of increased capacitances of apparatuses

to be horizontal throughout). The substation is of polygon connection haying four apparatuses in each branching: two disconnecting s,'.-itches, a current transformer and a circuit breaker. The capacitance of these four elements was considered as a single concentrated capacitance of 1200 pF because of computer storage problems. So in the calculation the characteristic impedance of the equivalent line was Z = 16.7 ohms at the used time step of 0.02 ,us.

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24 ^-4.^{DERI and}^E.^VOROS

In Fig. 6 the volt ages in the substation nodes are seen for the case without taking into consideration the capacitances. The numbers of the nodes given on the curves wrrespond to the topology of Fig. 5. The highest voltages oc- curred at the transformers (nodes 7 and 15).

The curves in Fig. 7 were computed and plotted with taking into consideration the capacitances of the circuit breaker, disconnecting s,vitches and current transformer. As it is seen on the curves, here too the highest voltage values occur at the transformers (nodes 7 and 15), but the maximal value is lower by about 16 per cent. The initial part of the curves flattened, the average rate of rise decreased and the imaginal average curves were lower than that of the curves in Fig. 6. Taking into consideration the capacitance of the voltage transformers in the nodes modifies in the same manner the node voltages, so there is a reduction of 20 per cent in the maximal values of the voltages com- pared ,vith the curves in Fig. 6.

Acknowledgements

The authors wish to thank Dr. G. BAc"'<, Associate Professor at the Department of Electric Power Systems, Poly technical University, Budapest, for directing their work and also wish to thank the staff of the Computing Centre of VEIKI and especially to head of section P. BRAUN for their assistance in the computations.

Summary

The study deals with overvoltages on high voltage power transmission networks due to lightning surges. The effect of substation capacitances on the wave phenomena in substations was analysed by means of a digital computer program based on Bergeron's method.

References

1. GESZTI O. P.: Villamosmuvek. Tankonyvkiad6, Budapest 1967.

2. BEWLEY, L. V.: Travelling Waves on Transmission Systems. John WHey and Sons, New York 1951.

3. KiN G.: Villamos ha.l6zatok tranziens folyamatai. Tankonyvkiad6. Budapest 1970.

4. BERGERON, L.: Waterhammer in Hydraulics and Wave Surge in Electricity. John Wiley and Sons, New York 1961.

_>ignes DiRI }

Erno VOROS H-1521 Budapest