Phase-to-phase switching surges on 500 kVunloaded transmission line
Ahdab M.K. El-Morshedy. M.Sc, Ph.D., Mem.I.E.E.E.
Indexing terms: Power system protection, Power transmission and distribution, Computer applications
Abstract: With the use of a digital computer, a comprehensive study of phase-to-phase switching surges on500 kV unloaded transmission line were studied. Investigations have been carried out on the distribution ofphase-to-phase overvoltages and the corresponding time-to-crest values during line energisation andre-energisation. Switching-surge control, using preinsertion resistors and shunt compensation and its effect onthe voltage magnitude and time-to-crest value, have been investigated. The phase-to-phase risk of failurefunction has been estimated in each case, given the effect of wave shape under consideration.
1 Introduction
Switching operations in three-phase systems result in switchingovervoltages to ground on all three phases. As these over-voltages are not synchronous and have different polarity andshapes, they also cause overvoltage stresses between phases;bearing in mind that a phase-to-phase overvoltage is the differ-ence of the two phase-to-ground components.
A number of investigations by TNA, as well as in realnetworks, have shown that the phase-to-ground overvoltages oftwo phases in the same system nearly always have oppositepolarity at the times at which the overvoltages to ground reachtheir peak values. This means that the overvoltage stressbetween phases is generally much higher than that to ground.
From the experimental point of view, the interphaseproblem is much more difficult than the phase-to-ground case.It is not so clear how to determine the laboratory impluseequivalent to the waveshape recorded in the network.
This paper presents the results of an analytical study of thephase-to-phase overvoltages, based on digital computation ofthe switching surges. The results are used to estimate thephase-to-phase risk of failure function considering the randomdistribution of both overvoltage magnitudes and time-to-crest values.
2 System studied
The circuit configuration used in this study simulates a typicalEgyptian 500 kV line. Fig. 1 illustrates the single-line diagramof the system. The equipment parameters used in the studywere:
Paper 2082C (P9, Pll), first received 15th February and in revisedform 20th May 1982The author is with the Electrical Engineering Department, Faculty ofEngineering, Cairo University, Cairo, Egypt
Switching overvoltages due to line energisation and re-energisation have been investigated. Two possible modes of athree-phase circuit breaker (CB) closure have been considered:
Mode 1: Simultaneous mechanical closure of the CB polesMode 2: Nonsimultaneous mechanical closure of the CB
poles, in which the three poles are operated sequentially andseparated by 3.33 ms (60 degrees at 50 Hz).
The closing and reclosing angles for the three-phase CB aregenerated at random, according to Gaussian distribution. Themean value of the distribution is zero and the standard devi-ation is 20 degrees (1.11 ms based on 50 Hz). For both modesof switching, a random-number generator is used to generate10 switching angles in the range of ± 60 degrees. The breakerpoles are closed at the angles selected, and the phase-to-phasevoltages at the receiving end are computed.
3 Calculations and results
3.1 Transient calculationsIt is well known that the properties of transmission lines canbe represented approximately by the use of models comprisingnumbers of lumped elements; chiefly resistors, inductors andcapacitors. It should always be remembered that such lineshave parameters which are essentially distributed over wholelengths. To accurately represent the behaviour of a long trans-mission line to transient disturbances, using the model tech-nique, one must ensure that sufficient numbers of sections areprovided so that the accuracy of the results is acceptable.
In this study, the long transmission line was represented byone hundred IT sections connected in tandom, with each nsection equivalent to 6 km length of line. Appendix 10describes the method of representing the line.
The breaker poles are closed at the angles selected and thephase-to-ground voltages at the receiving end are computed;they are denoted by VA VB and Vc.
As the phase-to-phase voltages consist of the individualphase-to-ground components, VAB, VBC and VCA, areobtained in the main computer program by finding thedifference between the corresponding phase-to-groundcomponents, VA, VB and Vc.
Switching-overvoltage computations, with nonsimultaneousclosure of CB poles, are described in Reference 1.
Peaks greater than 1.73 p.u., during the 0—100 ms period,are monitored and the time-to-crest value of each peak iscalculated. Figs. 2 and 3 show typical oscillations withswitching angles 6 = — 7.29° for mode 1 and 0 = 8 ° formode 2. Fig. 2 shows that the maximum phase-to-phase over-voltage is 3.1 p.u., and the steady-state value is 2.2 p.u. fromabout t = 0.35 s. In Fig. 3 the maximum value is 4.1 p.u., andthe steady-state value is 1.9 p.u. from about / = 0.30
IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982 0143- 7046/82/050199 + 07 $01.50/0 199
The individual phase-to-ground components are asimportant as the magnitude and wavefront of surges, since thepolarity is of prime significance in the breakdown mechanismof gaps.
Tables 1 and 2 list some individual phase-to-groundcomponents, for the two possible modes of CB poles, whichadd to yield the maximum phase-to-phase surge in each case.The switching angle 0 is 14.55°, tx is the time at which themaximum phase-to-phase overvoltage occurs and t is the time-to-crest value of each surge.
Table 1: The peak values of phase-to-phase switching surgesmode 1,0 = 14.55°
VAB VA V*
p.u.3.092.222.762.562.312.71
p.u.1.68
— 0.471.74
- 0.871.67
- 1.18
0.550.210.630.340.720.44
p.u.— 1.41
1.75— 1.02
1.69- 0 . 6 4
1.53
0.450.790.370.660.280.56
ms5.9
18.425.237.644.756.9
ms3.775.733.854.873.774.50
Tabie 2: ihe peak values of phase-to-phase switching surgesmode 2,0 = 14.55°
Analysis of the component voltages adding to produce themaximum phase-to-phase voltage indicates a maximumpolarity difference on phase-to-phase make up of 0.79 of onepolarity and 0.21 of the other polarity for mode 1, and 0.89of one polarity and 0.11 of the other for mode 2.
Fig. 4 gives the overvoltage factors aik and theircorrelations Mik for mode 1,0 = — 7.29°.
0.5
-0.5
. P-U-
Fig. 4A Phase-to-phase overvoltage factors and their components,mode 1, 6 = -7.29°
i max • k max'
Fig. 4B Ratio between the phase-to-phase and phase-to-ground over-voltages, mode Id = —7.29°
The method adopted for calculating aik and Mik is given ina recent paper [2].
It is clear that, for high phase-to-phase overvoltages, a tendsto ±0.5 and the M values fall as the phase-to-ground over-voltages rise.
200
0 20 £0 60 80 100percentage higher than the ordinate, %>
Fig. 5 Statistical occurrence of surges and wave shapes
IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982
3.2 Statistical occurrence of surges and waveshapesFor self-restoring insulation, the statistical occurrence of surgemagnitudes and waveshapes is of equal, if not greater, import-ance to the maximum surges, which may occur under specificsystem conditions. Examples of statistical distributions ofphase-to-phase switching surges and time-to-crest values areshown in Fig. 5. These curves were obtained under theassumption that the closing of the CB poles is at random.The surge maxima occurred in less then 1 percent of theoperations. The frequency of occurrence is, therefore,relatively low and thus may have a pronounced effect oninsulation considerations, particularly on self-restoringinsulation.
The cumulative distributions of both the voltage amplitudeU and time-to-crest value t are calculated, and given in Figs. 6and 7 for the two possible modes of CB poles.
3.3 Calculation of risk-of-failure functionRecently, statistical methods have made their way to the fieldof insulation design. The main reason for the application ofstatistical insulation co-ordination in EHV systems is the factthat the behaviour of the air insulation under switching surgestress is much more uncertain than under lightning over-voltages. A central concept in the statistical insulation co-ordination is the risk of failure, i.e. the failure probabilitycaused by different voltage stresses.
In such statistical studies, it is necessary to investigate theinfluence of both the overvoltage magnitude and the wave-form of a switching overvoltage on the phase-to-phase risk-of-failure function.
The distribution of phase-to-phase overvoltages is describedby the bivariate stress distribution F(U, t)[3], where C/is thephase-to-phase overvoltage amplitude and t is the corres-ponding time-to-crest value.
In addition to the crest value, the front time is an importantparameter affecting the withstand voltage of an air gap. The50% flashover voltage of an air gap between phases has beendescribed as a function of front time in many papers alreadypublished [4, 5] .
The flashover probability distribution function of thephase-to-phase insulation may be defined as a bivariate
99.99r
99
9590
50
3 Uvoltage ,p.u.
Fig. 6 Cumulative frequency distributions of overvoltage magnitudesof receiving end phase-to-phase surges
mode 1; mode 2a Phase-to-phase overvoltages, R = 0b With R = 300 flc With shunt reactorsd With trapped charge
function P{U, t) of surge magnitude U and its time-to-crestvalue t.
Finally, the risk-of-failure function R may be calculated byintegrating the bivariate-stress-distribution function F{U, t)and the flashover probability distribution function of thephase-to-phase insulation P(U, t).
The function F{U, t) is formulated for each mode of CBpoles; there are about 300 paired (U, t) phase-to-phase over-voltages, which is a sufficiently large number to formulate thefunction F(U,t).
Figs. 8 and 9 show a cluster of (£/, t) points for the two
2 3 4 5 6 7 8t ime-to- crest, ms
Fig. 7 Cumulative frequency distributions of time-to-crest values ofreceiving end phase-to-phase surges
mode 1; mode 2a Phase-to-phase overvoltages, R = 0b With R - 300 ftc With shunt reactorsd With trapped charge
U. Or
3.5
3.0
= 2.5a.
O^ 2.0
1.5
1.0
t(U)
U(t)
X X X
3 Utime ms
Fig. 8 Bivariate distribution contours, mode I, four cumulativeprobabilities are marked
IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982 201
possible modes of CB poles, with the bivariate and marginaldistributions of the overvoltages. The fitted distributionF(U, t) takes the form of concentric elliptic contours. Thevalue marked on each contour is the probability for a surge tohave magnitude and time-to-crest values within the boundaryof that contour.
4.0
3.5
3.0
2.0
1 5
1 .0
90°/.80°/o
70°/.90°/.
2 3 4time . ms
Fig. 9 Bivariate distribution contours, mode 2, four cumulativeprobabilities are marked
Table 3 lists the relevant statistics of the function F(U, t)for.the two different modes of switching. The function P{U, t)is obtained from the available data in the literature [5 ,6] . Thephase-to-phase clearance is 10 m for this study.
Table 3: Statistics of bivariate phase-to-phase overvoltages with andwithout preinsertion resistors
Correlation coefficientAverage value ofphase-to-phaseovervoltages U, p.u.Average value oftime to crest 7, msStandard deviation ofvoltage distributionay, p.u.Standard deviation oftime-to-crest distributionOf. ms
Withtf
mode 1
- 0 . 5 3
2.56
4.401
0.42
1.001
= 0
mode 2
— 0.21
2.49
3.115
0.62
0.855
Withfl =
mode 1
-0.55
2.48
4.554
0.41
1.082
300 £1
mode 2
- 0 . 2 9
2.39
3.114
0.48
0.857
The risk of failure between phases varies from one front tothe other, as not all the phase-to-phase switching surges havethe same time-to-crest values. The integrated risk of failurefunction R is determined considering the effect of thewavefront:
R = I ~ f F(U, 0 • P(U, t)dUdt
The risk of failure as a function of the time to crest will be
R(t) = F(t)
(1)
(2)
where f(U/t) is the conditional voltage distribution betweenphases, for a given value of t.
As both the F(U, t) and P{U, t) are assumed normally distri-buted, the risk-of-failure function will be
(3)
where
Z =
U(t) and ov are the mean value and standard deviation,respectively, of the conditional distribution f(U/t). Us0(t) ando{i) are the mean value and standard deviation, respectively, ofthe function P(U, t).
The integrated risk of failure is
u(t) R = P R(t\itJo
(4)
The risk-of-failure function R(t) is plotted in Fig. 10 for bothmode 1 and mode 2. The integrated risk of failure of phase-to-phase insualtion is found to be 12.35 x 10~8, for mode 1, and36.4 xlO"7, for mode 2.
x10' 60
20
2 A 6time - to - crest , ms
Fig. 10 Risk of failure function
.mode 2mode 1; _a Phase-to-phase overvoltages, R = 0 SIb With R = 300 SIc With trapped charge
4 Overvoltages on reclosing
The reclosing of transmission lines is the most criticaloperation as regards to insulation co-ordination. This isbecause the trapped charge on a transmission line prior to itsreclosing has a significant effect on the overvoltages produced.The value of the trapped charge is very much dependent onthe equipment permanently connected to the line, as thisdetermines the decay mechanism.
If no power transformers or reactors are connected the lineholds its trapped charge, the only losses being due to coronaand leakage, and thus the decay is very much weatherdependent. In good weather conditions the time constant ofthe decay is of the order of 10—100 s, so that no appreciabledischarge will occur in automatic-reclosure sequence.
When re-energising a transmission line, the trapped-chargevoltages at the receiving end of the line may be + 1, + 1 and— 1 p.u. on all three phases [7]. Figs. 11 and 12 show theeffect of the presence of trapped charge on the receiving-endphase-to-phase switching surges. It is clear that the presence oftrapped charge increases the magnitude of phase-to-phase over-voltages. In Table 4, the effect of the presence of trappedcharge on the statistics of the bivariate probability is listed.The mean value of overvoltage magnitude, the mean value oftime to crest and their corresponding standard deviations are
202 IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982
Table 4: Statistics of bivariate phase-to-phase overvoltages with shuntreactors and trapped charge
Correlation coefficient rAverage value ofphase-to-phaseovervoltages U, p.u.Average value oftime to crest 7, msStandard deviation ofvoltage distributionau. p.u.Standard deviation oftime-to-crest distributiona^ ms
with shunt reactors
Mode 1
- 0 . 5 1
1.98
4.393
0.16
1.103
Mode 2
-0 .47
2.33
1.967
0.57
1.093
with trapped charge
Mode 1
- 0 . 5 5
2.64
4.523
0.48
1.038
Mode 2
0.63
3.46
3.241
1.14
1.212
It is the most effective means for producing substantialreductions in surge voltages appearing on transmission lines.
To study the effect of preinsertion resistors on the phase-to-phase overvoltages and the risk of failure function, a 300 £2resistor is inserted in each phase on closing. The insertiontimes are 10 ms, for mode 1, and 15 ms, for mode 2. Theeffect of preinsertion resistors on the relevant statistics of thephase-to-phase bivariate overvoltage distribution is shown inTable 3, and its effect on the overvoltage magnitude is shownin Figs. 13, 14 and 15.
With preinsertion resistors, the risk of failure is reducedfrom 12.35 x 10"8 to 3.5 x 10~8, in mode 1, and from36.4 x 10"7 to 2.6 x 10~7, in mode 2. The effect of preinsertionresistor on the phase-to-phase risk-of-failure function R(t) isshown in Fig. 10.
increased with the presence of trapped charge. This increasesthe phase-to-phase risk-of-failure function.
The cumulative distributions of both the overvoltagemagnitude and time to crest with the presence of trappedcharge are given in Fig. 6, for overvoltages, and in Fig. 7, forwavefronts. The effect of the presence of trapped charge onphase-to-phase risk-of-failure function is shown in Fig. 10 forboth mode 1 and mode 2. The integrated risk of failureincreases from 12.35 x 10"8 to 96.5 x 10"8, in mode 1, andfrom 36.4 x 10"7 to 203.5 x 10"7, in mode 2.
Consequently, the elimination of trapped charge isnecessary to reduce the severity of re-energising overvoltages,and to decrease the phase-to-phase risk-of-failure function.
5 Switching-surge control
With the advent of 500 kV systems, it became technically andeconomically desirable to further control and reduce switching-surge severities. This was done through the use of CBs withone-step preinsertion resistors, and with the presence of shuntreactors. Overvoltage reduction is vital to economic design ofnew EHV and UHV systems. This can be obtained by usingpreinsertion resistors across the main circuit-breaker contacts.
Fig. 15 Typical receiving-end phase-to-phase voltages, mode 2,6=8°, with preinsertion resistor R = 300 fl
IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982 203
5. / Shunt reactorsThe adoption of shunt reactors, to compensate for a portion ofthe line charging MVAr, is an indispensable method for control-ling excessive voltages and the leading currents flowingthrough the EHV system.
For the study of the phase-to-phase switching-surge charac-teristics of an unloaded shunt-compensated 500 kV trans-mission line, the system illustrated in Fig. 1 was used. High-voltage shunt reactors were connected to ground at thesending and receiving ends of the line. The degree of compen-sation, i.e. the reactive power of the reactors, is expressed as apercentage of the charging power of the line, and is 75%.
Figs. 16 and 17 show the effect of shunt reactors on thephase-to-phase switching overvoltages for modes 1 and 2,respectively. It is clear that the presence of shunt reactorsreduces the phase-to-phase overvoltage magnitudes and theircorresponding standard deviations (Table 4).
Fig. 16 shows that the maximum phase-to-phase over-voltage is 2.5 p.u. and the steady-state value is 1.85 p.u., fromabout t = 0.12 s. However, from Fig. 16, the maximumphase-to-phase overvoltage is 3.0 p.u. and the steady-statevalue is 1.58 p.u., from about t = 0.10 s.
The cumulative distributions of both the overvoltagemagnitude and time-to-crest values with shunt reactors aregiven in Fig. 6, for overvoltages, and Fig. 7, for wavefronts.
The effect of shunt compensation on the phase-to-phaserisk-of-failure function R(t) is shown in Fig. 18 for the twopossible modes of CB poles.
With shunt reactors, the line risk of failure is greatlyreduced from 12.35 x 10"8 to 16.7 x 10~10, in mode 1, andfrom 36.4 x 10"7 to 3.5 x 10"9, in mode 2.
6 Voltage against time-to-crest relation
For each mode of CB switching there are about 300 paired(U, t) overvoltages, a number sufficiently large to determinethe correlation between the voltage magnitude U and time-to-crest value t.
Figs. 8 and 9 display a cluster of {U, t) stress pointsobtained with both modes 1 and 2, respectively. A voltageagainst time to crest curve is shown, under which practicallyall (U, t) points are located. This curve gives the upper limitbetween the overvoltage magnitude and time-to-crest value.Fig. 19 shows the corresponding relations for modes 1 and 2.
10
*~ 8T3OE 6
x10 -10 x10' 20
16 <uO12 I
8 ccr
0 2 U 6time -to-crest # ms
Fig. 18 Risk of failure function, with shunt reactors
mode 1 > mode 2
0 1 2 3 U 5 <time-to-crest , ms
Fig. 19 Voltage against time-to-crest relation
-mode 2mode 1; -a Phase-to-phase overvoltages, R = 0b With R = 300 SIc With shunt reactorsd With trapped charge
7 Conclusions
The risk of failure of phase-to-phase insulation can beaccurately calculated if the magnitude and the waveshape ofenergising surges are available.
Energising transmission lines with nonsimultaneous closureproduces larger maximum and mean values of overvoltages,than when energising takes place with simultaneous closure. Asa result the nonsimultaneous closure gives a higher phase-to-phase risk of failure.
The overvoltage magnitude and front distributions areinfluenced by various network parameters, such as trappedcharge on reclosing, preinsertion resistors and shunt reactors.
On reclosing transmission lines, the presence of trappedcharge gives rise to higher values of mean and standarddeviation, of both overvoltages and front distributions. Thisleads to a higher phase-to-phase risk of failure.
A great reduction of phase-to-phase risk of failure isobtained with preinsertion resistors. The mean and standard-deviation values of the overvoltage distribution decrease.
204 IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBER 1982
Shunt reactors are highly effective in lowering switching-surge magnitudes as well as steady-state values. The phase-to-phase risk of failure is greatly reduced, as a result of thereduction in the mean and standard deviation of both the over-voltage magnitudes and fronts. Therefore line compensatingshunt reactors are required for EHV and UHV transmissionsystems.
8 Acknowledgments
The author wishes to thank Prof. S. A. Sebo for usefuldiscussions and advice throughout this work. Thanks are alsodue to the Egyptian Government and the Department ofElectrical Engineering at the Ohio State University forsupporting this work.
References
1 EL-MORSHEDY, A., and SEBO, S.A: 'Risk of failure for phase-to-phase over voltages'. 1980 Midwest power symposium, PurdueUniversity, Lafayette, Indiana, October 1980
2 CIGRE working group 33-02: 'Switching overvoltages in three-phasesystems', Electro, 1979, (64), pp. 138-157
3 ANIS, H., RADWAN, R., and EL-MORSHEDY, A.: 'Effect of over-voltage transients on the risk of insulation failure'. 1978 IEEEwinter power meeting, Paper A78 154—7
4 CORTINA, R., FARZINI, M.S., and TASHINI, A.: 'Strength charac-teristics of air gaps subjected to interphase switching surges', IEEETrans., 1970, PAS-89, pp. 448-456
5 COLOMBO, A., SARTORIO, G., and TASCHINI, A.: 'Phase-to-phase air clearances in EHV substations as required by switchingsurges'. CIGRE Paper 33-11,1972
6 MENEMENLIS, C, ANIS, H., and HARBEC, G.: 'Phase-to-phaseinsulation - Pt. II: Required clearances and co-ordination with phase-to-ground insulation', IEEE Trans., 1976, PAS-95, pp. 651-659
7 RUOSS, E.: 'Overvoltages on energizing HV lines', Brown BoveriRev., 1979,66, pp. 262-270
10 Appendix: Transmission-line representation
A general line may be represented by N equivalent 7r sections.The equivalent n representation is the basis for the applicationof a digital computer dealing with long transmission lines, thenthese cascade-connected line sections can be represented by anexact equivalent single T section, using a simple digital
computer program. This equivalent T section permits thecalculation of switching surges at the receiving end of the line,Fig. 20.
Fig. 20 Representation of a single-phase transmission line
a N IT sections; b One equivalent T sectionR = resistance per unit lengthL — inductance per unit lengthC = capacitance per unit length
The long transmission line used in this study is representedby 100 7T sections. Each section represents 6 km length of line.With a DO loop in which N changes from 2 to 101, then:
Z3(N-l)Z(N) = Z2(N-\)
Z2(AO = [{Z2(N-\)+A}'B]IZ(N)
Z3(N) = [Z3(N-\)-B]IZ(N)
and A - R + jcoL, B = 2//coc, when
N = 1:Z, = Z2 = 0,Z3 = 5
Finally, the impedances of the equivalent T will be101
Z\T = I ZX{N)N= 2
Z2T = Z2(101)
and
Z 3 T = Z3(101)
This method of representation can also be used if theimpedances of the individual sections are not identical.
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