Engineering method for high-voltage substations lightning performance estimation. Prof. M.S. Savic. Indexing terms: Lightning and lightning protection, Cables ...
Engineering method for high-voltage substations lightning performance estimation Prof. M.S. Savic
Indexing terms: Lightning and lightning protection, Cables and overhead lines
Abstract: A computer method for estimating the lightning performance of high-voltage substations has been developed and modified for simple engineering applications in the substation design. The main substation element representation and the equivalent circuit choice are suggested. The method is illustrated by the example of a 110 kV substation with a cable entrance. Both shielding failures and lightning strikes to the towers or the earth wires, causing back-flashovers on the incoming overhead lines, have been analysed and the best variant of the overvoltage protection suggested.
1
Introduction
In the design of high-voltage substations one of the very important tasks is to perform insulation coordination by the correct selection and location of the surge arresters. Recently two kinds of methodologies for insulation coordination have been recognised. In the case of an untypical high-voltage substation layout a comprehensive study for estimating the expected number of failures due to over-voltage occurrence has been performed. On the other hand, in the case of a typical substation the simplified methods for overvohage protection design have been applied. In this paper a general methodology for high-voltage substation lightning performance estimation, convenient for engineering applications, will be described. The method is illustrated by the example of the 110 kV substation of the power plant 'Nikola Tesla' in Yugoslavia. The method is based on the travelling-wave technique. Wave distortion due to the corona losses is taken into account [I]. Frequency-dependent line parameters can be involved in the computation procedure [2]. The probability method of 'limiting parameters' described in References 3 and 4 is used for estimating the risk of insulation failure at a certain place in the substation. This method is based on computation of the critical value of the lightning current amplitude which, if applied at a certain point in front of the substation, causes greater overvoltage than the basic insulation level (BIL) at the inspected part of the insulation in the substation. The computation is repeated for various lightning current gradients to obtain the relation between the current gradient and the critical current magnitude causing insulation failure. It is Paper 6725C (P7, P1 l), received 16th January 1989 Prof. Savik is with the Faculty of Electrical Engineering, University of Belgrade, Bulevar Revolucije 73, PO Box 816, 1101 Belgrade, Yugoslavia
presumed that every overvoltage exceeding the BIL causes an insulation failure. 2
Computation methodology
2.1 Equivalent circuit choice One of the most important tasks in the lightning performance of a high-voltage substation estimation is the correct choice of the substation element representation and the selection of an equivalent circuit. (a) Usually the monophase representation of all conductors by positive sequence surge impedance can be satisfactory for a short-distance propagation process. The ground return frequency-dependent parameters cause a decay of the wave crest of a few percent. This effect can be neglected for the sake of simplicity and safety. The mutual influence of the phase conductor and the earth wire can be modelled by a coupling factor C, in the following way:
where U , is the earth wire surge voltage and U p , is the surge voltage of the phase conductor. Factor C, can be taken from the range 0.2-0.3. (b) A power transformer can be represented as an equivalent surge capacitance given by the manufacturers. Some authors use a surge impedance 2, = of the transformer in parallel with the surge capacitance. This surge impedance can cause a decrease in the crest voltage at the transformer terminal of less than 3%, and usually it can be neglected. (c) Current transformers, voltage transformers, circuit breakers, disconnectors and even insulator strings can be represented by equivalent capacitances. In that case equivalent circuit would become very complex and the results would become optimistic. Owing to this it has been decided to neglect all capacitances except power transformer surge capacitance. (d) In the case of a strike to the earth wire causing back-flash it is sufficient to investigate strikes to the first two spans in front of the substation. Strikes to the other spans causing back-flashovers are not dangerous for the substation insulation, owing to the wave distortion along the line. (e) Every tower can be modelled as a short line with a constant surge impedance dependent on the tower geometry, as described in Reference 5. ( f ) The number of back flashes is strongly dependent on the value of the tower impulse-footing resistance. This parameter is a function of the ligh,tning current magnitude and waveshape owing to ionisation effects, change of moisture content in the soil during the lightning discharge, and the presence of the propagation process in the case of the long buried conductors. For a simplified
a
IEE PROCEEDINGS, Vol. 136, Pt. C , No. 4 , JULY 1989
lightning performance estimation in Reference 5 the application of a constant tower im pulse-foo ting resistance equal to the low-frequency resistance is suggested. (g) There are two different insulation characteristic models: for air insulation and for solid dielectrics. A line insulation flashover voltage is computed by the constant area criterion [6] with the following mathematical formulation :
(h) The numerical corona model is described in Reference 1. It is based on the empirical formula given in Reference 8 for the increase of the wave front duration
1 current
wave
where uo is the reference voltage,
E, is the mean electrical field along the air gap at 50% flashover probability level, d is the air gap length, u(t) is the transient voltage across the air gap, to is the time instant when u(t) exceeds the reference voltage and t, is the moment of flashover when the computed area A becomes greater than A,, . The flashover criterion can be written in the following form : The critical area A,, can be calculated from the following relation : A,, = Cd
(5)
where C is the empirical constant deduced from experimental data. The constants C and E, are computed to obtain the 50% flashover voltage from a standard laboratory test o n the completely equipped insulator string with the standard 1.2/5Ops lightning wave. The computed constants from the test results described in Reference 7 are C = 677 kV ps/mm and E, = 5.067 kV/mm. In this way all possible air insulation weak points (line or busbar insulators) are modelled. It is supposed that the solid dielectric breakdown voltage in such high-voltage equipment as power transformers, current or voltage transformers, high-voltage cables or other equipment can be modelled by constant voltage-time characteristics equal to the BIL. Any lightning overvoltage exceeding the BIL is considered an insulation failure. If the method of limiting parameters is applied, whenever a computed surge for a certain current gradient at a inspected part of the equipment becomes greater than the BIL, the transient process computation is stopped for this current gradient and the current magnitude sufficient to produce this voltage is computed as
where t, is the time interval from the moment of occurrence of the voltage surge at the observed part of the substation equipment to the moment of insulation breakdown. t, is the time interval from the moment of the lightning strike (to the top of the tower or earth wire) to the moment of back-flashover o n the tower in front of the substation. I' is the linearised wavefront current gradient. In Fig. 1 the computation of the current magnitude sufficient to cause insulation failure is explained. The time interval t, sufficient to cause back-flashover on the tower, together with the time interval t, from the appearance of the voltage wave on the inspected part of the insulation to the moment of reaching the BIL, gives the total linearised front time duration of the current wave, sufficient to produce insulation failure at the inspected place. IEE PROCEEDINGS, Vol. 136, Pt. C , No. 4, J U L Y 1989
Fig. 1 Equivalent computation
circuit to explain procedure of current crest
d B = vt,; d , = ut, c = propagation speed u , = line insulation flashover voltage u , = transformer BIL
owing to the corona effect. The applied empirical formula is At
=2 U
[J(l
+ Bu) - I] (ps),
for
u > U,,
where d is the propagation distance (m). zj is the propagation speed (300 m/ps). B is the empirical coefficient dependent on the conductor radius given in Fig. 2 (l/kV).
Fig. 2
Dependence of coeflcient of corona on conductor radius
is the instantaneous value of the voltage (kV) and U,, is the corona inception voltage (kV).
u
2.2 Computation of risk of substation insulation failure due to back-flashover on incoming line In the statistical estimation method of the substation lightning performance due to direct strikes to the earth wire or tower and back-flashover, the place of the discharge is varied along the first few spans, as presented in Fig. 3. Usually two spans are enough.
Instead of a continuous variation of the point of discharge along the span only a few (usually 5) equidistant points of discharges at every span are analysed. The
flashovers, is N
=
1/R
2.3 Computation of risk of substation insulation failure due to shielding failure on incoming line
Fig. 3
Variation of place of discharge
mean value of the probability of occurrence of overvoltages exceeding the BIL of the equipment in the substation due to a strike somewhere on the analysed span, denoted P,, can be computed by means of the trapezoidal rule In the following form:
Pti (i = 1, n) is the probability of occurrence of the lightning over-voltages exceeding the BIL of the equipment in the substation if the strike hit the top of tower 1 or n in Fig. 3, causing back-flashover. Pi (i = 2, 3, . . ., n - 1) is the probability of occurrence of the over-voltage exceeding the BIL in the substation if the strike hit certain points (2, 3, .. ., n - 1) on the span, causing backflashover on the nearest tower. Kt is the coefficient of correction of the discharge probability to the top of the tower, which is presumed to be 1.3. In this way it is supposed that the probability of discharge to the top of the tower is 30% greater than that to the span. The risk of occurrence of lightning overvoltages exceeding the BIL of the equipment in the substation can be computed in the following way: R
=
In estimating the risk of occurrence of lightning overvoltages exceeding the substation equipment BIL due to the shielding failures on the line, it is supposed that a direct strike hits the substation entrance or overhead line cable junction in the case of cable entrance. The probability of strike penetration to the shielding zone denoted Psh as a function of the lightning current magnitude can be computed by means of the electrogeometrical method described in References 10 and 11. A direct strike to the phase conductor causes an overvoltage wave propagating to the substation. This overvoltage can be computed by means of the travelling-wave technique. The probability of' exceeding the BIL of the substation equipment for a strike at the substation entrance can be calculated in the following manner: P, =
I
f(I, I1)PSh(I)dI dI1
f(I, 1') is the joint frequency distribution of the lightning current magnitudes and wave front gradients. Psh(I)is the probability of the shielding failure as a function of the current magnitude. D is the failure zone, limited by the minimum lightning current magnitudes and rates of rise causing the insulation failure. The limiting set of parameters forming the failure zone is illustrated in Fig. 4.
1 Peq dj Sat Ng
1;
j
r;
I , kA/ps
P,, is the mean probability of occurrence of overvoltages exceeding the BIL of some equipment in the substation if the discharge hit the jth span. dj is the length of the jth span. Sat is the attractive area of the overhead line per unit length. N g is the annual lightning density of the discharges to the ground per km2. rn is the number of observed spans. The attractive area of the overhead line is a band on both sides of the line in which the most of the lightning discharges occur to the line and the minority to the ground. It can be estimated for a line of unit length as Sat = 6 he/ 10 - (km)
(10)
where hel is the effective height of the earth wire along the span (m). The mean number of years without lightning overvoltages exceeding the BIL of the substation equipment, due to strikes to the towers or earth wire causing back-
Fig. 4
Method of limiting parameters
The failure zone D can be expressed as a sum of elementary zones AD,, AD,, . . . , AD,, presented in Fig. 4.
The curve of lightning limiting parameters can be defined by sets of limiting values (I,, I;), (I,, I;), .. ., (I,, I;), or corresponding overvoltage wave parameters on the phase conductor at the struck point defined by Ui = Z, IJ4
and
U: = Zc11/4
(13)
where Z, is the surge impedance of the phase conductor, Ui is the overvoltage wave magnitude and U: is the overvoltage wave gradient. IEE PROCEEDINGS, Vol. 136, PC.C , No. 4, J U L Y 1989
In the case of a strike at a certain distance from the substation entrance, the incoming wave gradient is reduced. The distance of this point from the substation entrance can be determined in such a way as to reduce
Fig. 5
substation if shielding failure occurred at points j and + 1 in front of the substation. The total risk R of substation insulation failure due to shielding failure on the line in front of the substation can
j
Equivalent circuit
the overvoltage wave gradient from the given value U; at the point to the value U; at the substation entrance, both belonging to the sets of limiting values of the curve of limiting parameters computed for the case of discharge at the substation entrance. The wave front is prolonged owing to corona distortion for the time increment Atj.
The value T = Ul/U; is a front time of the voltage wave at the point, and T + Atj = Uj/UJ is a voltage wave front time at the substation entrance after propagation along distance dj. It is supposed that the wave front remains linear after corona distortion. The distance dj necessary to reduce voltage wave gradient from U; to Ui can be calculated from eqn. 7 for the front of wave time increase Atj owing to the corona.
The probability of occurrence of lightning parameters causing substation insulationfailure for the case of a point struck at distance dj from the substation entrance, denoted Pi, can be computed by the application of eqn. 12 in the areas ADj, ADj+ l, . . . , AD,. Eqn. 12 is applied only to lightning current rate rise greater than IJ or corresponding lightcing overvoltage wave gradients UJ at the point. Discharge with the lightning current gradient less than I;, causing corresponding overvoltage wave gradient to be less than U;, is reduced, owing to propagation at the station entrance, to voltage wave gradient less than U;. This voltage gradient is -not enough to cause insulation failure in the substation. The risk of insulation failure due to a lightning strike to the line length Adj = (dj+, - di) is
where P j and P j + , are the probabilities of occurrence of overvoltages exceeding the BIL of some equipment in the IEE P R O C E E D I N G S , Vol. 136, P t . C , N o . 4, J U L Y 1989
be computed as the sum of the risks of failure due to strikes to certain parts of line Adj ( j = 1,2, . . . , n). (17) R = ~ R , This method is pessimistic because wave distortion due to other effects is neglected. 3
Computation of lightning performances of 110 kV substation w i t h cable entrance
3.1 System data
The equivalent circuit of the analysed 110 kV system is presented in Fig. 5. The 110 kV cable is analysed in 5 uniformly distributed points to get the maximum voltage distribution along the cable due to the lightning strike. All system parameters taken from the substation layout or estimated are given in Table 1. A lightning strike to the earth wire on the first and second spans, and to the phase conductor in front of the substation, owing to shielding failure is analysed. In Fig. 5 and Table 1 system data for a strike to the second span in front of the cable are presented. In the case of the element modelled as an equivalent line, the surge impedance and the line length are also presented in Table 1. The system rated voltage is 110 kV. The BIL of all equipment is 550 kV. Classical S i c surge arresters of the type H M M 108, rated voltage 108 kV, [14] are modelled with the voltageltime characteristic of the spark gap given in Table 2. The current/voltage characteristics of the surge arrester nonlinear resistor is given in Table 3. The characteristics are linearly extrapolated for smaller current magnitudes.
3.2 Lightning parameters The joint log-normal lightning current magnitude and front of wave gradient distribution suggested in Reference 9 is in the following form : F(x, y) =
(
1 2
q
/
i
~
x2 + Y2 - ~ P X Y ) dx 2(1 - ~ 2 ) 225
Table 1 : Substation layout parameters Branch Type o f element - -
Resistance,
n
standard deviation p = correlation coefficient of I and I'
-
earth wire tower height t o cross arm tower grounding resistance earth wire support cross arm air gap after back-flash phase conductor part of earth wire lightning channel part of earth wire tower height t o cross arm tower grounding resistance earth wire support cross arm air gap after back-flash phase conductor earth wire portal tower grounding resistance horizontal part of portal air gap after back-flash phase conductor connection conductor busbars connection conductor lead t o the surge arrester conductor t o cable termination 30, 3 2 parts of cable phase conductor lead t o the surge arrester connection t o the power transformer Capacitance, nF -
-
35
power transformer surge capacitance voltage transformer surge capacitance
36
,,= current gradient logarithmic
a,, Length, m
Fig. 6
Transient voltage at place
Fig. 7
Transient voltage on phase conductor at place of backjlash
cf
cross arm
5
The presumed lightning strike parameters corresponding to Berger's measuring results according to Reference 9 are
3
Table 2: Voltageltime characteristic of surge arrester Front of wave spark-over voltage at instant Minimum 1 0 0 % sparkover voltage at instant Minimum switching spark over voltage at instant
r, = 0.324 p s
U,
t2=1.2ps
U2=248kV
a,, = 0.68
r, = 2 5 0 p s
U,
a,,
=
292 kV
= 259
kV
, ,,= 0.55
p = 0.38 Table 3: Currentlvoltage surge arrester characteristic Current, k A Residual voltage, kV
5 227
10 20 248 281
where I = random current amplitude = mean current amplitude I' = random current gradient i' = mean current gradient a,, = current magnitude logarithmic standard deviation
I
,
3.3 Classical approach to overvoltage computation The classical approach to overvoltage computation of choosing the representative current magnitude and mean waveform gradient is used to investigate the voltage distribution along the cable, and to investigate the voltage waveforms in different points of the equivalent circuit. In the classical methodology of overvoltage computation the critical lightning parameters with the probability of exceeding the chosen values by 2% are determined. The computed critical values are
1,
=
121 kA
and
1;
= 43.2 kA/ps
IEE PROCEEDINGS, Vol. 136, Pt. C , No. 4 , J U L Y 1989
Lightning channel surge impedance is presumed to be 300 R. It is supposed that the lightning strike happened at the middle of the second span to the earth wire. Three differ-
(a) A surge arrester is placed in front of the junction of the cable and the overhead line. (b) A surge arrester is placed at the other end of the cable.
Y varlant
Fig. 8
b
Transient voltaye at d ~ f i r e n points t on cable
Fig. 10 Peak voltage distribution along cable for various overuoltage protection variants
0
0
10
5
15
t , PS
Fig. 9
Transformer terminal overvoltaye
Table 4: Overvoltages at different points Nodeno.
11
Variant (a) (6) (c)
24
25
26
27
28
31
976 425 489 550 557 528 659 976 595 579 493 485 449 417 975 333 339 354 359 352 404
0
50
100
150
200
struck p o ~ n td~stance,m
ent overvoltage protection variants are analysed. In the first variant the surge arrester was connected only in front of the overhead line-cable junction. In Fig. 6 the transient response of the tower computed at the cross arm is presented. In Fig. 7 the transient voltage on the phase conductor at the place of back-flashover is presented; the infinitely steep wavefront after backflash can be seen. There is an overvoltage on the cross arm exceeding the BIL after back-flashover, owing to the large current wave magnitude. In Fig. 8 the transient overvoltages at different places along the cable are presented. The surge front gradient is decreased owing to the cable capacitance charging effect and wave distortion owing to the corona. The transformer terminal voltage is presented in Fig. 9. Three analysed overvoltage protection variants were investigated : IEE PROCEEDINGS, Vol. 136, Pt. C , No. 4, J U L Y 1989
Fig. 11 Expected number of strikes causing overvoltages less than the power transformer BI L as a function of position of strike
(c) A surge arrester is placed on each end of the cable. The computed overvoltages of the three protection variants analysed are presented in Table 4. The peak voltage distributions along the cable are presented in Fig. 10 for overvoltage protection variants (a), (b) and (c). 3.4 Estimation of risk of power transformer insulation failure 3.4.1 Risk of power transformer insulation failure due to the back-flashover: In the statistical approach to the risk of occurrence of overvoltages exceeding the power transformer BIL the annual lightning density N , = 4.5 (11 year x km2) is taken according to the meteorological
data [12]. The analysis is performed for the same three variants of overvoltage protection. The point of discharge to the earth wire is varied along the first two spans. In Fig. 11 the expected number of strikes causing one overvoltage exceeding the transformer BIL as a function of the position of the strike is presented. It can be seen that the most dangerous point of strike is the first tower just in front of the cable termination. The expected number of strikes causing one overvoltage exceeding the BIL increases for strikes to the earth wire in the middle of the span and decreases again for strikes to the top of the second tower. Strikes to the earth wire on the second span produce overvoltages which are sufficiently damped owing to propagation that dangerous overvoltages are extremely seldom. Discharges to the top of the third tower or even further away cannot cause dangerous overvoltages at all. The total risk of occurrence of overvoltages exceeding the power transformer BIL is presented in Table 5. The
system elements and the equivalent circuit selection is especially emphasised. The results of lightning performance studies show that strikes to the earth wire or tower in the vicinity of the
Table 5 : Risk of power transformer insulation failure Variant
Risk, 1/year
N = 1/Risk, year
(a) (6) (c)
6.01 x 1664 5 . 0 9 ~ 1 0 - ~196 1.88 x 10 - 6 0.532
x
1O6 Fig. 12
Line geometry with eflective dimensionsfor whole span
expected number of years without transformer insulation failure as a reciprocal value of the risk of insulation failure is also presented. In Reference 13 an equipment failure rate of N = 800 years or N = 400 years, depending on the equipment importance, is suggested. According to this criterion, variant (a) with only one set of surge arresters in front of the cable and overhead line junction can be recommended.
3.4.2Risk of power transformer insulation failure due to incoming overhead line shielding failures: An inves-
tigation of the risk of exceeding the power transformer BIL due to shielding failures on the line and substation was performed. The analysed line configuration with the effective heights of the earth wire and phase conductor is presented in Fig. 12. The probability of shielding failures on the line is analysed by means of the electrogeometrical method described in References 5, 10 and 11. The probability of occurrence of lightning current magnitude penetrating the shielding zone and hitting the phase conductor in front of the cable and overhead line junction is presented in Fig. 13. It can be seen that the greatest lightning current magnitude which can cause shielding failure is 11.1 kA. This current magnitude is not sufficient to cause dangerous overvoltage for transformer insulation; the minimum current magnitude which can produce overvoltage equal to the transformer BIL is 24 kA. The probability of penetration of lightning into the shielding zone of the substation is extremely small, due to the effective shielding geometry with negative shielding angles, and it will not be presented here. 4
Conclusion
In this paper the general methodology of the risk of the lightning outage estimation is presented and illustrated with the example of a 110 kV substation with cable entrance. The importance of the correct modelling of
Fig. 13 Probability of penetration of lightning currents of certain magnitude into shielding zone and hitting phase conductor
substation entrance or the overhead line and cable junction causing back-flashover are most dangerous for the transformer insulation in the analysed case of a 110 kV system. Strikes on the third tower or further from the substation entrance are not dangerous for the substation insulation. The overvoltages produced by shielding failures on the line are not dangerous for the substation equipment. Shielding failllres in a substation with effective shielding geometry, realised with negative shielding angles, are impossible. 5
Acknowledgment
I acknowledge the support of 'Energoprojekt, Department of thermal and nuclear plants', and in particular IEE PROCEEDINGS, Vol. 136, Pt. C , N o . 4, J U L Y 1989
Engineer M. PekoviC for obtaining all the necessary data and the late Engineer B. MiletiC for study organisation. I very grateful to the Community Of Science Of the am Republic of Serbia for the financial support of this study. 6
References
1 BICKFORD, J., and SAVIC, M.: 'Some aspects of system modelling for the estimation of lightning performance of high voltage substations', IEE Proc. C, Gener., Transm. Distrib., 1984, 131, ( 9 , pp. 204-209 2 AMETANI, A.: 'Modified travelling wave techniques to solve electrical transients on lumped and distributed constant circuits', Proc. IEE, 1973,120, (4), pp. 497-504 3 COOPER, J., and HILEMAN, A.: 'A probabilistic approach in estimating the BIL for 1200 kV gas insulated stations'. CIGRE Session 1982, Paper 33-02 4 BAZUTKIN, V., LARIONOV, V., and PINTALJ, J.: 'High-voltage technique-Insulation and Overvoltages in Power Systems' (Moskva, Energoatomizdat 1986), pp. 258-266 (in Russian) 5 IEEE working group: 'A simplified method lor estimating lightning performance of transmission lines', IEEE Trans. Power Appara. Syst., 1983, PAS-164, (4), pp. 919-927
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6 THIONE, L.: 'The dielectric strength of large air insulation' in RAGALLER, K. (Ed.): 'Surges in High Voltage Networks' (Plenum Press, New York and London, 1979), pp. 197-200 7 'Laboratory testing of the insulator strings for unpoluted areas'. Internal report No. 1986, 'Energoinvest', Sarajevo, 1978 8 DOLGINOV, A.: 'High voltage technique in electrical power systems', Energy (Moskow), 1968, pp. 28CL282 9 BROWN, G.: 'Joint frequency distributions of stroke current rates of rise and crest magnitudes to transmission lines', IEEE Trans. Power Appara. Syst., 1978, PAS-97, (I), pp. 53-58 WHITEHEAD, E.: 'Protection of transmission lines' in GOLDE, R.H. (Ed.): 'Lightning', Vol. 2: 'Lightning protection' (Academic Press, London, 1977),pp. 699-706. BERGER, K.: 'Lightning surges' in RAGALLER, K. (Ed.): 'Surges in high voltage networks' (Plenum Press, New York and London, 1979), pp. 42-49 PLAZINIC, S.: 'Metereological parameters for transmission lines design', Engineering-transmission of El. Energy, 1978, (22), pp. 103115 (in Serbo-Croatian) 'Draft - Revision of the application guide for insulation coordination' (IEC Publication 71-2 and 71-3), IEC/TC-28, 1987, pp. 341C
JJ
14 Lightning Arrester type HMM, Minel Belgrade, Catalogue OP-50402-1/1980
