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Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding
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Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding Alberto Borghetti, Fabio Napolitano, Carlo Alberto Nucci, Fabio Tossani ∗ University of Bologna, Italy
a r t i c l e
i n f o
Article history: Received 15 May 2016 Received in revised form 19 October 2016 Accepted 7 December 2016 Available online xxx Keywords: Electromagnetic transients Lightning induced overvoltages Lightning protection Overhead distribution lines Surge arresters
a b s t r a c t The paper deals with the response of distribution networks to direct and indirect lightning. The response of the network is analyzed with the aim of inferring the mean time between failures of the connected transformers. This is accomplished taking into account the voltage at the utility frequency, the flashovers occurrence in the line insulators, the location of surge arresters, and the shielding provided by nearby buildings. Two different transformer failure criteria are assumed: a critical value and a disruptive effect model. The results make reference to multi-conductor overhead systems with two different topologies: simple straight line and a real feeder with laterals. It is shown that such a detailed lightning performance analysis is useful in order to select the most appropriate strategy for the installation of surge arresters, which may allow the achievement of the desired mean time between failures at affordable costs. © 2016 Published by Elsevier B.V.
1. Introduction The protection methods of medium voltage (MV) power distribution lines are described in the Cigré brochure 441 [1] and references therein, which account also economical aspects and power quality. One of the important issues to be addressed is the protection of the connected distribution transformers against lightning, which is in several cases accomplished by means of surge arresters (SAs). In this respect, the interest by power utilities to investigate the possibility of reducing the number of installed surge arresters is justified. This may be the case, for example, when the change of the neutral earthing method from solidly earthed to resonant one is planned [2], and the reduction of the number of installed surge arresters becomes therefore a possibility worth of investigation as, in principle, all SAs would need to be replaced. Such a reduction is possible only after the accurate assessment of the protection distance of the SAs, which has to make reference to the most realistic representation of the phenomena involved.
∗ Corresponding author. E-mail addresses: [email protected] (A. Borghetti), [email protected] (F. Napolitano), [email protected] (C.A. Nucci), [email protected] (F. Tossani).
In this study, the effectiveness of location of SAs for the protection of the connected medium voltage/low voltage (MV/LV) transformers has been assessed by developing a procedure able to take into account both direct and indirect lightning strikes, the bus voltage at the utility frequency, the flashovers occurrence in the line insulators, and the shielding provided by nearby buildings. This paper presents such a procedure and the results obtained for two different topologies: a simple straight line and a more complex one, represented by a feeder with laterals. Also, two different transformer failure criteria are assumed: a critical withstand voltage and a disruptive effect model. The structure of the paper is the following. Section 2 describes the main characteristics and assumptions of the calculation procedure. Section 3 presents the results of the analysis for the case of a straight multiconductor line with typical pole configuration. Section 4 presents the results for the case of a realistic feeder. Section 5 concludes the paper. 2. Calculation method and simulation environment The approach adopted for the estimation of the lightning performance is based on the application of the Monte Carlo method, as presented in Refs. [3,4]. The developed procedure can be summarized as follows. A large number ntot of lightning events is randomly generated. Each event is characterized by four parameters: lightning current amplitude Ip , time to peak tf and stroke location with
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coordinates x and y. The lightning current parameters are assumed to follow the Cigré log-normal probability distributions [5,6] for negative first strokes, with a correlation coefficient between tf and Ip equal to 0.47. The effects of the presence of positive flashes and of subsequent strokes in negative flashes on the lightning performance of the feeder are assumed to be negligible. The stroke locations are assumed to be uniformly distributed in a striking area, having a size large enough to contain the entire network and all the lightning events that could cause voltages larger than the minimum voltage value of interest for the analysis. In general (e.g. Ref. [7]), the lightning performance is expressed by means of a curve providing the expected annual numbers of lightning events Fp that cause voltages with amplitude larger than the insulation voltage value reported in abscissa: Fp =
n ANg ntot
(1)
where n is the number of events causing overvoltages higher than the considered insulation level, A is the striking area and Ng is the annual ground flash density (assumed equal to 1 flash/km2 /yr in the results shown in this paper). If referred to a single straight line, the lightning performance is usually expressed in terms of number of events per year per unit length of line (e.g., 100 km of line, as usually done for transmission lines). However, the indirect lightning performance of a network with complex topology (e.g. a distribution feeder with several laterals) may significantly deviate from the one of a straight line of equal length [4]. Therefore, since the project that motivates this paper is focused on the protection of MV/LV transformers, such a performance is here expressed with the expected values of mean time between failures (MTBF), which are given by the inverse of the relevant Fp values calculated by applying Eq. (1) to each MV bus where a transformer is connected, where n is calculated by comparing the lightning voltage with the relevant withstand voltage. The withstand voltage of the transformers is assumed to be known (in order to take into account the withstand probability distribution of transformer insulation a more complex procedure would need to be applied [8]). In this paper, the lightning current waveform at the channel base is approximated by a ramp up to the peak value Ip at time tf , followed by a constant value. In Ref. [9] a Monte Carlo procedure able to take into account the typical functions adopted to represent the waveform of the lightning current at the channel base (e.g., the Heidler function and the Cigré function) has been proposed. The comparison between the results obtained by using different current waveforms shows that the simple trapezoidal current waveform represents a good compromise between computational effort and conservative assessment of the lightning performance. 2.1. Calculation of the overvoltages due to indirect lightning events From the total set of ntot lightning events, the ones relevant to indirect lightning are selected by using a lightning incidence model for the line. For the calculations of this paper, we have adopted the electro-geometric model suggested in Ref. [7]. In the literature, several approaches have been proposed for the evaluation of the lightning electromagnetic pulse (LEMP) response of distribution networks (e.g., Nucci et al. [10], Orzan et al. [11], Høidalen [12], Perez et al. [13], Andreotti et al. [14]). To obtain the results shown in this paper, the calculation of the induced voltages caused by indirect lightning strikes are performed by using the LIOV–EMTP-RV code [15,16]. It allows for the evaluation of the voltages induced by lightning return strokes on multi-conductor overhead lines above lossy ground by using a finite-difference time-domain (FDTD) solution method of the
Agrawal et al. field-to-line coupling model [17]. The LEMP is calculated by using the analytical formulation presented in Ref. [18] with the assumption that the lightning return stroke current pulse propagates along a straight vertical channel according to the transmission line (TL) model [19]. The assumed value for the returnstroke propagation speed is 1.5 × 108 m/s. The lossy ground effect on the LEMP are accounted by means of the Cooray–Rubinstein formula [20–22]. The bus voltage at the utility frequency is taken into account by using the procedure described in Ref. [23]. In order to appraise the indirect lightning performance in a reasonably low computational time also for the case of large networks equipped with SAs, the heuristic technique proposed in Ref. [2] has been applied. The procedure avoids to perform the time-domain simulation for the events that are expected to be less harmful than previously calculated ones that have not caused flashovers, i.e., those characterized by lower Ip , greater tf and greater distance between the stroke location and the nearest SAs than a previously calculated event that causes a current in the SAs below a predefined minimum value (assumed equal to 100 A). SAs of 15 kV class are considered in the simulation and the relevant voltage–current characteristic is reported in Ref. [24]. 2.2. Calculation of the overvoltages due to direct lightning events The overvoltages corresponding to each of the events classified as direct strikes to a line conductor by using the electro-geometric model are calculated by using an EMTP-RV model. The direct strikes are represented by current sources connected to the pole closest to the randomly-generated stroke location coordinates. Direct strikes to distribution overhead lines are always expected to cause flashovers at line insulators, unless very close SAs are installed [7], even in presence of ground wires [25,26]. The overvoltages at buses not equipped by SAs are greatly influenced by the occurrence of flashovers at the line insulators and by the number of SAs along the path from the stricken point to the observed buses. The insulators flashovers is represented by means of ideal switches that close according to the disruptive effect criterion [27]: a flashover occurs if the time integral D of the line-to-ground voltage exceeds a given value DE. Integral D is given by the following expression
t k [|v(t)| − V0 ] dt
D=
(2)
t0
where v(t) is the voltage at the pole insulator, V0 is the minimum voltage to be exceeded before any breakdown process can start, k is a dimensionless factor, and t0 is the time at which |v(t)| becomes greater than V0 . The effect of soil ionization at the grounded poles is accounted by using the Weck’s approximation [6], with soil breakdown gradient taken equal to 400 kV/m. 3. Single multiconductor overhead distribution line with typical pole configuration Recent papers addressed the issue of the lightning performance of distribution lines appraisal taking into account both direct and indirect lightning events [28,29]. When assessing the lightning performance of distribution lines, major attention is in general devoted to calculation of the induced voltages from nearby strikes rather than to those caused by direct strikes to the line since the latter are all expected to cause a fault in the line. However, a detailed calculation of the overvoltages due to direct strikes is needed when for the evaluation of the expected frequency of faults at specific locations of medium voltage distribution networks [24].
Please cite this article in press as: A. Borghetti, et al., Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2016.12.009
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Fig. 1. Direct strike overvoltage at the stricken point in absence of SAs and flashovers.
Here, we consider a single line composed by three overhead conductors of diameter equal to 1 cm and assumed horizontally placed at 9.3 m above ground. The distances between the lateral conductors and the central one are 1.5 m and 0.7 m. The soil conductivity is equal to 1 mS/m. The grounding resistance provided by concrete poles not equipped by SAs is assumed equal to 400 . The SAs grounding resistance is equal to 10 . 3.1. Results of time domain simulations The distance between subsequent poles is 35 m. A set of three SAs is installed every 10 spans. The overall length of the line is 3.5 km. A direct lightning strike is assumed to hit the central phase in the middle point of the line (phase 2), equidistant to the nearest SAs locations. At each pole of the line the flashovers are simulated by means of ideal switches between the line conductors and the grounding resistance. The flashover switches close when the integral D in Eq. (2), equals DE, with k = 1, V0 = 164 kV and DE = 255 kV s for the insulators of the external phase conductors and V0 = 90 kV and DE = 60.9 kV s for the central one. These parameters are chosen according to the values proposed in Ref. [30] from the results of laboratory tests performed on a 15 kV pin-type ceramic insulator taking into account the 60 cm long wooden crossarm that supports each external insulator. A channel-base current with a peak value of 31 kA and a maximum time-derivative of 26 kA/s, assumed as typical of a first negative return stroke, is represented by using the Cigré current
3
functions [6]. The channel impedance is assumed equal to 1 k. The stroke location in the LEMP calculation is assumed to be 10 m far from the line, in order to avoid numerical singularities. Fig. 1 shows the overvoltages calculated at the stricken point of the line due to a direct event, under the assumptions of absence of SAs and flashovers. In Fig. 1 the solid thin line represents the direct overvoltage when the effect of the LEMP is neglected. In this paper, we focus on the study of negative flashes only; therefore, the polarity of the overvoltage is negative. The thin dashed line represents the effect of the LEMP, which polarity is opposite to the direct overvoltage. The LEMP effect on the direct overvoltage, therefore, appears to slightly decrease the voltage amplitude at the stricken point. Farther from the observation point, the peak of the induced voltage is expected to reduce quickly. At 350 m from the stricken point, the effect of the LEMP is no more appreciable if flashovers are neglected. Fig. 2 shows the overvoltage at a point 350 m far from the direct strike obtained by disregarding the effects of the LEMP. In Fig. 2a flashovers are disregarded, while in Fig. 2b they are accounted for. The flashovers occurrence along the line results in a decrease of the peak of the overvoltage. In Fig. 3 the same calculation is repeated considering the LEMP effect. The comparison between Figs. 2 and 3 shows that the influence of the LEMP on the line response to a direct strike is more evident in presence of flashovers. 3.2. Monte Carlo simulations In this section a 2 km-long three phase overhead line is considered. The distance between subsequent poles is 50 m. Striking area A is chosen as a 1 km band from the line. The number of generated events in the Monte Carlo procedure is 20,000. Direct events nd are 1208. Indirect events nd are 18,792. The considered rated voltage at the utility frequency is 13.8 kV. The results are reported for different distances d between consecutive SAs, namely 100 m, 200 m, 300 m and 400 m. The Monte Carlo analysis has been performed for two different CFO of the line insulators, namely 100 kV and 165 kV. The relevant disruptive effect models are implemented by adopting the following parameters for all the three phases: a) k = 1, V0 = 90 kV and DE = 60.9 kV s, for CFO equal to 100 kV; b) k = 1, V0 = 132 kV and DE = 255 kV s, for CFO equal to 165 kV. We assume the presence of a pole transformer in the middle point of the line. There are no SAs at the pole with the transformer and the adjacent poles with SAs are equidistant. The transformer
Fig. 2. Overvoltage at 350 m far from the stricken point, in absence of LEMP: (a) disregarding flashover occurrence, (b) taking into account flashover occurrence.
Please cite this article in press as: A. Borghetti, et al., Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2016.12.009
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Fig. 3. Overvoltage at 350 m far from the stricken point, with LEMP effect: (a) disregarding flashover occurrence, (b) taking into account flashover occurrence.
Table 1 MTBF (in years) of the transformer for different distances between consecutive SAs, CFO of the insulators and withstand voltage model. Insulators CFO
Transformer fault model
Without SA
With SA
d = 100 m
100 kV 165 kV 100 kV 165 kV
FMa FMa FMb FMb
d = 200 m
d = 300 m
d = 400 m
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
4.3 4.3 4.3 4.3
3.2 2.8 10.2 3.4
1.8 1.7 3.0 1.9
25.3 22.3 25.1 24.4
Inf Inf Inf Inf
25.3 22.3 25.1 24.4
9.9 11.5 13.0 13.0
250 333 1250 1000
9.6 11.1 12.9 12.8
6.9 7.7 9.2 8.8
87.7 89.3 294 217
6.4 7.1 9.0 8.5
5.2 5.7 6.6 6.3
39.7 41.3 96.2 76.9
4.6 5.0 6.2 5.8
failures are accounted in two different ways, indicated as FMa and FMb. FMa: the transformer failure is expected to occur if the voltage amplitude exceeds, independently from its duration, the withstand voltage of the transformers taken equal to 110 kV, as suggested in Ref. [31]. FMb: A disruptive effect model is adopted for assessing the transformers faults. The relevant parameters are V0 = 100.5 kV, k = 1 and DE = 40.9 kV s, which predict breakdown at 3 s and 8 s in case of standard lightning waveform with crest value equal to 121 kV and 110 kV, respectively. These time to breakdown values are chosen according to the volt-time curve recommended in [32,33], in per unit of the insulation level, for the case of 1 insulation failure out of 1000 applications. The transformer grounding resistance is assumed equal to 10 . Table 1 shows the mean time between failures (MTBF) values calculated for a transformer connected to the middle of the line for the two different insulators described, with CFO equal to 100 kV and 165 kV, respectively. For case FMa, Table 1 shows that with SAs at d = 200 m and above, the MTBF values calculated for insulator CFO = 165 kV are higher than those calculated for CFO = 100 kV, whilst the opposite happens without SAs or with d = 100 m. Such a difference is due to additional flashovers near the transformer for the case of 100 kV CFO insulators with respect to the case with 165 kV CFO insulators. The oscillatory transients originated by these insulator flashovers and by the associated reflections at the surrounding SAs cause voltages, at the transformer location, with peak value higher than without flashovers. These overvoltages may exceed the withstand voltage value, if the distance between the protective devices is significant, e.g. d = 200 m and above, as illustrated in Figs. 4 and 5. Fig. 4 refers to an indirect event (one of the generated Monte Carlo events) and Fig. 5 to a direct one. In particular, Fig. 4 shows the induced voltages at the three phase terminals of the transformer due to an indirect strike characterized by a trapezoidal wave-
form with the following parameters: Ip = 172.3 kA, tf = 21.26 s. The stroke location is 244 m from the transformer and 239 m from the line. The distance between consecutive SAs is d = 200 m. With CFO = 100 kV the pole closest to the stroke location experiences a flashover at about 27 s. At the transformer terminals, as shown in Fig. 4a, the reflections between the two SAs, on the right and on the left side, result in an overvoltage exceeding 120 kV, whilst without flashover (i.e., CFO = 165 kV) the overvoltage amplitude is lower than 100 kV as shown by Fig. 4b. Fig. 5 shows the overvoltages at the three phase terminals of the transformer due to a direct strike characterized by a trapezoidal waveform with the following parameters: Ip = 39.4 kA, tf = 8.4 s. The stroke location is 400 m from the transformer. The distance between consecutive SAs is d = 200 m. With CFO = 100 kV, the pole closest to the stroke location experience a flashover at about 26 s. At the transformer terminals, the reflections between the two SAs, on the right and on the left side, result in an overvoltage with a peak amplitude of about 120 kV (Fig. 5a) whilst without flashovers (i.e., CFO = 165 kV) the overvoltage does not exceed 100 kV (Fig. 5b). By applying FMa, the transformer failure is expected to occur if the voltage amplitude exceeds the withstand voltage of the transformers even for a very short time interval; the more complex transformer withstand model provided by FMb, instead, prevents the failure in case of spikes of overvoltages. Indeed, as shown in Table 1, with FMb the MTBF values calculated for CFO = 100 kV are always larger than in the case of CFO = 165 kV, so the insulator flashovers provide some protection to the transformer.
4. Real distribution network This Section describes the evaluation of the lightning performance of a real three-phase distribution 13.8 kV feeder located in Brazil. The feeder is composed mainly by three-phase overhead lines, with the configuration described in the previous Section, for a total length of almost 13.9 km. The span between subsequent poles
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Fig. 4. Indirect lightning event: (a) line CFO = 100 kV; (b) line CFO = 165 kV.
Fig. 5. Direct lightning event: (a) CFO = 100 kV; (b) CFO = 165 kV.
is 40 m. The topology has been acquired directly from the geographic information system (GIS) data of the network, with only a small adjustment so that the length of each line is an integer multiple of the spatial integration step of the FDTD algorithm chosen equal to 5 m. The network topology is shown in Fig. 6. The primary substation is located at the origin of the coordinate system. The total number of MV/LV transformers is 80, 55 of which are utility transformers and 25 are of private customers. We describe here the results of the calculations for a configuration in which the SAs are installed at the MV terminals of all the private transformers and at the terminals of 16 out 55 utility transformers as shown in Fig. 6. Additional results have been presented in Ref. [2]. Insulator flashovers are represented by using the disruptive effect model described in Section 3.1. The failures of the transformers are calculated by assuming the simplified criterion named FMa in the previous Section. The presence of buildings, trees and other structures close to the overhead line is expected to reduce the number of direct strikes to the line conductors. This reduction is represented by using an environmental shielding factor Sf , i.e. the per-unit portion of the distribution line shielded by nearby objects [7]. The calculations have been repeated for three different values: Sf = 0 (no shield-
ing), Sf = 0.91 (that corresponds to the case of shielding provided by objects having the same height of the lines) and Sf = 1 (complete shielding provided by taller nearby objects). The effects on the lightning performance of the direct events that do not hit the line thanks to the environmental shielding are accounted for by calculating the voltages induced by the LEMP, which for simplicity is considered not affected by the metallic parts of the objects and by the multiple reflections along the struck objects.1 For the cases with Sf greater than 0, the shielding objects are assumed to be uniformly distributed in the whole area and placed at distance d = 10 m from the overhead lines. The events with a randomly-generated stroke location at a distance di ≤ d are repositioned at a distance equal to d. The total number of Monte Carlo events is ntot = 200,000, 14,685 of which are direct strikes to line conductors. The events are generated uniformly over a striking area A = 19 km2 with borders at least 1 km far from the network.
1 The influence of the attenuation of the LEMP due to the presence of the buildings is dealt with in e.g., Refs. [35–37], and references therein.
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Fig. 6. Top view of the network topology. Locations of the distribution transformers and SAs.
Fig. 7. Influence of different environmental shielding factors Sf on the number of unprotected transformers with MTBF value lower than abscissa calculated for transformer withstand voltage equal to 110 kV and g = 1 mS/m.
The number of time-domain simulated events is 60,471 out of the 185,315 indirect ones. The reduction in the number of simulations is due the application of the heuristic technique described in Section 2 that allows a calculation time reduction of about 67%. Fig. 7 shows the effect of the environmental shielding factor Sf on the MTBF values of the transformers not equipped with SAs. The MTBF are calculated taking into account both direct and indirect lightning, for the case of Sf = 0, Sf = 1 and Sf = 0.91, respectively, and they refer to transformer withstand voltage = 110 kV and ground conductivity g = 1 mS/m. The possibility to defer the installation of SAs in some transformers is strongly dependent on the Sf value. Fig. 8 compares the results obtained for different withstand voltage values of the transformers. The assumed environmental
shielding factor is Sf = 1 and the ground conductivity is g = 1 mS/m. The withstand voltage of the transformers has a significant effect on the MTBF values: the number of transformers with MTBF value lower than 20 years is 29, 26, 19 and 7 for withstand voltage equal to 95, 110, 125 and 150 kV, respectively. The same calculations have been repeated for a higher value of the ground conductivity ( g = 10 mS/m) and the results are summarized in Figs. 9 and 10. The higher soil conductivity results in higher MTBF values for the unprotected transformers. As an example, by assuming Sf = 1 and withstand voltage = 110 kV, the number of transformers with MTBF value lower than 20 years is 26 for g = 1 mS/m and 7 for g = 10 mS/m.
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Fig. 8. Influence of the different withstand voltage values of the transformers on the number of unprotected transformers with MTBF value lower than abscissa calculated for Sf = 1 and g = 1 mS/m.
Fig. 9. Influence of different environmental shielding factors Sf on the number of unprotected transformers with MTBF value lower than abscissa calculated for transformer withstand voltage equal to 110 kV and g = 10 mS/m.
5. Conclusions In this paper the influence of the location and characteristics of surge arresters (SAs) on the MTBF values of the MV/LV transformers connected to distribution lines is analyzed by means of a Monte Carlo approach taking into account both direct and indirect lightning strikes to the line conductors, the bus voltage at the utility frequency, the flashovers occurrence in the line insulators, and the shielding of nearby buildings. The analysis has been carried out for the case of a single multiconductor line and of a real feeder with complex topology. The results obtained show that it is only by means of a detailed lightning performance analysis that it is possible to select the most appropriate strategy for the installation of SAs. It has been shown that insulator flashovers and the operation of nearby SAs can provide some protection to transformers not
equipped with SA. The representation of the transformer failure is of importance, as it has an effect on the MTBF assessment. The results obtained for the real feeder show that, for the case of high values of environmental shielding factors and high values of ground conductivity, it is possible to obtain an acceptable protection level even by avoiding the installation of the SAs at some transformers.
Acknowledgments This paper has further analyzed and characterized some of the results that have been obtained in the framework of a research project carried out in collaboration with the colleagues of the Federal University of Itajubá (Brazil) and AES Sul (Brazil): Gustavo Paiva Lopes and Manuel Luis Barreira Martinez (Federal University of Itajubá), Donorvan R. Fagundes, Gilnei J. G. Dos Santos, and Juliana
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Fig. 10. Influence of the different withstand voltage values of the transformers on the number of unprotected transformers with MTBF value lower than abscissa calculated for Sf = 1 and g = 10 mS/m.
Izabel Lara Uchôa (AES Sul). A preliminary version of this paper has been presented at the 2015 International Symposium on Lightning Protection (SIPDA) [34].
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[15] F. Napolitano, A. Borghetti, C.A. Nucci, M. Paolone, F. Rachidi, J. Mahseredjian, An advanced interface between the LIOV code and the EMTP-RV, in: Proc. 29th Int. Conf. Light. Prot., Uppsala, Sweden, 2008. [16] C.A. Nucci, F. Rachidi, Interaction of electromagnetic fields generated by lightning with overhead electrical networks, in: V. Cooray (Ed.), Light. Flash. 2nd ed., IET—Power and Energy Series, vol. 69, 2014, pp. 559–610. [17] A.K. Agrawal, H.J. Price, S.H. Gurbaxani, Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field, IEEE Trans. Electromagn. Compat. EMC-22 (1980) 119–129. [18] F. Napolitano, An analytical formulation of the electromagnetic field generated by lightning return strokes, IEEE Trans. Electromagn. Compat. 53 (2011) 108–113. [19] M.A. Uman, D.K. Mclain, Magnetic field of lightning return stroke, J. Geophys. Res. 74 (1969) 6899–6910. [20] V. Cooray, Horizontal fields generated by return strokes, Radio Sci. 27 (1992) 529–537. [21] M. Rubinstein, An approximate formula for the calculation of the horizontal electric field from lightning at close intermediate, and long range, IEEE Trans. Electromagn. Compat. 38 (1996) 531–535. [22] V. Cooray, Some considerations on the Cooray–Rubinstein formulation used in deriving the horizontal electric field of lightning return strokes over finitely conducting ground, IEEE Trans. Electromagn. Compat. 44 (2002) 560–566. [23] F. Napolitano, A. Borghetti, C.A. Nucci, M.L.B. Martinez, G.P. Lopes, G.J.G. Dos Santos, Protection against lightning overvoltages in resonant grounded power distribution networks, Electr. Power Syst. Res. 113 (2014) 121–128. [24] F. Tossani, F. Napolitano, A. Borghetti, C.A. Nucci, G.P. Lopes, M.L.B. Martinez, G.J.G. dos Santos, Estimation of the influence of direct strokes on the lightning performance of overhead distribution lines, in: 2015 IEEE Eindhoven PowerTech Conf., Eindhoven, Netherlands, 2015. [25] K. Nakada, H. Sugimoto, S. Yokoyama, Experimental facility for investigation of lightning performance of distribution lines, IEEE Trans. Power Deliv. 18 (2003) 253–257. [26] T. Miyazaki, S. Okabe, A detailed field study of lightning stroke effects on distribution lines, IEEE Trans. Power Deliv. 24 (2009) 352–359. [27] M. Darveniza, A.E. Vlastos, The generalized integration method for predicting impulse volt-time characteristics for non-standard wave shapes—a theoretical basis, IEEE Trans. Electr. Insul. 23 (1988) 373–381. [28] P.N. Mikropoulos, T.E. Tsovilis, Statistical method for the evaluation of the lightning performance of overhead distribution lines, IEEE Trans. Dielectr. Electr. Insul. 20 (2013) 202–211. [29] J. Chen, M. Zhu, Calculation of lightning flashover rates of overhead distribution lines considering direct and indirect strokes, IEEE Trans. Electromagn. Compat. 56 (2014) 668–674. [30] A. De Conti, E. Perez, E. Soto, F.H. Silveira, S.S. Visacro, H. Torres, Calculation of lightning-induced voltages on overhead distribution lines including insulation breakdown, IEEE Trans. Power Deliv. 25 (2010) 3078–3084. [31] IEEE Standard for insulation coordination—definitions, principles, and rules, IEEE Std C62.82, 1-2010 (Revision IEEE Std 1313.1-1996) (2011). [32] P.M. Balma, R.C. Degeneff, H.R. Moore, L.B. Wagenaar, The effects of long term operation and system conditions on the dielectric capability and insulation coordination of large power transformers, IEEE Trans. Power Deliv. 14 (1999) 960–971.
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[33] IEEE Guide to describe the occurrence and mitigation of switching transients induced by transformers, switching device, and system interaction, IEEE Std C57, 142-2010 (2011). [34] A. Borghetti, F. Napolitano, C.A. Nucci, F. Tossani, Advancements in insulation coordination for improving lightning performance of distribution lines, 2015 Int. Symp. Light. Prot. (XIII SIPDA) (2015) 21–31. [35] A. Piantini, J.M. Janiszewski, A. Borghetti, C.A. Nucci, M. Paolone, A scale model for the study of the LEMP response of complex power distribution networks, IEEE Trans. Power Deliv. 22 (2007) 710–720.
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[36] A. Borghetti, F. Napolitano, C.A. Nucci, M. Paolone, Effects of nearby buildings on lightning induced voltages on overhead power distribution lines, Electr. Power Syst. Res. 94 (2013) 38–45. [37] F. Tossani, A. Borghetti, F. Napolitano, C.A. Nucci, A. Piantini, Lightning induced overvoltages on overhead lines shielded by nearby buildings, in: Proc. 33rd Int. Conf. Light. Prot., Estoril, Portugal, 2016.
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Contents lists available at ScienceDirect
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Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding Alberto Borghetti, Fabio Napolitano, Carlo Alberto Nucci, Fabio Tossani ∗ University of Bologna, Italy
a r t i c l e
i n f o
Article history: Received 15 May 2016 Received in revised form 19 October 2016 Accepted 7 December 2016 Available online xxx Keywords: Electromagnetic transients Lightning induced overvoltages Lightning protection Overhead distribution lines Surge arresters
a b s t r a c t The paper deals with the response of distribution networks to direct and indirect lightning. The response of the network is analyzed with the aim of inferring the mean time between failures of the connected transformers. This is accomplished taking into account the voltage at the utility frequency, the flashovers occurrence in the line insulators, the location of surge arresters, and the shielding provided by nearby buildings. Two different transformer failure criteria are assumed: a critical value and a disruptive effect model. The results make reference to multi-conductor overhead systems with two different topologies: simple straight line and a real feeder with laterals. It is shown that such a detailed lightning performance analysis is useful in order to select the most appropriate strategy for the installation of surge arresters, which may allow the achievement of the desired mean time between failures at affordable costs. © 2016 Published by Elsevier B.V.
1. Introduction The protection methods of medium voltage (MV) power distribution lines are described in the Cigré brochure 441 [1] and references therein, which account also economical aspects and power quality. One of the important issues to be addressed is the protection of the connected distribution transformers against lightning, which is in several cases accomplished by means of surge arresters (SAs). In this respect, the interest by power utilities to investigate the possibility of reducing the number of installed surge arresters is justified. This may be the case, for example, when the change of the neutral earthing method from solidly earthed to resonant one is planned [2], and the reduction of the number of installed surge arresters becomes therefore a possibility worth of investigation as, in principle, all SAs would need to be replaced. Such a reduction is possible only after the accurate assessment of the protection distance of the SAs, which has to make reference to the most realistic representation of the phenomena involved.
∗ Corresponding author. E-mail addresses: [email protected] (A. Borghetti), [email protected] (F. Napolitano), [email protected] (C.A. Nucci), [email protected] (F. Tossani).
In this study, the effectiveness of location of SAs for the protection of the connected medium voltage/low voltage (MV/LV) transformers has been assessed by developing a procedure able to take into account both direct and indirect lightning strikes, the bus voltage at the utility frequency, the flashovers occurrence in the line insulators, and the shielding provided by nearby buildings. This paper presents such a procedure and the results obtained for two different topologies: a simple straight line and a more complex one, represented by a feeder with laterals. Also, two different transformer failure criteria are assumed: a critical withstand voltage and a disruptive effect model. The structure of the paper is the following. Section 2 describes the main characteristics and assumptions of the calculation procedure. Section 3 presents the results of the analysis for the case of a straight multiconductor line with typical pole configuration. Section 4 presents the results for the case of a realistic feeder. Section 5 concludes the paper. 2. Calculation method and simulation environment The approach adopted for the estimation of the lightning performance is based on the application of the Monte Carlo method, as presented in Refs. [3,4]. The developed procedure can be summarized as follows. A large number ntot of lightning events is randomly generated. Each event is characterized by four parameters: lightning current amplitude Ip , time to peak tf and stroke location with
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coordinates x and y. The lightning current parameters are assumed to follow the Cigré log-normal probability distributions [5,6] for negative first strokes, with a correlation coefficient between tf and Ip equal to 0.47. The effects of the presence of positive flashes and of subsequent strokes in negative flashes on the lightning performance of the feeder are assumed to be negligible. The stroke locations are assumed to be uniformly distributed in a striking area, having a size large enough to contain the entire network and all the lightning events that could cause voltages larger than the minimum voltage value of interest for the analysis. In general (e.g. Ref. [7]), the lightning performance is expressed by means of a curve providing the expected annual numbers of lightning events Fp that cause voltages with amplitude larger than the insulation voltage value reported in abscissa: Fp =
n ANg ntot
(1)
where n is the number of events causing overvoltages higher than the considered insulation level, A is the striking area and Ng is the annual ground flash density (assumed equal to 1 flash/km2 /yr in the results shown in this paper). If referred to a single straight line, the lightning performance is usually expressed in terms of number of events per year per unit length of line (e.g., 100 km of line, as usually done for transmission lines). However, the indirect lightning performance of a network with complex topology (e.g. a distribution feeder with several laterals) may significantly deviate from the one of a straight line of equal length [4]. Therefore, since the project that motivates this paper is focused on the protection of MV/LV transformers, such a performance is here expressed with the expected values of mean time between failures (MTBF), which are given by the inverse of the relevant Fp values calculated by applying Eq. (1) to each MV bus where a transformer is connected, where n is calculated by comparing the lightning voltage with the relevant withstand voltage. The withstand voltage of the transformers is assumed to be known (in order to take into account the withstand probability distribution of transformer insulation a more complex procedure would need to be applied [8]). In this paper, the lightning current waveform at the channel base is approximated by a ramp up to the peak value Ip at time tf , followed by a constant value. In Ref. [9] a Monte Carlo procedure able to take into account the typical functions adopted to represent the waveform of the lightning current at the channel base (e.g., the Heidler function and the Cigré function) has been proposed. The comparison between the results obtained by using different current waveforms shows that the simple trapezoidal current waveform represents a good compromise between computational effort and conservative assessment of the lightning performance. 2.1. Calculation of the overvoltages due to indirect lightning events From the total set of ntot lightning events, the ones relevant to indirect lightning are selected by using a lightning incidence model for the line. For the calculations of this paper, we have adopted the electro-geometric model suggested in Ref. [7]. In the literature, several approaches have been proposed for the evaluation of the lightning electromagnetic pulse (LEMP) response of distribution networks (e.g., Nucci et al. [10], Orzan et al. [11], Høidalen [12], Perez et al. [13], Andreotti et al. [14]). To obtain the results shown in this paper, the calculation of the induced voltages caused by indirect lightning strikes are performed by using the LIOV–EMTP-RV code [15,16]. It allows for the evaluation of the voltages induced by lightning return strokes on multi-conductor overhead lines above lossy ground by using a finite-difference time-domain (FDTD) solution method of the
Agrawal et al. field-to-line coupling model [17]. The LEMP is calculated by using the analytical formulation presented in Ref. [18] with the assumption that the lightning return stroke current pulse propagates along a straight vertical channel according to the transmission line (TL) model [19]. The assumed value for the returnstroke propagation speed is 1.5 × 108 m/s. The lossy ground effect on the LEMP are accounted by means of the Cooray–Rubinstein formula [20–22]. The bus voltage at the utility frequency is taken into account by using the procedure described in Ref. [23]. In order to appraise the indirect lightning performance in a reasonably low computational time also for the case of large networks equipped with SAs, the heuristic technique proposed in Ref. [2] has been applied. The procedure avoids to perform the time-domain simulation for the events that are expected to be less harmful than previously calculated ones that have not caused flashovers, i.e., those characterized by lower Ip , greater tf and greater distance between the stroke location and the nearest SAs than a previously calculated event that causes a current in the SAs below a predefined minimum value (assumed equal to 100 A). SAs of 15 kV class are considered in the simulation and the relevant voltage–current characteristic is reported in Ref. [24]. 2.2. Calculation of the overvoltages due to direct lightning events The overvoltages corresponding to each of the events classified as direct strikes to a line conductor by using the electro-geometric model are calculated by using an EMTP-RV model. The direct strikes are represented by current sources connected to the pole closest to the randomly-generated stroke location coordinates. Direct strikes to distribution overhead lines are always expected to cause flashovers at line insulators, unless very close SAs are installed [7], even in presence of ground wires [25,26]. The overvoltages at buses not equipped by SAs are greatly influenced by the occurrence of flashovers at the line insulators and by the number of SAs along the path from the stricken point to the observed buses. The insulators flashovers is represented by means of ideal switches that close according to the disruptive effect criterion [27]: a flashover occurs if the time integral D of the line-to-ground voltage exceeds a given value DE. Integral D is given by the following expression
t k [|v(t)| − V0 ] dt
D=
(2)
t0
where v(t) is the voltage at the pole insulator, V0 is the minimum voltage to be exceeded before any breakdown process can start, k is a dimensionless factor, and t0 is the time at which |v(t)| becomes greater than V0 . The effect of soil ionization at the grounded poles is accounted by using the Weck’s approximation [6], with soil breakdown gradient taken equal to 400 kV/m. 3. Single multiconductor overhead distribution line with typical pole configuration Recent papers addressed the issue of the lightning performance of distribution lines appraisal taking into account both direct and indirect lightning events [28,29]. When assessing the lightning performance of distribution lines, major attention is in general devoted to calculation of the induced voltages from nearby strikes rather than to those caused by direct strikes to the line since the latter are all expected to cause a fault in the line. However, a detailed calculation of the overvoltages due to direct strikes is needed when for the evaluation of the expected frequency of faults at specific locations of medium voltage distribution networks [24].
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Fig. 1. Direct strike overvoltage at the stricken point in absence of SAs and flashovers.
Here, we consider a single line composed by three overhead conductors of diameter equal to 1 cm and assumed horizontally placed at 9.3 m above ground. The distances between the lateral conductors and the central one are 1.5 m and 0.7 m. The soil conductivity is equal to 1 mS/m. The grounding resistance provided by concrete poles not equipped by SAs is assumed equal to 400 . The SAs grounding resistance is equal to 10 . 3.1. Results of time domain simulations The distance between subsequent poles is 35 m. A set of three SAs is installed every 10 spans. The overall length of the line is 3.5 km. A direct lightning strike is assumed to hit the central phase in the middle point of the line (phase 2), equidistant to the nearest SAs locations. At each pole of the line the flashovers are simulated by means of ideal switches between the line conductors and the grounding resistance. The flashover switches close when the integral D in Eq. (2), equals DE, with k = 1, V0 = 164 kV and DE = 255 kV s for the insulators of the external phase conductors and V0 = 90 kV and DE = 60.9 kV s for the central one. These parameters are chosen according to the values proposed in Ref. [30] from the results of laboratory tests performed on a 15 kV pin-type ceramic insulator taking into account the 60 cm long wooden crossarm that supports each external insulator. A channel-base current with a peak value of 31 kA and a maximum time-derivative of 26 kA/s, assumed as typical of a first negative return stroke, is represented by using the Cigré current
3
functions [6]. The channel impedance is assumed equal to 1 k. The stroke location in the LEMP calculation is assumed to be 10 m far from the line, in order to avoid numerical singularities. Fig. 1 shows the overvoltages calculated at the stricken point of the line due to a direct event, under the assumptions of absence of SAs and flashovers. In Fig. 1 the solid thin line represents the direct overvoltage when the effect of the LEMP is neglected. In this paper, we focus on the study of negative flashes only; therefore, the polarity of the overvoltage is negative. The thin dashed line represents the effect of the LEMP, which polarity is opposite to the direct overvoltage. The LEMP effect on the direct overvoltage, therefore, appears to slightly decrease the voltage amplitude at the stricken point. Farther from the observation point, the peak of the induced voltage is expected to reduce quickly. At 350 m from the stricken point, the effect of the LEMP is no more appreciable if flashovers are neglected. Fig. 2 shows the overvoltage at a point 350 m far from the direct strike obtained by disregarding the effects of the LEMP. In Fig. 2a flashovers are disregarded, while in Fig. 2b they are accounted for. The flashovers occurrence along the line results in a decrease of the peak of the overvoltage. In Fig. 3 the same calculation is repeated considering the LEMP effect. The comparison between Figs. 2 and 3 shows that the influence of the LEMP on the line response to a direct strike is more evident in presence of flashovers. 3.2. Monte Carlo simulations In this section a 2 km-long three phase overhead line is considered. The distance between subsequent poles is 50 m. Striking area A is chosen as a 1 km band from the line. The number of generated events in the Monte Carlo procedure is 20,000. Direct events nd are 1208. Indirect events nd are 18,792. The considered rated voltage at the utility frequency is 13.8 kV. The results are reported for different distances d between consecutive SAs, namely 100 m, 200 m, 300 m and 400 m. The Monte Carlo analysis has been performed for two different CFO of the line insulators, namely 100 kV and 165 kV. The relevant disruptive effect models are implemented by adopting the following parameters for all the three phases: a) k = 1, V0 = 90 kV and DE = 60.9 kV s, for CFO equal to 100 kV; b) k = 1, V0 = 132 kV and DE = 255 kV s, for CFO equal to 165 kV. We assume the presence of a pole transformer in the middle point of the line. There are no SAs at the pole with the transformer and the adjacent poles with SAs are equidistant. The transformer
Fig. 2. Overvoltage at 350 m far from the stricken point, in absence of LEMP: (a) disregarding flashover occurrence, (b) taking into account flashover occurrence.
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Fig. 3. Overvoltage at 350 m far from the stricken point, with LEMP effect: (a) disregarding flashover occurrence, (b) taking into account flashover occurrence.
Table 1 MTBF (in years) of the transformer for different distances between consecutive SAs, CFO of the insulators and withstand voltage model. Insulators CFO
Transformer fault model
Without SA
With SA
d = 100 m
100 kV 165 kV 100 kV 165 kV
FMa FMa FMb FMb
d = 200 m
d = 300 m
d = 400 m
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
Direct
Indirect
Both
4.3 4.3 4.3 4.3
3.2 2.8 10.2 3.4
1.8 1.7 3.0 1.9
25.3 22.3 25.1 24.4
Inf Inf Inf Inf
25.3 22.3 25.1 24.4
9.9 11.5 13.0 13.0
250 333 1250 1000
9.6 11.1 12.9 12.8
6.9 7.7 9.2 8.8
87.7 89.3 294 217
6.4 7.1 9.0 8.5
5.2 5.7 6.6 6.3
39.7 41.3 96.2 76.9
4.6 5.0 6.2 5.8
failures are accounted in two different ways, indicated as FMa and FMb. FMa: the transformer failure is expected to occur if the voltage amplitude exceeds, independently from its duration, the withstand voltage of the transformers taken equal to 110 kV, as suggested in Ref. [31]. FMb: A disruptive effect model is adopted for assessing the transformers faults. The relevant parameters are V0 = 100.5 kV, k = 1 and DE = 40.9 kV s, which predict breakdown at 3 s and 8 s in case of standard lightning waveform with crest value equal to 121 kV and 110 kV, respectively. These time to breakdown values are chosen according to the volt-time curve recommended in [32,33], in per unit of the insulation level, for the case of 1 insulation failure out of 1000 applications. The transformer grounding resistance is assumed equal to 10 . Table 1 shows the mean time between failures (MTBF) values calculated for a transformer connected to the middle of the line for the two different insulators described, with CFO equal to 100 kV and 165 kV, respectively. For case FMa, Table 1 shows that with SAs at d = 200 m and above, the MTBF values calculated for insulator CFO = 165 kV are higher than those calculated for CFO = 100 kV, whilst the opposite happens without SAs or with d = 100 m. Such a difference is due to additional flashovers near the transformer for the case of 100 kV CFO insulators with respect to the case with 165 kV CFO insulators. The oscillatory transients originated by these insulator flashovers and by the associated reflections at the surrounding SAs cause voltages, at the transformer location, with peak value higher than without flashovers. These overvoltages may exceed the withstand voltage value, if the distance between the protective devices is significant, e.g. d = 200 m and above, as illustrated in Figs. 4 and 5. Fig. 4 refers to an indirect event (one of the generated Monte Carlo events) and Fig. 5 to a direct one. In particular, Fig. 4 shows the induced voltages at the three phase terminals of the transformer due to an indirect strike characterized by a trapezoidal wave-
form with the following parameters: Ip = 172.3 kA, tf = 21.26 s. The stroke location is 244 m from the transformer and 239 m from the line. The distance between consecutive SAs is d = 200 m. With CFO = 100 kV the pole closest to the stroke location experiences a flashover at about 27 s. At the transformer terminals, as shown in Fig. 4a, the reflections between the two SAs, on the right and on the left side, result in an overvoltage exceeding 120 kV, whilst without flashover (i.e., CFO = 165 kV) the overvoltage amplitude is lower than 100 kV as shown by Fig. 4b. Fig. 5 shows the overvoltages at the three phase terminals of the transformer due to a direct strike characterized by a trapezoidal waveform with the following parameters: Ip = 39.4 kA, tf = 8.4 s. The stroke location is 400 m from the transformer. The distance between consecutive SAs is d = 200 m. With CFO = 100 kV, the pole closest to the stroke location experience a flashover at about 26 s. At the transformer terminals, the reflections between the two SAs, on the right and on the left side, result in an overvoltage with a peak amplitude of about 120 kV (Fig. 5a) whilst without flashovers (i.e., CFO = 165 kV) the overvoltage does not exceed 100 kV (Fig. 5b). By applying FMa, the transformer failure is expected to occur if the voltage amplitude exceeds the withstand voltage of the transformers even for a very short time interval; the more complex transformer withstand model provided by FMb, instead, prevents the failure in case of spikes of overvoltages. Indeed, as shown in Table 1, with FMb the MTBF values calculated for CFO = 100 kV are always larger than in the case of CFO = 165 kV, so the insulator flashovers provide some protection to the transformer.
4. Real distribution network This Section describes the evaluation of the lightning performance of a real three-phase distribution 13.8 kV feeder located in Brazil. The feeder is composed mainly by three-phase overhead lines, with the configuration described in the previous Section, for a total length of almost 13.9 km. The span between subsequent poles
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Fig. 4. Indirect lightning event: (a) line CFO = 100 kV; (b) line CFO = 165 kV.
Fig. 5. Direct lightning event: (a) CFO = 100 kV; (b) CFO = 165 kV.
is 40 m. The topology has been acquired directly from the geographic information system (GIS) data of the network, with only a small adjustment so that the length of each line is an integer multiple of the spatial integration step of the FDTD algorithm chosen equal to 5 m. The network topology is shown in Fig. 6. The primary substation is located at the origin of the coordinate system. The total number of MV/LV transformers is 80, 55 of which are utility transformers and 25 are of private customers. We describe here the results of the calculations for a configuration in which the SAs are installed at the MV terminals of all the private transformers and at the terminals of 16 out 55 utility transformers as shown in Fig. 6. Additional results have been presented in Ref. [2]. Insulator flashovers are represented by using the disruptive effect model described in Section 3.1. The failures of the transformers are calculated by assuming the simplified criterion named FMa in the previous Section. The presence of buildings, trees and other structures close to the overhead line is expected to reduce the number of direct strikes to the line conductors. This reduction is represented by using an environmental shielding factor Sf , i.e. the per-unit portion of the distribution line shielded by nearby objects [7]. The calculations have been repeated for three different values: Sf = 0 (no shield-
ing), Sf = 0.91 (that corresponds to the case of shielding provided by objects having the same height of the lines) and Sf = 1 (complete shielding provided by taller nearby objects). The effects on the lightning performance of the direct events that do not hit the line thanks to the environmental shielding are accounted for by calculating the voltages induced by the LEMP, which for simplicity is considered not affected by the metallic parts of the objects and by the multiple reflections along the struck objects.1 For the cases with Sf greater than 0, the shielding objects are assumed to be uniformly distributed in the whole area and placed at distance d = 10 m from the overhead lines. The events with a randomly-generated stroke location at a distance di ≤ d are repositioned at a distance equal to d. The total number of Monte Carlo events is ntot = 200,000, 14,685 of which are direct strikes to line conductors. The events are generated uniformly over a striking area A = 19 km2 with borders at least 1 km far from the network.
1 The influence of the attenuation of the LEMP due to the presence of the buildings is dealt with in e.g., Refs. [35–37], and references therein.
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Fig. 6. Top view of the network topology. Locations of the distribution transformers and SAs.
Fig. 7. Influence of different environmental shielding factors Sf on the number of unprotected transformers with MTBF value lower than abscissa calculated for transformer withstand voltage equal to 110 kV and g = 1 mS/m.
The number of time-domain simulated events is 60,471 out of the 185,315 indirect ones. The reduction in the number of simulations is due the application of the heuristic technique described in Section 2 that allows a calculation time reduction of about 67%. Fig. 7 shows the effect of the environmental shielding factor Sf on the MTBF values of the transformers not equipped with SAs. The MTBF are calculated taking into account both direct and indirect lightning, for the case of Sf = 0, Sf = 1 and Sf = 0.91, respectively, and they refer to transformer withstand voltage = 110 kV and ground conductivity g = 1 mS/m. The possibility to defer the installation of SAs in some transformers is strongly dependent on the Sf value. Fig. 8 compares the results obtained for different withstand voltage values of the transformers. The assumed environmental
shielding factor is Sf = 1 and the ground conductivity is g = 1 mS/m. The withstand voltage of the transformers has a significant effect on the MTBF values: the number of transformers with MTBF value lower than 20 years is 29, 26, 19 and 7 for withstand voltage equal to 95, 110, 125 and 150 kV, respectively. The same calculations have been repeated for a higher value of the ground conductivity ( g = 10 mS/m) and the results are summarized in Figs. 9 and 10. The higher soil conductivity results in higher MTBF values for the unprotected transformers. As an example, by assuming Sf = 1 and withstand voltage = 110 kV, the number of transformers with MTBF value lower than 20 years is 26 for g = 1 mS/m and 7 for g = 10 mS/m.
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Fig. 8. Influence of the different withstand voltage values of the transformers on the number of unprotected transformers with MTBF value lower than abscissa calculated for Sf = 1 and g = 1 mS/m.
Fig. 9. Influence of different environmental shielding factors Sf on the number of unprotected transformers with MTBF value lower than abscissa calculated for transformer withstand voltage equal to 110 kV and g = 10 mS/m.
5. Conclusions In this paper the influence of the location and characteristics of surge arresters (SAs) on the MTBF values of the MV/LV transformers connected to distribution lines is analyzed by means of a Monte Carlo approach taking into account both direct and indirect lightning strikes to the line conductors, the bus voltage at the utility frequency, the flashovers occurrence in the line insulators, and the shielding of nearby buildings. The analysis has been carried out for the case of a single multiconductor line and of a real feeder with complex topology. The results obtained show that it is only by means of a detailed lightning performance analysis that it is possible to select the most appropriate strategy for the installation of SAs. It has been shown that insulator flashovers and the operation of nearby SAs can provide some protection to transformers not
equipped with SA. The representation of the transformer failure is of importance, as it has an effect on the MTBF assessment. The results obtained for the real feeder show that, for the case of high values of environmental shielding factors and high values of ground conductivity, it is possible to obtain an acceptable protection level even by avoiding the installation of the SAs at some transformers.
Acknowledgments This paper has further analyzed and characterized some of the results that have been obtained in the framework of a research project carried out in collaboration with the colleagues of the Federal University of Itajubá (Brazil) and AES Sul (Brazil): Gustavo Paiva Lopes and Manuel Luis Barreira Martinez (Federal University of Itajubá), Donorvan R. Fagundes, Gilnei J. G. Dos Santos, and Juliana
Please cite this article in press as: A. Borghetti, et al., Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2016.12.009
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Fig. 10. Influence of the different withstand voltage values of the transformers on the number of unprotected transformers with MTBF value lower than abscissa calculated for Sf = 1 and g = 10 mS/m.
Izabel Lara Uchôa (AES Sul). A preliminary version of this paper has been presented at the 2015 International Symposium on Lightning Protection (SIPDA) [34].
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Please cite this article in press as: A. Borghetti, et al., Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2016.12.009