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Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach
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Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach Fernando H. Silveira ∗ , Silvério Visacro, Ronaldo E. Souza LRC – Lightning Research Center, UFMG – Federal University of Minas Gerais, Brazil
a r t i c l e
i n f o
Article history: Received 14 April 2016 Received in revised form 26 August 2016 Accepted 3 January 2017 Available online xxx Keywords: Backflashover Grounding Lightning performance of transmission lines Traditional methodologies
a b s t r a c t This paper presents a critical review of CIGRE and IEEE traditional methodologies for calculating the backflashover outage rate (BFOR) of transmission lines, considering their adopted simplifications. These methodologies, along with an advanced computational approach named HEM-DE, were applied to a real 138-kV line to determine its backflashover rate. The quality of the results produced by the methodology at each step of their calculation procedure was assessed and discussed, taking as reference the accurate results provided by the advanced approach, based on the application of the hybrid electromagnetic model (HEM) and disruptive effect model (DE). According to this assessment, in the 40-to-10- range of tower footing grounding resistance, the CIGRE methodology overestimates outage rate of the line in relation to the reference values (98–21% larger in the 40-to-10- range of tower footing grounding resistance). The IEEE methodologies underestimates the BFOR, yielding rates 47–23% lower in the same resistance range. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The lightning performance of transmission lines is evaluated by means of the outage rate of the line per 100 km per year, including outages resulting from backflashover and shielding failures [1,2]. Backflashover prevails in lines installed over moderate and high resistivity soils [3]. Estimating this outage rate is relevant to defined the required protective practices to ensure a target performance of the line. Fig. 1 depicts the common procedure for calculating the backflashover rate in studies of the lightning performance of highvoltage transmission lines. This procedure begins with the modeling of line components, such as conductors, tower and grounding. Also, the main characteristics of the lightning return stroke current assumed to be impressed on the simulated system are defined, including its waveform and front time parameters. Following, the overvoltages developed across line insulator strings are calculated assuming lightning striking the tower top.
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (F.H. Silveira).
Applying a flashover criterion on the calculated overvoltages, the minimum peak current leading the insulators to flashover is determined. Such peak current is called critical current (IC ). Then, the percentage of lightning currents able to flashover the insulators is determined, taking as reference the estimated critical current in a cumulative distribution function of first return stroke peak currents. The outage rate is estimated as the product of this percentage by the expected number of lightning strikes to the line. It is worth mentioning that only first return stroke currents are considered for calculating backflashover rate, though the contribution of subsequent strokes could be relevant for specific conditions of lines with low tower-footing grounding resistances, as recently discussed by Silveira et al. [4,5]. The inclusion of subsequent return stroke currents on the calculation of BFOR is out of the scope of this paper. The most used approaches to calculate the transmission line outage rate consists of traditional methodologies proposed by CIGRE [2] and IEEE [6,7], based on analytical formulations. The easiness of application of such methodologies is responsible for their wide dissemination. On the other hand, some simplifications and approximations assumed in the methodologies to speed up the calculation process, responsible for this characteristic, are questionable, for instance the modeling of the impulsive behavior of grounding system, the representation of lightning currents and the
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Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005
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Fig. 2. CIGRE and IEEE cumulative first lightning stroke current distributions.
Fig. 1. Procedure for calculating backflashover outage rate.
criteria to define the insulator flashover. They can affect the calculated outage rate and harm the quality of the estimated line performance [10]. The purpose of this paper is to present a critical review of the main aspects of CIGRE and IEEE methodologies to estimate the backflashover rate and to evaluate the impact of some adopted approximations on the calculated rate. To assess the quality of the results provided by such methodologies, the accurate results obtained from the application of an elaborate computational approach, called HEM-DE methodology, is taken as reference. In this approach, the hybrid electromagnetic model (HEM) [8] is used to calculate the lightning overvoltage across line insulators and the disruptive effect model (DE) [9] is used to assess the flashover occurrence, as discussed in Section 4.2. The results for assessing the methodologies were developed for a typical configuration of a 138-kV transmission line. The text is organized as follows. Section 2 describes the main aspects of CIGRE and IEEE methodologies. The conditions and parameters required for implementing the simulated results are presented in Section 3. Section 4 is dedicated to the analyses and discussion of results. Section 5 presents the Summary and conclusions of the paper. 2. Traditional methodologies for calculating the lightning performance of high voltage transmission lines: CIGRE and IEEE The methodologies of CIGRE and IEEE consists of a set of analytical expressions intended to describe the transient behavior of the overvoltages across insulator strings due to direct lightning strikes to the line and to determine the resulting outage rate. The main aspects of each methodology are compiled in a series of published works. Specifically, the CIGRE methodology is described in CIGRE brochure 63 Guide to procedures for estimating the lightning performance of transmission lines [2], published in 1991. The IEEE methodology was first described in chapter 12 of the Transmission line reference book, written by Anderson [6], and was later included in the IEEE standard 1243 [7]. The most relevant features of CIGRE and IEEE methodologies in terms of the calculation of backflashover outage rates are described below. 2.1. Modeling of system components CIGRE and IEEE methodologies model line conductors and towers by means of surge impedances. Specifically concerning tower
modeling, CIGRE and IEEE consider the tower as a uniform constant surge impedance. While IEEE methodology provides a set of expressions to determine it, according to the geometrical arrangement of the tower, following the developments of Sargent and Darveniza [11], CIGRE suggests the use of a formula proposed by Chisholm et al. [12]. Both CIGRE and IEEE model the transmission line grounding modeling as a resistance, corresponding to the low frequency resistance. Soil ionization effect can be included, using Weck’s formula [13]. The frequency-dependence effect of soil parameters (resistivity and permittivity) is not considered. 2.2. Representation of lightning return-stroke current: waveform and front time CIGRE and IEEE methodologies calculate the lightning overvoltage across insulator due to a return stroke current assuming a linearly rising wavefront, though recommending different values of current front time. IEEE recommends the use of a 2-s-front time, while CIGRE allows the use to arbitrate a value of Td30, the virtual front duration calculated from time interval between the instants the current achieves 30% and 90% of the first peak value (Td30 = T30/0.6), for instance the median value of the front-time distribution of Berger´ıs measurements [14]. 2.3. Estimation of insulation strength CIGRE methodology adopts the so-called non-standard critical flashover overvoltage (CFONS ) as the withstand voltage for line insulators. The CFONS depends on the line critical flashover overvoltage (CFO), tower-footing grounding resistance and the span length between adjacent towers [2]. IEEE methodology follows the volt–time curve concept to estimate the flashover of insulators. This curve relates the peak overvoltage with the time to flashover, which depends on the length of line insulator [6,7]. As a simplification of the methodology, IEEE also presents the 2-point method that considers the estimation of the insulation in the volt–time curve for 2 and 6 s [6,7]. 2.4. Cumulative first return stroke current distribution The CIGRE and IEEE cumulative first return stroke current distributions are mostly based on first stroke data compiled in Anderson and Eriksson [14]. Fig. 2 illustrates both current distributions. CIGRE cumulative current distribution is obtained from the integration of the probability density function indicated in [2]. IEEE cumulative current distribution is reproduced by Eq. (1), where I means the peak current, and PI is the probability of a given current overpass the value of I. PI =
1
1+
I 2.6
(1)
31
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Table 1 Peak overvoltage across line insulator strings calculated by CIGRE and IEEE methodologies. RG = 20 . Insulator string
Vp (kV) CIGRE
Vp (kV) IEEE
Upper Intermediate Lower
487.8 501.4 515.0
498.0 513.5 525.9
Table 2 Peak overvoltage across line insulator strings calculated by CIGRE and IEEE methodologies. RG = 10 and 40 . Fig. 3. Lightning striking the 138-kV-single circuit transmission line.
Rg ()
Insulator string
Vp (kV) CIGRE
Vp (kV) IEEE
10
Upper Intermediate Lower
297.0 302.2 307.4
301.1 307.0 311.1
40
Upper Intermediate Lower
818.2 846.3 874.4
844.2 877.5 905.7
Table 3 Percentage of currents exceeding the peak required to flashover the lower insulator string determined by CIGRE and IEEE methodologies. RG = 10, 20, 40 .
Fig. 4. Geometry of the 138-kV transmission line tower considered in simulations.
2.5. Backflashover outage rate (BFOR) The resulting backflashover outage rate calculated by both methodologies is defined as BFOR = 0.6 × NL × PI , where NL is the rate of strokes hitting the line. Since the calculated overvoltages across insulator strings is only related to lightning striking the tower top, the 0.6-correction factor is applied to take into account the effect of the lower overvoltages yielded by lightning striking along the line span [9].
3. Developments The simulations considered a lightning striking the top of a tower, flanked by similar towers, of a typical 138-kV single-circuit transmission line illustrated in Fig. 3. The critical flashover overvoltage (CFO) is 650 kV. The towers are 30-m high and the span between adjacent towers is 400-m long. The radii of ground wire and phase cables are 0.397 cm and 0.914 cm, respectively. Fig. 4 depicts the geometry of the simulated tower. The tower surge impedance was assumed as 160 , the value provided by the expressions of CIGRE and IEEE methodologies for the characteristic of the represented tower. The tower-footing electrodes were simulated as a concentrated resistance, without considering soil ionization. The lightning current was simulated as a triangular waveform with 31-kA peak, 3.8-s Td30 front time, and 75-s T50 tail time. These values correspond to the median parameters measured by K. Berger at Mount San Salvatore station [14].
Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
CIGRE IEEE
66.4 108.4
12.7 3.7
– −71
20
CIGRE IEEE
41.1 64.1
36.4 13.1
– −64
40
CIGRE IEEE
25.9 37.2
66.1 38.3
– −42
4. Results and analysis 4.1. Peak overvoltage, critical current, and backflashover rate calculated according to CIGRE and IEEE methodologies Table 1 indicates the peak overvoltages at the upper, medium and lower insulator strings of the line calculated by CIGRE and IEEE methodologies considering tower-footing resistance of 20 . The resulting peak overvoltages are larger when applying IEEE methodology though the results are very close (2% difference). Similar behavior is observed for 10-- and 40--tower-footing grounding resistance as indicated in Table 2. For both methodologies application, larger overvoltages across the lower insulator string are observed. Table 3 shows the estimated critical currents and the corresponding percentage of current expected to flashover calculated by CIGRE and IEEE methodologies based on the overvoltages developed across the lower insulator string for 10--, 20-- and 40--tower-footing grounding resistance. In spite of the very similar peak overvoltages calculated by CIGRE and IEEE methodologies, the resulting lightning performance of the transmission line is quite different and strongly dependent on tower-footing grounding resistance. For all simulated tower-footing grounding resistance, the backflashover expectation calculated by IEEE methodology is lower. Taking as reference the results for 20--grounding resistance, CIGRE methodology estimates a 41-kA critical current, which means approximately 36% of currents exceeding such value. The application of IEEE methodology leads to critical current of 64 kA and about 13% of currents exceeding it. These results imply on an expectation of backflashover rate about 64% lower for IEEE. The increase of tower-footing grounding resistance contributes to diminish the difference between the outage rates calculated by CIGRE and IEEE.
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Table 4 Critical voltages estimated by CIGRE and IEEE methodologies as function of towerfooting grounding resistance. Rg ()
CIGRE CFOns (kV)
IEEE volt–time curve (kV)
Variation (%)
10 20 40
658.9 682.7 730.3
1088 1088 1088
+65.1 +59.4 +49.0
Fig. 5. Resulting outage rate (BFOR) assuming uniform distribution of tower-footing grounding resistance.
Fig. 6. Resulting outage rate (BFOR) assuming lognormal distribution of towerfooting grounding resistance.
The differences on the resulting outage rate are mainly due to the criteria adopted by each methodology to determine insulator’s flashover. While CIGRE considers the non-standard critical flashover overvoltage (CFONS ) that increases with the increase of tower-footing grounding resistance, IEEE adopts the volt–time curve concept that only depends on the line insulator length. Table 4 compares the critical overvoltage values estimated by each criterion as function of the tower-footing grounding resistance. As can be seen from the results of Table 4, the use of volt–time curve results on a fixed value of critical overvoltage that is 65%to-49% larger in comparison to those estimated by the CIGRE CFONS criterion for the 10-to-40 grounding resistance range. This behavior reflects on the corresponding critical currents, leading to lower outage rates estimated by IEEE methodology. Fig. 5 summarizes the resulting line outage rate calculated by CIGRE and IEEE methodologies as function of tower-footing grounding resistance assuming a rate (NL ) of 30 flashes striking the line per 100 km per year. In order to complement the previous analysis, further simulations were performed considering three lognormal distributions of tower-footing grounding resistance with median values of 10, 20, and 40 and standard deviation of 1. The resulting outage rates are presented in Fig. 6. The results confirm the lower outage rates related to the application of IEEE methodology and denotes the larger difference among the results for distributions in which low values of tower-footing grounding resistance prevail.
4.2. Application of HEM-DE methodology The occurrence of backflashover depends on a balance between the overvoltages resulting across line insulators and withstand of insulator. This makes the quality of the assessment of the backflashover rate strongly dependent of two key-points, the accuracy of the estimated overvoltage wave and the effectiveness of the criterion to determine whether this overvoltage leads the insulator to flashover (or not). This context reinforces the need of applying accurate and physically consistent models on the evaluation of the lightning performance of transmission lines. In this section, a comparison of results calculated by the traditional methodologies proposed by CIGRE and IEEE and those obtained by the application of an advanced methodology based on accurate modeling of system elements and the use of an elaborate criterion to verify the flashover occurrence across line insulators is presented. This methodology, named HEM-DE methodology, adopts the hybrid electromagnetic model (HEM) to calculate the overvoltages across insulator strings [8] and the disruptive effect model (DE) [9] to verify the flashover occurrence. The HEM model [8] is an electromagnetic model wide applied in literature to lightning-related studies. Its results are provided in terms of circuital quantities (voltages and currents) that are more suitable for engineering applications. The high accuracy of the results provided by this model has been assessed by means of comparison with experimental data [8,15] and with results calculated by other computational models, such as the Numerical Electromagnetics Code (NEC) and the finite difference time domain method (FDTD) [15,16]. Details of the application of the HEM model are presented in Refs. [4,5,8,15–17]. The use of electromagnetic models allows representing the physical system directly from the geometry of the elements and from the constitutive parameters of the media (air, soil), avoiding the simplified expressions of analytical approaches such as those considered by CIGRE and IEEE methodologies. Also, electromagnetic coupling among elements and propagation effects are accurately considered. This electromagnetic representation does not require the verification of consistency for each specific application/configuration, as required by representations of models based on distributed circuit or analytical approaches. Definitely, the quality of overvoltages calculated by an electromagnetic model is incomparable higher than that estimated by other approaches, such as distributed circuit approaches (including those based on the application of EMTP platform) and analytical ones. Nevertheless, the great improvement of the quality of the overvoltage calculated by an electromagnetic model has a high cost. As disadvantage, such models require long processing time. The disruptive effect (DE) model [9] integrates the overvoltage waveform during the interval in which the overvoltage across insulator is higher than a threshold value. If the result of the integral is equal or larger than a base DE (a value related to the CFO of line insulator), it assumes the occurrence of backflashover. The major advantage of such criterion is considering the whole overvoltage waveform to assess the insulator flashover (not only the peak overvoltage), with experimental support. The DE parameters are obtained from laboratorial tests and the application of such modeling reflects somehow the physical process involved in the insulator flashover [18–20]. The considerations above give the required support to use the results provided by HEM-DE methodology as reference for comparison in this work.
Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005
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Vp (kV) HEM
Upper 551.2 Intermediate 562.3 570 Lower
Vp (kV) CIGRE
487.8 501.4 515.0
Vp (kV) IEEE
498.0 513.5 525.9
Difference (CIGRE in relation to HEM) (%)
Difference (IEEE in relation to HEM) (%)
−11.5 −10.8 −9.6
−9.7 −8.7 −7.7
Table 6 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X CIGRE). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE CIGRE
83.7 66.4
6.4 12.7
– +98%
20
HEM-DE CIGRE
50.2 41.1
21.5 36.4
– +69%
40
HEM-DE CIGRE
31 25.9
54.7 66.1
– +21%
4.2.1. Comparison of peak overvoltages The peak overvoltages across insulator strings of the simulated transmission line calculated by HEM-DE methodology considering 20--tower footing grounding resistance are indicated in Table 5 along with the results previously calculated by CIGRE and IEEE methodologies. As can be noted from the results, the peak overvoltages calculated by the analytical formulations of CIGRE and IEEE are about 12-to-10% and 10-to-8% lower, respectively, than those calculated by the HEM model. The larger differences were observed at the upper insulator string. 4.2.2. Comparison in terms of critical currents and backflashover outage rates The resulting critical currents and the corresponding probability of backflashover occurrence determined by HEM-DE and CIGRE methodologies for the 10-to-40 -tower footing grounding resistance range are presented in Table 6. Both methodologies considered CIGRE cumulative return-stroke current distribution in this analysis. The application of HEM-DE methodology leads to larger critical current and, consequently, lower backflashover-rate expectation. Taking as reference the 20- grounding resistance case, the probability of occurring backflashover is about 22% and 36% for HEM-DE and CIGRE methodologies, respectively. If one considers a rate of 30 flashes striking the line per 100 km per year, the estimated backflashover rate of the line would be about 3.9 and 6.6 outages, respectively. In this case, CIGRE methodology estimates a 69% larger outage rate. The observed difference in terms of outage rate is not only related to the estimated overvoltages, but mainly due to the flashover requirement adopted by each methodology. To clarify this analysis, Table 7 indicates the resulting lightning performance if CIGRE CFONS criterion were applied to determine the critical current related to the HEM model overvoltage. As can be noted, the resulting critical current would be about 37 kA (Rg of 20 ), which represents a 40% probability of backflashover occurrence against the 22%-probability related to the application of the DE model. In terms of outage rate, this means an increase from 3.9 to 7.1 outages/100 km/year (increase of 84%), indicating that the use of CFONS criterion overestimates the resulting BFOR in relation to the DE model application. For tower-footing grounding resistance of 10 and 40 , the observed increase on the backflashover probability when considering the CFONS is about 175% and 19%, respectively.
5
Table 7 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X HEM-CFONS ). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE HEM-CFONS
83.7 54.4
6.4 17.6
– +175%
20
HEM-DE HEM-CFONS
50.2 37.1
21.5 39.5
– +84%
40
HEM-DE HEM-CFONS
31 24.9
54.7 65.1
– +19%
Table 8 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X IEEE). RG = 10, 20, 40 . Rg ()
Methodology
10
HEM-DE IEEE
Ic (kA) 83.7 108.4
%I > Ic 7 3.7
Variation (%) – −47%
20
HEM-DE IEEE
50.2 64.1
22.2 13.1
– −41%
40
HEM-DE IEEE
31 37.2
50 38.3
– −23%
Table 9 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X HEM-volt–time curve). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE HEM-volt–time curve
83.7 89.8
7 5.9
– −16%
20
HEM-DE HEM-volt–time curve
50.2 59.2
22.2 15.7
– −29%
40
HEM-DE HEM-volt–time curve
31 37.1
50 38.6
– −23%
Table 8 summarizes the critical current and corresponding probability of backflashover occurrence determined by HEM-DE and IEEE methodologies for the 10-to-40 range of tower footing grounding resistance. In this analysis, the cumulative return-stroke current distribution recommended by IEEE is considered by both methodologies. It is observed that the application of HEM-DE methodology leads to lower critical current and, consequently, larger probability of backflashover. Considering the 20- grounding resistance case, the backflashover probability of occurrence is around 22% and 13% for HEM-DE and IEEE methodologies, respectively. For a rate of 30 flashes striking the line per 100 km per year, the estimated backflashover rates are 4 and 2.4, respectively. The result considering the volt–time curve as the flashover criterion to calculate the critical current from the HEM overvoltage is indicated in Table 9. In this analysis, critical current related to HEM model increases from 50 to 59 kA (Rg of 20 ), decreasing the backflashover probability from 22% (4 outages) to 16% (2.8 outages), a reduction about 29%. For tower-footing grounding resistance of 10 and 40 , the observed decrease on the backflashover probability when considering the volt–time curve is about 16% and 23%, respectively. This result indicates that the use of volt–time curve criterion underestimates the resulting BFOR in relation to the DE model application. 4.2.3. Effect of the cumulative return stroke current distribution In order to evaluate the effect of the cumulative return stroke current distribution on the backflashover outage rate, HEM-DE methodology were applied for 10-to-40- tower-footing grounding resistance assuming both current distributions. The evaluation
Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005
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Fig. 7. Effect of the cumulative return stroke current distribution on the backflashover rate estimated by HEM-DE.
overestimates, respectively, the resulting critical currents in relation to the application of the DE model as the flashover criterion. Hence, the backflashover outage rate estimated following such requirements leads to larger and lower outage rates, respectively in relation to the application of the HEM-DE methodology. This analysis indicates that the trends of overestimation and underestimation observed in the results respectively for the CIGRE and IEEE methodologies are not specific of the 138-kV tested line. Also, the specific aspects of both methodologies leading to their response tend to affect in the same way the calculated BFOR of lines in general. This reveals a certain generality of the trends of overestimation of BFOR calculated by CIGRE methodology and underestimation of the results provided by IEEE methodology. Acknowledgments
assumed a rate of 30 flashes striking the line per 100 km per year. The results are presented in Fig. 7. Nearly the same outage rates are obtained. The IEEE current distribution leaded to about 10% lower outage rate for Rg of 20 and 40 (4 × 4.5 outages, and 9 × 9.9 outages, respectively), and 10% larger for Rg of 10 (1.3 × 1.2 outages). For this very low tower footing grounding resistance, the 10% difference in terms of outage rate is not significant since in a quantitative perspective the number of outages is still very low for a 138-kV transmission line, which means a favorable condition in terms of its lighting performance. To complement this analysis, it is important to note that the larger critical current related to the results of Fig. 7 is about 80 kA (for the 10- tower footing grounding resistance case), and, for currents larger than this value, the IEEE cumulative current distribution is characterized by probability of occurrence larger than those related to CIGRE distribution. This explains the calculation of larger outage rates associated with IEEE current distribution for lower values of tower-footing grounding resistance. 5. Summary and conclusions This work developed an objective review of CIGRE and IEEE traditional methodologies for calculating the backflashover outage rate (BFOR) of transmission lines. The quality of results provided by these methodologies were assessed taken as reference the accurate results provided by an advanced approach, based on the application of the hybrid electromagnetic model (HEM) and disruptive effect model (DE), described in Section 4.2. According to this assessment developed for a real 138-kV transmission line, in the 40-to-10- range of tower footing grounding resistance, the CIGRE methodology overestimates outage rate of the line in relation the reference values (98–21% larger in the 40to-10- range of tower footing grounding resistance). The IEEE methodologies underestimates the BFOR, yielding rates 47–23% lower in the same resistance range. In this work, each partial result obtained during the implementation of the methodology was analyzed and discussed in order to clarify the reasons for differences in relation to the reference results. Though the application of CIGRE and IEEE methodologies results in the same peak overvoltages across line insulator, their calculated outage rates are quite different. This results from the distinct flashover criteria adopted by each methodology. While CIGRE adopts the CFONS criterion, which depends on the tower-footing grounding resistance and other factors, IEEE uses the volt–time curve criterion that gives a fixed value of critical overvoltage related to the length of insulator string. For the 10-to-40- tower-footing grounding resistance range, IEEE estimated outage rates of the tested 138-kV line about 71%–42% lower in relation to the ones calculated by CIGRE methodology. As shown, the CFONS criterion of CIGRE and the volt–time criterion of IEEE underestimates and
Fernando H. Silveira would like to thank the National Council of Scientific and Technological Development (CNPq), grant 309326/2015-0, and The State of Minas Gerais Research Foundation (FAPEMIG), grants TEC APQ-02141-14 and TEC PPM-00491-16. References [1] IEEE Working Group on Lightning Performance of Transmission Lines, A simplified method for estimating the lightning performance of transmission lines, IEEE Trans. Power Appar. Syst. 104 (April (4)) (1985) 919–932. [2] CIGRE WG 33-01, Guide to Procedures for Estimating the Lightning Performance of Transmission Lines, Cigre Brochure 63, October 1991. [3] S. Visacro, Direct strokes to transmission lines: considerations on the mechanisms of overvoltage formation and their influence on the lightning performance of lines, J. Light. Res. 1 (2007) 60–68. [4] F.H. Silveira, S. Visacro, A. De Conti, Lightning performance of 138-kV transmission lines: the relevance of subsequent strokes, IEEE Trans. Electromagn. Compat. 55 (December) (2013) 1195–1200. [5] F.H. Silveira, S. Visacro, A. De Conti, C.R. Mesquita, Backflashovers of transmission lines due to subsequent lightning stroke, IEEE Trans. Electromagn. Compat. 54 (2) (2012) 316–322. [6] J.G. Anderson, Lightning performance of transmission lines, in: Transmission Line Reference Book −345 kV and Above, 2nd ed., Electric Power Research Institute–EPRI, California, 1982, pp. 545–597. [7] IEEE, Guide for Improving the Lightning Performance of Transmission Lines, IEEE Std. 1243, 1997. [8] S. Visacro, A. Soares Jr., HEM: a model for simulation of lightning-related engineering problems, IEEE Trans. Power Deliv. 20 (April (2)) (2005) 1026–1028. [9] H. Hileman, Insulation Coordination for Power Systems, CRC, Boca Raton, FL, 1999, pp. 627–640. [10] F.H. Silveira, S. Visacro, R. Souza Filho, Calculation of backflashover outage rate of transmission lines: a discussion on traditional methodologies and recent advances, in: Proceedings of 2015 International Symposium on Lightning Protection (XIII SIPDA), Brazil, 2015, pp. 315–319. [11] M.A. Sargent, M. Darveniza, Tower surge impedance, IEEE Trans. Power Appar. Syst. PAS-88 (May) (1969) 680–687. [12] W.A. Chisholm, Y.L. Chow, K.D. Srivastava, Lightning surge response of transmission towers, IEEE Trans. Power Appar. Syst. PAS-102 (September (9)) (1983) 3232–3242. [13] A.J. Eriksson, K.H. Weck, Simplified procedures for determining representative substation impinging lightning overvoltages, in: International Conference on Large High Voltage Electric Systems, CIGRE 33-16, Paris, 1988. [14] R.B. Anderson, A.J. Eriksson, Lightning parameters for engineering application, Electra 69 (1980) 65–102. [15] F.H. Silveira, S. Visacro, J. Herrera, H. Torres, Evaluation of lightning-induced voltages over lossy ground by the hybrid electromagnetic model, IEEE Trans. Electromagn. Compat. 51 (February (1)) (2009) 156–160. [16] F.H. Silveira, S. Visacro, The influence of attachment height on lightning-induced voltages, IEEE Trans. Electromagn. Compat. 50 (August (3)) (2008) 743–747. [17] A. Soares Jr., M.A.O. Schroeder, S. Visacro, Transient voltages in transmission lines caused by direct lightning strikes, IEEE Trans. Power Deliv. 20 (April (2)) (2005) 1447–1452. [18] R.O. Caldwell, M. Darveniza, Experimental and analytical studies of the effect of non-standard waveshapes of the impulse strength of external insulations, IEEE Trans. Power Appar. Syst. 92 (July (4)) (1973) 1420–1428. [19] 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 (June (3)) (1988). [20] W.A. Chisholm, New challenges in lightning impulse flashover modeling of air gaps and insulators, IEEE Electr. Insul. Mag. 26 (2) (2010) 14–25.
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Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach Fernando H. Silveira ∗ , Silvério Visacro, Ronaldo E. Souza LRC – Lightning Research Center, UFMG – Federal University of Minas Gerais, Brazil
a r t i c l e
i n f o
Article history: Received 14 April 2016 Received in revised form 26 August 2016 Accepted 3 January 2017 Available online xxx Keywords: Backflashover Grounding Lightning performance of transmission lines Traditional methodologies
a b s t r a c t This paper presents a critical review of CIGRE and IEEE traditional methodologies for calculating the backflashover outage rate (BFOR) of transmission lines, considering their adopted simplifications. These methodologies, along with an advanced computational approach named HEM-DE, were applied to a real 138-kV line to determine its backflashover rate. The quality of the results produced by the methodology at each step of their calculation procedure was assessed and discussed, taking as reference the accurate results provided by the advanced approach, based on the application of the hybrid electromagnetic model (HEM) and disruptive effect model (DE). According to this assessment, in the 40-to-10- range of tower footing grounding resistance, the CIGRE methodology overestimates outage rate of the line in relation to the reference values (98–21% larger in the 40-to-10- range of tower footing grounding resistance). The IEEE methodologies underestimates the BFOR, yielding rates 47–23% lower in the same resistance range. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The lightning performance of transmission lines is evaluated by means of the outage rate of the line per 100 km per year, including outages resulting from backflashover and shielding failures [1,2]. Backflashover prevails in lines installed over moderate and high resistivity soils [3]. Estimating this outage rate is relevant to defined the required protective practices to ensure a target performance of the line. Fig. 1 depicts the common procedure for calculating the backflashover rate in studies of the lightning performance of highvoltage transmission lines. This procedure begins with the modeling of line components, such as conductors, tower and grounding. Also, the main characteristics of the lightning return stroke current assumed to be impressed on the simulated system are defined, including its waveform and front time parameters. Following, the overvoltages developed across line insulator strings are calculated assuming lightning striking the tower top.
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (F.H. Silveira).
Applying a flashover criterion on the calculated overvoltages, the minimum peak current leading the insulators to flashover is determined. Such peak current is called critical current (IC ). Then, the percentage of lightning currents able to flashover the insulators is determined, taking as reference the estimated critical current in a cumulative distribution function of first return stroke peak currents. The outage rate is estimated as the product of this percentage by the expected number of lightning strikes to the line. It is worth mentioning that only first return stroke currents are considered for calculating backflashover rate, though the contribution of subsequent strokes could be relevant for specific conditions of lines with low tower-footing grounding resistances, as recently discussed by Silveira et al. [4,5]. The inclusion of subsequent return stroke currents on the calculation of BFOR is out of the scope of this paper. The most used approaches to calculate the transmission line outage rate consists of traditional methodologies proposed by CIGRE [2] and IEEE [6,7], based on analytical formulations. The easiness of application of such methodologies is responsible for their wide dissemination. On the other hand, some simplifications and approximations assumed in the methodologies to speed up the calculation process, responsible for this characteristic, are questionable, for instance the modeling of the impulsive behavior of grounding system, the representation of lightning currents and the
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Fig. 2. CIGRE and IEEE cumulative first lightning stroke current distributions.
Fig. 1. Procedure for calculating backflashover outage rate.
criteria to define the insulator flashover. They can affect the calculated outage rate and harm the quality of the estimated line performance [10]. The purpose of this paper is to present a critical review of the main aspects of CIGRE and IEEE methodologies to estimate the backflashover rate and to evaluate the impact of some adopted approximations on the calculated rate. To assess the quality of the results provided by such methodologies, the accurate results obtained from the application of an elaborate computational approach, called HEM-DE methodology, is taken as reference. In this approach, the hybrid electromagnetic model (HEM) [8] is used to calculate the lightning overvoltage across line insulators and the disruptive effect model (DE) [9] is used to assess the flashover occurrence, as discussed in Section 4.2. The results for assessing the methodologies were developed for a typical configuration of a 138-kV transmission line. The text is organized as follows. Section 2 describes the main aspects of CIGRE and IEEE methodologies. The conditions and parameters required for implementing the simulated results are presented in Section 3. Section 4 is dedicated to the analyses and discussion of results. Section 5 presents the Summary and conclusions of the paper. 2. Traditional methodologies for calculating the lightning performance of high voltage transmission lines: CIGRE and IEEE The methodologies of CIGRE and IEEE consists of a set of analytical expressions intended to describe the transient behavior of the overvoltages across insulator strings due to direct lightning strikes to the line and to determine the resulting outage rate. The main aspects of each methodology are compiled in a series of published works. Specifically, the CIGRE methodology is described in CIGRE brochure 63 Guide to procedures for estimating the lightning performance of transmission lines [2], published in 1991. The IEEE methodology was first described in chapter 12 of the Transmission line reference book, written by Anderson [6], and was later included in the IEEE standard 1243 [7]. The most relevant features of CIGRE and IEEE methodologies in terms of the calculation of backflashover outage rates are described below. 2.1. Modeling of system components CIGRE and IEEE methodologies model line conductors and towers by means of surge impedances. Specifically concerning tower
modeling, CIGRE and IEEE consider the tower as a uniform constant surge impedance. While IEEE methodology provides a set of expressions to determine it, according to the geometrical arrangement of the tower, following the developments of Sargent and Darveniza [11], CIGRE suggests the use of a formula proposed by Chisholm et al. [12]. Both CIGRE and IEEE model the transmission line grounding modeling as a resistance, corresponding to the low frequency resistance. Soil ionization effect can be included, using Weck’s formula [13]. The frequency-dependence effect of soil parameters (resistivity and permittivity) is not considered. 2.2. Representation of lightning return-stroke current: waveform and front time CIGRE and IEEE methodologies calculate the lightning overvoltage across insulator due to a return stroke current assuming a linearly rising wavefront, though recommending different values of current front time. IEEE recommends the use of a 2-s-front time, while CIGRE allows the use to arbitrate a value of Td30, the virtual front duration calculated from time interval between the instants the current achieves 30% and 90% of the first peak value (Td30 = T30/0.6), for instance the median value of the front-time distribution of Berger´ıs measurements [14]. 2.3. Estimation of insulation strength CIGRE methodology adopts the so-called non-standard critical flashover overvoltage (CFONS ) as the withstand voltage for line insulators. The CFONS depends on the line critical flashover overvoltage (CFO), tower-footing grounding resistance and the span length between adjacent towers [2]. IEEE methodology follows the volt–time curve concept to estimate the flashover of insulators. This curve relates the peak overvoltage with the time to flashover, which depends on the length of line insulator [6,7]. As a simplification of the methodology, IEEE also presents the 2-point method that considers the estimation of the insulation in the volt–time curve for 2 and 6 s [6,7]. 2.4. Cumulative first return stroke current distribution The CIGRE and IEEE cumulative first return stroke current distributions are mostly based on first stroke data compiled in Anderson and Eriksson [14]. Fig. 2 illustrates both current distributions. CIGRE cumulative current distribution is obtained from the integration of the probability density function indicated in [2]. IEEE cumulative current distribution is reproduced by Eq. (1), where I means the peak current, and PI is the probability of a given current overpass the value of I. PI =
1
1+
I 2.6
(1)
31
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Table 1 Peak overvoltage across line insulator strings calculated by CIGRE and IEEE methodologies. RG = 20 . Insulator string
Vp (kV) CIGRE
Vp (kV) IEEE
Upper Intermediate Lower
487.8 501.4 515.0
498.0 513.5 525.9
Table 2 Peak overvoltage across line insulator strings calculated by CIGRE and IEEE methodologies. RG = 10 and 40 . Fig. 3. Lightning striking the 138-kV-single circuit transmission line.
Rg ()
Insulator string
Vp (kV) CIGRE
Vp (kV) IEEE
10
Upper Intermediate Lower
297.0 302.2 307.4
301.1 307.0 311.1
40
Upper Intermediate Lower
818.2 846.3 874.4
844.2 877.5 905.7
Table 3 Percentage of currents exceeding the peak required to flashover the lower insulator string determined by CIGRE and IEEE methodologies. RG = 10, 20, 40 .
Fig. 4. Geometry of the 138-kV transmission line tower considered in simulations.
2.5. Backflashover outage rate (BFOR) The resulting backflashover outage rate calculated by both methodologies is defined as BFOR = 0.6 × NL × PI , where NL is the rate of strokes hitting the line. Since the calculated overvoltages across insulator strings is only related to lightning striking the tower top, the 0.6-correction factor is applied to take into account the effect of the lower overvoltages yielded by lightning striking along the line span [9].
3. Developments The simulations considered a lightning striking the top of a tower, flanked by similar towers, of a typical 138-kV single-circuit transmission line illustrated in Fig. 3. The critical flashover overvoltage (CFO) is 650 kV. The towers are 30-m high and the span between adjacent towers is 400-m long. The radii of ground wire and phase cables are 0.397 cm and 0.914 cm, respectively. Fig. 4 depicts the geometry of the simulated tower. The tower surge impedance was assumed as 160 , the value provided by the expressions of CIGRE and IEEE methodologies for the characteristic of the represented tower. The tower-footing electrodes were simulated as a concentrated resistance, without considering soil ionization. The lightning current was simulated as a triangular waveform with 31-kA peak, 3.8-s Td30 front time, and 75-s T50 tail time. These values correspond to the median parameters measured by K. Berger at Mount San Salvatore station [14].
Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
CIGRE IEEE
66.4 108.4
12.7 3.7
– −71
20
CIGRE IEEE
41.1 64.1
36.4 13.1
– −64
40
CIGRE IEEE
25.9 37.2
66.1 38.3
– −42
4. Results and analysis 4.1. Peak overvoltage, critical current, and backflashover rate calculated according to CIGRE and IEEE methodologies Table 1 indicates the peak overvoltages at the upper, medium and lower insulator strings of the line calculated by CIGRE and IEEE methodologies considering tower-footing resistance of 20 . The resulting peak overvoltages are larger when applying IEEE methodology though the results are very close (2% difference). Similar behavior is observed for 10-- and 40--tower-footing grounding resistance as indicated in Table 2. For both methodologies application, larger overvoltages across the lower insulator string are observed. Table 3 shows the estimated critical currents and the corresponding percentage of current expected to flashover calculated by CIGRE and IEEE methodologies based on the overvoltages developed across the lower insulator string for 10--, 20-- and 40--tower-footing grounding resistance. In spite of the very similar peak overvoltages calculated by CIGRE and IEEE methodologies, the resulting lightning performance of the transmission line is quite different and strongly dependent on tower-footing grounding resistance. For all simulated tower-footing grounding resistance, the backflashover expectation calculated by IEEE methodology is lower. Taking as reference the results for 20--grounding resistance, CIGRE methodology estimates a 41-kA critical current, which means approximately 36% of currents exceeding such value. The application of IEEE methodology leads to critical current of 64 kA and about 13% of currents exceeding it. These results imply on an expectation of backflashover rate about 64% lower for IEEE. The increase of tower-footing grounding resistance contributes to diminish the difference between the outage rates calculated by CIGRE and IEEE.
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Table 4 Critical voltages estimated by CIGRE and IEEE methodologies as function of towerfooting grounding resistance. Rg ()
CIGRE CFOns (kV)
IEEE volt–time curve (kV)
Variation (%)
10 20 40
658.9 682.7 730.3
1088 1088 1088
+65.1 +59.4 +49.0
Fig. 5. Resulting outage rate (BFOR) assuming uniform distribution of tower-footing grounding resistance.
Fig. 6. Resulting outage rate (BFOR) assuming lognormal distribution of towerfooting grounding resistance.
The differences on the resulting outage rate are mainly due to the criteria adopted by each methodology to determine insulator’s flashover. While CIGRE considers the non-standard critical flashover overvoltage (CFONS ) that increases with the increase of tower-footing grounding resistance, IEEE adopts the volt–time curve concept that only depends on the line insulator length. Table 4 compares the critical overvoltage values estimated by each criterion as function of the tower-footing grounding resistance. As can be seen from the results of Table 4, the use of volt–time curve results on a fixed value of critical overvoltage that is 65%to-49% larger in comparison to those estimated by the CIGRE CFONS criterion for the 10-to-40 grounding resistance range. This behavior reflects on the corresponding critical currents, leading to lower outage rates estimated by IEEE methodology. Fig. 5 summarizes the resulting line outage rate calculated by CIGRE and IEEE methodologies as function of tower-footing grounding resistance assuming a rate (NL ) of 30 flashes striking the line per 100 km per year. In order to complement the previous analysis, further simulations were performed considering three lognormal distributions of tower-footing grounding resistance with median values of 10, 20, and 40 and standard deviation of 1. The resulting outage rates are presented in Fig. 6. The results confirm the lower outage rates related to the application of IEEE methodology and denotes the larger difference among the results for distributions in which low values of tower-footing grounding resistance prevail.
4.2. Application of HEM-DE methodology The occurrence of backflashover depends on a balance between the overvoltages resulting across line insulators and withstand of insulator. This makes the quality of the assessment of the backflashover rate strongly dependent of two key-points, the accuracy of the estimated overvoltage wave and the effectiveness of the criterion to determine whether this overvoltage leads the insulator to flashover (or not). This context reinforces the need of applying accurate and physically consistent models on the evaluation of the lightning performance of transmission lines. In this section, a comparison of results calculated by the traditional methodologies proposed by CIGRE and IEEE and those obtained by the application of an advanced methodology based on accurate modeling of system elements and the use of an elaborate criterion to verify the flashover occurrence across line insulators is presented. This methodology, named HEM-DE methodology, adopts the hybrid electromagnetic model (HEM) to calculate the overvoltages across insulator strings [8] and the disruptive effect model (DE) [9] to verify the flashover occurrence. The HEM model [8] is an electromagnetic model wide applied in literature to lightning-related studies. Its results are provided in terms of circuital quantities (voltages and currents) that are more suitable for engineering applications. The high accuracy of the results provided by this model has been assessed by means of comparison with experimental data [8,15] and with results calculated by other computational models, such as the Numerical Electromagnetics Code (NEC) and the finite difference time domain method (FDTD) [15,16]. Details of the application of the HEM model are presented in Refs. [4,5,8,15–17]. The use of electromagnetic models allows representing the physical system directly from the geometry of the elements and from the constitutive parameters of the media (air, soil), avoiding the simplified expressions of analytical approaches such as those considered by CIGRE and IEEE methodologies. Also, electromagnetic coupling among elements and propagation effects are accurately considered. This electromagnetic representation does not require the verification of consistency for each specific application/configuration, as required by representations of models based on distributed circuit or analytical approaches. Definitely, the quality of overvoltages calculated by an electromagnetic model is incomparable higher than that estimated by other approaches, such as distributed circuit approaches (including those based on the application of EMTP platform) and analytical ones. Nevertheless, the great improvement of the quality of the overvoltage calculated by an electromagnetic model has a high cost. As disadvantage, such models require long processing time. The disruptive effect (DE) model [9] integrates the overvoltage waveform during the interval in which the overvoltage across insulator is higher than a threshold value. If the result of the integral is equal or larger than a base DE (a value related to the CFO of line insulator), it assumes the occurrence of backflashover. The major advantage of such criterion is considering the whole overvoltage waveform to assess the insulator flashover (not only the peak overvoltage), with experimental support. The DE parameters are obtained from laboratorial tests and the application of such modeling reflects somehow the physical process involved in the insulator flashover [18–20]. The considerations above give the required support to use the results provided by HEM-DE methodology as reference for comparison in this work.
Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005
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Vp (kV) HEM
Upper 551.2 Intermediate 562.3 570 Lower
Vp (kV) CIGRE
487.8 501.4 515.0
Vp (kV) IEEE
498.0 513.5 525.9
Difference (CIGRE in relation to HEM) (%)
Difference (IEEE in relation to HEM) (%)
−11.5 −10.8 −9.6
−9.7 −8.7 −7.7
Table 6 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X CIGRE). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE CIGRE
83.7 66.4
6.4 12.7
– +98%
20
HEM-DE CIGRE
50.2 41.1
21.5 36.4
– +69%
40
HEM-DE CIGRE
31 25.9
54.7 66.1
– +21%
4.2.1. Comparison of peak overvoltages The peak overvoltages across insulator strings of the simulated transmission line calculated by HEM-DE methodology considering 20--tower footing grounding resistance are indicated in Table 5 along with the results previously calculated by CIGRE and IEEE methodologies. As can be noted from the results, the peak overvoltages calculated by the analytical formulations of CIGRE and IEEE are about 12-to-10% and 10-to-8% lower, respectively, than those calculated by the HEM model. The larger differences were observed at the upper insulator string. 4.2.2. Comparison in terms of critical currents and backflashover outage rates The resulting critical currents and the corresponding probability of backflashover occurrence determined by HEM-DE and CIGRE methodologies for the 10-to-40 -tower footing grounding resistance range are presented in Table 6. Both methodologies considered CIGRE cumulative return-stroke current distribution in this analysis. The application of HEM-DE methodology leads to larger critical current and, consequently, lower backflashover-rate expectation. Taking as reference the 20- grounding resistance case, the probability of occurring backflashover is about 22% and 36% for HEM-DE and CIGRE methodologies, respectively. If one considers a rate of 30 flashes striking the line per 100 km per year, the estimated backflashover rate of the line would be about 3.9 and 6.6 outages, respectively. In this case, CIGRE methodology estimates a 69% larger outage rate. The observed difference in terms of outage rate is not only related to the estimated overvoltages, but mainly due to the flashover requirement adopted by each methodology. To clarify this analysis, Table 7 indicates the resulting lightning performance if CIGRE CFONS criterion were applied to determine the critical current related to the HEM model overvoltage. As can be noted, the resulting critical current would be about 37 kA (Rg of 20 ), which represents a 40% probability of backflashover occurrence against the 22%-probability related to the application of the DE model. In terms of outage rate, this means an increase from 3.9 to 7.1 outages/100 km/year (increase of 84%), indicating that the use of CFONS criterion overestimates the resulting BFOR in relation to the DE model application. For tower-footing grounding resistance of 10 and 40 , the observed increase on the backflashover probability when considering the CFONS is about 175% and 19%, respectively.
5
Table 7 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X HEM-CFONS ). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE HEM-CFONS
83.7 54.4
6.4 17.6
– +175%
20
HEM-DE HEM-CFONS
50.2 37.1
21.5 39.5
– +84%
40
HEM-DE HEM-CFONS
31 24.9
54.7 65.1
– +19%
Table 8 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X IEEE). RG = 10, 20, 40 . Rg ()
Methodology
10
HEM-DE IEEE
Ic (kA) 83.7 108.4
%I > Ic 7 3.7
Variation (%) – −47%
20
HEM-DE IEEE
50.2 64.1
22.2 13.1
– −41%
40
HEM-DE IEEE
31 37.2
50 38.3
– −23%
Table 9 Critical currents and percentage of currents exceeding the peak required to flashover the lower insulator string (HEM-DE X HEM-volt–time curve). RG = 10, 20, 40 . Rg ()
Methodology
Ic (kA)
%I > Ic
Variation (%)
10
HEM-DE HEM-volt–time curve
83.7 89.8
7 5.9
– −16%
20
HEM-DE HEM-volt–time curve
50.2 59.2
22.2 15.7
– −29%
40
HEM-DE HEM-volt–time curve
31 37.1
50 38.6
– −23%
Table 8 summarizes the critical current and corresponding probability of backflashover occurrence determined by HEM-DE and IEEE methodologies for the 10-to-40 range of tower footing grounding resistance. In this analysis, the cumulative return-stroke current distribution recommended by IEEE is considered by both methodologies. It is observed that the application of HEM-DE methodology leads to lower critical current and, consequently, larger probability of backflashover. Considering the 20- grounding resistance case, the backflashover probability of occurrence is around 22% and 13% for HEM-DE and IEEE methodologies, respectively. For a rate of 30 flashes striking the line per 100 km per year, the estimated backflashover rates are 4 and 2.4, respectively. The result considering the volt–time curve as the flashover criterion to calculate the critical current from the HEM overvoltage is indicated in Table 9. In this analysis, critical current related to HEM model increases from 50 to 59 kA (Rg of 20 ), decreasing the backflashover probability from 22% (4 outages) to 16% (2.8 outages), a reduction about 29%. For tower-footing grounding resistance of 10 and 40 , the observed decrease on the backflashover probability when considering the volt–time curve is about 16% and 23%, respectively. This result indicates that the use of volt–time curve criterion underestimates the resulting BFOR in relation to the DE model application. 4.2.3. Effect of the cumulative return stroke current distribution In order to evaluate the effect of the cumulative return stroke current distribution on the backflashover outage rate, HEM-DE methodology were applied for 10-to-40- tower-footing grounding resistance assuming both current distributions. The evaluation
Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005
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ARTICLE IN PRESS F.H. Silveira et al. / Electric Power Systems Research xxx (2016) xxx–xxx
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Fig. 7. Effect of the cumulative return stroke current distribution on the backflashover rate estimated by HEM-DE.
overestimates, respectively, the resulting critical currents in relation to the application of the DE model as the flashover criterion. Hence, the backflashover outage rate estimated following such requirements leads to larger and lower outage rates, respectively in relation to the application of the HEM-DE methodology. This analysis indicates that the trends of overestimation and underestimation observed in the results respectively for the CIGRE and IEEE methodologies are not specific of the 138-kV tested line. Also, the specific aspects of both methodologies leading to their response tend to affect in the same way the calculated BFOR of lines in general. This reveals a certain generality of the trends of overestimation of BFOR calculated by CIGRE methodology and underestimation of the results provided by IEEE methodology. Acknowledgments
assumed a rate of 30 flashes striking the line per 100 km per year. The results are presented in Fig. 7. Nearly the same outage rates are obtained. The IEEE current distribution leaded to about 10% lower outage rate for Rg of 20 and 40 (4 × 4.5 outages, and 9 × 9.9 outages, respectively), and 10% larger for Rg of 10 (1.3 × 1.2 outages). For this very low tower footing grounding resistance, the 10% difference in terms of outage rate is not significant since in a quantitative perspective the number of outages is still very low for a 138-kV transmission line, which means a favorable condition in terms of its lighting performance. To complement this analysis, it is important to note that the larger critical current related to the results of Fig. 7 is about 80 kA (for the 10- tower footing grounding resistance case), and, for currents larger than this value, the IEEE cumulative current distribution is characterized by probability of occurrence larger than those related to CIGRE distribution. This explains the calculation of larger outage rates associated with IEEE current distribution for lower values of tower-footing grounding resistance. 5. Summary and conclusions This work developed an objective review of CIGRE and IEEE traditional methodologies for calculating the backflashover outage rate (BFOR) of transmission lines. The quality of results provided by these methodologies were assessed taken as reference the accurate results provided by an advanced approach, based on the application of the hybrid electromagnetic model (HEM) and disruptive effect model (DE), described in Section 4.2. According to this assessment developed for a real 138-kV transmission line, in the 40-to-10- range of tower footing grounding resistance, the CIGRE methodology overestimates outage rate of the line in relation the reference values (98–21% larger in the 40to-10- range of tower footing grounding resistance). The IEEE methodologies underestimates the BFOR, yielding rates 47–23% lower in the same resistance range. In this work, each partial result obtained during the implementation of the methodology was analyzed and discussed in order to clarify the reasons for differences in relation to the reference results. Though the application of CIGRE and IEEE methodologies results in the same peak overvoltages across line insulator, their calculated outage rates are quite different. This results from the distinct flashover criteria adopted by each methodology. While CIGRE adopts the CFONS criterion, which depends on the tower-footing grounding resistance and other factors, IEEE uses the volt–time curve criterion that gives a fixed value of critical overvoltage related to the length of insulator string. For the 10-to-40- tower-footing grounding resistance range, IEEE estimated outage rates of the tested 138-kV line about 71%–42% lower in relation to the ones calculated by CIGRE methodology. As shown, the CFONS criterion of CIGRE and the volt–time criterion of IEEE underestimates and
Fernando H. Silveira would like to thank the National Council of Scientific and Technological Development (CNPq), grant 309326/2015-0, and The State of Minas Gerais Research Foundation (FAPEMIG), grants TEC APQ-02141-14 and TEC PPM-00491-16. References [1] IEEE Working Group on Lightning Performance of Transmission Lines, A simplified method for estimating the lightning performance of transmission lines, IEEE Trans. Power Appar. Syst. 104 (April (4)) (1985) 919–932. [2] CIGRE WG 33-01, Guide to Procedures for Estimating the Lightning Performance of Transmission Lines, Cigre Brochure 63, October 1991. [3] S. Visacro, Direct strokes to transmission lines: considerations on the mechanisms of overvoltage formation and their influence on the lightning performance of lines, J. Light. Res. 1 (2007) 60–68. [4] F.H. Silveira, S. Visacro, A. De Conti, Lightning performance of 138-kV transmission lines: the relevance of subsequent strokes, IEEE Trans. Electromagn. Compat. 55 (December) (2013) 1195–1200. [5] F.H. Silveira, S. Visacro, A. De Conti, C.R. Mesquita, Backflashovers of transmission lines due to subsequent lightning stroke, IEEE Trans. Electromagn. Compat. 54 (2) (2012) 316–322. [6] J.G. Anderson, Lightning performance of transmission lines, in: Transmission Line Reference Book −345 kV and Above, 2nd ed., Electric Power Research Institute–EPRI, California, 1982, pp. 545–597. [7] IEEE, Guide for Improving the Lightning Performance of Transmission Lines, IEEE Std. 1243, 1997. [8] S. Visacro, A. Soares Jr., HEM: a model for simulation of lightning-related engineering problems, IEEE Trans. Power Deliv. 20 (April (2)) (2005) 1026–1028. [9] H. Hileman, Insulation Coordination for Power Systems, CRC, Boca Raton, FL, 1999, pp. 627–640. [10] F.H. Silveira, S. Visacro, R. Souza Filho, Calculation of backflashover outage rate of transmission lines: a discussion on traditional methodologies and recent advances, in: Proceedings of 2015 International Symposium on Lightning Protection (XIII SIPDA), Brazil, 2015, pp. 315–319. [11] M.A. Sargent, M. Darveniza, Tower surge impedance, IEEE Trans. Power Appar. Syst. PAS-88 (May) (1969) 680–687. [12] W.A. Chisholm, Y.L. Chow, K.D. Srivastava, Lightning surge response of transmission towers, IEEE Trans. Power Appar. Syst. PAS-102 (September (9)) (1983) 3232–3242. [13] A.J. Eriksson, K.H. Weck, Simplified procedures for determining representative substation impinging lightning overvoltages, in: International Conference on Large High Voltage Electric Systems, CIGRE 33-16, Paris, 1988. [14] R.B. Anderson, A.J. Eriksson, Lightning parameters for engineering application, Electra 69 (1980) 65–102. [15] F.H. Silveira, S. Visacro, J. Herrera, H. Torres, Evaluation of lightning-induced voltages over lossy ground by the hybrid electromagnetic model, IEEE Trans. Electromagn. Compat. 51 (February (1)) (2009) 156–160. [16] F.H. Silveira, S. Visacro, The influence of attachment height on lightning-induced voltages, IEEE Trans. Electromagn. Compat. 50 (August (3)) (2008) 743–747. [17] A. Soares Jr., M.A.O. Schroeder, S. Visacro, Transient voltages in transmission lines caused by direct lightning strikes, IEEE Trans. Power Deliv. 20 (April (2)) (2005) 1447–1452. [18] R.O. Caldwell, M. Darveniza, Experimental and analytical studies of the effect of non-standard waveshapes of the impulse strength of external insulations, IEEE Trans. Power Appar. Syst. 92 (July (4)) (1973) 1420–1428. [19] 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 (June (3)) (1988). [20] W.A. Chisholm, New challenges in lightning impulse flashover modeling of air gaps and insulators, IEEE Electr. Insul. Mag. 26 (2) (2010) 14–25.
Please cite this article in press as: F.H. Silveira, et al., Lightning performance of transmission lines: Assessing the quality of traditional methodologies to determine backflashover rate of transmission lines taking as reference results provided by an advanced approach, Electr. Power Syst. Res. (2016), http://dx.doi.org/10.1016/j.epsr.2017.01.005