2012 International Conference on Lightning Protection (ICLP), Vienna, Austria Frequency Dependence of Soil Parameters: The Influence on the Lightning Performance of Transmission Lines Silvério Visacro, Fernando H. Silveira, Sillas Xavier, Henrique B. Ferreira LRC – Lightning Research Center UFMG – Federal University of Minas Gerais Brazil E-mail:
[email protected] Abstract— The impact of the frequency dependence of soil parameters on the lightning response of transmission lines was assessed by simulation, taking an existing 138-kV line as reference. This can be important for overvoltages experienced across insulators due to lightning strikes, in particular of first strokes and soil resistivity above 300 Ωm. The effect causes a percentage decrease of the backflashover rate expected under the assumption of constant soil parameters of around 8%, 20% and 25% for values of soil resistivity of 300, 1000 and 2000 Ωm. Keywords-Lightning; Performance of transmission lines; Soil resistivity and permittivity; Impact of frequency dependent soil parameters on backflashover. I. INTRODUCTION Lightning is a frequent cause of transmission line outages. Direct strikes to the line develop overvoltages across insulator strings that might result in electrical discharges, leading to faults [1,2]. Backflashover largely prevails as the main mechanism responsible for lightning-related outages of lines below 500 kV installed in regions of unfavorable soil- resistivity. Therefore, this mechanism, which is mainly governed by tower-footing grounding impedance, is the main focus of practices intended to improve the lightning performance of lines. In most cases, such practices consist basically in reducing this impedance. The use of surge arresters to prevent flashovers is an increasing alternative practice. Once a tower or the shield wires close to the tower are stricken by lightning, the balance between the amplitude of the overvoltage experienced across insulator strings and the insulation withstand determine whether a backflashover occurs or not. Some lightning current parameters have influence on the resulting overvoltage wave and therefore affect the probability of backflashover, notably the peak current that is almost proportional to the overvoltage peak. The current waveform has also great influence on overvoltage amplitude and waveform. In respect to line parameters, insulation withstand that is strongly influenced by the voltage level of the line and tower- footing grounding impedance have remarkable influence on backflashover occurrence. Other parameters that affect the overvoltage amplitude have also some influence, such as tower configuration, the distance between adjacent towers and their grounding impedance, the number of shielding wires and the geometrical disposal of line conductors. In order to determine the developed overvoltage, typically, the severe condition illustrated in Figure 1, corresponding to a direct strike to the line is simulated, assuming a given waveform and amplitude for the return stroke current. Figure 1. Simulated condition: direct strike to the tower. The evaluation of flashover occurrence is usually done by means of the integration method (also called Disruptive Effect (DE) method) [3,4]. This method considers the waveform and amplitude of overvoltage to determine whether they might cause electrical arcs across insulators. Different approaches can be used to simulate the overvoltage developed in response to direct strikes to the line. The authors frequently employ a field approach based on the application of the Hybrid Electromagnetic Model (HEM) [5]. The relevant effect of the grounding impedance to decrease the amplitude of lightning overvoltage is illustrated in Figure 2, which shows voltage waves resulting across the upper insulator string due to a direct strike to the tower top. The incident lightning current is approached by a triangular 2/50 µs wave 978-1-4673-1897-6/12/$31.00 ©2012 IEEE with a 50-kA peak current. It is worth mentioning that reducing grounding resistance is an indirect way to decrease the tower- footing grounding impedance, as explained in [6]. The overvoltages of Figure 2, taken from [2], were calculated varying the tower-footing grounding resistance (Rg) from 10 to 80 Ω for the same arrangement of electrodes (50 m long counterpoise shown in Figure 1), considering different values of soil resistivity. 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 0 2 4 6 8 10 Time (µµµµs) V o lt a g e ( k V ) Rg = 40 ΩΩΩΩ - ρρρρ = 3200 ΩΩΩΩ.m Rg = 30 ΩΩΩΩ - ρρρρ = 2400 ΩΩΩΩ.m Rg = 20 ΩΩΩΩ - ρρρρ = 1600 ΩΩΩΩ.m Rg = 10 ΩΩΩΩ - ρρρρ = 800 ΩΩΩΩ.m Rg = 80 ΩΩΩΩ - ρρρρ = 6400 ΩΩΩΩ.m Figure 2. Overvoltage across upper insulator string for different grounding- resistance values (2/50-µs triangular current wave). Adapted from [2]. While the resistance is decreased from 80 to 10 Ω, the overvoltage vary from the order of 2.25 MV to around 0.75 MV, achieving an overvoltage reduction of around 66%. Though this simplified simulation denotes the relevant role of the grounding resistance to decrease the overvoltage amplitude, an accurate evaluation of the overvoltage developed in response to direct lightning strikes requires a realistic representation of the impressed lightning current, of the arrangement of tower, conductors and electrodes and of the soil where electrodes are buried. The latter is the focus of this paper. In particular, this work investigates how the frequency dependence of soil parameters (resistivity ρ and permittivity ε) affects the lightning overvoltage across insulators due to direct strikes to the line and the expectation of backflashover. II. DEVELOPMENTS A. Frequency dependence of soil parameters In spite of the well-known fact that soil resistivity and permittivity present significant frequency dependence, the response of grounding electrodes is calculated assuming constant values of both soil parameters. In the lack of accurate formulation to express the frequency dependence of such parameters, this effect is usually neglected. In a conservative approach, the resistivity is assumed as the value measured at low frequency and the relative permittivity of soil is considered to vary from 4 to 81, according to the soil humidity [6]. Recently, a new methodology for measuring the frequency variation of soil resistivity and permittivity in field conditions was developed and experimentally validated [7]. It was systematically applied to different soils in order to allow deriving general expressions (1) and (2) to estimate this parameters variation in the typical range of frequency content of lightning currents [8]: 6 0.73 0.65 1 0 0{1 [1.2 10 ] [( 100) ]}fρ ρ ρ − −= + ⋅ ⋅ ⋅ − (1) 3 0.47.6 10 1.3r fε −= ⋅ + (2) where ρ is the soil resistivity at frequency f in Hz, ρ0 is the soil resistivity at 100 Hz and εr is the soil relative permittivity at frequency f. Expression (1) is valid in the 100-Hz to 4-MHz range and expression (2) is valid in the 10-kHz to 4-MHz range. Below 10 kHz, using the value of relative permittivity given by (2) at 10 kHz is suggested. B. The simulation of lightning overvoltage The Hybrid Electromagnetic Model [5] was employed to simulate the overvoltage developed across the insulators of an existing 138-kV-transmission line in response to lightning strikes to the tower top, as depicted in Figure 1. The typical 30- m high self-sustained tower of this line, supporting four aerial cables (one ground wire and three phase conductors) is represented in Figure 3. Figure 4 shows the two arrangements of grounding electrodes used at the line tower-footing, according to the local soil resistivity. 2.9 m 1.65 m 2 3 .2 5 m 3 0 m 0.8 m 3.03 m 3.72 m 1.86 m 6.0 m Figure 3. Tower configuration. L 6 m 6 m 10 m 6 m 6 m L (a) (b) Figure 4. Grounding electrode arrangement: type I (a) and II (b). The current waves represented in Figure 5 that closely reproduce the median peak currents and front times parameters of first and subsequent strokes measured at Mount San Salvatore [9] were supposed to be impressed on the tower top, in order to simulate the developed lightning overvoltage. Three values of low-frequency soil resistivity in the range of 300 to 2000 Ωm were considered in simulations, that explored the results of two assumptions for soil parameters: constant soil parameters (ρ=ρ0; εr=10) and frequency dependent soil parameters determined from expressions (1) and (2) [8]. In order to analyze the effect of frequency dependent soil parameters, two kind of simulated results were developed: the grounding potential rise GPR at the tower footing and the overvoltage across insulator strings. 0 5 10 15 20 25 30 35 0 10 20 30 40 Time (µµµµs) C u rr e n t (k A ) 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Time (µµµµs) C u rr e n t (k A ) (a) (b) Figure 5. Representative current waveforms impressed on the tower top with median peak currents and front times of first (a) and subsequent (b) strokes. FST: Ip = 31.1 kA, Td30=3.83 µs, SUB: Ip = 11.8 kA, Td30 = 0.67 µs. Adapted from [10]. III. RESULTS AND ANALYSIS A. Simulated response of grounding electrodes The impulse grounding impedance ZP, given by the ratio of the peak values of developed GPR and impressed current, was calculated from each simulated tower-footing grounding potential rise, considering both assumptions of soil parameters. The results obtained for different values of low-frequency soil resistivity are summarized in Table I, which comprises the arrangement of electrodes, the low-frequency resistance Rg and the impulse impedance. TABLE I. GROUNDING PARAMETERS DETERMINED FOR THE IMPRESSION OF FIRST- AND SUBSEQUENT-STROKE CURRENTS OF FIGURE 5 CONSIDERING CONSTANT AND FREQUENCY DEPENDENT SOIL PARAMETERS. First-stroke current Impedance Zp (Ω) Subsequent-stroke current Impedance Zp (Ω) ρ0 (Ω.m) Type L (m) Rg (Ω) (ρ=ρ0, εr=10) ρ=ρ(ω), ε(ω)) % (ρ=ρ0, εr=10) (ρ=ρ(ω), ε(ω)) % 300 I 10 11,1 10,66 10,28 -3,6 9,46 8,42 -11 1000 II 50 12,5 12,06 10,47 -13,2 18,21 12,16 -33 2000 II 70 19,5 18,56 15,28 -17,7 27,31 15,40 -44 The impulse impedance of a given grounding arrangement depends on the current assumed to be impressed on electrodes. The results in Table I show clearly that the frequency dependence of soil parameters causes a general decrease of impulse impedance that becomes more evident with increasing low-frequency soil resistivity. This decrease is much larger for subsequent strokes due to their frequency content that includes higher frequency components. Reductions of grounding impedance of around 11% to around 44% are observed while soil resistivity varies from 300 to 2000 Ωm for subsequent strokes. Such reductions are decreased to the order of 3.6% to 18% respectively for first strokes. B. Overvoltages across insulator strings Figure 6 shows the overvoltage waves experienced across the upper insulator strings for the same conditions considered in Table I. Table II summarizes the values of peak overvoltages of the waves shown in Figure 6. 0 100 200 300 400 500 600 0 5 10 15 20 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) 0 100 200 300 400 500 600 0 2 4 6 8 10 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) (a) (b) 0 100 200 300 400 500 600 700 0 5 10 15 20 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) 0 100 200 300 400 500 600 700 0 2 4 6 8 10 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) (c) (d) 0 100 200 300 400 500 600 700 0 5 10 15 20 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) 0 100 200 300 400 500 600 700 0 2 4 6 8 10 Time (µµµµs) V o lt a g e ( k V ) ρ ρ ρ ρ = ρρρρ0000 , ε , ε , ε , εr = 10 ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω)ρ = ρ(ω) , ε(ω) (e) (f) Figure 6. Developed overvoltage waves across upper insulator string of line under the assumption of constant and frequency-dependent soil parameters for different values of soil resistivity ρ0. (Left column:First stroke; Right column: Subsequent stroke). (a)-(b) 300 Ω.m, (c)-(d) 1000 Ω.m, (e)-(f) 2000 Ω.m. TABLE II. PEAK OVERVOLTAGE ACROSS THE UPPER INSULATOR STRING OF THE 138-KV LINE FOR DIFFERENT VALUES OF SOIL RESISTIVITY ρ0. First-stroke current Overvoltage (kV) Subsequent-stroke current Overvoltage (kV) ρ0 (Ω.m) L (m) (ρ=ρ0, εr=10) (ρ=ρ(ω), ε(ω)) % (ρ=ρ0, εr=10) (ρ=ρ(ω), ε(ω)) % 300 10 531.54 518.48 -2.46 595.42 593.78 -0.28 1000 50 582.48 537.83 -7.67 605.57 598.00 -1.25 2000 70 674.97 571.22 -15.37 609.27 596.97 -2.02 The results of Table II show that, as expected, the frequency dependence of soil parameters causes a general reduction of overvoltages and this effect becomes more relevant as the low-frequency resistivity is increased. This reduction is much more pronounced for overvoltages yielded by first strokes, ranging from around 2.5% to 15% for soils with ρ0 varying from 300 to 2000 Ωm. It is worth mentioning that, for soils of 1000 Ωm and above, the frequency dependence effect causes the amplitude of voltage wave to remain decreased during a period along the wave after the peak, as depicted in Figure 6, and this reduces the potential to flashover across insulators. On the other hand, Table II shows that this effect is negligible for subsequent strokes, in spite of the much stronger reduction of impulse grounding impedance it yields for currents of subsequent strokes. This behavior can be partially attributed to the weak effect of decreasing grounding impedance to diminish the amplitude of overvoltages yielded by subsequent strokes, as discussed in [10]. The results obtained for first strokes suggest that the frequency dependence of soil resistivity and permittivity might contribute to diminish the number of backflashovers, once the area to be integrated in the application of the DE method is significantly decreased, as shown in Figure 6 for soils of 1000 Ωm and above. This finding motivated assessing the impact of the frequency dependent soil parameters on backflashover. Taking the overvoltage waveformes of Figure 6 for each value of ρ0 as reference, the DE method was applied to determine the peak voltage (and therefore the peak current) required to flashover. Then, considering the cumulative distribution of first-stroke peak currents measured at Mount San Salvatore [9], the percentages of currents expected to overpass the value (critical peak current) required to flashover were determined for both assumptions, constant and frequency dependent soil parameters. This percentage equals the expectation of backflashover per strike to the tower. The results are summarized in Table III. TABLE III. CRITICAL PEAK CURRENTS OF FIRST STROKES REQUIRED TO FLASH OVER THE UPPER INSULATOR STRING OF THE 138-KV LINE FOR DIFFERENT VALUES OF SOIL RESISTIVITY ρ0. (ρ = ρ0, εr = 10) (ρ = ρ(ω), ε(ω)) ρ0 (Ω.m) L(m) Ip (kA) (%) Ip (kA) (%) ∆ (%) 300 10 76.6 8.7 79.4 8.0 8.1 1000 50 68.8 11.2 75.3 9.0 20 2000 70 47.1 25.2 54.3 18.9 25 The content of Table III shows that the frequency dependence of soil parameters causes a decrease on the expectation of backflashover for soil resistivity of ρ0 300 Ωm and above that becomes more significant as ρ0 is increased. This reduction ranges from 8.1% to 25% for values of resistivity varying from 300 to 2000 Ωm. IV. CONCLUSIONS This paper assessed the impact of the frequency dependence of soil parameters on the lightning response of transmission lines, taking an existing 138-kV line as reference. It was shown that this impact, quantified in terms of backflashover expectation of the tower per strike, is negligible for subsequent strokes and much reduced for first strokes specifically for soil resistivity ρ0 below 300 Ωm. However, the impact can be important for first strokes for soil resistivity ρ0 larger than 300 Ωm and becomes more relevant for increasing soil resistivity. The effect causes a percentage decrease of the backflashover rate expected under the assumption of constant soil parameters of around 8%, 20% and 25% for values of soil resistivity ρ0 of 300, 1000 and 2000 Ωm. The results suggest it is recommended to take the frequency dependence of soil resistivity and permittivity into account on accurate calculations of the lightning performance of transmission lines installed in regions of moderate and high soil resistivity. REFERENCES [1] 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., vol. 1, pp. 60–68, 2007, [2] S. Visacro, F.H. Silveira, and A. De Conti, “The use of underbuilt wires to improve the lightning performance of transmission lines,” IEEE Trans. Power Del., vol. 27, no. 1, pp. 205-213, Jan. 2012 [3] M. Darveniza and A. E. Vlastos, “The generalized integration method for predicting impulse volt-time characteristics for non-standard wave shapes—A theoretical basis,” IEEE Trans. Elect. Insul., vol. 23, no. 3, pp. 373–381, Jun. 1988. [4] A. H. Hileman, Insulation coordination for power systems. Boca Raton, FL: CRC, 1999, pp. 627–640. [5] S. Visacro and A. Soares Jr., "HEM: a model for simulation of lightning- related engineering problems," IEEE Trans. Power Del., vol. 20, no. 2, pp. 1026–1208, Apr. 2005. [6] S. Visacro, “A comprehensive approach to the grounding response to lightning currents,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 381–386, Jan. 2007. [7] S. Visacro, R. Alipio, M. H. Murta Vale, and C. Pereira, “The response of grounding electrodes to lightning currents: the effect of frequency- dependent soil resistivity and permittivity,” IEEE Trans. Electromagn. Compat., vol. 53, no. 2, pp. 401–406, May 2011. [8] S. Visacro and R. Alipio, “Frequency dependence of soil parameters: Experimental results, predicting formula and influence on the lightning response of grounding electrodes,” 2012, DOI: 10.1109/TPWRD.2011.2179070. [9] R. B. Anderson and A. J. Eriksson, “Lightning parameters for engineering application,” Electra, vol.69, pp. 65-102, 1980. [10] F.H. Silveira, S. Visacro, A. De Conti, C.R. Mesquita, “Backflashovers of transmission lines due to subsequent lightning strokes”, IEEE Trans. Electromagn. Compat, vol.54, no.2, pp. 316-322, Apr. 2012. doi:10.1109/TEMC.2011.2181851. ACKNOWLEDGMENT The participation of Prof. Visacro and both undergraduate students Sillas Xavier and Henrique B. Ferreira has been partially supported by grants provided by CNPq.