1. Introduction

For a distribution network protection from lightning, several combinations from surge arresters (SAs), overhead ground wires (OHGWs), and grounding system can be used. In case of Korea Electric Power Company (KEPCO), a distribution network utility of South Korea, all of them have been used with multi-grounded system until 2021. However, it has always been debatable whether installing all of the equipment or not since there is a trade-off issue between an economic efficiency and an acceptable lightning performance by utilities.

A lightning performance evaluation has been studied in many literatures. Reference ^[1] carried out a study to test how the presence of the buildings nearby the overhead lines influences the lightning performance of the lines. The authors focused on the lightning electromagnetic pulse (LEMP) attenuation of indirect strokes provided by the buildings to evaluate the lightning performance. The results show that the LEMP effect provided by the buildings significantly improves the lightning performance, therefore, the LEMP reduction effect must be considered to calculate the lightning performance accurately. However, the lightning performance is evaluated for a single conductor with a 150kV withstand voltage. Therefore, it is not possible to estimate the lightning performance reflected the LEMP effect for multi-conductor lines with lateral.

Reference ^[2] suggested the stratified sampling technique application to the assessment of the indirect lightning performance of low voltage (LV) distribution lines. They experiment three different neutral grounding configurations to analyze the effect of the neutral grounding of the line against the indirect lightning. The results show that neutral grounding improves the LV line performance whereas additional neutral grounding appears to worsen the induced voltage stress at the customers' connection point. However, the line is composed of four unshielded insulated wires except for the overhead ground wire.

Reference ^[3] proposed the recursive stratified sampling technique to reduce the computational time for the lightning performance of the distribution. The Standard Monte Carlo (MC) and Stratified Sampling methods are compared, and the results show that the proposed procedure has the advantages of not only reducing computational time but also reducing the importance of the choice of the smallest area including the perspective stroke locations of the events. However, the proposed procedure is considered according to the SAs installation interval for a single overhead line and network composed by a main feeder, and laterals without SAs.

Reference ^[4] addressed the influence of reflecting on actual insulation volt-time curves and suggested reducing the threshold level – 1.2 times critical flash over voltage (1.2CFO) in the paper – to estimate a more realistic flashover rate of distribution lines. They conduct the different flashover criteria of multiply factors 1.5 and 1.2, respectively. The results show that the threshold level of the simplified 1.5CFO criterion traditionally used is capable to underestimate the flashover rate of the line due to indirect stroke. However, the results did not reflect the realistic conditions of the distribution network including the equipment such as the shielding wires and SAs.

Reference ^[5] calculated the flashover rate due to direct negative lightning and considered the 6.6kV distribution lines with SAs and OHGW installing intervals. The flashover rate of distribution line is calculated for the negative first strokes and negative subsequent stroke. However, the ground resistance of SA and OHGW is used as a fixed value. Therefore, the effect of the grounding resistance on the flashover rate cannot be confirmed. In addition, the LV line was modeled except for the transformer model.

Reference ^[6] proposed the analytical approach to reduce the required computer resources significantly and investigated the influences of the shield wires in lightning performance. The simulation is reflected in a vertical line and horizontal line configurations by adding multiple shield wires. The results show that adding multiple shield wires can improve the lightning performance. However, it is limited in deriving a realistic operation plan for insulation coordination between devices because it does not reflect the devices such as insulators, SAs, and transformers.

Reference ^[7] investigated indirect lightning flashover rate considering first and subsequent strokes. Furthermore, analysis of the parameters affecting the flashover rate, such as front-time value of the current, soil resistivity, stroke velocity, is also performed. However, a simplified line model is considered to calculate the lightning performance: a single overhead line from the Cigré model, 2km long, 10m high.

Reference ^[8] proposed a statistical method to estimate the lightning performance associated with the lightning interception probability distribution of the line conductors not using the MC method traditionally used in the relevant studies. In addition, they analyze the effects of the line parameters, shielding of nearby objects, soil resistivity, and the lightning crest current distribution on the lightning performance of distribution lines quantitatively. However, the simplified coupling model of IEEE std. 1410 and statistical lightning attachment model are implemented to assess and expected the lightning performance.

In this paper, to overcome the limitations of the previous works, we focus on the consideration of both MV and LV lines for lightning performance evaluation of KEPCO distribution lines and the analysis of the sensitivity of the lightning performance of the distribution lines to different configuration of LV and MV grounding systems, distance between SAs, as well as presence of OHGWs.

The rest of the paper is structured as follows. Section 2 thoroughly describes the models adopted in the study. Section 3 presents the time domain simulations for indirect lightning events with an analysis of the influence of the grounding resistance and the presence of medium voltage/low voltage (MV/LV) transformers and lines. Section 4 presents the calculation of the lightning performance of the LV lines. Section 5 outlines the conclusion.

2.Models of MV/LV Distribution Lines and Components

This section describes the geometrical configuration of the line and all the components adopted in the EMTP simulations.

2.3 Surge Arresters and Surge Protective Devices

The current-voltage characteristic of the MV SA is shown in Fig. 1.

Fig. 1. MV SAs characteristic

According to the characteristic the SA has a nominal discharge current of 10kA corresponding to a lightning impulse protection level equal to 64.2kV. The SA can be therefore considered of distribution class with high duty. The reference voltage corresponding to 1mA is equal to 39.8kV that correspond to a RMS voltage equal to 28.2kV, that is larger than the system rated voltage of 22.9kV, and is consistent with a MV distribution system with resonant or insulated neutral.

By comparison with technical data of SAs of rated voltage 21kV with similar residual voltages at 8/20μs discharge currents, the residual voltage at 10kA steep front discharge current is of about 71kA. This value, together allow to estimate the dynamic response of the SA by using the model proposed by ^[11].

2.4 Distribution Transformer Model

We used a black box transformer model inferred by using admittance matrices at logarithmically spaced frequencies between 1kHz and 1MHz measured on a distribution transformer. The transformer has rated power 100kVA, rated voltages 15/0.4kV and is an oil insulated pole mounted.

The admittances of the transformer were measured by a virtual instrument composed by an oscilloscope and a signal generator driven by a Labview environment. The measurement and identification procedure are the same presented in ^[12].

The transformer has 3MV terminals and 4LV terminals. So, the transformer has 7 terminals plus the tank ground terminal. The neutral is assumed grounded. The admittance matrices have therefore order 6. In particular, denoting the MV terminals by the symbols 1, 2, 3, and the LV terminals by 4, 5, 6, the transformer admittance matrices, one for each frequency can be expressed as:

(3)

where each element has the following relationships:

(4)

The frequency responses were fitted by rational functions by using a Vector Fitting tool ^[13] and an enforcing passivity procedure that implements the method proposed in ^[14]. The fitted rational functions are used to define the admittances of the multi-port equivalent network of the transformer by means of the following relationship:

(5)

$y_{ii,\: \pi}\simeq\sum_{j=1}^{m}Y_{ij}$

(6)

$y_{ii,\: \pi}\simeq -Y_{ij}$

The multi terminal π-equivalent circuit can be implemented in EMTP-like programs by means of frequency dependent equivalent networks, i.e. equivalent circuits with lumped parameters such as resistances, inductances and capacitances whose frequency response match the fitted admittances of the multi-port network, schematically shown in Fig. 2.

Fig. 2. Generic structure of a FDB (Frequency Dependent Branch) in EMTP

The procedure for the selection of the parameters of the equivalent network is the same illustrated in ^[15].

3.Overvoltages in MV and LV Lines Due to Indirect Lightnings

3.1 Transferred Overvoltages Due to Indirect Lightnings

In this subsection, the overvoltages transferred to the secondary side of the distribution transformer and the response of the line are presented. An external electromagnetic field originated by a lightning return stroke in the vicinity of the line is considered. Fig. 3 shows the topology of the line and a lightning stroke location. The red circles indicate the poles grounded with $R_{ga}$= 25Ω and all the other poles are grounded with $R_{gb}$= 300Ω. The line length is 2000m. The line terminations are connected to the matrix of the line surge impedances. 40 poles are considered. The stroke location is at 50m away from the center of the line and equidistant to the line terminations.

Fig. 3. Top view of the line and the strike location (X) for the first simulation case

It is assumed that the return stroke velocity is 1.5×108m/s and the Transmission Line (TL) model is adopted for the return stroke. The channel-base current is assumed to has a 12kA peak amplitude and a maximum time derivative of 40kA/μs, which are the medians of subsequent return strokes ^[16] and are represented as:

(7)

$i(0,\: t)=\dfrac{I_{0}}{\eta}\dfrac{(t/\tau_{1})^{n}}{(t/\tau_{1})^{n}+1}\exp(-t/\tau_{2})$

where

(8)

$\eta =\exp\left[\left(-\dfrac{\tau_{1}}{\tau_{2}}\right)\left(\dfrac{\tau_{2}n}{\tau_{1}}\right)^{1/n}\right]$

Equations (7) and (8) have the following parameters ^[17]:

$I_{01}=10.7$ kA, $\tau_{11}=0.25\mu s$, $\tau_{21}=2.5\mu s$, $n_{1}=2$,

$I_{02}=6.5$ kA, $\tau_{12}=2.1\mu s$, $\tau_{22}=230\mu s$, $n_{2}=2$.

The electromagnetic field is calculated by using the model described in ^[18].

In the following figures, both the total voltages and the voltages across the insulators are reported. The former is the voltages respect to the remote far ground assumed as undisturbed, the latter is the voltages across the MV insulators. The insulator voltages are equal to the voltage between the MV phase conductors and the steel arm of the pole, due to the presence of the grounding lead, there is a little difference between the voltage of the OHGW (or shield wire) and the neutral, therefore the insulator voltage has been taken equal to the voltage between the MV phase wires and the neutral wire. The ground resistivity of the ground σg is 1mS/m and the relative permittivity $\epsilon_{rg}$ is equal to 10.

Fig. 4 shows the overvoltages on the MV side due to a subsequent stroke, while Fig. 5 shows the voltages transferred on the LV-side of the transformer. The neutral voltage is the same in both figures. In Fig. 5(a), the overvoltages are calculated with respect to the voltage of the neutral conductor. The same comparison is provided in Fig. 6 and Fig. 7 for the case of a first return stroke. In all the cases, the grounding resistance $R_{ga}$ is set to 25Ω.

Fig. 4. Overvoltages on the MV side due to a subsequent stroke. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$

Fig. 5. Overvoltages on the LV side due to a subsequent stroke. (a) total voltage, (b) phase-to-neutral. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$

Fig. 6. Overvoltages on the MV side due to a first stroke. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$

Fig. 7. Overvoltages on the LV side due to a first stroke. (a) total voltage, (b) phase-to-neutral. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$

3.2 A Case of MV and LV Lines on the Same Poles

The presence of the LV conductors does not affect the overvoltages induced on the MV line. On the other hand, in order to calculate the accurate response of the LV line to an external electromagnetic field, it is necessary to consider both the MV and LV wires in the same lightning-induced overvoltage-line model.

Fig. 8 shows the topology of the considered double circuit line and the stroke location. The poles in which Rga is varied are indicated in red. The simulations are repeated in case MVSAs are installed at the poles indicated by the blue circles.

Fig. 9 shows the overvoltage induced by a first stroke at 50m from the line center, as represented in Fig. 8. Fig. 10 shows the same overvoltages but referred to the neutral voltage, it is the same as in Fig. 6 since the LV phase conductors do not affect the overvoltages in the MV ones and the neutral.

In this case, very dangerous overvoltages arise in the LV conductors, which could also result in flashovers of the cable insulation. The presence of SAs on the MV line is only partially effective in reducing the overvoltages on the LV conductors, as the peak reduces from 25kV to slightly less than 15kV.

Fig. 8. Top view of the line and the strike location (X) for the second simulation case

Fig. 9. Overvoltages on the LV conductors due to a first stroke. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$, $R_{ga}$=25Ω. (a) without MV SAs installed, (b) with MV SAs installed

Fig. 10. Phase-to-neutral overvoltages on the LV conductors due to a first stroke. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$, $R_{ga}$= 25Ω. (a) without MV SAs installed, (b) with MV SAs installed

3.2.1 Effect of the Grounding Resistance of the Poles

Fig. 11 shows the overvoltages peaks on the LV line induced by a first stroke for different values of Rga. Also in this case, lowering the grounding resistance has a beneficial effect on the total overvoltages, as it lowers the voltage of the neutral conductor, but is not effective in reducing the phase-to-neutral voltages, which instead increase as the value of Rga decreases. The comparison is repeated in Fig. 12 for the case in which MV SAs are installed.

Fig. 11. Overvoltages peaks on the LV line induced by a first stroke for different values of $R_{ga}$. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$ without MV SAs installed

Fig. 12. Overvoltages peaks on the LV line induced by a first stroke for different values of $R_{ga}$. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$ with MV SAs installed

3.2.2 Effect of the Transformer on the LV over voltages

Fig. 13 and Fig. 14 show the same comparisons of Fig. 9 and Fig. 10 in which no transformer was considered. With respect to the previous case the phase to ground overvoltage peaks are lower, while the neutral voltage is practically unchanged.

Fig. 13. Overvoltages on the LV conductors due to a first stroke with pole transformer. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$, $R_{ga}$= 25Ω. (a) without MV SAs installed, (b) with MV SAs installed

Fig. 14. Phase-to-neutral overvoltages on the LV conductors due to a first stroke with pole transformer. $\sigma_{g}=1$mS/m, $\epsilon_{rg}=10$, $R_{ga}$= 25Ω. (a) without MV SAs installed, (b) with MV SAs installed

4.Indirect Lightning Performance of LV Lines

The lightning performance evaluation is conducted through the MC method, as presented in ^[19-20]. Generally (e.g. ^[21]), the lightning performance is evaluated by drawing of a curve providing the expected annual number of lightning events $F_{p}$ that cause voltages larger than the insulation voltage on abscissa:

where $n$ is the number of events causing voltages higher than the insulation level, $A$ is the area of striking and $N_{g}$ is the annual ground flash density (which is assumed equal to 1flash/km$^{2}$/yr).

In the following simulations, 64,000 MC events (63,654 indirect events, 346 direct events) are considered. The bounds of area $A$ are 4km far from the lines. The topology of the considered MV and LV lines is shown in Fig. 15. MV SAs are placed every 500m, in correspondence of every pole grounded with $R_{ga}$.

Fig. 15. Topology of the MV+LV network and location of the groundings and SAs

In this Section, in order to assess the influence of different value of the grounding resistance and of the ground conductivity, the following Cases are considered:

1. $R_{ga}$ = 25Ω, LV-line A grounded at 250m and 500m with $R_{ga}$, $R_{gn}$ = 25Ω, $\sigma_{g}=1$mS/m.

2. $R_{ga}$ = 10Ω, LV-line A grounded at 250m and 500m with $R_{ga}$, $R_{gn}$ = 10Ω, $\sigma_{g}=10$mS/m.

3. $R_{ga}$ = 10Ω, LV-line A grounded only at 500m with $R_{ga}$, $R_{gn}$ = 10Ω, $\sigma_{g}=10$mS/m.

Fig. 16 shows the indirect lightning performance of the LV line evaluated at the following observation points:

– transformer LV terminals

– the line center

– the LV-line terminals

Fig. 16. Case 1. (a) total voltages (b) phase-to-neutral voltages

The calculation results are obtained by using (9) and refer to the total voltages (phase respect to the far ground) and the phase-to-neutral voltages for the configuration of Case 1.

Fig. 17 reports the same results but for Case 2. By comparing the results of Case 2 respect to those of Case 1, it can be observed that the lightning performance is significantly improved by the higher value of the ground conductivity and the lower value of the grounding resistances in the configuration of Case 2.

Fig. 18 refers to the configuration of Case 3, in which the neutral conductor is grounded only at the line end. In this configuration, the performance at the line center, calculated by making reference to the total voltages, is worse than that calculated at the line termination. The lightning performance calculated at the termination is not meaningfully influenced by the presence of the grounding at the mid-point of the line.

Fig. 17. Case 2. (a) Total voltages (b) Phase-to-neutral voltages

Fig. 18. Case 3. (a) total voltages (b) phase-to-neutral voltages

5. Conclusion

In this paper, the focus was on the definition of the main calculation models for the assessment of the lightning performance of the LV distribution lines, also on the indirect lightning performance with different configurations of lighting protection equipment.

In the simulations, we considered at least two groundings of the LV neutral: at the transformer and at the termination of the line. The case of a single grounding of the neutral is not considered because it worsens too much the indirect lightning performance. Many distribution system operators adopting TN distribution for the grounding system type, all the more reason, have multiple grounding also for safety reasons.

From the simulation results, it can be observed that the presence of SAs on the MV line is only partially effective in reducing the overvoltages on the LV conductors. And obviously, the lightning performance is significantly improved by the higher value of the ground conductivity and the lower value of the grounding resistances. It is noteworthy that the LV line lightning performance calculated at the termination is not meaningfully influenced by the presence of the grounding at the mid-point of the line.