Influence of lightning current waveforms of cloud-to-ground lightning with multi-return strokes on the lightning withstand level of 500 kV transmission lines

The most common factor causing line tripping is lightning strokes, and it is necessary to conduct research on the lightning withstand level (LWL). The statistical results of lightning location systems (LLS) in various regions of China indicate that the total proportion of cloud-to-ground lightning with multi-return strokes in nature is 30% to 50%. The traditional method of lightning protection design for 500 kV lines based on the current waveform of single lightning strokes is no longer enough to effectively protect existing transmission lines. Therefore, in this paper an electromagnetic transient simulation model for 500 kV lines was established, to compare the LWL difference between single and multiple lightning strokes. The influence of the tower height, the grounding resistance, and the lightning current waveforms are all simulated and discussed. It is found that the back flashover LWL of 500 kV lines is significantly influenced by the lightning current waveforms. Meanwhile, reducing the grounding resistance cannot effectively increase the LWL of 500 kV lines when the tower is too high and the rise time of the lightning current is too short. It is proposed that the lightning current waveforms should be fully considered while calculating the LWL of 500 kV lines, both single and multiple lightning currents, providing a reference for practical engineering construction.


1.Introduction
China's power system is developing rapidly now, and the requirements for power supply reliability are becoming increasingly high, which puts forward higher requirements for the LWL of power lines [1].At present, the lightning protection performance for transmission lines is mostly calculated with standard lightning current waveforms 2.6/50 μs [2].However, the statistical results of LLS in various regions of China indicate that the total proportion of cloud-to-ground lightning with multi-return strokes in nature is over 30% [3][4][5].Therefore, it is necessary to calculate the LWL of 500 kV transmission lines under different lightning current waveforms, which include cloud-to-ground lightning with multi-return strokes.The safety and stability of the power system can only be guaranteed.
The LWL of transmission lines is influenced by tower height, tower grounding resistance, and lightning current waveform.Based on it, this paper established an electromagnetic transient simulation model for 500 kV lines, to compare the LWL difference between single and multiple lightning strokes.The effects of the tower height, grounding resistance, and lightning current waveforms on the back 2 flashover, as well as the effects of different lightning current waveforms on the shielding failure LWL of the line, are all simulated and discussed.

2.Modeling methods
A 500 kV lines model with 7 towers was established in this paper by the PSCAD/EMTDC program.The span of the tower was set to 400 m.Double circuit lines were adopted and double lightning conductors were erected throughout the entire line.To avoid the impact of lightning current refraction and reflection at the end of the transmission line on the calculation results, the length of the end of the line was set to 10 km.The criterion of insulator flashover adopted the CIGRE Antecedent Development model.A frequency-dependent model was used for the transmission line.
In this paper, different lightning current waveforms were used to simulate the LWL of 500 kV lines, including lightning current waveform 2.6/50 μs (standard [6] lightning current waveform), 1/200 μs (first re-stroke), 0.25/100 μs (subsequent re-stroke) and the measured waveform obtained by Huang et al. [7] in the artificial triggered lightning test in Conghua district, including 3.5/75 μs (first re-stroke) and 0.4/18 μs (subsequent re-stroke).A dual exponential model was used to simulate lightning current waveform: where Im is the amplitude of lightning current, kA.K is the fitting coefficient of the double exponential model.a and b are a parameter of a double exponential function.Fitting different waveforms with different parameters.The impedance of the lightning current channel was taken as 300 Ω and 800 Ω respectively in the model of back flashover and shielding failure.The tower model adopted the multiconductor layered wave impedance model, as shown in Figure 1.

Back flashover lightning withstand level of 500 kV transmission line
The top of the transmission line tower is located at the top of the transmission system, which is the most vulnerable part to lightning strokes.After lightning strikes the tower, due to the impedance of the tower itself and the impedance of the grounding body, the potential at the top of the tower rises, and the potential difference between the two ends of the insulator also increases, resulting in a back striking overvoltage that may cause the insulator to flash over.According to the recommended calculation method in GB/T 50064-2014, the impulse grounding resistance is set to 7 Ω.The tower heights are set as 50 m, 65 m, and 75 m respectively, and the lightning stroke point is located on the top of Tower #4.Simulations were conducted on the back flashover LWL of the line under different waveforms including 2.6/50 μs (standard lightning current waveform), 1/200 μs (standard first re-stroke), 0.25/100 μs (standard subsequent re-stroke), 3.5/75 μs (measured first restroke), and 0.4/18 μs (measured subsequent re-stroke) as shown in Table 1 and Figure 1.As shown in Table 1, the wavefront time of the lightning current waveform of cloud-to-ground lightning with multi-return strokes is generally smaller than the standard lightning current waveform.Therefore, the calculated data when the back flashover LWL of the line generally cannot reach the standard lightning current waveform.When the tower height is 50 m, and the lightning current waveform is the standard single lightning stroke waveform 2.6/50 μs, the back flashover LWL of the line is 294 kA.When the lightning current waveform is the subsequent waveform 0.25/100 μs recommended by standard, that is 143 kA.Compared to the standard lightning current waveform, it has decreased by 51.36%.When the lightning current waveform is the measured subsequent waveform 0.4/18 μs, that is 169 kA, which has decreased by 42.52%.This indicates that when considering the waveform of multiple lightning strokes, there is a significant difference in the LWL of 500 kV transmission lines when considering only the standard lightning current waveform.The shorter the wavefront time of the lightning current is, the more the lightning resistance level decreases, and the greater the difference is.
Further as shown in Figure 2, the influence of tower height on the back flashover LWL of the line under the waveform of multiple lightning strokes will also decrease.For example, under the standard lightning current waveform 2.6/50 μs, if the tower height is increased from 50 m to 75 m, the corresponding LWL is 220 kA, about a 25.17% decrease.But under the lightning current waveform 0.25/100 μs, it decreases by about 18.18%.According to the GB/T 50064-2014, the back flashover LWL of the 500 kV line should not be less than 162 kA when the grounding resistance is 7 Ω.However, under the waveform of multiple lightning strokes, the back flashover LWL the most cannot meet this standard.If only considering the standard lightning current waveform 2.6/50 μs, the tower design and insulation coordination of the transmission line may result in inadequate lightning protection due to insufficient LWL of the transmission line.Therefore, the calculation of back flashover LWL should include consideration of cloud-to-ground lightning with multi-return strokes.
In addition, this paper sets the impulse grounding resistance to 30 Ω, 15 Ω, 10 Ω, and 7 Ω, and then simulates the LWL of the line under different waveforms mentioned above, as shown in Table 2 and Figure 3.As shown in Table 2, although it can increase the LWL of the line by reducing the grounding resistance, the improvement is not significant when the tower is high, and this phenomenon is more prominent under the waveform of multiple lightning strokes with short wavefront time.
Under standard lightning current waveform 2.6/50 μs, when the impulse grounding resistance is 30 Ω, the corresponding LWL of the line is 140 kA.When the impulse grounding resistance is respectively 15 Ω, 10 Ω and 7 Ω, the back flashover LWL of the line are 186 kA, 206 kA, and 220 kA, respectively.It increases by 32.86%, 47.14%, and 57.14% respectively compared to the grounding resistance of 30 Ω.But under the measured subsequent stroke waveform 0.4/18 μs with shorter wavefront time, the LWL of the corresponding line has only respectively increased by 19.80%, 26.73%, and 29.70%, compared to the grounding resistance of 30 Ω.This indicates that although reducing the impulse resistance can improve the LWL of 500 kV transmission lines to some extent, there are significant differences in the degree of improvement under different lightning current waveforms.
Further as shown in Figure 3, the back flashover LWL of the line increases with the decrease of grounding resistance, and the increase is relatively small when the tower is higher.Moreover, there is a significant difference between the measured lightning current waveform of multiple lightning strokes and the recommended lightning current waveform of the standard in back flashover LWL.Compared to the standard lightning current waveform, even if the grounding resistance is further reduced, it cannot meet the minimum standard of LWL required in the standard when considering the actual measurement of multiple lightning strokes or the recommended subsequent lightning stroke waveform in the standard.

Shielding failure lightning withstand level of 500 kV transmission line.
This paper further studied the effect of different lightning current waveforms on the shielding failure LWL of the 500 kV line.The lightning stroke point is located on the A-phase conductor of Tower #4, and the simulation data results are shown in Table 3.As shown in Table 3, the lightning current waveform of cloud-to-ground lightning with multi-return strokes with a longer pulse width results in a lower shielding failure LWL.Among them, the shielding failure LWL of the line under the lightning current waveform of the first stroke is 21 kA, while that under the lightning current waveform of the subsequent stroke is 23 kA, with a difference of nearly 10% between the two.There is also a certain difference, which should be considered for cloud-to-ground lightning with multi-return strokes.

4.Conclusions
A simulation model for a 500 kV transmission line was established in this paper.The effect of single and multiple lightning current waveforms on the LWL was calculated.The influence of the tower heights and grounding resistances was also discussed.The main conclusions are as follows: 1) There is a significant difference in the lightning current waveforms between single and multiple lightning strokes, which has a significant influence on the back flashover LWL of the line.For example, the back flashover LWL under the current waveform 0.25/100 μs of multiple lightning strokes is more than 50% lower than that under the current waveform of a single lightning stroke under the same other conditions.
2) The standard GB/T 50064-2014 requires that the back flashover LWL of 500 kV transmission lines should not be less than 162 kA when the grounding resistance is 7 Ω.However, the influence of tower height and grounding resistance is minimal under the lightning current waveforms with short wavefront time of cloud-to-ground lightning with multi-return strokes, making it difficult to meet this requirement.
3) The difference in shielding failure LWL of 500 kV transmission lines with different lightning current waveforms of cloud-to-ground lightning with multi-return strokes is close to 10%, and certain differences cannot be ignored.
4) Currently, most lightning protection calculations only consider the current waveform of a single lightning stroke, which will result in insufficient lightning protection effectiveness.It is necessary to consider the waveform parameters of multiple lightning strokes in lightning protection calculation and design to improve the effectiveness of lightning protection measures.

Table 1 .
The back flashover LWL at different tower heights.

Table 2 .
LWL of 500 kV line under different grounding resistances.

Table 3 .
Shielding failure LWL of 500 kV transmission line.