On the Relation between Ground Resistivity and Lightning Induced Voltage Evaluation on the

Distribution Lines M. Izadi1,2*, M. Z. A. Ab Kadir3

1,3Centre for Electromagnetic and Lightning Protection Research (CELP), Faculty of Engineering, Universiti Putra Malaysia, UPM, 43400 Serdang, Selangor, Malaysia

2Aryaphase Company, Tehran, Iran *Email: aryaphase@yahoo.com

Abstract - In this paper, the values of lightning induced voltage associated with a typical measured lightning current from triggered lightning experiment on the distribution line are evaluated where the ground reflection at channel base is taken into account. The relation between the peak of lightning induced voltage and the ground reflection factors at channel base, as well as ground impedance and ground resistivity at connection point are also considered and the results are discussed accordingly. The results showed that the values of lightning induced voltage are depend on the ground reflection factor and ground resistivity at the strike point. These information are very important for loghtning performance of distribution system especially for setting up an appropriate protection level on the line, considering the local information of soil is very important and can be helpful for estimation accurate lightning induced voltage.

Keywords: Lightning induced voltage, Ground resistivity, Ground reflection, lightning performance

I. INTRODUCTION

Lightning is a natural phenomenon for which the impact can be affected on the stability of power networks. One of the important effects of lightning is the lightning induced voltage that occurs due to the electromagnetic coupling between the lightning channel and the line conductor [1-5] i.e. when the lightning strikes to the ground or any nearby object to the power lines [6-7]. The amplitude of lightning induced voltage is depend on the lightning current wave shape at channel base and the shapes of current at different heights along lightning channel, as well as the lightning electromagnetic fields due to lightning channel. On the other hand, the ground impedance at striking point can also influence the value of lightning currents at different heights along lightning channel where the reflected currents due to the difference between channel impedance and ground impedancewill be used in the calculation. Furthermore, the values of lightning electromagnetic fields are directly dependent on the current values along lightning channel [8-11]. Likewise, this information will also affect on the evaluated values of lightning electromagnetic fields and lightning induced voltage [12-14]. Therefore, it is very crucial

to consider the ground resistivity data for an accurate estimation of lightning induced voltage, which is mostly ignored in the previous studies. The same thing goes to the ground impedance, which depends on the values of ground resistivity in that area. Therefore, this paper considers on the effect of ground resistivity on the lightning induced voltages with some basic assumptions are listed as follow;

1- The lightning channel is a vertical channel 2- The ground conductivity is perfect 3- The effect of lightning branches is ignored 4- The surface of the ground is assumed to be flat

II. RETURN STROKE CURRENT

In this study, the lightning return stroke current at channel base is simulated using double Heidler functions as expressed by equation(1)[15-17].

I 0, t = [!!"η!

!τ!!

!!

!! !τ!!

!! exp!!τ!"

+ !!"η!

!τ!"

!!

!! !τ!"

!! exp!!τ!!

] (1)

Where:

i 0, t is the channel base current,

t is the time step,

i!"/  i!"is the amplitudes of the channel base current,

τ!!/τ!" is the first/second front time constant,

τ!"/τ!! is the first/second decay- time constant,

n!/  n!is the first/second exponent (2~10),

η! = exp  [− τ!! τ!" n!τ!"τ!!

!!!] ,

η! = exp  [− τ!" τ!! n!τ!!τ!"

!!!] .

Moreover, the typical values of lightning current parameters are listed in Table 1 as follow;

Table 1. The channel base current parameters[16]

i!" (kA)

i!" (kA)

τ!! (µs)

τ!" (µs)

τ!" (µs)

τ!! (µs)

n! n!

10.7 6.5 0.25 2.5 2 230 2 2

On the other hand, the current waveshapes at different heights along lightning channel are modeled based on equation (2) as follow [13-14, 18];

i!" z ′, t = [P z ′ i 0, t − !′

!+ ρ!  i 0, t −

!′

!]U t − !′

!!

(2)

Where:

z’ is the temporary charge height along lightning channel,

I(0,t) is channel base current,

P(z’) is the attenuation height dependent factor,

v is the current-wave propagation velocity,

v!is the upward propagating front velocity,

u is the Heaviside function as defined by

u t −z ′

v!=

1                    for  t ≥z′v!

0                    for  t <z′v!

ρ!  is ground reflection coefficient equal to !!"!!!!!"!!!

,

z!"  is the surge impedance of return stroke channel,

z! is the ground impedance,

i!" z ′, t is the return stoke current at different heights along channel in presence of ground reflection factor.

It should be mentioned that MTLE model is considered in this paper and the attenuation height dependent function is expressed by equation (3) as follow [11, 19];

P(z’)=exp(-z'/𝜆) (3)

Where:

λ is the constant parameter between 1000m to 2000m.

III. GROUND REFLECTION FACTOR

The value of ground reflection factor depends on the channel impedance (typically equal to 330Ω) and the ground impedance a striking point as expressed by equation (4) [18].

 ρ! =!!"!!!!!"!!!

(4)

On the other hand, the ground impedance can be represented with the values of ground resistivity at striking point, as expressed by equation (5).

z! =ρ!π!ln  (!"

!− 1) (5)

Where:

ρ is the ground resistivity,

l is the depth of rod (connection point),

r is the radius of rod(connection point).

IV. LIGHTNING INDUCED VOLTAGE

In order to evaluate the lightning induced voltage at different points along power line, the geometry of problem is shown in Figure 1 [20];

Figure 1. The geometry of problem

Noted that the values of v and λ are set on the 1.5×10!m/s and 1500m, respectively. Figure 2 shows the waveshape of channel base current where the current parameters are obtained from Table 1.

Figure 2. The channel base current wave shape

Figure 3 illustrates the waveshapes of lightning induced voltage at the middle of the power line where the length of line is 2000m, the conductor height is 10m above the ground surface and the striking distance is 50 m.

Figure 3. The lightning induced voltages for different ground reflection factors

Figure 3 demonstrates the values of lightning induced voltage which directly proportional to the ground reflection values at the channel base. It shows that the peak value of lightning induced voltage increases about 35% at  ρ! = 0.6 as compared to the case where the ground reflection is neglected (  ρ! = 0).

Figure 4. The behaviour of ground impedance against ground resistivity changes

On the other hand, using equations 4 and 5 and by setting the channel surge impedance equal to 330Ω and both l and r at 0.5m, the behaviour of ground impedance against the ground resistivity is shown in Figure 4, which illustrates that the ground impedance has a direct relationship with the values of ground resistivity.

Figure 5. The behaviour of ground reflection factor

against ground impedance changes

Whilst Figure 5 shows the behaviour of ground reflection against ground impedance. The higher the ground impedance, the lower the ground reflection factors (as demonstrated by equation 4). Moreover, the effect of ground resistivity on the values of lightning induced voltage is illustrated in Figure 6. Result demonstrates that by increasing the ground resistivity, the lightning induced voltage will be reduced. Another results on the behaviour of lightning induced voltage versus ground resistivity and also ground impedance are shown in Figures 7 and 8, respectively.

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

Time(µs)

Cha

nnel

bas

e cu

rrent

(kA)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20

40

60

80

100

120

140

Time(µs)

Ligh

tnin

g In

duce

d Vo

ltage

(kv)

pg=0pg=0.2pg=0.4pg=0.6

200 300 400 500 600 700 80050

100

150

200

250

300

ρ(Ω.m)

Z g(Ω)

50 100 150 200 250 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Zg(Ω)

p g

Figure 6. The lightning induced voltages for different

values of ground resistivity

Figure 7. The behaviour of lightning induced voltage

versus ground resistivity changes

Figure 8. The behaviour of lightning induced voltage versus ground impedance changes at striking point

Figure 7 shows that by increasing the values of ground resistivity and ground impedance, the peak value of lightning induced voltages has shown a decreasing trend. The results illustrate that the values of lightning induced voltages are strongly depended on the values of ground reflection, ground impedance and ground resistivity at striking point. By taking into account on the soil condition surrounding the power line and the fact that those values will be used in the calculation, the evaluated lightning induced voltage will be affected. In contrast, the previous studies mostly ignored this condition for the ease of calculation.

V. CONCLUSION This paper provides the significant relation and effect of ground reflection (due to difference between channel and ground impedances) on the values of lightning induced voltage. Moreover, the effect of ground resistivity on the values of lightning induced voltage was also considered and the results were discussed accordingly. Without all these considerations, the determination of the appropriate protection scheme can be affected due to the inaccurate evaluation of the induced voltage which will result in the poor lightning performance of the distribution lines.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20

40

60

80

100

120

140

Time(µs)

Ligh

tnin

g In

duce

d Vo

ltage

(kv)

ρ=200 Ω .m ρ=300 Ω .m ρ=400 Ω .m ρ=500 Ω .m ρ=600 Ω .m ρ=700 Ω .m ρ=800 Ω .m

200 300 400 500 600 700 80095

100

105

110

115

120

125

130

ρ(Ω.m)

V peak(kv)

50 100 150 200 250 30095

100

105

110

115

120

125

130

Zg(Ω)

V peak(kv)

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