validating the effect of rise-slope in transient response of grounding system

8/2/2019 Validating the Effect of Rise-slope in Transient Response of Grounding System

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Fig. 1. Transmission line circuit for an electrode

The equations (1) can be presented by a equivalent circuit in Fig.1. In this,R,L(x,t), G(x,t) and

C(x,t) are per-unit length resistance, inductance, conductance and capacictance of the electrode,

respectively. These parameters are functions of space and time which can be calculated detailedly in

[1].

The grounding system and lightning current used for simulation

A typical grounding system under towers of telecomunication or wireless systems is presented

in Fig. 2. The three vertical grounding copper electrodes are 7.5mm in radius and 15m long. They

are connected by copper wires which are 5mm in radius. The electrodes resistivity used in

calculation is . The grouding system is buried at 0.5m depth in the soil which

has relative permittivity and resistivity . In simulation, the lightning current is

assumed to be conducted into the injected point and the mutual effect of the uper-soil structures as

well as the skin-effect is neglected.


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Fig. 2. A grounding system for simulation

The lightning currents are described as a double exponetial function () ( )

with the rise-time, changing in a range from 1s to 8s. Besides, in oder to compare the effect of

the lightning currents rise-time, these currents all have the same peak value of 1 kA. These

ligntning currents parameters and wave-forms are shown in Tab. 1 and Fig. 3.

Table 1. Parameter of lightning currents

Num (s) Im(kA) a(s-1) b(s-1)

1 1 1.029 23925 5452900

2 2 1.062 24779 2287300

3 3 1.101 25696 1345000

4 4 1.146 26685 908650

5 5 1.199 27750 662230

6 6 1.261 28896 506050

7 7 1.336 30150 3991908 8 1.426 31511 322060

-5

0

5

-5

0

5

-20

-15

-10

-5

0

5

x(m)y(m)

z(m)

3 vertical

groudingcopperelectrodes

Connecting

copper wires

3m

3m

3mair

15m 15m

15m

soil

injectedpoint


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Fig. 3. Lightning current wave forms

Simulation results

Table 2. Peak value of over-voltages at the injected point when the rise-time changes from

1s to 8s

( s ) 1 2 3 4 5 6 7 8

Peak value (kV) 6,722 4,543 3,662 3,177 2,929 2,823 2,692 2,539

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10-5

0

0.2

0.4

0.6

0.8

1

1.2

t(s)

Is(kA)

1

2

34

5

6

7

8


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Fig. 4. Over-voltage at the injected point when the rise-time changes from 1s to 8s

Fig. 5. Peak value of over-voltage at the injected point varies with the rise-time

0 2 4 6 8

x 10-6

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

s(s)

Upeak(kV)


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From the simulation results in Fig. 4, 5 and Tab. 2, the smaller the rise-time is, the higher the

over-voltage on the grounding systems is. That means the transient response on grounding systems

is affected significantly by the rise-slope of the lightning current. The reason is that the inductance

along electrodes of grounding systems can prevent the impulse current from passing by, and hence

decrease the ability of grounding systems in dissipating this current into the surrounding ground.

Conclusion

Non-uniform transmission line model is applied to simulate the transient phenomenon of

grounding systems in this research. Through the simulation results, the considerable effect of the

rise-slope of the lightning currents to this issue can be clarify. This influcence can be sumarized

briefly as the steeper this parameter is, the less effective the grounding systems are in distributing

the lightning currents into the ground. Hence, grounding systems used for lightning protection have

to be limited in their length or their building area to reduce the effect of inductances along their

component electrodes.

References

[1]Yaqing Liu, Nelson Theethayi, and Rajeev Thottappillil, Member, IEEE An engineering modelfor transient analysis of grounding system under lightning strikes: Nonuniform transmission-line

approach, IEEE Trans. Power Del, vol. 20, no. 2, pp. 722 730 , Apr 2005

validating the effect of rise-slope in transient response of grounding system

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