**8. Conclusion**

20 Computational and Numerical Simulationse

**Figure 9.** The distribution of the SEP *ϕ* on the ground surface (f=800 kHz)

**Figure 10.** The distribution of the EFI *Ex* on the ground surface (f=16.7 kHz)

which clearly shows that the region of maximum electrical field shifts from the edge of the

The distribution of the x-componential of MFI *Bx* is given in Figs. 13–15. We can also see that as in the ground SEP rise case, the maximum value of the x-componential of the MFI *Bx* is dependent on the magnitude of the injecting current. Unlike the distribution of the x-componential of the EFI *Ex*, the distribution of the x-componential of the MFI *Bx* is along the y-direction, which can be easily explained in that the distribution of the electrical field is perpendicular to that of the magnetic field. Meanwhile, the distribution of the electrical

grid to the injection point location as the frequency increases from low to high.

A novel mathematical model for accurately computing the lightning currents flowing in the grounding system of a high voltage a.c. substation, buried in multilayered earth, has been developed in this paper. Together with the FFT, not only the conducting effect of harmonic wave components of these currents, but also capacitive and inductive effects from the interface between different soil layers have been analyzed in the frequency domain. To

**Figure 15.** The distribution of the MFI *Bx* on the ground surface (f=800 kHz)

Zhong-Xin Li, Ke-Li Gao, Yu Yin, Cui-Xia Zhang and Dong Ge

China Electrical Power Research Institute, Beijing, China

vol. 20, no. 3, pp. 2160–2165, Jul. 2005.

Foundation of China under Grant 51177153.

This work was funded by the Science and Technology Projects of State Grid Corporation of China under Contract Number: GY172011000JD and the National Natural Science

Numerical Calculation for Lightning Response to Grounding Systems Buried in Horizontal Multilayered Earth Model

Based on Quasi-Static Complex Image Method

http://dx.doi.org/10.5772/57049

415

[1] E. D. Sunde. *Earth Conduction Effects in Transmission Systems*, New York: Dover, 1968.

[2] L. V. Bewley, *Traveling Waves on Transmission Systems*, 2nd ed. New York: Wiley, 1951

[4] A. P. Meliopoulos, *Power System Grounding and Transients*. New York: Marcel-Dekker,

[5] A. C. Liew and M. Darveniza, "Dynamic model of impulse characteristics of

[6] J. Wang, A. C. Liew, and M. Darveniza, "Extension of dynamic model of impulse behavior of concentrated grounds at high currents", *IEEE Transactions on Power Delivery*,

[3] R. Rudenberg, *Electrical ShockWaves in Power Systems*. Harvard Univ. Press, 1968.

concentrated earths", *Proc. Inst. Elect. Eng.*, vol. 121, pp. 123–135, Feb. 1974.

**Acknowledgment**

**Author details**

**References**

1988.

**Figure 13.** The distribution of the MFI *Bx* on the ground surface (f=16.7 kHz)

**Figure 14.** The distribution of the MFI *Bx* on the ground surface (f=250 kHz)

accelerate the calculation, the QSCIM and a closed form of Green's function were introduced. With the inverse FFT, the model can calculate the distribution of lightning currents in any configuration of the grounding system. This can be used for studying the performance of transient lightning responses to grounding systems. Last, the model has been validated through some numerically simulated and experimental results from open published paper, and some numerical results have been discussed in this paper.

<sup>414</sup> Computational and Numerical Simulations Numerical calculation for lightning response to grounding systems buried in horizontal multilayered earth model based on quasi-static Numerical Calculation for Lightning Response to Grounding Systems Buried in Horizontal Multilayered Earth Model Based on Quasi-Static Complex Image Method http://dx.doi.org/10.5772/57049 415

**Figure 15.** The distribution of the MFI *Bx* on the ground surface (f=800 kHz)
