Numerical calculation of grounding system buried in vertical earth model in low frequency domain based on the boundary element method

Abstract

SUMMARYTo solve a grounding problem which describes a grounding system with floating metallic conductors buried in vertical multilayer earth model under a high voltage a.c. substation, a new mathematical model for accurately computing currents flowing along conductors of the grounding system has been developed in this paper, which is hybrid of Galerkin's type Boundary Element Method and conventional nodal analysis method. Propagation effect of electromagnetic wave within the substation has been neglected due to its limited area. A quasi-static complex image method and new closed form of Green's function for the vertical multilayer earth model are introduced into this model to accelerate mutual impedance and induction coefficients calculation. The model is then implemented in a computer program, which can be used to calculate currents distribution of any configuration of grounding system, and with or without floating metallic conductors buried in the vertical multilayer earth model.

A novel mathematical model for the lightning response of a grounding system buried in multilayered earth based on the quasi‐static complex image method

“…The formula for self impedance and self induction can be found in [28][29][30][31], here, we give the formula for mutual induction: [29][30][31][32] The formula for self impedance and self induction can be found in [28][29][30][31], here, we give the formula for mutual induction: [29][30][31][32] …”

“…Meliopoulos also discusses the hybrid method based on quasi-static electromagnetic field theory in [26]; Huang and Kasten developed a new hybrid model to calculate the current distribution in both the grounding system and the metallic support conductors, while considering the voltage drop along the grounding system conductors [27]. This confine in the frequency domain promoted the development of a novel mathematical model in [29][30][31][32], which introduced the quasi-static complex image method (QSCIM) for calculating the current distribution in a grounding system buried in both horizontal and vertical multilayered earth in the frequency domain. Meanwhile, leakage currents and longitudinal currents within the grounding system are separately considered in the calculation, their mutual coupling influence is neglected, and the capacitive coupling effect of the earth is also neglected.…”

“…[29][30][31][32] The matrix above includes the conductive and capacitive effects of the earth, and its elements are the mutual impedance coefficients Z i,j .…”

Quasi-Static Complex Image Method for a Current Point Source in Horizontally Stratified Multilayered Earth

“…Although the hypothesis for the electrostatic field theory can be accepted under 50 Hz or 60 Hz work frequency condition, restrictions for the model will be evident for more general cases. For example, if a large resistivity of earth is observed for a buried grounding grid, the imaginary number of grounding impedance will be large [9]. In this case, grounding resistance substituting for grounding impedance will be inappropriate.…”

“…To better describe the grounding problem in low frequency domain (50 or 60 Hz and higher harmonic wave), in recent years the quasistatic electric field theory has been utilized to combine with the equal potential model [10][11][12][13][14] and unequal potential model [9,[15][16][17][18][19][20][21][22]. In these models, only the propagation effect of electromagnetic wave is ignored.…”