Finite-length horizontal conductor

In the case of perfectly conducting earth (p =0), the substitution of =0 into M, in the earlier equation gives the following expression  

Substituting x,i = 0 and Xa=Xi and taking the limit of angle 0 to zero with tan-iz= n /2-l/2 ( z 1) in Equation 1.245, the impedance formula of a parallel horizontal conductor is obtained in the following form  

When x i is taken to be zero, the earlier equation becomes identical to that given in Ref. [37]. Also, the substitution of x j=0 and x 2=Xj into the earlier equation gives the same formula as that derived in Ref. [42]. 

In the case that X i=Xyi = 0 and Xa=Xy2=x in Equations 1.245 and 1.246, that is, the case of a parallel horizontal conductor with the same length, the earlier formula is simplified as follows  

Taking a limit of distance x to infinite, the earlier equation per unit length is reduced to only the second term, that is. 

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The admittance of a finite-length horizontal conductor is evaluated by the potential coefficient of a perfecdy conducting earth [1] ... 

Let us consider the vertical multiconductor system illustrated in Figure 1.61. In the same manner as the finite-length horizontal conductor, the following impedance formula is obtained ... 

This section explains impedance and admittance formulas of nonuniform lines, such as finite-length horizontal and vertical conductors based on a plane wave assumption. The formulas are applied to analyze a transient on a nonuniform line by an existing circuit theory-based simulation tool such as the EMTP [9,11]. The impedance formula is derived based on Neumann s inductance formula by applying the idea of complex penetration depth explained earlier. The admittance is obtained from the impedance assuming the wave propagation velocity is the same as the light velocity in free space in the same manner as an existing admittance formula, which is almost always used in steady-state and transient analyses on an overhead line. 

Rogers, E. J. and J. F. White. 1989. Mutual coupling between finite length of parallel or angled horizontal earth return conductors. IEEE Trans. Power Deliv. 4(1) 103-113. 

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