A New Method for Fast Evaluation of the Cooray–Rubinstein Formula in Time Domain

An improved method for expressing the transient ground resistance of overhead transmission lines by exponential polynomial

“…Thus, the poles for any ground parameters and line geometry can be easily evaluated by p k = ap k * (17) In fact, the property above mentioned can be also explained in the time domain, rewriting (7) as…”

“…Because the time-dependent terms is proportional to a, the value of p k in (11) will be also proportional to a and can be evaluated by (17).…”

“…In general, once the 'normalised poles' p k * have been evaluated, the p k corresponding to any ground conductivity, permittivity and line geometry can be evaluated directly by (17) for the early time response and by (20) for the late time response.…”

“…Step I: According to given ground parameters and line geometry, calculating the poles p k using (17) and (20).…”

“…In order to overcome the above mentioned issues, based on the Tossani et al formula, an improved and simple method is proposed to express the transient ground resistance by the exponential polynomial. The main contribution of this paper is that the relation between the ground parameters and the poles resulting from the rational approximation of the ground resistance is fully discussed and a concept named as 'normalised poles' [16,17] is introduced, which makes it easy to evaluate the poles according to any ground parameters and line geometrical configuration. The implementation procedures summarised in this paper show that the approximation of the transient ground resistance can be achieved by the 'normalised poles' and least squares method in the time domain, thus the VF method would be no longer required.…”