Time-Domain Implementation of Cooray–Rubinstein Formula via Convolution Integral and Rational Approximation

A New Formulation of the Cooray–Rubinstein Expression in Time Domain

“…The CR expression has been originally obtained in the frequency domain, but its counterpart in the time-domain is important when dealing with codes for the analysis of electromagnetic transients in power networks. For this reason, an effort has been made in that respect [18], [19]. In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved.…”

“…For this reason, an effort has been made in that respect [18], [19]. In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved. An in-depth analysis of the formulation presented in [18] and [19] reveals that the kernel of the convolution integral is characterized by a class of functions describing a Dirac delta function.…”

“…In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved. An in-depth analysis of the formulation presented in [18] and [19] reveals that the kernel of the convolution integral is characterized by a class of functions describing a Dirac delta function. It is well known, e.g., [20], that, in this case, any numerical algorithm for the solution of the convolution integral requires a preliminary extraction of the Dirac pulse (irregular term) in order for the algorithms to work on a regular function, and hence to converge according to a desired accuracy.…”

“…In Section II, a review of the results obtained in [18] and [19] is presented. In Section III, a new formulation for the CR expression in the time domain will be derived.…”

“…In Section IV, the numerical treatment for the new formulation is described. In Section V, this formulation is compared with the one proposed in [18] and [19]. Conclusions are drawn in Section VI.…”