Including high order rational functions in EMTP: a comparison between alternative methods with emphasis on accuracy

Rational functions are used as a simplified representation of complex network functions in time domain calculations. The rational functions are established either in the z-domain or in the s-domain. This paper shows that the poles and zeros in the z-domain can be derived from the corresponding quantities in the s-domain. This relation is based on an approximation which is equivalent to the linearization assumed within each time step in EMTP. High order z-domain functions may fail to give an acceptable result due to roundoff errors. This problem can be omitted by performing a partial fraction expansion in the frequency domain