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 sdomain. 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 zdomain 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.