A Robust Phase-Coordinates Frequency Dependent Underground Cable Model (Zcable) for the EMTP

A major difficulty in multiphase cable modeling with traditional electromagnetic transient program like the EMTP is the synthesis of the frequency-dependent transformation matrix that relates modal and phase domain variables. This paper presents a new model (zCable) to represent the frequency-dependence of cable parameters directly in phase coordinates, thus avoiding the problems related to frequency-dependent transformation matrices. The cable model is split into two parts: a constant ideal line section and a frequency-dependent loss section. A pi-correction is proposed to solve the problem of different traveling times in the ideal line section. The main advantage of the proposed model as compared to existing frequency-dependent transformation matrix models is the model´s absolute numerical stability for strongly asymmetrical cable configurations and for arbitrary fault conditions. The model parameters are easy to obtain with robust algorithms, and the model can be efficiently implemented in the context of a real-time PC-cluster simulator.