Wide-band modeling of cables based on the fractional order differential theory

Research on the wide-band modelling method of the cable and the analysis of the electromagnetic transients on the cable systems has significant practical meaning on the engineering problems, e.g. overvoltage protection, insulation coordination and electromagnetic interference, with the growing use of cable systems and the increasing levels of capacity in the power and communication systems. In the transient analysis of the cable system, such as lighting transient simulations, the skin effect of the conductor and the ground should be considered, which materializes as a frequency domain variation in the cables´ impedance matrix. In order to treat this frequency dependent problem for the time domain simulation, the vector fitting method is widely used, in which the frequency dependent parameter is approximated by a rational function. However, a high order rational function is usually needed in order to obtain an accurate approximation because the fractional order characteristic of the skin effect is neglected in the vector fitting method. In this paper, a novel wide-band model of cables is presented based on the fractional order differential theory. In this method, the fractional order irrational functions are adopted to approximate the frequency dependent parameter, which makes the fitting order much lower than the conventional vector fitting method. In order to validate the presented method, an example is considered and the transient responses are compared with the results obtained by EMTP.