Simulation of transients on frequency dependent transmission lines using an improved multipoint Padé approximation technique

Transmission line structures are commonly found in electrical power delivery systems. Efficient transient simulations of transmission line networks are important for characterization of power system performance. Conventionally, transients on power transmission lines are computed using time domain techniques such as PSCAD simulator [1] and the computational effort associated is generally high. In the last decade, model order reduction techniques, such as multipoint Padé approximation method, have been introduced for the analysis of interconnect networks containing transmission lines and have demonstrated a high computational efficiency as compared to conventional circuit simulation methods [2]-[5]. Multipoint Padé approximation method employs all moment sets available at all updated frequency expansion points and can be used to efficiently obtain a closed-form solution of the linear networks in the presence of distributed transmission line models. Despite its success in solving interconnect circuit problems, applications of multipoint Padé approximations to transients simulation of power transmission lines are not always straightforward. This is because transmission lines in power systems are generally high frequency dependent as compared to those found in typical high-speed interconnect circuits, resulting in solution instability of multipoint Padé approximations. More specifically, the matrix that is used to yield coefficients of Padé rational transfer function is prone to be ill-conditioned when multipoint Padé approximation method is applied to simulate frequency dependent power transmission lines.