Numerically stable, computationally efficient, filter bank based modeling of transfer functions for power system transient simulation

A numerically robust, computationally efficient method for modeling a high order system by means of low order transfer functions using a perfect reconstruction filter bank (PR-FB) is proposed. Modeling the transfer functions associated with the characteristic impedance and propagation/weighting function of a frequency dependent transmission line (FDTL) over a wide range of frequencies typically involves rational function approximations (RFAs) of high order. Discretization of the high order RFAs is prone to numerical instability, especially when the ratio of the maximum pole over the minimum pole (condition number) is large. The proposed method improves numerical stability by employing several narrowband (subband), low-order RFAs using a logarithmic tree-structured perfect reconstruction filter bank. Moreover, the method is computationally efficient, since simulation of each subband is of low complexity and very suitable for parallel (multi-core) processing.