Periodic steady-state solution of power systems with nonlinearities

Power systems are becoming more and more polluted by harmonics which are produced by nonlinear and/or switching devices. Steady-state analysis of such systems is needed for proper initialization of transient simulations as well as for harmonic studies. A periodic steady-state response can be obtained by simply integrating the differential equations until all transients disappear from the periodic signal. However, this may take unacceptably long time for lightly damped systems. Direct calculation of the periodic steady-state response of nonlinear systems is investigated in this paper. The problem is formulated as an asymptotic waveform evaluation problem where the linear part of the original network is replaced by an equivalent. The equivalent network has identical steady-state but much faster transient response, allowing the periodic state-state to be reached efficiently by time domain simulation. The proposed method is applied to various test systems and simulation results from these are shown in the paper