Exact approach to determining power system responses on periodic discontinuous excitations

The paper is focused on presentation of a new approach to exact solutions of periodic states in power systems working under discontinuous excitation. It avoids completely the Fourier series calculations of the input and output system quantities. The periodic state of the power system output is formulated directly in the time domain as a superposition of the zero-input response and forced output for each continuous piecewise segments of the excitation quantity, separately. The whole periodic output is reached by taking into account the continuity and periodicity conditions at instants of discontinuities of the input quantity and then using the concatenation procedure for all segments. The method can be applied efficiently to continuous and discontinuous input quantities equally well. Moreover, when comparing with all up-to-date used approaches the presented here newly elaborated method can be applied more efficiently to determine the one-period energy for each of particular system elements. Solutions are exact and there is no need to apply any of the widely up-to-date used frequency approaches. The Fourier series is completely cut out of the presented system analysis.