Arbitrary polynomial chaos expansion and its application to power flow analysis-Fast approximation of probability distribution by arbitrary polynomial expansion

This paper introduces an arbitrary polynomial chaos expansion method for performing probabilistic power flow analysis in power systems. The proposed method is used for uncertainty analysis, expressing the uncertainty of a system as random variables with an arbitrary output distribution based on orthogonal polynomial expansion. This method is advantageous because of its calculation speed and accuracy. This study expresses probabilistic power flow in a power system with many uncertain power sources using linear combination polynomial expansion. The orthogonal polynomial system employed is generated by moment analysis from renewable energy output data, with the polynomial coefficients derived from a collocation method. Simulation of probabilistic power flow using the proposed method is applied to a 29-bus transmission network model including three renewable energies, and the calculation speed and accuracy are evaluated by changing the expansion order of the polynomial. In addition, the influence on the polynomial coefficient is assessed when the system topology is changed due to a line fault. Therefore, since the arbitrary polynomial chaos expansion method can represent complex networks by linear combination of orthogonal polynomial sets, calculation based on it is several hundred times faster than the conventional Monte Carlo method. The results demonstrate that the proposed method is very useful for analyzing the probabilistic power distribution and that third-order expansion is practically appropriate.