Abstract: With more and more photovoltaic renewable energy integrated into the power system, the traditional deterministic power flow can not accurately describe the actual operation state of the power system. We present a probabilistic power flow analysis method which combines semi invariant method, Copula theory and Gaussian mixture approximation method. This method overcomes the shortcoming that the existing series expansion method can not approximate the multimodal probability distribution. The mixture of Gaussian, non Gaussian and discrete probability distributions of input bus power is considered. Without using any series expansion method, the probability distributions of multi-mode bus voltage and line power flow with these correlated inputs are obtained accurately. Multi input correlation is considered. The performance of this method is verified in IEEE14 and IEEE57 bus system. Experimental results show that the multi-modal distribution of the expected random variables is accurately established, and the running time of the proposed method is reduced by 76% compared to the Gram-Charlier method.

Key words: related items, semi-invariant, Gaussian mixture approximation, photovoltaic power generation;probabilistic power flow