Combined cumulant and Gaussian mixture approximation for correlated probabilistic load flow studies: a new approach

In this paper, a probabilistic load flow analysis technique that combines the cumulant method and Gaussian mixture approximation method is proposed. This technique overcomes the incapability of the existing series expansion methods to approximate multimodal probability distributions. A mix of Gaussian, non-Gaussian, and discrete type probability distributions for input bus powers is considered. Probability distributions of multimodal bus voltages and line power flows pertaining to these inputs are precisely obtained without using any series expansion method. At the same time, multiple input correlations are considered. Performance of the proposed method is demonstrated in IEEE 14 and 57 bus test systems. Results are compared with cumulant and Gram Charlier expansion, cumulant and Cornish Fisher expansion, dependent discrete convolution, and Monte Carlo simulation. Effects of different correlation cases on distribution of bus voltages and line power flows are also studied.