Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources

Context: The electric parameters of the power networks are usually analysed through deterministic power flows; however, the variation in load demands and power fluctuation of renewable generators cannot be considered with the deterministic power flows because it uses specific power values. The probabilistic power flow methods are better for this purpose since they apply techniques to include and reflect the uncertainty of input variables on the results obtained. Objective: This paper extends the Point Estimate Method (PEM) applied to the probabilistic power flow of an unbalanced power distribution system with dispersed generation and variable power factors. This method is applied to include uncertainties of loads and power sources such as wind and solar. As PEM requires independent input random variables, but usually there is spatial correlation between loads or power sources; therefore, Cholesky decomposition is applied to deal with this situation. Method: In this paper are combined the scheme 2m+1 of the Point Estimate Method with the Cholesky decomposition and some approximation methodologies to estimate the cumulative distribution function of some electrical parameters. Results: The results obtained are the moments about the mean of the output variables, which are used in conjunction with some approximation methodologies to obtain an estimation of the Cumulative Distribution Function for nodes or branch parameters. The proposed methodology is tested on the three-phase unbalanced IEEE 123-node test system, and results are compared with those obtained from the benchmark Monte Carlo simulation. Conclusions: There are comments on some pertinent information about Point Estimate Method performance on this kind of power systems. 2014 Elsevier Ltd. All rights reserved.