The increasing penetration of wind power brings great uncertainties into power systems, which poses challenges to system planning and operation. This paper proposes a novel probabilistic load flow (PLF) method based on clustering technique to handle large fluctuations from large-scale wind power integration. The traditional cumulant method (CM) for PLF is based on the linearization of load flow equations around the operating point, therefore resulting in significant errors when input random variables have large fluctuations. In the proposed method, the samples of wind power and loads are first generated by the inverse Nataf transformation and then clustered using an improved K-means algorithm to obtain input variable samples with small variances in each cluster. With such pre-processing, the cumulant method can be applied within each cluster to calculate cumulants of output random variables with improved accuracy. The results obtained in each cluster are combined according to the law of total probability to calculate the final cumulants of output random variables for the whole samples. The proposed method is validated on modified IEEE 9-bus and 118-bus test systems with additional wind farms. Compared with the traditional CM, 2m?1 point estimate method (PEM), Monte Carlo simulation (MCS) and Latin hypercube sampling (LHS) based MCS, the proposed method can achieve a better performance with consideration of both computational efficiency and accuracy.
Abstract:The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush-Kuhn-Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish-Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS).
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