Three-stage relaxation-weightsum-correction based probabilistic reactive power optimization in the distribution network with multiple wind generators - Chen, Shuheng; Hu, Weihao; Du, Yuefang; Wang, Shixing; Zhang, Chenxuan; Chen, Zhe (International journal of electrical power & energy systems, 2022)
•The improved Nataf transformation-based point estimate method for the equivalent transformation of uncertain wind speeds.•The mathematical formulation of reactive power optimization of the distribution network with the consideration of active utilization of reactive power capability of DFIG based wind generators.•The three-stage relaxation-weightsum-correction solution scheme for the reactive power optimization problem of the distribution network. The uncertainty of wind powers complicates the reactive power optimization in the distribution network. In this paper, the authors proposed a three-stage relaxation-weightsum-correction (TSRWC) based probabilistic reactive power optimization method to deal with the uncertainty and correlation of DFIG based wind generators in the distribution network. Firstly, by the inverse NataF transformation, an improved point estimate method is proposed to transform the uncertain wind speeds into a series of data samples with weights. The digital integral technology and root search method are employed to calculate the correlation matrix in the standard normal space. Then, with the consideration of active utilization of reactive power capability of DFIG based wind generators, the reactive power optimization problem in the distribution network corresponding to each data sample is formulated. Further, the three-stage relaxation-weightsum-correction solution method is proposed to solve the probabilistic reactive power optimization problem. Finally, the numerical simulation experiments are conducted on the real 19-node distribution network and the modified PG&E 69-node distribution network, respectively. The experimental results verified that by the proposed TSRWC based probabilistic reactive power optimization method, the expectation and deviation of power loss are more adjacent to the results from the Monte Carlo Simulation experiments than the scenario without the consideration of correlation. Meanwhile, no obvious increasement of consumed time appeared. © 2017 Elsevier Inc. All rights reserved.