Optimization of Static Voltage Stability Margin Considering Uncertainties of Wind Power Generation

An optimal static voltage stability margin (SVSM) control model considering the uncertain wind farm output is proposed, in which the probability distribution of SVSM is required to satisfy the chance and variance constraints. A probabilistic distribution control method is proposed to solve the model. First, a linear weighted sum of B-spline basic functions is introduced to approximate the analytical function between the probability density function (PDF) of SVSM and control variables. Next, the analytical expression of the PDF of SVSM corresponding to a control variables’ sample is derived, and the sample of corresponding B-spline function weights is obtained, thus forming a series of ‘control variables-weights’ samples. Then, the analytic functions between weights and control variables are obtained using the generated samples to train a radial basis function neural-network, and the analytical function between the PDF of SVSM and control variables is obtained. After that, the chance and variance constraints are transformed into general nonlinear constraints with respect to control variables. Moreover, a method of selecting key control variables by calculating sensitivities is proposed to increase computational efficiency. Test results on the IEEE-39 bus system and an actual provincial power grid demonstrate the feasibility and effectiveness of the proposed method.