Risk assessment of distribution network based on sparse polynomial chaos expansion with Lasso regression

Under the context of energy decarbonization and transformation, addressing the issues of flow uncertainty characterization and quantification in risk assessment of distribution networks with a high proportion of new energy sources, a method based on Lasso regression and sparse polynomial chaos expansion for risk assessment of distribution networks has been proposed. By introducing polynomial chaos expansion theory, an auxiliary model is established to replace the traditional nonlinear power flow calculation model in stochastic power flow analysis. Since the auxiliary model introduces a large number of polynomials that do not affect the response as the number of variables increases, a polynomial sparsification method is proposed. Firstly, by analyzing the polynomial expansion coefficients, the sensitivity of variables to first-order linear, first-order quadratic, and second-order polynomials is evaluated, and sparsification is performed from the perspective of polynomial sensitivity. Subsequently, based on Lasso regression, the variables are ranked and selected according to their impact magnitude, allowing for sparsification from the perspective of the contribution of variables. Then, static security risk assessment indices for the distribution network were established, and the proposed method was used to quantify these risk indices. Finally, case simulations were conducted using the IEEE 33-node and IEEE 118-node test systems to verify the effectiveness of the proposed sparsification method. This method significantly improved the efficiency of online risk assessment for the distribution network while maintaining computational accuracy.