A Novel Economic Dispatch Method in Active Distribution Grids with Correlated Uncertain Power Injections

Solving the correlated uncertain power injections of wind power generations and photovoltaic power generations is a tough challenge for economic dispatch in active distribution grids. Although the chance-constrained method can solve this problem, it takes more time to determine the chance constraints. Therefore, a cumulant-based optimal method is proposed to solve the chance-constrained model for the economic dispatch problem with correlated uncertain power injections. Firstly, we set power injection adjustments as variables and established the economic dispatch model. Secondly, based on the Cholesky decomposition and the Cornish-Fisher series expansion, we calculate the cumulants of correlated uncertain power injections and establish the explicit expressions of chance constraints in power injection spaces. Thirdly, combined with the cumulants, a heuristic algorithm is used to solve the economic dispatch model. Optimization results for the modified PG&E69-bus distribution grid are given to verify the effectiveness of the proposed method.