Nonlinearity-Adaptive Data-Driven Power Flow Constraint for Distribution Network Optimization

Data-driven power flow (PF) analysis methods have higher practical value to deal with the inaccurate branch parameters in medium and low-voltage distribution networks, which can be easily integrated into the classic optimization framework as a constraint. However, the PF mapping relationship of the measurement data shows stronger nonlinearity, with the high penetration of distributed generation (DG), leading to the low accuracy of the linear PF constraint. To this end, we propose an incomplete dimension lifting (IDL) data-driven PF method for distribution network optimization. The state variables are divided into optimization variables and uncontrollable variables, among them, the optimization variables keep the original linear state space or converted into quadratic space to simplify the optimization solution; and the uncontrollable variables is dimension lifted to fit the nonlinearity of PF. In addition, in order to deal with the problem of gradient direction error caused by nonlinear model overfitting, the first-order sensitivity constraint is involved in parameter regression process. The standard IEEE cases with high penetration of DG demonstrate that the proposed method can achieve higher accurate PF constraint and better optimization results, compared to the existing data-driven PF constrain.