A Linear Probabilistic Optimal Power Flow Model with Linearization Error Checking

With the integration of renewable energy, probabilistic optimal power flow (POPF) becomes an important tool to analyze system uncertainty. To relieve the computational burden of POPF, a linear OPF model is proposed. To make the linear OPF accurate, an optimization method is proposed to obtain the worst-case error of the used linear power flow (LPF) model. When the worst-case error is unacceptable, a min-max two-levels optimization problem is proposed to obtain the optimal LPF model (i.e., in terms of minimizing the worst-case error) over a defined linearization range. To solve the difficult min-max problem, an analytical approximation method is proposed to reformulate the min-max problem as a tractable one-level linear program. By applying the error checking, the proposed linear OPF yields better solutions. Several standard systems are tested and the results verify the effectiveness of the proposed method.