Improving Linear OPF Model via Incorporating Bias Factor of Optimality Condition

The linearization of the optimal power flow (OPF) model is widely-used to meet the computational demands of power system dispatch. To improve the accuracy of the OPF solution, existing studies are devoted to reducing the linearization error of nonlinear power flow constraints. However, the linearization accuracy of model fractions does not necessarily represent the linearization error of the OPF result. In this paper, an improved linear OPF formulation is derived from the optimality condition of the OPF solution. Based on the Karush–Kuhn–Tucker (KKT) condition, we transform the OPF optimization into solving a set of nonlinear equations, which consists of non-gradient and gradient terms. The traditional approach to linearize OPF constraints is regarded as deriving the first-order and zero-order Taylor expansions of non-gradient and gradient terms, respectively. The missing first-order component of gradient terms causes considerable linearization error. We formulate it as a bias factor in the OPF objective to improve the accuracy and maintain linearity of the OPF model. By considering the bias factor, the performance of linear OPF optimization is notably improved, which is illustrated in theory and verified in numerous IEEE and Polish test systems.