A novel network model for optimal power flow with reactive power and network losses

To improve the accuracy of the DC network model, we re-examine the power flow equations and propose an improved network model for optimal power flow (OPF) calculation with reactive power and network losses. Voltage angle and the square of voltage magnitude are used as independent variables. A mathematical transformation of the nonlinear voltage magnitude term is used, which decomposes the voltage magnitude term to a linear expression and a quadratic expression. The quadratic expression presents the influence of voltage magnitude on network losses. To handle the non-convexity of the OPF model caused by the network losses, a convex relaxation method is used. The relaxed model and the proposed OPF model are typically equivalent in transmission systems. Methods of restricting the potential relaxation errors are introduced. It is shown that the accuracy of the proposed network model can be further improved with initial points of voltage angles. Case studies in several IEEE benchmark systems validate the performance of the proposed formulation and approach.