Optimal reactive power flow with exact linearized transformer model in distribution power networks

Optimal reactive power flow (ORPF) in distribution power networks is to optimize the operation of reactive power devices to minimize the total operation cost or power loss. As the optimization model is constructed with AC power flow constraints and the strategies of compensating capacitor and transformer are discrete, ORPF problem in distribution power networks is essentially a Mixed Integer Nonconvex Nonlinear Programming (MINNLP) problem which is hard to solve mathematically. Based on the Branch Flow Model of distribution power networks, we proposed a method to exactly linearize the transformer model using piecewise linear technique. To efficiently solve the problem, the latest second-order cone (SOC) relaxation technique is adopted and the ORPF is relaxed to a Mixed Integer Second-order Cone Programming (MISOCP) problem. Further, the exactness of the SOC relaxation is discussed in this paper and the modified IEEE 33 and 69 bus system are employed to study the effectiveness of the proposed method.