Linear AC Three-Phase OPF Model for Active Distribution Networks with Unbalanced ZIP Loads

Although nonlinear Alternating Current (AC) Optimal Power Flow (OPF) may provide more accurate results compared to linearized OPF models, many ACOPF problems are complex and may require high, sometimes infeasible, computational time. The linear Direct Current OPF (DCOPF) has been widely used in power system analysis; however, it has limitations regarding reactive power analysis, and it may cause significant error in distribution networks with a high R/X ratio of feeders. Moreover, most of the existing formulations for the linear ACOPF do not consider mutual impedance for the lines and simplify the network as a single-phase system, which does not significantly represent unbalanced loads. This paper proposes a novel linear AC three-phase OPF formulation for unbalanced ZIP loads using current injection and considering delta and wye loads. The formulation is extended to include shunt capacitors, voltage regulators, and mutual impedance. The proposed methodology is illustrated using the IEEE 123-bus test system in case studies including/not-including voltage regulators, distributed generation, high R/X ratio, and mutual impedance. The results are very accurate compared with a nonlinear three-phase ACOPF model. The high computational performance and the accuracy of the proposed model considering distributed generation and high R/X ratio show its effectiveness in active distribution networks.