A Linear AC Three-Phase Optimal Power Flow Model for Active Distribution Networks and Microgrids

Distribution networks typically have unbalanced loads; however, most works on Active Distribution Networks (ADNs) use single-phase representations. This paper proposes a linear alternate current (AC) three-phase optimal power flow (OPF) for a day-ahead operation planning of ADNs and microgrids. The proposed AC linear three-phase optimal power flow model is based on polar coordinate systems and considering some consistent approximations for linearization of power flow equations. The shunts admittances of the network and the mutual impedances between phases of the three-phase lines are considered in the model. In this paper, the proposed linear AC three-phase OPF model is used to define the optimal day-ahead operation planning of active distribution systems and microgrids with three-phase feeders and three-phase distributed generators (DG) and energy storage (ES). Since this model proposes a three-phase representation of the system, it provides more accurate results, making it an effective tool for optimal planning of the ADN operation. The proposed model is illustrated using the IEEE 34-bus test system and results show its effectiveness and excellent performance, presenting an error of less than 4% for the voltage magnitude of the buses and less than 2% for the apparent power flow of the lines, when compared with non-linear models.