Active and Reactive Power Coordinated Optimization of Distribution Network–Microgrid Clusters Considering Three-Phase Imbalance Mitigation

With the continuous increase in the penetration of single-phase microgrids in low-voltage distribution networks (LVDNs), the phase asymmetry of source–load distribution has made the problem of three-phase imbalance increasingly prominent. To address this issue, this paper proposes an active–reactive power coordinated optimization model for distribution network–microgrid clusters considering three-phase imbalance mitigation. The model is formulated within a master–slave game framework: in the upper level, the distribution network acts as the leader, formulating time-of-use prices for active and reactive power based on day-ahead forecast data with the objective of minimizing operating costs. These price signals guide the flexible loads and photovoltaic (PV) inverters of the lower-level microgrids to participate in mitigating three-phase imbalance. In the lower level, each microgrid responds as the follower, minimizing its own operating cost by determining internal scheduling strategies and power exchange schemes with the distribution network. Finally, the resulting leader–follower game problem is transformed into a unified constrained model through strong duality theory and formulated as a mixed-integer second-order cone programming (MISOCP) problem, which is efficiently solved using the commercial solver Gurobi. Simulation results demonstrate that the proposed model fully exploits the reactive power compensation potential of PV inverters, significantly reducing the degree of three-phase imbalance. The maximum three-phase voltage unbalance factor decreases from 3.98% to 1.43%, corresponding to an overall reduction of 25.87%. The proposed coordinated optimization model achieves three-phase imbalance mitigation by leveraging existing resources without the need for additional control equipment, thereby enhancing power quality in the distribution network while ensuring economic efficiency of system operation.