Voltage Unbalance-Aware AC Optimal Power Flow in Distribution Networks

The increasing penetration of single-phase loads and distributed generation exacerbates voltage unbalance (VU) in distribution grids, raising concerns about power quality and complicating network operation. However, most market-clearing models and price-based coordination frameworks do not enforce VU limits within a three-phase AC representation, so the implications for grid-code compliance, numerical scalability, and economic signals remain unclear. This paper embeds VU in a three-phase AC optimal power flow market-clearing model and benchmarks two treatments: strict VU limit enforcement and objective function penalization. Building on these insights, an Improved Hybrid Limits (IHL) formulation is proposed that preserves compliance while using a smooth unbalance proxy in the objective to guide the optimization solver. Case studies on a European low-voltage feeder show that IHL maintains feasible operating points, yields price and curtailment signals consistent with conventional hybrid formulations, and converges substantially faster and more reliably than a penalization based on the exact unbalance metric. These results support IHL as a practical and scalable mechanism for VU mitigation in market-based operation of unbalanced distribution systems.