Operational Cost Optimization of Rural LV Distribution Systems Considering Power Quality Constraints

High penetration of residential photovoltaic (PV) systems frequently causes voltage violations and three-phase unbalance in rural low-voltage distribution systems (LVDS). These issues directly result in large-scale PV curtailment and significantly increase the operating costs of the rural LVDS. To address these issues, this paper proposes an operational cost optimization model and a corresponding solution method for the rural LVDS, explicitly considering power quality constraints. The decision variables of the model include the three-phase active and reactive power outputs of the distributed PV inverters and the energy storage system (ESS). The optimization objective is to minimize the total electricity cost of the rural LVDS, incorporating the operational cost of the ESS, subject to power quality constraints such as voltage limits and three-phase unbalance margins. Given the non-convex nature of the original model, second-order cone relaxation (SOCR) is employed to reformulate it as a convex optimization problem, which can be solved efficiently and robustly to global optimality. Simulation results based on real-world case studies demonstrate the effectiveness of the proposed method in mitigating voltage violations, reducing three-phase unbalance, and enabling economical operation. Overall, the proposed approach facilitates the high-penetration integration of distributed PV in the rural LVDS.