Coordinated Active-Reactive BESS Scheduling via Convex Optimization with Degradation Costs

Abstract

The increasing penetration of renewable energy sources in distribution networks, coupled with the growing deployment of battery energy storage systems (BESS), necessitates advanced operational frameworks that can effectively coordinate active and reactive power dispatch while accounting for battery degradation and economic constraints. This paper proposes a novel convex optimization framework for the optimal day-ahead scheduling of BESS in active distribution networks. The problem is formulated as a mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes the coordinated active and reactive power dispatch of BESS units while enforcing the power balance equation at each time interval for an aggregated single-node representation of the distribution network. Unlike most existing approaches that treat active and reactive power independently, the proposed formulation fully exploits the inverter capabilities of modern BESS units, enabling them to provide both energy arbitrage and reactive power support services simultaneously. A detailed battery degradation cost model is incorporated using an equivalent full-cycle counting approach based on the cumulative variation of the state-of-charge trajectory, capturing the economic impact of cycling on battery lifetime. The resulting MINLP is exactly reformulated as a mixed-integer second-order cone program (MISOCP) through the convex reformulation of the apparent power constraints and the linearization of the absolute value terms in the degradation cost, preserving convexity and enabling efficient solution using state-of-the-art optimization solvers. The framework is implemented using MATLAB CVX with the Gurobi solver and validated on a modified 33-bus radial distribution network incorporating three PV generation units and three BESS units, with detailed time-varying load profiles, solar irradiance profiles, and energy price data representing realistic Colombian distribution system conditions. The computational analysis is organized around seven distinct scenarios that progressively introduce distributed energy resources and reactive power control capabilities. Numerical results demonstrate that the proposed framework achieves a total daily cost reduction of up to 50.28% compared to the base case without distributed resources, with PV integration alone reducing costs by 29.70%, and enabling reactive power control from PV inverters providing an additional 19.40\% cost reduction. Furthermore, while BESS units operating with active power-only services provide minimal economic benefits, enabling reactive power control from BESS units yields a 10.37% cost reduction, and the full integration of both PV and BESS with coordinated active-reactive control achieves the best performance with a 50.28% cost reduction. The results confirm that coordinated active-reactive power dispatch, combined with degradation-aware scheduling, provides significant economic benefits for distribution systems with integrated renewable sources and energy storage. The proposed framework offers a computationally efficient and practical tool for distribution system operators, enabling them to fully utilize the capabilities of distributed energy resources while maintaining system security and economic efficiency.