A federated game-theoretic strategy for three-phase voltage unbalance mitigation via dynamic pricing and demand response

This paper introduces a federated game-theoretic framework to mitigate the three-phase voltage unbalance in power distribution systems through a fully distributed demand response (DR) program where users act as autonomous agents. Conventional voltage balancing methods rely on supply-side interventions. However, the human-centered approach proposed in this article leverages the inherent flexibility of user-side loads across networked buildings to achieve a system-wide three-phase voltage balance, while respecting individual preferences. Conventional demand response programs consider users as passive load tweakers responding to centralized price signals. In contrast, our approach empowers users as autonomous decision-makers who maintain control over their consumption patterns while contributing to system-wide voltage stability. A mathematical model of user-side grid elements, including various classes of household appliances, energy storage systems (ESS), and distributed energy resources (DER) is developed. This model provides insights on how human consumption behaviors can be effectively integrated into power system operations. A novel three-phase dynamic pricing mechanism is designed to incentivize phase-specific consumption adjustments, encouraging users to adopt load patterns that contribute to a balanced three-phase voltage state without compromising comfort preferences. Each user controls a personalized trade-off parameter (λk) that serves as an adjustable dial to balance economic objectives against individual comfort requirements. In this way, traditional cost-versus-reliability dichotomies can be overcome by enabling simultaneous optimization of both system-level voltage stability and user-specific preferences. The proposed approach serves as a proof of concept for human-centered design in smart grids, operating entirely on the demand side while being robust, scalable, and privacy-preserving, with low computational complexity for users. Simulations illustrate that strategic load scheduling on each phase, driven by the proposed multi-agent model, significantly improves voltage balance, maintains customer comfort, and supports ancillary services such as peak shaving. The results of our simulations demonstrate that the balanced strategy delivers 23.91 % cost reduction while improving phase matching by 30.12 % on average, confirming simultaneous achievement of economic efficiency and voltage stability objectives.