A game-theoretic approach to fair and grid-aware load flexibility allocation in residential distribution networks

This article evaluates the potential of thermostatically controlled loads (TCL) as flexible resources to improve power quality―particularly phase unbalance―in low-voltage residential distribution networks while ensuring fair consumer participation. To address both grid-level and social objectives, the adaptive fairness and grid-aware allocation (AFGA) algorithm is proposed. This algorithm integrates cooperative game theory and Nash bargaining principles to jointly optimize phase balancing and consumer utility. The proposed approach dynamically allocates residential consumer flexibility by accounting for phase-level constraints, individual flexibility capacity, and historical participation, thereby preventing the persistent overuse of specific consumers and promoting equitable long-term engagement. Simulation results on a representative residential network with 100 households demonstrate that, with only 20% participation, the AFGA algorithm reduces the unbalance load factor (ULF) to below 10%, achieves a highly equitable distribution of benefits (Gini index = 0.065), and effectively enforces adaptive fairness through penalty-feedback mechanisms. Furthermore, the algorithm completes a full-day simulation in 102 s with only 0.24 MB of peak memory usage. These findings position the AFGA algorithm as an effective and scalable solution for integrating fairness-aware residential flexibility into the operation of low-voltage residential distribution networks.