A Stochastic MILP Framework for Risk-Aware and Degradation-Conscious Energy Management in Residential Multi-Home Systems

The integration of photovoltaic (PV) systems, energy storage systems (ESSs), and electric vehicles (EVs) in residential communities introduces challenges from renewable-generation uncertainty, load variability, and battery degradation. This paper proposes a stochastic mixed-integer linear programming (MILP) framework for centralized multi-home energy management with aggregated PV and ESS resources and household EVs. The framework minimizes expected electricity cost while controlling operational risk, quantified by Conditional Value-at-Risk (CVaR), and shared-ESS cycling-related degradation, represented by the equivalent full cycle (EFC) metric. An ε-constraint formulation with a causal-adaptive ESS dispatch coordinates these requirements, and static and adaptive strategies are evaluated on independent test scenarios. For the 10-home case, the proposed strategy reduces expected cost by 0.24%, CVaR0.90 by 2.18%, and ESS EFC by 4.37% relative to the static baseline. Relative to the adaptive baseline, it reduces ESS EFC by 4.46% for a 1.12% cost increase, with a practically unchanged CVaR0.90 and no increase in EV throughput; the CVaR reduction arises mainly from the adaptive recourse. Scalability tests with up to 50 households confirm computational practicality for 24 h day-ahead scheduling.