Comparative Residential Energy Management with Behind-the-Meter Battery and Vehicle-to-Home Operation Under Prescribed PV and Demand Deviations

Residential photovoltaic generation and household demand are temporally mismatched, affecting grid dependence and local storage use. This study formulates a 24 h mixed-integer linear programming model for a grid-connected residential prosumer with rooftop PV, a stationary behind-the-meter battery, and an electric vehicle capable of vehicle-to-home operation. Four configurations are compared under common external inputs: no storage, battery only, V2H only, and a hybrid battery–V2H system. The model resolves the main power routes, enforces charging, discharging, and cyclic state-of-charge constraints, allows grid charging, and excludes storage-to-grid export. PV generation is reduced, and residential demand is increased through a prescribed deviation-scaling parameter evaluated at five levels for clear-day and synthetic partly cloudy profiles. Numerical consistency is checked using an independent no-storage calculation and equation residuals. At ρ = 0.3 under the clear-day profile, the hybrid configuration reduces daily operating cost from USD 26.113 to USD 17.807, increases PV self-consumption from 69.684% to 89.121%, lowers utility purchase from 106.380 to 88.700 kWh/day, and reduces export from 36.170 to 12.980 kWh/day. Under the partly cloudy profile, all storage-based configurations reach 100% PV self-consumption and zero export, while the hybrid case retains the lowest operating cost. The results are conditional on the adopted capacities, continuous EV connection, tariff structure, and exclusion of degradation and investment costs.