Two-stage optimization of appliance scheduling and BESS capacity with comfort level

Abstract

Residential photovoltaic (PV)–battery energy storage system (BESS) planning often neglects impact of comfort level. We propose a two-stage framework that jointly selects BESS capacity and appliance start-up schedules while accounting for appliance-use comfort, thermal comfort, and BESS degradation. Annual days are clustered by k-means to select a set of typical days. Stage 1 performs a discrete capacity scan (coarse grid plus local refinement). For each candidate, Stage 2 solves a typical day mixed-integer linear programming problem with a linear fractional cost–comfort objective via Dinkelbach’s method, maps the resulting binary schedules to all natural days by cluster membership, and then solves an annual rolling linear programming problem for dispatch and degradation-inclusive evaluation. In the baseline case, the selected capacity is 10.75 kWh with an annual total cost of 2623.2 CNY and comfort indices of 0.793 and 0.788; degradation cost is 404.3 CNY. Without the comfort term, the preferred capacity increases to 16.5 kWh and the annual total cost decreases to 2265.9 CNY, while degradation cost rises to 555.1 CNY. Sensitivity analyses show that outcomes vary with comfort settings and time-of-use prices. Overall, the framework quantifies annual cost-comfort-degradation trade-offs and recommends a feasible BESS size and appliance schedules.

HIGHLIGHTS • Two-stage framework jointly optimizes BESS capacity and appliance schedules with comfort. • k-means typical days enable tractable annual MILP and rolling LP evaluation. • Baseline selects 10.75 kWh, 2623.2 CNY, with comfort indices 0.793 and 0.788. • Removing comfort changes preferred BESS capacity and appliance start-up schedules. • Sensitivity analyses quantify impacts of comfort weights, bounds, price.