Optimal Equipment Sizing and Investment Timing for a Residential Energy System Considering Uncertainty

This paper proposes a method for determining the optimal investment timing and capacity of photovoltaic (PV) and battery energy storage (ES) systems for residential use, considering uncertainties in energy demand, solar irradiance, and equipment costs. Energy demand is forecasted based on probabilistic changes in household composition using the cohort method, and solar irradiance scenarios are generated from historical weather data with Markov-chain-based weather sequence prediction. The equipment investment problem is formulated as a mixed-integer linear programming problem that allows separate optimization of PV and ES investment timing over a 20-year planning horizon. Numerical simulations show that PV installation in the first year is cost-optimal regardless of conditions, while ES investment can be deferred by approximately 10 years at a 4% discount rate, demonstrating the value of investment deferral flexibility.