Optimal Sizing of Residential PV and Battery Systems Under Grid Export Constraints: An Estonian Case Study

This study investigates the optimal sizing of photovoltaic (PV) and battery storage (BAT) systems for Estonian households operating under grid constraints that prevent selling surplus energy. We develop and compare three sizing models of increasing complexity, ranging from a simple heuristic to a full simulation based optimization. Their performance is evaluated using a multi-criteria decision analysis (MCDA) framework that integrates Net Present Value (NPV), Internal Rate of Return (IRR), Profitability Index Ratio (PIR), and payback period. Sensitivity analyses are used to test the robustness of each configuration against electricity price shifts and market volatility. Our findings reveal that standalone PV-only systems are the most economically robust investment. They consistently outperform combined PV + BAT and BAT-only configurations in terms of investment efficiency and overall financial attractiveness. Key results demonstrate that the simplest heuristic-based model (Model 1) identifies configurations with a better balance of financial returns and capital efficiency than the more complex simulation-based approach (Model 3). While the optimization model achieves the highest absolute NPV, it requires significantly higher investment and results in lower overall efficiency. The economic case for batteries remains weak, with viability depending heavily on price volatility and arbitrage potential. These results provide practical guidance, suggesting that for grid constrained households, a well-sized PV-only system identified with a simple model offers the most effective path to cost savings and energy self-sufficiency.