Optimization of residential rooftop PV configurations for maximum energy efficiency and economic viability

This paper proposes an integrated optimization model for residential rooftop photovoltaic (PV) systems, aiming to balance economic viability and operational performance. The problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) model that captures seasonal variations and incorporates reliability indicators such as the Loss of Power Supply Probability (LPSP) and energy density. To efficiently solve the model, a hybrid approach is used: the Relax-and-Fix (R&F) heuristic generates an initial feasible layout, which is subsequently refined using the Branch-and-Bound (B&B) algorithm. In addition, variability in energy density is addressed by constructing an empirical probability distribution, which guides the determination of optimal inter-row spacing across different seasonal conditions. To enhance performance, the model determines the optimal number of PV panels, tilt angle, and inter-row spacing. A case study of a residential building in eastern Saudi Arabia assesses the model's practicality. Sensitivity analysis examines the impact of economic and design factors, such as inflation dynamics and tilt angles, on system viability. Findings reveal that at low interest rates (0%–5%), larger PV systems achieve a lower levelized cost of energy (LCOE) and greater grid independence, whereas interest rates above 7% lead to system downsizing, making solar investments unviable. An optimal tilt angle range of 20°–40° balances energy generation, cost, and land-use efficiency across seasonal variability, while extreme angles degrade economic and operational performance.