Mathematical modeling and optimization of crop-PV index for photovoltaic greenhouses

Photovoltaic (PV) greenhouses provide a sustainable route to dual-purpose land use by merging food production with renewable energy production. This work presents a unified mathematical framework for the modeling and optimization of the Crop-PV Index (CPVI) — a compound performance index combining crop yield and PV electricity output subject to real-world conditions. The model integrates solar radiation breakdown, microclimatic equilibrium, and crop growth processes, and is tuned to three globally important staple crops: maize, wheat, and rice. These three cereal crops were chosen to represent differential thermal and photosynthetic demands: wheat (cool season), rice (moderate season), and maize (warm season). Simulations are conducted under different PV coverage fractions, greenhouse transmissivity rates, and climatic conditions. A nonlinear optimization algorithm determines the design parameters maximizing CPVI subject to critical light and thermal condition thresholds. Results indicate up to 22.4 % improvement in CPVI, with increased water-use efficiency and carbon savings as compared to baseline case. Sensitivity analysis indicates PV coverage ratio, transmissivity, and irrigation efficiency as the most sensitive parameters. The optimization framework presented provides a scalable tool for achieving maximum agronomic and energy productivity in integrated PV greenhouse systems in various agro-ecological zones.