Optimal Sizing of Grid-Connected Photovoltaic and Battery Energy Storage Systems Under Environmental Constraints
Rapid growth in grid-connected photovoltaic (PV) deployment supports decarbonization goals but creates planning challenges due to PV variability and the cost of meeting explicit environmental targets. A key limitation in many PV-battery energy storage system (BESS) sizing studies is that carbon impacts are often evaluated as a post-processing metric or treated as a soft objective, which does not guarantee compliance with mandated carbon budgets. This paper proposes a two-stage techno-economic optimization framework that minimizes total PV-BESS investment and operating cost while enforcing an annual carbon-emission cap on grid electricity imports as a hard constraint. To solve the resulting large-scale, time-coupled problem over an hourly annual horizon, a Benders decomposition approach separates long-term capacity decisions from short-term operational dispatch. Using real-world PV availability and a realistic load and tariff profile, the case study shows that the carbon cap directly shapes both optimal sizing and dispatch behavior: the optimized configuration reduces grid energy consumption and achieves the prescribed emission limit (e.g., $100,000 \text{kg} \mathbf{C O}_{\mathbf{2}} /$ year) compared with a grid-only benchmark, while quantifying the corresponding cost implications. Unlike existing approaches that treat emissions as soft objectives requiring post-optimization trade-off analysis, this framework enforces carbon limits as binding constraints within cost minimization, ensuring guaranteed environmental compliance. The proposed framework provides a practical decision-support tool for planners and policymakers seeking cost-effective PV-BESS deployment that is explicitly compliant with emissions targets The case study demonstrates that enforcing a 100,000 kg $\mathbf{C O}_{\mathbf{2}}$ /year emission limit yields an optimal configuration of 423 kW PV capacity and 1,027 kWh battery storage, reducing grid energy consumption by 71% (from 792,198 to 227,632 kWh annually) and achieving 68% emission reduction while simultaneously lowering total annual costs by 34% (from $396,099 to $259,496) compared to grid-only supply.