Optimal sizing of a PV–wind–battery hybrid system considering performance degradation and embodied energy under LPSP and battery State of Health constraints

Abstract

This paper proposes an optimal sizing of a hybrid energy system comprising photovoltaic (PV), Wind Turbines (WT), a Battery Energy Storage System (BESS), and loads. The optimization simultaneously minimizes the global cost, integrating the life cycle cost and the Ecological Cost (EC), while preserving the battery State of Health (SoH). The EC is evaluated through the embodied energy, which quantifies the total amount of energy consumed throughout the entire life cycle of each component. Key technical constraints include a Loss of Power Supply Probability (LPSP) below 5% and the SoH degradation limit of 5% over 2 years. The problem is solved using a Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP), comparing their complexity and robustness. The sizing parameters are the PV area (A_PV), WT swept area (A_WT), and battery capacity (C_BESS). The model uniquely incorporates performance degradation of PV (−2%/year) and WT (−1.8%/year) for realistic design. The optimal configuration (A_PV-opt = 6.5 m², A_WT-opt = 3.5 m², C_BESS-opt = 158.77 Ah) achieves a minimal global cost of €18,997.9, with a SoH of 95.03 % and LPSP of 4.541 %, effectively balancing economic, environmental, and operational criteria. Both methods converge to the same optimal solution, with SQP being faster but sensitive to the initial vector, while GA is more robust but computationally intensive. This makes SQP suitable for simple problems and GA preferable for complex or non-convex ones.