Optimizing PHEV Electric Range with Battery Degradation

Lin, Alexander; Lin, Zhenhong · 2025 · Crossref

DOI: 10.21203/rs.3.rs-7914876/v1

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Summary

This study addresses the optimization of electric range (battery capacity) for plug-in hybrid electric vehicles (PHEVs) by integrating battery degradation mechanisms into existing cost models. While PHEVs offer decarbonization benefits and range assurance, previous optimization efforts ignored the impact of battery wear on total ownership costs. The authors argue that optimizing battery size is critical for reducing consumer costs, minimizing greenhouse gas emissions associated with battery production, and alleviating pressure on lithium supply chains. The research aims to develop a modeling framework that accounts for both cycle-based and calendar-based degradation to determine the optimal battery capacity that minimizes total range-related costs over a vehicle’s lifetime. The authors expanded the Market-oriented Optimal Range for PHEV (MOR-PHEV) model to include dynamic battery capacity calculations. The objective function minimizes the net present value of six cost components: upfront battery cost, electricity cost, gasoline cost, gasoline refueling behavior cost, electricity recharging behavior cost, and vehicle cost. The model incorporates a degradation equation that reduces available battery capacity daily based on depth of discharge and calendar aging. Using Microsoft Excel and Solver, the authors simulated a base case assuming a 10-year vehicle lifetime, U.S. average driving patterns, and specific energy prices. Parameters included a battery cost of $115/kWh, electricity price of $0.175/kWh, and gasoline price of $0.87/L. The model assumes a Gamma distribution for daily driving distances and calculates costs based on the evolving electric range as the battery degrades. The results indicate that the optimal battery capacity for the base case is 47.43 kWh, providing an electric range of 99.5 km. This configuration minimizes the total range-related cost to $20,192, composed primarily of electricity (43%), battery (27%), and recharging behavior costs (26%). The optimization yields significant savings, reducing battery costs by $3,000 to $5,000 compared to non-optimized scenarios, such as a misguided 90 kWh battery. Sensitivity analysis reveals that the optimal results are robust against variations in exogenous parameters, with annual distance, gasoline consumption, and battery unit cost being the most influential factors. Notably, the model identifies a "discreteness point" where small batteries degrade completely within the vehicle's life, suggesting that faster degradation can sometimes be economically beneficial by allowing the vehicle to operate earlier as a non-plug-in hybrid, thereby avoiding recharging hassles. The study concludes that incorporating battery degradation into PHEV range optimization is essential for accurate cost assessment and vehicle design. The findings imply that automakers and policymakers should consider degradation effects to maximize consumer value and social efficiency. By optimizing battery size, the industry can reduce material demand and lifecycle emissions without compromising utility. The robustness of the optimal capacity against parameter changes suggests that standardized optimization strategies can be effectively applied across varying market conditions, supporting more sustainable and cost-effective PHEV adoption.

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