Equivalent Circuit Modeling of Sodium-Ion Batteries Incorporating Temperature Effects: A Comprehensive Investigation

<div class="section abstract"><div class="htmlview paragraph">The transition from Internal Combustion Engine (ICE) Vehicles to Electric Vehicles (EVs) has catalyzed significant advancements in battery technology, prioritizing safer and more reliable energy storage solutions. Although Lithium Iron Phosphate (LFP) batteries are recognized for their safety, they rely on critical and market-volatile elements such as copper, lithium, and graphite. To address these challenges, sodium-ion batteries (SIBs) have emerged as sustainable alternatives that are particularly suited for low-speed EVs. Ensuring the seamless integration of SIBs into EV battery packs necessitates preparedness for the rapid evolution of SIB technology. Model-based approaches, including Equivalent Circuit Models (ECMs), are crucial for developing advanced Battery Management Systems (BMSs) and State of Charge (SoC) estimation algorithms that enable precise battery control. This study comprehensively evaluates various order Resistance-Capacitance (RC) ECM configurations to accurately estimate the terminal voltage for a 10Ah commercial 33140 SIB. The tests were conducted at Charge/Discharge Rates (CDR) of 0.375C/0.5C, 0.75C/1C, and 1.125C/1.5C, incorporating the effects of temperatures at 10, 25, 40, and 55°C. The Worldwide Harmonized Light Vehicle Test Procedure (WLTP), modified for cell-level testing, was used to validate the model-predicted voltage against experimental results, with accuracy assessed through Root Mean Square Error (RMSE). The findings indicate that the first-order RC ECM at 0.375C/0.5C CDR yields a minimum RMSE of 13 mV for the WLTP at 25°C using the non-linear least square method as a parameter estimation technique. Furthermore, Incorporating the temperature effects for the first order RC ECM at 0.5C/0.375C CDR resulted in an RMSE of 10.6 mV at 15°C and 3.8 mV at 45°C when validated using WLTP, highlighting the model's reliability across varying temperatures.</div></div>