A comparative study of reduced-order equivalent circuit models for state-of-available-power prediction of lithium-ion batteries in electric vehicles

Lithium-ion batteries (LIBs) definitely belong to the most promising commercially available energy storage systems (ESS) for use in electric vehicles (EVs). Their higher specific volumetric and gravimetric energy and power density, higher cycle lifetime and lower self-discharge rate in contrast to settled ESS (e.g., lead-acid batteries, nickel cadmium or nickel-metal hydride) have gained the attention of many vehicle manufacturers, suppliers and research institutions in order to explore and improve different LIB technologies in recent years. Battery management systems (BMS) consisting of both hardware and hardware are responsible for reliable and safe operation of LIBs in EVs. State-of-Charge (SoC), State-of-Health (SoH) and State-of-Available-Power (SoAP) are the major battery states that must be determined by means of so-called monitoring algorithms. The main focus of the present study lies on on-board SoAP prediction of LIBs in EVs. The prediction of the maximum power that can be applied to the battery by (dis)charging it during acceleration, regenerative braking and gradient climbing is definitely one of the most challenging tasks of BMS. The available battery power is limited by the safe operating area (SOA), where SOA is defined by battery temperature, current, voltage and SoC. Accurate SoAP prediction allows the energy management system to regulate the power flow of the vehicle more precisely and optimize battery performance and improve its lifetime accordingly. In this study, LIBs at different aging states using various active materials are investigated whereby the primary focus lies on investigating the electrical behavior of LIBs using lithium titanium oxide, Li4Ti5O12 (LTO) anodes. In addition, other LIB technologies such as lithium nickel cobalt manganese oxide, Li(Ni1/3Co1/3Mn1/3)O2 (NMC) and lithium iron phosphate, LiFePO4 (LFP) are examined. Characterization tests are performed over a wide temperature range (- 20 °C⋯+40 °C) by employing electrochemical impedance spectroscopy and current pulse tests. Furthermore, the behavior of battery impedance parameters and open-circuit voltage over the battery lifetime with regard to temperature, SoC is investigated comprehensively. The closed-loop model-based approaches using reduced order equivalent circuit models (ECM) for battery state estimation have received increasing attention in recent scientific publications due to their simple nature and the possibility for implementation on low cost embedded systems. The aforementioned techniques are often reliable and can track the changes of impedance characteristics over the battery lifetime. However, most of the methods presented in the literature are often validated under nominal conditions using standardized load profiles and neglect major internal and external factors, among others, extreme temperature variation or adaptability of the applied algorithm to present operating condition and aging state of the battery. In this study, a comparative study of a wide range of impedance-based ECMs for on-board SoAP prediction is carried out. In total, seven dynamic ECMs including ohmic resistance, RC-elements, ZARC elements connected in series with a voltage source are implemented. The investigated ECMs are verified under varying conditions (different temperatures and wide SoC range) using real vehicle data obtained in an EV prototype and current pulse tests. Furthermore, the current dependence of the charge transfer resistance is considered by applying the Butler-Volmer equation. The dependence of voltage estimation and SoAP prediction accuracy for different prediction time horizons on SoC, temperature and applied current rate is examined