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Accurate prediction of range of an electric vehicle (EV) is a significant issue and a key market qualifier. EV range forecasting can be made practicable through the application of advanced modelling and estimation techniques. Battery modelling and state-of-charge estimation methods play a vital role in this area. In addition, battery modelling is essential for safe charging/discharging and optimal usage of batteries. Much existing work has been carried out on incumbent Lithium-ion (Li-ion) technologies, but these are reaching their theoretical limits and modern research is also exploring promising next-generation technologies such as Lithium-Sulfur (Li-S). This study reviews and discusses various battery modelling approaches including mathematical models, electrochemical models and electrical equivalent circuit models. After a general survey, the study explores the specific application of battery models in EV battery management systems, where models may have low fidelity to be fast enough to run in real-time applications. Two main categories are considered: reducedorder electrochemical models and equivalent circuit models. The particular challenges associated with Li-S batteries are explored, and it is concluded that the state-of-the-art in battery modelling is not sufficient for this chemistry, and new modelling approaches are needed.

Lithium-sulfur (Li-S) batteries are described extensively in the literature, but existing computational models aimed at scientific understanding are too complex for use in applications such as battery management. Computationally simple models are vital for exploitation. This paper proposes a non-linear state-of-charge dependent Li-S equivalent circuit network (ECN) model for a Li-S cell under discharge. Li-S batteries are fundamentally different to Li-ion batteries, and require chemistry-specific models. A new Li-S model is obtained using a ‘behavioural’ interpretation of the ECN model; as Li-S exhibits a ‘steep’ open-circuit voltage (OCV) profile at high states-of-charge, identification methods are designed to take into account OCV changes during current pulses. The prediction-error minimization technique is used. The model is parameterized from laboratory experiments using a mixed-size current pulse profile at four temperatures from 10 °C to 50 °C, giving linearized ECN parameters for a range of states-of-charge, currents and temperatures. These are used to create a nonlinear polynomial-based battery model suitable for use in a battery management system. When the model is used to predict the behaviour of a validation data set representing an automotive NEDC driving cycle, the terminal voltage predictions are judged accurate with a root mean square error of 32 mV

Lithium-Sulfur (Li-S) battery technology is considered for an application in an electric-vehicle energy storage system in this study. A new type of Li-S cell is tested by applying load current and measuring cell's terminal voltage in order to parameterize an equivalent circuit network model. Having the cell's model, the possibility of state-of-charge (SOC) estimation is assessed by performing an observability analysis. The results demonstrate that the Li-S cell model is not fully observable because of the particular shape of cell's open-circuit voltage curve. This feature distinguishes Li-S batteries from many other types of battery, e.g., Li-ion and NiMH. As a consequence, a Li-S cell's SOC cannot be estimated using existing methods in the literature and special considerations are needed. To solve this problem, a new framework is proposed consisting of online battery parameter identification in conjunction with an estimator that is trained to use the identified parameters to predict SOC. The identification part is based on the well-known prediction-error minimization algorithm; and the SOC estimator part is an adaptive neuro-fuzzy inference system in combination with coulomb counting. Using the proposed method, a Li-S cell's SOC is estimated with a mean error of 4% and maximum error of 7% in a realistic driving scenario.

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