Electric Vehicles - Using physics-based battery models for an improved estimation of state of charge.

Adrien Bizeray's picture

Low battery

The last two decades have seen a renewed interest in battery research due to the commercial development of electric and hybrid electric cars. Indeed, the use of batteries for electric vehicles raises issues that were not encountered in previous applications, such as electronics. On the one hand, a large area of research is aimed at increasing battery energy density – the amount of energy stored per kilogram of battery – by focusing on new materials and chemistries. On the other hand, many researchers are now focusing on optimising battery use and monitoring to get the most out of current battery technology notably by improving Battery Management Systems.

A Battery Management System (BMS) is a device that monitors battery state and ensures that the battery operates in safe conditions. One of the most important battery parameters monitored by the BMS is the state of charge (SOC), which is the percentage of the remaining energy compared to the energy available in a fully charged battery. An accurate and trustworthy state of charge estimation is of major importance for automotive applications since it is the 'fuel gauge' of the electric vehicle. However, it cannot be measured directly but can only be calculated from voltage and current measurements using a mathematical model.

Currently, battery state of charge is mainly estimated using empirical models that are simple to implement in embedded systems. Simple models include measuring the battery terminal voltage, which is directly related to state of charge (see voltage discharge curves obtained experimentally on Figure 1) or ‘counting’ electrons passing through the external circuit by a technique called “Coulomb counting”. However, these techniques are limited by the high dependency of the battery behaviour on current, temperature and ageing of the battery. The wide operating range in terms of temperature and current and the high commercial constraints on electric vehicles make empirical models insufficient for automotive applications.

Discharge curves of a lithium-ion battery at different C-rates

Figure 1: Battery terminal voltage at different discharge currents. In battery terminology, it is common to express electric current in terms of C-rate. A current of 1C is the current that will discharge the battery in one hour. In this case, the battery has a nominal capacity of 4.8Ah, which means that a 4.8A current discharges the battery in one hour.


A possible solution consists of using theoretical battery models derived from principles of physics instead of empirical models. The most widely used battery electrochemical model is based on transport of ions and was derived by Newman of Berkeley Lab (California) in the early 1990s. This model is based on equations governing the transport of charges in the electrodes and electrolyte (see Figure 2). In his model, Newman relates the transport of ions (microscopic scale) to the voltage and current (macroscopic scale) in order to estimate the concentration of lithium ions in electrodes, which is a more accurate estimation of state of charge.

Transport of charges in a lithium-ion battery

Figure 2: Transport of charges in lithium-ion battery. During discharge, due to the difference in electrochemical potential between the two electrodes, deinsertion of lithium occurs spontaneously at the anode (negative electrode) and electrons are released in the external circuit (1). Lithium ions migrate in the electrolyte through the separator (2) while electrons, which cannot flow into the non-conductive electrolyte, flow through the external circuit and the load (3) creating a current. At the cathode (positive electrode), electrons are consumed and lithium is reinserted (4). This process is reversed during battery charge by externally applying a potential difference between the electrodes.


Physic-based models have been widely used for battery design but cannot be easily implemented in embedded systems due to their high computational requirements. A current avenue of research aims at reducing the computational cost of physics-based models to allow their use in embedded Battery Management Systems for optimising batteries’ utilization.