A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation
Journal of Power Sources
In this paper, we survey two kinds of mathematics-based battery models intended for use in hybrid and electric vehicle simulation. The first is circuit-based, which is founded upon the electrical behaviour of the battery, and abstracts away the electrochemistry into equivalent electrical components. The second is chemistry-based, which is founded upon the electrochemical equations of the battery chemistry. In this paper we focus on the field of battery modelling for automotive electric vehicle
... imulation, with an aim to help engineers and scientists become familiar with the field of battery modelling and the different models and techniques that are commonly used. Because the field of battery modelling is so extensive, we limit ourselves to considering only the most common battery chemistries and modelling techniques. We also limit ourselves to acausal, physics-based battery models. This means our batteries use voltage, current, and temperature as the physical quantities of interest, and that they can be written as a system of continuous-time equations. This is in contrast to causal, signal-based battery models that typically use discrete-time equations in an iterative solution, and power as the main physical quantity of interest. The most commonly used batteries in electric vehicles today are the Nickel-Metal-Hydride (NiMH) and Lithium-Ion (Li-ion) chemistries  . In the past, Lead-Acid batteries (PbA) were used, but these are falling out of favour to the higher energy and power densities of the Ni-MH and Li-ion chemistries. However many of the techniques developed for modelling these PbA batteries are applicable to more modern chemistries. In the future, Li-ion is a very promising chemistry that is light weight and has high energy and power densities; however more research needs to be done to drive down the cost of these batteries and to increase their safety  and performance, particularly at relatively high and low temperatures. In Section 2 we survey battery models as they apply to various battery modelling tasks. Section 3 focuses on equivalent circuit models in particular, and surveys different modelling techniques and considerations. Section 4 surveys electrochemical battery modelling, and Section 5 briefly compares an equivalent circuit and electrochemical battery under pulse discharge, shows the results of a sensitivity analysis of the two battery models, and finally shows the results of an electric vehicle simulation. The paper is finished off by the conclusions, acknowledgements, references, and appendices. Battery Modelling The two most common techniques we encountered for modelling batteries in automotive applications are equivalent electric circuit and electrochemical modelling. Some models [7-9] combine elements of both chemistry and circuit-based modelling techniques. Equivalent circuit modelling techniques abstract away the electrochemical nature of the battery and represent it solely as electrical components  . Sometimes these contain non-linear components like diodes that strive to better approximate the electrochemical nature of the battery. The structure of the model depends on the type of experimental method used to determine the parameters of the model -which is usually either electrochemical impedance spectroscopy or measuring pulse discharge behaviour -as well as the desired fidelity and goals of the modelling effort. Electrochemical modelling techniques are all based on the highly non-linear equations that describe the electrochemical physics of the battery, and employ many different approximations to simplify the equations and the solutions thereof, depending on the level of fidelity one requires and the goals of modelling the battery. Generally, the simpler the model, the faster it will simulate, but the lower its fidelity. This is an important trade-off that one must consider when choosing a battery model to suit one's application, particularly if real-time simulation is a requirement.