Mathematical based modelling and simulation software from Maplesoft is being used to develop high-fidelity models of hybrid-electric and fully electric vehicle batteries
In the fast-moving hybrid-electric and fully electric vehicle market, manufacturers are being forced to come up with new designs faster than ever before. So, the industry is turning to math-based physical modelling techniques which allow engineers to accurately describe the behaviour of the components that comprise the system and the physical constraints on it. These model equations are then used to develop, test, and refine designs quickly, and without the expense and time required to build physical prototypes.
The battery is one of the most important components of a hybrid-electric or fully electric vehicle. Having a good virtual model of the battery is essential so that both its behaviour and the physical interaction of the battery with all the other components are properly reflected in the model. Capturing these interactions is essential to designing an efficient, effective electric vehicle.
In such an application, Dr. Thanh-Son Dao and Mr. Aden Seaman are working with Dr. John McPhee, the NSERC/Toyota/Maplesoft Industrial Research Chair for Mathematics-based Modelling and Design, to develop high-fidelity models of hybrid-electric and electric vehicles, including the batteries. For this, the team chose MapleSim, multi-domain physical modelling and simulation software from Maplesoft.
Capturing effects
Being light while providing high levels of power, lithium-ion batteries are a good solution for electric vehicles. Batteries in vehicles are subject to periods of high current draw and recharge and large temperature variations, which can have a significant effect on the performance and lifespan of the batteries.
To capture these effects, McPhee and Seaman needed a model of lithium-ion battery chemistry over a wide state-of-charge range, widely varying currents, and various temperatures. Starting with the electric circuit battery model of Chen and Rincón-Mora, they implemented the components in MapleSim, using a custom function component to represent the nonlinear relationship between the state of charge and the electrical components. They then modified the battery equations to simulate a battery pack that is composed of series and parallel combinations of single cells. Next, they developed a power controller model in order to connect the battery pack to a motor, and then incorporated a one-dimensional vehicle model into the model. The simple vehicle model drives on an inclined plane, which is in turn controlled by a terrain model. A drive cycle model was included to control the desired speed of the vehicle. The resulting differential equations, generated by MapleSim, were simplified symbolically and then simulated numerically.
A variety of driving conditions were simulated, such as hard and gentle acceleration and driving up and down hills – the results were physically consistent and clearly demonstrated the tight coupling between the battery and the movement of the vehicle. This model will form the basis for a more comprehensive vehicle model, which will include a more sophisticated power controller and more complex motor, terrain, and drive-cycle models.
Development
McPhee, Dao and Seaman used MapleSim to develop a multi-domain model of a series HEV, including an automatically generated optimised set of governing equations. The HEV model consists of a mean-value internal combustion engine (ICE), DC motors driven by a chemistry-based NiMH battery pack, and a multibody vehicle model. They chose a Ni-MH battery because of its widespread use in hybrid-electric vehicles.
Furthermore, they used a chemistry-based modelling approach that captures the chemical and electrochemical processes inside the battery, enabling them to modify the physical parameters of the battery as needed to meet their overall vehicle design requirements. They modelled the battery inside MapleSim by placing the governing equations of the battery processes directly inside MapleSim custom components.
MapleSim automatically generated an optimised set of governing equations for the entire HEV system, which combined mechanical, electrical, chemical, and hydraulic domains. Simulations were then used to demonstrate the performance of the developed HEV system.
Simulation results showed that the model is viable and, as a result of MapleSim’s lossless symbolic techniques for automatically producing an optimal set of equations, the number of governing equations was significantly reduced, resulting in a computationally efficient system. This HEV model can be used for design, control, and prediction of vehicle handling performance under different driving scenarios. The model can also be used for sensitivity analysis, model reduction, and real-time applications such as hardware-in-the-loop (HIL) simulations.
McPhee commented: “We firmly believe that a math-based approach is the best and quite possibly the only feasible approach for tackling the design problems associated with complex systems such as electric and hybrid-electric vehicles.”
MapleSoft solutions are available in the UK from Adept Scientific.
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