By Saurabh Mahapatra, The MathWorks
Figure 1: This simplified diagram of an HEV vehicle illustrates one possible arrangement of system elements.
The general concept of a hybrid electric vehicle is to combine the right proportion of an electric drive with an internal combustion engine depending on driving conditions, so both can work in their optimal operating range as much as possible.
Figure 1 shows a simplified schematic of one possible arrangement for an HEV. The electric motor and the gasoline engine are coupled through a power splitter and supply energy to the driveshaft. In practice, planetary gears are used for the power-splitter function. This leads to coupling of the nonlinear dynamical equations governing the electromechanical components, leading to added mathematical complexity of the system. To improve fuel efficiency, the design requires a strategy for managing these coupled power sources. To increase the energy density further, permanent magnet synchronous machines (PMSM) are often used. Also, optimizing the core design of the various components such as the engine, the motor, the planetary gear, the generator, and the battery can also bring about significant fuel savings.
HEV Design Challenges
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Figure 2: This diagram shows in componentized form a system-level model realization of the hybrid electric vehicle design.
Traditional approaches such as paper-based processes with linear workflows increase the possibility that design bugs will be detected late in the development process, leading to higher costs. Such a process is not amenable to implementing an HEV design that requires nonlinear workflows. Even with design approaches based on software tools, the diversity of development environments used by the different teams can make it very challenging to create interfaces for the different component designs.
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Figure 3: This illustration shows the synchronous generator and drive in the system-level model. The associated controllers for the torque and speed control are simple PI controllers.
Using Model-Based Design for highly complex systems such as an HEV, with its highly specialized functional components, typically fits into the "divide and conquer" methodology. The initials steps are to come up with an executable specification for a model of the overall system with the interconnected components that meets broad-level requirements. With the right level of detail or model fidelity, faster simulations can be carried out to address feasibility concerns early in the development process. Specialist teams can then elaborate on the component designs by using these executable specifications as a guideline. As model elaboration progresses, the requirements undergo refinement both at the system and the component levels. After design iterations, the components are integrated to form the final solution. In the next section, a case study illustrates how Model-Based Design supports these key ideas.
Case StudyThe case study is based on a design experiment to understand how Model-Based Design, in particular the use of an executable specification and design with simulation, along with the latest design tools can be effectively applied to HEV development.
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Figure 4 shows the implementation of the system power management algorithm.
• Fuel efficiency: Greater than 36.5 mpg
• 0-1/4 mile in 25s: Initial acceleration helps in identifying the motor requirements because the engine cannot provide torque at low speeds, and most of the power is supplied by the motor.
• Top speed of 120 mph: Maximum velocity is necessary because the power required at this speed should be met by the combination of the engine and the motor supply. It guarantees that all speeds between rest and this maximum speed can be attained by the combination of electric battery and gasoline engine power sources.
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Next, we illustrate the design of the synchronous generator and drive component with Simulink. Figure 3 shows a low-fidelity model based on mathematical relationships between the generator drive torque, speed, and control voltages. This level of detail greatly enhanced the speed of simulation, because we did not have to deal with the high-frequency switching that would be present in the associated power electronics circuitry.
In Figure 4(A), we show the conceptual framework consisting of ON/OFF states of the engine, motor, and generator. We define the vehicle modes as follows:
• Low speeds/Start: The electric motor provides all the torque for initial acceleration.
•Acceleration: As the vehicle reaches a predefined speed, the engine kicks in to supply power along with the motor.
• Cruising: If the car maintains constant speed, the motor is switched off and the generator is switched on. A portion of the engine's power is used by the generator to recharge the battery.
• Braking: If brakes are applied, the engine and the generator are switched off. The motor is made to behave like a generator to recharge the battery.
Figure 4a. On the left is the conceptual framework (A), and on the right is the associated executable specification in Stateflow (B).
In Figure 4b, we translated this conceptual design into a hierarchical state chart modeled in Stateflow. This executable specification is simulated and tested with the rest of the model.
The following results came from simulating and testing the system-level model compared with the requirements:
• Fuel efficiency greater than 6.5 mpg (requirement met)
• 0-1/4 mile in 25s: 0-1/5 mile in 25 s (requirement not met)
• Top speed of 120 mph: top speed of 100 mph (requirement not met)
Since fuel economy is more important for us than performance, we leaned toward compromising the last two requirements. Once we were satisfied with the level of fidelity and the results, the components in the system-level model were handed over to the domain specialists to elaborate on them.
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Figure 5: This diagram shows the model elaboration of the synchronous generator and the drive. The associated control loops are shown in pink.
Figure 5 shows the elaborated model consisting of the machine, power electronics circuitry, and the associated controllers. The use of a three-phase AC permanent magnet synchronous machine with a DC battery source entailed the use of a three-phase inverter/rectifier. As the machine design was elaborated, the associated controllers became increasingly complex with the use of speed and multiple control loops.
These elaborated designs were integrated into the same system-level model by replacing each of the components piece by piece. Here is a snapshot of the results of the first design iteration of the elaborated system-level model:
• efficiency greater than 36.5 mpg (requirement not mpg)
•0-1/4 mile in 25s: Requirement met
• Top speed of 120 mph: top speed of 96 mph (Requirement not met)
Through this first iteration of the design, it is clear that model elaboration has led to many requirements not being met. Using a model as the executable specification and design with simulation helped us to detect these difficulties early. Also, using a collaborative environment enabled us to be innovative with our choices to relax system-level requirements, to redo the entire system-level design with better requirements, or to redo the component design. In this case, we found that power losses in the synchronous machine and drive were primarily responsible for the deterioration in performance, and we focused our limited resources more on improving that aspect of the design. Going through several more design iterations helped us to meet our design requirements.
SummaryHEVs have become an important trend in the automotive industry. However, compared to traditional gasoline vehicles, their designs are significantly more complex. HEV development requires collaboration and optimization across multiple engineering domains. Model-Based Design allows for the reuse of design information across all teams and through various stages of development. This approach modeling and simulating the system behavior prior to building the actual hardware leads to the added benefits of lower costs, increased time savings, and customer satisfaction.
Saurabh Mahapatra is a product manager at The MathWorks, Natick, Mass. He holds a Masters degree in Mechanical Engineering from Cornell University and a Bachelors degree in Electrical Engineering from the Indian Institute of Technology (IIT). He can be reached at firstname.lastname@example.org