This work introduces a novel method for the simultaneous optimization of energy management and powertrain components sizing of a parallel plug-in hybrid electric vehicle. The problem is formulated as a convex optimization problem to minimize an objective function, which is a weighted sum of operational and component costs. The former includes the consumed fossil fuel and electrical energy, whereas the latter includes the cost of battery, electric motor, and internal combustion engine. The powertrain model includes quadratic losses for the powertrain components.Moreover, the combustion engine and the electric motor losses are assumed to scale linearly with respect to the size and the losses of baseline components.The result of the optimization is the variables of the global optimal energy management for every time instant and optimal component sizes. Due to the dependency of the result on the driving cycle, a long real-life cycle with its charging times is chosen to represent a general driving pattern. The method allows studying the effect of some performance requirements, namely acceleration, top speed, and all electric range, on the component sizes and total cost.
I. IntroductionInterest in the electrification of vehicles is growing as a result of the environmental benefits that can be achieved regarding emissions and fuel consumption. Hybrid electric vehicles (HEV) are the first generation of electrified vehicles that, in addition to an internal combustion engine (ICE), have an electric motor (EM) and electric energy storage. HEVs can improve fuel efficiency owing to the possibility of downsizing the engine, the ability to recover braking energy, the extra power control freedom gained by the two power sources, and the ability to stop the engine when idle. The next generation of electrified vehicles, plug-in hybrid electric vehicles (PHEV), have the additional ability to store energy from the electricity grid using large capacity batteries. The stored energy can propel the vehicle on short trips, thereby reducing vehicle dependency on petroleum and potentially CO 2 emissions.The extent to which this can be achieved depends on the size of the battery and the driving habits of the vehicle owner. There is clearly a trade-off between improved fuel economy and battery cost (size). This is one of the many design trade-offs involved with PHEVs when taking into account both cost effectiveness and performance of the vehicle [1]. These trade-offs are highly sensitive to the varying prices of energy and components, and the driving and charging patterns. Finding the proper balance between different objectives is also related to customers' October 15, 2012 DRAFT
Building a plug-in hybrid electric vehicle that has a low fuel consumption at low hybridization cost requires detailed design optimization studies. This paper investigates optimization of a PHEV with a series powertrain configuration, where plant and control parameters are found concurrently. In this work two often used methods are implemented to find optimal energy management with component sizes. In the first method, the optimal energy management is found simultaneously with the optimal design of the vehicle by using convex optimization to minimize the sum of operational and component costs over a given driving cycle. To find the integer variable, i.e., engine on-off, dynamic programming and heuristics are used. In the second method, particle swarm optimization is used to find the optimal component sizing, together with dynamic programming to find the optimal energy management. The results show that both methods converge to the same optimal design, achieving a 10.4% fuel reduction from the initial powertrain design. Additionally, it is highlighted that the usage of each of the method poses challenges, such as computational time (where convex optimization outperforms particle swarm optimization by a factor of 20) and the tuning effort for the particle swarm optimization and the ability to handle integer variables of convex optimization.
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