This paper presents a formalization of the energy management problem in hybrid electric vehicles and a comparison of three known methods for solving the resulting optimization problem. Dynamic programming (DP), Pontryagin’s minimum principle (PMP), and equivalent consumption minimization strategy (ECMS) are described and analyzed, showing formally their substantial equivalence. Simulation results are also provided to demonstrate the application of the strategies. The theoretical background for each strategy is described in detail using the same formal framework. Of the three strategies, ECMS is the only implementable in real time; the equivalence with PMP and DP justifies its use as an optimal strategy and allows to tune it more effectively.

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Driving style, road geometry, and traffic conditions have a significant impact on vehicles' fuel economy. In general, drivers are not aware of the optimal velocity profile for a given route. Indeed, the global optimal velocity trajectory depends on many factors, and its calculation requires intensive computations. In this paper, we discuss the optimization of the speed trajectory to minimize fuel consumption and communicate it to the driver. With this information the driver can adjust his/her speed profile to reduce the overall fuel consumption. We propose to perform the computation-intensive calculations on a distinct computing platform called the "cloud." In our approach, the driver sends the information of the intended travel destination to the cloud. In the cloud, the server generates a route, collects the associated traffic and geographical information, and solves the optimization problem by a spatial domain dynamic programming (DP) algorithm that utilizes accurate vehicle and fuel consumption models to determine the optimal speed trajectory along the route. Then, the server sends the speed trajectory to the vehicle where it is communicated to the driver. We tested the approach on a prototype vehicle equipped with a visual interface mounted on the dash of a test vehicle. The test results show 5%-15% improvement in fuel economy depending on the driver and route without a significant effect on the travel time. Although this paper implements the speed advisory system in a conventional vehicle, the solution is generic, and it is applicable to any kind of powertrain structure.

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This paper proposes a new method for solving the energy management problem for hybrid electric vehicles (HEVs) based on the equivalent consumption minimization strategy (ECMS). After discussing the main features of ECMS, an adaptation law of the equivalence factor used by ECMS is presented, which, using feedback of state of charge, ensures optimality of the strategy proposed. The performance of the A-ECMS is shown in simulation and compared to the optimal solution obtained with dynamic programming.