John Kessels

Energy management in hybrid electric vehicles: benefit of prediction

Hybrid vehicles require a supervisory algorithm, often referred to as energy management strategy, which governs the drivetrain components. In general the energy management strategy objective is to minimize the fuel consumption subject to constraints on the components, vehicle performance and driver comfort. Typically, we have to deal with two difficulties in the design of an energy management strategy. Firstly, the nonlinear behavior of the components results in a nonconvex cost function, complicating the use of optimization methods. Different approaches to deal with the nonconvexity are discussed. Secondly, the future power and velocity trajectories are unknown. Prediction of the future trajectories, based upon either past or predicted vehicle velocity and road grade trajectories, could help in obtaining a solution close to optimal. The benefit of prediction, compared to a heuristic and an optimal control strategy that uses only actual vehicle data, is shown with an example of a hybrid truck at a highway trajectory in a hilly environment. Results indicate that prediction has benefits only when the slopes have sufficient grade and length, such that the battery state-of-charge boundaries are reached.

Implementation of an optimal control energy management strategy in a hybrid truck

Energy Management Strategies for hybrid powertrains control the power split, between the engine and electric motor, of a hybrid vehicle, with fuel consumption or emission minimization as objective. Optimal control theory can be applied to rewrite the optimization problem to an optimization independent of time. Estimation of the Lagrange parameter, e.g., by feedback on the battery State-Of-Charge (SOC), can be used to arrive at a real-time implementable strategy. Nevertheless, it is still required to solve a nonconvex optimization problem with limited onboard computational power. This paper suggests to solve this optimization problem, offline, for different values of the Lagrange parameter, crankshaft rotational speed, and torque request. The resulting strategy is evaluated with simulations of a hybrid distribution truck on two different velocity trajectories. The influence of several control parameters is investigated also.

Experimental Case Studies

This chapter illustrates, with the help of two case studies, both involving design, implementation and experimental validation, the design process for energy management strategies. The first case is for a micro hybrid vehicle. Here, another method to numerically solve the optimization problem is introduced, namely Quadratic Programming, to handle the multiple decision variables used in the problem set-up for this case. The optimal solution for the powersplit is embedded in a Model Predictive Control frame work. The numerical solution allows a comparison between an optimal numerical strategy and a real-time strategy, as implemented in the vehicle. The implementation uses computing facilities that go beyond the standard ones in one of the vehicle’s computational units. The second case study is for a heavy-duty freight vehicle, namely a delivery truck. The implementation in this case uses a standard computational unit of the vehicle, which is possible by using a map-based approach. The experimental results show that the implementation of the optimal strategy is feasible and that this strategy achieves a better fuel economy than the built-in rule-based strategy.

Real-Time Implementable Strategies

This chapter provides a supervisory control algorithm that deals with the balanced generation and re-use of stored energy using the powersplit between engine and electric machine as control variable. Hereby taking into account only real-time available information such as the gas pedal position, the state-of-energy of the battery, vehicle velocity, and possibly road slope.

Cyber-physical Modeling of Hybrid Vehicles

This chapter presents models for power converters (combustion engines and electric machines), storage devices (batteries), and driving conditions (drive cycles). Models of limited complexity that are accurate enough for sizing problems, control design, and embedded control get the most attention. We prefer analytical models that allow further comprehensive analysis, and so provide a better integration between physical and computational processes.

Analytical Solution Methods

This chapter focuses on analytical solutions for the powersplit control problem defined in the previous chapter. Two well known solution concepts will be considered: the method of Lagrange multipliers and Pontryagin’s Minimum Principle. Both concepts have in common that they obtain the necessary conditions for an optimal solution by evaluating where the first differential of the augmented objective function becomes equal to zero. Illustrative examples are used to introduce each solution concept. Next, analytical expressions will be derived that solve the optimal powersplit problem under consideration. This chapter ends with a summary for both solution concepts and demonstrates the coherence between their respective optimality conditions.

Numerical Solutions for Known Trajectories

This chapter deals with numerical solutions for the powersplit problem for hybrid vehicles using predefined power and velocity trajectories. Two numerical solution methods are pursued: an indirect method that uses the necessary conditions for optimality obtained with Pontryagin’s Minimum Principle, and a direct method using the Dynamic Programming algorithm which is based on Bellman’s Principle of Optimality. Both methods are illustrated with an example.