Optimization of power management in an hybrid electric vehicle using dynamic programming

Hybrid electric vehicles are those powered from two different sources. Typically, they are equipped with an internal combustion engine, and also with an electrical storage system, such as a bank of batteries or ultra-capacitors. While braking, these vehicles may convert kinetic energy to electrical energy and send it back to the electrical storage system (regenerative braking). The whole vehicle system may be abstracted to one consisting of two energy sources, one of them rechargeable and the other consumable, that feed or receive energy from an energy consumer. A centralized control strategy is required to define the instantaneous power flows among these three main components. In this work, we derive the power split between the two sources such that fuel consumption is minimized, while the vehicle performs a given velocity cycle. Bounds on the power flows from both sources are considered. There is also a constraint of an integral nature that arises from the fact that the energy of the electrical storage system must remain between proper limits, in order to avoid physical damage. The problem is posed as a finite horizon dynamical optimization problem with constraints and solved by a dynamic programming (DP) approach. The hybrid electrical vehicle being developed in the University of Rio Cuarto, Argentina is taken as the case study.