An Equivalent Consumption Minimisation Strategy based on 1-Step Look-Ahead Stochastic Dynamic Programming∗

In this paper, a systematic procedure to determine the equivalence factor in the equivalent consumption minimisation strategy (ECMS) is proposed. This is relevant when ECMS is not only used for controlling the power split between the internal combustion engine and the electric machine of a hybrid electric vehicle (HEV), but also for controlling several auxiliary systems. In this case, the number of controlled components and energy buffers increases, which causes the number of tunable equivalence factors to increase. The procedure to determine the equivalence factors proposed in this paper is based on the observation that ECMS can be considered as a time-invariant feedback policy and dynamic programming (DP) also yields a time-invariant feedback policy when the time horizon of the control problem approaches infinity and the disturbances are constant or absent. As the drive cycle can be considered as a (stationary stochastic) disturbance, we propose to formulate ECMS as the solution of a 1-step look-ahead stochastic dynamic program (1slSDP). This strategy results in an energy management strategy that performs close to optimal and yields similar fuel consumption results, when compared to a well-tuned ECMS. The absence of any parameters to be tuned and the fact that fuel consumption is similar to a well-tuned ECMS makes 1slSDP a useful strategy for energy management of HEVs.