Optimal Energy Management of Hybrid Storage Systems Using an Alternative Approach of Pontryagin's Minimum Principle

Evaluating performances of real-time strategies for hybrid energy storage systems (HESSs) of electric vehicles (EVs) always requires optimal energy management strategies (EMSs) as offline benchmarks. Dynamic programming (DP) is well-known due to its ability to obtain global optimal solutions based on the numerical searching technique. Nevertheless, DP accuracy depends on the numericalization fineness. Analytical optimal control methods, typically Pontryagin's minimum principle (PMP), are also frequently used as effective counterparts. However, solving optimal control problems based on these methods often depends on the complexity and the characteristic of the system model; basically, it is sophisticated since there is no general way to solve the issue. This article proposes an alternative approach of using PMP to develop an optimal EMS for battery/supercapacitor HESSs. The novel strategy is based on formulating the problem in terms of power and energy, which forms a state-constrained optimal control problem. PMP is then applied with a penalty function, in which the inequality state constraints are reformulated to deduce a new state-unconstrained problem. The proposed optimal EMS is hundreds of times faster than DP with better results. Moreover, the optimal solution is piecewise constant that could give significant insights to develop real-time strategies in future studies.