**Zeyu Chen \*, Jiahuan Lu, Bo Liu, Nan Zhou and Shijie Li**

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; jhlu@stu.neu.edu.cn (J.L.); Boliu@stu.neu.edu.cn (B.L.); nanzhou@mail.neu.edu.cn (N.Z.); shijie02@stu.neu.edu.cn (S.L.)

**\*** Correspondence: chenzy@mail.neu.edu.cn; Tel.: +86-(024)-8369-1095

Received: 31 March 2020; Accepted: 10 May 2020; Published: 17 May 2020

**Abstract:** The performance of lithium-ion batteries will inevitably degrade during the high frequently charging/discharging load applied in electric vehicles. For hybrid electric vehicles, battery aging not only declines the performance and reliability of the battery itself, but it also affects the whole energy efficiency of the vehicle since the engine has to participate more. Therefore, the energy management strategy is required to be adjusted during the entire lifespan of lithium-ion batteries to maintain the optimality of energy economy. In this study, tests of the battery performances under thirteen different aging stages are involved and a parameters-varying battery model that represents the battery degradation is established. The influences of battery aging on energy consumption of a given plug-in hybrid electric vehicle (PHEV) are analyzed quantitatively. The results indicate that the variations of capacity and internal resistance are the main factors while the polarization and open circuit voltage (OCV) have a minor effect on the energy consumption. Based on the above efforts, the optimal energy management strategy is proposed for optimizing the energy efficiency concerning both the fresh and aging batteries in PHEV. The presented strategy is evaluated by a simulation study with different driving cycles, illustrating that it can balance out some of the harmful effects that battery aging can have on energy efficiency. The energy consumption is reduced by up to 2.24% compared with that under the optimal strategy without considering the battery aging.

**Keywords:** battery aging; plug-in electric vehicles; energy management; global optimization; state of health; particle swarm algorithm; genetic algorithm
