# An Optimal Sizing Design Approach of Hybrid Energy Sources for Various Electric Vehicles
## 1 Introduction  
Due to the stringent transportation laws legislated, especially for fuel economy, electric vehicles (EVs) have attracted much more attention recently due to their characteristics of zero pollutants, low noise, high efficiency, and rapid acceleration compared to traditional engine vehicles [1]. The most popular EV type is the battery EV (BEV) with one type of battery, such as LiFePO4 batteries, lithium titanate oxide (LTO) batteries, nickel manganese cobalt (NMC) batteries, or nickel cobalt aluminium (NCA) batteries [2]. Each batterytype is characterized by specific energy, specific power, cell voltage, C-rate for charge and discharge, life cycle, inner resistance, cost, etc. [3]. Hence, choosing the correct type of battery according to the requirements and specifications of the target vehicle is crucial. Recently, a hybridization concept for the powertrains or energy sources has been needed due to the physical constraints of a sole power source or single energy source that limit the performance of EVs. To solve this problem, the most popular hybrid powertrains are an engine/motor/generator hybrid system such as the full hybrid system (i.e., Toyota THS) and a power-assist hybrid system (i.e., Honda Insight). The electric power devices effectively compensate for the inefficient operation and high pollution at low-power or low-speed conditions, recover the braking energy from generation, and properly assist the traction torque in low-torque areas [4]. Hybrid electric energy sources such as the fuel cell (FC)/battery system [5], the battery/SC system [6], the fuel cell/SC system [7], and even the FC/battery/SC hybrid system [8] have been employed to EVs. The FC system provides the stable output power to the out load; meanwhile, it charges the energy storage devices (such as batteries and SCs) when the State-Of-Charges (SOCs) of the energy storage devices are low [9]. Contrarily, the SC system plays the role of providing the boost power while the vehicle accelerates with high power, or receiving the brake regeneration power with high efficiency due to low inner resistance [10]. The battery system is able to drive the vehicle at a wide-power-range operation while storing the extra or recovered energy from outside [11]. To extend the life cycle and maintain the state-of-health (SOH) of the battery, SCs compensate the peak power to avoid the high C-rate discharge or even high C-rate charge. For hybrid electric energy systems (HEESs), two main approaches are utilized to enhance the system performance to increase the overall system efficiency. The first approach is the energy management control. Three categories are summarized for the control. The first is the rule-based control [12], where the flowchart decision making [13] (if-else control, fuzzy logic control [14], etc.) relies on engineering intuition. The second is the theoretical-based control, such as deterministic dynamics programming (DDP) or the Genetic Algorithm (GA), where the computational resource is extremely high [15]. It leads to the offline optimization [16]. The third is the online optimization, which combines the theories integrated into rules such as stochastic dynamics programming (SDP) [17] bionic optimization [18], the equivalent consumption minimization strategy [19; 20], etc. Though the energy management control improves the system performance, the second approach, system design, is more crucial, as the optimal sizing of an HEES directly influences the maximal output performance, total stored energy, and even the cost, occupied space, and the gross weight [21]. For HEES sizing, in [22], a hybrid battery system (HBS) with NCA and LTO batteries of an EV was evaluated to reduce battery aging and extend the life cycle. Four structures, mono battery, passive HBS, active HBS with one DC/DC converter, and active HBS with two DC/DC converters, were compared. In [23], a high energy storage and a high power storage were combined.