*1.1. Literature Review*

Nowadays the new technologies applied in batteries manufacturing industry "often demand more compact, higher capacity, safe and rechargeable batteries" [1]. The batteries vary by different chemistries and "generate the basic cell voltages typically in the 1.0 to 3.6 V range" [1]. The required voltages and the currents of a battery pack are obtained by adding up the number of the cells in a series connection to increase the voltage and parallel connection to enhance the current. It is important to

note that when driving on the road, electric car batteries "need to be recharged relatively quickly", which is one of the key requirements for a Li-ion battery [2]. The maximum power required by a Li-ion battery pack for charging is calculated by using the following formula [2]:

$$P\_{\text{max}} = V\_{\text{bat,max}} \times N\_{\text{cells}} \times I\_{\text{bat,max}} \tag{1}$$

where *Vbat*,*max* is the maximum terminal voltage of the cell, *Ncells* is the number of cells in the pack and *Ibat*,*max* is the maximum charging current allowed per cell.

In contrast to other electric vehicles, "the fuel cell electric vehicles (FCEVs) produce, cleanly and e fficiently, electricity using the chemical energy of a fuel cell powered by hydrogen, rather than drawing electricity from only a battery" [3,4]. A hybrid FCEV (HFCEV) can be designed "with plug-in capabilities to charge the battery", since "most HFCEVs today use the battery for recapturing braking energy, providing extra power during short acceleration events, and to smooth out the power delivered from the fuel cell" [3]. Compared to "conventional internal combustion engine vehicles", the HFCEVs "are more e fficient and produce no harmful tailpipe emissions" [3].

Fuel cells (FC) "work like batteries, but they do not run down or need recharging; they produce electricity and heat as long as fuel is supplied" [4]. Among "the most common types of fuel cell for vehicle applications is the polymer electrolyte membrane (PEM) [3,4]. The most recent HFCEVs "are equipped with advanced technologies to increase e fficiency, such as regenerative braking systems, which capture the energy lost during braking and store it in a battery" [3]. In the case study of a small hybrid electric vehicle (HEV) car (HEV-SMCAR), the fuel cell battery is "designed to meet the average load power, while batteries and supercapacitors provide extra power during transients and overload" [5]. This reduces drastically "the size of the fuel cell system" and also "improve the dynamic response of hybrid power system" [5]. As a new improvement of HEV performance it is more appropriate to consider a "hybridization of the on-board energy source, i.e., to combine the Li-ion battery, and energy source, with a component that is more power dense" [6].

The supercapacitor (SC) is used in this combination, since it is "able to provide high power for short periods of time without damaging their internal structure" and also works for a long life-cycle with a high e fficiency, which exceeds the Li-ion battery performance [6–10]. Also, the SC keeps the discharging Li-ion battery current within battery limits given in specifications, such that to "extend the Li-ion battery life cycle by compensating "the high current of the load" [6]. To reach this objective an energy managemen<sup>t</sup> system (EMS) is required [5–11]. In [5,6], the EMS is conceived as an algorithmic procedure for developing five EMS techniques, to optimize the hydrogen consumption, and to assure a high overall system e fficiency, as well as a long-life cycle. In [7,11] a detailed diagram of an EMS system is presented, for an FC, UC, and Li-ion battery hybrid energy storage, to rationalize both power density and energy density, which can be adapted such that to be useful for a small hybrid electric car (SMCAR) proposed in our case study. To simplify the Simulink diagram of the EMS, the authors use Simscape components such as Li-ion battery, supercapacitor, and FCPEM [8]. The battery state of charge (SOC) is an essential internal parameter of the battery and SC/UC that is under observation constantly by a battery managemen<sup>t</sup> system (BMS) to "prevent hazardous situations and to improve battery and SC/UC performance" [12–14]. Typically, for calculation, SOC is "tracking according to the discharging current" [14–16].

### *1.2. Li-Ion Battery Models Reported in the Literature—Brief Presentation*

In the absence of a measurement sensor, the SOC cannot be measured directly, thus its estimation using Kalman filter estimation techniques is required [17–29], a topic that is detailed in Part 2 [30]. Furthermore, an accurate Li-ion battery model is essential in SOC estimation of the model-based BMS in electric vehicles (EVs)/HEVs. A complete analysis of the current state of the SOC estimation of the Li-ion battery for EVs is presented in [28]. In the paper it is stated that for EV/HEVs battery systems, "an accurate SOC can prevent battery discharge and charging, thus ensuring the safety of

the battery system, more e fficiently using limited energy and extending battery life". It can also "support the accurate calculation of the driving range of the vehicle, provide a better discharge or charging strategy, improve the e fficiency of other energy sources and make balancing strategies work more e fficiently". The same research paper [28] emphasizes that the design of the Li-ion battery model and the real-time implementation of adequate SOC estimation in EV/HEVs applications is a challenging task due to the "complexity of electrochemical reactions and performance degradation caused by various factors". Design and implementation in real time of stable, accurate and robust SOC estimation algorithms encounter some critical issues, such as hysteresis and the flat aspect of the open-circuit controlled voltage (OCV) = f(SOC) characteristic curve, Li-ion battery model, ageing, choice of estimation algorithm and imbalance cell [28]. Therefore, these issues require a comprehensive analysis to consider their impact on solving the correct and accurate battery SOC estimation. At the end of this section, a brief review is given of some linear and non-linear analytic battery models of di fferent chemistries reported in the literature well-suited for "battery design, performance estimation, prediction for real-time power management, and circuit simulation", such as is done in [17,18,28]. These models can be categorized into five categories: electrochemical models, computational intelligence-based models, analytical models, stochastic models, and electrical circuit models, as is mentioned [17].
