*6.1. Battery Degradation Due to Changes in Ambient Temperature*

The performance of lithium-ion batteries and their lifespan is significantly influenced by temperature. When exposed to high temperatures, its rate of degradation is significantly accelerated. Li-Ion batteries are temperature-sensitive [9], and their performance is affected not only by the temperature of the cell itself but also by the environment in which it is located. Battery degradation is caused by a combination of the SEI and the loss of active material. The one brought about by SEI is the most common and fundamental cause of capacity fade rate in batteries. As a result of the high temperature, the surface particles of the electron undergo a rapid development of SEI, thereby causing the battery's capacity to reduce [94]. According to some literature [95] on the systematic establishment of the theory on SEI growth and reduction in battery capacity, it was asserted that temperature changes trigger capacity fade due to alterations in the SEI layer. Incidentally, SEI growth can occur in idle situations, during the cycle, and during temperature changes. Some literature [96] clearly stated that temperature changes severely affect battery degradation. This process is of two types, namely actual and temporary capacity fading and loss. The actual capacity fading suggests that there has been irreversible cell loss due to the ingestion of lithium-ion. The high temperature of the battery accelerates the rapid rate of cell deterioration. On the other hand, a temporary capacity loss is caused by a drop in temperature during a specific cycle. It can be restored if the battery temperature returns to a certain level.

The literature [97] focuses on the ambient temperature impact on a battery's lifespan. The formation of the film on the electrodes of Li-Ion batteries explains the effect that the surrounding temperature has on its lifespan. This is because of the oxidation of the cell, proven by the film produced on the electrodes. It causes an irreversible increase in the Li-Ion battery's internal resistance, ultimately leading to damage. The findings on the simulation process show that higher temperatures during idle battery scenarios resulted in extreme capacity loss and self-discharge.

Some studies on calendar aging reported that it is related to temperature. Battery aging testing is performed at different temperatures, SOC, and end-of-life. The tests were conducted in a laboratory with temperature control facilities and charging or discharge operations. In reality, the battery is in extremely harsh operational conditions. The results of Li-Ion testing for EVs are reported to last 2000 and 800 cycles at temperatures of 25 ◦C and 55 ◦C, respectively [98]. Additionally, testing the influence of battery temperature due to discharge rate differences such as 1C, 2C, 3C, and 4C was also conducted [99]. It is possible to determine the varying contours due to the changing temperatures of the battery cells and their discharge at a consistent rate.

The pace at which capacity is lost is significantly affected by the temperature of the surrounding environment. Meanwhile, when it is greater than 35 degrees Celsius, it triggers more changes in the composition of the electrolyte due to the substantial temperature rise. This causes the process at which active lithium is utilized to quickly move forward [100]. As a result, the battery's capacity starts to decrease at various room temperatures, as shown in Figure 10. It is evident that when the perimeter temperature is greater than 35 ◦C, the capacity fades level drops significantly during the first 50 cycles. This phenomenon occurs while the battery is being used. When the temperature is 55 ◦C, the maximum capacity fades, while the temperatures of 25 ◦C and 35 ◦C are projected to be the same [100].

Characteristics of the capacity fade rate of the battery which is affected by the ambient temperature as shown in Figure 11. Yuhan Wu et al. [31] stated that LiFePO4 battery degradation caused by the average temperature in BESS is modeled by combining calendar and cycle aging. This model is depicted by a single operating cycle, as shown in Equations (3)–(8). By knowing the characteristics of the battery aging cycle to set the optimal operating temperature of BESS, it can reduce the battery degradation rate so that the battery life is longer.

$$\mathfrak{g}^{\mathfrak{x}} = \mathfrak{g}\_{\text{cal}} + \mathfrak{g}\_{\text{cyc}} \tag{3}$$

$$
\xi\_{cyc} = f\_{d,soc} \left( SOC\_{avg} \right) \tag{4}
$$

$$\mathcal{J}\_{\rm cal} = \sum\_{i=1}^{n} f\_{d,dod}(DOD\_i) f\_{d,T}(T\_{i,\rm avg}) \tag{5}$$

$$f\_{d, \text{soc}}(\text{SOC}\_{\text{avg}}) = k\_1 \text{SOC}\_{\text{avg}}^2 + k\_2 \text{SOC}\_{\text{avg}} \tag{6}$$

$$f\_{d,dod}(DOD\_i) = k\_3 DOD^2 + k\_4 DOD \tag{7}$$

$$f\_{d,T}(T\_{i, \text{avg}}) = \begin{cases} e^{k5 \text{\textdegree T}} / k\_{6 \text{\textdegree}} \text{\textdegree 298K} \ge T \ge 273K \\ e^{k\_7 \text{\textdegree T}} / k\_{8 \text{\textdegree}} \text{\textdegree 333K} \ge T \ge 298K \end{cases} \tag{8}$$

where *ξ* represent of battery degradation from calendar aging (*ξcal*) and cyclic aging (*ξcyc*). *n* is the number of cycles charged or discharged in one day. *SOCavg* represents the average SOC, *DODi* depicts the difference between the i-th charge and discharge cycles DOD, and *Ti*,*avg* is the average temperature in BESS. In most cases, the value of the k parameter is determined by the experimental observation [31,35].

**Figure 10.** Capacity fade rate of LiFePO4 battery at each temperature during cycling [100].

**Figure 11.** Characteristic cycle aging battery [31].

#### *6.2. Battery Thermal Management*

Complex electrochemical reactions and electric-to-thermal conversion determine the thermal characteristics of a battery [101]. The production of heat by Li-Ion batteries is a complex process that involves a knowledge of how the rate of electrochemical reaction varies with time and temperature, in addition to how current flows within the battery [102]. Simply, heat generation of the battery is written as Equation (9):

$$Q = I(\mathcal{U} - V) - I\left(T\frac{d\mathcal{U}}{dT}\right) \tag{9}$$

where *Q* denotes the rate of heat generation, *I* denotes the electric current flowing through the cell, *U* denotes the open-circuit voltage, and *V* represents the voltage of each individual cell in the Li-Ion batteries. In general, the thermal model of a battery has been examined according to the dimensions of the battery as well as the physical mechanism (electrothermal model, electrochemical thermal model, and thermal runaway propagation model) (lumped model, 1D, 2D, and 3D). In most cases, the charging and discharging procedures for Li-Ion batteries result in the production of three distinct types of heat. These forms of heat include activation of irreversible heat as a result of the polarization of an electrochemical reaction, joule heating as a result of ohmic losses, and reversible reaction heat as a result of the change in entropy that takes place during the charging and discharging processes. Consequently, if the heat created by the battery while charging or discharging is not correctly dissipated, the temperature of the battery may grow because of heat accumulation, which may have a severe influence on the battery's performance, life, and safety [102].

The thermal management process, which is a critical component of the battery management system, is most concerned with estimating the precise state of temperature (SOT). Using more traditional measurement methods, such as thermocouples, it is simple to obtain an accurate reading of the temperature at the surface of the battery. Nevertheless, the temperature on the inside of the cell during transients is significantly different [103]. In general, the SOT estimation methods can be broken down into four categories: the direct measurement method, the electrochemical impedance-based method, the model-based estimation method, and the data-driven method.

Using a direct measurement methodology, researchers proposed ways for monitoring the temperature of a battery's internal layers. Temperature micro-sensors are integrated into the interior layers of the battery cells in these technologies. Thermocouples and resistance thermometers are the two most common types of sensors used to indicate the temperature of a battery's interior. The model-based estimation approach typically makes extensive use of numerical thermoelectric and thermal models when attempting to determine an object's internal temperature. To construct thermoelectric and thermal models such as the lumped-parameter battery model and the distributed battery thermal model, it is very required to understand heat generation, conduction, dissipation, balancing, and thermal boundary conditions. A few different approaches for calculating the temperature of a battery based on electrochemical impedance spectroscopy EIS measurements have been proposed in the electrochemical impedance-based approach without first constructing a thermal model. Temperature can be linked to impedance indicators acquired via EIS. These indicators include phase shift, real part amplitude, and imaginary part amplitude, per the most recent data-driven strategies. Data-driven approaches were used to estimate the temperature of the batteries inside [103].

#### **7. Objective, Design Constraint, and Algorithm BESS Optimization**

This section explains the objective functions frequently reported by previous studies, design constraints, algorithms used for BESS optimization, and a review of its state-the-art development. The steps involved in BESS optimization are depicted in the flowchart shown in Figure 12. This starts with collecting input system data, then determining the direction of the model development, selecting an objective function and design constraints, optimizing strategy and algorithm, and finally evaluating the optimization results.

**Figure 12.** Flowchart of optimization of BESS.
