Meta-Heuristic Optimization and Comparison for Battery Pack Thermal Systems Using Simulink

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Electric Vehicle, Data Center, Simulink, etc.

Abstract

This study examines the use of meta-heuristic algorithms, specifically particle swarm optimization and genetic algorithms, for optimizing thermal systems, addressing a research gap on their efficacy in larger systems. Utilizing MATLAB’s Simulink and Simscape, the research initially targets an electric vehicle thermal system model, emphasizing the optimization of a Li-ion battery pack and associated cooling components, like chillers, pumps, and cooling plates, during operation. One consideration is the use of a glycerol–water mixture in the chiller pump, which demands the use of an optimal control algorithm that adjusts to outdoor temperatures and control strategies. This study focuses on computational efficiency reflecting the complexity of system simulations. Challenges related to applying particle swarm optimization and genetic algorithms to these systems are scrutinized, leading to the establishment of a new objective function to pinpoint target values for system optimization. This research aims to refine design methodologies for engineers by harmonizing optimal design with computational expediency, thereby enhancing the engineering design process in thermal management. This integrative approach promises to yield practical insights, benefiting engineers dedicated to the advancement of thermal system design and optimization. The results show that, compared to the base model, 1% of the overall state of charge could be saved, and the battery temperature could also be cooled by more than 4 °C compared to the initial temperature.

1. Introduction

Thermal system design and optimization have played a critical role in enhancing the efficiency and performance of various engineering applications. The thermal system presents a unique characteristic that differentiates it from conventional thermal devices such as heat exchangers and heat pipes [1,2]. While the performance of individual devices is undeniably crucial, the interconnectivity between these devices assumes an even greater significance. Finding the optimal engineering point within the operational range is a challenging endeavor, one that requires a meticulous analysis of the intricate relationships between thermal components [3,4,5].

Thus far, a significant amount of research has focused on lithium-ion (Li-ion) batteries and their arrays, leading to notable progress in the domain of battery pack thermal management systems (BTMS). Such scholarly efforts have not only diminished thermal burden but also broadened the exploration of battery attributes, especially those related to cooling mechanisms. These studies include a wide array of experimental and numerical techniques aimed at advancing cooling technologies [6,7,8,9]. Jilte et al. [10] investigated this area by developing a Li-ion battery thermal management system using air cooling under high discharge rates. By utilizing computational fluid dynamics (CFD), they tracked temperature patterns in the air and throughout the battery pack at varying airflow rates. Sun and associates [11] extended this line of inquiry by creating a sub-model for a three-dimensional battery pack and applied simulation methods to assess the thermal behavior of battery cells under convective heat exchange scenarios. Their work involved analyzing the impact of different airflows over the battery pack and confirming the thermal consistency within the cells. Furthermore, a combination of computational and practical experiments were undertaken to evaluate the use of heat pipes with lithium-ion battery cells [12]. This line of research focuses on heat transference from the battery cells to a heat sink and tests a battery pack system that integrates passive cooling strategies for potential future applications. The system in question comprises passive cooling units that can remove heat from individual battery cells and heat pipe segments that are capable of managing heat over extended distances and dispelling intense heat loads. While current research trends heavily emphasize the examination of singular thermal devices, this focused approach does not often lead to a meaningful improvement in the thermal performance or efficiency of the systems. This issue is particularly evident in the case of electric vehicles, where aspects such as the operation of the liquid pump and properties of the ethylene glycol solution become more critical.

The understanding of the entire thermal system, including the battery’s operating conditions, emerges as an urgent concern. Such an approach demands an integration between diverse components and processes, acknowledging the complex interplay that governs the thermal behavior within these systems. In the ever-evolving era of electric vehicles, this comprehensive perspective between the optimization of thermal system is crucial, underscoring the need for a nuanced appreciation of both individual elements and their synergistic interactions. The meta-heuristic optimization method is widely used for the optimization of thermal devices. Meta-heuristic optimization techniques have emerged as a prominent alternative to conventional optimization methods, particularly in complex multi-objective problems where the search space is large and the landscape is non-continuous [13,14,15]. These techniques are renowned for their adaptability and capability to escape local optima, making them suitable for the non-linear and intricate nature of BTMS. In the context of BTMS, meta-heuristic optimization techniques can provide dynamic solutions, adapting to various operational constraints and environmental conditions. These techniques, such as genetic algorithms (GAs) and particle swarm optimization (PSO) are capable of exploring a vast search space to find near-optimal solutions that balance various objectives like energy consumption, thermal comfort, environmental considerations, and cost-effectiveness [15,16,17,18,19]. Particle swarm optimization (PSO) and genetic algorithms (GAs) are popular optimization algorithms inspired by social–psychological behaviors, such as those seen in bird flocks and individuals. They are viewed as simpler and more intuitive compared to other heuristic optimization methods. For a similar example, a three-fluid cross-flow plate-fin heat exchanger with offset strip fins is optimized, focusing on maximizing hot fluid effectiveness and minimizing entropy generation [19]. Finite element method (FEM) is used to solve the governing equations and determine the rate of entropy generation and effectiveness. The optimization uses genetic algorithm (GA) and particle swarm optimization (PSO) to find optimal geometric parameters, achieving nearly identical design values for both objectives, with PSO being effective [19].

However, a limitation of these algorithms is their susceptibility to low optimization precision. This can result in rapid convergence to local minima, potentially leading to suboptimal solutions [19,20,21,22,23,24]. To this end, the application of meta-heuristic techniques has garnered significant attention, aiming to maximize system performance, while considering complex design constraints. Previous studies have explored the utilization of particle swarm optimization and genetic algorithms for optimizing thermal devices. However, limited attention has been given to their suitability for large-scale devices or thermal systems.

In recent studies focusing on thermal systems and battery pack thermal management, a notable drawback is the limited presentation of open platforms. To address this issue, leveraging recently developed tools such as Simulink and Simscape by MATLAB could prove to be an excellent solution [4,25,26]. These platforms offer numerous advantages and hold the potential to fill the research gap in thermal system simulations and battery pack thermal management. As an illustration of similar studies, several investigations, specifically concerning battery packs, have been conducted using Simulink. For instance, the simulation procedure involved applying pulse current–voltage conditions to lithium battery cells under various scenarios [5,25,26,27]. The battery thermal model employed is based on electrochemical knowledge, where the voltage changes exhibits non-linear characteristics in response to the current input. As a result, certain simplifications are necessary, especially when considering factors like battery-related resistance correlation. The commonly used equivalent circuit model (ECM) model is used to establish the relationship between battery currents, voltages observed at the battery terminals, and coulomb accumulation. This includes accounting for open-circuit voltage based on current history, encompassing self-discharge, and current charge inefficiency [28,29]. The ECM model effectively captures the phenomenological behavior of the battery and facilitates the estimation of the state of charge (SOC) through coulomb counting methods [5,13,29,30]. In addition, an example of the thermal management of a battery pack in an EV model from the Simulink database is provided, along with a suitable approach for configuring a thermal system in a liquid-cooled battery pack that is currently in operation. Consequently, by incorporating PSO and GA algorithms into these hybrid thermal systems that blend model-based and non-model-based approaches, researchers can anticipate gaining a more intuitive understanding of the optimal design direction for the thermal system. Addressing this research gap, this study focuses on the application of meta-heuristic techniques for optimizing thermal systems, specifically targeting the design of components in electric vehicles. Electric vehicles rely on advanced Li-ion battery packs, and the effective cooling of these battery packs is essential for their performance and longevity. Therefore, optimizing the design of components, such as the chiller, pump, and cooling plate becomes paramount during vehicle operation operated in Simulink.

Therefore, the main objective of this simulation study is to investigate the fundamental principles governing thermal devices, with a primary focus on the ultimate goal of becoming fully operational thermal systems. Throughout the engineering process of a thermal system, the quest for an optimal design remains a continuous pursuit, regardless of theoretical equations. This research explores the intricate relationship between thermal devices and thermal systems in Simulink operated by MATLAB, elucidating how the realization of a thermal system culminates in the attainment of the desired optimal design. The study draws upon various case studies and theoretical analyses to demonstrate the significance of this engineering objective. By comprehending the interplay between thermal devices and thermal systems, we can optimize designs to maximize efficiency and performance. This research began as an exploration of whether meta-heuristic algorithms could be applied in Simulink. To directly compare PSO and GA algorithms, we aimed to stay as close as possible to the “fundamental” and “original” algorithms in terms of their direction. Consequently, our study did not involve modifications to the algorithms, and only pre-designed algorithms were utilized.

Additionally, the applicability of a genetic algorithm (GA) and particle swarm optimization (PSO) are explored for optimizing a thermal system simulated using Simulink. These two popular optimization algorithms have long been utilized by engineers to enhance system performance. To evaluate their suitability for thermal systems, a battery pack is chosen from an electric vehicle as a representative case, utilizing a pre-existing Simulink model provided by MATLAB. By applying GA and PSO to this model, we assess their effectiveness in determining the optimal thermal management strategies for the battery pack. The study aims to identify the most appropriate algorithm for enhancing the thermal performance of the battery pack and the role that each thermal management device plays in achieving this objective. Through this investigation, we can contribute valuable insights into the selection of optimization algorithms for thermal systems and their implications in forward-thinking designs.

2. Numerical Methods for Simulink

2.1. Liquid Cooling Module

The Simulink model used in this study presents a comprehensive simulation of an Electric Vehicle (EV) battery cooling system, an overall aspect of contemporary EV technology. We aimed to work with the “sscfluids_ev_battery_cooling” example in MATLAB shown in Figure 1. When actual speed and input values corresponding to the FTP-75 drive cycle are inputted, the model employs a liquid pump to cool the battery pack. Notably, regarding battery pack modules, many manufacturers cannot perform a direct validation due to confidentiality constraints. Therefore, to assess the thermal system, we rely on MATLAB’s basic tutorial-level model to validate the optimal algorithm, whose approach seems prudent only for the study of the optimization algorithm. In this configuration, the battery packs are situated atop a strategically engineered cold plate, encompassing designed cooling channels. These channels guide the cooling liquid flow beneath the battery packs, ensuring effective heat transfer.

Three-dimensional interpolated properties such as density, specific heat, specific internal energy, kinematic viscosity, thermal conductivity, etc., are also provided by Simulink. In Figure 2, data are represented in a multi-dimensional variable, including the volume fraction of each ethylene glycol. Since the data are functionalized and grouped as a graphic user interface (GUI), based on each calculation, it allows for the accessible and easy acquisition of the required values in Simulink. These data are provided based on temperature and pressure. For temperature, it can be applied from extreme low temperatures of 250 K to high temperatures of 373 K, offering a range that can be used in virtually all BTMS research contexts might affect thermal runaway [31,32,33].

The heat absorbed by the cooling liquid is subsequently transported to a multifunctional heating–cooling unit (HCU). Uniquely composed of three distinct branches, the HCU can switch between operating modes to both cool and heat the battery as required. The heater branch incorporates an electrical heater, produced by the battery pack, facilitating the rapid heating of the batteries in low-temperature conditions, thus ensuring an optimal performance across a wide range of environmental circumstances.

As shown in Figure 1b, the radiator employs both air-cooling mechanisms, this branch offers stable temperature control when the batteries are in regular operation, enhancing both efficiency and longevity. The refrigerant system is particularly engaged for cooling overheated batteries, a critical safeguard for both safety and functionality. The heat extraction process is quantitatively represented by the amount of heat flow removed from the cooling liquid, reflecting a precise control over the thermal management process. The entire system is subjected to rigorous simulations under varying conditions, including the FTP-75 drive cycle and diverse fast charge scenarios, across a spectrum of environmental temperatures. This detailed simulation offers valuable insights into the dynamic performance and adaptability of the cooling system, contributing to the ongoing development of efficient and sustainable EV technologies.

Figure 1c illustrates the configuration of the battery pack. In the basic model presented, the pump operates independently from the battery, thereby necessitating an additional power input. Considering that battery power is depleted, as highlighted when the torque produced by the pump is multiplied by its rotational speed and then fed into the battery, we derived an optimal design strategy to minimize the battery’s usage during the pump’s operation.

When the current value required for the FTP-75 driving cycle of the EV is entered, the battery temperature increases. The elevated battery temperature then interacts with the pump response delay control in Figure 1d, which is based on the preset temperature value, T_set. Consequently, the pump’s power is determined over time. As the pump operates, it circulates the refrigerant liquid of water–glycol mixture, ultimately cooling the battery pack again. The environmental temperature is set at 30 °C and the target temperature, T_set, that the battery should aim for is fixed at 20.5 °C. Those values remain unchanged even when considering optimization. The difference between the battery’s initial temperature, T_init, and T_set is factored into the pump speed. The pump response delay value is determined as a first-order transfer function of 1/(a × s + 1), where a is the time constant, which in turn defines the pump’s torque and power. A larger value of ‘a’ corresponds to a quicker pump system response. Consequently, the pump’s operational speed or cycle is adjusted based on the battery’s temperature, facilitating its cooling.

Figure 2 serves as proof that the used MATLAB Simulink model incorporates temperature-variant properties. It can display a three-dimensional graph showing how thermal conductivity changes with temperature and pressure in a solution mixed with ethylene glycol, depending on the volume fraction. This inclusion demonstrates that, even with varying temperatures, Simulink and Simscape can calculate other necessary properties through interpolation. This capability allows us to predict how properties are adjusted in our simulations, ensuring accuracy and relevance in our modeling.

2.2. Battery Configuration

In Simulink, the equivalent circuit model (ECM) utilizes a consolidated resistance–capacitance (RC) unit, as recommended by Huria and colleagues [5]. Displayed in Figure 2 is a schematic of a battery cell and its corresponding Simulink implementation. This schematic features a voltage source labeled Em, an RC segment composed of a capacitor (C₁) and a resistor (R₁), in addition to a separate resistor in series (R₀). The values for each component within this analogous circuit are affected by the battery cell’s temperature (T) and its state of charge (SOC), as outlined in Equations (1)–(3) referenced from sources [28,29,34].

$$V-E_{\mathrm{m}}=I{R}_0+\left(I-I_1\right)R_1,$$

(1)

$$I_1=C_1\frac{d{V}_1}{dt},$$

(2)

$$R=R_0+R_1\left(1-e^{-t/C_1{R}_1}\right),$$

(3)

Within the ECM framework in Simulink, the thermal assessment is integrated, as shown in Figure 3b. The temperature of the cell is calculated using a thermal equation that takes into account the uniform heat transfer between the cell body and its environment.

$$c_{\mathrm{p}}\frac{dT}{dt}=-\frac{T-T_a}{R_{\mathrm{t}}}+Q,$$

(4)

C_p denotes the specific heat capacity and R_t refers to the resistance to heat transfer [5]. The calculation of temperatures can be performed through a Laplace transform, as indicated in Equation (4). Information on the characteristics of Li-ion batteries was obtained from MathWorks’ open database, and these characteristics are detailed in

Table 1. Battery properties utilized in this study. The rows indicate the state of charge, and the columns indicate cell temperature.

R0/SOC	5 °C	20 °C	40 °C	R1/SOC	5 °C	20 °C	40 °C
0	0.0117 Ω	0.0085 Ω	0.009 Ω	0	0.0109 Ω	0.0029 Ω	0.0013 Ω
10%	0.011 Ω	0.0085 Ω	0.009 Ω	10%	0.0069 Ω	0.0024 Ω	0.0012 Ω
25%	0.0114 Ω	0.0087 Ω	0.0092 Ω	25%	0.0047 Ω	0.0026 Ω	0.0013 Ω
50%	0.0107 Ω	0.0082 Ω	0.0088 Ω	50%	0.0034 Ω	0.0016 Ω	0.001 Ω
75%	0.0107 Ω	0.0083 Ω	0.0091 Ω	75%	0.0033 Ω	0.0023 Ω	0.0014 Ω
100%	0.0116 Ω	0.0085 Ω	0.0089 Ω	100%	0.0028 Ω	0.0017 Ω	0.0011 Ω
Em/SOC	5 °C	20 °C	40 °C	C1/SOC	5 °C	20 °C	40 °C
0	3.497 V	3.506 V	3.515 V	0	1913 F	12,447 F	30,609 F
10%	3.552 V	3.566 V	3.565 V	10%	4625.7 F	18,872 F	32,995 F
25%	3.618 V	3.634 V	3.640 V	25%	23,306 F	40,764 F	47,535 F
50%	3.707 V	3.713 V	3.721 V	50%	10,736 F	18,721 F	26,325 F
75%	3.913 V	3.926 V	3.938 V	75%	18,036 F	33,630 F	48,274 F
100%	4.192 V	4.193 V	4.193 V	100%	9023 F	23,394 F	30,606 F

. The focus is on temperatures ranging from 5 °C to 40 °C. For temperatures outside of this interval, Simulink allows for linear extrapolation.

With the assumption that battery materials are homogeneously isotropic, they exhibit a consistent specific heat capacity of 800 J/K. This assumption, together with the values for specific heat and thermal conductivity, confirms the applicability of the lumped system analysis [10,35]. The precision of the model generally enhances with the incorporation of more RC network elements. Yet, for cells with a high coulombic efficiency, a single RC (1RC) network model proves to be adequate [3,5,29,33,34]. Upon configuring the equivalent circuit model (ECM) block as shown in Simulink, its schematic is represented in Figure 1b. The model’s construction can proceed, drawing on the aspect of geometric resemblance. Temperature-dependent variations in physical properties are managed by interpolating values over time using data from Table 1. The setup includes four battery packs, each comprising twenty cells wired in series, which aligns with the configuration in the example model. The starting temperature for the cells is not specified, making it an adjustable parameter to be optimized in line with the external conditions experienced during the optimization trials.

3. Meta-Heuristic Methods

3.1. Particle Swarm Optimization

Particle swarm optimization is nature-inspired and mirrors the swarm dynamics observed in bird flocks or fish schools to solve optimization problems with specific constraints [18]. The genetic algorithm is rooted in evolution, whereas PSO is a swarm-centric search optimization methodology. The operational structure of PSO and GA is depicted in the flowchart in Figure 4. Within the PSO algorithm, each particle solution navigates the search space at a certain velocity, influenced by both local and global optimum positions. When these positions change, the relevant parameters update. The velocity describes the particle’s movement pace and is determined by its current position, the global optimum, and random fluctuations. Consequently, particles closer to the local and global optimums tend to move slower.

Kennedy and Eberhart first introduced the basic particle swarm optimization algorithm [36]. Figure 1 provides a schematic representation of this basic PSO algorithm. Initially, the algorithm generates a distributed population of potential solutions, known as particles. In the search space, the current position x_ij of a particle can move until the algorithm reaches a predetermined maximum iteration, t_max. As one particle identifies the best global positions within the entire swarm, other particles tend to follow its lead. Throughout the iterative process, every particle evaluates its performance and updates its personal best, or Pbest. Subsequently, the particle shares the most recent global best, Gbest, with all other particles and transitions to a new position. The velocity vector of individual particles, v_ij(t + 1), can be determined. Following this, x_ij(t + 1) is updated, as outlined in [36,37].

v_ij(t + 1) = w × v_ij(t) + c₁r₁[p_i − x_ij(t)] + c₂r₂[p_g − x_ij(t)]

(5)

x_ij(t + 1) = x_ij(t) + v_ij(t + 1)

(6)

In this context, p_i represents the personal best position of each particle (Pbest), while p_g stands for the global best position amongst all particles (Gbest). Specifically, p_i = [p₁, p₂, …, p$Np$] indicates the Pbest of the ith particle. The variables r₁ and r₂ are random numbers uniformly distributed between 0 and 1. The coefficient c₁ signifies the particle’s cognitive component, whereas c₂ represents the social collaboration coefficient. The inertia weight, denoted as w, plays a critical role in convergence. It serves as a pivotal parameter in striking a balance between the exploration (Pbest) and exploitation (Gbest) behaviors. This weight influences the proportion of particle velocity that contributes to the new velocity in each iteration. Although often set to a constant value of 1, we’ve chosen to model the inertia weight as a function that linearly decreases over time to optimize convergence, as described below.

$$w=w_{max}-\left(w_{max}-w_{min}\right)\times \frac{t}{t_{max}}$$

(7)

where w_min and w_max represent the initial and final values of inertia weight, respectively. For this study, they are adopted as 0 and 1 in this study [37].

3.2. Genetic Algorithm

The genetic algorithm is inspired by the evolutionary principles of genes, mirroring how DNA determines an individual’s structure. Its primary mechanisms are evaluation, ordering, crossover, and mutation. The evaluation step calculates the fitness value of the function slated for optimization. In GA, solutions or individuals are selected based on their fitness value. A pure elitist GA transfers only the top organisms to the subsequent generation without gene alterations, which can reduce population diversity. Conversely, the controlled elitist GA retains some organisms with lower fitness values to enhance diversity, aiding in convergence to an optimal Pareto front. To grasp GA methodologies, one can refer to the flowchart in Figure 4.

3.3. Applications of Optimization Approaches

We implemented constraint handling methods in our optimization algorithms. These measures were specifically designed to be solved within the feasible space using an adapted fitness function [38]:

$$\min f(x_{ij})=\left\{\begin{array}{ll}f(x_{ij})\hfill & \mathrm{if}{x}_{ij}\in \mathsf{\Omega }\hfill \\ f(x_{ij})+\mathrm{penalty}(x_{ij})\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(8)

A penalty function serves as a tool to determine the number of feasible particles within Ω. In thermal system engineering challenges, similar to our study of the thermal management of a battery pack in Simulink, the terms x_ij, v_ij, and p_ij comprise multi-variable or multi-dimensional vectors, leading to the potential filtering of numerous particles. In our research, we employed two repair strategies. The initial step seeks solutions for each variable within the specified upper (UB) and lower (LB) bounds. If x_ij falls outside of these bounds, the subsequent repair strategy is invoked.

$$V_j=\left\{\begin{array}{ll}{V}_j=L{B}_j\hfill & \mathrm{if}{V}_j<L{B}_j\hfill \\ V_j=U{B}_j\hfill & \mathrm{if}{V}_j>U{B}_j\hfill \end{array}\right.$$

(9)

The second step involves verifying if the decision variable g(x_ij) adheres to the bounded inequalities [38].

$$\min f(x_{ij})=\left\{\begin{array}{ll}f(x_{ij})\hfill & \mathrm{if}g(x_{ij})\in \mathsf{\Omega }\hfill \\ f(x_{ij})+q\cdot g(x_{ij})\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(10)

where q is a arbitrary constant as 100,000 in this study.

Due to its constraints, not all parameters of the thermal system could be addressed for the optimization. Instead, five variables were selected based on their relevance to battery liquid cooling to check the optimal function and their significance in Simulink through the provided input data. The Simulink results were then evaluated to define a new objective function, upon which further calculations were conducted. Five variables are selected as referred in Figure 1:

• T_init: initial battery temperature.
• Radiator.solution.glycol: the glycol volume fraction.
• Pump.omega: the pump revolution speed.
• Pump.response.delay: a variable used to regulate the pump speed, incorporating an unknown value as the denominator coefficient.
• Pump.displacement: the volume of fluid that a pump moves during a single cycle or revolution.

Finally, the objective function can be defined as:

$$f(x_{ij})=\frac{1}{{\mathrm{SOC}}_{end}}\times \frac{P_{\mathrm{pump}}}{T_{\mathrm{init}}-T_{\mathrm{final}}}$$

(11)

The objective function seeks to ensure that the battery’s final state of charge value during the FTP-75 driving cycle [39], i.e., the battery’s ultimate consumption, is minimized. Additionally, the use of the pump and the temperature differential should also be minimized, reflecting the underlying principle that certain aspects need to be kept at a minimum. The lower bound and upper bound of each parameter are listed in

Table 2. Lower and upper bound to find optimal value.

	LB	UB
1. Initial battery temperature	25 °C	40 °C
2. Radiator.solution.glycol	0.1 (10%)	0.9 (90%)
3. Pump.omega	1000 rpm	4000 rpm
4. Pump.response.delay	10	40
5. Pump.displacement	10 m	30 m

.

As shown in

Table 3. Pseudo-code for particle swarm optimization and the genetic algorithm for Simulink.

Particle Swarm Optimization	Genetic Algorithm
1. Initialize parameters	2. Initialize parameters
num_particles = 100; num_dimensions = 2; num_iterations = 100; % Initialize particle positions and velocities for i = 1:num_particles for j = 1:num_dimensions particle(i).position(j) = random_value(); % Initialize with a random value particle(i).velocity(j) = random_value(); % Initialize with a random value sim(‘sscfluids_ev_battery_cooling’) end particle(i).best_position = particle(i).position; end global_best = particle(1).best_position;	num_particles = 100; num_generations = 1000; num_dimensions = 2; % Initialize population for i = 1:num_particles for j = 1:num_dimensions population(i).gene(j) = random_value(); % Initialize with a random value sim(‘sscfluids_ev_battery_cooling’) end population(i).fitness = fitness_function(population(i).gene); end
3. Main loop	4. Main loop
for iter = 1:num_iterations for i = 1:num_particles % Update velocity for j = 1:num_dimensions particle(i).velocity(j) = inertia_weight * particle(i).velocity(j) + c1 * rand() * (particle(i).best_position(j)—particle(i).position(j)) + c2 * rand() * (global_best(j)—particle(i).position(j)); End % Update position for j = 1:num_dimensions particle(i).position(j) = particle(i).position(j) + particle(i).velocity(j); sim(‘sscfluids_ev_battery_cooling’) end % Update personal best if fitness_function(particle(i).position) < fitness_function(particle(i).best_position) particle(i).best_position = particle(i).position; end % Update global best if fitness_function(particle(i).best_position) < fitness_function(global_best) global_best = particle(i).best position; end end end	for gen = 1:num_generations % Selection for i = 1:num_particles parent1 = tournament_selection(population); parent2 = tournament_selection(population); % Update position by crossover [child1, child2] = crossover(parent1, parent2); % Mutation child1 = mutate(child1); % Function, needs to be defined child2 = mutate(child2); % Fitness Evaluation sim(‘sscfluids_ev_battery_cooling’) child1.fitness = fitness_function(child1.gene); child2.fitness = fitness_function(child2.gene); % Replacement population = replace_worst(population, child1, child2); end end

, these generic codes are provided for a specific implementation in Simulink, adding a random function for generating a random number within a suitable range. For a particle swarm optimization, this code assumes that we have defined a fitness function fitness_function which takes a position vector as input and returns a fitness value. inertia_weight, c₁ and c₂ are the inertia weight, cognitive, and social parameters, respectively. The cognitive and social parameters (c₁ and c₂) are set as 2 for code simplicity, but the exploration versus exploitation aspects of the search are balanced, and the inertia weight can help maintain momentum. Additionally, note that the random function is a placeholder for generating a random number within a suitable range. This range should be defined based on your problem space.

For a genetic algorithm, this modified code uses the term num_particles instead of pop_size for consistency with the PSO pseudocode. This will allow a more direct comparison between the two algorithms. Additionally, it assumes the existence of tournament_selection, crossover, mutate, and replace_worst functions. These need to be changed according to your specific problem.

The fitness function fitness_function should be defined along with the Simulink. This function can be designed according to the problem at hand and should take a gene vector as input and return a fitness value. When comparing the scripts used for integrating Simulink in MATLAB, there is not a significant difference in the number of lines in each code. Both represent simplified algorithms that are capable of executing optimization in Simulink. The model can be then integrated before the fitness evaluation process in the particle swarm optimization (PSO) or genetic algorithm (GA). This would involve using the position vectors (for PSO) or gene vectors (for GA) as inputs for the Simulink model, and then using the output of the model to calculate the fitness of each particle or individual. The pseudo-code for these algorithms would then change in the fitness calculation step. In MATLAB, you could use the “sim” function to run your Simulink model with the given inputs and gather the output.

4. Results and Discussion

4.1. Comparison between PSO and GA

In this study, the primary aim is to establish a novel framework for analyzing optimized results and understanding their implications. Compared to equation-based thermal device models, which typically resolve within 5 s, a single Simulink case run requires approximately 20–33 s. This is compounded by the variable time-step, which can change from as short as 0.001 s to as long as 2500 s. Such variability introduces significant fluctuations in computation times across different cases at every iteration considering optimization. Consequently, achieving thermal system optimization might demand considerable time, especially when seeking optimal values with fewer particles and iterations. Initially, it is intended to compare the differences in results among the basic case in Simulink at T_init = 30 °C, optimized PSO, and optimized GA results. Given the high time consumption of model, it is wise to categorize them by particle size and iteration effect within both PSO and GA. This will help determine which optimization technique is most suitable for the current phase.

In the initial scenario, a fixed constant provided in Simulink was used, yielding a result of 0.00122 kW/K. We then compared the outcomes from both the PSO (particle swarm optimization) and GA (genetic algorithm) techniques, utilizing the predefined lower and upper bounds. Figure 5 presents a comparison of the results with those obtained from 10 particles incorporated by 10 iterations. A critical aspect of this study is the emphasis on optimal results, as the complex modeling environment is inherent to the thermal system. The extended simulations required approximately 2814 s for the PSO and 2791 s for the GA to execute their respective optimization cases. The simulations were conducted on a computer equipped with a Ryzen Threadripper 5950× processor, boasting 16 cores. MATLAB R2023a was utilized for the simulations, and no parallel processing was employed.

In the initial stages of optimization, both optimization models yielded results that were inferior to the baseline case. However, with subsequent iterations, they progressively approached the optimal outcome. When benchmarked against the basic model, the PSO demonstrated a marginally better performance than the GA. With PSO, there was a clear continuous effort to identify the local minimum through rapid convergence and persistent random functions.

Figure 6 examines the relationship between the number of particles and iterations for both GA and PSO. Drawing from the results shown in Figure 5, this study explores the potential improvements as both particles and iterations are increased. It is evident that as the sizes of particles and iterations increase, the numerical analysis yields increasingly optimized results. While increasing the number of iterations may lead to somewhat shorter computation times compared to increasing particles, the best outcomes arise when the number of particles is increased. Notably, in this study, calculations were limited to 50 particles to avoid unnecessary computational overhead without a substantial improvement in results. While PSO and GA have comparable computation times, PSO displays slightly better computational efficiency and an increase of over 14% in result differentiation.

Conversely, while the GA exhibits a similar trend, it does not seem to make a further effort to seek optimal results. PSO generally converges faster than GA, due to the cooperative behavior of particles, where each particle adjusts its path based on its own experience and the experience of its neighbors. This sharing of information can speed up convergence. PSO focuses on a balance between the exploration of new areas of the search space and the refinement of the search around the best solutions, whereas GA uses crossover and mutation to explore and exploit the search space. Depending on the problem, the balance struck by PSO might be more effective than GA. It is worth noting that the superiority of PSO over GA is problem-dependent. While PSO might be better suited for solving some problems, GA might outperform PSO in solving others. There were some studies where PSO outperformed the GA algorithm to some extent [18,19,40,41]. When examining the basic optimization model, it is evident that if the number of particles calculated in each iteration increases, making a judicious decision regarding those particles early on can influence subsequent steps, potentially resulting in more optimal values. Conversely, as the number of iterations grows, decision making within a limited number of particles becomes necessary. While this trend is understandable, it might impose limitations on the choices available. Hence, it is advantageous that PSO optimization is emphasized as the number of particles increases, compared to the GA heuristics. Especially when faced with a situation with fewer particles and iterations, if we must make a choice, increasing the number of particles may be necessary for accuracy. However, from an engineering perspective, increasing the number of iterations could offer the advantage of faster computations with an acceptable fitness value.

To delve deeper into these reasons, Figure 7 illustrates the particle variations for the two algorithms, PSO and GA. PSO demonstrates directionality due to the synergistic movements of individual particles. Figure 7a, depicts a coalescence at T_init = 40 °C that converges into optimal results. When values are not found within the upper or lower bounds, such as with pump displacement in Figure 7b, particles tend to move towards the nearest possible value. This observation aligns with the finding that computational outcomes improve as the numbers of particles or iterations increase, as shown in Figure 6.

For the GA algorithm, the results tended to be largely spread between upper and lower bounds, deviating from the optimal value. As illustrated in Figure 7c,d, this even distribution likely arises from the algorithm’s reliance on individual crossover, mutation, and selection processes, rather than inter-particle interactions. Nonetheless, these outcomes might improve with different schemes or enhanced GA methods. Therefore, it is important to note that these findings are based on a fundamental GA environment and might present a limited perspective. When examining Figure 7a,c, despite only four iterations being completed, we can assess the ability of these algorithms to move particles toward the final objective. In the case of Figure 7c, it is evident that even as the iterations progress, more than half of the particles are unable to converge to a solution, or they fail to gather and find the remaining solutions. It is also observed that this aspect does not improve significantly with repeated iterations.

Based on the aforementioned results, the optimal findings can be summarized in

Table 4. Optimized results by PSO and GA at 20 particles and 10 iterations.

	Initial Condition	PSO	GA
1. Initial battery temperature	30 °C	40 °C	40 °C
2. Radiator.solution.glycol	0.5 (50%)	0.1 (10%)	0.1 (10%)
3. Pump.omega	4000 rpm	1000 rpm	1000 rpm
4. Pump.response.delay	20	20.5	19
5. Pump.displacement	20 m	12.7 m	19.8 m
Fitness	1.22 × 10−4 kW/K	0.356 × 10−3 kW/K	0.406 × 10−3 kW/K

. For both PSO and GA, given computational constraints, it is believed that 20 particles and 10 iterations can yield satisfactory outcomes. While parameters such as initial battery temperature or radiator glycol solution range between the upper and lower bounds, factors like pump displacement and response delay are intermediary values. It is suggested that further research should employ enhanced algorithms, rather than solely relying on the foundational PSO or GA algorithms.

4.2. Optimized Results Analysis

This analysis starts with understanding how meta-heuristic optimization data influence optimal design and its tangible physical implications. A primary aspect to evaluate is the efficacy of the PSO or GA algorithms in optimizing battery consumption, temperature, and pump usage, given that the distance covered by the electric car remains constant. We begin by examining a graph, as depicted in Figure 8, which compares battery consumption to a baseline scenario over a span of 2500 s for a distance of 17.7 km, based on the FTP-75 standard. The results from both graphs indicate comparable EV performance, with negligible differences, with an error rate of less than 1.5%. Thus, while the data can produce consistent outcomes, the optimization results can vary, indicating the potential gains in battery efficiency, reduced pump usage, and improved heat transfer.

State of charge (SOC) refers to the used battery gauge equivalent to a fuel gauge in a traditional gasoline-powered vehicle in the context of batteries, especially rechargeable batteries like those found in electric vehicles or renewable energy storage systems. It represents the current battery capacity as a percentage of its maximum capacity. If it is 50% or 0.5, the battery is half-charged; if it is 0%, the battery is completely discharged. Figure 9 displays the SOC results over time, segmented into basic, PSO, and GA outcomes. As illustrated, the battery’s consumption seems to significantly improve in the optimized results compared to the basic results. While the basic case ends with an SOC of 0.76, the PSO outcome yields a SOC of 0.77, a 1% difference. This 1% variance might appear minimal, but in practical terms, it equates to an additional driving distance of between 4 and 6 km. Hence, this underlines that the battery’s overall reliability and driving performance are enhanced through optimal design using meta-heuristics.

Figure 10 depicts the cooling achieved due to the influence of battery cell temperature in each scenario. As illustrated, in scenarios where the battery temperature begins at a relatively higher level, such as in the PSO and GA cases, the temperature consistently decreases over time. This trend occurs because, while the battery’s temperature rises due to resistance during its use in driving, it cools down more rapidly due to the activation of the liquid pump. Conversely, in the basic scenario, the battery temperature only experiences a brief decline during driving due to the pump’s operation.

Additionally, when the temperature of a battery increases, its internal resistance generally decreases. This reduction in resistance means that, for a given load, the battery can deliver the required power with less internal energy loss. As a result, less energy is wasted in the form of heat within the battery, leading to a potentially slower rate of SOC consumption. Additionally, at higher temperatures, the electrolyte’s ionic conductivity increases, further aiding in efficient charge and discharge processes. However, it is crucial to note that consistently operating a battery at elevated temperatures can lead to a reduced lifespan and potential safety concerns. Therefore, while short-term energy efficiency might improve at higher temperatures, there could be long-term drawbacks to this approach.

Figure 11 delivers a comparison of pump power usage over time, further elaborating on the observations from Figure 10. The pump instant power graph in Figure 11a indicates that, in the basic scenario, the pump is excessively utilized between 0 to 500 s. Despite employing a pump capable of reaching its maximum specified performance, the control was inefficient, resulting in an undue reduction in battery cell temperature. In contrast, the PSO and GA outcomes reveal that, by maintaining a steady pump use at 1000 rpm, effective cooling capacity control is achievable. This optimization results in comparable, if not better, battery usage, solidifying the benefits of the continuous engagement of the battery cooling mechanism.

This is further corroborated by Figure 11b. These data aggregate and accumulate the torque and revolution values of the pump over time for each scenario. Observing the cumulative pump usage, it is evident that efficient cooling was achieved even with the pump’s sustained operation. Consequently, the objective value was decreased by using the PSO and GA algorithms, ensuring a more effective maintenance of battery temperature alongside efficient pump utilization.

What makes PSO more advantageous than GA in terms of battery cell temperature, as observed in Figure 9, Figure 10 and Figure 11, is its ability to reduce pump usage further, lower the temperature slightly, and simultaneously save more on battery SOC. This confirms that the target pursued by the PSO algorithm chose to sacrifice lowering the temperature for the overall objective function. However, in the case of the GA algorithm, its focus on optimizing temperature cooling had a negative impact on the overall objective function. Therefore, it can be confirmed that although PSO may consume some computational time, the optimization algorithm operated in a way that took into account all the overall parameters.

Additionally, the concentration of glycol significantly influences the thermal system. As illustrated in Figure 2, water possesses superior thermal conductivity compared to glycol. Thermal conductivity gauges a material’s heat transfer capability. Hence, a fluid with high thermal conductivity is more adept at heat transmission. A mixture leaning towards water rather than glycol inherently boasts better heat conduction. Water stands out for its remarkable specific heat capacity, one of the highest known for any substance. This implies it can store substantial heat without a notable rise in temperature. A mixture with a high water content retains this trait, allowing for more heat transfer. Conversely, a high glycol concentration can make the mixture more viscous, hindering fluid motion and diminishing convective heat transfer. The lower the glycol concentration, the more it favors turbulent flow, which increases convective heat transfer.

Notably, water is generally denser than glycol, impacting the mixture’s heat transfer traits. While glycol’s inclusion in cooling systems primarily offers antifreeze properties and combats corrosion, it can compromise the fluid’s thermal efficiency. Hence, for prime heat transfer, minimizing the glycol fraction is recommended, a fact underscored by optimization outcomes, provided that freezing protection remains uncompromised. Furthermore, while glycol’s detrimental effect on thermal transfer is acknowledged, the fluid composition in a thermal system can extend beyond glycol, potentially involving multiple fluids. The optimal ratio in such blends can be pinpointed through heuristic optimization strategies.

5. Conclusions

In this research, we utilized a non-model-based battery pack thermal system from Simulink to develop and implement both the PSO and GA methods. Our goal was to devise an optimal thermal system. Key takeaways from our application to Simulink include:

For both PSO and GA, the calculation time is critical when integrating into Simulink. We found that controlling the particle size yields better accuracy when aiming to achieve an objective function, especially in a scenario with fewer particles and iterations. In our findings, the PSO method slightly outperformed the GA approach. However, this superiority might be due to the specific constraints of our study. As more researchers contribute and share their methodologies, we anticipate even more refined and enhanced results.

This integrative approach offers tangible benefits for engineers focusing on advancing thermal system design and optimization. Our results indicate that, in comparison to the base model in Simulink, there is a saving of 1% in the overall state of charge of a battery and a reduction in battery temperature by over 4 °C compared to the initial temperature.

Upon integrating and verifying computational outcomes, we observed an enhancement in the SOC by applying both PSO and GA results to the sample EV—this was achieved without altering its driving performance or battery voltage. By efficiently modulating the pump’s performance, we were able to consistently regulate the battery pack temperature to the desired level. Notably, by managing the pump’s functionality, we discerned that the optimal point within the thermal system model of Simulink can be identified using meta-heuristic approaches.