Optimization of an Air-cooling Thermal Management System for Lithium-ion Battery Packs via Particle Swarm Algorithm

Recently, lithium-ion batteries have attracted many researchers and their safety issues such as overheating, combustion and explosion continue to further limit battery application scenarios. These issues are mainly caused by unoptimized battery structure parameters or cooling methods. In this paper, an integrated approach has been proposed to design an efficient air-cooling system using the particle swarm algorithm to find an optimal relationship between air flow rate and battery temperature. Firstly, this method can adjust an optimized air flow rate to ensure that the battery temperature is minimized with the lowest energy consumption via the particle swarm algorithm. Additionally, an optimized air flow rate can still be obtained with the change of structure parameters such as the radius in a lithium-ion battery pack via this novel algorithm. Then, we demonstrate the feasibility of this integrated method in simulations. Compared with the previous work, this method can employ the continuous modulation of the particle swarm algorithm, realizing both the best cooling capacity of the battery cooling system and simultaneously the lowest energy consumption for cooling in cell heat regulation systems. Meanwhile, temperature variations of the entire cell pack are also shown in simulations. In contrast to previous approaches, this integrated method may provide more dynamic thermal management inspirations for designing novel battery thermal management systems.


Introduction
Due to the increasing energy shortage and environmental problems, electric vehicles are developing rapidly worldwide, among which lithium-ion batteries are usually employed as the mainstream energy source in the field of electric vehicles over the past decades [1].This is owing to the undoubted fact that it has superior cycle performance, quick charge and discharge, high output power and long cycle life [2].Moreover, the lithium battery has better economy and safety performance.More importantly, it does not contain toxic and harmful substances and is known as a sustainable paradigm.However, the thermal regulation of the battery is restricted to the unoptimized cell structure parameters and cooling methods [3].Currently, a more intelligent approach is urgently needed to be introduced to address the above unoptimized parameter issues in lithium batteries [4,5].
Recently, in the rapid charge and discharge cycle, the thermal energy caused by the chemical reaction inside the lithium-ion cell can easily lead to heat accumulation in a confined space, which may cause overheating, combustion, and explosion [6].Therefore, thermal regulation of lithium cells is quite necessary.The lithium cell model [7] studied in this work uses an air-cooling system because of its lower fabrication cost and better manufacturing technology.However, the air-cooling system may not ensure the best cooling capability with the lowest energy consumption under various operating conditions such as fast charge and discharge cycles.Therefore, our work hopes to optimize the battery structure through an intelligent algorithm to ensure the best cooling capacity of our cooling system with the lowest energy consumption.Herein, the particle swarm algorithm is employed in this study, and it belongs to a class of uncertain algorithms.For certain tasks, uncertain algorithms perform better than deterministic ones.The benefit of non-deterministic algorithms such as particle swarm algorithms is that they can increase the likelihood that the algorithm is able to find the overall best results.Meanwhile, particle swarm algorithms have a larger possibility of finding the overall best solution, which is their main benefit.With this method, we may effectively determine the cell's ideal configuration even under large ambiguity.It is also an artificial intelligence-based bionic optimization technique.As a result, the particle swarm algorithm's separate intelligence can render the capacity to collaborate with the battery structure to engage with it.
Herein, we propose an integrated approach to design an efficient air-cooling system using the particle swarm algorithm to find an optimal relationship between cell temperature and air flow rate.It is found that the temperature inside the cell decreases as the flow rate increases.The faster the flow rate is, the better the cooling capacity is.But a faster flow rate also means higher power consumption, which is what the battery design wants to avoid.The temperature is stabilized in the range of 17 o C while consuming less energy.Then, we demonstrate this efficient air-cooling system in simulations.A particle swarm algorithm has been first used to find an ideal air flow rate, leading to a balance between energy consumption and cooling performance.Meanwhile, the variations of the internal temperature of the cell along the air flow rate are simultaneously shown in simulations.This method is more intelligent and efficient for the optimization of air-cooling heat regulation systems.

2.Theoretical analysis
According to Gu and Wang's work [7], the steady-state conductive heat equation can be expressed as: where U b , b C and b k are the density, heat capacity and thermal conductivity of the battery, respectively; T and Q are the temperature and electrochemical heat of the battery, respectively.Then, for the air, the governing equation of Equation ( 1) can be written as: where U a , a C and a k are the density, heat capacity and thermal conductivity of the air, respectively; T and a v are the temperature and flow rate of air, respectively.1a and 1b.Three cells are located inside the battery module.The battery module has dimensions of 90 mm, 27 mm, and 65 mm.The cells' radius is 9 mm, and their spacing is 27 mm.Graphite serves as the positive electrode of the cells, lithium manganate serves as the negative electrode, and LiPF6 serves as the liquid electrolyte material.The air flow rate used to cool the cells can be changed in accordance with the demands of the actual usage.Then, we can obtain the general solutions of this air-cooling system just as: where P is the dynamic viscosity of the air.For minimizing the temperature decrease (TD) of the battery and energy consumption (Es) of our cooling system, a particle swarm algorithm can be introduced into the battery cooling system (Figure 2).According to Xun et al.'s work [4], the corresponding equations are then: where b r , W , S and h are the battery radius, the air-cooling work, the battery surface area and the battery height, respectively.Then, we can employ the particle swarm algorithm in the entire region shown as: X and 1 i j X are the velocity, the next velocity, the position and next position of these particles in the physical space K (i = 1, ..., n or j = 1, ..., n), respectively; w, ws and we are the inertia weight, the original inertia weight and end inertia weight, respectively; i and Imax are the iteration number and the maximum iteration number, respectively.

Results and discussion
First, when the cell radius is 9 mm as shown in Figure 1a, the temperature profiles of the cell operating in the air-cooling system with a flow rate of 0 m/s are shown in Figure 3a(I) and (II), respectively.Currently, the air-cooling system does not work.When the battery starts to operate, its temperature rises rapidly and rises to a maximum temperature of 65 o C at 1500 s (Figure 3a(I)).The cell temperature then begins to drop and drops to 55 o C at 3000 s (Figure 3a(I)).As shown in Figure 3a(II), the high temperature inside the cell, which is caused by the air-cooling system not operating, prevents the cell from dissipating heat internally.Figures 3b(I) and (II) show temperature variations of the cell in our system with an air flow rate of 10 m/s.This speed is the ideal air flow rate as determined by the particle swarm algorithm and it can consume less energy to ensure that the battery has the best cooling capacity.When the battery starts to operate, from 0 to 1500 s, the temperature of the cell shows a fluctuating increase with the maximum temperature of the cell rising to around 7.1 o C and the minimum temperature of the battery remaining below 1.3 o C. The average temperature of the cell remains between 2.7 o C and 5.2 o C. Currently, the battery load is operating normally with an operating voltage between -7.5 V and 7.5 V with periodic variations.To verify that the best flow rate is 10 m/s when the battery cooling system is at its optimum with the lowest energy consumption, temperature variations of the cell under different air-cooling speeds have been carried out in the simulation.Figures 3c(I) and (II) show temperature variations of the cell in our designed cooling system with a flow rate of 13 m/s.When the battery starts to operate, from 0 to 1500 s, the temperature of the cell shows a fluctuating increase, the maximum temperature of the battery rises to about 6.9 o C, and the average temperature of the cell is maintained between 2 o C and 4.9 o C, and the minimum temperature of the cell is maintained below 1.1 o C. At this point, the battery load is working normally, the operating voltage is between -7.5 V and 7.5 V and varies periodically.Therefore, we can see that increasing the flow rate from 10 m/s to 13 m/s does not have a significant cooling effect on the cell and cell temperature is only reduced by 0.2 o C.However, increasing the flow rate boosts more energy consumption of our designed system, which violates the principle of pursuing the best utilization of the energy.Therefore, we believe that the cooling system of the battery acquires the best cooling effect while it keeps the lowest energy consumption with an air flow rate of 10 m/s, indicating that the particle swarm algorithm is reliable and correct.To further verify the relationship between air-cooling speed and cell radius via the particle swarm algorithm, we adjusted the size of the cell radius and observed the internal thermal distribution of cells when operating at different air flow rates for cells with different radii.For the cell radius of 9 mm, the particle swarm algorithm optimizes the ideal air flow rate to be 10 m/s, ensuring the cooling capacity of the cell while preventing high energy consumption.At this point, the maximum battery temperature is around 7.1 o C, ensuring proper battery operation while consuming less energy.When the air flow speed is increased to 14 m/s, the maximum temperature of the battery is 6.9 o C. As we can see, increasing the flow rate from 10 m/s to 14 m/s does not have a significant cooling effect on the cell and battery temperature can only be reduced by 0.2 o C.However, increasing the flow rate boosts more energy consumption of our designed cooling system.Therefore, it is the best choice that the ideal air flow rate is optimized to be 10 m/s by the particle swarm algorithm.When the radius of the battery is 10 mm, the particle swarm algorithm optimizes the ideal air flow rate to be 12 m/s.Currently, the maximum temperature of the battery is around 7.6 o C, which ensures the best cooling performance of the cooling system for the battery while consuming less energy.When the air flow speed is increased to 14 m/s, the maximum temperature of the battery is 7.5 o C. Increasing the air flow rate from 10 m/s to 14 m/s does not have a significant cooling effect on the cell and battery temperature can be only reduced by 0.1 o C. Therefore, it is the best choice that the ideal air flow rate is optimized to be 12 m/s by the particle swarm algorithm.Increasing the cell radius to 11 mm, the particle swarm algorithm optimises the ideal air flow rate to be 13 m/s.At this point, the maximum cell temperature is around 8.2 o C, ensuring the best cooling capacity of the cooling system for the battery while consuming less energy.When the air velocity is increased to 14 m/s, the maximum temperature of the battery is 8.1 o C. Increasing the air flow rate from 10 m/s to 14 m/s does not have a significant cooling effect on the battery and the battery temperature can be only reduced by 0.1 o C. Therefore, it is the best choice that the ideal air flow rate is optimized to be 13 m/s by the particle swarm algorithm.Overall, in order to maintain cooling capacity, the air flow rate must increase equally as the cell radius becomes larger.This shows that as the cell radius increases, the cooling efficiency of cooling the battery decreases with the increase in air velocity.However, this is not the best choice, because we acquire the best cooling performance at the cost of quite large energy consumption.Thus, it is necessary to introduce the particle swarm algorithm in battery thermal management, leading to a more intelligent approach to not only optimize the cooling capacity of the cell cooling system but also to prevent the consumption of useless energy and thus improve battery efficiency.

4.Conclusion
Figure 4 a, b, and c exhibit an overhead view of three battery configurations with different radii in the air-cooling system.Figure 5 (I), (III), and (V) show the temperature distribution of the batteries under three optimized flow rates.These flow rates, namely 10 m/s, 12 m/s, and 13 m/s, were obtained using the particle swarm algorithm for battery radii of 9 mm, 10 mm, and 11 mm, respectively.Figure 5 (II), (IV), and (VI) present the temperature distribution for battery radii of 9 mm, 10 mm, and 11 mm, respectively, when the flow rate va is 14 m/s.It is evident that the batteries have reached a steady thermal state at this point, and further increasing the va has a negligible impact on the cooling effectiveness of the batteries.
Herein, we propose an integrated approach to design an efficient air-cooling system using the particle swarm algorithm to find an optimal relationship between air flow rate and battery temperature.Firstly, this method can adjust an optimized air flow rate to ensure that the battery temperature is minimized with the lowest energy consumption via the particle swarm algorithm.Additionally, an optimized air flow rate can still be obtained with the change of structure parameters such as radius in a lithium-ion battery system via this novel algorithm.Then, we demonstrate the feasibility of this integrated method in simulations.Compared with the previous work, this method can employ the continuous modulation of the particle swarm algorithm, realizing not only the best cooling capacity of the battery cooling system but also simultaneously the lowest energy consumption for cooling in battery thermal management.Meanwhile, temperature variations in the entire cell pack are also shown in simulations.In contrast to previous approaches, this integrated method may provide more dynamic thermal management inspirations for designing novel air-cooling cell heat regulation systems.

Figure 1 .
Figure 1.a) 3D schematic setup of batteries in our air-cooling system.b) The top view of batteries in the air-cooling system.

Figure 2 .
Figure 2. The flow diagram of our proposed particle swarm algorithm.

Figure 3 .
Figure 3.The temperature curves (I) and temperature distributions (II) of the cell under three different flow speeds va of a) 0 m/s, b) 10 m/s (The optimized value by the particle swarm algorithm), and c) 13 m/s, respectively.

Figure 4 .Figure 5
Figure 4.The three top views of the batteries in the air-cooling system with three different radii of a) 9 mm, b) 10 mm, and c) 11 mm, respectively.