Category Lithium ion power battery life estimation and optimization

Lithium-ion power battery cells generally adopt a constant current-constant voltage charging method, that is, first use a fixed rate of current (0.3C or 1C, etc.) to charge, reach the set charging cut-off voltage (3.6V, 4.0V, etc.) For constant voltage charging, the charging is completed after the charging current is lower than a certain value (such as 0.03C). Relevant studies have shown that the charging current and charging cut-off voltage not only have a significant impact on the charging time and charging energy of lithium-ion power batteries, but also have an important impact on their service life. Lithium-ion power battery systems are generally used in groups of multiple cells in series. If the constant current-constant voltage charging method is still used, it may cause overcharging of some battery cells. On the basis of studying the influence of charging current, charging voltage, overcharge and other charging factors on the service life, with the purpose of prolonging the service life of the battery, an optimized charging method for lithium-ion power battery cells and battery packs is proposed.

1. Influence of charging factors on the life of lithium-ion power batteries

1) Influence of overcharging on the life of lithium-ion power batteries
When the lithium-ion power battery is overcharged, a lot of heat is generated inside the battery, and at the same time, a lot of bubbles are generated in the electrolyte, which causes the active material on the positive and negative plates of the lithium-ion power battery to peel off, which seriously affects the activity of the battery and increases the internal resistance. Capacity has also dropped. At the same time, overcharging may also cause the battery to expand and deform, and even cause serious consequences such as fire and explosion. Research by Wang Hongwei et al. shows that at an ambient temperature of 20°C to 40°C, overcharging will cause the lithium-ion power battery to expand and deform, and the higher the temperature, the faster the temperature rises when the lithium-ion power battery is overcharged, and the higher the maximum temperature. more likely to be dangerous. Therefore, during the use of the lithium-ion power battery, it is necessary to ensure the normal operation of the charger and the protection circuit to avoid overcharging.

2) Influence of charging current and charging voltage on battery life
The charging voltage and charging current directly affect the charging energy and charging speed of the lithium-ion battery. Taking a certain lithium-ion power battery as an example, as shown in Figure 1, as the charging current increases, the charging capacity in the constant current stage becomes smaller, and the constant current charging capacity at 100A charging current is reduced by 8.36% compared with 20A charging current. The total charging time of the battery decreases with the increase of charging current, and the total charging time of 100A constant current charging is reduced by 76.1% compared with the total charging time of 20A charging current. This shows that increasing the charging current has little effect on the total energy charged, but can significantly improve the charging speed. However, high-rate charge-discharge current will cause the battery system to deviate from the equilibrium state, and accelerate the aging of positive and negative materials, thereby shortening the battery life. Therefore, power battery manufacturers need to comprehensively consider charging time and battery life when designing charging strategies. Two charging modes can be set: under normal circumstances, low-current charging should be selected as far as possible when charging lithium-ion power batteries, so as to prolong the battery life; in urgent cases, high-current charging can be used to shorten the charging time, although this will damage battery life.

In general, when the charging current is the same, the higher the charging cut-off voltage, the greater the total energy charged by the lithium-ion power battery. However, the higher charge cut-off voltage will cause partial decomposition of the battery cathode material, the performance of the electrolyte will also decline, and the separator will also be oxidized due to contact with the high-potential cathode material. Taking a lithium-ion power battery as an example, as shown in Figure 2, when the charging voltage is reduced from 4.2V to 4.1V, the capacity retention of the lithium-ion battery is better as the number of charging and discharging increases, that is, the battery Longer cycle life. Relevant studies have shown that reducing the charge cut-off voltage by 0.1~0.3V can prolong the battery cycle life by 2~5 times.

2. Charging strategy based on lifetime optimization
By studying the influence of charging current, charging voltage and overcharge on the life of lithium-ion power battery, in order to prolong the service life of lithium-ion power battery cells and battery packs, this paper proposes the optimization of lithium-ion power battery cells and battery packs. charging strategy.

1) Charging strategy of lithium-ion power battery cells
In order to prolong the service life of the battery, the charger and the charging protection circuit should be safe and reliable. The thermistor can be used to detect the temperature of the battery, and stop charging when the battery temperature exceeds the high temperature threshold to prevent overcharging. After the battery is fully charged, disconnect the voltage in time, otherwise, metal lithium will be generated inside the battery, resulting in permanent capacity loss, and may cause a short circuit inside the battery.

According to different positive and negative materials and battery structure, the charging parameters of lithium-ion power batteries will be different. When determining the charging method of a single battery, factors such as the composition material and structure of the battery, charging time, charging capacity and battery life should be comprehensively considered, and parameters such as charging current, charging cut-off voltage and charging termination current should be optimized and designed. The charging methods of lithium-ion batteries can be divided into ordinary charging and fast charging: ordinary charging is suitable for general household charging or long-term parking charging, using small rate charging current and charging cut-off voltage, charging voltage can be 3.8~4.0V, And use a small charging termination current (such as C/10 or less) to strengthen the protection of the battery; fast charging is suitable for charging in emergency situations, which will greatly damage the battery life, use a large rate current for a short time (1h) Charge more than 90% of the battery inside. The number of fast charging times should be minimized during use.

Appropriately reducing the charge cut-off voltage can significantly improve the service life of the battery. In order to take into account the charging time, the cut-off voltage can be set according to the depth of discharge (DOD): when the depth of discharge is 100%, in order to shorten the charging time, the cut-off voltage can be increased, such as 3.8V; when the depth of discharge is 0, set the cut-off voltage The voltage is 3.5V. In this way, when the depth of discharge is between 0 and 100%, the charge cut-off voltage can be set between 3.5 and 3.8V according to a linear relationship. This approach helps extend battery life and can reduce the overall charging time for Li-ion power batteries.

2) Charging strategy of lithium-ion power battery pack
When charging a lithium-ion power battery pack, if a single constant current-constant voltage charging is used, it is likely to cause some cells to be overcharged. Therefore, the charging of the battery pack needs to be controlled according to the state of the lithium-ion power battery cells to prevent overcharging of the cells, protect the cycle life of the single cells, and help prolong the cycle life of the battery pack. Taking the charging process of a lithium-ion power battery system as an example, the standard charging steps are: charging with a constant current of 1C, when the voltage of a single battery reaches 3.5V or more, the charging current is reduced to C/2. When the voltage of the single battery reaches 3.55V or more, reduce the charging current to C/4, when the voltage of a single battery reaches 3.6V, reduce the charging current to C/8, when the highest voltage of the single battery reaches the cut-off voltage (3.65V) or the battery pack The charging process is completed after the total voltage reaches a certain cut-off voltage.

When the vehicle is parked for a long time, the power supply should be cut off, and the vehicle should be parked in a ventilated, rain-proof, moisture-proof, sun-proof, and fire-fighting place, and should be kept away from flammable and corrosive items. When the vehicle is parked for more than a month, the battery pack must be kept at a state of charge of about 50%, the connecting wire of the battery pack must be unplugged, and the power battery system must be charged and discharged with a small current every three months for maintenance.

The consistency of lithium-ion power batteries means that after the cells are used in groups, the voltage, internal resistance, capacity and other parameters of each cell are not exactly the same due to the influence of factors such as production and use environment. The performance parameters such as charge-discharge capacity and cycle life of a lithium-ion power battery are generally determined by the worst-performing monomer in the battery. Therefore, the consistency of the battery pack plays an extremely important role in its performance and cycle life. The impact of consistency on battery life will be discussed and ways to improve consistency will be suggested.

1. The impact of consistency on the life of the power battery pack
The consistency of lithium-ion power batteries mainly includes voltage consistency, capacity consistency and internal resistance consistency. As the power battery usage time increases, the degree of inconsistency will gradually increase. The most intuitive reflection is that the degree of inconsistency of the cell voltages in the battery pack increases. There are two main reasons for the poor consistency of lithium-ion power batteries: one is the production and manufacturing reasons. Due to slight differences in electrode plate thickness, chemical activity, microporosity, etc., there are some differences in parameters such as internal resistance and capacity of single cells. The second is the inconsistency in the use process. Lithium-ion power batteries have complex operating conditions, long-term work under harsh conditions such as high-rate charge and discharge current, vibration, etc., coupled with the structural layout of the battery system and the design of the heat dissipation system, which lead to the temperature, self-discharge degree, and electrolyte activity of each battery cell. There are differences, and the inconsistency of lithium-ion power battery packs gradually increases as the number of uses increases. It can be seen that the inconsistency of lithium-ion power batteries is inevitable. Figure 1 shows the causes of battery pack inconsistency and its transmission process.

As the inconsistency of the power battery pack increases, the performance and life of the battery pack are seriously affected. Scholars from various countries have already made some research results on the impact of inconsistency on the life of power batteries. Wang Zhenpo et al. [71] proposed a formula for calculating the remaining capacity of the battery pack after n times of use under the influence of inconsistency:
C(n)=fn(△C)(1-nP/N)C0

In the formula, C(n) represents the remaining capacity of the battery pack after n times of use; f(△C) represents the maximum value of the damage coefficient of the battery charge and discharge capacity during each charge and discharge process, which is a positive number less than 1; N represents the battery pack The service life of the battery pack; P indicates the specified capacity decay percentage at the end of the battery pack life; C0 indicates the initial capacity of the battery pack.

If f(△C) takes the maximum value of 0.999, the end of battery life is defined as the capacity decay of 20%. Assuming that there are three single cells with cycle life of 300 times, 600 times, and 1200 times, respectively, according to the formula, the cycle life when they are used in groups can be calculated as shown in Table 1.

sample	Monomer cycle life (times)	Battery pack cycle life (times)
1#	300	132
2#	600	167
3#	1200	191

According to the calculation results, the cycle life of the lithium-ion power battery pack is much lower than that of the corresponding monomer. Due to the inconsistency, the cycle life of the single cell is doubled, and the life of the battery pack can only be improved by dozens of times. If the battery pack is not repaired and maintained in time, the life of the battery pack can only reach a fraction of the life of the single unit. The lithium-ion power battery used in the demonstration operation of Beijing’s public transport has a single cell life of more than 1,000 times. The capacity of the power battery system applied to the vehicle will be seriously attenuated after 150 times of charging and discharging, and the capacity of some cells has been lower than 80% of rated capacity.

2. Measures to improve battery consistency
The cycle life of the battery pack is increased by increasing the cycle life of the lithium-ion power battery cells, which is ineffective and expensive. By optimizing the charging and discharging method of the battery pack, reducing the inconsistency caused by charging and discharging, and regularly repairing and maintaining the battery pack during use, the electrical performance of the lithium-ion power battery pack can be effectively guaranteed and the service life of the battery pack can be improved. Combined with the research on the life characteristics of lithium-ion power batteries for vehicles and the actual use of vehicles, the following measures can be taken to prevent the expansion of inconsistencies in the use of battery systems.

(1) To ensure the delivery quality of lithium-ion power battery cells, the initial voltage of each cell needs to be consistent, and the same batch of cells must be correlated with voltage, internal resistance and other data before leaving the factory to ensure the same batch of cells. performance as consistent as possible. The battery cells of the same batch, the same specification, and the same type must be selected when assembling the battery.

(2) Adopt practical battery balancing system and energy management system. At present, the most effective and practical equalization method is to equalize the voltage of each cell during the charging process of the battery pack, so that the cell voltage is as consistent as possible, and equalization management is realized from the source. Charging is terminated when the cell voltage reaches the charge cut-off voltage. Charge equalization is to use an active or passive equalization method to make the voltage of each cell consistent before charging is terminated, and the passive equalization method is currently used more. The principle of passive balancing is shown in Figure 2. Each cell is connected to a load resistor and controlled by a switch. According to the result of the cell voltage detection in the battery system, the balance management system closes the switch connected to the cell with the faster voltage rise during charging, thereby maintaining the consistency of the cell voltage and improving the electrical performance of the entire battery pack. Passive equalization is carried out by means of heat dissipation, the discharge current is generally controlled at about 0.1A, and the charging equalization takes several hours to complete. Active charge equalization requires an energy storage element (capacitor, magnetic field, etc.) to transfer energy between cells. The equalizing current is large and the power consumption is small, and no special cooling measures are required, which is beneficial to improve the consistency of the battery pack. However, this method has a complex structure and high cost.

The purpose of the battery management system (BMS) is to avoid premature failure of battery cells due to excessive use, so that the main electrical performance of the battery pack can reach and maintain the performance level of poor cells. Its main task is to prevent overcharge and overdischarge. , which provides status information such as voltage, current, temperature, and remaining power. Using thermal resistance, semiconductor refrigeration device for temperature control, etc., and controlling the charging and discharging state of the power battery pack through BMS can effectively increase the cruising range of the vehicle, prolong the service life of the battery system, and at the same time ensure the safety and reliability of the battery pack during use. Sex is important.

(3) Strengthen the maintenance and maintenance of the battery pack during use. During the use of the battery pack, it is necessary to avoid the contamination of the battery poles by water and dust as much as possible, to ensure a good working environment for the battery pack, and to avoid excessive use as much as possible. The power battery pack should be maintained regularly, and the cells with poor performance should be replaced or adjusted in time through the analysis of parameters such as the voltage of each single cell of the battery pack. The power battery pack is charged with a small current at regular intervals to promote its balance and performance recovery.

1. Flow field design of battery pack thermal management system
The rate of heat dissipation per unit area of ​​the battery pack to the heat transfer medium is expressed as
^·Q=h(T_bat-T_amb)

Among them, h represents the convective heat transfer coefficient on the surface of the battery pack, and the subscripts bat and amb represent the surface of the battery pack and the heat transfer medium, respectively.

First, the design of the flow field determines the order in which the heat transfer medium flows through different positions of the battery pack, which will affect the value of the T_bat-T_amb term, thereby affecting the local heat dissipation rate at different positions. Second, the design of the flow field determines the flow velocity of the heat transfer medium at different locations, and the flow velocity will affect the h term of the local convective heat transfer coefficient. Third, the design of the flow field determines the local shape of the flow channel, which will also affect the value of the local convective heat transfer coefficient h. Therefore, the rationality of the flow field design has a significant impact on the thermal management effect of the battery pack.

(1) Path design of flow field – serial flow channel and parallel flow channel. According to the passage of the heat transfer medium inside the battery pack, the flow field can be divided into serial flow channel type and parallel flow channel type, as shown in Figure 1. In the serial flow channel design, the heat transfer medium passes through each single cell or battery module in strict order, while in the parallel flow channel design, the heat transfer medium enters the battery pack box and passes through the parallel flow channels. Divide the current through different battery sub-modules in parallel. For serial runner designs, the battery modules behind the runners will not be able to dissipate heat effectively because the medium will gradually be heated in the serial runners. It has been pointed out that the parallel flow channel design results in better temperature uniformity at different locations of the battery pack compared to the serial flow channel.

(2) Velocity design of flow field—speed regulation and pressure regulation of parallel flow channels. For the parallel flow channel design, the flow rates of different flow channels must be as uniform as possible to reduce the non-uniformity of temperature at different positions inside the battery pack. Two methods to ensure uniform flow rate: speed regulation method and pressure regulation method, and the optimal combination of the two methods is given. The speed regulation method refers to reducing the width of each channel in turn in the direction of increasing the number of parallel channels to adjust the flow resistance of the heat transfer medium, so that the heat transfer medium can redistribute its flow according to the resistance of each channel, so as to achieve the purpose of adjusting the flow rate distribution. The pressure regulation method changes the pressure difference on both sides of different channels by changing the inclination angle of the inlet and outlet collector plates, thereby indirectly adjusting the flow rates of different channels.

The thermal management system of the lithium-ion power battery system is mainly divided into air cooling and liquid cooling according to the different cooling media. Among them, liquid cooling has better cooling effect, but it needs to arrange special pipes, has many parts, complicated control and high cost. The gas cooling system has low heat transfer rate and low volumetric efficiency, but is widely adopted due to its simple design, simple control and low cost. Due to the small convective heat transfer coefficient of gas, it is more difficult to use gas to heat or cool battery systems than liquids. Therefore, the design of gas cooling systems should be optimized to the greatest extent possible for battery packs. Taking the development of a power battery cooling system for an electric vehicle as an example, the optimization scheme of the air-cooled cooling system is proposed, and the final optimization scheme is determined by the simulation results.

2. Problems and solutions of cooling system
The air-cooled cooling system of an electric vehicle power battery is shown in Figure 2. There are two main problems in this cooling system: one is that the temperature difference between the battery modules is too large; the other is that the pressure loss is too large, and the structure of the air channel needs to be optimized. The main reasons for these two problems are: the arrangement of the battery modules is asymmetric, and the air flow between the battery modules is inconsistent; the battery module adopts a double-layer structure, which generates heat accumulation; there is a sudden contraction or expansion in the air channel. The cross section changes suddenly, the structure does not have enough corner radius at the corner, and the air cannot transition smoothly. In order to solve these two problems, the air-cooled heat dissipation system of the battery system is optimized: the battery module is arranged in a single-layer structure, the structure of the air channel is arranged symmetrically, and the cross-section is changed by using a small shrinkage angle and multiple cross-sections. , and design a large corner radius at the corner. There are two types of improved schemes: scheme one, the air inlet of the air channel is set at the top left side, the air outlet is set at the bottom end of the right side, and the air inlet and outlet are located on both sides; scheme two, the air inlet port of the air channel is located at the top left side, The air outlet is at the bottom left side, and the air inlet and outlet are at the left end. In the two schemes, the battery modules are arranged in a single-layer symmetrical arrangement, and a large rounded transition is designed at the turn of the air inlet, and a small-angle contraction is used to reduce the pressure loss. The improved scheme is shown in Figure 3 and Figure 4.

3. Evaluation indicators of air-cooled cooling system
In the design process of the air cooling system of the battery pack, it is necessary to evaluate it with relevant indicators to determine whether the optimization scheme is feasible. The main indicators are the maximum temperature difference of the system, the maximum temperature of the system, and the pressure difference between the inlet and outlet. The maximum temperature difference of the system refers to the difference between the highest temperature and the lowest temperature of all the cells in the lithium-ion power battery system, which reflects the uniformity of the cooling system and ensures that the cooling effect of each cell is consistent. The maximum temperature of the system refers to the maximum temperature of all cells in the lithium-ion power battery system, which can represent the cooling effect of the cooling system to a certain extent. The inlet and outlet pressure difference refers to the pressure difference between the air inlet and the air outlet in the air cooling system, which is closely related to the structure of the air flow channel of the cooling system.

4. Simulation analysis
The flow field and thermal field simulation are carried out for the two optimization schemes respectively, and the temperature cloud map, pressure cloud map and velocity cloud map are formed, as shown in Figure 5, Figure 6, and Figure 7. By comparing and analyzing the simulation results of flow, pressure, temperature, etc., the advantages and disadvantages of the two schemes are judged according to the evaluation indicators of the cooling system, and the one with better cooling effect is selected. The key parameters of the two optimization schemes are compared in Table 1. From the data in Table 1, it can be seen that the maximum temperature difference of the system, the maximum temperature of the system, and the flow uniformity of the scheme 2 are better than those of the scheme 1, but the pressure difference between the inlet and the outlet of the scheme 2 is slightly different. Therefore, the second solution with the same side design of the air inlet and outlet has a better heat dissipation effect, and further optimization design can be made on the basis of the second solution to obtain a better heat dissipation effect.

Scheme	Maximum temperature difference (K)	Maximum temperature (K)	Inlet and outlet pressure difference (Pa)	Flow unevenness (%)
Scheme 1	14.2	326.3	11.88	0.08604
Scheme 2	13	325.8	11.89	0.06196

Lithium-ion power battery is an electrochemical battery based on Li+ concentration difference. The level of ambient temperature during operation directly affects the activity of positive and negative electrode materials and electrolyte, and has an important impact on its life. The electrical performance and service life of the same lithium-ion power battery at different operating temperatures are very different. Generally, the lithium-ion power battery can exert its maximum efficiency at a room temperature of about 25 °C. When the ambient temperature is too low, the activity of the electrolyte is affected, and the internal resistance increases significantly, resulting in difficult battery charging, reduced power, reduced usable capacity, and impaired battery life. When used at high temperature, the heat dissipation of the battery system will be affected. When the internal temperature of the battery exceeds the limit temperature, the internal chemical balance will be destroyed, resulting in corrosion and aging of battery materials, seriously aggravating the battery life decay process, and causing the battery to fail prematurely.

Figure 1 shows the relationship between the capacity retention rate and the number of cycles of a lithium-ion power battery cell at different temperatures. In the cyclic charge-discharge test, the discharge system is: 1C constant current discharge to voltage 2.5V; charging system: 1C constant current charge to 3.7V, transfer to constant voltage 3.7V to charge until the current drops to 1/30C, stop charging, and complete the charging process. After charging, let it stand for 1h, and then re-charge and discharge test. The remaining capacity of the monomer was measured every 20 charge-discharge cycles completed.

It can be seen from Figure 1 that when the high temperature is 40~60°C, the battery decays faster as the temperature increases, especially when the battery is at an ambient temperature of 60°C, the battery discharge capacity decays to 80.63 after 20 charge-discharge cycles. %. When the low temperature is -10~10℃, with the decrease of the ambient temperature, the battery attenuation speed is accelerated, and the battery capacity attenuation speed is significantly accelerated in the -10℃ environment. Moreover, it can be seen that the high temperature environment has a greater impact on the life attenuation than the low temperature environment, which is more detrimental to the life of the battery. The temperature of the battery increases rapidly in the high temperature environment. When the charge and discharge test is carried out in the environment of 40°C, the temperature of the battery increases by 20°C after 7 cycles of charge and discharge.

In order to protect the lithium-ion battery and improve the service life of the battery, the ambient temperature of the lithium-ion power battery should be controlled within the range of 0~40 °C, and it is forbidden to work in a high temperature environment above 50 °C. In order to further ensure that the battery capacity decay rate is within a certain range, the working temperature of the battery should preferably be controlled at 0~25℃.

When the lithium-ion power battery cells are connected in series and parallel to form a power battery pack, the temperature field of the power battery pack is not a simple superposition of the temperature field of the single cell, and the temperature distribution of the battery pack is not as uniform as that of the battery cells. The stability is also not as good as the monomer. The non-uniformity of the temperature distribution of the battery pack leads to inconsistent cell activity at different positions inside the battery pack, thereby aggravating the expansion of the inconsistency. Therefore, the power battery system needs to design a special thermal management system to ensure that the battery works in an appropriate temperature range and the uniformity of the battery temperature distribution.

1. Research background of lithium-ion power battery thermal management system
The performance, life and safety of lithium-ion power batteries are closely related to the temperature of the battery. If the temperature is too high, the side reactions will be accelerated, the decay will be accelerated (every time the temperature increases by 15°C, the life span will be reduced by half), and even safety accidents will occur. If the temperature is too low, the power and capacity of the battery will be significantly reduced. If the power is not limited, it may lead to the precipitation of lithium ions, causing irreversible attenuation and burying potential safety hazards. Generally, the suitable working temperature of lithium-ion power battery is between 10°C and 30°C. The operating ambient temperature of the lithium-ion battery for electronic products is not much different from this suitable temperature range, and no or only simple heat dissipation components are required. Vehicle power batteries are used in a wide range of ambient temperatures (-20°C to 50°C), and the thermal environment around the battery in the vehicle is often very uneven, which poses a serious challenge to the thermal management of the battery pack. The large-scale and grouped use of power batteries has led to the fact that the heat dissipation capacity of the battery (group) is much lower than the heat generation capacity. Especially for HEVs and PHEVs characterized by high-rate discharge, a complex heat dissipation system needs to be designed. When the single cells are used in parallel (the internal pole pieces of the single cells are also connected in parallel), the uneven temperature of the individual cells will cause thermoelectric coupling, that is, the battery (or part) with a high temperature has a smaller internal resistance and will share more current, resulting in The state of charge is not uniform, thereby accelerating the deterioration of the battery pack. Therefore, the thermal management technology of the power battery system is one of the key technologies to ensure its performance, life and safety.

The thermal management system of the power battery mainly realizes the following functions: first, heat dissipation when the temperature of the battery pack is high to prevent safety accidents caused by overheating of the battery; second, heating the battery pack when the temperature of the battery pack is low to ensure that the battery is in a low temperature environment The safety and use efficiency of lower charging and discharging; third, make the temperature difference between different positions of the battery and different parts of the battery as small as possible, suppress the formation of local hot spots or hot spots, and make the thermally induced decay rates of the batteries at different positions close to Consistent. Generally, the internal temperature difference of the battery pack is less than 5℃. GM’s Volt adopts a water-cooling design of thermoelectric integration, which can control the maximum temperature difference within 2℃, which strongly supports the 8-year life guarantee period (GM’s guarantee period for the internal combustion engine power system is 5 years). Table 4-1 shows typical automobile thermal management methods in the United States and Japan.

2. Research content of thermal management system of lithium-ion power battery
1) The main components of the thermal management system for lithium-ion power batteries
(1) Heat transfer medium: a medium in contact with the heat exchange surface of the battery pack, through which the heat generated in the battery pack is dissipated to the external environment through the flow of the medium.

(2) Flow field environment: the path through which the heat transfer medium flows and the distribution of velocity and pressure along the way.

(3) Temperature measuring element and control circuit: The temperature measuring element is used to measure the real-time temperature of different positions of the battery pack; the control circuit makes the action decision of the cooling actuator according to the real-time temperature.

(4) Heat dissipation actuator: The device that drives the heat transfer medium to circulate, with fans and pumps being the most common. Thermal management systems with natural ventilation do not contain thermal actuators.

2) The main heat transfer medium of the thermal management system of the lithium-ion power battery pack
(1) Air is used as the heat transfer medium. In a thermal management system that uses air as the heat transfer medium, the air from the outside environment or the passenger compartment enters the flow channel of the thermal management system, directly contacts the heat exchange surface of the battery pack, and takes away heat through the air flow. According to the spontaneous degree of air flow, it is divided into two categories: natural ventilation and forced ventilation. Natural ventilation includes natural convection and air movement that occurs with the vehicle. Forced ventilation is primarily driven by fans whose instantaneous power is determined by the control circuit of the thermal management system.

(2) Use liquid as heat transfer medium. Thermal management systems using liquid as heat transfer medium are mainly divided into contact and non-contact thermal management systems. The contact type uses highly insulating liquids such as silicon-based oil, mineral oil, etc., and the battery pack can be directly immersed in the heat transfer liquid. The non-contact type uses conductive liquids such as water, ethylene glycol or coolant, and the battery pack cannot be in direct contact with the heat transfer liquid. At this time, distributed closed pipes must be arranged inside the battery pack, and the heat transfer liquid flows through the pipes to take away the heat. The material of the pipe and its tightness ensure the electrical insulation between the conductive liquid and the battery body. The liquid flow in the contact or non-contact liquid cooling system is mainly driven by oil pumps/water pumps.
Since the specific heat capacity and thermal conductivity of liquid are much higher than that of air, the heat dissipation effect of liquid-cooled thermal management system is theoretically better than that of air-cooled system. However, the following two characteristics of the liquid cooling system reduce its heat dissipation efficiency in practical use:
①The heat transfer medium insulating oil of the contact liquid cooling system has a high viscosity, which requires a high oil pump power to maintain the required flow rate.
②The non-contact liquid cooling system needs to design distributed closed flow channels inside the battery pack, which increases the overall mass of the battery pack and reduces the heat transfer efficiency between the battery surface and the heat transfer medium.

(3) The phase change material is used as the heat transfer medium. Certain substances undergo a phase change at a specific temperature and absorb or release energy, and these substances are called phase change materials (PCM). The phase change temperature can be adjusted near the upper limit of the suitable working range of the battery by adjusting the types and composition ratios of phase change materials and additives. Using this type of phase change material to wrap the battery pack, when the battery temperature rises to the phase change temperature, the phase change material will absorb a large amount of latent heat, so that the battery temperature is maintained within the suitable working range of the battery, and the battery pack is effectively prevented from overheating.
The thermal management system using phase change material as heat transfer medium has the advantages of simple overall structure, high system reliability and safety. At 40℃~45℃ and high rate discharge, the effect of using composite PCM material to dissipate heat from the battery pack is better than using a fan within the general power range for air cooling. At present, paraffin wax (and its additives) has received more attention as the mainstream battery thermal management phase change material, because the phase change temperature of paraffin wax is close to the upper limit of the optimal operating temperature of the battery, and the cost is low and the latent heat is high. But the main problem is its low thermal conductivity. Therefore, other substances with high thermal conductivity are often added to paraffin to make composite PCM materials. The results show that the mechanical properties are gradually improved with the increase of the paraffin mass fraction at low temperature, while the mechanical properties are gradually deteriorated with the increase of the paraffin mass fraction at high temperature. In addition, adding heat pipes, foamed aluminum and aluminum heat sinks inside the battery pack phase change material can further improve the heat dissipation capacity of the PCM.

Using the data obtained from the lithium-ion power battery pack cycle life test, combined with the Matlab genetic algorithm toolbox, the functional relationship between the battery system capacity retention rate η and the number of charge-discharge cycles n was fitted. Referring to the research methods of general engineering problems, combined with the observation of the relationship between the capacity retention rate and the number of cycles in Figure 1, a 3rd degree polynomial can be used to fit the relationship between the two, namely:
η=a₀+a₁n+a₂n²+a₃n³——(1)

According to a certain test result, we can know the test data [η_i, n_i ] of the capacity retention rate η and the number of charge-discharge cycles n. In order to prevent the magnitude of the undetermined coefficients a₀, a₁, a₂, and a₃ from being too small, the number of cycles of charge and discharge is converted to 1000 times as a unit. The data of η_i,n_i are shown in Table 1.

Number of cycles ni (1000 times)	Capacity retention rate ηi (%)
0.001	103.53034
0.36	98.451615
0.72	96.411574
1.08	94.625677
1.44	93.271964
1.8	92.118205
2.16	90.863933
2.52	89.384969

1 Steps for fitting based on Matlab genetic algorithm toolbox
The following describes the process of using the Matlab Genetic Algorithm Toolbox to determine the undetermined coefficients a₀, a₁, a₂, a₃ in the polynomial (1):

① Determine the fitness function. The fitness function designed in Matlab Genetic Algorithm can only obtain its minimum value. If the maximum value is to be solved, appropriate changes must be made. Let η’²_i be the capacity decay rate corresponding to the number of cycles n_i calculated by the fitting function formula (3-26), then the sum of squares of the total errors of η_i and η’_i is

Generally, it can be considered that the smaller the error squared sum e, the better the fitting effect, even if the values ​​of the undetermined coefficients a0, a1, a2, and a3 with the smallest e are the optimal results.

② Write the m file of the fitness function and save it to the Matlab working path with the function name “bat_cyclelife3”. The function written in this article is as follows:
function y=bat_cyclelife3(a)
C=[103.53035498.45161596.41157494.62567793.27196492.11820590.86393389.384969]; Ne=[0.001, 0.36, 0.72, 1.08, 1.44, 1.80, 2.16, 2.52];
[r, s] = size(c);
y=0
For i=1: s
y=y+(C(i)-(a(1)+a(2)Ne(i)+a(3)(Ne(i)^2)+a(4)*(Ne(i)^ 3)))^2
% Error sum of squared minimization principle
end

③ Open the Matlab Genetic Algorithm Toolbox to make relevant settings, run and obtain the test results. Enter the handle of the fitness function “@bat_cyclelife3” in the Fitness function, enter “4” for the number of variables, check Best fitness and Best individual in the running display (Plots), and set the Selection function in the selection parameter (Selection) to roulette For Roulette, in Stopping Criteria, Generations is set to 100, Fitness limit is set to 0, Stall generations is set to 100, and Stall time limit is set to Inf. The parameters such as crossover and mutation are default values, which are set in the default toolbox. After completing the settings, click the “Start” button, and the genetic algorithm starts to operate.

2 Algorithm calculation process and results
When the maximum number of iterations (Generations) of the stopping condition is set to 100, the display of the best fitness and the current best individual during the calculation process is shown in Figure 2. It can be seen from this that the optimal fitness (that is, the sum of squares of errors) gradually decreases as the number of iterations progresses, and the optimal fitness of each generation is gradually approaching the average fitness, indicating that the algorithm is constantly being optimized. The best fitness after 100 iterations is 21542.86, and the values ​​of a₀, a₁, a₂, and a₃ are shown in Table 2.

number of iterations	a0	a1	a2	a3	total error sum of squares
100	17.2614	13.55584	12.16966	-1.00239	21541.8613
300	60.74951	31.81238	8.51764	-7.23103	2947.9990
2191	102.5959	-10.7985	3.99807	-0.7087	1.5282

It can be seen from Figure 2 that the optimal fitness continues to decrease in the process of 100 iterations, indicating that the optimization can be continued by increasing the number of iterations. Set the “Selection” to Stochastic uniform, the Generations in the Stopping Criteria to “Inf”, the Time limit to “Inf”, the Stall Generations to “Inf”, and then click “Start” restarts the operation. Through the display of the best fitness in Plots, we can see the change between the fitness and the best individual. When the desired effect is achieved, click “Stop” in the toolbox to stop the operation, and record the optimization results of the algorithm as shown in Table 2.

After 2191 iterations, the best approximations of the coefficients a₀, a₁, a₂, and a₃ are 102.5959, -10.7985, 3.99807, and -0.7087, respectively, which is the difference between the capacity retention rate η of the lithium-ion power battery pack and the number of charge-discharge cycles n. The functional relationship between them is shown in formula (2). The maximum value of the error between the calculated value of the fitting equation (2) and the actual capacity retention rate obtained by the experiment is 0.9, and the sum of squares of the total error is only 1.5282, indicating that the equation (2) has a good degree of fit. Using the Matlab function to program and draw, the data points obtained from the experiment and the curve of the fitting function are shown in Figure 3. According to the capacity retention rate lower than 80% as the end of life, the total cycle life of the lithium-ion power battery pack is calculated to be 3836 times according to formula (2).
η=102.5959-10.7985n+3.99807n²-0.7087n³——(3)

What is the Matlab genetic algorithm toolbox?

Genetic algorithm has the advantages of simple thinking and obvious application effect. Experts and scholars in various fields have conducted in-depth research on it, and used C, C++ and other programming languages ​​to implement algorithms. However, these languages ​​require users to write genetic algorithm programs, which brings certain difficulties to researchers who are not familiar with programming languages. The genetic algorithm toolbox of Matlab can realize the operation of genetic algorithm through a graphical user interface (GUI) . The problem can be quickly defined by writing a small amount of fitness function program and setting the corresponding parameters in the toolbox. Flexible, easy to use, and easy to modify parameters.

This article takes the genetic algorithm toolbox in Matlab7.1 version as an example to introduce the structure and parameter settings of the toolbox. Type “gatool” in the Matlab working window. After the command is run, you can open the Genetic Algorithm Tool box, or find and open the tool box in the Start menu in Matlab. The operation interface is shown in Figure.

The genetic algorithm toolbox is divided into 5 parts from left to right, mainly including defining function handles and variable numbers, running displays (Plots), constraints (Constraints), running commands and results (Run Solver), parameter settings (Options), etc.

(1) When solving actual problems, first determine the fitness function of the problem, and write it as an M file and store it on the working path of Matlab. Fill in the handle of the compiled fitness function in Fitness Function, the format is “@funtname”, and enter the number of variables to be solved in Number of vari.

(2) Constraints include constraints such as Linear inequalities, Linear equalities, and Bounds. For example, boundary constraints limit the minimum and maximum values ​​of variables, and the maximum value constraints of multiple variables can be expressed in matrix form.

(3) Operation display (Plots) displays the operation process of the selected item in image form during operation. For example, after checking Best fitness, the algorithm operation process will display the best function value and average value in each generation of the group; checking Best individual will display the individual corresponding to the best fitness value under the current iteration number.

(4) The run command and result (Run solver) includes operation buttons such as run, pause, stop, etc. The number of iterations and operation status will be displayed during the running process, and the final optimization result will be displayed in the final point after the algorithm stops.

(5) Parameter settings (Options) mainly affect the calculation speed and accuracy of the algorithm, mainly including population (Population), fitness scale (Fitness scaling), selection (Selection), mutation (Mutation), stop condition (Stopping Criteria), Crossover (Crossover) and other parameter settings. The relevant parameters can be selected and set through the drop-down menu.

What is genetic algorithm fitting?

Genetic Algorithm (Genetic Algorithm, GA) is a global optimization algorithm, which is based on the evolutionary theory of natural selection and genetics to find the optimal solution to the function problem. It is not only suitable for general fitting problems, but also can solve the traditional fitting methods. Deal with non-linear and highly complex data fitting problems.

Therefore, this paper uses genetic algorithm to fit the test data obtained from the lithium-ion power battery cycle life test, and obtain the optimal coefficient and equation between the capacity retention rate and the number of cycles.

Genetic algorithm (GA) simulates the evolutionary process of gene recombination and mutation in the process of biological reproduction. When solving actual problems, the potential solution of the problem (randomly generated) is used as the initial population of the algorithm. The population is used as an individual after binary coding by a computer. These individuals perform operations similar to natural selection, crossover, and mutation in biological evolution, and reproduce according to the rule of survival of the fittest, and finally obtain the optimal individual that meets the convergence condition is the optimization result of the problem.

When the genetic algorithm is used for curve fitting, the algorithm uses group evolution to process multiple individuals at the same time. It does not need to know the derivative of the problem to be sought, does not depend on the complexity of the problem, and the initial population, recombination, mutation and other operations in the genetic algorithm It is performed randomly, which can avoid the local optimum in the optimization process and achieve the global optimum effect, and can effectively solve the optimal estimation problems such as polynomial coefficients.

The main calculation steps of genetic algorithm are:

① Randomly generate an initial population based on actual problems.

②Use the designed fitness function to calculate the fitness of the individual.

③ Perform operations such as selection, crossover, and mutation.

Selection refers to the use of certain methods to select individuals with high adaptability to inherit to the next generation according to the fitness of the individual.
Crossover refers to selecting two individuals with higher probability from the group, and exchanging part of the genes in each pair of individuals.
Commonly used methods such as single-point crossover and multi-point crossover. Variation refers to changing the value of part of the gene position of the individual in the population after crossover with a small probability.

④ Determine whether the convergence conditions are met.

When the set convergence conditions are met, the individual with the greatest fitness is the optimal solution to the problem, otherwise, proceed to steps ③ and ④.

The fitness function is used to measure the fitness of an individual, which is equivalent to the objective function in actual problems. It can only find the minimum value in the Matlab genetic algorithm toolbox. The genetic algorithm controls the operation of the algorithm through the fitness function, uses the size of the individual fitness to determine the probability of an individual being inherited to the next generation, and then changes the group structure. It is the basis for the algorithm’s natural selection and the driving force of evolution. When the genetic algorithm is used to fit the function, the fitness function f(x) that can be selected is as shown in the formula (formula diagram), where C_max is a sufficiently large positive number, and ER is the objective function.

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