Category Lithium ion power battery life estimation and optimization

What is the research status of lithium-ion power battery thermal management system?

What is the research status of lithium-ion power battery thermal management system?

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.

What is the research status of lithium-ion power battery thermal management system?
battery thermal management system

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.

What is the research status of lithium-ion power battery thermal management system?
lithium-ion power battery thermal management system

(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.

Lithium-ion power battery system cycle life fitting

Lithium-ion power battery system cycle life fitting

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:

Lithium-ion power battery system cycle life fitting
Figure 1 Relationship between the capacity retention rate of lithium-ion power battery system and the number of cycles of charge and discharge

According to a certain test result, we can know the test data [ηi, ni ] 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 ηi,ni are shown in Table 1.

Number of cycles ni (1000 times)Capacity retention rate ηi (%)
Table 1 Experimental data of cycle times and capacity retention

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’²i be the capacity decay rate corresponding to the number of cycles ni calculated by the fitting function formula (3-26), then the sum of squares of the total errors of ηi 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);
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

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 iterationsa0a1a2a3total error sum of squares
Table 2 Coefficient optimization results based on genetic algorithm
Lithium-ion power battery system cycle life fitting
Figure 2 The best/average fitness and the best individual for 100 iterations of the algorithm

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).

Lithium-ion power battery system cycle life fitting
Figure 3 GA fitting curve of cycle life of lithium-ion power battery
Matlab genetic algorithm toolbox

Matlab Genetic Algorithm Toolbox

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.

Matlab genetic algorithm toolbox
Figure Matlab genetic algorithm toolbox

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.

Genetic Algorithm Fitting

Genetic Algorithm Fitting

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 Cmax is a sufficiently large positive number, and ER is the objective function.

Fitness function
Fitness function

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