Method for rapidly measuring open-circuit voltage

Abstract

The invention relates to a rapid measurement method for open-circuit voltage, belongs to the technical field of battery measurement, and solves the problems that in the prior art, battery open-circuit voltage measurement is long in time and large in error. Comprising the following steps: establishing a calculation mode of open-circuit voltage, identifying the open-circuit voltage on line, and further establishing an open-circuit voltage precision evaluation model based on the offset degree; applying a preset number of positive and negative pulses to the battery to obtain a relation model between the open-circuit voltage precision evaluation model and the number of positive and negative pulses, and further obtaining an expected number of pulses; positive and negative pulses with the expected pulse number are applied to the battery, online identification is carried out based on a calculation mode of the open-circuit voltage, and measurement of the open-circuit voltage is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of battery measurement, and in particular to a method for quickly measuring open circuit voltage. Background Art

[0002] Lithium-ion-based batteries have been widely used in electric vehicles, microgrids, handheld devices and other fields. To maximize the performance of the battery, it is necessary to obtain the battery state parameters, and the identification of battery model parameters, especially open-circuit voltage (OCV), is the basis for obtaining the battery state parameters. Since there is a one-to-one correspondence between OCV and state of charge (SOC), accurately measuring the OCV of the battery helps to improve the accuracy of SOC estimation. In addition, the battery's state of power (SOP) and state of health (SOH) are also related to SOC and OCV, so the identification of OCV is the basis for accurately estimating the battery's SOC, SOP and SOH.

[0003] OCV is mainly obtained by standing still for 1 hour at zero output and zero input. Although this method is widely used, it takes too long and can only be used in laboratories or special test sites, and is not suitable for use in actual working conditions. OCV can also be obtained by charging and discharging the battery with a small current (less than 0.05C), but this test method takes at least 40 hours and can only be used in laboratories or special test sites, and cannot be used in actual working conditions. Although online identification of OCV can also be achieved through the equivalent circuit model, the identified OCV is affected by the current amplitude, battery charging and discharging status and test conditions, and the OCV obtained by this method has a large error and cannot be used in practice.

[0004] Therefore, a method that can quickly and accurately measure the open circuit voltage of a battery is urgently needed. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a method for quickly measuring open circuit voltage, so as to solve the problem that the existing open circuit voltage measurement of a battery takes a long time and has large errors.

[0006] An embodiment of the present invention provides a method for quickly measuring an open circuit voltage, comprising:

[0007] Establish a calculation method for open circuit voltage, identify open circuit voltage online, and then establish an open circuit voltage accuracy evaluation model based on the degree of offset;

[0008] By applying a preset number of positive and negative pulses to the battery, a relationship model between the open circuit voltage accuracy evaluation model and the number of positive and negative pulses is obtained, and then the expected number of pulses is obtained;

[0009] By applying positive and negative pulses of the expected number to the battery, online identification is performed based on the calculation method of the open circuit voltage to achieve the measurement of the open circuit voltage.

[0010] Furthermore, the calculation method of the open circuit voltage is expressed as:

[0011]

[0012] Among them, λ0 and λ1 satisfy the following formula:

[0013]

[0014] Where U ocv (k) represents the open circuit voltage at time k, λ0, λ1, λ2 and λ3 represent the first, second, third and fourth coefficients respectively, U(k) and U(k-1) represent the battery terminal voltage at time k and k-1 respectively, I(k) and I(k-1) represent the input or output current of the battery at time k and k-1 respectively, and θ represents the coefficient matrix.

[0015] Furthermore, the open circuit voltage accuracy evaluation model based on the offset degree is expressed as:

[0016]

[0017] Where, ODE represents the open circuit voltage accuracy evaluation value based on the degree of offset, OCV 辨识 Indicates the open circuit voltage, OCV, identified online 实际 Indicates the actual open circuit voltage.

[0018] Further, the expected number of pulses is obtained by performing the following steps:

[0019] Applying a preset number of positive and negative pulses to the battery, obtaining a curve of the relationship between ODE and the number of pulses, and then obtaining a relationship between ODE and the number of pulses;

[0020] The expected number of pulses is obtained according to the relationship between ODE and the number of pulses.

[0021] Furthermore, if the relationship curve is described by a relationship between ODE and the number of pulses, the number of pulses when ODE is zero in the relationship is taken as the expected number of pulses;

[0022] If the relationship curve is described by multiple relationship equations between ODE and the number of pulses, the average value of the number of pulses obtained when the ODE is zero in the relationship equations between the ODE and the number of pulses is taken as the expected number of pulses.

[0023] Furthermore, the relationship curve between the ODE and the number of pulses includes polynomial, exponential and logarithmic relationships.

[0024] Furthermore, the positive and negative pulses are positive and negative pulses of equal amplitude, the amplitude is 2C, and the duration is 10s; wherein C represents the current ratio.

[0025] Furthermore, the preset number of pulses is set to 15.

[0026] Furthermore, the online identification of the coefficient matrix θ is performed online, and then the online identification of the open circuit voltage is realized according to the calculation method of the open circuit voltage, wherein the online identification of the coefficient matrix θ includes an adaptive differential evolution algorithm, a least squares algorithm, a model reference adaptation and an intelligent algorithm.

[0027] Furthermore, the coefficient matrix θ is identified online through an adaptive differential evolution algorithm, including initializing the population based on the coefficients in the coefficient matrix, and then calculating the objective function after mutation, crossover, selection, and boundary condition processing until the termination criterion requirements are met, and the values ​​of the coefficients in the coefficient matrix are obtained; wherein the objective function is the sum of squares of the battery terminal voltage residuals.

[0028] Compared with the prior art, the present invention can at least achieve the following beneficial effects:

[0029] The present invention provides a rapid measurement method for open circuit voltage. The open circuit voltage is identified online by establishing a calculation method for the open circuit voltage, and then an open circuit voltage accuracy evaluation model based on the degree of offset is established. Then, a relationship model between the open circuit voltage accuracy evaluation model and the number of positive and negative pulses is obtained by applying a preset number of positive and negative pulses to a battery, and an expected number of pulses is obtained. Finally, after applying an expected number of positive and negative pulses to the battery, online identification is performed based on the calculation method for the open circuit voltage to achieve open circuit voltage measurement. The open circuit voltage of a battery can be measured rapidly and accurately in any state, thereby laying a foundation for accurately estimating the SOC, SOP and SOH of the battery.

[0030] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0032] Figure 1 A schematic flow chart of a method for quickly measuring open circuit voltage provided in an embodiment of the present invention;

[0033] Figure 2 A schematic diagram of the flow of the ADE algorithm provided in an embodiment of the present invention;

[0034] Figure 3 This is a relationship curve between ODE and the number of positive and negative pulses provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0036] A specific embodiment of the present invention discloses a method for quickly measuring open circuit voltage. Figure 1 As shown, including:

[0037] S1. Establish a calculation method for open circuit voltage, identify the open circuit voltage online, and then establish an open circuit voltage accuracy evaluation model based on the degree of offset.

[0038] During implementation, the open circuit voltage is calculated as:

[0039]

[0040] Among them, λ0 and λ1 satisfy the following formula:

[0041]

[0042] Where U ocv (k) represents the open circuit voltage at time k, λ0, λ1, λ2 and λ2 represent the first, second, third and fourth coefficients respectively, U(k) and U(k-1) represent the battery terminal voltage at time k and time k-1 respectively, I(k) and I(k-1) represent the input or output current of the battery at time k and time k-1 respectively.

[0043] It should be noted that the calculation method of the open circuit voltage is established in the following way:

[0044] Establish the equivalent circuit model of the battery, specifically:

[0045] The Thevenin model of a battery is:

[0046]

[0047] Where U represents the terminal voltage of the battery, U ocv Represents the open circuit voltage of the battery, R o Represents the ohmic internal resistance of the battery, R p Represents the polarization internal resistance of the battery, C prepresents the polarization capacitance of the battery, I represents the input or output current of the battery, and U p Represents the polarization voltage of the battery.

[0048] The Thevenin model of the battery is transformed into an identifiable difference equation using a direct discrete method, specifically:

[0049] The formula for converting a differential equation into a difference equation is:

[0050]

[0051] In the formula, y represents the variable to be transformed, and ΔT represents the sampling interval.

[0052] According to formula (3), formula (2) can be directly transformed into:

[0053]

[0054] in,

[0055]

[0056] Where U ocv (k) represents the open circuit voltage at time k, U(k) represents the battery terminal voltage at time k, I(k) and I(k-1) represent the input or output current of the battery at time k and time k-1 respectively, and U p (k) U p (k-1) represents the polarization voltage of the battery at time k and time k-1, respectively, T s Indicates the sampling time.

[0057] Substituting the first term in equation (4) into the second term, after rearrangement, we get:

[0058] U(k)=U ocv (k)-aU ocv (k-1)+aU(k-1)+R o I(k)+(b-aR o )I(k-1) (5)

[0059] Where U ocv (k-1) represents the open circuit voltage at time k-1.

[0060] In a very short time (such as 1s), the open circuit voltage hardly changes, that is, U ocv (k)≈U ocv (k-1), then formula (5) can be transformed into:

[0061] U(k)=(1-a)U ocv (k)+aU(k-1)+R oI(k)+(b-aR o )I(k-1) (6)

[0062] By transforming equation (6) into the least squares format, the identifiable difference equation of the battery Thevenin model can be obtained as follows:

[0063]

[0064] Wherein, λ0, λ1, λ2 and λ3 represent the first, second, third and fourth coefficients respectively. It should be noted that 1(k) represents a constant 1, and the suffix (k) means that it is 1 at any time.

[0065] Thus, the calculation method of the battery open circuit voltage is obtained:

[0066]

[0067] During implementation, the coefficient matrix θ is identified online, and then the open circuit voltage is identified online according to the calculation method of the open circuit voltage. The online identification of the coefficient matrix θ includes an adaptive differential evolution algorithm, a least squares algorithm, a model reference adaptation and an intelligent algorithm.

[0068] Preferably, the coefficient matrix θ is identified online by an adaptive differential evolution algorithm, such as Figure 2 As shown, the population is initialized based on each coefficient in the coefficient matrix, and then the objective function is calculated after mutation, crossover, selection, and boundary condition processing until the termination criterion is met to obtain the value of each coefficient in the coefficient matrix.

[0069] When implementing it, Figure 2 As shown, the adaptive differential evolution algorithm includes initializing the population based on each coefficient in the coefficient matrix, and then calculating the objective function after mutation, crossover, selection, and boundary condition processing until the termination criterion requirements are met to obtain the value of each coefficient in the coefficient matrix, wherein the objective function is the sum of squares of the battery terminal voltage residuals.

[0070] Specifically, the population is initialized in the following way:

[0071] The adaptive differential evolution algorithm uses a population of NP real-valued parameter vectors with dimension D = 4 as the population of each generation. The target vector of each individual is expressed as:

[0072] x i,g (i=1,2,…,NP) (9)

[0073] In the formula, i represents the sequence of individuals in the population, and g represents the current evolutionary generation.

[0074] In order to establish a starting point for the optimization search, the population must be initialized. Let the bounds on the parameter variables be but

[0075]

[0076] In the formula, x j represents the jth parameter, x ji,0 represents the initial target vector of the jth parameter of the individual with sequence i in the population, and rand[0,1] represents a uniform random number generated between [0,1]; represents the search lower bound, Represents the search upper bound, which is within [0,1].

[0077] Mutation is performed in the following ways:

[0078] For each individual target vector x i,g (i=1,2,…,NP), the mutation vector of the adaptive differential evolution algorithm is generated by the following formula:

[0079]

[0080] In the formula, v i,g+1 represents the mutation vector of the individual with sequence i in the population in the next evolutionary generation, i≠r1≠r2≠r3 (i=1,2,…,NP), and r1, r2 and r3 are all random integers in [1,NP], and F represents the adaptive mutation operator.

[0081] Crossover is done in the following way:

[0082] In order to increase the diversity of the interference parameter vector, a crossover operation is introduced, and the test vector becomes:

[0083] u i,g+1 =(u 1i,g+1 ,u 2i,g+1 ,…,u Di,g+1 ) (12)

[0084] in,

[0085]

[0086] In the formula, u i,g+1 represents the test vector of the individual with sequence i in the population in the next evolutionary generation, u ji,g+1 represents the test vector of the jth parameter of the individual with sequence i in the population in the next evolutionary generation, v ji,g+1 represents the mutation vector of the jth parameter of the individual with sequence i in the population in the next evolutionary generation, which can be obtained from formula (11); x ji,g+1represents the target vector of the jth parameter of the individual with sequence i in the population in the next evolutionary generation, which can be obtained by formula (9); randb(j) represents the jth estimated value of the random number generator between [0,1]; rnbr(i)∈(1,2,…,D) represents a randomly selected sequence to ensure that u i,g+1 At least from v i,g+1 Get a parameter; C r represents the cross factor.

[0087] Make your selection by:

[0088] To determine the test vector u i,g+1 Will it become a member of the next generation? The adaptive differential evolution algorithm compares the test vector with the target vector x in the current population according to the greedy criterion. i,g If the objective function is to be minimized, then the vector with the smaller objective function value will appear in the next generation population. All individuals in the next generation are better or at least the same as the corresponding individuals in the current population, where the objective function is the sum of squares of the battery terminal voltage residuals.

[0089] The boundary conditions are handled in the following way:

[0090] In problems with boundary constraints, it is necessary to ensure that the parameter values ​​of the generated new individuals are in the feasible domain of the problem. The new individuals that do not meet the boundary constraints can be replaced by parameter vectors randomly generated in the feasible domain, that is: or So

[0091]

[0092] Set the termination criteria as follows:

[0093] If g exceeds the maximum evolutionary number G m Or when the solution accuracy reaches the requirement, the search is stopped; otherwise, mutation, crossover and selection operations will be performed on the population again until the conditions are met.

[0094] More specifically, in the adaptive differential evolution algorithm, the population size NP = 200, the crossover factor C r = 0.6, termination criterion to achieve the maximum evolutionary generation G m =100, the adaptive mutation operator F is:

[0095] F=2 ρ F0 (14)

[0096] in,

[0097]

[0098] Wherein, F0 represents the initial mutation operator, preferably, F0=0.2; and ρ is the attenuation factor.

[0099] During implementation, the open circuit voltage accuracy evaluation model based on the offset degree is expressed as:

[0100]

[0101] Where, ODE represents the open circuit voltage accuracy evaluation value based on the degree of offset, OCV 辨识 Indicates the open circuit voltage, OCV, identified online 实际 Indicates the actual open circuit voltage.

[0102] Specifically, the actual open circuit voltage OCV 实际 It is the voltage obtained after the battery is left standing for at least 1 hour without input or output current.

[0103] It is understandable that there is an error between the open circuit voltage obtained through online identification and the actual open circuit voltage. In this embodiment, the error is evaluated by establishing an open circuit voltage accuracy evaluation model based on the degree of offset.

[0104] S2. A relationship model between an open circuit voltage accuracy evaluation model and the number of positive and negative pulses is obtained by applying a preset number of positive and negative pulses to the battery, thereby obtaining an expected number of pulses.

[0105] During implementation, the expected number of pulses is obtained by executing the following steps:

[0106] Applying a preset number of positive and negative pulses to the battery, obtaining a curve of the relationship between ODE and the number of pulses, and then obtaining a relationship between ODE and the number of pulses;

[0107] The expected number of pulses is obtained according to the relationship between ODE and the number of pulses.

[0108] In a specific implementation, if a relationship curve is described by a relationship between ODE and the number of pulses, the number of pulses when the ODE in the relationship is zero is taken as the expected number of pulses;

[0109] If the relationship curve is described by multiple relationship equations between ODE and the number of pulses, the average value of the number of pulses obtained when the ODE is zero in the relationship equations between the ODE and the number of pulses is taken as the expected number of pulses.

[0110] Specifically, the relationship curve between the ODE and the number of pulses includes a polynomial, an exponential and a logarithmic relationship.

[0111] Specifically, the positive and negative pulses are positive and negative pulses of equal amplitude. It can be understood that after applying positive and negative (PN) pulses of equal amplitude, the ODE calculated based on the open circuit voltage obtained by online identification in step S1 is the smallest, and as the number of positive and negative pulses increases, the ODE gradually decreases.

[0112] Specifically, the amplitudes of the positive and negative pulses can be arbitrarily selected under a current rate that ensures battery safety. Preferably, the amplitude is 2C, where C represents the current rate.

[0113] Specifically, the duration of the positive and negative pulses can be arbitrarily selected. Preferably, the duration of the positive and negative pulses is 10 seconds, that is, the duration of the positive pulse and the duration of the negative pulse are both 10 seconds.

[0114] Preferably, the preset number of pulses is set to 15.

[0115] For example, 15 positive and negative pulses are applied to the LiFePO4 battery to obtain a relationship curve between ODE and the number of pulses, such as Figure 3 As shown, f(N) represents the function of the number of pulses N, that is, the relationship expression between ODE and the number of pulses N; R represents the correlation coefficient. The closer R is to 1, the greater the correlation between ODE and the number of pulses N.

[0116] Optionally, the relationship curve between ODE and the number of pulses can be described by the following formula:

[0117] ODE=αln(N)+β (16)

[0118] In the formula, α and β are coefficients.

[0119] Depend on Figure 3 The relationship curve in is fitted to obtain the specific values ​​of the coefficients in formula (16), which are α=0.588 and β=-2.3731.

[0120] Let ODE = 0 in equation (16), then we can get N = 56.6;

[0121] For ease of implementation, the expected number of pulses is an integer, and thus the expected number of pulses is N=56.

[0122] Optionally, the relationship curve between ODE and the number of pulses can also be described by the following formula:

[0123]

[0124] In the formula, γ, μ, and η are coefficients.

[0125] Depend on Figure 3The relationship curve in is fitted to obtain the specific values ​​of the coefficients in formula (17), which are γ = -0.2894, μ = 0.6319, and η = 1.1608.

[0126] Let ODE = 0 in equation (17), then we can get N = 57.3;

[0127] For ease of implementation, the expected number of pulses is an integer, and thus the expected number of pulses is N=57.

[0128] Preferably, in implementation, the relationship curve between ODE and the number of pulses can be simultaneously described by equations (16) and (17), and the first number of pulses is 56.6 and the second number of pulses is 57.3, and the average of the first number of pulses and the second number of pulses is obtained, and the average is rounded to the expected number of pulses, that is, the expected number of pulses is 57.

[0129] S3. By applying a desired number of positive and negative pulses to the battery, online identification is performed based on the calculation method of the open circuit voltage to achieve the measurement of the open circuit voltage.

[0130] It can be understood that by obtaining the expected number of pulses through steps S1 and S2 and finally performing the final open circuit voltage identification through step S3, the open circuit voltage can be quickly measured.

[0131] To verify the effectiveness of the battery open circuit voltage measurement method in this embodiment, in this embodiment, the LiFePO4 battery is charged at different SOC points at different rates, and 57 positive and negative pulses are applied. The calculation method in step S1 is combined to identify the open circuit voltage online and calculate the ODE. The verification results are shown in Table 1.

[0132] Table 1 OCV measurement accuracy

[0133]

[0134] It can be seen from Table 1 that, using the measurement method in this embodiment, the maximum ODE is only -0.098%, and the average value is only -0.03% (error is about 1 mV), which can achieve fast and accurate measurement of the battery open circuit voltage.

[0135] Compared with the prior art, the present embodiment provides a method for rapid measurement of open circuit voltage, which performs online identification of open circuit voltage by establishing a calculation method for open circuit voltage, and then establishes an open circuit voltage accuracy evaluation model based on the degree of offset, and then obtains a relationship model between the open circuit voltage accuracy evaluation model and the number of positive and negative pulses by applying a preset number of positive and negative pulses to the battery, and obtains the expected number of pulses; finally, after applying an expected number of positive and negative pulses to the battery, online identification is performed based on the calculation method of open circuit voltage to achieve open circuit voltage measurement, which can achieve rapid and accurate measurement of the open circuit voltage of the battery in any state, thereby laying the foundation for accurately estimating the SOC, SOP and SOH of the battery.

[0136] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0137] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for quickly measuring open circuit voltage, characterized in that: include: Establish a calculation method for open circuit voltage, identify open circuit voltage online, and then establish an open circuit voltage accuracy evaluation model based on the degree of offset; By applying a preset number of positive and negative pulses to the battery, a relationship model between the open circuit voltage accuracy evaluation model and the number of positive and negative pulses is obtained, and then the expected number of pulses is obtained; By applying positive and negative pulses of the expected number to the battery, online identification is performed based on the calculation method of the open circuit voltage to achieve the measurement of the open circuit voltage.

2. The method for rapid measurement of open circuit voltage according to claim 1, characterized in that: The calculation method of the open circuit voltage is expressed as: Among them, λ0 and λ1 satisfy the following formula: Where U ocv (k) represents the open circuit voltage at time k, λ0, λ1, λ2 and λ3 represent the first, second, third and fourth coefficients respectively, U(k) and U(k-1) represent the battery terminal voltage at time k and k-1 respectively, I(k) and I(k-1) represent the input or output current of the battery at time k and k-1 respectively, and θ represents the coefficient matrix.

3. The method for rapid measurement of open circuit voltage according to claim 1, characterized in that: The open circuit voltage accuracy evaluation model based on the offset degree is expressed as: Where, ODE represents the open circuit voltage accuracy evaluation value based on the degree of offset, OCV 辨识 Indicates the open circuit voltage, OCV, identified online 实际 Indicates the actual open circuit voltage.

4. The method for rapid measurement of open circuit voltage according to claim 3, characterized in that: The expected number of pulses is obtained by performing the following steps: Applying a preset number of positive and negative pulses to the battery, obtaining a curve of the relationship between ODE and the number of pulses, and then obtaining a relationship between ODE and the number of pulses; The expected number of pulses is obtained according to the relationship between ODE and the number of pulses.

5. The method for rapid measurement of open circuit voltage according to claim 4, characterized in that: If the relationship curve is described by a relationship between ODE and the number of pulses, the number of pulses when ODE is zero in the relationship is taken as the expected number of pulses; If the relationship curve is described by multiple relationship equations between ODE and the number of pulses, the average value of the number of pulses obtained when the ODE is zero in the relationship equations between the ODE and the number of pulses is taken as the expected number of pulses.

6. The method for rapid measurement of open circuit voltage according to claim 4, characterized in that: The relationship curve between the ODE and the number of pulses includes polynomial, exponential and logarithmic relationships.

7. The method for rapid open circuit voltage measurement according to claim 4, characterized in that: The positive and negative pulses are positive and negative pulses of equal amplitude, with an amplitude of 2C and a duration of 10s; wherein C represents the current ratio.

8. The method for rapid open circuit voltage measurement according to claim 1, characterized in that: The preset number of pulses is set to 15.

9. The method for rapid open circuit voltage measurement according to claim 2, characterized in that: The online identification of the coefficient matrix θ is performed online, and then the online identification of the open circuit voltage is realized according to the calculation method of the open circuit voltage. The online identification of the coefficient matrix θ includes an adaptive differential evolution algorithm, a least squares algorithm, a model reference adaptation and an intelligent algorithm.

10. The method for rapid open circuit voltage measurement according to claim 9, characterized in that: The coefficient matrix θ is identified online through an adaptive differential evolution algorithm, including population initialization based on the coefficients in the coefficient matrix, and then the objective function is calculated after mutation, crossover, selection, and boundary condition processing until the termination criterion is met to obtain the value of each coefficient in the coefficient matrix; wherein the objective function is the sum of squares of the battery terminal voltage residuals.

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