A method and apparatus for estimating state of charge of a battery

Abstract

The application provides a method and device for estimating battery state of charge, and mainly relates to the technical field of batteries. The method comprises the following steps: establishing a battery equivalent circuit model; identifying the battery equivalent circuit model by using two groups of least square methods to obtain an open circuit voltage and battery model parameters, wherein the least square methods are least square methods with forgetting factors; and estimating the battery state of charge by using an extended Kalman filtering algorithm according to the open circuit voltage and the battery model parameters. The battery equivalent circuit model is identified by using two groups of least square methods with forgetting factors, so that reliable battery model parameters and stable open circuit voltage can be obtained, and then the battery state of charge is estimated by using the extended Kalman filtering algorithm, so that the SOC estimation accuracy is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery, in particular to a method and device for estimating state of charge of battery. BACKGROUND

[0002] The state of charge (SOC) of a new energy vehicle power battery is the basis for energy management and energy decision of the vehicle. The accuracy of SOC estimation affects the service life and safety of the battery, and directly affects the applicability and safety of the vehicle. Therefore, the accuracy of SOC estimation is extremely important.

[0003] In the prior art, Kalman filtering algorithm is usually used to estimate SOC, and least square method is needed to continuously output reliable battery model identification parameters and stable open circuit voltage (OCV) values. However, in the operation of the system, there will always be an unbalanced state, which cannot continuously output reliable battery model identification parameters and stable OCV values at the same time, resulting in increased SOC estimation error. SUMMARY

[0004] Therefore, the embodiments of the present application provide a method and device for estimating state of charge of battery, aiming to improve the estimation accuracy of state of charge of battery.

[0005] In a first aspect, the embodiments of the present application provide a method for estimating state of charge of battery, comprising:

[0006] building a battery equivalent circuit model;

[0007] using two groups of least square methods to respectively identify the battery equivalent circuit model, to obtain an open circuit voltage and battery model parameters, the least square method being a least square method with a forgetting factor;

[0008] using an extended Kalman filtering algorithm to estimate the state of charge of battery according to the open circuit voltage and the battery model parameters.

[0009] Optionally, the using two groups of least square methods to respectively identify the battery equivalent circuit model, to obtain an open circuit voltage and battery model parameters comprises:

[0010] using a least square method with a first forgetting factor to identify the battery equivalent circuit model, to obtain the open circuit voltage;

[0011] using a least square method with a second forgetting factor to identify the battery equivalent circuit model, to obtain the battery model parameters, wherein the first forgetting factor is greater than the second forgetting factor.

[0012] Optionally, the using an extended Kalman filtering algorithm to estimate the state of charge of battery according to the open circuit voltage and the battery model parameters comprises:

[0013] obtaining a relationship curve of a battery state of charge and an open circuit voltage;

[0014] determining an open circuit voltage interval in which an extended Kalman filter algorithm is started according to the open circuit voltage and the relationship curve, the relationship curve being used to represent a corresponding relationship between the battery state of charge and the open circuit voltage;

[0015] taking the battery model parameters as inputs of the extended Kalman filter algorithm to estimate the battery state of charge in the open circuit voltage interval.

[0016] Optionally, the battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model is as follows:

[0017]

[0018] wherein, U oc is the open circuit voltage of the battery, U p is a polarization voltage of the battery, R0 is an ohmic internal resistance of the battery, U t is an output voltage of the battery, R p is a polarization internal resistance of the battery, C p is a polarization capacitance of the battery, i L is a current flowing through the battery, is a differential of the polarization voltage of the battery with respect to time;

[0019] the Thevenin first-order equivalent circuit model is solved by a constant variable method to obtain:

[0020]

[0021] Δt is a sampling period, U p,k , U t,k , U oc,k , i L,k is U p , U t , U oc , i L a sampling value at k moment.

[0022] Optionally, the battery model parameters include:

[0023]

[0024] wherein, Δt is a sampling period.

[0025] In a second aspect, an embodiment of the present application provides a device for estimating a battery state of charge, and the device comprises:

[0026] A building module is configured to build a battery equivalent circuit model;

[0027] An identification module is configured to identify the battery equivalent circuit model by using two sets of least square methods respectively to obtain an open circuit voltage and battery model parameters, the least square methods being least square methods with forgetting factors;

[0028] An estimation module is configured to estimate a battery state of charge by using an extended Kalman filter algorithm according to the open circuit voltage and the battery model parameters.

[0029] Optionally, the identification module comprises:

[0030] A first identification unit is configured to identify the battery equivalent circuit model by using a least square method with a first forgetting factor to obtain the open circuit voltage;

[0031] A second identification unit is configured to identify the battery equivalent circuit model by using a least square method with a second forgetting factor to obtain the battery model parameters, wherein the first forgetting factor is greater than the second forgetting factor.

[0032] Optionally, the estimation module comprises:

[0033] A first estimation unit is configured to obtain a relationship curve of a battery state of charge and an open circuit voltage, and determine an open circuit voltage interval in which an extended Kalman filter algorithm is started according to the open circuit voltage and the relationship curve, the relationship curve being used to represent a corresponding relationship between the battery state of charge and the open circuit voltage;

[0034] A second estimation unit is configured to take the battery model parameters as inputs of the extended Kalman filter algorithm to estimate the battery state of charge in the open circuit voltage interval.

[0035] Optionally, the battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model is as follows:

[0036]

[0037] wherein, U oc is an open circuit voltage of the battery, U p is a polarization voltage of the battery, R0 is an ohmic internal resistance of the battery, U t is an output voltage of the battery, R p is a polarization internal resistance of the battery, C p is a polarization capacitance of the battery, i L is a current flowing through the battery, is a differential of the polarization voltage of the battery with respect to time;

[0038] The Thevenin first-order equivalent circuit model is solved by a constant variable method to obtain:

[0039]

[0040] Δt is the sampling period, U p,k 、U t,k 、U oc,k 、i L,k For U p 、U t 、U oc 、i L Sample value at time k.

[0041] Optionally, the battery model parameters include:

[0042]

[0043] in, Δt is the sampling period.

[0044] The embodiment of the present application provides a method and device for estimating the state of charge of a battery. When executing the method, a battery equivalent circuit model is first constructed, and then two sets of least squares methods with forgetting factors are used to identify the battery equivalent circuit model respectively to obtain the open circuit voltage and battery model parameters. Finally, based on the open circuit voltage and the battery model parameters, the extended Kalman filter algorithm is used to estimate the battery state of charge to achieve the estimation of the battery state of charge. In this way, by using two sets of least squares methods with forgetting factors to identify the battery equivalent circuit model respectively, reliable battery model parameters and stable open circuit voltage can be obtained, and then the extended Kalman filter algorithm is used to estimate the battery state of charge, thereby improving the accuracy of SOC estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in this embodiment or the prior art, the following briefly introduces the drawings required for use in the embodiment or the prior art description. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 A flowchart of a method for estimating the state of charge of a battery provided in an embodiment of the present application;

[0047] Figure 2 A circuit diagram of a Thevenin first-order equivalent circuit model provided in an embodiment of the present application;

[0048] Figure 3 A schematic diagram of the structure of a device for estimating the state of charge of a battery provided in an embodiment of the present application. DETAILED DESCRIPTION

[0049] It is apparent that the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0050] Reference is made to Figure 1 , Figure 1 A flowchart of a method for estimating the state of charge of a battery according to an embodiment of the present application is shown in FIG. 1. The method comprises the following steps.

[0051] S101: Establishing a battery equivalent circuit model.

[0052] A high-order resistance-capacitance equivalent circuit model has many parameters and is complex to operate. The battery equivalent circuit model used in the embodiments of the present application is a Thevenin first-order equivalent circuit model. Reference is made to Figure 2 , Figure 2 A circuit diagram of a Thevenin first-order equivalent circuit model according to an embodiment of the present application is shown in FIG. 2.

[0053] In a possible implementation provided by an embodiment of the present application, the battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model formula 1 is as follows:

[0054]

[0055] wherein U oc is an open-circuit voltage of the battery, U p is a polarization voltage of the battery, R0 is an ohmic internal resistance of the battery, U t is an output voltage of the battery, R p is a polarization internal resistance of the battery, C p is a polarization capacitance of the battery, i L is a current flowing through the battery, and is a differential of the polarization voltage of the battery with respect to time.

[0056] The above formula 1 is a first-order ordinary differential equation. The solution of formula 1 is obtained by the constant variation method, and the general solution formula 2 is as follows:

[0057] Formula 2:

[0058]

[0059] wherein Δt is a sampling period, U p,k , U t,k , U oc,k , i L,k , U p , U t , U oc , iL The sampling value at the kth moment.

[0060] Then, a discretization operation is performed according to formula 2 to obtain a discretized measurement voltage formula 3:

[0061]

[0062] The formula 3 is arranged, and a symbol replacement is performed by using formula 4.

[0063] The formula 4 is:

[0064]

[0065] Wherein,

[0066] The replacement obtains:

[0067] U t,k = φ k Θ k ;

[0068] It should be noted that, in the running process of the battery, the battery system will continuously and slowly change. In order to make the battery model more close to the actual situation, a white noise e k is introduced, and the above formula is rewritten as:

[0069] U t,k = φ k Θ k + e k ;

[0070] S102: The battery equivalent circuit model identification is performed by using two sets of least square methods respectively to obtain an open circuit voltage and a battery model parameter.

[0071] The least square method is a least square method with a forgetting factor. By introducing the least square method with the forgetting factor, and the value range of the forgetting factor is between 0.95-1, the smaller the value is, the lower the influence of old data on parameter estimation is, the greater the influence of new data is, the algorithm can track time-varying parameters well, and the greater the value is, the greater the influence of old data on parameter estimation is, the smaller the influence of new data is, and the algorithm can obtain stable parameters.

[0072] In a possible implementation provided in the application, the battery equivalent circuit model identification is performed by using two sets of least square methods respectively to obtain an open circuit voltage and a battery model parameter, and the method comprises the following steps.

[0073] The battery equivalent circuit model identification is performed by using a least square method with a first forgetting factor to obtain the open circuit voltage.

[0074] The battery equivalent circuit model identification is performed by using the least square method with a second forgetting factor, the battery model parameters are obtained, wherein the first forgetting factor is greater than the second forgetting factor.

[0075] By introducing the first forgetting factor and the second forgetting factor, calculation is performed according to formula 5, and two groups of least square method Θ k are obtained, formula 5 is as follows:

[0076]

[0077] Based on formula 5 and two groups of least square method Θ k , the battery model parameters and the open circuit voltage can be obtained respectively:

[0078]

[0079] Wherein, Δt is a sampling period.

[0080] The least square method with the second forgetting factor is used for online parameter identification, the parameters change in real time with input information, and more reliable battery model parameters are obtained. The least square method with the first forgetting factor can output a more stable open circuit voltage Uoc,k.

[0081] S103: According to the open circuit voltage and the battery model parameters, the battery state of charge is estimated by using the extended Kalman filtering algorithm.

[0082] The system of the battery is a nonlinear system, the extended Kalman filtering algorithm is used for first-order Taylor expansion of the battery equivalent model, and the battery equivalent model is approximated as a linear system. The battery state of charge is discretized to obtain formula 6:

[0083]

[0084] Wherein, SOC k is the battery state of charge at k, Q max is the total capacity of the battery pack.

[0085] According to formula 2 and formula 6, the state space equation and the observation equation of the battery system are obtained, formula 7 is as follows:

[0086]

[0087] U oc (SOC k ) is the open circuit voltage corresponding to k, ω k is the system noise and υ kFor observation noise, both are Gaussian white noise, Q and R are covariance, Q and R in extended Kalman filter are initialized as constant.

[0088] Matrices needed in extended Kalman filter algorithm include:

[0089]

[0090]

[0091] According to the above matrix, formula 7 is simplified as:

[0092]

[0093]

[0094] First, the SOC is predicted, and the system state estimation and covariance matrix P k Update:

[0095] State prior estimation:

[0096] State estimation error covariance matrix:

[0097] Then, the SOC is error corrected, and the actual observation y k Correct the state estimation and covariance estimation, the corrected state estimation Covariance matrix is

[0098] Update Kalman gain matrix K k :

[0099]

[0100] Update the actual observation y k Deviation e of observation equation k :

[0101]

[0102] Update the system state estimation

[0103]

[0104] Recalculate the current covariance matrix As the input of the next time prior estimation. Where I is the unit matrix,

[0105]

[0106] By comparing the relationship curve of the battery state of charge and the open circuit voltage with the open circuit voltage identified by the least square method with the first forgetting factor, the correction interval with the largest deviation is obtained, thereby determining the open circuit voltage interval in which the extended Kalman filtering algorithm is started. It can be seen that when starting to enter the correction interval (voltage interval), the larger the absolute value of K k e k is, the larger the correction is. When starting to enter the correction interval, P and R are set as initial values, that is, the larger the absolute value of the deviation e k between the actual observation y k and the observation equation is, the larger the correction is. Therefore, the time when entering the correction interval and the deviation e k in the correction interval should be kept at a larger value.

[0107] In a possible implementation provided by the present application, the battery state of charge is estimated by using the extended Kalman filtering algorithm according to the open circuit voltage and the battery model parameter, including:

[0108] obtaining a relationship curve of the battery state of charge and the open circuit voltage;

[0109] determining an open circuit voltage interval in which the extended Kalman filtering algorithm is started according to the open circuit voltage and the relationship curve, the relationship curve being used to represent the corresponding relationship between the battery state of charge and the open circuit voltage;

[0110] taking the battery model parameter as an input of the extended Kalman filtering algorithm, and estimating the battery state of charge in the open circuit voltage interval.

[0111] When the correction interval is selected, because the current observation voltage value is affected by the working condition and changes in real time, the voltage deviation also changes in real time. If the current observation voltage value is used as the selection judgment condition of the correction interval, the correction interval will be frequently entered and exited. The OCV (open circuit voltage) identified by the least square method with the first forgetting factor is more stable than the current observation voltage value output, and thus the voltage interval in which the Kalman filtering is started for correction is found according to the OCV (open circuit voltage), and the correction interval can be stably maintained after entering the correction interval.

[0112] By comparing the relationship curve of the battery state of charge and the open circuit voltage with the open circuit voltage identified by the least square method with the first forgetting factor, the correction interval with the largest deviation is obtained, thereby determining the open circuit voltage interval in which the extended Kalman filtering algorithm is started. As an example, the relationship curve of the battery state of charge and the open circuit voltage can be obtained through the current charge and discharge experiment of the lithium iron phosphate battery cell. In the open circuit voltage interval, the convergence speed is fast, the battery parameter model is taken as the input of the extended Kalman filtering algorithm, the battery state of charge is estimated in the open circuit voltage interval, and the estimated battery state of charge is more close to the real battery state of charge.

[0113] In the embodiment of the present application, the battery equivalent circuit model is first built, and then two sets of least square methods with forgetting factors are used to respectively identify the battery equivalent circuit model, to obtain the open circuit voltage and the battery model parameters. Finally, the state of charge of the battery is estimated by using the extended Kalman filtering algorithm according to the open circuit voltage and the battery model parameters, so as to realize the estimation of the state of charge of the battery. In this way, the reliable battery model parameters and the stable open circuit voltage can be obtained by using the two sets of least square methods with forgetting factors to respectively identify the battery equivalent circuit model, and then the state of charge of the battery is estimated by using the extended Kalman filtering algorithm, so as to improve the estimation accuracy of the state of charge of the battery.

[0114] The above is some specific implementation manners of the method for estimating the state of charge of the battery provided by the embodiment of the present application. Based on this, the corresponding device is also provided by the present application. The device provided by the embodiment of the present application will be introduced from the perspective of functional modularization.

[0115] Referring to Figure 3 , Figure 3 The device 300 for estimating the state of charge of the battery provided by the embodiment of the present application is a structural schematic diagram of the device, which comprises a building module 301, an identification module 302 and an estimation module 303.

[0116] The building module 301 is used to build the battery equivalent circuit model.

[0117] The identification module 302 is used to use two sets of least square methods to respectively identify the battery equivalent circuit model, to obtain the open circuit voltage and the battery model parameters, wherein the least square method is a least square method with forgetting factors.

[0118] The estimation module 303 is used to estimate the state of charge of the battery by using the extended Kalman filtering algorithm according to the open circuit voltage and the battery model parameters.

[0119] In a possible implementation manner provided by the present application, the identification module 302 comprises:

[0120] The first identification unit is used to identify the battery equivalent circuit model by using the least square method with the first forgetting factor, to obtain the open circuit voltage.

[0121] The second identification unit is used to identify the battery equivalent circuit model by using the least square method with the second forgetting factor, to obtain the battery model parameters, wherein the first forgetting factor is greater than the second forgetting factor.

[0122] In a possible implementation manner provided by the present application, the estimation module 303 comprises:

[0123] The first estimation unit is configured to obtain a relationship curve of the battery state of charge and the open circuit voltage, and determine an open circuit voltage interval in which an extended Kalman filter algorithm is started according to the open circuit voltage and the relationship curve, the relationship curve being used to represent a corresponding relationship between the battery state of charge and the open circuit voltage.

[0124] The second estimation unit is configured to take the battery model parameters as inputs of the extended Kalman filter algorithm, and estimate the battery state of charge in the open circuit voltage interval.

[0125] In a possible implementation provided by the present application, the battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model is as follows:

[0126]

[0127] wherein U oc is the open circuit voltage of the battery, U p is the polarization voltage of the battery, R0 is the ohmic resistance of the battery, U t is the output voltage of the battery, R p is the polarization resistance of the battery, C p is the polarization capacitance of the battery, i L is the current flowing through the battery, is the differential of the polarization voltage of the battery with respect to time;

[0128] The Thevenin first-order equivalent circuit model is solved by a constant variable method to obtain:

[0129]

[0130] Δt is a sampling period, U p,k , U t,k , U oc,k , i L,k is U p , U t , U oc , i L is a sampling value at k moment.

[0131] In a possible implementation provided by the present application, the battery model parameters include:

[0132]

[0133] wherein, Δt is a sampling period.

[0134] The embodiment of the present application provides a device for estimating battery state of charge. A battery equivalent circuit model is built, then two sets of least square methods with forgetting factors are used for battery equivalent circuit model identification respectively, open circuit voltage and battery model parameters are obtained, finally, the battery state of charge is estimated by using extended Kalman filtering algorithm according to the open circuit voltage and the battery model parameters, so as to realize the estimation of the battery state of charge. In this way, the reliable battery model parameters and stable open circuit voltage can be obtained by using two sets of least square methods with forgetting factors for battery equivalent circuit model identification, and then the battery state of charge is estimated by using the extended Kalman filtering algorithm, so that the SOC estimation accuracy is improved.

[0135] The embodiment of the present application also provides a corresponding device and a computer storage medium for realizing the scheme provided by the embodiment of the present application.

[0136] The embodiment of the present application provides a device, which comprises a memory and a processor, the memory is used for storing instructions or codes, and the processor is used for executing the instructions or codes, so that the device executes the method for estimating battery state of charge in any one of the preceding first aspects.

[0137] The embodiment of the present application provides a computer storage medium, which stores codes, when the codes are executed, a device executing the codes realizes the method for estimating battery state of charge in any one of the preceding first aspects.

[0138] The device comprises a memory and a processor, the memory is used for storing instructions or codes, and the processor is used for executing the instructions or codes, so that the device executes the method for estimating battery state of charge in any one of the embodiments of the present application.

[0139] The computer storage medium stores codes, when the codes are executed, a device executing the codes realizes the method for estimating battery state of charge in any one of the embodiments of the present application.

[0140] The "first", "second" in the names mentioned in the embodiments of the present application are only used for name identification, and do not represent the first and second in order.

[0141] Through the description of the above embodiments, it can be known that those skilled in the art can clearly understand that all or part of the steps in the above embodiment methods can be implemented by means of software plus a general hardware platform. Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a storage medium, such as a read-only memory (ROM) / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network communication device such as a router) to execute the methods described in each embodiment or certain parts of the embodiments of the present application.

[0142] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple. For the relevant parts, refer to the partial description of the method embodiment. Some or all of the modules can be selected according to actual needs to achieve the purpose of the embodiment. Those of ordinary skill in the art can understand and implement it without paying any creative work.

[0143] The above description is merely an exemplary embodiment of the present application and is not intended to limit the scope of protection of the present application.

Claims

1. A method of estimating a state of charge of a battery, characterized by, The method comprises: building a battery equivalent circuit model; performing battery equivalent circuit model identification using least squares method with a first forgetting factor to obtain an open circuit voltage; performing battery equivalent circuit model identification using least squares method with a second forgetting factor to obtain the battery model parameters, wherein the first forgetting factor is greater than the second forgetting factor, and the least squares method is least squares method with a forgetting factor; estimating the state of charge of the battery according to the open circuit voltage and the battery model parameters using extended Kalman filtering algorithm; the battery model parameters comprise: ； wherein , , , , is a sampling period.

2. The method of claim 1, wherein, the estimation of the state of charge of the battery according to the open circuit voltage and the battery model parameters using extended Kalman filtering algorithm comprises: obtaining a relationship curve of the state of charge of the battery and the open circuit voltage; determining an open circuit voltage interval in which extended Kalman filtering algorithm is started according to the open circuit voltage and the relationship curve, wherein the relationship curve is used to represent the corresponding relationship between the state of charge of the battery and the open circuit voltage; taking the battery model parameters as the input of the extended Kalman filtering algorithm to estimate the state of charge of the battery in the open circuit voltage interval.

3. The method according to claim 1 or 2, characterized in that, The battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model is: ； wherein, Vopen is the open circuit voltage of the battery, Vpolar is the polarization voltage of the battery, Rohm is the ohmic internal resistance of the battery, Vout is the output voltage of the battery, Rpolar is the polarization internal resistance of the battery, Cpolar is the polarization capacitance of the battery, I is the current flowing through the battery, dVpolar / dt is the differential of the battery polarization voltage over time; the solution of the equation obtained by the constant variation method for the Thevenin first-order equivalent circuit model is: ； for the sampling period, , , , for the sampling period, , , , sample value at k.

4. An apparatus for estimating a state of charge of a battery, characterized by The device comprises: a building module configured to build a battery equivalent circuit model; an identification module comprising a first identification unit and a second identification unit; the first identification unit is configured to perform battery equivalent circuit model identification using least squares method with a first forgetting factor to obtain an open circuit voltage; the second identification unit is configured to perform battery equivalent circuit model identification using least squares method with a second forgetting factor to obtain the battery model parameters, wherein the first forgetting factor is greater than the second forgetting factor, and the least squares method is least squares method with a forgetting factor; an estimation module configured to estimate the state of charge of the battery according to the open circuit voltage and the battery model parameters using extended Kalman filtering algorithm; the battery model parameters comprise: ； wherein , , , , is a sampling period.

5. The apparatus of claim 4, wherein, the estimation module comprises: a first estimation unit configured to obtain a relationship curve of the state of charge of the battery and the open circuit voltage, and determine an open circuit voltage interval in which extended Kalman filtering algorithm is started according to the open circuit voltage and the relationship curve, wherein the relationship curve is used to represent the corresponding relationship between the state of charge of the battery and the open circuit voltage; a second estimation unit configured to take the battery model parameters as the input of the extended Kalman filtering algorithm to estimate the state of charge of the battery in the open circuit voltage interval.

6. The apparatus of claim 4 or 5, wherein, The battery equivalent circuit model is a Thevenin first-order equivalent circuit model, and the Thevenin first-order equivalent circuit model is: ； wherein, Vopen is the open circuit voltage of the battery, Vpolar is the polarization voltage of the battery, Rohm is the ohmic internal resistance of the battery, Vout is the output voltage of the battery, Rpolar is the polarization internal resistance of the battery, Cpolar is the polarization capacitance of the battery, I is the current flowing through the battery, dVpolar / dt is the differential of the battery polarization voltage with respect to time; the solution of the equation obtained by the constant variation method for the Thevenin first-order equivalent circuit model is: ； for the sampling period, , , , for , , , sample value at k.

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