CN114740385A - Self-adaptive lithium ion battery state of charge estimation method - Google Patents

Self-adaptive lithium ion battery state of charge estimation method Download PDF

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CN114740385A
CN114740385A CN202210212196.5A CN202210212196A CN114740385A CN 114740385 A CN114740385 A CN 114740385A CN 202210212196 A CN202210212196 A CN 202210212196A CN 114740385 A CN114740385 A CN 114740385A
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battery
charge
state
lithium ion
voltage
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张晓勇
宋诗语
蒋富
黄志武
李烁
高凯
李恒
刘伟荣
彭军
杨迎泽
关凯夫
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Central South University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E60/10—Energy storage using batteries

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Abstract

The invention discloses a self-adaptive lithium ion battery state of charge estimation method, which comprises the following steps: establishing a second-order RC equivalent circuit model of the lithium ion battery, and identifying parameters of the second-order RC equivalent circuit model in an off-line manner; fitting a correlation curve between the open-circuit voltage and the state of charge of the lithium ion battery; verifying the accuracy of the model through a dynamic stress test; performing online identification on the model parameters according to a recursive least square method containing forgetting factors; and determining an estimated value of the state of charge of the lithium ion battery by using an adaptive extended Kalman particle filter algorithm. According to the method, the stability and the accuracy of the charge state estimation result are improved by outputting the weighted average value of a plurality of particles; the importance of the particles is sampled through the adaptive extended Kalman filtering algorithm, so that the operation efficiency of the algorithm is improved while the charge state of the lithium ion battery is accurately estimated.

Description

Self-adaptive lithium ion battery state of charge estimation method
Technical Field
The invention belongs to the technical field of lithium ion batteries, and particularly relates to a self-adaptive lithium ion battery state of charge estimation method.
Background
The lithium battery has the advantages of high energy density, high working voltage, low self-discharge rate, long service life and the like, and is widely applied to the fields of new energy automobiles, mobile robots, new energy sources and the like. However, lithium batteries also have many disadvantages, such as high internal resistance leading to higher temperatures at high charge and discharge rates. Meanwhile, overcharge and overdischarge may damage the battery, shorten the life of the battery, and even cause accidents such as explosion. Therefore, the working state of the lithium battery is detected, and the performance and the service life of the lithium battery can be obviously improved.
The state of charge (SOC) of a lithium battery is an important index for measuring the state of the lithium battery, and directly represents the remaining capacity of the battery. SOC is defined as the percentage of the remaining charge after a lithium battery is fully charged. Accurate SOC estimation can prevent the battery from over-charging and over-discharging, improve the performance of the battery and prolong the service life of the battery. SOC cannot be measured directly by the sensor due to the non-linear characteristics of the lithium ion battery. Currently, methods commonly used in the field of SOC estimation include a data-driven method, a direct estimation method, and a model-based estimation method.
The SOC estimation method based on the equivalent circuit model simulates the battery dynamics by establishing the equivalent circuit model, has strong robustness, and is very suitable for SOC estimation of the lithium ion battery. In addition, the equivalent circuit model based method also needs to be combined with a filtering algorithm to estimate the SOC of the battery. In the invention patent "power lithium battery SOC estimation method based on adaptive kalman filtering method" with patent application number CN201910567240.2, an adaptive extended kalman filtering algorithm is used to estimate the battery SOC. Although the adaptive extended kalman filter algorithm is not computationally complex, the algorithm cannot handle non-gaussian noise and has model linearization errors if the system is strongly non-linear. In the invention patent "state of charge estimation method and battery management system based on adaptive particle filtering", with patent application number CN201910567240.2, a particle filtering algorithm is used to estimate the SOC of the battery. Although the particle filter algorithm can deal with the situations of system nonlinearity and noise non-Gaussian, the particle degradation causes the high calculation complexity of the algorithm.
Disclosure of Invention
The invention aims to provide a self-adaptive lithium ion battery state of charge estimation method, which aims to solve the problems in particle filtering and self-adaptive extended Kalman filtering: the method not only can process the conditions of system nonlinearity and noise non-Gaussian, but also can ensure the operation efficiency of the algorithm.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a self-adaptive lithium ion battery state of charge estimation method comprises the following steps:
s1, establishing a second-order RC equivalent circuit model of the lithium ion battery, performing an HPPC cycle condition experiment, and performing off-line identification on parameters of the equivalent circuit model by using an exponential fitting method;
step S2, obtaining a correlation curve of the open-circuit voltage and the state of charge of the battery according to the result of the HPPC cycle condition experiment;
step S3, inputting the correlation curves of current, open-circuit voltage and state of charge of the battery dynamic stress test and the equivalent circuit model parameters of off-line identification into the battery equivalent circuit model to obtain the corresponding equivalent circuit model output voltage; comparing the error between the output voltage of the equivalent circuit model and the actual dynamic stress test voltage, and verifying the accuracy of the equivalent circuit model;
step S4, updating the equivalent circuit model parameters on line by using a recursive least square method containing forgetting factors;
and step S5, deducing a state space equation and an observation equation of the battery according to the mathematical expression of the equivalent circuit model, and estimating the state of charge of the lithium ion battery by using the adaptive extended Kalman particle filter.
In a more preferred embodiment, the mathematical expression of the equivalent circuit model in step S1 is:
Figure BDA0003532115740000031
wherein, UocIs the open circuit voltage of the battery; r0Ohmic internal resistance of the battery; r1And C1Is the resistance and capacitance representing the electrochemical polarization reaction of the cell; r2And C2Is the resistance and capacitance representing the concentration polarization reaction of the cell; u shapetIs the terminal voltage of the battery.
In a more preferred technical solution, the specific process of the HPPC experiment in step S1 is as follows: after the battery is kept stand for 5 minutes, when the voltage of the battery is charged to 4.2V by the current with the constant current of 0.5C, the battery is converted into a constant voltage charging mode; in the constant voltage charging mode, after the current of the battery is charged to be lower than 0.05C, the charging is stopped, and the battery is kept stand for 2 hours; discharging at 3C, standing the battery for 1 hour when the charge state is reduced by 10%, measuring the corresponding open-circuit voltage, and repeating the steps until the charge state of the battery is 0%.
In a more preferred embodiment, the offline identification process of the parameters in step S1 is as follows:
(1) according to the terminal voltage V1 second before the lithium ion battery is loaded with the HPPC pulse1Terminal voltage V at moment of loading HPPC pulse2End voltage V at the moment of finishing HPPC pulse loading3And terminal voltage V1 second after the end of the HPPC pulse loading4And calculating ohmic resistance R in the lithium ion equivalent circuit0Meter for measuringThe calculation formula is as follows:
Figure BDA0003532115740000041
(2) the zero input voltage response of the battery in the standing process of the HPPC pulse charge-discharge experiment is as follows:
Figure BDA0003532115740000042
wherein, U1(0) And U2(0) Terminal voltages, τ, of two RC networks, respectively1＝R1C1，τ2＝R2C2(ii) a Fitting the above formula by using a fitting tool box of matlab, and calculating two time constants tau1And τ2The specific value of (a);
(3) the zero state response of the RC network in the HPPC pulse charging and discharging experiment process of the battery is as follows:
Figure BDA0003532115740000043
similarly, the above formula is fit in the matlab fitting tool box to obtain the specific R1And R2Taking the value of (A);
(4) according to the relation1＝R1C1，τ2＝R2C2And R already obtained1And R2Solve for C1And C2The specific value of (a).
In a more preferred technical solution, the specific model of the open-circuit voltage and state of charge correlation curve in step S2 is:
Uoc＝k1SOC6-k2SOC3+k3SOC4-k4SOC3+k5SOC2+k6SOC+k7
wherein k is1，k2…k7For the coefficient to be fitted, 1The open circuit voltage points are obtained by fitting 10 charge states.
In a more preferred embodiment, the dynamic stress test in step S3 refers to: carrying out a cycle test on the battery under the dynamic stress working condition until the voltage is less than 3V; the dynamic stress working condition test method comprises the following steps that (1) one dynamic stress working condition comprises a plurality of charging and discharging pulses, 360 seconds are consumed when each dynamic stress working condition test is carried out, and the battery still needs to stand for 120 seconds before the next dynamic stress working condition test is carried out; the shortest duration time of a single discharge pulse in the dynamic stress working condition is 8 seconds, the longest duration time can reach 40 seconds, the maximum discharge current is 2C, and the maximum charge current is 0.5C.
In a more preferred embodiment, the step S4 includes the following steps:
(1) calculating the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor:
Figure BDA0003532115740000051
wherein y (k) is the real battery voltage at the current moment,
Figure BDA0003532115740000052
the vector is measured for the current time instant,
Figure BDA0003532115740000053
e (k) the error between the model output voltage and the actual battery output voltage obtained by the parameter identification result at the last moment;
(2) updating a gain matrix
Figure BDA0003532115740000054
Wherein, P (k-1) is a covariance matrix at the last moment, lambda is a forgetting factor, and K (k) is a gain matrix at the current moment;
(3) updating the covariance matrix for calculating the gain matrix at the next time instant
Figure BDA0003532115740000055
(4) Updating the current time parameter identification result by using the gain matrix and the error
Figure BDA0003532115740000056
In a more preferred embodiment, the state space equation and the observation equation of the battery in step S5 are respectively:
Figure BDA0003532115740000061
Ut,k＝Uoc,k-U1,k-U2,k-IkR0
wherein T is sampling time, k is discrete time variable, and Q is battery rated capacity.
In a more preferred technical solution, the particles of the adaptive extended kalman particle filter described in step S5 are a series of random samples with weights, and the specific steps are as follows:
(1) initializing a set of particles
Figure BDA0003532115740000062
And particle weight is set to
Figure BDA0003532115740000063
(2) Taking adaptive extended Kalman filtering as importance sampling function
Figure BDA0003532115740000064
(3) The particle weights are updated according to:
Figure BDA0003532115740000065
(4) normalizing the weights:
Figure BDA0003532115740000066
(5) the effective number of particles was calculated according to the following formula:
Figure BDA0003532115740000067
wherein N iseffIs the effective number of particles, if NeffIf the sampling rate is less than 0.7N, resampling is needed;
(6) obtaining a current time estimation result:
Figure BDA0003532115740000068
(7) returning to the step (2), setting k to k +1 until the loop is finished.
The invention has the beneficial effects that: the invention establishes a second-order RC equivalent circuit model of the lithium ion battery, and offline identification is carried out on model parameters by adopting an exponential fitting method; OCV and SOC correlation curves were then fitted using HPPC cycle behavior experiments. The model parameters are identified online by adopting a recursive least square method containing forgetting factors, and the state of charge estimation of the lithium ion battery is realized by combining an adaptive extended Kalman particle filter algorithm based on the identified model parameters online. The method combines the adaptive extended Kalman filter algorithm and the particle filter algorithm, and improves the stability and the accuracy of the SOC estimation result by outputting the weighted average value of a plurality of particles; the adaptive extended Kalman filtering is used as an importance sampling function, so that the operation efficiency of the algorithm is improved.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of a second-order RC equivalent circuit model in the present invention.
Detailed Description
The present invention is described in detail with reference to the following embodiments, which are developed based on the technical solutions of the present invention, and the detailed embodiments and specific operating procedures are given to further explain the technical solutions of the present invention.
As shown in fig. 1, the state of charge estimation method based on adaptive extended kalman particle filter according to the present invention includes the following steps:
in step S1, a second-order RC equivalent circuit model of the lithium ion battery is first established, and the equivalent circuit model is shown in fig. 2. Wherein R is0Expressing ohmic internal resistance; first RC network, R1And C1For describing the electrochemical polarization reaction of the cell; second RC network, R2And C2For describing the cell concentration polarization reaction; u shapetIs the battery terminal voltage; u shapeocAn open circuit voltage for the battery; i is the battery load current. According to kirchhoff's current-voltage law, a mathematical expression of a second-order RC equivalent circuit model can be obtained:
Figure BDA0003532115740000081
to identify the unknown parameters R in the model0、R1、R2、C1、C2The invention adopts an off-line parameter identification method. The parameters can be identified by using terminal voltage data of the HPPC cycle working condition and combining with a fitting tool box of matlab.
Before parameter identification, an HPPC pulse charge-discharge experiment needs to be carried out, and the process is as follows: the battery was left to stand for 5 minutes, and then when the battery voltage was charged to 4.2V with a constant current of 0.5C, the mode was changed to the constant voltage charging mode. And (3) after the current of the battery is charged to be lower than 0.05 ℃ in a constant voltage charging mode, stopping charging, and standing the battery for 2 hours. After this time, the cell was discharged at 3C, allowed to stand for 1 hour for each 10% drop in state of charge, and the corresponding open circuit voltage was measured. This procedure was repeated until the battery state of charge was 0%.
Thereafter, forAnd performing off-line identification on the initial values of the model parameters. According to terminal voltage V1 second before loading HPPC pulse1Terminal voltage V at the moment of loading HPPC pulse2Terminal voltage V at the moment of end of loading HPPC pulse3Terminal voltage V1 second after the HPPC pulse is loaded4Then the ohmic resistance R in the lithium ion equivalent circuit can be calculated0The calculation formula is as follows:
Figure BDA0003532115740000082
then, two time constants tau can be calculated by fitting zero input voltage response of the battery in the standing process of the HPPC pulse charge-discharge experiment1And τ2The specific values of (A):
Figure BDA0003532115740000083
fitting the zero state response of the RC network can obtain R1And R2The value of (A) is as follows:
Figure BDA0003532115740000084
due to tau1＝R1C1，τ2＝R2C2And R is1And R2Now known, so that C can be solved1And C2And therefore, the initial parameter value identification of the second-order RC equivalent circuit model is completed.
And step S2, fitting a correlation curve of the open-circuit voltage and the state of charge. Firstly, 10 data points, namely open-circuit voltage corresponding to 100% of charge state and open-circuit voltage corresponding to 90% of charge state … 0% of charge state, are calibrated by using an HPPC cycle working condition experiment. Then, fitting the 10 data points by using a sixth-order polynomial model, wherein the expression of the sixth-order polynomial model is as follows:
Uoc＝k1SOC6-k2SOC3+k3SOC4-k4SOC3+k5SOC2+k6SOC+k7
after the fitting of the open-circuit voltage and the charge state calibration point is completed, k can be obtained1,k2…k7The value of (a). I.e. the dependence of the open circuit voltage and the state of charge.
And step S3, carrying out a dynamic stress test working condition cycle test on the battery, and verifying the accuracy of the established model. Firstly, a dynamic stress condition test is carried out, namely, the applied pulse current has different duration and different magnitude in 360 seconds. The shortest duration time of a single discharge pulse is 8 seconds, the longest duration time can reach 40 seconds, the maximum discharge current is 2C, and the maximum charge current is 0.5C. And then carrying out the next dynamic stress working condition test after 120 seconds till the terminal voltage of the battery is lower than 3V.
The expression for the output terminal voltage from the battery model is:
Ut＝Uoc-U1-U2-IR0
wherein, UocCan be obtained by the correlation curve of the state of charge and the open circuit voltage, while U1And U2Can pass through the already identified R1、R2、C1、C2And (4) calculating. Therefore, the current of the battery dynamic stress test is input into the battery model, and the corresponding model output voltage can be obtained. And then verifying the accuracy of the model by comparing the error between the output voltage of the model and the actual dynamic stress test voltage.
In step S4, performing online identification on the model parameters by using recursive least squares including a forgetting factor, the main steps including:
(1) calculating the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor
Figure BDA0003532115740000101
Wherein y (k) is the real battery voltage at the current moment,
Figure BDA0003532115740000102
the vector is measured for the current time instant,
Figure BDA0003532115740000103
e (k) the error between the model output voltage obtained by the parameter identification result at the previous moment and the actual battery output voltage.
(2) Updating a gain matrix
Figure BDA0003532115740000104
Wherein, P (k-1) is the covariance matrix of the last time, λ is the forgetting factor, and K (k) is the gain matrix of the current time.
(3) Updating the covariance matrix for calculating the gain matrix at the next time instant
Figure BDA0003532115740000105
(4) Updating the current time parameter identification result by using the gain matrix and the error
Figure BDA0003532115740000106
In step S5, the state of charge of the lithium ion battery is estimated based on the adaptive extended kalman particle filter. Before a specific filtering algorithm is carried out, related state equations and measurement equations need to be established. For a discrete control system, its state equations and observation equations can be expressed as:
xk＝Ak-1xk-1+Bk-1uk-1+wk-1
yk＝Ckxk+Dkuk+vk
wherein x iskThe system state vector at the kth moment is obtained; y iskThe measurement vector at the kth moment is taken as the measurement vector; u. ofkThe input vector at the k-th moment is; w and v are the process noise and the measurement noise of the system, respectively; A. b, C, D matrix is the parameter matrix of the system. The invention converts SOC (k +1) U1(k+1) U2(k+1)TAs state vector of the system, UtAs the output of the system, I is the input of the system. Writing a state equation and an observation equation according to a mathematical expression of a second-order RC equivalent circuit model and a definition formula of the SOC:
Figure BDA0003532115740000111
Ut,k＝Uoc,k-U1,k-U2,k-IkR0
wherein T is sampling time, k is discrete time variable, Q is rated capacity of battery,
Figure BDA0003532115740000112
Dk＝-R0。
then, estimating the state of charge of the lithium ion battery by using self-adaptive extended Kalman particle filtering, wherein the particles are a group of random samples with weights, and the method comprises the following specific steps:
(1) initializing a set of particles
Figure BDA0003532115740000113
And the particle weight is set to
Figure BDA0003532115740000114
(2) Generating importance sampling functions using adaptive extended Kalman filtering
Figure BDA0003532115740000115
The ABCD matrix derived as described above needs to be used. Since the adaptive extended kalman filter is a prior art, a repeated explanation is not given in the present invention；
(3) The particle weights are updated according to:
Figure BDA0003532115740000116
(4) normalizing the weights:
Figure BDA0003532115740000121
(5) the effective number of particles was calculated according to the following formula:
Figure BDA0003532115740000122
wherein N iseffIs the effective number of particles, if NeffIf the sampling rate is less than 0.7N, resampling is needed;
(6) obtaining a current time estimation result:
Figure BDA0003532115740000123
(7) returning to step (2), setting k to k +1 until the loop is ended.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.

Claims (9)

1. A self-adaptive lithium ion battery state of charge estimation method is characterized by comprising the following steps:
s1, establishing a second-order RC equivalent circuit model of the lithium ion battery, performing an HPPC cycle condition experiment, and performing off-line identification on parameters of the equivalent circuit model by using an exponential fitting method;
step S2, obtaining a correlation curve of the open-circuit voltage and the state of charge of the battery according to the result of the HPPC cycle condition experiment;
step S3, inputting the correlation curves of current, open-circuit voltage and state of charge of the battery dynamic stress test and the equivalent circuit model parameters of off-line identification into the battery equivalent circuit model to obtain the corresponding equivalent circuit model output voltage; comparing the error between the output voltage of the equivalent circuit model and the actual dynamic stress test voltage, and verifying the accuracy of the equivalent circuit model;
step S4, updating the equivalent circuit model parameters on line by using a recursive least square method containing forgetting factors;
and step S5, deducing a state space equation and an observation equation of the battery according to the mathematical expression of the equivalent circuit model, and estimating the state of charge of the lithium ion battery by using the adaptive extended Kalman particle filter.
2. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the mathematical expression of the equivalent circuit model in step S1 is as follows:
Figure FDA0003532115730000011
wherein, UocIs the open circuit voltage of the battery; r0Ohmic internal resistance of the battery; r is1And C1Is the resistance and capacitance representing the electrochemical polarization reaction of the cell; r2And C2Is the resistance and capacitance representing the concentration polarization reaction of the cell; u shapetIs the terminal voltage of the battery.
3. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific process of the HPPC experiment in step S1 is as follows: after the battery is kept stand for 5 minutes, when the voltage of the battery is charged to 4.2V by the current with the constant current of 0.5C, the battery is converted into a constant voltage charging mode; in the constant voltage charging mode, after the current of the battery is charged to be lower than 0.05C, the charging is stopped, and the battery is kept stand for 2 hours; discharging at 3C, standing the battery for 1 hour when the charge state is reduced by 10%, measuring the corresponding open-circuit voltage, and repeating the steps until the charge state of the battery is 0%.
4. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the offline identification process of the parameters in step S1 is as follows:
(1) according to the terminal voltage V1 second before the lithium ion battery is loaded with the HPPC pulse1Terminal voltage V at moment of loading HPPC pulse2End voltage V at the moment of finishing of loading HPPC pulse3And terminal voltage V1 second after the end of the HPPC pulse loading4Calculating ohmic resistance R in the lithium ion equivalent circuit0The calculation formula is as follows:
Figure FDA0003532115730000021
(2) the zero input voltage response of the battery in the standing process of the HPPC pulse charge-discharge experiment is as follows:
Figure FDA0003532115730000022
wherein, U1(0) And U2(0) Terminal voltages, τ, of two RC networks, respectively1＝R1C1，τ2＝R2C2(ii) a Fitting the above formula by using a fitting tool box of matlab, and calculating two time constants tau1And τ2The specific value of (a);
(3) the zero state response of the RC network in the HPPC pulse charging and discharging experiment process of the battery is as follows:
Figure FDA0003532115730000023
likewise, the above equation was fit in the matlab fitting toolsetTo obtain a specific R1And R2Taking the value of (A);
(4) according to the relation1＝R1C1，τ2＝R2C2And R already obtained1And R2Solve for C1And C2The specific value of (a).
5. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific model of the open-circuit voltage and state of charge correlation curve in step S2 is:
Uoc＝k1SOC6-k2SOC3+k3SOC4-k4SOC3+k5SOC2+k6SOC+k7
wherein k is1，k2…k7The coefficient to be fitted is obtained by fitting the open circuit voltage points at 10 states of charge.
6. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the dynamic stress test in step S3 refers to: carrying out a cyclic test on the battery under the dynamic stress working condition until the voltage is less than 3V; the dynamic stress working condition test method comprises the following steps that (1) one dynamic stress working condition comprises a plurality of charging and discharging pulses, 360 seconds are consumed when each dynamic stress working condition test is carried out, and the battery still needs to stand for 120 seconds before the next dynamic stress working condition test is carried out; the shortest duration time of a single discharge pulse in the dynamic stress working condition is 8 seconds, the longest duration time can reach 40 seconds, the maximum discharge current is 2C, and the maximum charge current is 0.5C.
7. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific step of step S4 includes:
(1) calculating the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor:
Figure FDA0003532115730000031
wherein y (k) is the real battery voltage at the current moment,
Figure FDA0003532115730000032
the vector is measured for the current time instant,
Figure FDA0003532115730000033
e (k) the error between the model output voltage and the actual battery output voltage obtained by the parameter identification result at the last moment;
(2) updating a gain matrix
Figure FDA0003532115730000034
Wherein, P (k-1) is a covariance matrix at the last moment, lambda is a forgetting factor, and K (k) is a gain matrix at the current moment;
(3) updating the covariance matrix for calculating the gain matrix at the next time instant
Figure FDA0003532115730000041
(4) Updating the current time parameter identification result by using the gain matrix and the error
Figure FDA0003532115730000042
8. The adaptive lithium ion battery state-of-charge estimation method of claim 1, wherein the state space equation and the observation equation of the battery in step S5 are respectively:
Figure FDA0003532115730000043
Ut,k＝Uoc,k-U1,k-U2,k-IkR0
wherein T is sampling time, k is discrete time variable, and Q is battery rated capacity.
9. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the particles of the adaptive extended kalman particle filter of step S5 are a series of random samples with weights, and the specific steps are as follows:
(1) initializing a set of particles
Figure FDA0003532115730000044
And the particle weight is set to
Figure FDA0003532115730000045
(2) Adaptive extended Kalman filtering as an importance sampling function
Figure FDA0003532115730000046
(3) The particle weights are updated according to:
Figure FDA0003532115730000047
(4) normalizing the weights:
Figure FDA0003532115730000048
(5) the effective number of particles was calculated according to the following formula:
Figure FDA0003532115730000049
wherein N iseffIs the effective number of particles, if NeffIf the sampling rate is less than 0.7N, resampling is needed;
(6) obtaining a current time estimation result:
Figure FDA0003532115730000051
(7) returning to step (2), setting k to k +1 until the loop is ended.
CN202210212196.5A 2022-03-04 2022-03-04 Self-adaptive lithium ion battery state of charge estimation method Pending CN114740385A (en)

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CN115469236A (en) * 2022-10-28 2022-12-13 北京航空航天大学 Battery SOC estimation method and device and electronic equipment

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