CN114779105A - Lithium battery pack inconsistency estimation method - Google Patents

Lithium battery pack inconsistency estimation method Download PDF

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CN114779105A
CN114779105A CN202210396495.9A CN202210396495A CN114779105A CN 114779105 A CN114779105 A CN 114779105A CN 202210396495 A CN202210396495 A CN 202210396495A CN 114779105 A CN114779105 A CN 114779105A
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battery pack
lithium battery
equivalent circuit
inconsistency
soc
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李刚
刘晗
曹馨予
孙彩棠
周逢道
韩滔
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Jilin University
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    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
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Abstract

The invention relates to the field of lithium batteries, in particular to an inconsistency estimation method of a lithium battery pack, which comprises the steps of discretizing a continuous time model of an equivalent circuit established based on a second-order RC equivalent circuit model and kirchhoff's law, and establishing an equivalent circuit discrete time model; the method comprises the steps of fitting parameter data of a lithium battery pack by adopting a least square method to obtain an initial value of a state variable of an equivalent circuit discrete time model, updating a coefficient matrix of the equivalent circuit discrete time model by adopting extended Kalman filtering to obtain SOC estimation values of a plurality of single batteries, calculating parameter values influencing the inconsistency of the battery pack by inductive transfer learning according to the SOC estimation values, and integrating the inconsistency parameters influencing the battery pack by adopting integrated learning to obtain adaptive weighted values. The accuracy of the SOC estimation value can be improved to a certain extent.

Description

Lithium battery pack inconsistency estimation method
Technical Field
The invention relates to the field of lithium batteries, in particular to an inconsistency estimation method of a lithium battery pack.
Background
With the rapid development of large-scale lithium battery energy storage systems, the management of the lithium battery energy storage system becomes one of the core technologies of the energy storage system, and the inconsistency estimation problem of the lithium battery pack is a technical difficulty in the management of the lithium battery energy storage system. There are many factors that cause inconsistency of the battery pack, for example, in the production process of the lithium battery, the steps and processes experienced are numerous and cumbersome, and thus, when the lithium battery pack is shipped, the lithium batteries themselves in the lithium battery pack have a difference problem. Because the self-discharge rate of different batteries causes the capacity loss of the batteries in the energy storage process, the batteries have the problem of inconsistency. In the process of charging and discharging, the lithium battery has the phenomenon of life decline. However, the operating temperature, depth of discharge, etc. of the unit cells in the battery pack cannot be maintained completely uniform. Therefore, the deterioration of each unit cell in the battery pack is also inconsistent.
In a large-scale energy storage process, the problem of inconsistency among batteries brings higher challenges to battery management systems, energy storage converters and other management systems of a battery system. The inconsistency problem of the energy storage battery system is mainly reflected in the inconsistency of parameters such as battery capacity, internal resistance and temperature. The inconsistency of the batteries can cause the problems of incomplete charging, incomplete discharging, non-uniform current among clusters and the like of an energy storage system.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an inconsistency estimation method for a lithium battery pack, which can improve the accuracy of an SOC estimation value to a certain extent.
The present invention is achieved in such a way that,
a method for estimating inconsistency of a lithium battery pack, comprising:
discretizing a continuous time model of the equivalent circuit established based on a second-order RC equivalent circuit model and kirchhoff's law, and then establishing an equivalent circuit discrete time model; the method comprises the steps of fitting parameter data of the lithium battery pack by adopting a least square method to obtain a state variable initial value of an equivalent circuit discrete time model, updating a coefficient matrix of the equivalent circuit discrete time model by adopting extended Kalman filtering to obtain SOC estimated values of a plurality of single batteries, calculating parameter values influencing the inconsistency of the battery pack through inductive transfer learning according to the SOC estimated values, and integrating the inconsistency parameters influencing the battery pack by adopting integrated learning to obtain adaptive weighted values.
Further, the single lithium battery is equivalent to internal resistance R1C1Ring and R2C2The continuous time model of the equivalent circuit is represented by the loop:
Figure BDA0003597426820000021
UL(t)＝OCV(SOC(t))-I(t)R0-URC1(t)-URC2(t)
where SOC (k) is an SOC estimation value at time k, UL(t) is terminal voltage of equivalent circuit terminal, OCV (. cndot.) is open-circuit voltage of lithium battery, URCIs R1C1Terminal voltage of URC2Is R2C2Terminal voltage of R0Is the internal resistance of the lithium battery, R1And R2For polarizing internal resistance, capacitance C1And C2A polarization capacitance;
obtaining an equivalent circuit discrete time model after dispersion:
Figure BDA0003597426820000022
Figure BDA0003597426820000023
wherein the matrix is replaced by a parameter such that,
Figure BDA0003597426820000031
Figure BDA0003597426820000032
SOC (k) is the SOC estimate at time k, URC1(k) Is at time k R1C1Terminal voltage of (U)RC2(k) Is R2C2Terminal voltage of Ak、BkAre coefficient matrices.
Further, parameters of the lithium battery pack in the model are obtained: 1) at room temperature, a brand-new lithium battery pack is fully charged according to an explanation mode; 2) standing for 1 h; 3) passing a constant current pulse test; 4) discharging 10% SOC; 5) standing for 1 h; 6) and repeating the steps of 3) and 5) until the electric quantity of the battery is consumed by 90%, and repeatedly testing the terminal voltage of the lithium battery pack, the terminal voltage of the single lithium battery and the load current data in the process.
Further, the obtained data are preprocessed: data preprocessing is carried out on the data by adopting a z-score standardization method, after an initial data set is obtained, whether voltage and current data are missing or not is judged, if the data are missing, a missing data reconstruction method is adopted to process the actual voltage and current, and then a complete data set is output; and if the data set does not have the data missing phenomenon, directly outputting the preprocessed data set.
Further, obtaining the SOC estimation value of the unit battery includes:
carrying out terminal voltage test on the single batteries in the battery pack to obtain the terminal voltage U of the single batteriesocThen pass through UocInquiring an initial value SOC (0) from a relation table of the SOC, and acquiring an initial value theta (0) of a state variable, wherein the initial value theta (0) of the state variable comprises a terminal voltage U of the single batteryoc(0) By internal resistance R of the battery0(0) (ii) a Internal resistance of polarization R1(0)，R2(0) (ii) a And a polarization capacitance, C1(0)，C2(0)；
Determining the state variable based on the initial value theta (0)Coefficient matrix A of equivalent circuit continuous time modelk、Bk；
Updating the coefficient matrix to A by adopting extended Kalman filteringk+1、Bk+1；
And repeating the updating process of the coefficient matrix to obtain SOC estimated values of the plurality of single batteries.
Further, updating the coefficient matrix using extended kalman filtering includes:
the lithium battery nonlinear system state equation and the observation equation are respectively expressed as follows:
Figure BDA0003597426820000041
the system state equation and the observation equation are developed by adopting a first-order Taylor formula to obtain:
Figure BDA0003597426820000042
Figure BDA0003597426820000043
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003597426820000044
measuring the updated state estimation value for the k moment;
Figure BDA0003597426820000045
Figure BDA0003597426820000046
and (3) performing linearization processing on a system state equation and an observation equation to obtain:
Figure BDA0003597426820000047
wherein
Figure BDA0003597426820000048
Comprises the following steps:
Figure BDA0003597426820000049
the initial conditions adopted are:
Figure BDA00035974268200000410
adopting a system equation and an observation equation to perform prior estimation and state prediction:
updating system state time: x is a radical of a fluorine atomk|k-1＝f(xk-1,uk-1)；
Updating the state covariance:
Figure BDA0003597426820000051
kalman gain:
Figure BDA0003597426820000052
posterior estimation and state correction:
and (3) updating the system state:
Figure BDA0003597426820000053
updating an error state matrix:
Figure BDA0003597426820000054
wherein, XkAnd ZkRespectively is a state vector and an observation vector at the kth moment; u. ukIs a control vector; w is akRepresenting process noise due to sensor error, wk～N(0,Qk),E(wk)＝0，QkIs a process noise covariance matrix; v. ofkRepresenting system noise due to uncertainty, vk～N(0,Rk)，E(vk)＝0，RkA covariance matrix which is the system noise; f (-) represents a non-linear mapping equation from the current state to the next state; h (-) represents a nonlinear mapping equation between the state quantity and the measurement quantity.
Further, the integration of the parameters affecting the inconsistency of the battery pack by adopting integrated transfer learning comprises the step of carrying out weighted voting by adopting AdaBoost classification, and the final strong classifier adopts a formula:
Figure BDA0003597426820000055
wherein α represents a weak learner weight coefficient, Gn(. -) represents a weak learner.
Compared with the prior art, the invention has the beneficial effects that:
compared with an ampere-hour integration method and a single extended Kalman filtering method, the method can estimate the SOC value more accurately and efficiently in real time.
Drawings
FIG. 1 is a schematic flow chart of the extended Kalman filtering and integrated transfer learning combined method of the present invention;
FIG. 2 is a schematic diagram of an ensemble learning process according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The invention provides a lithium battery pack inconsistency estimation method which comprises the following steps: discretizing a continuous time model of the equivalent circuit established based on a second-order RC equivalent circuit model and kirchhoff's law, and then establishing an equivalent circuit discrete time model; the method comprises the steps of fitting parameter data of the lithium battery pack by adopting a least square method to obtain a state variable initial value of an equivalent circuit discrete time model, updating a coefficient matrix of the equivalent circuit discrete time model by adopting extended Kalman filtering to obtain SOC estimated values of a plurality of single batteries, calculating parameter values influencing the inconsistency of the battery pack through inductive transfer learning according to the SOC estimated values, and integrating the inconsistency parameters influencing the battery pack by adopting integrated learning to obtain adaptive weighted values.
The second-order RC equivalent circuit model refers to that a single lithium battery is equivalent to internal resistance and two RC rings.
The parameters required by the second-order RC equivalent circuit model include: internal resistance R of lithium battery0Internal resistance to polarization R1And R2Polarization capacitance C1And C2. Using the state vector representation as: state vector θ ═ UocR0R1R2C1C2]T。
The continuous-time model of the equivalent circuit is as follows:
Figure BDA0003597426820000061
UL(t)＝OCV(SOC(t))-I(t)R0-URC1(t)-URC2(t)
where SOC (k) is an SOC estimation value at time k, UL(t) is the terminal voltage of the equivalent circuit, OCV (. cndot.) is the open-circuit voltage of the lithium battery, URC1Is R1C1Terminal voltage of URC2Is R2C2Terminal voltage of
The above model dispersion is: equivalent circuit discrete time model, as follows:
Figure BDA0003597426820000071
Figure BDA0003597426820000072
where SOC (k) is an SOC estimation value at time k, URC1(k) Is at time k R1C1Terminal voltage of URC2(k) Is R2C2The terminal voltage of (c).
The matrix is represented as:
Figure BDA0003597426820000073
Figure BDA0003597426820000074
the parameter acquisition process of the model comprises the following steps: 1) at room temperature, a brand-new lithium battery pack is fully charged according to an explanation mode; 2) standing for 1 h; 3) passing a constant current pulse test; 4) discharging 10% SOC; 5) standing for 1 h; 6) repeating 3) to 5) until the battery power is consumed by 90%. Repeatedly testing the terminal voltage of the lithium battery pack, the terminal voltage of the single lithium battery, load current data and the like in the process; normalization by z-score method:
Figure BDA0003597426820000075
normalizing the terminal voltage of the single lithium battery and then arranging the terminal voltage into a data set;
fitting the parameter data of the lithium battery pack by adopting a least square method to obtain a state variable initial value theta (0) of an equivalent circuit discrete time model; obtaining terminal voltage UocThen pass through UocThe initial value SOC (0) is looked up in the relation table with SOC.
Determining a coefficient matrix A by a mathematical expression of the equivalent circuit continuous time model according to the initial value theta (0) of the state variablek、Bk；
Updating coefficient matrix A by using extended Kalman filteringk+1、Bk+1(ii) a And repeating the process to obtain SOC estimated values of a plurality of single batteries.
Calculating parameter values influencing the inconsistency of the battery pack through a learning algorithm according to the SOC estimation value;
and integrating the parameters influencing the inconsistency of the battery pack through ensemble learning.
The method adopts extended Kalman filtering to process a nonlinear system of the lithium battery, and comprises the following system equations:
Figure BDA0003597426820000081
the system equation is developed by adopting a first-order Taylor formula to obtain:
Figure BDA0003597426820000082
Figure BDA0003597426820000083
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003597426820000084
measuring the updated state estimation value at the k moment;
Figure BDA0003597426820000085
Figure BDA0003597426820000086
system equation and observation equation ZkObtaining the following products after linearization treatment:
Figure BDA0003597426820000087
wherein
Figure BDA0003597426820000091
Comprises the following steps:
Figure BDA0003597426820000092
wherein x iskAnd zkRespectively is a state vector and an observation vector at the kth moment; u. ofkIs a control directionAn amount; w is akRepresenting process noise due to sensor error, wk～N(0,Qk),E(wk)＝0，QkIs a process noise covariance matrix; v. ofkRepresenting system noise, v, due to uncertainties such as system modelingk～N(0,Rk)，E(vk)＝0，RkA covariance matrix which is the system noise; f (-) represents a non-linear mapping equation from the current state to the next state; h (-) represents a nonlinear mapping equation between the state quantity and the measurement quantity.
The core part of the extended Kalman algorithm is as follows:
a) initial conditions:
Figure BDA0003597426820000093
b) prior estimation and state prediction:
updating system state time: x is the number ofk|k-1＝f(xk-1,uk-1)；
Updating the state covariance:
Figure BDA0003597426820000094
kalman gain:
Figure BDA0003597426820000095
c) posterior estimation and state correction:
and (3) updating the system state:
Figure BDA0003597426820000096
updating an error state matrix:
Figure BDA0003597426820000097
and expanding the SOC estimation value output by the Kalman filtering algorithm based on a characteristic mode, and adding the SOC estimation value into a target learning model to perform inductive transfer learning, wherein the target learning model is transfer learning.
The transfer learning is to transfer the knowledge in the source field to the target field, so that the target field can obtain better learning effect.
And sorting the learning results by adopting an AdaBoost classification method in an integrated algorithm to obtain an adaptive weight value and improve the accuracy of the result.
The AdaBoost classification carries out weighting voting, and the final strong classifier adopts a formula:
Figure BDA0003597426820000101
wherein α represents a weak learner weight coefficient, Gn(. cndot.) represents a weak learner.
Referring to fig. 2, an implementation flow of AdaBoost classification is as follows:
1. training using multiple loop iterations
2. Aggregating the weak classifiers trained for multiple times, and combining the weak classifiers into a strong classifier
3. And outputting a final prediction result.
Examples
In the embodiment, a research is carried out by taking a panasonic lithium ion battery 18650B as an object, the nominal voltage is 3.7V, and the rated capacity of the battery is 3400 mAh. And (3) after the battery pack is fully filled in a CC-CV mode and stands for one hour, carrying out HPPC test on the battery pack until the voltage is reduced to cut-off voltage, and repeating the experiment.
The method comprises the following steps: step 1) acquiring data such as voltage, current, temperature and the like of a lithium battery pack through a charge-discharge experiment; step 2) preprocessing the data, constructing an initial data set (corresponding to a lithium battery pack), and dividing the data into n initial subdata sets (corresponding to each single lithium battery); step 3) processing the initial subdata set through an extended Kalman filtering transfer learning algorithm to form a new subdata set (updated data); and 4) setting different weight values for the sub-data sets through integrated learning, and obtaining a real-time SOC value of the lithium battery pack for estimating the inconsistency of the lithium battery pack.
The process for acquiring the parameters of the lithium battery pack comprises the following steps: 1) at room temperature, a brand-new lithium battery pack is fully charged according to an explanation mode; 2) standing for 1 h; 3) passing a constant current pulse test; 4) discharging 10% SOC;
5) standing for 1 h; 6) repeating 3) to 5) until the battery power is consumed by 90%. Repeatedly testing the terminal voltage of the lithium battery pack, the terminal voltage of the single lithium battery, load current data and the like in the process;
normalization method by z-score:
Figure BDA0003597426820000111
normalizing the terminal voltage of the single lithium battery and then sorting the terminal voltage into a data set;
and establishing an equivalent circuit continuous time model of the single battery by utilizing the kirchhoff voltage law based on a second-order RC equivalent circuit model. Establishing a second-order equivalent circuit model according to the internal structure and the internal reaction of the circuit, namely, the battery model is equivalent to an internal resistance and an RC ring; the more RC rings, the more the dynamic characteristics of the battery can be simulated, and in consideration of actual use, in order to avoid overlarge calculation amount, two-order RC rings are selected.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

Claims (7)

1. A method for estimating inconsistency of a lithium battery pack, comprising:
discretizing a continuous time model of the equivalent circuit established based on a second-order RC equivalent circuit model and kirchhoff's law, and establishing an equivalent circuit discrete time model; the method comprises the steps of fitting parameter data of the lithium battery pack by adopting a least square method to obtain a state variable initial value of an equivalent circuit discrete time model, updating a coefficient matrix of the equivalent circuit discrete time model by adopting extended Kalman filtering to obtain SOC estimated values of a plurality of single batteries, calculating parameter values influencing the inconsistency of the battery pack through inductive transfer learning according to the SOC estimated values, and integrating the inconsistency parameters influencing the battery pack by adopting integrated learning to obtain adaptive weighted values.
2. The method of estimating the inconsistency of a lithium battery pack according to claim 1, wherein a single lithium battery is equivalent to an internal resistance, R1C1Ring and R2C2The continuous time model of the equivalent circuit is represented by the loop:
Figure FDA0003597426810000011
UL(t)＝OCV(SOC(t))-I(t)R0-URC1(t)-URC(t)
where SOC (k) is an SOC estimation value at time k, UL(t) is the terminal voltage of the equivalent circuit, OCV (. cndot.) is the open-circuit voltage of the lithium battery, URC1Is R1C1Terminal voltage of (U)RC2Is R2C2Terminal voltage of R0Is the internal resistance of the lithium battery, R1And R2For polarizing internal resistance, C1And C2Is a polarization capacitance;
obtaining an equivalent circuit discrete time model after the dispersion:
Figure FDA0003597426810000021
Figure FDA0003597426810000022
wherein the matrix is replaced by a parameter such that,
Figure FDA0003597426810000023
Figure FDA0003597426810000024
SOC (k) is the estimated value of SOC at time k, URC1(k) Is at time k R1C1Terminal voltage of URC2(k) Is R2C2Terminal voltage of Ak、BkAre coefficient matrices.
3. The lithium battery pack inconsistency estimation method according to claim 1, wherein the parameters of the lithium battery pack in the model are obtained by: 1) at room temperature, a brand-new lithium battery pack is fully charged according to an explanation mode; 2) standing for 1 h; 3) passing a constant current pulse test; 4) discharging 10% SOC; 5) standing for 1 h; 6) and repeating 3) -5) until the electric quantity of the battery is consumed by 90%, and repeatedly testing the terminal voltage of the lithium battery pack, the terminal voltage of the single lithium battery and the load current data in the process.
4. The lithium battery pack inconsistency estimation method according to claim 3, wherein the obtained data is preprocessed: data preprocessing is carried out on the data by adopting a z-score standardization method, after an initial data set is obtained, whether voltage and current data are missing or not is judged, if the data are missing, a missing data reconstruction method is adopted to process the actual voltage and current, and then a complete data set is output; and if the data set does not have the data missing phenomenon, directly outputting the preprocessed data set.
5. The lithium battery pack inconsistency estimation method according to claim 2, wherein obtaining the SOC estimation value of the unit cell comprises:
carrying out terminal voltage test on the single batteries in the battery pack to obtain the terminal voltage U of the single batteriesocThen pass through UocAnd the initial value SOC (0) is inquired in the relation table of the SOC, and the initial value theta (0) of the state variable is obtained, wherein the initial value theta (0) of the state variable comprises the terminal voltage U of the single batteryoc(0) By internal resistance R of the battery0(0) (ii) a Internal resistance to polarization R1(0)，R2(0) (ii) a And polarized electricityC of container1(0)，C2(0)；
Determining a coefficient matrix A of the equivalent circuit continuous time model based on the initial value theta (0) of the state variablek、Bk；
Updating coefficient matrix to be A by adopting extended Kalman filteringk+1、Bk+1；
And repeating the updating process of the coefficient matrix to obtain SOC estimated values of the plurality of single batteries.
6. The lithium battery pack inconsistency estimation method according to claim 5, wherein updating the coefficient matrix using extended kalman filtering comprises:
the lithium battery nonlinear system state equation and the observation equation are respectively expressed as follows:
Figure FDA0003597426810000031
the system state equation and the observation equation are developed by adopting a first-order Taylor formula to obtain:
Figure FDA0003597426810000032
Figure FDA0003597426810000033
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003597426810000034
measuring the updated state estimation value for the k moment;
Figure FDA0003597426810000035
Figure FDA0003597426810000036
the system state equation and the observation equation are subjected to linearization treatment to obtain:
Figure FDA0003597426810000037
wherein
Figure FDA0003597426810000041
Comprises the following steps:
Figure FDA0003597426810000042
the initial conditions adopted are:
Figure FDA0003597426810000043
adopting a system state equation and an observation equation to perform prior estimation and state prediction:
updating system state time: x is a radical of a fluorine atomk|k-1＝f(xk-1，uk-1)；
Updating the state covariance:
Figure FDA0003597426810000044
kalman gain:
Figure FDA0003597426810000045
posterior estimation and state correction:
and (3) updating the system state:
Figure FDA0003597426810000046
updating an error state matrix:
Figure FDA0003597426810000047
wherein XkAnd ZkRespectively a state vector and an observation vector at the kth moment; u. ukIs a control vector; w is akRepresenting process noise due to sensor error, wk～N(0，Qk)，E(wk)＝0，QkIs a process noise covariance matrix; v. ofkRepresenting system noise, v, due to uncertaintyk～N(0，Rk)，E(vk)＝0，RkA covariance matrix which is the system noise; f (-) represents a non-linear mapping equation from the current state to the next state; h (-) represents a nonlinear mapping equation between the state quantity and the measurement quantity.
7. The lithium battery pack inconsistency estimation method according to claim 1, wherein the integration of the battery pack inconsistency affecting parameters by means of ensemble transfer learning comprises weighted voting by means of AdaBoost classification, and a final strong classifier adopts a formula:
Figure FDA0003597426810000051
wherein α represents a weak learner weight coefficient, Gn(. -) represents a weak learner.
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CN117590259A (en) * 2023-11-22 2024-02-23 昆明理工大学 Migration model-based lithium battery pack full-life wide-temperature SOC efficient estimation method

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