CN111581904A - Lithium battery SOC and SOH collaborative estimation method considering influence of cycle number - Google Patents

Lithium battery SOC and SOH collaborative estimation method considering influence of cycle number Download PDF

Info

Publication number
CN111581904A
CN111581904A CN202010306668.4A CN202010306668A CN111581904A CN 111581904 A CN111581904 A CN 111581904A CN 202010306668 A CN202010306668 A CN 202010306668A CN 111581904 A CN111581904 A CN 111581904A
Authority
CN
China
Prior art keywords
estimation
state
battery
lithium battery
soc
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010306668.4A
Other languages
Chinese (zh)
Other versions
CN111581904B (en
Inventor
庞辉
牟联晶
武龙星
郭龙
晋佳敏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xian University of Technology
Original Assignee
Xian University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xian University of Technology filed Critical Xian University of Technology
Priority to CN202010306668.4A priority Critical patent/CN111581904B/en
Publication of CN111581904A publication Critical patent/CN111581904A/en
Application granted granted Critical
Publication of CN111581904B publication Critical patent/CN111581904B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • 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
    • 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]
    • G01R31/392—Determining battery ageing or deterioration, e.g. state of health
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Abstract

The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number comprises the following steps: step 1, constructing a lithium battery equivalent circuit model considering cycle times; step 2, identifying model parameters; step 3, carrying out simulation verification on the model established in the step 1; and step 4, constructing an SOC/SOH collaborative estimator. The method can finally realize the estimation of the State-of-charge (SOC) and the State-of-health (SOH) of the battery in the full life range of the lithium battery, has great significance for the State estimation and the energy management of the battery management system of the electric vehicle, solves the problems of large State estimation error and the like caused by inaccurate models in different life cycles, effectively improves the utilization efficiency of the power battery pack, and ensures the service life of the battery pack.

Description

Lithium battery SOC and SOH collaborative estimation method considering influence of cycle number
Technical Field
The invention belongs to the technical field of power battery management systems, and particularly relates to a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times.
Background
With the vigorous development of the electric automobile market, the lithium battery is widely used as a power source of the electric automobile. In order to ensure safe and reliable operation of the Battery pack, good monitoring, control, and management by a Battery Management System (BMS) are required. For battery management systems, the core function is to provide accurate estimation of the State-of-charge (SOC) and State-of-health (SOH) of the battery, which is a huge challenge. Since the existing vehicle-mounted sensor cannot observe these two states, it is necessary to develop a feasible state estimation algorithm.
The state of charge is a key factor of the residual capacity of the battery system, and is helpful for predicting the residual driving mileage and the endurance time of the electric automobile. At present, research on SOC estimation algorithms is abundant, and common algorithms include coulomb counting method, model-based open circuit voltage method, neural network method and kalman filtering method. The Kalman filtering is a comprehensive algorithm comprising a coulomb counting method and an OCV prediction method based on a model, has the advantages of high precision, strong robustness and the like, and is widely applied in recent years.
State of health describes the degree of battery aging, which can be generally reflected by a loss of capacity or an increase in resistance. The existing estimation method mainly comprises the following steps: direct measurement, voltage trajectory, compatibilization analysis, differential voltage analysis, kalman filtering, particle filtering, neural network, vector machine, genetic algorithms, and artificial intelligence algorithms.
However, as the battery is cycled, the battery parameters, including capacity and impedance, may change as the battery degrades, thereby affecting the accuracy of the algorithm's estimation of the battery SOC and SOH. Therefore, in order to improve the estimation performance of SOC and SOH, it is necessary to consider the cycle aging of the lithium battery and propose a cooperative estimator that monitors the state of charge and the state of health of the battery at the same time.
In summary, a combined state estimation scheme capable of estimating SOC and SOH simultaneously is an urgent problem to be solved in the technical field of power battery management systems at present. The method has great significance for protecting the battery system, improving the performance of the whole vehicle and improving the economy.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, overcomes the limitation that the traditional equivalent circuit model is only suitable for a certain life cycle range, and greatly improves the applicability of BMS state calculation and energy management in the whole life cycle.
In order to achieve the purpose, the invention adopts the technical scheme that: the lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number comprises the following steps:
step 1, constructing a lithium battery equivalent circuit model considering cycle times;
step 2, identifying model parameters by adopting a recursive least square method;
step 3, carrying out simulation verification on the lithium battery equivalent circuit model established in the step 1 under a constant current working condition;
and 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery.
The lithium battery equivalent circuit model constructed in the step 1 has a mathematical relation as follows:
Figure BDA0002456034770000021
in the formula (1), UtIs the battery terminal voltage; u shapeOC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r0Ohmic internal resistance; r1And C1Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r2And C2Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be0(Cyc),R1(Cyc),C1(Cyc),R2(Cyc),C2(Cyc) is written as R0,R1,C1,R2And C2，ItRepresents the operating current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
And 2, identifying the parameters of the model in the step 2 by adopting a Recursive least square method (RLS) to obtain the model parameters under different cycle times, wherein the specific formula comprises the following steps:
the terminal voltage is subjected to laplace transform:
Figure BDA0002456034770000031
it is provided that,
E＝Ut-UOC(3)
the model transfer function is:
Figure BDA0002456034770000032
the method is simplified as follows:
Figure BDA0002456034770000033
the Tustin transform maps the s-plane based system equation to the z-plane:
Figure BDA0002456034770000034
the discrete transfer function based on the z-plane is:
G(z-1)＝[a3+a4z-1+a5z-2]/[1-a1z-1-a2z-2](7)
the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:
E(l)＝a1E(l-1)+a2E(l-2)+a3I(l)+a4I(l-1)+a5I(l-2) (8)
defining a data variable Ψ for a systemlAnd parametersVariable thetalComprises the following steps:
Figure BDA0002456034770000035
the time domain difference equation (8) can be rewritten as:
zl＝Ψlθl+eLs,l(10)
the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:
Figure BDA0002456034770000041
the parameter variables and error covariance are initialized as:
Figure BDA0002456034770000042
inverse transformation using equation (6)
Figure BDA0002456034770000043
Then, equation (7) can be rewritten as:
Figure BDA0002456034770000044
comparing equation (7) and equation (14), we can obtain:
Figure BDA0002456034770000045
in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is1＝R1C1，τ2＝R2C2(ii) a T is the sampling interval time of the system; a is1,a2,a3,a4And a5Unknown parameters related to model parameters; ΨlRepresenting system data variables; thetalRepresenting a parameter variable; in the formula zlAn output variable representing the system; e.g. of the typeLs,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 106And I represents an identity matrix.
And 3, performing simulation verification on the lithium battery equivalent circuit model, specifically:
under MATLAB/Simulink environment, build the lithium cell equivalent circuit model that considers the cycle number influence, wherein the input is: current, cycle number, output as voltage; the verification is carried out under seven different circulation times of [301002003006008001000] respectively by using a Constant current condition test (CCC).
In step 4, a cooperative estimator considering the cycle number is constructed to estimate the SOC and the SOH of the lithium battery, and the method specifically comprises the following steps:
step 4.1, establishing a discrete state space model of the lithium battery system:
according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the lithium battery are calculated1Concentration polarization voltage U2Ohmic internal resistance R0And reciprocal 1/C of capacitycapSelecting measurable battery terminal voltage U as state variabletAs observed quantity, a state prediction equation and an observation equation (16) are established,
Figure BDA0002456034770000051
first, a system state matrix x is definedkDefining the system output ykAnd system input uk：
Figure BDA0002456034770000052
Figure BDA0002456034770000053
Figure BDA0002456034770000054
Figure BDA0002456034770000055
The algorithm formula is as follows:
Figure BDA0002456034770000056
in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. thek-1Is a system matrix; b isk-1Is a control matrix; ckOutputting a matrix for the system; u. ofkInputting for the system; t isSFor a sampling period, P-And P+Respectively state estimation covariance prior estimation and posterior estimation, K is Kalman gain, e is innovation matrix, I is unit matrix, η is Coulomb efficiency, and assuming 1 during charging and 0.98 during discharging, Ccap,kThe maximum available capacity of the battery under the current cycle; cfreshThe maximum available capacity of the battery when leaving the factory; rfreshInternal resistance for the first cycle of the battery; reolIndicating the internal resistance of the battery at the end of its life; r0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,
Figure BDA0002456034770000061
step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the SOC and SOH collaborative estimation of the lithium battery is carried out by using a self-adaptive extended Kalman filter:
1) initialization:
at t0At time, i.e., when k is 0, an initial value x of the state observer is set0,P0,Q0,R0；
2) A priori estimate-predict: time update [ State Slave time (k-1)+Arrival time (k)-Is calculated by]
For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)+Reckoning to the current time (k)-The time update equation of the adaptive extended kalman filter is expressed as follows:
and (3) system state estimation:
Figure BDA0002456034770000062
estimating error covariance:
Figure BDA0002456034770000063
wherein, f (x)k-1,uk-1) Representing a system equation of state function;
3) a posteriori estimation-correction: measurement update [ State Slave time (k)-Arrival time (k)+Is calculated by]
This step uses the measured value y at the time kkCorrecting state estimation and covariance estimation, the estimation results being used separately
Figure BDA0002456034770000064
And
Figure BDA0002456034770000065
expressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:
an innovation matrix:
Figure BDA0002456034770000071
kalman gain matrix:
Figure BDA0002456034770000072
adaptive noise covariance matching:
Figure BDA0002456034770000073
and (3) correcting the system state:
Figure BDA0002456034770000074
error covariance correction:
Figure BDA0002456034770000075
4) time scale update
Time of day (k)+The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.
Compared with the prior art, the invention can obtain the following technical effects:
the invention provides a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, overcomes the limitation that the traditional model is only suitable for a certain specific cycle range, and greatly improves the applicability of a Battery Management System (BMS) in the full life cycle range in state calculation and energy management. The estimator constructed by the invention can more accurately describe the external characteristics of the power battery, and has positive significance for improving state calculation and energy management in the BMS and subsequent battery thermal management and safety management. Therefore, the lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number has good practicability and application value in BMS and engineering.
The method can finally realize the estimation of the state of charge and the state of health of the battery in the whole life cycle range, has great significance for the state estimation and the energy management of the battery management system of the electric vehicle, solves the problems of large SOC/SOH estimation error and the like caused by inaccurate models due to different cycle times, and effectively improves the utilization efficiency of the power battery pack and the real-time monitoring of the service life of the battery. In an electric automobile, the protection of a battery system, the improvement of the performance of the whole automobile and the improvement of the economical efficiency are all significant.
Drawings
FIG. 1 is a schematic diagram of SOC and SOH estimation process according to the present invention.
Fig. 2 is a schematic diagram of a battery model according to the present invention.
FIG. 3 is a schematic diagram of the OCV-SOC curves for different cycles of the present invention.
Fig. 4 is a schematic diagram of the variation of the battery voltage under the constant current discharge condition of the invention.
FIG. 5 is a graph showing a comparison curve between a measured voltage and a simulated voltage in model verification according to the present invention.
FIG. 6 is a schematic diagram of an error curve of the measured voltage and the simulated voltage according to the present invention.
Fig. 7 is a diagram illustrating the maximum available capacity at different cycles of the present invention.
FIG. 8 is a schematic diagram of a SOC and SOH co-estimation process according to the present invention.
FIG. 9 is a diagram illustrating a comparison curve between the experimental SOC and the estimated SOC under the CCC condition according to the present invention.
FIG. 10 is a schematic diagram of an experimental SOC versus estimated SOC error curve according to the present invention.
FIG. 11 is a graphical representation of measured versus estimated capacity curves for the CCC condition of the present invention.
FIG. 12 is a graph illustrating measured capacity versus estimated capacity error curves in accordance with the present invention.
FIG. 13 is a schematic diagram of capacity and SOH estimation according to the present invention.
FIG. 14 is a graphical illustration of a comparison of the identified internal resistance to the estimated internal resistance for the CCC condition of the present invention.
FIG. 15 is a schematic diagram of an error curve of identifying the internal resistance and estimating the internal resistance according to the present invention.
FIG. 16 is a schematic diagram of the internal resistance and SOH estimation of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention discloses a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, the realization process is shown in figure 1, and the method specifically comprises the following steps:
step 1, constructing a lithium battery equivalent circuit model considering cycle times;
the universal second-order RC equivalent circuit model has the advantages of high calculation efficiency, easiness in engineering realization, good battery dynamic behavior simulation and the like, and is widely applied to power battery modeling and state estimation. However, as the battery is recycled, especially after hundreds of cycles of charge and discharge, the battery capacity is attenuated, the internal resistance is increased, and the accuracy of the battery model is reduced, the invention provides an improved second-order RC circuit model considering different cycles on the basis of the second-order RC model, as shown in FIG. 2, wherein the model parameter R0(Cyc),R1(Cyc),C1(Cyc),R2(Cyc),C2(Cyc) is a function of the Cycle number, and for the sake of brevity, the parameters are each written as R0,R1,C1,R2,C2(ii) a In addition, the difference of the OCV-SOC relationship under different Cycle times is considered, the consideration on the OCV-SOC is increased, the OCV-SOC-Cycle relationship is established, as shown in FIG. 3, according to kirchhoff's law, the mathematical relationship is shown as formula (1),
Figure BDA0002456034770000091
in the formula (1), UtIs the battery terminal voltage; u shapeOC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r0Ohmic internal resistance; r1And C1Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r2And C2Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be0(Cyc),R1(Cyc),C1(Cyc),R2(Cyc),C2(Cyc) is written as R0,R1,C1,R2And C2，ItRepresents the operating current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
Step 2, identifying model parameters by adopting a recursive least square method;
in the step 2 of the invention, model parameters are identified by using a Recursive least square method (RLS), and model parameters under different cycle times are respectively obtained by using constant current discharge working conditions (shown in figure 4) under different cycles [301002003006008001000], wherein the specific formula is as follows:
the terminal voltage is subjected to laplace transform:
Figure BDA0002456034770000092
it is provided that,
E＝Ut-UOC(3)
the model transfer function is:
Figure BDA0002456034770000101
the method is simplified as follows:
Figure BDA0002456034770000102
the Tustin transform maps the s-plane based system equation to the z-plane:
Figure BDA0002456034770000103
the discrete transfer function based on the z-plane is:
G(z-1)＝[a3+a4z-1+a5z-2]/[1-a1z-1-a2z-2](7)
the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:
E(l)＝a1E(l-1)+a2E(l-2)+a3I(l)+a4I(l-1)+a5I(l-2) (8)
defining a data variable Ψ for a systemlAnd a parameter variable thetalComprises the following steps:
Figure BDA0002456034770000104
the time domain difference equation (8) can be rewritten as:
zl＝Ψlθl+eLs,l(10)
the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:
Figure BDA0002456034770000105
the parameter variables and error covariance are initialized as:
Figure BDA0002456034770000106
inverse transformation using equation (6)
Figure BDA0002456034770000107
Then, equation (7) can be rewritten as:
Figure BDA0002456034770000108
comparing equation (7) and equation (14), we can obtain:
Figure BDA0002456034770000111
in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is1＝R1C1，τ2＝R2C2(ii) a T is the sampling interval time of the system; a is1,a2,a3,a4And a5Unknown parameters related to model parameters; ΨlRepresenting system data variables; thetalRepresenting a parameter variable; in the formula zlAn output variable representing the system; e.g. of the typeLs,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 106And I represents an identity matrix.
And 3, carrying out simulation verification on the model established in the step 1 under the constant-current working condition, specifically:
the parameters R under different cycles can be obtained through the parameter identification in the step 20、R1、C1、R2、C2Numerical value of (1). Then, under the MATLAB/Simulink environment, a lithium ion battery equivalent circuit model considering the influence of different cycle times is built, wherein the input is as follows: current, cycle number, output is terminal voltage. The Constant Current Condition (CCC) is respectively tested at [301002003006008001000]]Performing simulation under seven different Cycle times, taking Cycle30 as an example, as shown in fig. 5, comparing the measured voltage with the simulated voltage, and obtaining a corresponding error of 0.019 as shown in fig. 6; other cycles [ 1002003006008001000]The lower errors are respectively [ 0.0190.0180.0160.0210.0220.019]；
Step 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery, specifically:
step 4.1, establishing a discrete state space model of the lithium battery system:
according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the battery are calculated1Concentration polarization voltage U2Ohmic internal resistance R0And reciprocal 1/C of capacitycapSelecting measurable battery terminal voltage U as state variabletAs observed quantity, a state prediction equation and an observation equation (16) are established,
Figure BDA0002456034770000112
first, a system state matrix x is definedkDefining the system output ykAnd system input uk：
Figure BDA0002456034770000121
Figure BDA0002456034770000122
The SOH is defined in terms of the remaining capacity of the battery, which can be measured directly after the battery has been used for a certain period of time. The invention is provided with CfreshIs the maximum available capacity, C, of the battery when leaving the factorycap,kFor the current maximum available capacity of the battery, the change at different cycles is shown in FIG. 7, and then the SOH[Ccap]Is defined as:
Figure BDA0002456034770000123
since the battery SOH is attenuated as the internal resistance of the battery gradually increases, the battery SOH may be defined according to this relationship, wherein R isfreshInternal resistance for the first cycle of the battery; reolIndicating the internal resistance of the battery at the end of its life; r0,kThe internal resistance of the battery in the current state is the battery SOH[R0]Is defined as:
Figure BDA0002456034770000124
the algorithm formula of the self-adaptive extended Kalman filter is as follows:
Figure BDA0002456034770000125
in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. thek-1Is a system matrix; b isk-1Is a control matrix; ckOutputting a matrix for the system; u. ofkInputting for the system; t isSFor a sampling period, P-And P+Respectively state estimation covariance prior estimation and posterior estimation, K is Kalman gain, e is innovation matrix, I is unit matrix, η is Coulomb efficiency, and assuming 1 during charging and 0.98 during discharging, Ccap,kThe maximum available capacity of the battery under the current cycle; cfreshThe maximum available capacity of the battery when leaving the factory; rfreshInternal resistance for the first cycle of the battery; reolIndicating the internal resistance of the battery at the end of its life; r0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,
Figure BDA0002456034770000131
step 4.2, aiming at the model constructed in step 4.1, a specific process shown in fig. 8 is implemented for the cooperative estimation implementation flow of the SOC and SOH of the lithium battery by using an Adaptive Extended Kalman Filter (AEKF):
1) initialization:
at t0At time, i.e., when k is 0, the initial value of the state observer is set: x is the number of0,P0,Q0,R0；
2) A priori estimate-predict: time update [ State Slave time (k-1)+Arrival time (k)-Is calculated by]
For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)+Reckoning to the current time (k)-The time update equation of the adaptive extended kalman filter is expressed as follows:
and (3) system state estimation:
Figure BDA0002456034770000132
estimating error covariance:
Figure BDA0002456034770000133
wherein, f (x)k-1,uk-1) Representing a system equation of state function;
3) a posteriori estimation-correction: measurement update [ State Slave time (k)-Arrival time (k)+Is calculated by]
This step uses the measured value y at the time kkCorrecting state estimation and covariance estimation, the estimation results being used separately
Figure BDA0002456034770000134
And
Figure BDA0002456034770000135
expressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:
an innovation matrix:
Figure BDA0002456034770000141
kalman gain matrix:
Figure BDA0002456034770000142
adaptive noise covariance matching:
Figure BDA0002456034770000143
and (3) correcting the system state:
Figure BDA0002456034770000144
error covariance correction:
Figure BDA0002456034770000145
4) time scale update
Time of day (k)+The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.
In order to verify the accuracy of the constructed SOC and SOH collaborative estimator, a second-order RC equivalent circuit model considering the influence of different cycle times is firstly established in an MATLAB/Simulink environment, and a measured constant-current working condition experimental curve is compared with a model simulation curve by identifying model parameters and simulating the accuracy of a verification model. Finally, constructing a SOC and SOH co-estimator, wherein the SOH estimation comprises estimating the SOH as a representation of the maximum available capacity of the battery[Ccap]And estimating SOH for battery internal resistance characterization[R0]. For simplicity, a cyclic Cycle30 is used as an example, wherein the comparison curve of the experimental SOC and the estimated SOC is shown in FIG. 9, and the average absolute error is 0.26% as shown in FIG. 10. In addition, the average absolute error under constant current working condition in other cycles [ 1002003006008001000]]Respectively, the content of the components is [ 0.24%, 0.22%, 0.20%, 0.86%, 1.14%, 1.36%]. A graph of measured versus estimated capacity under cyclic 30 conditions is shown in FIG. 11, with an average absolute error of 0.018Ah as shown in FIG. 12. In addition, other cycles [ 1002003006008001000] may also be obtained]The lower errors are respectively [ 0.0160.0190.0200.0190.0210.022]Ah. Wherein, according to equation (19), a SOH estimation diagram characterized by capacity can be obtained, as shown in fig. 13. A graph of the comparison curve of the identified internal resistance and the estimated internal resistance under the condition of the cyclic 30 is shown in FIG. 14, and the error of the comparison curve is 0.00142 Ω shown in FIG. 15. In addition, other cycles [ 1002003006008001000] may also be obtained]The lower errors are respectively [ 0.001330.001500.001560.001580.001670.00187]Omega. Wherein, according to equation (20), a SOH estimation diagram characterized by internal resistance can be obtained, as shown in fig. 16. As can be seen from the error range, the estimator of the invention has long application period and has great significance for BMS state estimation and energy management.
The simulation and estimation data show that the estimation method provided by the invention can be controlled within a smaller error range in SOC estimation, capacity and resistance estimation, so that the effectiveness and the accuracy of the estimation method are verified, the application of the electric vehicle in the whole life cycle range is improved, the problems of larger state estimation error and the like caused by inaccurate models due to different life cycles are solved, and the method has great significance for state estimation and energy management of a battery management system of the electric vehicle; the method plays an important role in the utilization efficiency, the service life and the performance of the whole power battery pack.
While the foregoing specification illustrates and describes several preferred embodiments of the invention, it is to be understood, as noted above, that the invention is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number is characterized by comprising the following steps of:
step 1, constructing a lithium battery equivalent circuit model considering cycle times;
step 2, identifying model parameters by adopting a recursive least square method;
step 3, carrying out simulation verification on the lithium battery equivalent circuit model established in the step 1 under a constant current working condition;
and 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery.
2. The lithium battery SOC and SOH collaborative estimation method considering influence of cycle times according to claim 1, wherein a mathematical relation of the lithium battery equivalent circuit model constructed in the step 1 is as follows:
Figure FDA0002456034760000011
formula (1)) In, UtIs the battery terminal voltage; u shapeOC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r0Ohmic internal resistance; r1And C1Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r2And C2Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be0(Cyc),R1(Cyc),C1(Cyc),R2(Cyc),C2(Cyc) is written as R0,R1,C1,R2And C2，ItRepresents the operating current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
3. The lithium battery SOC and SOH collaborative estimation method considering cycle frequency influence according to claim 1, wherein the model parameters are identified in step 2 by using a recursive least square method to obtain model parameters under different cycle frequencies, and the specific formula comprises:
the terminal voltage is subjected to laplace transform:
Figure FDA0002456034760000021
it is provided that,
E＝Ut-UOC(3)
the model transfer function is:
Figure FDA0002456034760000022
the method is simplified as follows:
Figure FDA0002456034760000023
the Tustin transform maps the s-plane based system equation to the z-plane:
Figure FDA0002456034760000024
the discrete transfer function based on the z-plane is:
G(z-1)＝[a3+a4z-1+a5z-2]/[1-a1z-1-a2z-2](7)
the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:
E(l)＝a1E(l-1)+a2E(l-2)+a3I(l)+a4I(l-1)+a5I(l-2) (8)
defining a data variable Ψ for a systemlAnd a parameter variable thetalComprises the following steps:
Figure FDA0002456034760000025
the time domain difference equation (8) can be rewritten as:
zl＝Ψlθl+eLs,l(10)
the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:
Figure FDA0002456034760000026
the parameter variables and error covariance are initialized as:
Figure FDA0002456034760000027
inverse transformation using equation (6)
Figure FDA0002456034760000031
Then, equation (7) can be rewritten as:
Figure FDA0002456034760000032
comparing equation (7) and equation (14), we can obtain:
Figure FDA0002456034760000033
in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is1＝R1C1，τ2＝R2C2(ii) a T is the sampling interval time of the system; a is1,a2,a3,a4And a5Unknown parameters related to model parameters; ΨlRepresenting system data variables; thetalRepresenting a parameter variable; in the formula zlAn output variable representing the system; e.g. of the typeLs,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 106And I represents an identity matrix.
4. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number according to claim 1, wherein the simulation verification is performed on the lithium battery equivalent circuit model in the step 3, and specifically comprises the following steps:
under MATLAB/Simulink environment, build the lithium cell equivalent circuit model that considers the cycle number influence, wherein the input is: current, cycle number, output as voltage; the test is carried out under seven different circulation times by using a constant-current working condition test respectively [301002003006008001000 ].
5. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle times as claimed in claim 1, wherein the step 4 is to construct a collaborative estimator considering the cycle times to estimate the SOC and the SOH of the lithium battery, specifically:
step 4.1, establishing a discrete state space model of the lithium battery system:
according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the lithium battery are calculated1Concentration polarization voltage U2Ohmic internal resistance R0And reciprocal 1/C of capacitycapSelecting measurable battery terminal voltage U as state variabletAs observed quantity, a state prediction equation and an observation equation (16) are established,
Figure FDA0002456034760000041
first, a system state matrix x is definedkDefining the system output ykAnd system input uk：
Figure FDA0002456034760000042
Figure FDA0002456034760000043
Figure FDA0002456034760000044
Figure FDA0002456034760000045
The algorithm formula is as follows:
Figure FDA0002456034760000046
in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. thek-1Is a system matrix; b isk-1Is a control matrix; ckOutputting a matrix for the system; u. ofkInputting for the system; t isSFor a sampling period, P-And P+Respectively state estimation covariance prior estimation and posterior estimation, K is cardThe Lrman gain, e is the innovation matrix, I is the identity matrix, η is the coulombic efficiency and assumes a value of 1 at charge and 0.98 at discharge, Ccap,kThe maximum available capacity of the battery under the current cycle; cfreshThe maximum available capacity of the battery when leaving the factory; rfreshInternal resistance for the first cycle of the battery; reolIndicating the internal resistance of the battery at the end of its life; r0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,
Figure FDA0002456034760000051
step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the SOC and SOH collaborative estimation of the lithium battery is carried out by using a self-adaptive extended Kalman filter:
1) initialization:
at t0At time, i.e., when k is 0, an initial value x of the state observer is set0,P0,Q0,R0；
2) A priori estimate-predict: time update [ State Slave time (k-1)+Arrival time (k)-Is calculated by]
For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)+Reckoning to the current time (k)-The time update equation of the adaptive extended kalman filter is expressed as follows:
and (3) system state estimation:
Figure FDA0002456034760000052
estimating error covariance:
Figure FDA0002456034760000053
wherein, f (x)k-1,uk-1) Representing the system stateA program function;
3) a posteriori estimation-correction: measurement update [ State Slave time (k)-Arrival time (k)+Is calculated by]
This step uses the measured value y at the time kkCorrecting state estimation and covariance estimation, the estimation results being used separately
Figure FDA0002456034760000054
And
Figure FDA0002456034760000055
expressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:
an innovation matrix:
Figure FDA0002456034760000056
kalman gain matrix:
Figure FDA0002456034760000057
adaptive noise covariance matching:
Figure FDA0002456034760000061
and (3) correcting the system state:
Figure FDA0002456034760000062
error covariance correction:
Figure FDA0002456034760000063
4) time scale update
Time of day (k)+The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.
CN202010306668.4A 2020-04-17 2020-04-17 Lithium battery SOC and SOH collaborative estimation method considering cycle number influence Active CN111581904B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010306668.4A CN111581904B (en) 2020-04-17 2020-04-17 Lithium battery SOC and SOH collaborative estimation method considering cycle number influence

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010306668.4A CN111581904B (en) 2020-04-17 2020-04-17 Lithium battery SOC and SOH collaborative estimation method considering cycle number influence

Publications (2)

Publication Number Publication Date
CN111581904A true CN111581904A (en) 2020-08-25
CN111581904B CN111581904B (en) 2024-03-22

Family

ID=72119770

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010306668.4A Active CN111581904B (en) 2020-04-17 2020-04-17 Lithium battery SOC and SOH collaborative estimation method considering cycle number influence

Country Status (1)

Country Link
CN (1) CN111581904B (en)

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112051511A (en) * 2020-08-26 2020-12-08 华中科技大学 Power battery state of health estimation method and system based on multichannel technology
CN112305440A (en) * 2020-09-27 2021-02-02 精进电动科技股份有限公司 Battery remaining capacity and health state joint estimation method
CN112327195A (en) * 2020-09-29 2021-02-05 浙江南都电源动力股份有限公司 Battery health degree detection method
CN112765794A (en) * 2021-01-05 2021-05-07 国网辽宁省电力有限公司经济技术研究院 Reliability analysis method of lithium iron phosphate battery based on accelerated life test
CN112946480A (en) * 2021-01-28 2021-06-11 中国矿业大学 Lithium battery circuit model simplification method for improving SOC estimation real-time performance
CN113420444A (en) * 2021-06-23 2021-09-21 南通大学 Lithium ion battery SOC estimation method based on parameter online identification
CN113466710A (en) * 2021-08-17 2021-10-01 南京工程学院 SOC and SOH collaborative estimation method for energy storage battery in receiving-end power grid containing new energy
CN114089191A (en) * 2021-11-17 2022-02-25 浙大城市学院 Method for estimating health condition of composite lithium ion battery
CN114578708A (en) * 2022-01-26 2022-06-03 吉林大学 Aerocar working condition recognition system based on Matlab/Simulink
CN114791993A (en) * 2022-05-16 2022-07-26 江苏大学 SOH prediction method and system for power battery pack
CN115291130A (en) * 2022-10-09 2022-11-04 江苏正力新能电池技术有限公司 Battery pack parameter monitoring method and device, storage medium and electronic equipment
CN116401497A (en) * 2023-06-08 2023-07-07 上海泰矽微电子有限公司 SOH estimation method for feature fusion
CN116840699A (en) * 2023-08-30 2023-10-03 上海泰矽微电子有限公司 Battery health state estimation method and device, electronic equipment and medium

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110172939A1 (en) * 2010-01-08 2011-07-14 Sandip Uprety System and Method to Determine an Internal Resistance and State of Charge, State of Health, or Energy Level of a Rechargeable Battery
WO2013072927A2 (en) * 2011-09-30 2013-05-23 Kpit Cummins Infosystems Limited System and method for battery monitoring
US20140180614A1 (en) * 2012-12-26 2014-06-26 Robert Bosch Gmbh System And Method For Selective Estimation Of Battery State With Reference To Persistence Of Excitation And Current Magnitude
CN109143097A (en) * 2018-09-05 2019-01-04 合肥工业大学 It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method
CN110221221A (en) * 2019-04-24 2019-09-10 吉林大学 Charge states of lithium ion battery and health status combined estimation method
CN110261779A (en) * 2019-06-25 2019-09-20 西安石油大学 A kind of ternary lithium battery charge state cooperates with estimation method with health status online
CN110346734A (en) * 2019-06-19 2019-10-18 江苏大学 A kind of lithium-ion-power cell health status evaluation method based on machine learning

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110172939A1 (en) * 2010-01-08 2011-07-14 Sandip Uprety System and Method to Determine an Internal Resistance and State of Charge, State of Health, or Energy Level of a Rechargeable Battery
WO2013072927A2 (en) * 2011-09-30 2013-05-23 Kpit Cummins Infosystems Limited System and method for battery monitoring
US20140180614A1 (en) * 2012-12-26 2014-06-26 Robert Bosch Gmbh System And Method For Selective Estimation Of Battery State With Reference To Persistence Of Excitation And Current Magnitude
CN109143097A (en) * 2018-09-05 2019-01-04 合肥工业大学 It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method
CN110221221A (en) * 2019-04-24 2019-09-10 吉林大学 Charge states of lithium ion battery and health status combined estimation method
CN110346734A (en) * 2019-06-19 2019-10-18 江苏大学 A kind of lithium-ion-power cell health status evaluation method based on machine learning
CN110261779A (en) * 2019-06-25 2019-09-20 西安石油大学 A kind of ternary lithium battery charge state cooperates with estimation method with health status online

Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112051511A (en) * 2020-08-26 2020-12-08 华中科技大学 Power battery state of health estimation method and system based on multichannel technology
CN112305440A (en) * 2020-09-27 2021-02-02 精进电动科技股份有限公司 Battery remaining capacity and health state joint estimation method
CN112327195A (en) * 2020-09-29 2021-02-05 浙江南都电源动力股份有限公司 Battery health degree detection method
CN112765794A (en) * 2021-01-05 2021-05-07 国网辽宁省电力有限公司经济技术研究院 Reliability analysis method of lithium iron phosphate battery based on accelerated life test
CN112946480A (en) * 2021-01-28 2021-06-11 中国矿业大学 Lithium battery circuit model simplification method for improving SOC estimation real-time performance
CN113420444A (en) * 2021-06-23 2021-09-21 南通大学 Lithium ion battery SOC estimation method based on parameter online identification
CN113466710A (en) * 2021-08-17 2021-10-01 南京工程学院 SOC and SOH collaborative estimation method for energy storage battery in receiving-end power grid containing new energy
CN114089191A (en) * 2021-11-17 2022-02-25 浙大城市学院 Method for estimating health condition of composite lithium ion battery
CN114578708A (en) * 2022-01-26 2022-06-03 吉林大学 Aerocar working condition recognition system based on Matlab/Simulink
CN114791993A (en) * 2022-05-16 2022-07-26 江苏大学 SOH prediction method and system for power battery pack
CN114791993B (en) * 2022-05-16 2022-11-11 江苏大学 Power battery pack SOH prediction method and system
CN115291130A (en) * 2022-10-09 2022-11-04 江苏正力新能电池技术有限公司 Battery pack parameter monitoring method and device, storage medium and electronic equipment
CN115291130B (en) * 2022-10-09 2023-01-20 江苏正力新能电池技术有限公司 Battery pack parameter monitoring method and device, storage medium and electronic equipment
CN116401497A (en) * 2023-06-08 2023-07-07 上海泰矽微电子有限公司 SOH estimation method for feature fusion
CN116401497B (en) * 2023-06-08 2023-09-26 上海泰矽微电子有限公司 SOH estimation method for feature fusion
CN116840699A (en) * 2023-08-30 2023-10-03 上海泰矽微电子有限公司 Battery health state estimation method and device, electronic equipment and medium
CN116840699B (en) * 2023-08-30 2023-11-17 上海泰矽微电子有限公司 Battery health state estimation method and device, electronic equipment and medium

Also Published As

Publication number Publication date
CN111581904B (en) 2024-03-22

Similar Documents

Publication Publication Date Title
CN111581904B (en) Lithium battery SOC and SOH collaborative estimation method considering cycle number influence
Lin et al. State of charge estimation with the adaptive unscented Kalman filter based on an accurate equivalent circuit model
Xu et al. State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter
Ouyang et al. Improved parameters identification and state of charge estimation for lithium-ion battery with real-time optimal forgetting factor
CN111337832B (en) Power battery multidimensional fusion SOC and SOH online joint estimation method
CN110261778B (en) SOC estimation algorithm of lithium ion battery
Li et al. Comparative study of the influence of open circuit voltage tests on state of charge online estimation for lithium-ion batteries
CN111060834A (en) Power battery state of health estimation method
CN108732508B (en) Real-time estimation method for lithium ion battery capacity
He et al. State-of-charge estimation of lithium ion batteries based on adaptive iterative extended Kalman filter
CN110703114B (en) Power battery SOC and SOT combined state estimation method based on electricity-heat-neural network coupling model
CN109633472B (en) State of charge estimation algorithm of single lithium battery
CN111781503B (en) On-line estimation method for SOC of lithium ion energy storage battery
Li et al. A novel parameter and state-of-charge determining method of lithium-ion battery for electric vehicles
CN109839599B (en) Lithium ion battery SOC estimation method based on second-order EKF algorithm
CN111856282B (en) Vehicle-mounted lithium battery state estimation method based on improved genetic unscented Kalman filtering
CN113777510A (en) Lithium battery state of charge estimation method and device
CN111142025A (en) Battery SOC estimation method and device, storage medium and electric vehicle
CN112269133B (en) SOC estimation method based on pre-charging circuit model parameter identification
CN113156321A (en) Estimation method for state of charge (SOC) of lithium ion battery
Biswas et al. Simultaneous state and parameter estimation of li-ion battery with one state hysteresis model using augmented unscented kalman filter
CN114114038A (en) Lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions
Wu et al. State-of-charge estimation of lithium-ion batteries based on MCC-AEKF in non-Gaussian noise environment
Havangi Adaptive robust unscented Kalman filter with recursive least square for state of charge estimation of batteries
CN115047357A (en) Combined estimation method for lithium ion battery state

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant