CN111707953A - Lithium battery SOC online estimation method based on backward smoothing filtering framework - Google Patents

Lithium battery SOC online estimation method based on backward smoothing filtering framework Download PDF

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CN111707953A
CN111707953A CN201911160898.8A CN201911160898A CN111707953A CN 111707953 A CN111707953 A CN 111707953A CN 201911160898 A CN201911160898 A CN 201911160898A CN 111707953 A CN111707953 A CN 111707953A
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soc
lithium battery
square root
estimation
voltage
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汪双凤
丘祥晖
陈凯
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South China University of Technology SCUT
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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
    • 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
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements

Abstract

The invention discloses a lithium battery SOC online estimation method based on a backward smoothing filtering framework, which comprises the following steps of: the method comprises the following steps of firstly, testing a lithium battery to obtain a function of open-circuit voltage about a state of charge, and obtaining an initial SOC of the lithium battery through the open-circuit voltage; establishing an equivalent circuit model of the lithium battery, and determining a discrete state equation and an observation equation of the lithium battery; identifying model parameters, and identifying the equivalent circuit model parameters of the lithium battery; step four, establishing a backward smooth square root volume Kalman filter; and step five, collecting real-time voltage and current data of the lithium battery, and estimating the SOC of the battery. The algorithm is based on the traditional square root volume Kalman algorithm, combines a backward smoothing filtering frame and utilizes the latest measurement information to perform backward smoothing recursive operation, thereby reducing the influence of factors such as observation noise, observation error and the like, improving the estimation precision and accelerating the convergence speed.

Description

Lithium battery SOC online estimation method based on backward smoothing filtering framework
Technical Field
The invention relates to the field of battery management systems of electric automobiles, in particular to a lithium battery SOC online estimation method based on a backward smoothing filtering framework.
Background
In recent years, pure electric vehicles and hybrid electric vehicles, in which a battery is a main power source, have been widely used. The emerging vehicle is emphasized by people due to the characteristics of low carbon emission, energy conservation and portability. The lithium ion battery is used as an energy storage device of an electric automobile and a hybrid electric automobile, and an effective battery management method is needed to slow down the capacity attenuation of the battery, prolong the service life of the battery and ensure the reliability and safety of the electric automobile. The battery state of charge (SOC) estimation is always a hotspot problem in the battery management research direction, and the accurate estimation of the SOC of the battery can be used for preventing the overcharge and the overdischarge of the battery, reducing the damage to the battery, further improving the service performance of the battery and playing a vital role in a management system of the battery.
In general, methods for estimating SOC can be classified into model and non-model methods. The modeless approach refers to an estimation method that does not rely on any model type, typically an open-loop algorithm. Of these methods, ampere-hour integration and open circuit voltage are the most widely used. The accuracy of the ampere-hour integration method is greatly influenced by the initial SOC estimation value and the current observation accuracy. The principle of the open-circuit voltage method is to estimate the state of charge according to the simple correspondence between the open-circuit voltage and the state of charge of the battery. The method has the disadvantages that the battery needs to be idle and placed for a long time in order to obtain the open-circuit voltage of the battery, and the open-circuit voltage curve of part of the battery has an obvious 'plateau period', and the change of the open-circuit voltage along with the SOC is not obvious in the 'plateau period', so that the SOC estimated in the 'plateau period' has a large error.
Model-based methods can be further divided into two categories. The first type describes the nonlinear relationship between the battery SOC and the influence factors thereof based on a black box model; the second category is a method that combines various electrical characteristic models with filtering algorithms. The former depends on the quantity and quality of training data, the training period is long, the calculation amount is large, and the method is not suitable for online real-time estimation of the SOC. The latter has certain requirements on the calculation speed of a processor and higher calculation cost, but compared with an ampere-hour integral method, the method has the advantage of closed-loop feedback correction, so that the method is more suitable for online real-time estimation of the SOC. Methods based on Equivalent Circuit Models (ECM) and using kalman filtering and its derived algorithms are common today.
However, based on the SOC estimation of the Extended Kalman Filter (EKF), linearization errors are inevitably introduced in the process of linearizing the highly nonlinear lithium battery system by using a first-order taylor formula, and instability of filtering is caused; although the Unscented Kalman Filter (UKF) overcomes the error caused by EKF local linearization and avoids the inconvenience of solving the jacobian matrix, the central point weight of the UKF during Unscented Transformation (UT) may be negative, resulting in unstable UKF or UT transformation value. The literature (gajianin, tan \23468, sun pavo, towns. estimation of power lithium battery state of charge [ J ] based on volume kalman filtering algorithms the integration technique, 2018,7(06):31-38.) uses volume kalman filtering (CKF) in SOC estimation. Compared with EKF and UKF, CKF has better numerical stability and higher filtering precision. However, CKF also has problems that the spherical volume point may exceed the integration area, the positive nature of the covariance matrix may be destroyed during the calculation process, and the like. Square root volume kalman filtering (SRCKF) is proposed in the literature (cold inflammation, CKF-based SOC estimation of lithium batteries and battery management system research [ D ]. jiangsu university, 2016), which solves the problem of the CKF that the normality of covariance matrix is destroyed in the calculation process, but still does not solve the problems of filter divergence, general convergence rate, etc.
In order to obtain the SOC online estimation method with high precision, good stability and high convergence rate, the invention combines the backward smoothing filtering frame with square root volume Kalman filtering, and provides the lithium battery SOC online estimation method based on the backward smoothing filtering frame. The method has the characteristics of high precision, strong robustness and strong white noise resistance, and is easy to realize.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a lithium battery SOC online estimation method based on a backward smoothing filtering framework. Compared with the traditional square root cubature Kalman filtering method, the method has higher precision and better robustness, and the calculated amount is not obviously increased.
The invention is realized by at least one of the following technical schemes.
A lithium battery SOC online estimation method based on a backward smoothing filtering framework comprises the following steps:
the method comprises the steps that firstly, a lithium battery is tested to obtain a function of open-circuit voltage about state of charge (SOC), and the initial SOC of the lithium battery is obtained through the initial open-circuit voltage;
establishing a lithium battery equivalent circuit model to obtain a lithium battery dynamic characteristic equation;
thirdly, identifying parameters of the lithium battery equivalent circuit model on line by adopting a recursive least square method containing forgetting factors;
step four, establishing a backward smooth square root volume Kalman observer by taking the SOC value and the second-order polarization voltage of the lithium battery as a discrete state equation of an equivalent circuit model and taking a terminal voltage equation of the equivalent circuit model as an observation equation;
and step five, collecting real-time voltage and current data of the lithium battery, estimating the SOC of the battery through a backward smooth square root volume Kalman filter established in the previous step, preventing overcharge and overdischarge of the battery, and providing important reference for the battery health condition estimation and equalization functions of a battery management system.
Further, the first step specifically comprises: open circuit voltage U of the battery is measured every 10% SOC from 0% to 100% SOCocObtaining the battery U by utilizing the fitting of a fifth-order polynomialoc-a calibration curve function of SOC, the fifth order polynomial being:
Uoc(SOC)＝a0+a1*SOC+a2*SOC2+a3*SOC3+a4*SOC4+a5*SOC5
wherein, aiI is 0,1,., 5 is a polynomial coefficient, and SOC is the state of charge of the lithium battery; by first-collected electricityPressing data, using UocAnd (SOC) obtaining an SOC value as an initial value of the SOC estimation of the lithium battery.
Further, the equivalent circuit model of the lithium battery in the second step comprises a voltage source UocOhmic resistance R0A first polarization resistor Rp1And a second polarization resistance Rp2And a first polarization resistor Rp1Parallel first polarization capacitor Cp1And a second polarization resistance Rp2Second polarization capacitor C connected in parallelp2(ii) a First polarization resistance Rp1And a first polarization capacitor Cp1Forming a first RC branch, a second polarization resistor Rp2And a second polarization capacitor Cp2Forming a second RC branch, a voltage source UocFor open circuit voltage, the voltage at two ends of the whole circuit model is ULI.e., terminal voltage; the ohmic resistance R0Voltage source UocThe first RC branch and the second RC branch are connected in series, and a lithium battery dynamic characteristic equation is obtained according to kirchhoff's theorem:
Figure BDA0002286120370000041
where T is the sampling time interval, ILFor load current, Up1Is the voltage across the first RC branch, Up2Is the voltage across the second RC branch, ULIs the load voltage.
Further, the parameters in the third step include ohmic resistance R0A first polarization resistor Rp1And a second polarization resistance Rp2A first polarization capacitor Cp1And a second polarization capacitor Cp2。
Further, the third step specifically comprises: for the observation equation of the equivalent circuit model, the recurrence formula is as follows:
Figure BDA0002286120370000042
wherein the content of the first and second substances,
Figure BDA0002286120370000043
is a parameter vector, biI is 0,1, 5 is a constant, y is an actual observed value of the terminal voltage of the lithium battery, y (k +1) is an observed value of the terminal voltage of the lithium battery at the moment (k +1), and H is a constantT(k +1) is a state transfer matrix, H (k +1) ═ y (k), y (k-1), IL(k+1),IL(k),IL(k-1)]TK (K +1) is the calculated gain matrix, P (K) is the estimated error matrix, and must be given before parameter estimation begins
Figure BDA0002286120370000051
And initial value of P
Figure BDA0002286120370000052
And P (0) and (C) in the above,
Figure BDA0002286120370000053
is an arbitrary value, P (0) is α I, α is the coefficient of the unit matrix, I is the unit matrix, lambda is the forgetting factor, the value range is [0.95,1]；
Parameter vector
Figure BDA0002286120370000054
The following relationship exists between the parameters of the lithium battery equivalent circuit model:
Figure BDA0002286120370000055
wherein the coefficient b1～b5Is found by a recursive algorithm, taup1、τp2The method is an unknown parameter of the lithium battery equivalent circuit model, and the process of identifying the parameters by the recursive least square method with the forgetting factor is completed.
Further, the backward-smoothed square-root volume kalman observer of step four comprises the following discrete state equations and observation equations:
Figure BDA0002286120370000056
wherein x isk+1Is a state vector, yk+1To observe in the directionAmount ukAs input variable, ωkIs the process noise, upsilon, with mean 0 and variance QkIs the observation noise with the mean value of 0 and the variance of R, and f (-) and h (-) are the state transfer function and the observation function respectively; specifically, in combination with the lithium battery dynamic characteristic equation in the second step, the discrete state equation of the backward smooth square root volume kalman observer is established as follows:
Figure BDA0002286120370000061
wherein C is the rated capacity of the lithium battery, T is the sampling interval of the voltage and the current of the lithium battery, and SOCk+1Is SOC at (k +1), Up1,k+1Is the voltage across the first RC branch at time (k +1), Up2,k+1The voltage across the second RC branch at time (k +1), IL,kLoad current at time k;
the observation equation taking the equivalent circuit model terminal voltage equation as the backward smooth square root volume Kalman filter is as follows:
UL,k＝Uoc(SOCk)+IL,kR0+Up1,k+Up2,k
wherein U isoc(SOCk) Open circuit voltage, U, corresponding to SOC at time kL,kThe load voltage at time k.
Further, step five specifically is to update the model parameters and the U obtained in step one in real time by means of the recursive least square method containing the forgetting factor in step threeoc(SOC) as an important item in an observation equation of a backward smooth square root volume Kalman filter, establishing estimation of the backward smooth square root volume Kalman filter on the SOC of the battery, and comprising the following steps:
(1) setting the initial value of the discrete state equation and the process noise Q0Observation noise R0Covariance value P of sum state error0；
(2) Calculating and propagating volume points, wherein the expression is as follows:
Figure BDA0002286120370000062
Figure BDA0002286120370000063
where j is 1, 2n, n is the dimension of the system state vector, xj,kIs the volume point at time k, SkIs a Cholesky decomposition of the State error covariance matrix, Sk＝chol(Pk)，
Figure BDA0002286120370000064
Is the system state vector estimate at time k,
Figure BDA0002286120370000071
is xj,kThe propagated volume point, f (-) is the state transfer function, ζ is the volume point set, ζjColumn j, ζ, is defined as:
Figure BDA0002286120370000072
wherein [1 ]]jIs the j column of the n × n identity matrix;
(3) time updating and obtaining a prediction of the state vector at the current time, predicting x, and a prediction of the square root of the state error covariance matrixk+1The expression of (a) is:
Figure BDA0002286120370000073
where n is the dimension of the system state vector;
square root of state error covariance matrix
Figure BDA0002286120370000074
The prediction expression of (a) is:
Figure BDA0002286120370000075
where Tria () denotes QR decomposition of a matrix, the matrix
Figure BDA0002286120370000076
And SQThe definition is as follows:
Figure BDA0002286120370000077
SQ＝chol(Q)
wherein j is 1, 2n, SQIs the Cholesky decomposition, S, of the process noise matrix QQ＝chol(Q)；
(4) Recalculating and propagating volume points according to the prediction of the square root of the state error covariance matrix in the step (3), wherein the expression is as follows:
Figure BDA0002286120370000078
(5) according to the volume points updated in the step (4), carrying out observation updating to obtain observation vector prediction and square root prediction of observation error covariance and cross covariance matrix, and carrying out observation updating and calculating the expression of the observation vector prediction at the current moment as follows:
Zj,k+1＝h(xj,k+1,uk)
Figure BDA0002286120370000081
wherein j is 1, 2n, Zj,k+1Is xj,k+1The corresponding observation vector is then calculated,
Figure BDA0002286120370000082
is a prediction of the observation vector at the current time;
square root of the covariance matrix of the observed errors Szz,k+1The expression of (a) is:
Figure BDA0002286120370000083
wherein the content of the first and second substances,
Figure BDA0002286120370000084
and SRThe definition is as follows:
Figure BDA0002286120370000085
SR＝chol(R)
wherein j is 1, 2n, SRIs a Cholesky decomposition, S, of the observed noise matrix RR＝chol(R)；
The expression for the cross covariance matrix prediction is:
Figure BDA0002286120370000086
in the formula, ξk+1And
Figure BDA0002286120370000087
is defined as follows:
Figure BDA0002286120370000088
Figure BDA0002286120370000089
wherein j is 1,2 n;
(6) obtaining square root volume Kalman gain at the current moment, wherein the expression is as follows:
Figure BDA00022861203700000810
(7) correcting the prior state vector by using a gain matrix to obtain the state vector estimation of the current moment and the square root estimation of an error covariance matrix, wherein the expression of the system state vector estimation is as follows:
Figure BDA00022861203700000811
wherein Z isk+1Is the actual value of the observation vector at the current time.
The expression for the square root estimate of the error covariance matrix is:
Figure BDA0002286120370000091
(8) performing backward filtering calculation by using the state vector prediction, estimation and error covariance matrix square root, prediction and estimation of cross covariance matrix square root obtained in the steps (2) to (7) to obtain smooth estimation of the state vector and the error covariance matrix square root at the previous moment;
the expression for the smooth estimation of the state vector at the last moment is:
Figure BDA0002286120370000092
in the formula, WkFor smoothing gain, the expression is:
Figure BDA0002286120370000093
the smooth estimate expression for the square root of the error covariance matrix at the previous time is:
Figure BDA0002286120370000094
(9) replacing the smooth estimation in the step (8) with the estimation of the previous moment, and updating the state vector estimation and the error covariance matrix square root estimation of the current moment to replace the result obtained in the step (7) in the steps (2) to (7);
(10) and (4) repeating the steps (2) to (9) by using the updated state vector estimation and the square root of the error covariance matrix, and estimating the next moment.
In summary, the advantages and effects of the invention are:
the invention has the beneficial effects that: the invention relates to a lithium battery SOC online estimation method based on a backward smoothing filter framework, which comprises the steps of testing a lithium battery to obtain a function of a UOC (unified extensible operating mode) about SOC (state of charge), and calculating the initial SOC of the lithium battery through the initial UOC; establishing an equivalent circuit model of the lithium battery, and determining a discrete state equation and an observation equation of the lithium battery; identifying model parameters, and identifying battery model parameters by adopting a recursive least square method; establishing a backward smooth square root volume Kalman filter; and collecting real-time voltage and current data of the lithium battery and estimating the SOC of the battery.
The invention utilizes the filtering result of the k-moment square root volume Kalman filtering (SRCKF) to perform measurement updating by backward smooth filtering and utilizing the observed value of the k-1 moment, and can obtain a more accurate state estimation value of the k-1 moment by utilizing the observed value information of the k-moment and the k-1 moment simultaneously, so that the more accurate estimation value of the current k moment can be obtained by taking the state estimation value as an initial condition to perform forward filtering again, and the accuracy and the convergence speed of the algorithm are improved. Meanwhile, a Q-R decomposition mode is adopted, and the square root of the error covariance is used for operation, so that the stability and the operation efficiency of the new algorithm are improved.
Drawings
Fig. 1 is a flowchart of an online estimation method for SOC of a lithium battery based on a backward smoothing filter framework according to the present embodiment;
FIG. 2 is a block diagram of the backward-smoothed square root volume Kalman observer of the present embodiment;
fig. 3 is a schematic diagram of an equivalent circuit model of a lithium battery provided in this embodiment;
fig. 4 is a comparison graph of SOC estimation errors between the lithium battery SOC online estimation method based on the backward smoothing filter framework and other methods according to the present embodiment.
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.
As shown in fig. 1, the method for estimating SOC of a lithium battery on line based on a backward smoothing filter frame in the present embodiment includes the following steps:
step one, testing the lithium battery to obtain UocFunction of SOC, and by initial UocObtaining the initial SOC of the lithium battery, which specifically comprises the following steps:
measuring the open-circuit voltage of the battery from 0% to 100% SOC every 10% SOC, and obtaining the battery U by utilizing the fifth-order polynomial fittingoc-a calibration curve for SOC, the fifth order polynomial being:
Uoc(SOC)＝a0+a1*SOC+a2*SOC2+a3*SOC3+a4*SOC4+a5*SOC5
wherein, ai(i ═ 0, 1., 5) is a polynomial coefficient, and SOC is the state of charge of the lithium battery.
Using the function U from the first acquired voltage dataocAnd (SOC) obtaining an SOC value as an initial value of the SOC estimation of the lithium battery.
Step two, establishing a lithium battery equivalent circuit model shown in fig. 3, and simulating the dynamic characteristics of the lithium battery by using a circuit model formed by a voltage source, an ohmic resistor, a polarization resistor and a polarization capacitor, wherein the circuit model comprises an ohmic resistor R0A first polarization resistor Rp1And a second polarization resistance Rp2A voltage source and a first polarization resistor Rp1Parallel first polarization capacitor Cp1And a second polarization resistor Rp2Second polarization capacitor C connected in parallelp2. First polarization resistance Rp1And a first polarization capacitor Cp1Forming a first RC branch, a second polarization resistor Rp2And a second polarization capacitor Cp2Constituting a second RC branch. UOcIs the voltage across the voltage source, i.e., the open circuit voltage. U shapeLIs the voltage across the entire circuit, i.e., the terminal voltage. The ohmic resistance R0The voltage source, the first RC branch and the second RC branch are connected in series, and then a lithium battery dynamic characteristic equation is obtained according to kirchhoff's theorem:
Figure BDA0002286120370000111
where T is the sampling time interval, ILFor load current, Up1Is the voltage across the first RC branch, Up2Is the voltage across the second RC branch.
Identifying model parameters, and identifying the lithium battery equivalent circuit model parameters on line by adopting a recursive least square method containing forgetting factors; the parameters mentioned in step three include ohmic resistance R0Polarization resistance Rp1And Rp2Polarization capacitance Cp1And Cp2. For an observation equation of a battery observation model equation, a recursion calculation formula is as follows:
Figure BDA0002286120370000121
wherein the content of the first and second substances,
Figure BDA0002286120370000122
is an estimation of a parameter vector, biI is 0,1, 5 is a constant. y is an actual observed value of the terminal voltage of the lithium battery, and y (k +1) is an observed value of the terminal voltage of the lithium battery at the moment (k + 1). H is a state transfer matrix, H (k +1) [ [ y (k) ], y (k-1) ], IL(k+1),IL(k),IL(k-1)]T. K is the calculated gain matrix and P is the estimated error matrix. Before the parameter estimation starts, it must be given
Figure BDA0002286120370000123
And initial value of P
Figure BDA0002286120370000124
And P (0).
Figure BDA0002286120370000125
For any value, P (0) ═ α i. α is the coefficient of the unit matrix, generally taken to be 5000, I is the unit matrix, λ is the forgetting factor, and the value range is [0.95,1]。
Parameter vector
Figure BDA0002286120370000126
The following relationship exists between the parameters of the lithium battery equivalent circuit model:
Figure BDA0002286120370000127
the coefficient on the right side of the equal sign of the formula is calculated by a recursion algorithm, and the left side of the equal sign is the unknown parameter of the model and comprises an ohmic resistor R0A first polarization resistor Rp1And a second polarization resistance Rp2First polarization capacitor Cp1And a second polarization capacitor Cp2. And completing the process of identifying parameters by the recursive least square method with forgetting factors.
Step four, establishing a backward smooth square root volume Kalman observer shown in FIG. 2 by taking the SOC value and the second-order polarization voltage of the lithium battery as a discrete state equation of an equivalent circuit model of the lithium battery and taking a terminal voltage equation of the equivalent circuit model as an observation equation;
the backward smoothing volume Kalman filter observer in the fourth step comprises the following discrete state equations and observation equations:
Figure BDA0002286120370000132
where x is the state vector, y is the observation vector, u is the input variable, ωkIs the process noise, upsilon, with mean 0 and variance QkIs the observation noise with mean 0 and variance R, and f (-) and h (-) are the state transfer function and the observation function, respectively. The discrete state equation of the backward smooth square root volume Kalman observer is established by combining a lithium battery dynamic characteristic equation as follows:
Figure BDA0002286120370000131
wherein C is the rated capacity of the lithium battery, and T is the sampling interval of the voltage and the current of the lithium battery. SOCk+1Is SOC at (k +1), Up1,k+1Is the voltage across the first RC branch at time (k +1), Up2,k+1The voltage across the second RC branch at time (k +1), IL,kThe load current at time k.
The observation equation is:
UL,k＝Uoc(SOCk)+IL,kR0+Up1,k+Up2,k。
wherein U isoc(SOCk) Is the open circuit voltage corresponding to the SOC at time k.
Updating the model parameters in real time by means of the recursive least square method containing the forgetting factor in the step three, and obtaining the U in the step oneoc(SOC) as an important item in an observation equation, establishing backward smooth square root volume Kalman filtering to estimate the SOC of the battery, and comprising the following steps:
(1) setting the initial value of the discrete state equation and the process noise Q0Observation noise R0Covariance value P of sum state error0；
(2) Calculating and propagating volume points, wherein the expression is as follows:
Figure BDA0002286120370000141
Figure BDA0002286120370000142
where j is 1, 2n, n is the dimension of the system state vector. x is the number ofj,kIs the volume point at time k, SkIs a Cholesky decomposition of the State error covariance matrix, Sk＝chol(Pk)，
Figure BDA0002286120370000143
Is the system state vector estimate at time k.
Figure BDA0002286120370000144
Is xj,kThe propagated volume point, f (-) is the state transfer function. Zeta is a set of volume points, zetajColumn j, ζ, is defined as:
Figure BDA0002286120370000145
wherein [1 ]]jIs the j-th column of the n × n identity matrix.
(3) Time updating and obtaining a prediction of the state vector at the current time, predicting x, and a prediction of the square root of the state error covariance matrixk+1The expression of (a) is:
Figure BDA0002286120370000146
where n is the dimension of the system state vector.
Square root of state error covariance matrix Sk+1The prediction expression of (a) is:
Figure BDA0002286120370000147
where Tria () denotes QR decomposition of a matrix, the matrix
Figure BDA0002286120370000148
And SQThe definition is as follows:
Figure BDA0002286120370000149
SQ＝chol(Q)
wherein j is 1, 2n, SQIs the Cholesky decomposition, S, of the process noise matrix QQ＝chol(Q)。
(4) Recalculating and propagating volume points according to the prediction of the square root of the state covariance in the step (3), wherein the expression is as follows:
Figure BDA0002286120370000151
(5) according to the volume points updated in the step (4), carrying out observation updating to obtain observation vector prediction and square root prediction of observation error covariance and cross covariance matrix, and carrying out observation updating and calculating the expression of the observation vector prediction at the current moment as follows:
Zj,k+1＝h(xj,k+1,uk)
Figure BDA0002286120370000152
wherein j is 1, 2n, Zj,k+1Is xj,k+1The corresponding observation vector.
Figure BDA0002286120370000153
Is a prediction of the observation vector at the current time.
Square root of the covariance matrix of the observed errors Szz,k+1The expression of (a) is:
Figure BDA0002286120370000154
wherein the content of the first and second substances,
Figure BDA0002286120370000155
and SRThe definition is as follows:
Figure BDA0002286120370000156
SR＝chol(R)
wherein j is 1, 2n, SRIs a Cholesky decomposition, S, of the observed noise matrix RR＝chol(R)。
The expression for the cross covariance matrix prediction is:
Figure BDA0002286120370000157
in the formula, ξk+1And
Figure BDA0002286120370000158
is defined as follows:
Figure BDA0002286120370000159
Figure BDA00022861203700001510
wherein j is 1,2 n.
(6) Obtaining square root volume Kalman gain at the current moment, wherein the expression is as follows:
Figure BDA0002286120370000161
(7) correcting the prior state vector by using a gain matrix to obtain the state vector estimation of the current moment and the square root estimation of an error covariance matrix, wherein the expression of the system state vector estimation is as follows:
Figure BDA0002286120370000162
wherein Z isk+1Is the actual value of the observation vector at the current time.
The expression for the square root estimate of the error covariance matrix is:
Figure BDA0002286120370000163
(8) and (3) performing backward filtering calculation by using the state vector prediction, estimation and error covariance matrix square root and the prediction and estimation of the cross covariance matrix square root obtained in the steps (2) to (7) to obtain the smooth estimation of the state vector and the error covariance matrix square root at the previous moment.
The expression for the smooth estimation of the state vector at the last moment is:
Figure BDA0002286120370000164
in the formula, WkFor smoothing gain, the expression is:
Figure BDA0002286120370000165
the smooth estimate expression for the square root of the error covariance matrix at the previous time is:
Figure BDA0002286120370000166
(9) and (3) replacing the smooth estimation in the step (8) with the estimation at the previous moment, and updating the state vector estimation and the error covariance matrix square root estimation at the current moment to replace the result obtained in the step (7) in the steps (2) to (7).
(10) And (4) repeating the steps (2) to (9) by using the updated state vector estimation and the square root of the error covariance matrix, and estimating the next moment.
And step five, acquiring real-time voltage and current data of the lithium battery in the battery charging and discharging process, and estimating the SOC of the battery through the backward smooth square root volume Kalman filter established in the previous step. The invention is realized in a main control module of the battery management system by taking the battery management system as a carrier.
FIG. 4 is a comparison diagram of SOC estimation errors of backward smoothing square root cubature Kalman filter and square root cubature Kalman filter under the same condition, Dynamic Stress Test (DST). As shown, the backward-smoothed square-root volumetric Kalman filter SOC estimation error is less than 1% most of the time, and is significantly smaller than the square-root volumetric Kalman filter SOC estimation error.
The above examples merely represent one embodiment of the present invention, which is described in more detail and in greater detail, but are not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims (7)

1. A lithium battery SOC online estimation method based on a backward smoothing filtering framework is characterized by comprising the following steps:
the method comprises the steps that firstly, a lithium battery is tested to obtain a function of open-circuit voltage about state of charge (SOC), and the initial SOC of the lithium battery is obtained through the initial open-circuit voltage;
establishing a lithium battery equivalent circuit model to obtain a lithium battery dynamic characteristic equation;
thirdly, identifying parameters of the lithium battery equivalent circuit model on line by adopting a recursive least square method containing forgetting factors;
step four, establishing a backward smooth square root volume Kalman observer by taking the SOC value and the second-order polarization voltage of the lithium battery as a discrete state equation of an equivalent circuit model and taking a terminal voltage equation of the equivalent circuit model as an observation equation;
and step five, collecting real-time voltage and current data of the lithium battery, estimating the SOC of the battery through a backward smooth square root volume Kalman filter established in the previous step, preventing overcharge and overdischarge of the battery, and providing important reference for the battery health condition estimation and equalization functions of a battery management system.
2. The lithium battery SOC online estimation method based on the backward smoothing filter framework as claimed in claim 1, wherein the step one specifically includes: open circuit voltage U of the battery is measured every 10% SOC from 0% to 100% SOCocObtaining the battery U by utilizing the fitting of a fifth-order polynomialoc-a calibration curve function of SOC, the fifth order polynomial being:
Uoc(SOC)＝a0+a1*SOC+a2*SOC2+a3*SOC3+a4*SOC4+a5*SOC5
wherein, aiI is 0,1,., 5 is a polynomial coefficient, and SOC is the state of charge of the lithium battery; by first collecting voltage data, U is utilizedocAnd (SOC) obtaining an SOC value as an initial value of the SOC estimation of the lithium battery.
3. The lithium battery SOC online estimation method based on the backward smoothing filter framework as claimed in claim 1, wherein the equivalent circuit model of the lithium battery in the second step includes voltageSource UocOhmic resistance R0A first polarization resistor Rp1And a second polarization resistance Rp2And a first polarization resistor Rp1Parallel first polarization capacitor Cp1And a second polarization resistance Rp2Second polarization capacitor C connected in parallelp2(ii) a First polarization resistance Rp1And a first polarization capacitor Cp1Forming a first RC branch, a second polarization resistor Rp2And a second polarization capacitor Cp2Forming a second RC branch, a voltage source UocFor open circuit voltage, the voltage at two ends of the whole circuit model is ULI.e., terminal voltage; the ohmic resistance R0Voltage source UocThe first RC branch and the second RC branch are connected in series, and a lithium battery dynamic characteristic equation is obtained according to kirchhoff's theorem:
Figure FDA0002286120360000021
where T is the sampling time interval, ILFor load current, Up1Is the voltage across the first RC branch, Up2Is the voltage across the second RC branch, ULIs the load voltage.
4. The lithium battery SOC online estimation method based on backward smoothing filter framework as claimed in claim 1, wherein the parameters in step three include ohmic resistance R0A first polarization resistor Rp1And a second polarization resistance Rp2A first polarization capacitor Cp1And a second polarization capacitor Cp2。
5. The lithium battery SOC online estimation method based on the backward smoothing filter framework as claimed in claim 1, wherein the third step specifically includes: for the observation equation of the equivalent circuit model, the recurrence formula is as follows:
Figure FDA0002286120360000022
wherein the content of the first and second substances,
Figure FDA0002286120360000023
is a parameter vector, biI is 0,1, 5 is a constant, y is an actual observed value of the terminal voltage of the lithium battery, y (k +1) is an observed value of the terminal voltage of the lithium battery at the moment (k +1), and H is a constantT(k +1) is a state transfer matrix, H (k +1) ═ y (k), y (k-1), IL(k+1),IL(k),IL(k-1)]TK (K +1) is the calculated gain matrix, P (K) is the estimated error matrix, and must be given before parameter estimation begins
Figure FDA0002286120360000031
And initial value of P
Figure FDA0002286120360000032
And P (0) and (C) in the above,
Figure FDA0002286120360000033
is an arbitrary value, P (0) is α I, α is the coefficient of the unit matrix, I is the unit matrix, lambda is the forgetting factor, the value range is [0.95,1]；
Parameter vector
Figure FDA0002286120360000034
The following relationship exists between the parameters of the lithium battery equivalent circuit model:
Figure FDA0002286120360000035
wherein the coefficient b1～b5Is found by a recursive algorithm, taup1、τp2The method is an unknown parameter of the lithium battery equivalent circuit model, and the process of identifying the parameters by the recursive least square method with the forgetting factor is completed.
6. The lithium battery SOC online estimation method based on the backward smoothing filter framework of claim 1, wherein the backward smoothing square root volume Kalman observer of step four comprises the following discrete state equation and observation equation:
Figure FDA0002286120360000036
wherein x isk+1Is a state vector, yk+1To observe the vector, ukAs input variable, ωkIs the process noise, upsilon, with mean 0 and variance QkIs the observation noise with the mean value of 0 and the variance of R, and f (-) and h (-) are the state transfer function and the observation function respectively; specifically, in combination with the lithium battery dynamic characteristic equation in the second step, the discrete state equation of the backward smooth square root volume kalman observer is established as follows:
Figure FDA0002286120360000041
wherein C is the rated capacity of the lithium battery, T is the sampling interval of the voltage and the current of the lithium battery, and SOCk+1Is SOC at (k +1), Up1,k+1Is the voltage across the first RC branch at time (k +1), Up2,k+1The voltage across the second RC branch at time (k +1), IL,kLoad current at time k;
the observation equation taking the equivalent circuit model terminal voltage equation as the backward smooth square root volume Kalman filter is as follows:
UL,k＝Uoc(SOCk)+IL,kR0+Up1,k+Up2,k
wherein U isoc(SOCk) Open circuit voltage, U, corresponding to SOC at time kL,kThe load voltage at time k.
7. The lithium battery SOC on-line estimation method based on the backward smoothing filtering framework as claimed in claim 1, wherein the step five is to update the model parameters and the U obtained in the step one in real time by means of recursive least square method containing forgetting factor in the step threeoc(SOC) as a backward smoothed square root volumetric Kalman filter viewThe method for establishing the estimation of the battery SOC by the backward smooth square root volume Kalman filtering comprises the following steps:
(1) setting the initial value of the discrete state equation and the process noise Q0Observation noise R0Covariance value P of sum state error0；
(2) Calculating and propagating volume points, wherein the expression is as follows:
Figure FDA0002286120360000042
Figure FDA0002286120360000043
where j is 1,2, …,2n, n is the dimension of the system state vector, xj,kIs the volume point at time k, SkIs a Cholesky decomposition of the State error covariance matrix, Sk＝chol(Pk)，
Figure FDA0002286120360000051
Is the system state vector estimate at time k,
Figure FDA0002286120360000052
is xj,kThe propagated volume point, f (-) is the state transfer function, ζ is the volume point set, ζjColumn j, ζ, is defined as:
Figure FDA0002286120360000053
wherein [1 ]]jIs the j column of the n × n identity matrix;
(3) time updating and obtaining a prediction of the state vector at the current time, predicting x, and a prediction of the square root of the state error covariance matrixk+1The expression of (a) is:
Figure FDA0002286120360000054
where n is the dimension of the system state vector;
square root of state error covariance matrix
Figure FDA0002286120360000055
The prediction expression of (a) is:
Figure FDA0002286120360000056
where Tria () denotes QR decomposition of a matrix, the matrix
Figure FDA0002286120360000057
And SQThe definition is as follows:
Figure FDA0002286120360000058
SQ＝chol(Q)
wherein j is 1,2, …,2n, SQIs the Cholesky decomposition, S, of the process noise matrix QQ＝chol(Q)；
(4) Recalculating and propagating volume points according to the prediction of the square root of the state error covariance matrix in the step (3), wherein the expression is as follows:
Figure FDA0002286120360000059
(5) according to the volume points updated in the step (4), carrying out observation updating to obtain observation vector prediction and square root prediction of observation error covariance and cross covariance matrix, and carrying out observation updating and calculating the expression of the observation vector prediction at the current moment as follows:
Zj,k+1＝h(xj,k+1,uk)
Figure FDA0002286120360000061
wherein j is 1,2, …,2n, Zj,k+1Is xj,k+1The corresponding observation vector is then calculated,
Figure FDA0002286120360000062
is a prediction of the observation vector at the current time;
square root of the covariance matrix of the observed errors Szz,k+1The expression of (a) is:
Figure FDA0002286120360000063
wherein the content of the first and second substances,
Figure FDA0002286120360000064
and SRThe definition is as follows:
Figure FDA0002286120360000065
SR＝chol(R)
wherein j is 1,2, …,2n, SRIs a Cholesky decomposition, S, of the observed noise matrix RR＝chol(R)；
The expression for the cross covariance matrix prediction is:
Figure FDA0002286120360000066
in the formula, ξk+1And
Figure FDA0002286120360000067
is defined as follows:
Figure FDA0002286120360000068
Figure FDA0002286120360000069
wherein j is 1,2, …,2 n;
(6) obtaining square root volume Kalman gain at the current moment, wherein the expression is as follows:
Figure FDA00022861203600000610
(7) correcting the prior state vector by using a gain matrix to obtain the state vector estimation of the current moment and the square root estimation of an error covariance matrix, wherein the expression of the system state vector estimation is as follows:
Figure FDA00022861203600000611
wherein Z isk+1Is the actual value of the observation vector at the current time.
The expression for the square root estimate of the error covariance matrix is:
Figure FDA0002286120360000071
(8) performing backward filtering calculation by using the state vector prediction, estimation and error covariance matrix square root, prediction and estimation of cross covariance matrix square root obtained in the steps (2) to (7) to obtain smooth estimation of the state vector and the error covariance matrix square root at the previous moment;
the expression for the smooth estimation of the state vector at the last moment is:
Figure FDA0002286120360000072
in the formula, WkFor smoothing gain, the expression is:
Figure FDA0002286120360000073
the smooth estimate expression for the square root of the error covariance matrix at the previous time is:
Figure FDA0002286120360000074
(9) replacing the smooth estimation in the step (8) with the estimation of the previous moment, and updating the state vector estimation and the error covariance matrix square root estimation of the current moment to replace the result obtained in the step (7) in the steps (2) to (7);
(10) and (4) repeating the steps (2) to (9) by using the updated state vector estimation and the square root of the error covariance matrix, and estimating the next moment.
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