CN111505506A - Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering - Google Patents

Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering Download PDF

Info

Publication number
CN111505506A
CN111505506A CN202010409709.2A CN202010409709A CN111505506A CN 111505506 A CN111505506 A CN 111505506A CN 202010409709 A CN202010409709 A CN 202010409709A CN 111505506 A CN111505506 A CN 111505506A
Authority
CN
China
Prior art keywords
battery
soc
state
parameter
value
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.)
Pending
Application number
CN202010409709.2A
Other languages
Chinese (zh)
Inventor
宋世欣
肖峰
彭思仑
段文献
安靖宇
孙发荣
宋传学
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.)
Jilin University
Original Assignee
Jilin University
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 Jilin University filed Critical Jilin University
Priority to CN202010409709.2A priority Critical patent/CN111505506A/en
Publication of CN111505506A publication Critical patent/CN111505506A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • 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
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computing Systems (AREA)
  • Operations Research (AREA)
  • Secondary Cells (AREA)

Abstract

The invention discloses a battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering, which comprises the following steps: step one, performing charge and discharge tests on a battery to be tested at different temperatures and under different working conditions through a battery charge and discharge test system and a temperature box, step two, constructing a battery actual capacity calculation model according to sample parameters of the battery to be tested collected in the test process, and calculating through the calculation model to obtain the actual capacity of the battery to be tested; step three, establishing a first-order RC equivalent circuit model of the storage battery to be tested according to the sample parameters of the battery collected in the testing process, and obtaining the state and observation equation of the first-order equivalent circuit model according to kirchhoff's law; and step four, performing state estimation by using a multi-scale self-adaptive unscented Kalman filtering algorithm, inputting test current and voltage, and obtaining an optimal estimation value of the SOC value of the storage battery to be measured, namely the SOC estimation value of the storage battery, by taking the minimum error between the actually measured terminal voltage and the estimation value as a target.

Description

Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering
Technical Field
The invention relates to the field of battery management of electric vehicles, in particular to a battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering.
Background
The battery management system is one of the key parts of the electric automobile, can effectively manage the working state of the power battery pack and provides safety guarantee for the normal running of the electric automobile. One of the main functions of the battery management system is to obtain the state of charge (SOC) of each battery cell and determine whether a balancing strategy is required to ensure that the entire battery pack is in a stable operating state.
However, during the driving of the vehicle, the internal operation state of the battery is a nonlinear electrochemical reaction and is easily affected by the external environment temperature and the self cycle life, so that it is very difficult to obtain an accurate SOC value. At present, the method for obtaining the battery SOC is mostly obtained by collecting the current and the voltage of a single battery and indirectly estimating the temperature of a working environment. The simplest method mainly comprises an ampere-hour integration method and an open-circuit voltage method. Although these methods are simple and feasible, they have their own drawbacks, and must obtain accurate SOC under specific conditions, for example, the ampere-hour integration method requires knowing an accurate initial value, and the open-circuit voltage method requires stopping charging and discharging of the battery for a long time. There are some methods for estimating the SOC of the battery by using neural networks, such as neural network algorithms (neural networks), wavelet neural network algorithms (wavelets neural networks), extreme learning machines (extreme learning machines), support vector machines (support vector machines), and so on.
The method comprises the steps of firstly, obtaining a state equation of a battery by using a battery model, obtaining a state parameter of the battery by using a filter algorithm, and then, updating the state parameter of the battery by using a self-adaptive unscented filter algorithm (FFR L S), wherein the state parameter of the battery is updated by using a filter algorithm with a time-varying unscented factor, and the like.
Disclosure of Invention
The invention designs and develops a battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering, combines EKF and AUKF, improves the convergence speed and SOC estimation precision of the algorithm at the initial stage, and greatly reduces the calculated amount.
The technical scheme provided by the invention is as follows:
a battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering comprises the following steps:
the method comprises the following steps that firstly, charging and discharging tests are carried out on a battery to be tested at different temperatures through a battery charging and discharging test system and a temperature box, and sample parameters of the battery to be tested are collected in the test process;
secondly, establishing a battery actual capacity calculation model according to sample parameters of the battery to be tested acquired in the testing process to obtain an end current estimation value of the battery to be tested; and
establishing a first-order RC equivalent circuit model of the battery to be tested according to the sample parameters of the battery to be tested collected in the testing process, and obtaining the state and observation equation of the first-order equivalent circuit model according to kirchhoff's law;
and step three, carrying out nonlinear transformation on the state of the first-order equivalent circuit model and an observation equation to obtain a state matrix and a parameter matrix, carrying out parameter estimation by using an extended Kalman filtering algorithm, carrying out state estimation by using a multi-scale self-adaptive unscented Kalman filtering algorithm, and obtaining an optimal estimation value of the SOC value of the battery to be measured by taking the minimum error between the actual measured current and the end current estimation value of the battery to be measured as a target.
Preferably, the charge and discharge test in the first step is performed at three temperatures of 0 ℃, 25 ℃ and 45 ℃ respectively, and data are collected.
Preferably, the charge and discharge test process in the first step includes the steps of:
step 1, fully charging the battery by using a standard constant-current constant-voltage charging mode, standing for 2 hours, and recording the measured terminal voltage of the battery as SOC (state of charge) 1;
step 2, carrying out constant current discharge by using the current of 1A, standing for 2h every 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to each SOC point during charging;
step 3, when discharging to a cut-off voltage of 2.5V, standing for 2h, then carrying out constant current charging on the battery by using a current of 1A, standing for 2h every 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to all SOC points during charging; and (3) standing for 2h every time the battery consumes 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to the SOC points during charging.
Preferably, the actual capacity calculation model of the battery to be tested is as follows:
SOC(t)＝SOC(t0)-∫ηiItdt/CN；
wherein SOC (t) is the battery capacity value of the battery at the time t, and SOC (t)0) For the battery at initial t0The battery capacity value at the moment, η, is the coulomb magnification, I, of the batterytThe current flowing through the battery and the load at time t, positive during discharging, negative during charging, CNIs the rated capacity of the battery.
Preferably, the state and observation equation of the first-order equivalent circuit model in step three is:
Figure BDA0002492743610000031
wherein, UtIs the voltage, U, measured at the battery terminal at time tp1Is the voltage, U, at one end of an RC network in an equivalent circuit modelp2Is the voltage at the other end of the RC network in the equivalent circuit model, ItCurrent flowing through battery and load at time t, R0Ohmic internal resistance, U, of equivalent circuit modelocOpen-circuit voltage source, U, for equivalent circuit modeloc＝ξ1SOC8+ξ2SOC7+ξ3SOC6+ξ4SOC5+ξ5SOC4+ξ6SOC3+ξ7SOC2+ξ8SOC+ξ9；ξi(i-1 … 9) is a fitting coefficient of a polynomial, RP1Is the internal resistance of polarization of one end of the cell, RP2Is the internal polarization resistance of the other end of the cell, CP1A polarization capacitor at one end of the battery, CP2Is the polarization capacitance at the other end of the cell.
Preferably, the third step includes:
step a, carrying out nonlinear transformation on the state of the first-order equivalent circuit model and an observation equation to obtain a battery model after nonlinear transformation;
Figure BDA0002492743610000041
where x is the state of the system, and x ═ SOC Up]T(ii) a Theta is a battery model parameter in the system, and theta is [ R ]0RpCp]T(ii) a k is a microscopic time scale, l is a macroscopic time scale, u is a current value input at the moment k, and y is a voltage value estimated in the system at the moment k; w is aθ,k-1Is the parameter Gaussian white noise, vkRepresenting white Gaussian noise, w, in the measurement equationx,k-1White Gaussian noise as a state parameter, vkWhite gaussian noise in the measurement equation;
step b, initializing states and parameters and corresponding covariance matrixes, wherein the noise values are as follows:
Figure BDA0002492743610000042
step c, predicting the state parameters and the parameter covariance matrix:
wherein the content of the first and second substances,
Figure BDA0002492743610000043
d, updating the state parameters with time to obtain parameter prediction values and parameter covariance prediction matrixes: firstly, calculating the weight of a sampling point corresponding to UT transform:
Figure BDA0002492743610000044
then, 2n +1 Sigma point sets were calculated:
Figure BDA0002492743610000045
Figure BDA0002492743610000051
in the formula: n represents the state dimension of the model, ωmRepresenting the weight coefficient, ω, corresponding to the meancRepresenting the weight coefficients corresponding to the covariance, λ is a scaling factor to reduce the total prediction error, α is selected to control the distribution of the sample points around the states, β is a non-negative weight coefficient to adjust the influence of the higher order terms, k is a secondary scaling parameter to ensure that the matrix (n + λ) P is a semi-positive matrix, where n is 3, α is 0.03, β is 2, and k is 0.
Next, a one-step prediction of the state values in the Sigma point set is performed:
Figure BDA0002492743610000052
and finally, solving the mean value and the covariance according to the one-step state prediction result:
Figure BDA0002492743610000053
Figure BDA0002492743610000054
e, performing next state measurement updating on the parameter predicted value to obtain a next parameter predicted value and a next state covariance matrix;
and performing UT transformation on the state result predicted in the one step again to generate a new Sigma point set:
Figure BDA0002492743610000055
the resulting new set of state Sigma points is substituted into the observation equation:
Figure BDA0002492743610000056
according to the observation predicted value of the Sigma point set, solving the mean value and covariance predicted by the system:
Figure BDA0002492743610000057
Figure BDA0002492743610000058
Figure BDA0002492743610000059
and (3) calculating innovation:
Figure BDA00024927436100000510
calculating a Kalman gain matrix:
Figure BDA00024927436100000511
update state and state covariance:
Figure BDA0002492743610000061
Figure BDA0002492743610000062
noise covariance update:
Figure BDA0002492743610000063
Qx,k＝Kx,kFk(Kx,k)T
Figure BDA0002492743610000064
step f, judging the time scaleIf k is l LθIterating the parameter gain matrix to obtain an updated state estimate, where k is a time scale and l is an integer LθIs a time parameter.
Preferably, the state estimation value updated in step f is:
parameter gain matrix:
Figure BDA0002492743610000065
updating parameters:
Figure BDA0002492743610000066
updating the parameter covariance matrix:
Figure BDA0002492743610000067
the invention has the advantages of
The invention combines EKF and AUKF, which not only improves the convergence speed and SOC estimation precision of the algorithm at the initial stage, but also greatly reduces the calculated amount.
The algorithm can obtain more accurate SOC than the EKF algorithm with fixed parameters in a mode of updating model parameters on line, and meanwhile, the EKF-AUKF algorithm added with the self-adaptive noise is more accurate than the estimation of the traditional algorithm.
According to the method, the robustness of the system can be improved through online updating iteration of the model, so that the system can run online, and the SOC state of the battery can be monitored in real time.
The algorithm does not need to update the model parameters periodically, is not influenced by the temperature on the model parameters and the open-circuit voltage, and can still have higher estimation precision under the condition of uncertain noise.
Drawings
Fig. 1 is a battery SOC estimation method based on the fusion of multi-scale kalman filtering and unscented kalman filtering according to the present invention.
Fig. 2 is a relationship between current and voltage in the pulse charge and discharge experiment described in the present invention.
Fig. 3 shows the correspondence between OCV and SOC at three temperatures according to the present invention.
Fig. 4 is a first-order equivalent circuit model of the power battery according to the invention.
FIG. 5 is a comparison of SOC estimates for three algorithms according to the present invention.
FIG. 6 shows SOC estimation errors in comparison of three algorithms according to the present invention.
Fig. 7 shows the voltage estimation values under comparison of the three algorithms according to the present invention.
FIG. 8 shows the voltage estimation error compared with the three algorithms according to the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
As shown in fig. 1, the method for estimating the SOC of a battery by fusing multi-scale kalman filtering and unscented kalman filtering provided by the present invention includes:
step one, through battery charge and discharge test system and temperature box, carry out the charge and discharge experiment to the battery under different temperatures and different operating modes and obtain the data collection, in this embodiment, all charge and discharge operating modes carry out the data collection respectively under three kinds of temperatures of 0 ℃, 25 ℃ and 45 ℃, and the sampling time is all 1 s.
Step two, an incremental OCV testing method is selected for experimental testing, and the specific testing steps are as follows:
step 1, fully charging the battery by using a standard constant-current constant-voltage charging mode, standing for a period of time, and recording the measured terminal voltage of the battery as SOC (state of charge) 1
Step 2, performing constant current discharge by using the current of 1A (C/2), unloading the current when the discharge reaches 10% of the rated capacity, and then standing for 2h to eliminate the polarization effect in the battery, wherein the measured terminal voltage of the battery is recorded as SOC (state of charge) 0.9;
step 3, repeating the step 2, and sequentially recording the open-circuit voltages corresponding to the SOC points;
and 4, discharging to a cut-off voltage of 2.5V, standing for 2h, then carrying out constant-current charging on the battery by using a current of 1A (C/2), standing for 2h every 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to each SOC point during charging.
Step three, building a battery model, and building an electrochemical equation corresponding to reaction conditions according to the internal reaction mechanism of the battery to obtain a more accurate residual capacity model; the SOC of the battery reflects the condition of the remaining capacity, and its value may be defined by the ratio of the remaining capacity to the rated capacity. In the working process of the battery, under the condition that the sampling time unit is very small, the current can be obtained by an ampere-hour integration method, and the calculation formula is as follows:
SOC(t)＝SOC(t0)-∫ηiItdt/CN；
wherein, SOC (t)0) Indicating the battery at an initial time t0The value of time, SOC (t), is the value of the battery at initial time t, ηiThe coulomb efficiency of the battery, ItFor the current flowing through the battery and the load, positive during discharge and negative during charge, CNIndicating the rated capacity of the battery.
As shown in fig. 4, in the fourth step, in this embodiment, a first-order battery model is selected as a research object, and the first-order RC battery model mainly has an open-circuit voltage source UocAn ohmic internal resistance R0An RC series network, RpIs the internal polarization resistance of the cell, CpIs the polarization capacitance of the cell.
The state and observation equation of the first-order equivalent circuit model can be obtained according to kirchhoff's law as follows:
Figure BDA0002492743610000081
wherein, UtRepresents the voltage, U, measured at the battery terminal at time tP1Is the voltage at one end of the RC network in the first-order battery model, UP2Is the voltage at the other end of the RC network in a first-order battery model, ItRepresenting the current flowing through the battery at time t, CP1Polarization capacitance, C, at one end of the first-order cell modelP2At the other end of the first-order cell modelPolarization capacitance, RP1Polarization resistance, R, at one end of the first order cell modelP2Polarization resistance at the other end in the first order cell model.
Before the equivalent circuit model is used for estimating the SOC and the voltage of the battery, in order to reduce the influence of uncertain parameters on the estimation effect, the parameters in the model need to be identified. The experimental measurement can show that a certain nonlinear relationship exists between the battery end open-circuit voltage and the SOC, and the relationship is determined by using an octave polynomial least square fitting method, wherein the expression is as follows:
Uoc＝ξ1SOC8+ξ2SOC7+ξ3SOC6+ξ4SOC5+ξ5SOC4+ξ6SOC3+ξ7SOC2+ξ8SOC+ξ9；ξi(i-1 … 9) is a fitting coefficient of a polynomial
In addition, the parameters to be identified in the model are also R0，Rp1，Rp2，Cp1And Cp2The SOC and the voltage are estimated mainly by using an EKF algorithm online identification mode, therefore, in order to reduce the complexity of the identification algorithm, an FFR L S method with simple principle is selected to perform offline identification in advance, before identifying parameters, necessary bilinear transformation is required to be performed on a first-order model state and an observation equation,
step five, for the first-order model, the parameters change slowly along with time, the SOC changes rapidly along with time, an AUKF algorithm is selected to carry out state estimation on a micro scale to obtain accurate SOC of the battery, in the process of updating the parameters by the EKF algorithm, the time scale needs to be redefined, and a time parameter is set to be Lθ，k＝lLθ(l ═ 1,2,3 …), if k can be LθInteger divide, then at time k to k + LθAnd (3) updating parameters of the EKF algorithm is not carried out within the moment, the model parameters are regarded as equal within the time scale, and the state and noise covariance matrix is updated at each k moment in the process of estimating the SOC of the battery by the AUKF algorithm, so that the dual-scale estimation of the parameters and the state is completed.
In order to apply the proposed algorithm to the battery SOC estimation, the formula in the battery model needs to be discretized.
Figure BDA0002492743610000091
Uk＝Uoc(SOCk)-Up1,k-Up2,k-R0,lIk+vk
In the formula:
Figure BDA0002492743610000092
the input of the system is current I, the output is voltage U, and the state matrix of the system is x ═ SOC Up1Up2]TThe parameter matrix is [ R ═ theta [ ]0R1R2C1C2]TThe correlation matrix used for the EKF-AUKF joint estimation algorithm is as follows, C used for parameter estimationθ,kCan be derived from a formula discretization battery model.
Figure BDA0002492743610000093
Figure BDA0002492743610000094
Figure BDA0002492743610000095
Dk＝[-R0]
Figure BDA0002492743610000096
In the formula: a. thek-1Jacobian matrix for state function with respect to state
BkJacobian matrix for a state function with respect to a parameter
Cx,kJacobian moment of state for observation functionMatrix of
DkJacobian matrix for the observation function with respect to the parameters
Figure BDA0002492743610000101
Figure BDA0002492743610000102
Figure BDA0002492743610000103
Figure BDA0002492743610000104
Figure BDA0002492743610000105
Figure BDA0002492743610000106
Figure BDA0002492743610000107
Figure BDA0002492743610000111
Performing nonlinear transformation on the state of the first-order equivalent circuit model and an observation equation to obtain a state matrix and a parameter matrix, performing parameter estimation by using an extended Kalman filtering algorithm, performing state estimation by using a multi-scale self-adaptive unscented Kalman filtering algorithm, inputting test current and voltage, and obtaining an optimal estimation value of the SOC value of the battery to be measured by taking the actually measured terminal voltage and the minimum error of the estimation value as a target, namely the SOC estimation value of the battery, wherein the specific steps are as follows:
step a, using a double Kalman filtering algorithm EKF for parameter estimation, using AUKF for state estimation (double scale), and using a state equation and an observation equation of a battery model as follows:
Figure BDA0002492743610000112
step b, initializing states and parameters and corresponding covariance matrix and noise value Qx,0Rx,0Qθ,0Rθ,0
Figure BDA0002492743610000113
Figure BDA0002492743610000114
Figure BDA0002492743610000115
For a parameter observer H∞FθParameter of middle system
Figure BDA0002492743610000116
An initial value of (1);
Figure BDA0002492743610000117
representing the parameter thetakAn estimated or expected value of;
Qθ,0for a parameter observer H∞FθMiddle matrix Qx,0An initial value of (1);
Qx,0a symmetric positive array designed for the designer based on the system noise p 1;
Rθ,0for a parameter observer H∞FθMiddle matrix Rx,0An initial value of (1);
Rx,0a symmetric positive array designed for the designer based on the measurement noise vk;
Fork＝1,2,3…
step c, updating parameter time
Wherein, the parameter prediction formula is as follows:
Figure BDA0002492743610000121
the parameter covariance matrix prediction formula is:
Figure BDA0002492743610000122
step d, updating the state time, which specifically comprises the following steps:
calculating the weight of the sampling point corresponding to the UT transform
Figure BDA0002492743610000123
Calculate 2n +1 Sigma point sets:
Figure BDA0002492743610000124
Figure BDA0002492743610000125
wherein: n represents the state dimension of the model, ωmRepresenting the weight coefficient, ω, corresponding to the meancRepresenting the weight coefficients corresponding to the covariance, λ is a scaling factor to reduce the total prediction error, α is selected to control the distribution of the sample points around the states, β is a non-negative weight coefficient to adjust the influence of the higher order terms, and k is a secondary scaling parameter to ensure that the matrix (n + λ) P is a semi-positive matrix, where n is 3, α is 0.03, β is 2, and k is 0.
The status values in the Sigma spot set are predicted in one step:
Figure BDA0002492743610000126
and (3) solving the mean value and the covariance according to the one-step state prediction result:
Figure BDA0002492743610000127
Figure BDA0002492743610000128
Figure BDA0002492743610000129
is the state prediction result mean;
Figure BDA0002492743610000131
predicting a result covariance for the state;
step e, state measurement updating:
and performing UT transformation on the state result predicted in the one step again to generate a new Sigma point set:
Figure BDA0002492743610000132
the resulting new set of state Sigma points is substituted into the observation equation:
Figure BDA0002492743610000133
according to the observation predicted value of the Sigma point set, solving the mean value and covariance predicted by the system:
Figure BDA0002492743610000134
Figure BDA0002492743610000135
Figure BDA0002492743610000136
Figure BDA0002492743610000137
for substituting the observation equation for a new set of state Sigma points
Figure BDA0002492743610000138
Updating the state covariance for the parameter;
and (3) calculating innovation:
Figure BDA0002492743610000139
ekestimating an innovation, i.e. an estimated error of the measured value, for the state;
calculating a Kalman gain matrix:
Figure BDA00024927436100001310
update state and state covariance:
Figure BDA00024927436100001311
Figure BDA00024927436100001312
Figure BDA00024927436100001313
updating a state matrix for the parameters;
Kx,kis a parameter gain matrix;
Figure BDA0002492743610000141
updating the state covariance for the parameter;
noise covariance update:
Figure BDA0002492743610000142
Qx,k＝Kx,kFk(Kx,k)T
Figure BDA0002492743610000143
Fkis a noise state matrix;
Qx,kis a noise gain matrix;
Rx,kis the noise state covariance;
making a time scale decision if k is divided by LθIf no remainder, the parameter measurement in step f is updated, otherwise, the step b is returned to continue updating the state.
F, updating the parameter measurement if k is l Lθ(l＝1,2,3…)，
Parameter gain matrix:
Figure BDA0002492743610000144
updating parameters:
Figure BDA0002492743610000145
updating the parameter covariance matrix:
Figure BDA0002492743610000146
the invention designs and develops a battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering, combines EKF and AUKF, improves the convergence speed and SOC estimation precision of the algorithm at the initial stage, and greatly reduces the calculated amount.
Summary of the experiments:
to verify the robustness of the proposed EKF + AUKF algorithm, FIGS. 5 and 6 show the estimated SOC and SOC error for the three algorithms at a given temperature. From fig. 6, it can be seen that all three algorithms have good robustness, and can quickly converge to the true SOC value under the condition that the initial SOC value is inaccurate. After converging on the reference value SOC value, SOC estimation error is within 0.02. Fig. 7 and 8 show the estimated voltage and voltage error for three algorithms at a given temperature. As can be seen from fig. 8, in the three algorithms, under the condition that the initial value of SOC is uncertain, the voltage error is very large in the initial stage of the FUDS operating condition, and after the estimated SOC value converges to the true value, the voltage error is also substantially controlled within 0.04V. However, the voltage errors of the three algorithms are obviously increased in the discharge period of 20% -10% of the capacity.
As can be seen from the results, the SOC estimation accuracy of the EKF-UKF algorithm and the EKF-AUKF algorithm is higher than that of the EKF algorithm at different temperatures. It shows that the online real-time updating of the parameters by the dual kalman filter algorithm is more accurate than the SOC value estimated by the fixed parameter values. The SOC estimation precision of the EKF-AUKF algorithm with the self-adaption is higher than that of the EKF-UKF algorithm without the self-adaption, which shows that the algorithm provided by the patent can update the noise value and the covariance matrix in the algorithm by using the self-adaption covariance matching mode, and further improves the SOC estimation precision.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (7)

1. A battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering is characterized by comprising the following steps:
the method comprises the following steps that firstly, charging and discharging tests are carried out on a battery to be tested at different temperatures through a battery charging and discharging test system and a temperature box, and sample parameters of the battery to be tested are collected in the test process;
secondly, establishing a battery actual capacity calculation model according to sample parameters of the battery to be tested acquired in the testing process to obtain an end current estimation value of the battery to be tested; and
establishing a first-order RC equivalent circuit model of the battery to be tested according to the sample parameters of the battery to be tested collected in the testing process, and obtaining the state and observation equation of the first-order equivalent circuit model according to kirchhoff's law;
and step three, carrying out nonlinear transformation on the state of the first-order equivalent circuit model and an observation equation to obtain a state matrix and a parameter matrix, carrying out parameter estimation by using an extended Kalman filtering algorithm, carrying out state estimation by using a multi-scale self-adaptive unscented Kalman filtering algorithm, and obtaining an optimal estimation value of the SOC value of the battery to be measured by taking the minimum error between the actual measured current and the end current estimation value of the battery to be measured as a target.
2. The method for estimating the SOC of the battery based on the fusion of the multi-scale Kalman filtering and the unscented Kalman filtering according to claim 1, wherein in the first step, the charging and discharging tests are respectively carried out at three temperatures of 0 ℃, 25 ℃ and 45 ℃ and data are acquired.
3. The method for estimating the SOC of the battery based on the fusion of the multi-scale kalman filter and the unscented kalman filter according to claim 2, wherein the charge and discharge test process in the first step includes the following steps:
step 1, fully charging the battery by using a standard constant-current constant-voltage charging mode, standing for 2 hours, and recording the measured terminal voltage of the battery as SOC (state of charge) 1;
step 2, carrying out constant current discharge by using the current of 1A, standing for 2h every 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to each SOC point during charging;
step 3, when discharging to a cut-off voltage of 2.5V, standing for 2h, then carrying out constant current charging on the battery by using a current of 1A, standing for 2h every 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to all SOC points during charging; and (3) standing for 2h every time the battery consumes 10% of rated capacity, and sequentially recording open-circuit voltages corresponding to the SOC points during charging.
4. The multi-scale Kalman filtering and unscented Kalman filtering integrated battery SOC estimation method according to claim 3, characterized in that the actual capacity calculation model of the battery to be measured is:
SOC(t)＝SOC(t0)-∫ηiItdt/CN；
wherein SOC (t) is the battery capacity value of the battery at the time t, and SOC (t)0) For the battery at initial t0The battery capacity value at the moment, η, is the coulomb magnification, I, of the batterytThe current flowing through the battery and the load at time t, positive during discharging, negative during charging, CNIs the rated capacity of the battery.
5. The method for estimating the SOC of the battery based on the fusion of the multi-scale kalman filter and the unscented kalman filter according to claim 1 or 4, wherein the state and observation equation of the first-order equivalent circuit model in the third step is as follows:
Figure FDA0002492743600000021
wherein, UtIs the voltage, U, measured at the battery terminal at time tp1Is the voltage, U, at one end of an RC network in an equivalent circuit modelp2Is the voltage at the other end of the RC network in the equivalent circuit model, ItCurrent flowing through battery and load at time t, R0Ohmic internal resistance, U, of equivalent circuit modelocOpen-circuit voltage source, U, for equivalent circuit modeloc＝ξ1SOC8+ξ2SOC7+ξ3SOC6+ξ4SOC5+ξ5SOC4+ξ6SOC3+ξ7SOC2+ξ8SOC+ξ9；ξi(i-1 … 9) is a fitting coefficient of a polynomial, RP1Is the internal resistance of polarization of one end of the cell, RP2Is the internal polarization resistance of the other end of the cell, CP1A polarization capacitor at one end of the battery, CP2Is the polarization capacitance at the other end of the cell.
6. The multi-scale Kalman filter and unscented Kalman filter fused battery SOC estimation method according to claim 5, characterized in that the third step comprises:
step a, carrying out nonlinear transformation on the state of the first-order equivalent circuit model and an observation equation to obtain a battery model after nonlinear transformation;
Figure FDA0002492743600000022
where x is the state of the system, and x ═ SOC Up]T(ii) a Theta is a battery model parameter in the system, and theta is [ R ]0RpCp]T(ii) a k is a microscopic time scale, l is a macroscopic time scale, u is a current value input at the moment k, and y is a voltage value estimated in the system at the moment k; w is aθ,k-1Is the parameter Gaussian white noise, vkRepresenting white Gaussian noise, w, in the measurement equationx,k-1White Gaussian noise as a state parameter, vkWhite gaussian noise in the measurement equation;
step b, initializing states and parameters and corresponding covariance matrixes, wherein the noise values are as follows:
Figure FDA0002492743600000031
Figure FDA0002492743600000032
for a parameter observer H∞FθParameter of middle system
Figure FDA0002492743600000033
An initial value of (1);
Figure FDA0002492743600000034
is a parameter thetakAn estimated or expected value of;
step c, predicting the state parameters and the parameter covariance matrix:
wherein the content of the first and second substances,
Figure FDA0002492743600000035
d, updating the state parameters with time to obtain parameter prediction values and parameter covariance prediction matrixes: firstly, calculating the weight of a sampling point corresponding to UT transform:
Figure FDA0002492743600000036
then, 2n +1 Sigma point sets were calculated:
Figure FDA0002492743600000037
Figure FDA0002492743600000038
in the formula: n is the state dimension of the model, ωmIs the weight coefficient, omega, corresponding to the mean valuecWeighting coefficients corresponding to the covariance, λ being a scaling factor, α selection controlling the distribution of sample points around the states, β being a non-negative weighting coefficient, k being a quadratic scaling parameter ensuring that the matrix (n + λ) P is a semi-positive definite matrix;
next, a one-step prediction of the state values in the Sigma point set is performed:
Figure FDA0002492743600000041
and finally, solving the mean value and the covariance according to the one-step state prediction result:
Figure FDA0002492743600000042
Figure FDA0002492743600000043
e, performing next state measurement updating on the parameter predicted value to obtain a next parameter predicted value and a next state covariance matrix;
and performing UT transformation on the state result predicted in the one step again to generate a new Sigma point set:
Figure FDA0002492743600000044
the resulting new set of state Sigma points is substituted into the observation equation:
Figure FDA0002492743600000045
according to the observation predicted value of the Sigma point set, solving the mean value and covariance predicted by the system:
Figure FDA0002492743600000046
Figure FDA0002492743600000047
Figure FDA0002492743600000048
and (3) calculating innovation:
Figure FDA0002492743600000049
calculating a Kalman gain matrix:
Figure FDA00024927436000000410
update state and state covariance:
Figure FDA00024927436000000411
Figure FDA00024927436000000412
noise covariance update:
Figure FDA0002492743600000051
Figure FDA0002492743600000052
f, judging the time scale, and if k is l LθIterating the parameter gain matrix to obtain an updated state estimate, where k is a time scale and l is an integer LθIs a time parameter.
7. The method for estimating battery SOC through fusion of multi-scale Kalman filtering and unscented Kalman filtering according to claim 6, wherein the state estimation value updated in the step f is:
parameter gain matrix:
Figure FDA0002492743600000053
updating parameters:
Figure FDA0002492743600000054
updating the parameter covariance matrix:
Figure FDA0002492743600000055
CN202010409709.2A 2020-05-15 2020-05-15 Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering Pending CN111505506A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010409709.2A CN111505506A (en) 2020-05-15 2020-05-15 Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010409709.2A CN111505506A (en) 2020-05-15 2020-05-15 Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering

Publications (1)

Publication Number Publication Date
CN111505506A true CN111505506A (en) 2020-08-07

Family

ID=71868323

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010409709.2A Pending CN111505506A (en) 2020-05-15 2020-05-15 Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering

Country Status (1)

Country Link
CN (1) CN111505506A (en)

Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111781503A (en) * 2020-06-15 2020-10-16 国网江苏省电力有限公司无锡供电分公司 Lithium ion energy storage battery SOC online estimation method
CN111983471A (en) * 2020-08-24 2020-11-24 哈尔滨理工大学 Lithium ion power battery safety degree estimation method and estimation device based on double Kalman filtering
CN112130077A (en) * 2020-09-30 2020-12-25 东风汽车集团有限公司 SOC estimation method of power battery pack under different working conditions
CN112234673A (en) * 2020-09-30 2021-01-15 长安大学 Battery energy balancing method suitable for balancing circuit
CN112485680A (en) * 2020-11-27 2021-03-12 浙江零跑科技有限公司 Battery SOC estimation method
CN112578286A (en) * 2020-11-23 2021-03-30 经纬恒润(天津)研究开发有限公司 Battery SOC estimation method and device
CN112816877A (en) * 2021-01-04 2021-05-18 东风柳州汽车有限公司 Current calibration method, device and storage medium for battery
CN112858929A (en) * 2021-03-16 2021-05-28 上海理工大学 Battery SOC estimation method based on fuzzy logic and extended Kalman filtering
CN113030752A (en) * 2021-04-12 2021-06-25 安徽理工大学 Online parameter identification and SOC joint estimation method based on forgetting factor
CN113204900A (en) * 2021-07-06 2021-08-03 湖北东湖实验室 Self-adaptive state estimation method for comprehensive power system of pure battery power ship
CN113625182A (en) * 2021-07-23 2021-11-09 北京理工大学 Method for on-line estimating battery state
CN113985292A (en) * 2021-06-24 2022-01-28 重庆大学 Lithium ion power battery SOC double-filtering estimation method based on improved coupling mode
CN114113929A (en) * 2021-11-12 2022-03-01 云南电网有限责任公司电力科学研究院 Method and system for acquiring real-time equivalent salt deposit density
CN114239463A (en) * 2021-12-16 2022-03-25 杭州科工电子科技有限公司 Battery cluster state of charge correction method based on big data
US11360147B2 (en) * 2020-03-03 2022-06-14 Karma Automotive Llc Method of determining the state of charge of a battery used in an electric vehicle
CN115201687A (en) * 2022-07-13 2022-10-18 西南交通大学 Battery model parameter and SoC joint estimation method based on online broadband impedance
CN115327385A (en) * 2022-07-29 2022-11-11 武汉理工大学 Power battery SOC value estimation method and system
CN116203432A (en) * 2023-03-23 2023-06-02 广东工业大学 CSO optimization-based unscented Kalman filtering method for predicting battery state of charge
CN116500466A (en) * 2023-06-28 2023-07-28 吉林大学 LXI bus-based integrated battery parameter measurement system and method
CN117074966A (en) * 2023-10-19 2023-11-17 东方电子股份有限公司 Battery SOC estimation method and system based on attenuation memory Kalman filter

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1903308A2 (en) * 2006-09-25 2008-03-26 Honeywell International Inc. Systems and methods for a hybrid state transition matrix
CN104714188A (en) * 2015-03-31 2015-06-17 桂林电子科技大学 Method and system for estimating measured noise variance matrix matched battery state of charge (SOC)
CN106443471A (en) * 2016-09-20 2017-02-22 首都师范大学 System on chip (SOC) estimation method for lithium ion battery and hardware implementation of estimation method
CN105378496B (en) * 2013-09-05 2017-08-18 日本康奈可株式会社 Estimation unit and method of estimation
CN108427079A (en) * 2018-06-11 2018-08-21 西南交通大学 A kind of power battery method for estimating remaining capacity
CN110395141A (en) * 2019-06-27 2019-11-01 武汉理工大学 Dynamic lithium battery SOC estimation method based on adaptive Kalman filter method
CN111060834A (en) * 2019-12-19 2020-04-24 中国汽车技术研究中心有限公司 Power battery state of health estimation method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1903308A2 (en) * 2006-09-25 2008-03-26 Honeywell International Inc. Systems and methods for a hybrid state transition matrix
CN105378496B (en) * 2013-09-05 2017-08-18 日本康奈可株式会社 Estimation unit and method of estimation
CN104714188A (en) * 2015-03-31 2015-06-17 桂林电子科技大学 Method and system for estimating measured noise variance matrix matched battery state of charge (SOC)
CN106443471A (en) * 2016-09-20 2017-02-22 首都师范大学 System on chip (SOC) estimation method for lithium ion battery and hardware implementation of estimation method
CN108427079A (en) * 2018-06-11 2018-08-21 西南交通大学 A kind of power battery method for estimating remaining capacity
CN110395141A (en) * 2019-06-27 2019-11-01 武汉理工大学 Dynamic lithium battery SOC estimation method based on adaptive Kalman filter method
CN111060834A (en) * 2019-12-19 2020-04-24 中国汽车技术研究中心有限公司 Power battery state of health estimation method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
YUJIE WANG: "Modeling and state-of-charge prediction of lithium-ion battery and ultracapacitor hybrids with a co-estimator", 《ENERGY》 *
张绍虹: "电动汽车锂离子电池SOH估算方法研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 *

Cited By (31)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11360147B2 (en) * 2020-03-03 2022-06-14 Karma Automotive Llc Method of determining the state of charge of a battery used in an electric vehicle
US11913995B2 (en) 2020-03-03 2024-02-27 Karma Automotive Llc Method of determining the state of charge of a battery used in an electric vehicle
CN111781503A (en) * 2020-06-15 2020-10-16 国网江苏省电力有限公司无锡供电分公司 Lithium ion energy storage battery SOC online estimation method
CN111781503B (en) * 2020-06-15 2023-09-22 国网江苏省电力有限公司无锡供电分公司 On-line estimation method for SOC of lithium ion energy storage battery
CN111983471A (en) * 2020-08-24 2020-11-24 哈尔滨理工大学 Lithium ion power battery safety degree estimation method and estimation device based on double Kalman filtering
CN111983471B (en) * 2020-08-24 2022-11-22 哈尔滨理工大学 Lithium ion power battery safety degree estimation method and estimation device based on double Kalman filtering
CN112234673A (en) * 2020-09-30 2021-01-15 长安大学 Battery energy balancing method suitable for balancing circuit
CN112234673B (en) * 2020-09-30 2022-04-22 长安大学 Battery energy balancing method suitable for balancing circuit
CN112130077A (en) * 2020-09-30 2020-12-25 东风汽车集团有限公司 SOC estimation method of power battery pack under different working conditions
CN112578286A (en) * 2020-11-23 2021-03-30 经纬恒润(天津)研究开发有限公司 Battery SOC estimation method and device
CN112485680B (en) * 2020-11-27 2024-04-23 浙江零跑科技股份有限公司 Battery SOC estimation method
CN112485680A (en) * 2020-11-27 2021-03-12 浙江零跑科技有限公司 Battery SOC estimation method
CN112816877A (en) * 2021-01-04 2021-05-18 东风柳州汽车有限公司 Current calibration method, device and storage medium for battery
CN112816877B (en) * 2021-01-04 2022-08-30 东风柳州汽车有限公司 Current calibration method, device and storage medium for battery
CN112858929A (en) * 2021-03-16 2021-05-28 上海理工大学 Battery SOC estimation method based on fuzzy logic and extended Kalman filtering
CN113030752A (en) * 2021-04-12 2021-06-25 安徽理工大学 Online parameter identification and SOC joint estimation method based on forgetting factor
CN113030752B (en) * 2021-04-12 2024-03-29 安徽理工大学 Online parameter identification and SOC joint estimation method based on variable forgetting factor
CN113985292A (en) * 2021-06-24 2022-01-28 重庆大学 Lithium ion power battery SOC double-filtering estimation method based on improved coupling mode
CN113985292B (en) * 2021-06-24 2024-04-19 重庆大学 Lithium ion power battery SOC double-filter estimation method based on improved coupling mode
CN113204900A (en) * 2021-07-06 2021-08-03 湖北东湖实验室 Self-adaptive state estimation method for comprehensive power system of pure battery power ship
CN113625182A (en) * 2021-07-23 2021-11-09 北京理工大学 Method for on-line estimating battery state
CN114113929A (en) * 2021-11-12 2022-03-01 云南电网有限责任公司电力科学研究院 Method and system for acquiring real-time equivalent salt deposit density
CN114239463A (en) * 2021-12-16 2022-03-25 杭州科工电子科技有限公司 Battery cluster state of charge correction method based on big data
CN115201687B (en) * 2022-07-13 2023-08-29 西南交通大学 Battery model parameter and SoC joint estimation method based on-line broadband impedance
CN115201687A (en) * 2022-07-13 2022-10-18 西南交通大学 Battery model parameter and SoC joint estimation method based on online broadband impedance
CN115327385A (en) * 2022-07-29 2022-11-11 武汉理工大学 Power battery SOC value estimation method and system
CN116203432A (en) * 2023-03-23 2023-06-02 广东工业大学 CSO optimization-based unscented Kalman filtering method for predicting battery state of charge
CN116203432B (en) * 2023-03-23 2023-10-20 广东工业大学 CSO optimization-based unscented Kalman filtering method for predicting battery state of charge
CN116500466A (en) * 2023-06-28 2023-07-28 吉林大学 LXI bus-based integrated battery parameter measurement system and method
CN116500466B (en) * 2023-06-28 2023-09-15 吉林大学 LXI bus-based integrated battery parameter measurement system and method
CN117074966A (en) * 2023-10-19 2023-11-17 东方电子股份有限公司 Battery SOC estimation method and system based on attenuation memory Kalman filter

Similar Documents

Publication Publication Date Title
CN111505506A (en) Battery SOC estimation method integrating multi-scale Kalman filtering and unscented Kalman filtering
CN109633477B (en) Real-time monitoring method for health state of battery pack based on EKF-GPR and daily fragment data
CN111781503B (en) On-line estimation method for SOC of lithium ion energy storage battery
CN112989690B (en) Multi-time-scale state-of-charge estimation method for lithium battery of hybrid electric vehicle
KR102246633B1 (en) Battery Output Voltage Response and State-of-Charge Forecasting Optimization Method using Hybrid VARMA and LSTM
CN109633470B (en) Estimation method for battery real-time full charge time based on EKF-GPR and daily segment data
CN112269133B (en) SOC estimation method based on pre-charging circuit model parameter identification
CN113868884B (en) Power battery multi-model fault-tolerant fusion modeling method based on evidence theory
Jin et al. SOC estimation of lithium-ion battery considering the influence of discharge rate
CN112098849A (en) Lithium battery residual capacity estimation method based on integral Kalman filtering
CN112379270A (en) Electric vehicle power battery state of charge rolling time domain estimation method
CN113466725B (en) Method and device for determining state of charge of battery, storage medium and electronic equipment
CN114114038A (en) Lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions
Tang et al. Modeling and estimation of nickel metal hydride battery hysteresis for SOC estimation
CN113805075A (en) BCRLS-UKF-based lithium battery state of charge estimation method
Ren et al. Novel strategy based on improved Kalman filter algorithm for state of health evaluation of hybrid electric vehicles Li-ion batteries during short-and longer term operating conditions
CN112946481A (en) Based on federation H∞Filtering sliding-mode observer lithium ion battery SOC estimation method and battery management system
CN115455842A (en) Method for estimating state of charge of super capacitor based on variable-temperature model weighted fusion
Wei et al. State-of-charge estimation for lithium-ion batteries based on temperature-based fractional-order model and dual fractional-order kalman filter
CN114839550A (en) UKF-AUKF-based lithium battery SOC joint estimation method
Feng et al. An adaptive state of charge estimation method of lithium-ion battery based on residual constraint fading factor unscented Kalman filter
CN114861545A (en) Lithium battery SOP online estimation method based on RNN neural network and multi-parameter constraint
Fornaro et al. State-of-Charge and State-of-Health variable-gain estimation based on tracking sliding mode differentiators for an electric vehicle Lithium-ion battery
CN113420444A (en) Lithium ion battery SOC estimation method based on parameter online identification
Li et al. Joint estimation of SOC and SOH for lithium-ion batteries based on EKF multiple time scales

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