CN111650517B - Battery state of charge estimation method - Google Patents

Battery state of charge estimation method Download PDF

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CN111650517B
CN111650517B CN202010309691.9A CN202010309691A CN111650517B CN 111650517 B CN111650517 B CN 111650517B CN 202010309691 A CN202010309691 A CN 202010309691A CN 111650517 B CN111650517 B CN 111650517B
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CN111650517A (en
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王伟达
杨超
项昌乐
刘金刚
韩立金
倪俊
张中国
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Beijing Institute of Technology BIT
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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]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables

Abstract

The invention discloses a battery state of charge estimation method, which aims at providing a nonlinear state relation existing in a battery model, provides a state of charge SOC estimation algorithm based on STF-SRUKF, combines a strong tracking filter theory STF algorithm with a square root unscented Kalman filter algorithm SR-UKF algorithm, on one hand, uses a covariance square root to replace a covariance matrix for recursive calculation, and strengthens the stability of iteration of the square root unscented Kalman filter algorithm SR-UKF algorithm, on the other hand, introduces a time-varying fading factor based on the idea of strong tracking filtering, and improves the robustness of the square root unscented Kalman filter algorithm SR-UKF algorithm on parameter perturbation, thereby improving the estimation precision of the battery state of charge SOC under the influence of complex working conditions and strong noise.

Description

Battery state of charge estimation method
Technical Field
The invention relates to the technical field of battery state of charge estimation, in particular to a battery state of charge estimation method.
Background
Based on lithium iron phosphate batteries which are widely used in electric vehicles nowadays, as shown in fig. 1. The lithium iron phosphate battery has high safety performance, long service life, good high-temperature performance and no memory effect, and meets the requirement of environmental protection. For a four-wheel hub motor-driven electric vehicle, a power battery pack is a core component of the electric vehicle, and directly determines the driving range and the control mode of the electric vehicle. In order to prevent overcharge and overdischarge of the battery during use, improve the service life of the battery and the drivability of the electric vehicle, it is necessary to estimate the state of charge SOC of the battery.
Disclosure of Invention
The invention aims to provide a SOC estimation algorithm based on STF-SRUKF aiming at a nonlinear state relation existing in a battery model, combine a strong tracking filter theory STF algorithm with a square root unscented Kalman filtering algorithm SR-UKF algorithm, on one hand, use a covariance square root to replace a covariance matrix for recursive calculation, and strengthen the iteration stability of the square root unscented Kalman filtering algorithm SR-UKF algorithm, on the other hand, introduce a time-varying fading factor based on the idea of strong tracking filtering, and improve the robustness of the square root unscented Kalman filtering algorithm SR-UKF algorithm on parameter perturbation, thereby improving the estimation precision of the battery SOC under the influence of complex working conditions and strong noise.
In order to solve the technical problems, the invention provides the following technical scheme:
a battery state of charge estimation method, comprising the steps of:
step 1, establishing a first-order RC model of the battery:
according to the circuit principle, a characteristic equation of a first-order RC model is deduced as shown in a formula 3-1:
Figure GDA0003116460020000011
the current is used as an input value of a system, the terminal voltage is used as a measured value of the system, the SOC and the polarization voltage of the battery are used as state quantities of the system, and a state equation of the power battery system can be established as follows, wherein the equation is shown in a formula 3-2:
Figure GDA0003116460020000012
Ul,krepresents the battery terminal voltage at time k; u shapep,kThe polarization voltage at time k; i.e. ikThe working current of the battery at the moment k; eta is the coulomb efficiency of charging and discharging the battery; t issIs a sampling time interval; tau ispIs a time constant; cnIs the rated capacity of the battery.
Wherein, the polarization capacitance C of the battery at the k momentpPolarization resistance RpAnd open circuit voltage UOCAll are SOC correlation functions, and an experimental method is needed for identification and fitting; open circuit voltage adopts OCV test to carry out point taking experiment; the remaining parameters of the cell model, e.g. polarization capacitance CpPolarization resistance RpThe time constant tau needs HPPC experiment to identify;
step 2, calculating the state estimation value of the system at the k moment according to the formula 3-2
Figure GDA00031164600200000210
And PkEstimating the state of the system at the moment k +1 according to the data;
for the Kalman filtering recursion system, the state estimation steps are as follows:
equation 3-3:
Figure GDA0003116460020000021
wherein
Figure GDA0003116460020000022
Is a residual sequence obtained by a state estimation filtering equation; under the condition that the Kalman filtering theory meets the formula 3-4, the strong tracking filter is added with the formula 3-5, so that residual sequences at different moments are orthogonal everywhere;
equations 3-4:
Figure GDA0003116460020000023
equations 3-5:
Figure GDA0003116460020000024
in order to establish the formulas 3-5, the STF algorithm introduces a time-varying fading factor lambda, and adjusts the covariance matrix of the prediction error in real time, so as to further update the Kalman gain; the calculation method of the fading factor λ is as follows:
equations 3-6:
Figure GDA0003116460020000025
equations 3-7:
Figure GDA0003116460020000026
equations 3-8:
Figure GDA0003116460020000027
equations 3-9:
Figure GDA0003116460020000028
wherein, VkFor the error covariance matrix, the following is defined, equations 3-10:
Figure GDA0003116460020000029
in the formula, rho is more than 0 and less than or equal to 1 and is a forgetting factor, beta is more than or equal to 1 and is a weakening factor, and the estimation result can be smoother by increasing the value of beta; f and H are Jacobian matrixes of a system state equation and an observation equation respectively;
constructing sigma points according to the mean of the state vector x
Figure GDA00031164600200000211
With covariance P, the sigma point set { ξ is selected as followsi1,2, …,2n, and the weight W corresponding to the point seti (m)And Wi (c)Equation 3-11:
Figure GDA0003116460020000031
wherein, kappa is a scale condition coefficient and determines the precision of a sampling value; at this time, sigma point set { ξi-approximation of the gaussian distribution of x;
the sigma point set is propagated through a nonlinear function, the selected sigma point set is calculated through a nonlinear function f (x), and the nonlinear propagated sigma point set { Y) is obtainediWhen the probability distribution of Y is close to the probability distribution of the non-linear function computed value Y ═ f (x):
formulas 3 to 12: y isi＝f(χi),i＝0,1,...,2n
Calculating the mean value and covariance value of the transformed point set, and performing sigma point set { Y after transformationiWeighting to obtain the mean value and covariance of the output variables by calculation, wherein the weight value is equal to that of the input variables:
equations 3-13:
Figure GDA0003116460020000032
equations 3-14:
Figure GDA0003116460020000033
wherein, Wi mAnd Wi cThe weighting coefficients used for calculating the mean and covariance of the y-values are:
equations 3-15:
Figure GDA0003116460020000034
wherein κ ═ α2The value of (n + lambda) -n, alpha is positive and is slightly less than 1; beta is a state distribution parameter, and the value of the parameter is 2 for a system with Gaussian distribution; λ is set to 0 or 3-n; the precision of variance transformation can be improved by adjusting the value of beta, and the precision of the estimated mean value can be improved by adjusting the values of alpha and lambda;
for nonlinear systems, equations 3-16:
Figure GDA0003116460020000035
the iteration steps of the square root unscented kalman filter are as follows:
initialization:
equations 3-17:
Figure GDA0003116460020000036
calculate Sigma point:
equations 3-18:
Figure GDA0003116460020000037
and step 3, updating the time as follows:
equations 3-19: chi shapek/k-1＝F[χk-1]
Formulas 3 to 20:
Figure GDA0003116460020000041
equations 3-21:
Figure GDA0003116460020000042
formulas 3 to 22:
Figure GDA0003116460020000043
equations 3-23: y isk/k-1＝H[χk/k-1]
Formulas 3 to 24:
Figure GDA0003116460020000044
wherein QR represents QR decomposition, cholepdate represents Cholesky first-order update, and the Cholesky first-order update are matlab executable function statements;
the measurement is updated as follows:
formulas 3 to 25:
Figure GDA0003116460020000045
equations 3-26:
Figure GDA0003116460020000046
step 4, calculating an fading factor:
equations 3-27:
Figure GDA0003116460020000047
equations 3-28:
Figure GDA0003116460020000048
formulas 3 to 29:
Figure GDA0003116460020000049
equations 3-30:
Figure GDA00031164600200000410
equations 3-31: sk＝cholupdate(Sk/k-1,U,-1)
Because SR-UKF also needs choleupdate in the iterative process, and the product of the column vector of U and its transposition in the formula 3-31 may have non-positive character, the square root S of covariance P after choleupdate also loses positive character; to avoid this, the following modifications are made to equations 3-31:
let R be U (: i)TIf R is a positive definite matrix, then equations 3-32:
Sk＝cholupdate(Sk/k-1,U(:,i),-1)
otherwise, equations 3-33:
Figure GDA00031164600200000411
similarly, equations 3-22 and equations 3-26 are modified as follows:
if sign (W)1 (c)) -1, then:
equations 3-34:
Figure GDA00031164600200000412
equations 3-35:
Figure GDA00031164600200000413
if not, then,
formulas 3 to 36:
Figure GDA0003116460020000051
equations 3-37:
Figure GDA0003116460020000052
step 5, calculating the square root of the covariance matrix of the state prediction error:
equations 3-38:
Figure GDA0003116460020000053
equations 3-39:
Figure GDA0003116460020000054
step 6, updating the system state and the square root of the covariance according to the formulas 3-27 to 3-31, namely the estimated value at the k +1 moment
Figure GDA0003116460020000055
Including the estimated value of the battery SOC at the current moment and the polarization voltage UpAn estimate of the current time.
Compared with the prior art, the invention has the following beneficial effects: the method is characterized in that a first-order RC model is used for modeling the power battery of the electric automobile, the parameters of the model are identified, and then a strong tracking filter theory (STF) and a square root unscented Kalman filter algorithm (SR-UKF) are combined, so that the stability of the filter algorithm is ensured, the tracking capability of the algorithm on emergency is improved, and the SOC of the battery is estimated based on the algorithm. And performing off-line simulation verification by using the acquired battery voltage and current data, and substituting three different estimation algorithms for result comparison. Simulation results show that stable, effective and accurate estimation can be performed on the SOC of the battery under the condition of large noise interference based on the STF-SRUKF algorithm.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic diagram of a lithium iron phosphate battery of an electric vehicle in the prior art.
Fig. 2 is a schematic diagram of an RC battery model in an embodiment of the invention.
Fig. 3 is a graph illustrating the relationship between the open-circuit voltage and the state of charge SOC of a battery cell according to an embodiment of the present invention.
FIG. 4 is a diagram comparing a battery simulation model with experimental data in an embodiment of the present invention.
FIG. 5 is a diagram illustrating a comparison between EKF algorithm and UT transformation error in an embodiment of the present invention.
Fig. 6 is a schematic diagram of a voltage signal with noise added as an input of a battery state of charge SOC estimation algorithm according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of a current signal with noise added as an input of a battery state of charge SOC estimation algorithm according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a battery SOC estimation result according to an embodiment of the present invention.
FIG. 9 is a flow chart of a method in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in FIG. 1, the allowable working temperature range of the iron phosphate lithium battery is-30 to 55 degrees. Because the electrochemical reaction in the battery is very complicated, the parameters of the battery can be changed under the influence of various external factors such as temperature, pressure and the like. Therefore, the robustness requirement for the battery state of charge SOC estimation algorithm is high. The following table shows the performance parameters of the lithium iron phosphate battery of fig. 1.
Figure GDA0003116460020000061
The invention provides a method for estimating the state of charge of a battery, which adopts a first-order RC battery model, also called Thevenin model, as shown in figure 2, wherein the model simulates the polarization phenomenon of the battery by using a resistor/capacitor parallel circuit and describes the internal resistance of the battery by using a resistor. Both of these parameters change as the state of charge, SOC, of the battery changes.
According to the circuit principle, the characteristic equation of a first-order RC model can be deduced to be formula 3-1:
Figure GDA0003116460020000062
the current is used as an input value of a system, the end circuit voltage is used as a measured value of the system, the battery SOC and the polarization voltage are used as state quantities of the system, and a state equation of the power battery system can be established as follows, wherein the equation is shown in a formula 3-2:
Figure GDA0003116460020000063
Ul,krepresents the battery terminal voltage at time k; u shapep,kThe polarization voltage at time k; i.e. ikThe working current of the battery at the moment k; eta is the coulomb efficiency of charging and discharging the battery; t issIs a sampling time interval; tau ispIs a time constant; cnIs electricityThe rated capacity of the pool.
Wherein, the polarization capacitance C of the battery at the k momentpPolarization resistance RpAnd open circuit voltage UOCAre all SOC related functions, and need to be identified and fitted by an experimental method. The open circuit voltage is subjected to a point-taking experiment by using an OCV test, and experimental data and a fitting curve are shown in FIG. 3.
The remaining parameters of the cell model, e.g. polarization capacitance CpPolarization resistance RpThe time constant τ is identified by HPPC experiments. Because the conventional HPPC experiment only performs 0.75C charging and 1C discharging, and for the vehicle power battery, under the working conditions of vehicle braking energy recovery and rapid acceleration, the short-time charging and discharging of the battery can reach 5C, and under the working conditions, if the conventional HPPC experiment mode is adopted, the charging and discharging behaviors of the battery cannot be accurately modeled. Therefore, the charging current and the discharging current of the HPPC experiment are respectively 3.75C and 5C, 10 points are sequentially taken from 100% to 10% according to the SOC, and the interval between each point is 10%.
According to current and voltage data acquired by experiments, combining a battery model state equation and performing off-line identification based on a least square method, thereby obtaining a polarization capacitor CpPolarization resistance RpWith respect to the time constant τ and SOC. A first-order RC model of the battery is established in Simulink based on the identification result, the simulation result is compared with the experimental data, the result is shown in figure 4, and it can be seen that in figure 4, the error between the simulation model result and the experimental result is small, so that the model precision is available.
First, strong tracking filter theory (STF):
the strong tracking filtering theory is firstly proposed by professor Zhouyanhua of Qinghua university in 1990, and the core idea is to introduce a time-varying fading factor, and correct a state prediction error covariance matrix and a corresponding Kalman gain matrix in a Kalman filtering recursion process so as to force a residual sequence to be orthogonal or approximately orthogonal. When the model or the measured value has uncertainty or mutation, the STF algorithm calculates an fading factor for ensuring the irrelevance of the innovation sequence, thereby weakening the influence of historical data on the current filtering calculation value and enabling the algorithm to have the capability of tracking the mutation state.
For the Kalman filtering recursion system, the state estimation steps are as follows, and the formula is 3-3:
Figure GDA0003116460020000071
wherein
Figure GDA0003116460020000072
Is the residual sequence found by the state estimation filter equation. Under the condition that the Kalman filtering theory meets the formula 3-4, the strong tracking filter is added with the formula 3-5, so that residual sequences at different moments are orthogonal everywhere.
Equations 3-4:
Figure GDA0003116460020000073
equations 3-5:
Figure GDA0003116460020000074
in order to make equations 3-5 hold, the STF algorithm introduces a time-varying fading factor λ, adjusting the prediction error covariance matrix in real time, and further updating the kalman gain. The calculation method of the fading factor λ is as follows:
equations 3-6:
Figure GDA0003116460020000075
equations 3-7:
Figure GDA0003116460020000076
equations 3-8:
Figure GDA0003116460020000081
equations 3-9:
Figure GDA0003116460020000082
wherein, VkFor the error covariance matrix, the following is defined, equations 3-10:
Figure GDA0003116460020000083
in the formula, rho is more than 0 and less than or equal to 1 and is a forgetting factor, beta is more than or equal to 1 and is a weakening factor, and the estimation result can be smoother by increasing the value of beta. F and H are Jacobian matrixes of a system state equation and an observation equation respectively.
II, square root unscented Kalman Filter (SR-UKF):
the extended Kalman filtering adopts Taylor expansion to carry out linearization, and high-order nonlinear terms above the second order are ignored. Therefore, when the degree of non-linearity of the system is high, the accuracy of the EKF algorithm is poor, and the calculation is complex and easy to make errors. In order to solve the problem of loss of precision of linearization of the EKF algorithm, Julian professor of the Oxford university proposes a non-linear Kalman filtering algorithm based on UT transformation in 1995, omits the process of solving the Jacobian matrix, and approximates the statistical characteristics of the state quantities by using a series of sigma sampling points, namely the mean and covariance distribution of the sampling points is equal to the mean and covariance distribution of the state quantities. And then carrying out nonlinear transformation on the group of sampling points according to a state space equation of the system, and taking weighted average on the transformed sampling points to obtain the statistical characteristic of the approximate variable after nonlinear transformation, wherein the statistical characteristic is also equal to the mean value and the covariance of the state quantity.
The core method of Unscented Kalman Filtering (UKF) is UT transform. Intuitively, it is easier to approximate a probability distribution than to approximate an arbitrary non-linear function. Assume the mean of the state vector x
Figure GDA0003116460020000084
And covariance P is known, a set of determined vectors is found, called sigma points, with mean and covariance of the set of sigma points as
Figure GDA0003116460020000085
And P, then each determined vector is known to be non-linearAnd f (x) and h (x) of the linear function obtain a transformed vector, namely substituting the sigma point into the nonlinear function for calculation. The mean value and covariance of the transformed vector can accurately approximate the real mean value and covariance of the original state vector after nonlinear function transformation. The UT transform can achieve the fourth order accuracy of a taylor series, as shown in fig. 5.
The specific steps of the UT conversion algorithm are as follows:
(1) constructing sigma points
According to the mean value of the state vector x
Figure GDA0003116460020000086
With covariance P, the sigma point set { ξ is selected as followsi1,2, …, and a weight W corresponding to the point seti (m)And Wi (c)Equation 3-11:
Figure GDA0003116460020000087
where κ is a scale condition coefficient, which determines the accuracy of the sample value. At this time, sigma point set { ξiThe gaussian distribution of x is approximated.
(2) The sigma point set is propagated by a non-linear function
Calculating the selected sigma point set through a nonlinear function f (x) to obtain a nonlinear propagated sigma point set { Y }iWhen the probability distribution of Y is close to the probability distribution of the nonlinear function calculation value Y ═ f (x), equations 3-12:
Yi＝f(χi),i＝0,1,...,2n
(3) mean and covariance value calculation of transformed point sets
For the transformed sigma point set { YiWeighting to obtain the mean value and covariance of the output variables by calculation, wherein the weight value is equal to that of the input variables:
equations 3-13:
Figure GDA0003116460020000091
equations 3-14:
Figure GDA0003116460020000092
wherein, Wi mAnd Wi cThe weighting coefficients used for calculating the mean and covariance of the y-values are:
equations 3-15:
Figure GDA0003116460020000093
wherein κ ═ α2(n + λ) -n, α is positive and is usually slightly less than 1. Beta is a state distribution parameter, which is typically 2 for a gaussian distributed system. λ is typically set to 0 or 3-n. Adjusting the value of β can improve the accuracy of variance transformation, and adjusting the values of α and λ can improve the accuracy of the estimated mean.
When calculating the Sigma point, the UKF algorithm needs Cholesky decomposition on the covariance matrix, that is, positive determination of the covariance matrix is required. In the computer calculation process, truncation errors can be generated due to the limitation of calculation accuracy. With the accumulation of truncation errors or stepwise changes of parameters, the covariance matrix will likely lose the positive nature, thereby making the filtering process impossible. The square root UKF algorithm iteratively propagates the square root matrix of the covariance matrix, thereby avoiding factorization in the iterative process.
For nonlinear systems, equations 3-16:
Figure GDA0003116460020000094
the iteration steps of the square root unscented kalman filter are as follows:
initialization:
equations 3-17:
Figure GDA0003116460020000095
calculate Sigma point:
equations 3-18:
Figure GDA0003116460020000096
the time is updated as:
equations 3-19: chi shapek/k-1＝F[χk-1]
Formulas 3 to 20:
Figure GDA0003116460020000097
equations 3-21:
Figure GDA0003116460020000101
formulas 3 to 22:
Figure GDA0003116460020000102
equations 3-23: y isk/k-1＝H[χk/k-1]
Formulas 3 to 24:
Figure GDA0003116460020000103
wherein QR represents QR decomposition, cholemount represents Cholesky first-order update, and both are matlab executable function statements.
The measurement is updated as follows:
formulas 3 to 25:
Figure GDA0003116460020000104
equations 3-26:
Figure GDA0003116460020000105
equations 3-27:
Figure GDA0003116460020000106
equations 3-28:
Figure GDA0003116460020000107
formulas 3 to 29:
Figure GDA0003116460020000108
equations 3-30:
Figure GDA0003116460020000109
equations 3-31: sk＝cholupdate(Sk/k-1,U,-1)
Since SR-UKF also needs to carry out choleupdate decomposition in the iterative process, the product of the column vector of U and its transpose in the formulas 3-31 may have non-positive character, and the square root S of covariance P after choleupdate decomposition also loses positive character. To avoid this, the following modifications are made to equations 3-31:
let R be U (: i)TIf R is a positive definite matrix, then equations 3-32:
Sk＝cholupdate(Sk/k-1,U(:,i),-1)
otherwise, equations 3-33:
Figure GDA00031164600200001010
similarly, equations 3-22 and equations 3-26 are modified as follows:
if sign (W)1 (c)) -1, then equation 3-34:
equations 3-34:
Figure GDA00031164600200001011
equations 3-35:
Figure GDA00031164600200001012
otherwise, equations 3-36:
formulas 3 to 36:
Figure GDA00031164600200001013
equations 3-37:
Figure GDA00031164600200001014
thirdly, STF-SRUKF algorithm:
in summary, as shown in fig. 9, the present invention includes the following steps:
step 1, establishing a first-order RC model of the battery: the state space equation of the SOC estimation system of the battery can be known by the formula 3-2 and is substituted into the STF-SRUKF algorithm;
step 2, calculating a state estimation value of the system at the k moment according to a system state equation and an initial value
Figure GDA0003116460020000115
And PkEstimating the state of the system at the moment k +1 according to the data;
and step 3, time updating: the state estimation and innovation covariance matrices for the system are calculated from equations 3-19 through equations 3-26. At the moment, a time-varying fading factor is not introduced into the prediction covariance matrix;
and 4, step 4: calculating an fading factor: obtaining a lambda value at the k +1 moment according to the formulas 3-6 to 3-10;
step 5, calculating the square root of the covariance matrix of the state prediction error: equations 3-25 and equations 3-26 are modified to:
equations 3-38:
Figure GDA0003116460020000111
equations 3-39:
Figure GDA0003116460020000112
step 6: the system state and the square root of the covariance are updated according to equations 3-27 through 3-31, i.e., the estimated value at time k +1
Figure GDA0003116460020000113
Including the estimated value of the battery SOC at the current moment and the polarization voltage UpAn estimate of the current time.
In order to verify the effect and the anti-interference capability of the battery SOC estimation method, Gaussian white noise interference with a mean value of zero and a variance of 1A is added to current signals collected by experimental equipment, Gaussian white noise interference with a mean value of zero and a variance of 50mV is added to collected voltage signals, and the voltage and current signals added with noise are used as the input of a battery SOC estimation algorithm, as shown in FIG. 6 and FIG. 7.
The traditional EKF algorithm, the original SR-UKF algorithm and the STF-SRUKF algorithm proposed in the chapter are respectively adopted to estimate the SOC of the battery, the results of FIG. 8 show that the STF-SRUKF algorithm proposed in the chapter can remarkably reduce the influence of measurement noise on the estimation of the SOC of the battery, the precision is greatly improved compared with the EKF algorithm and the SR-UKF algorithm, the estimation precision of the STF-SRUKF algorithm is the highest under the larger noise interference, and the error is within +/-0.07.
The error analysis is shown in the following table 2, and it can be seen that, no matter the Root Mean Square Error (RMSE) or the Maximum Error (ME), the estimation result of the STF-SRUKF algorithm provided by the invention on the battery SOC is greatly superior to the traditional EKF algorithm and the original SR-UKF algorithm.
TABLE 2 Battery SOC estimation result error
Figure GDA0003116460020000114
The method uses the first-order RC model to model the power battery of the electric automobile, identifies the parameters of the model, and then combines the strong tracking filter theory (STF) with the square root unscented Kalman filter algorithm (SR-UKF), thereby not only ensuring the stability of the filter algorithm, but also improving the tracking capability of the algorithm to emergencies, and estimating the SOC of the battery based on the algorithm. And performing off-line simulation verification by using the acquired battery voltage and current data, and substituting three different estimation algorithms for result comparison. Simulation results show that stable, effective and accurate estimation can be performed on the SOC of the battery under the condition of large noise interference based on the STF-SRUKF algorithm.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method of estimating state of charge of a battery, comprising the steps of:
step 1, establishing a first-order RC model of the battery:
according to the circuit principle, a characteristic equation of a first-order RC model is deduced as shown in a formula 3-1:
Figure FDA0003131613580000011
wherein, UOThe terminal voltage of the battery, namely the voltage between the positive pole and the negative pole of the power supply; u shapePIs a polarization voltage; rintOhmic internal resistance; i is the working current of the battery;
the current is used as an input value of a system, the terminal voltage is used as a measured value of the system, the SOC and the polarization voltage of the battery are used as state quantities of the system, and a state equation of the power battery system can be established as follows, wherein the equation is shown in a formula 3-2:
Figure FDA0003131613580000012
wherein, Ul,kRepresents the battery terminal voltage at time k; u shapep,kThe polarization voltage at time k; i.e. ikThe working current of the battery at the moment k; eta is the coulomb efficiency of charging and discharging the battery; t issIs a sampling time interval; tau ispIs a time constant; cnIs the rated capacity of the battery;
polarization capacitance C of battery at time kpPolarization resistance RpAnd open circuit voltage UOCAll are SOC correlation functions, and an experimental method is needed for identification and fitting; open circuit voltage is obtained by an OCV test and a point taking experiment;
step 2, calculating the state estimation value of the system at the k moment according to the formula 3-2
Figure FDA0003131613580000017
And PkEstimating the state of the system at the moment k +1 according to the data;
for the Kalman filtering recursion system, the state estimation steps are as follows:
equation 3-3:
Figure FDA0003131613580000013
wherein
Figure FDA0003131613580000014
Is a residual sequence obtained by a state estimation filtering equation; under the condition that the Kalman filtering theory meets the formula 3-4, the strong tracking filter is added with the formula 3-5, so that residual sequences at different moments are orthogonal everywhere;
equations 3-4:
Figure FDA0003131613580000015
equations 3-5:
Figure FDA0003131613580000016
in order to establish the formulas 3-5, the STF algorithm introduces a time-varying fading factor lambda, and adjusts the covariance matrix of the prediction error in real time, so as to further update the Kalman gain; the calculation method of the fading factor λ is as follows:
equations 3-6:
Figure FDA0003131613580000021
equations 3-7:
Figure FDA0003131613580000022
equations 3-8:
Figure FDA0003131613580000023
equations 3-9:
Figure FDA0003131613580000024
wherein, VkFor the error covariance matrix, the following is defined:
formula 3-10:
Figure FDA0003131613580000025
in the formula, rho is more than 0 and less than or equal to 1 and is a forgetting factor, epsilon is more than or equal to 1 and is a weakening factor, and the estimation result can be smoother by increasing the epsilon value; f and H are Jacobian matrixes of a system state equation and an observation equation respectively;
construct sigma point, let' siAs a set of sigma points { ξiThe ith sigma point in the sigma, according to the mean value of the state vector x
Figure FDA0003131613580000026
With covariance P, the sigma point set { ξ is selected as followsi0,1,2, …,2n, and the weight W corresponding to the point seti (m)And Wi (c)：
Equations 3-11:
Figure FDA0003131613580000027
wherein, kappa is a scale condition coefficient and determines the precision of a sampling value; at this time, sigma point set { ξi-approximation of the gaussian distribution of x;
the sigma point set is propagated through a nonlinear function, the selected sigma point set is calculated through a nonlinear function f (x), and the nonlinear propagated sigma point set { Y) is obtainediAt this time, the probability of YThe probability distribution of the distribution and the nonlinear function calculated value y ═ f (x) is similar:
formulas 3 to 12: y isi＝f(χi),i＝0,1,...,2n
Calculating the mean value and covariance value of the transformed point set, and performing sigma point set { Y after transformationiWeighting to obtain the mean value and covariance of the output variables by calculation, wherein the weight value is equal to that of the input variables:
equations 3-13:
Figure FDA0003131613580000028
equations 3-14:
Figure FDA0003131613580000029
wherein, Wi (m)And Wi (c)The weighting coefficients used for calculating the mean and covariance of the y-values are:
Figure FDA0003131613580000031
Figure FDA0003131613580000032
equations 3-15:
Figure FDA0003131613580000033
wherein κ ═ α2The value of (n + theta) -n, alpha is positive and is slightly less than 1; beta is a state distribution parameter, and the value of the parameter is 2 for a system with Gaussian distribution; the scaling factor θ is set to 0 or 3-n; the precision of variance transformation can be improved by adjusting the value of beta, and the precision of the estimated mean value can be improved by adjusting the values of alpha and theta;
for nonlinear systems, equations 3-16:
Figure FDA0003131613580000034
the iteration steps of the square root unscented kalman filter are as follows:
initialization:
equations 3-17:
Figure FDA0003131613580000035
calculate Sigma point:
equations 3-18:
Figure FDA0003131613580000036
and step 3, updating the time as follows:
equations 3-19: chi shapek/k-1＝F[χk-1]
Formulas 3 to 20:
Figure FDA0003131613580000037
equations 3-21:
Figure FDA0003131613580000038
formulas 3 to 22:
Figure FDA0003131613580000039
equations 3-23: y isk/k-1＝H[χk/k-1]
Formulas 3 to 24:
Figure FDA00031316135800000310
wherein QR represents QR decomposition, cholepdate represents Cholesky first-order update, and the Cholesky first-order update are matlab executable function statements;
the measurement is updated as follows:
formulas 3 to 25:
Figure FDA00031316135800000311
equations 3-26:
Figure FDA00031316135800000312
step 4, calculating an fading factor:
equations 3-27:
Figure FDA0003131613580000041
equations 3-28:
Figure FDA0003131613580000042
formulas 3 to 29:
Figure FDA0003131613580000043
equations 3-30:
Figure FDA0003131613580000044
equations 3-31: sk＝cholupdate(Sk/k-1,U,-1)
Because SR-UKF also needs choleupdate in the iterative process, and the product of the column vector of U and its transposition in the formula 3-31 may have non-positive character, the square root S of covariance P after choleupdate also loses positive character; to avoid this, the following modifications are made to equations 3-31:
let R be U (: i)TIf R is a positive definite matrix, then equations 3-32:
Sk＝cholupdate(Sk/k-1,U(:,i),-1)
otherwise, equations 3-33:
Figure FDA0003131613580000045
similarly, equations 3-22 and equations 3-26 are modified as follows:
if sign (W)1 (c)) -1, then:
equations 3-34:
Figure FDA0003131613580000046
equations 3-35:
Figure FDA0003131613580000047
if not, then,
formulas 3 to 36:
Figure FDA0003131613580000048
equations 3-37:
Figure FDA0003131613580000049
step 5, calculating the square root of the covariance matrix of the state prediction error:
equations 3-38:
Figure FDA00031316135800000410
equations 3-39:
Figure FDA00031316135800000411
step 6, updating the system state and the square root of the covariance according to the formulas 3-27 to 3-31, namely the estimated value at the k +1 moment
Figure FDA00031316135800000412
Including the estimated value of the battery SOC at the current moment and the polarization voltage UpAn estimate of the current time.
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