CN110502778B - Adaptive optimization method for estimating battery SOC based on Kalman filtering framework - Google Patents

Adaptive optimization method for estimating battery SOC based on Kalman filtering framework Download PDF

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CN110502778B
CN110502778B CN201910596702.3A CN201910596702A CN110502778B CN 110502778 B CN110502778 B CN 110502778B CN 201910596702 A CN201910596702 A CN 201910596702A CN 110502778 B CN110502778 B CN 110502778B
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何志刚
魏涛
盘朝奉
周洪剑
李尧太
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Jiangsu University
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention discloses a self-adaptive optimization method for estimating the SOC of a battery based on a Kalman filtering framework, which comprises the steps of taking a second-order RC equivalent circuit as a battery model, identifying parameters of the second-order RC equivalent circuit by using battery pulse experimental data and an MATLAB parameter identification tool box, constructing a state equation and an observation equation of the battery according to a kirchhoff voltage law, adding a self-adaptive optimization strategy into an extended Kalman filtering algorithm according to a difference value estimated by an observed quantity and the observation equation, and applying the optimized extended Kalman filtering algorithm to the estimation of the SOC of the battery. The results show that: compared with the traditional extended Kalman filtering algorithm, the method provided by the invention has the advantages that the precision is improved by 0.3%, the fluctuation is smaller, and the accuracy and the practicability are good.

Description

Adaptive optimization method for estimating battery SOC based on Kalman filtering framework
Technical Field
The invention belongs to the field of state estimation of battery management systems, and particularly relates to a self-adaptive optimization method for estimating battery SOC based on a Kalman filtering framework.
Background
In recent years, many studies have been conducted to search for a battery state of charge (SOC) estimation method. One is a model driven method, such as an electrochemical model, an equivalent circuit model. The electrochemical model utilizes a complex electrochemical reaction mechanism in the battery to establish the battery power loss relation, the accuracy is high, but the calculation is very complex, and the application to practical engineering is difficult. The equivalent circuit model estimates the SOC of the battery by utilizing the external characteristics of the battery and based on self-adaptive filtering methods such as ampere-hour integration, Kalman filtering or particle filtering, reduces estimation errors caused by an initial value of the model in a closed-loop mode, and has high precision and small calculation pressure; still another class is data-driven methods, such as neural networks, genetic algorithms, support vector machines. The data driving method does not need to understand the internal mechanism or external characteristics of the battery, uses a black box control as a principle, finds the corresponding relation between input and output through a large amount of sample training, and has poor universality and limited practical use.
On the basis, the estimation of the battery SOC by the equivalent circuit model is favored by many scholars, and a series of improved algorithms based on kalman filtering, such as Kalman Filtering (KF), Extended Kalman Filtering (EKF), volume kalman filtering (CKF), and the like, are continuously appeared. However, the kalman filter algorithm and the joint algorithm using the kalman filter algorithm as a framework have the biggest disadvantages: the only type of the observed values that can be filtered is gaussian white noise, so the precondition for applying the kalman filtering algorithm is to assume that the system noise processed by the kalman filtering algorithm follows gaussian distribution. However, the actual system may be gaussian white noise or colored noise, so its filtering effect is limited.
Disclosure of Invention
The invention provides a self-adaptive optimization method for estimating the SOC of a battery based on a Kalman filtering framework under the condition that the filtering effect is limited because the filtering type of the battery SOC is only white Gaussian noise when the battery SOC is estimated by the Kalman filtering algorithm framework, so that the noise parameters can be adaptively changed according to the change of measurement feedback when the battery SOC is estimated by the Kalman filtering framework, and the filtering effect is better.
A self-adaptive optimization method for estimating the SOC of a battery based on a Kalman filtering framework is characterized by establishing a battery second-order RC equivalent circuit model, identifying parameters of the battery second-order RC equivalent circuit model, adding a self-adaptive optimization strategy to an extended Kalman filtering algorithm, and applying the adaptively optimized extended Kalman filtering algorithm to the estimation of the SOC of the battery.
Further, the adaptive optimization strategy is as follows:
is provided with
Figure BDA0002115930380000021
If (Δ)k-Δk-1＜0)
Figure BDA0002115930380000022
Otherwise (Δ)k-Δk-1＝0)
Rk＝Rk-1
Otherwise (Δ)k-Δk-1＞0)
Figure BDA0002115930380000023
Wherein ΔkFor the difference between the observed quantity at time k and the estimated observation equation, zkIs the observed quantity of the battery at the time k,
Figure BDA0002115930380000024
for a priori estimation of the state of the battery at time k, RkThe equation noise variance is observed for time k.
Further, the specific process of applying the adaptively optimized extended kalman filter algorithm to the battery SOC estimation is as follows:
(1) establishing a state equation and an observation equation of a battery
Figure BDA0002115930380000025
Wherein:
Figure BDA0002115930380000026
xkstate variable, time constant tau, representing a model1＝R1C1、τ2＝R2C2Eta is coulombic efficiency, Ik-1Represents the actual current at time k-1, f (SOC)k) Represents the open circuit voltage UOCIn relation to the SOC function, R0Is the ohmic internal resistance, R, of the battery1,R2For electrochemical polarization internal resistance and concentration polarization internal resistance of the cell, U1For electrochemical polarization of voltage, U2Is a concentration polarization voltage, C1,C2For electrochemical polarization capacitance and concentration polarization capacitance, omega, of the cellkAs noise of the equation of state, gammakTo observe noise;
(2) for algorithm parameter x0、P0、R0Carry out initialization
x0＝[1 0.01 0.01]T
Figure BDA0002115930380000031
R0＝0.5
(3) Prior estimation of state and state covariance
xk -＝f(xk-1)
Figure BDA0002115930380000032
Wherein:
Figure BDA0002115930380000033
is a priori estimate of the state of the battery at time k, xk-1Is the state quantity of the battery at the moment k-1,
Figure BDA0002115930380000034
for the prior estimation of the covariance of the state of the system at time k, A is f (x) in the nonlinear systemk -Partial derivatives of (A), Pk-1A covariance matrix of a system state at the moment of k-1, and Q is a noise variance of a system state equation;
(4) difference value delta estimated according to observed quantity and observation equationkAnd an adaptive optimization strategy to calculate the observed noise variance
Figure BDA0002115930380000035
Rk＝Rk-1
Figure BDA0002115930380000036
(5) Calculating Kalman gain coefficients
Figure BDA0002115930380000037
Wherein: kkA Kalman gain coefficient matrix at time k, H being a nonlinear system H (x) at xk -Partial derivatives ofR is the system observation equation noise variance;
(6) correcting a priori estimates of state and state covariance according to Kalman gain coefficients
Figure BDA0002115930380000038
Figure BDA0002115930380000039
Wherein: i is the identity matrix, PkIs the covariance matrix of the system state at time k.
Further, the open circuit voltage UOCThe relation with the SOC function is as follows:
Figure BDA0002115930380000041
further, the extended kalman filter may be replaced with an unscented kalman filter or a volumetric kalman filter.
Furthermore, parameters of the battery second-order RC equivalent circuit model are identified to establish a Simscape parameter identification model, the current is input into the Simscape parameter identification model, the voltage is output from the Simscape parameter identification model, and a solver module is added to configure a model simulation solving mode.
By adopting the technical scheme, the invention has the following beneficial effects:
(1) the invention adopts two RC circuits and a resistor R0The series connection second order RC equivalent circuit model, one RC circuit is used for simulating the battery electrochemistry polarization phenomenon, the other RC circuit is used for simulating the battery concentration polarization phenomenon, the equivalent circuit model not only can well explain the battery external characteristics, but also has five parameters to be identified in total, and the calculation complexity is smaller than that of the third order RC equivalent circuit model.
(2) The method utilizes a parameter identification tool box integrated by MATLAB and a Simscape physical model of a second-order RC circuit of the battery, takes the current of a battery pulse experiment as the input of a parameter identification model, takes the voltage as the output of the parameter identification model, adopts a nonlinear least square method to identify five parameters of the battery, and can adjust the iteration step number and the iteration error in the identification process according to the requirement of estimation precision.
(3) The invention estimates the difference value delta according to the observed quantity and the observation equationkAnd the sigmoid function characteristic is used for updating the observation equation noise variance in the iterative process of the extended Kalman filtering algorithm in real time, and compared with the traditional Kalman filtering algorithm, the improved extended Kalman filtering algorithm is adopted, so that the adaptive optimization strategy is easy to implement, the filtering effect is better, and the precision is higher.
Drawings
FIG. 1 is a flow chart of a method for adaptive optimization of estimating battery SOC according to the present invention;
FIG. 2 is a diagram of a second order RC equivalent circuit model;
FIG. 3 is a graph of a voltage curve profile for a battery pulse experiment;
FIG. 4 is a graph of a current curve profile for a battery pulse experiment;
FIG. 5 is a model diagram of battery parameter identification, FIG. 5(a) is a simulation diagram of Simulink and Simscape for battery parameter identification, and FIG. 5(b) is a simulation diagram of Simscape for RC circuit of battery 2;
FIG. 6 is a flow chart of the method for estimating the SOC of the battery by the extended Kalman filtering algorithm of the adaptive optimization method of the present invention;
FIG. 7 is a comparison graph of EKF algorithm and adaptive optimization EKF algorithm estimation results;
FIG. 8 is a graph comparing EKF algorithm and adaptive optimization EKF algorithm estimated error.
Detailed Description
The technical solution of the present invention will be further described in more detail with reference to the following embodiments.
As shown in fig. 1, the adaptive optimization method for estimating the SOC of the battery based on the kalman filter framework of the present invention has the following implementation processes:
the method comprises the following steps: a second-order RC equivalent circuit model is adopted as a battery simulation model, and as shown in figure 2, two RC circuits are connected in series and then connected with a resistor R0Series, RC electricityThe circuit is formed by connecting a resistor and a capacitor in parallel; wherein R is0Is the ohmic internal resistance, R, of the battery1,R2For the electrochemical polarization internal resistance and concentration polarization internal resistance of the cell, C1,C2For electrochemical polarization capacitance and concentration polarization capacitance of the cell, UOCFor open circuit voltage of battery, U1For electrochemical polarization of voltage, U2Is a concentration polarization voltage, UtIs the battery terminal voltage.
Step two: after the battery simulation model is built in the first step, parameter identification is carried out on the model, the parameter identification data come from pulse experimental data of the battery, the battery is a ternary lithium battery, the rated capacity is 3.2Ah, and the specific experimental steps are as follows:
fully charging the battery in a normal constant-current constant-voltage charging mode, and standing for one hour;
discharging the battery at 1C multiplying power for 10% of discharging depth, and standing for one hour;
and thirdly, repeating the step II until the battery discharges 100 percent of discharge depth.
The current and voltage variation data of the battery are recorded, the experimental data are shown in fig. 3 and fig. 4, the voltage in fig. 3 is used as the output of the Simscape parameter identification model in fig. 5(a), and the current in fig. 4 is used as the input of the Simscape parameter identification model in fig. 5 (b).
Battery experimental data is imported into an MATLAB parameter identification toolbox, and a Simscape parameter identification model of the battery is established, wherein the model is shown in fig. 5 (a). The method is characterized in that current is input into the Simscape parameter identification model, voltage is output from the Simscape parameter identification model, and a solver f (x) 0 module is added to configure a solving mode of simulation of the Simscape parameter identification model.
Then, the parameter R of 2RC (see fig. 5(b)) in fig. 5 is subjected to the nonlinear least square method built in the parameter identification tool box0、R1、R2、C1、C2The identification is performed, and the identification result is shown in table 1.
TABLE 1 second order RC equivalent circuit model parameter identification results
Figure BDA0002115930380000051
Step three: the working principle of the extended Kalman method is to expand a nonlinear model near a state mean value according to Taylor formula, and take a first-order approximate term as a system state equation and a measurement equation, so that the extended Kalman method can extend a Kalman algorithm from a linear system to a nonlinear system. The Kalman filtering algorithm is an algorithm with the minimum mean square error as a criterion, and updates the system state according to the state estimation value of the system at the previous moment and the observation value at the current moment. The extended kalman filter of the present embodiment may be replaced with an unscented kalman filter or a volumetric kalman filter. The state equation and the observation equation of the battery are as follows:
xk -＝f(xk-1)+ωk (1)
Figure BDA0002115930380000061
wherein:
Figure BDA0002115930380000067
is a priori estimate of the state of the battery at time k, xk-1Is the state quantity, omega, of the battery at the moment k-1kAs noise of equation of state, zkIs the observed quantity of the battery at time k, gammakTo observe the noise.
The state and state covariance time are updated as:
xk -＝f(xk-1) (3)
Figure BDA0002115930380000062
wherein:
Figure BDA0002115930380000063
for the prior estimation of state covariance at time k, A is f (x) in a nonlinear systemk -Partial derivatives of (A), Pk-1Is a state covariance matrix at the time of k-1, and Q is the state equation noise variance. Time managementThe new process is mainly the prior estimation of the current time state and prepares for the measurement and correction of the next time.
Kalman gain coefficient calculation:
Figure BDA0002115930380000064
wherein: kkA Kalman gain coefficient matrix at time k, H being a nonlinear system H (x) at xk -And R is the observation equation noise variance. In the process of calculating the Kalman gain coefficient, when the battery system tends to be in a stable state, the Kalman coefficient can keep a smaller value.
State and state covariance measurement update:
Figure BDA0002115930380000065
Figure BDA0002115930380000066
wherein: i is the identity matrix, PkIs the state covariance matrix at time k. The process is mainly a feedback process, and the accurate estimated value of the state is obtained by adding the prior estimated value of the current state and the correction quantity of the actual measured value.
From equations (5) - (7), it can be seen that the battery system state is recurred through successive estimation-correction cycles, thereby approaching the true state. However, the method also has a disadvantage that the noise variance Q of the state equation and the noise variance R of the observation equation are constant values and do not modify themselves in real time along with the feedback process, so that the kalman gain coefficient of the extended kalman algorithm still keeps a small value when the fluctuation of the feedback process is large, and the system state with large fluctuation cannot be tracked. Aiming at the defects, the invention improves the extended Kalman filtering algorithm and provides a self-adaptive optimization strategy to improve the filtering effect of the extended Kalman, which comprises the following steps:
k-time observation quantity and observation partyDifference of range estimation
Figure BDA0002115930380000071
Figure BDA0002115930380000072
By using
Figure BDA0002115930380000073
The function can map the independent variable x to the function characteristic between (0, 1) and update the observation equation noise variance R in real time according to the observation feedback, so that the observation equation noise variance of Kalman filtering can adapt to the change of noise in the observation equation, and the adaptive optimization strategy is designed.
According to the adaptive optimization strategy described above, the observation equation noise variance R can modify itself according to the observation feedback value, when the observation feedback is large, i.e., ΔkIncrease (Δ)k-Δk-1> 0), according to
Figure BDA0002115930380000074
R can be reduced in real time, so that Kalman gain KkBecomes large so that the state estimation value depends on the observation value; and when the observed feedback is small, i.e. ΔkDecrease (Delta)k-Δk-1< 0), based on
Figure BDA0002115930380000075
R can be increased in real time, and then Kalman gain KkSmall, making the state estimate dependent on the a priori estimate.
Step four: establishing a state equation and an observation equation of the battery according to a second-order RC equivalent circuit model of the battery and kirchhoff's law:
Figure BDA0002115930380000081
wherein:
Figure BDA0002115930380000082
xkstate variable, time constant tau, representing a model1＝R1C1Time constant τ2＝R2C2Eta is coulombic efficiency, and the value range is generally 0.98-1, Ik-1Represents the actual current at time k-1, f (SOC)k) Represents according to the open circuit voltage UOCAs a function of SOC.
Open circuit voltage UOCThe relation with the SOC function is as follows:
Figure BDA0002115930380000083
the optimized extended kalman filtering algorithm is applied to the estimation of the SOC of the battery, and the flow chart is shown in fig. 6, and the specific process is as follows:
(1) firstly, establishing a state equation and an observation equation of the battery, wherein the state equation and the observation equation are shown in a formula (8);
(2) second pair of algorithm parameters x0、P0、R0Carrying out initialization;
x0＝[1 0.01 0.01]T (9)
Figure BDA0002115930380000084
R0＝0.5 (11)
(3) then, carrying out prior estimation on the state and the state covariance;
xk -＝f(xk-1) (12)
Figure BDA0002115930380000091
(4) then estimating the difference value delta according to the observed quantity and the observed equationkCalculating the noise variance of the observation equation by using a self-adaptive optimization strategy;
Figure BDA0002115930380000092
Rk＝Rk-1 (15)
Figure BDA0002115930380000093
(5) calculating a Kalman gain coefficient;
Figure BDA0002115930380000094
(6) and finally, correcting the state and the prior estimation of the state covariance according to the Kalman gain coefficient and the formulas (6) and (7).
Step five: the state quantity (namely the SOC estimation result) of the battery is obtained according to the self-adaptive optimization extended Kalman filtering algorithm in the fourth step, meanwhile, the state quantity is compared with the unmodified extended Kalman filtering estimation result, the fact that when the SOC of the battery is estimated through the self-adaptive optimization extended Kalman filtering algorithm is found, the accuracy is improved by 0.3%, the fluctuation is smaller, the accuracy and the errors of the two algorithms are compared and analyzed, the accuracy ratio is shown in figure 7, the error ratio is shown in figure 8, and the error mean value and the error root mean square are shown in table 2.
TABLE 2 EKF Algorithm versus adaptive optimization strategy EKF Algorithm estimation error comparison
Figure BDA0002115930380000095
From the estimation result and the estimation error, the adaptive optimization strategy added to the extended Kalman filtering algorithm provided by the invention has higher precision and better robustness than the traditional extended Kalman filtering algorithm, and from the aspect of the adaptive optimization strategy, the calculation is convenient, and the calculation complexity of the extended Kalman filtering algorithm cannot be increased.
It should be noted that the purpose of the present embodiment is to better explain the present invention, and not to limit the protection scope of the present invention. The algorithm parameter values and the specific battery parameters set in the embodiments are only required for the verification of the experiment, and based on the embodiments of the present invention, all other embodiments without creative work by those skilled in the art should belong to the protection scope of the present invention.

Claims (4)

1. A self-adaptive optimization method for estimating the SOC of a battery based on a Kalman filtering framework is characterized by establishing a battery second-order RC equivalent circuit model, identifying parameters of the battery second-order RC equivalent circuit model, adding a self-adaptive optimization strategy into an extended Kalman filtering algorithm, and applying the adaptively optimized extended Kalman filtering algorithm to the estimation of the SOC of the battery;
the specific process of applying the self-adaptive optimized extended Kalman filtering algorithm to the battery SOC estimation is as follows:
(1) establishing a state equation and an observation equation of a battery
Figure FDA0002995373160000011
Wherein:
Figure FDA0002995373160000012
xkstate variable, time constant tau, representing a model1＝R1C1、τ2＝R2C2Eta is coulombic efficiency, Ik-1Represents the actual current at time k-1, f (SOC)k) Represents the open circuit voltage UOCIn functional relation to SOC, SOCkIs state of charge at time k, R'0Is ohmic internal resistance of the battery, R'1、R′2For electrochemical polarization internal resistance and concentration polarization internal resistance of the cell, U1,kElectrochemical polarization voltage at time k, U2,kConcentration polarization voltage at time k, C1,C2For electrochemical polarization capacitance and concentration polarization capacitance, omega, of the cellkAs noise of the equation of state, gammakTo observe noise;
(2) for algorithm parametersx0、P0、R0Carry out initialization
x0＝[1 0.01 0.01]T
Figure FDA0002995373160000013
R0＝0.5
(3) Prior estimation of state and state covariance
xk -＝f(xk-1)
Figure FDA0002995373160000021
Wherein:
Figure FDA0002995373160000022
is a priori estimate of the state of the battery at time k, xk-1Is the state quantity of the battery at the moment k-1,
Figure FDA0002995373160000023
for the prior estimation of the covariance of the state of the system at time k, A is f (x) in the nonlinear systemk -Partial derivatives of (A), Pk-1A covariance matrix of a system state at the moment of k-1, and Q is a noise variance of a system state equation;
(4) difference value delta estimated according to observed quantity and observation equationkAnd calculating an observed noise variance using an adaptive optimization strategy;
is provided with
Figure FDA0002995373160000024
If Δk-Δk-1＜0，
Figure FDA0002995373160000025
If Δk-Δk-1＝0，
Rk＝Rk-1；
If Δk-Δk-1＞0，
Figure FDA0002995373160000026
Wherein ΔkFor the difference between the observed quantity at time k and the estimated observation equation, zkIs the observed quantity of the battery at time k, xkA priori estimate of the state of the battery at time k, RkObserving equation noise variance for k time;
(5) calculating Kalman gain coefficients
Figure FDA0002995373160000027
Wherein: kkA Kalman gain coefficient matrix at time k, H being a nonlinear system H (x) at xk -Partial derivatives of (c);
(6) correcting a priori estimates of state and state covariance according to Kalman gain coefficients
Figure FDA0002995373160000028
Figure FDA0002995373160000029
Wherein: i is the identity matrix, PkIs the covariance matrix of the system state at time k.
2. The Kalman filtering framework based adaptive optimization method for estimating battery SOC of claim 1, in which the open circuit voltage U isOCThe relation with the SOC function is as follows:
Figure FDA0002995373160000031
3. the Kalman filtering framework based adaptive optimization method for estimating battery SOC of claim 1, in which the extended Kalman filtering may be replaced by unscented Kalman filtering or volumetric Kalman filtering.
4. The Kalman filtering frame-based adaptive optimization method for estimating the SOC of the battery according to claim 1, wherein the parameters of the battery second-order RC equivalent circuit model are identified to establish a Simscape parameter identification model, the current is input into the Simscape parameter identification model, the voltage is output from the Simscape parameter identification model, and a solver module is added to configure a model simulation solving mode.
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