CN114114037A - Power battery SOC estimation method based on fuzzy PID-UKF - Google Patents

Power battery SOC estimation method based on fuzzy PID-UKF Download PDF

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CN114114037A
CN114114037A CN202111338805.3A CN202111338805A CN114114037A CN 114114037 A CN114114037 A CN 114114037A CN 202111338805 A CN202111338805 A CN 202111338805A CN 114114037 A CN114114037 A CN 114114037A
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范兴明
贠祥
张鑫
吴军科
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Guilin University of Electronic Technology
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    • 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]
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Abstract

The invention discloses a power battery SOC estimation method based on fuzzy PID-UKF, which comprises the following steps: (A) establishing a battery model for parameter identification; (B) acquiring a functional relation between OCV and SOC under an HPPC working condition; (C) performing SOC calculation by using an unscented Kalman filtering algorithm; (D) and correcting the error by adopting a fuzzy PID algorithm. The estimation algorithm is different from the traditional PID-UKF estimation method, the traditional PID-UKF aims at PID control of a parallel subsystem of a battery pack, the obtained SOC estimation result is not aimed at a single battery in the battery pack, the result has certain error, and the estimated SOC value can not be used as the balance management basis of the battery pack; meanwhile, different from a method for directly carrying out SOC by using fuzzy PID, UKF estimation is carried out firstly, the UKF is transformed by UT, a Jacobian matrix does not need to be calculated, the precision of the UKF can reach at least two orders, and PID coefficients are adjusted by fuzzy, so that the estimation method disclosed by the invention has better adaptability to nonlinear functions and higher estimation precision.

Description

Power battery SOC estimation method based on fuzzy PID-UKF
Technical Field
The invention relates to the technical field of lithium battery SOC estimation, in particular to an electric vehicle lithium battery SOC estimation method based on fuzzy PID-UKF.
Background
In recent electric automobile safety accidents, the pure electric power type is the main power of a fire accident, and the battery problem is the main reason. The improvement of the reliability of the battery management system is significant, particularly the accurate SOC estimation, many functions in the battery management system depend on the accurate estimation of the SOC, and the accurate estimation of the SOC of the power battery is the key for fully and reasonably utilizing the power battery and the key for establishing a good power battery management system.
The UKF is unscented Kalman filtering, is an algorithm combining unscented transformation and Kalman filtering, and is used for processing the nonlinear problem by adopting the idea of probability density distribution, so that the UKF is a nonlinear estimation algorithm with better development prospect. The PID is an automatic controller which is controlled according to proportion, integral and differential of deviation, and has the advantages of simple principle, easy realization, wide application range, mutually independent control parameters and the like.
Common SOC estimation methods include an ampere-hour integral method, a neural network method, extended Kalman filtering and the like. The ampere-hour integration method has high accuracy in the charge and discharge stage, but has the problems of difficulty in determining an initial value and accumulative error. The neural network model has good self-learning capability, can approximate nonlinear characteristics, and does not need prior knowledge of the model structure. Theoretically, when enough neurons exist, the neural network model can fully simulate the dynamic characteristics of the battery and has higher precision. The neural network method has the disadvantages that a large amount of experimental data is needed to train the parameters, and the SOC estimation error is greatly influenced by the training data and the training method. The extended kalman filter algorithm (EKF algorithm) is a first-order approximation algorithm that is linearized based on taylor series expansion of a nonlinear function, and if it is desired to improve the approximation accuracy, a reserved order may be added, for example, the order is expanded to two or higher orders to form a second-order or higher-order approximation algorithm, but this requires a higher-order matrix, which results in a substantial increase in the amount of computation and an insignificant improvement in the filter accuracy.
Disclosure of Invention
The invention provides a power battery SOC estimation method based on fuzzy PID-UKF, which aims to solve the problems of the common SOC estimation method.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a power battery SOC estimation method based on fuzzy PID-UKF comprises the following steps:
(A) establishing a battery model for parameter identification;
(B) acquiring a functional relation between OCV and SOC under an HPPC working condition;
(C) performing SOC calculation by using an unscented Kalman filtering algorithm;
(D) and correcting the error by adopting a fuzzy PID algorithm.
Further, the battery model in the step (a) is a second-order RC equivalent circuit model, and the identified parameters include battery internal resistance R0Polarization resistance R1Polarization resistance R2And a polarization capacitor C1And a polarization capacitor C2。
Further, in the step (a), the battery is identified by a forgetting factor least square method, and the forgetting factor recursive least square method formula is as follows:
Figure BDA0003351610000000021
in the formula
Figure BDA0003351610000000022
In the form of a vector of data,
Figure BDA0003351610000000023
a prediction of the observed value; y (k) is the actual observed value; k (k) is a gain term; λ is a forgetting factor, and is generally in the range of 0.95 ≦ λ ≦ 1; i is the identity matrix of the corresponding dimension.
Further, in the step (B), a functional relationship between OCV and SOC is obtained under the HPPC working condition, and a polynomial fitting function tool cftool in Matlab is used to perform 6 th order curve fitting on the data, where the functional relationship is as follows:
UOCV＝a1·SOC6+a2·SOC5+a3·SOC4+a4·SOC3+a5·SOC2+a6·SOC1+a7
wherein a is1～a7Is the fitting parameter and Uocv is the open circuit voltage.
Further, the step (C) of using the unscented kalman filter algorithm to perform SOC calculation includes the steps of:
(1) let E (x) be the expected value of the random variable, given an initial value
Figure BDA0003351610000000024
The initial value of covariance P0Comprises the following steps:
Figure BDA0003351610000000025
(2) selecting a Sigma point according to the optimal state variable and the error covariance at the current k momentiFor the selected particle, WiFor the corresponding weight values, the equation is as follows:
Figure BDA0003351610000000031
the corresponding weighting coefficients are:
Figure BDA0003351610000000032
wherein λ is a proportionality parameter, corresponding to: λ ═ α2(L+κ)-L，ω(m)Is the mean value of the particle points, ω(c)Is the weighted value corresponding to the variance of the particle point;
Figure BDA0003351610000000033
is (L + lambda) PXColumn i of the square root matrix; α is the molecular distance of the particle, β is used to reduce the high order term error, and L represents the dimension of the state variable;
(3) and calculating the sigma point at the k-1 moment as follows:
Figure BDA0003351610000000034
(4) according to the state variable of the sigma point at the k-1 moment, prediction is carried out through the state variable
Figure BDA0003351610000000035
(5) K-time covariance prediction according to k-time sigma point
Figure BDA0003351610000000036
(6) Estimating a measurement equation
Figure BDA0003351610000000037
(7) Obtaining the state variable gain K and the state variable at the time K
Figure BDA0003351610000000038
Covariance Pk，
Figure BDA0003351610000000039
Figure BDA0003351610000000041
Figure BDA0003351610000000042
Figure BDA0003351610000000043
Further, in the step (D), the fuzzy PID algorithm is adopted to correct the error, and the formula is as follows:
Δy(k)＝kp(ek-ek-1)+kIek+kD(ek-2ek-1+ek-2)
Figure BDA0003351610000000044
wherein ekFor the measured voltage ykAnd predicting terminal voltage
Figure BDA0003351610000000045
Δ y (K) is the product of the gain factor K and the innovation e, KPIs a proportionality coefficient, KIIntegral coefficient, KDIs a differential coefficient.
Further, the three parameters of the PID in the step (D) are realized by fuzzy control, and the realization steps are as follows:
1) determining input and output variables; the input variable being the measured voltage ykAnd predicting terminal voltage
Figure BDA0003351610000000046
Difference e and kalman gain kk，kP、kI、kDTo output, e includes ek-ek-1、ek、ek-2ek-1+ek-2；
2) Domain discourse and membership degree of each variable; e.g. of the typek-ek-1、ek、ek-2ek-1+ek-2Respectively of [ -0.01, 0.01]、[-0.02，0.02]、[-0.01，0.01]Output quantity kP、kI、kDHas a discourse field of [ -0.06, respectively]、[-0.06，0.06]、[-0.02，0.02]The fuzzy languages are { NB (negative big), NM (negative middle), NS (negative small), Z0 (zero), PS (positive small), PM (middle big), NB (positive big) }, kkHas a discourse field of [0, 1]The fuzzy language set is { Z0 (zero), PS (positive small), PM (positive middle), PB (positive large) }, and all the membership function corresponding to the fuzzy language is triangle membershipA function;
3) establishing a fuzzy rule; and (3) forming a control rule by a plurality of if-then conditional statements of the fuzzy control: ife and kk，then kP、kI、kDThe method is realized by utilizing a fuzzy control tool box in Matlab;
4) and carrying out fuzzy operation, and finally carrying out sharpening treatment by adopting a weighted average method.
The invention has the following beneficial effects:
1. and performing SOC estimation by using unscented Kalman filtering, controlling errors by using PID, and adjusting PID coefficients by using a fuzzy rule so as to realize dynamic error correction.
2. The fuzzy PID-UKF algorithm is adopted for the single battery, the application range of the PID algorithm is expanded, the algorithm extends from the battery pack to the single battery, and the estimation precision of the single battery is improved.
3. The estimation algorithm is different from the traditional PID-UKF estimation method, the traditional PID-UKF aims at PID control of a parallel subsystem of a battery pack, the obtained SOC estimation result is not aimed at a single battery in the battery pack, the result has certain error, and the estimated SOC value can not be used as the balance management basis of the battery pack; meanwhile, different from a method for directly carrying out SOC by using fuzzy PID, UKF estimation is carried out firstly, the UKF is transformed by UT, a Jacobian matrix does not need to be calculated, the precision of the UKF can reach at least two orders, and PID coefficients are adjusted by fuzzy, so that the estimation method disclosed by the invention has better adaptability to nonlinear functions and higher estimation precision.
Drawings
FIG. 1 is a flow chart of a power battery SOC estimation method based on fuzzy PID-UKF of the invention;
FIG. 2 is a second order RC equivalent circuit model diagram of the present invention;
FIG. 3 is a flow chart of the fuzzy PID of the invention with respect to e and K;
FIG. 4 is a comparison graph of fuzzy PID-UKF and UKF under the DST condition of the present invention;
FIG. 5 is a fuzzy PID-UKF and UKF error comparison diagram under the DST condition of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, technical solutions in embodiments of the present invention will be clearly and completely described below with reference to specific embodiments and with reference to the accompanying drawings. It should be noted that the described embodiments of the present invention are illustrative, but this is not a limitation of the present invention, and thus the present invention is not limited to the above-described embodiments. Other embodiments, which are within the scope of the invention, are contemplated by those skilled in the art, based on the teachings herein, and are obtained without the exercise of inventive faculty.
As shown in fig. 1, the present embodiment provides a power battery SOC estimation method based on fuzzy PID-UKF, which includes the following steps:
(A) establishing a battery model for parameter identification;
(B) acquiring a functional relation between OCV and SOC under an HPPC working condition;
(C) performing SOC calculation by using an unscented Kalman filtering algorithm;
(D) and correcting the error by adopting a fuzzy PID algorithm, and dynamically correcting the error value.
Battery modeling and parameter identification
Since the first-order equivalent circuit model cannot describe the polarization effect of the battery, a second-order RC equivalent circuit model is adopted, as shown in FIG. 2, wherein Uocv is the open-circuit voltage of the battery and the internal resistance R of the battery0Polarization resistance R1Polarization resistance R2And a polarization capacitor C1And a polarization capacitor C2K is time, U1、U2Is C1、C2I (k) is a current value at the k-th time, and u (k) is a terminal voltage.
The lithium battery is identified through a forgetting factor least square method, and the forgetting factor recursion least square method formula is as follows:
Figure BDA0003351610000000061
in the formula
Figure BDA0003351610000000062
In the form of a vector of data,
Figure BDA0003351610000000063
a prediction of the observed value; y (k) is the actual observed value; k (k) is a gain term; λ is a forgetting factor, and is generally in the range of 0.95 ≦ λ ≦ 1; i is the identity matrix of the corresponding dimension.
Second, SOC-OCV function relationship
Carrying out HPPC working condition experiment on the lithium battery, and carrying out 6-order relation curve fitting on data by utilizing a polynomial fitting function tool cftool in Matlab, wherein a1～a7Is a fitting parameter, Uocv is the open circuit voltage, and the functional relationship is as follows:
UOCV＝a1·SOC6+a2·SOC5+a3·SOC4+a4·SOC3+a5·SOC2+a6·SOC1+a7 (2)
third, using unscented Kalman filter algorithm to calculate SOC
The estimation with unscented kalman filtering steps are as follows:
(1) let E (x) be the expected value of the random variable, given an initial value
Figure BDA0003351610000000064
The initial value of covariance P0Comprises the following steps:
Figure BDA0003351610000000065
(2) selecting a Sigma point according to the optimal state variable and the error covariance at the current k momentiFor the selected particle, WiFor the corresponding weight values, the equation is as follows:
Figure BDA0003351610000000071
the corresponding weighting coefficients are:
Figure BDA0003351610000000072
wherein λ is a proportionality parameter, corresponding to: λ ═ α2(L+κ)-L，ω(m)Is the mean value of the particle points, ω(c)Is the weighted value corresponding to the variance of the particle point;
Figure BDA0003351610000000073
is (L + lambda) PXColumn i of the square root matrix; α is the molecular distance of the particle, β is used to reduce the high order term error, and L represents the dimension of the state variable.
(3) And calculating the sigma point at the k-1 moment as follows:
Figure BDA0003351610000000074
(4) according to the state variable of the sigma point at the k-1 moment, prediction is carried out through the state variable
Figure BDA0003351610000000075
(5) K-time covariance prediction according to k-time sigma point
Figure BDA0003351610000000076
(6) Estimating a measurement equation
Figure BDA0003351610000000077
(7) Obtaining the state variable gain K and the state variable at the time K
Figure BDA0003351610000000078
Covariance Pk，
Figure BDA0003351610000000079
Figure BDA0003351610000000081
Figure BDA0003351610000000082
Figure BDA0003351610000000083
Fourthly, in order to correct the error value more accurately, the fuzzy PID algorithm is adopted to correct the error, and the formula is as follows, wherein ekFor the measured voltage ykAnd predicting terminal voltage
Figure BDA0003351610000000084
Δ y (K) is the product of the gain factor K and the innovation e, KPIs a proportionality coefficient, KIIntegral coefficient, KDIs a differential coefficient.
Δy(k)＝kp(ek-ek-1)+kIek+kD(ek-2ek-1+ek-2) (14)
Figure BDA0003351610000000085
Three parameters of the PID are realized by fuzzy control, as shown in fig. 3, and the realization steps are as follows:
(1) determining input and output variables; the input variable of the invention is the measured voltage ykAnd predicting terminal voltage
Figure BDA0003351610000000086
Difference e and Carl ofMangan gain kk，kP、kI、kDTo output, e includes ek-ek-1、ek、ek-2ek-1+ek-2。
(2) Domain discourse and membership degree of each variable; e.g. of the typek-ek-1、ek、ek-2ek-1+ek-2Respectively of [ -0.01, 0.01]、[-0.02，0.02]、[-0.01，0.01]Output quantity kP、kI、kDHas a discourse field of [ -0.06, respectively]、[-0.06，0.06]、[-0.02，0.02]The fuzzy languages are { NB (negative big), NM (negative middle), NS (negative small), Z0 (zero), PS (positive small), PM (middle big), NB (positive big) }, kkHas a discourse field of [0, 1]The fuzzy language set is { Z0 (zero), PS (positive small), PM (positive middle), PB (positive large) }. All membership functions corresponding to the fuzzy languages are triangular membership functions.
(3) Establishing a fuzzy rule; and (3) forming a control rule by a plurality of if-then conditional statements of the fuzzy control: if e and kk，then kP、kI、kD. Implementation in Matlab is done with a fuzzy control toolbox.
(4) Then carrying out fuzzy operation, and finally carrying out sharpening processing by adopting a weighted average method.
According to the method, firstly, a battery model is established for parameter identification, the functional relation between OCV and SOC is solved through the working condition of HPPC, then the SOC is estimated by using unscented Kalman filtering, PID control is introduced on the basis of unscented Kalman filtering algorithm for error correction, and PID parameters are realized through fuzzy control. The DST working condition is injected into the algorithm of the invention for calculation, the SOC, UKF and the true value calculated in the embodiment are compared, and as shown in FIG. 4, the result shows that the algorithm of the invention has better tracking effect. The error ratio of the algorithm and the UKF is shown in FIG. 5, and the error result shows that compared with the 2.85% error of the UKF, the algorithm of the embodiment can effectively ensure that the SOC estimation error is within 2.24%, effectively improves the SOC estimation precision, improves the precision by 21.4%, and highlights the remarkable progress of the technology of the invention.
While there has been described and illustrated what are considered to be example embodiments of the present invention, it will be understood by those skilled in the art that various changes and substitutions may be made therein without departing from the spirit of the invention. In addition, many modifications may be made to adapt a particular situation to the teachings of the present invention without departing from the central concept described herein. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments and equivalents falling within the scope of the invention.

Claims (7)

1. A power battery SOC estimation method based on fuzzy PID-UKF is characterized by comprising the following steps:
(A) establishing a battery model for parameter identification;
(B) acquiring a functional relation between OCV and SOC under an HPPC working condition;
(C) performing SOC calculation by using an unscented Kalman filtering algorithm;
(D) and correcting the error by adopting a fuzzy PID algorithm.
2. The fuzzy PID-UKF-based power battery SOC estimation method of claim 1, wherein the battery model in step (A) is a second order RC equivalent circuit model, and the identified parameter includes battery internal resistance R0Polarization resistance R1Polarization resistance R2And a polarization capacitor C1And a polarization capacitor C2。
3. The fuzzy PID-UKF-based power battery SOC estimation method according to claim 1, wherein the battery parameter identification in step (A) is carried out by forgetting factor least square method, and the forgetting factor recursion least square method formula is as follows:
Figure FDA0003351609990000011
in the formula
Figure FDA0003351609990000012
In the form of a vector of data,
Figure FDA0003351609990000013
a prediction of the observed value; y (k) is the actual observed value; k (k) is a gain term; λ is a forgetting factor, and is generally in the range of 0.95 ≦ λ ≦ 1; i is the identity matrix of the corresponding dimension.
4. The fuzzy PID-UKF based power battery SOC estimation method of claim 1, wherein in step (B) the functional relationship between OCV and SOC is obtained under HPPC working condition, and a polynomial fitting function tool cftool in Matlab is used to fit the data with a 6 th order relation curve, the functional relationship is as follows:
UOCV＝a1·SOC6+a2·SOC5+a3·SOC4+a4·SOC3+a5·SOC2+a6·SOC1+a7
wherein a is1～a7Is the fitting parameter and Uocv is the open circuit voltage.
5. The fuzzy PID-UKF based power battery SOC estimation method of claim 1, wherein the SOC calculation using unscented Kalman filter algorithm in step (C) comprises the following steps:
(1) let E (x) be the expected value of the random variable, given an initial value
Figure FDA0003351609990000021
The initial value of covariance P0Comprises the following steps:
Figure FDA0003351609990000022
(2) selecting a Sigma point according to the optimal state variable and the error covariance at the current k momentiFor the selected particle, WiFor the corresponding weight values, the equation is as follows：
Figure FDA0003351609990000023
The corresponding weighting coefficients are:
Figure FDA0003351609990000024
wherein λ is a proportionality parameter, corresponding to: λ ═ α2(L+κ)-L，ω(m)Is the mean value of the particle points, ω(c)Is the weighted value corresponding to the variance of the particle point;
Figure FDA0003351609990000025
is (L + lambda) PXColumn i of the square root matrix; α is the molecular distance of the particle, β is used to reduce the high order term error, and L represents the dimension of the state variable;
(3) and calculating the sigma point at the k-1 moment as follows:
Figure FDA0003351609990000026
(4) according to the state variable of the sigma point at the k-1 moment, prediction is carried out through the state variable
Figure FDA0003351609990000027
(5) K-time covariance prediction according to k-time sigma point
Figure FDA0003351609990000028
(6) Estimating a measurement equation
Figure FDA0003351609990000031
(7) Obtaining the state variable gain K and the state variable at the time K
Figure FDA0003351609990000032
Covariance Pk，
Figure FDA0003351609990000033
Figure FDA0003351609990000034
Figure FDA0003351609990000035
Figure FDA0003351609990000036
6. The fuzzy PID-UKF based power battery SOC estimation method of claim 1, wherein the fuzzy PID algorithm is used to correct the error in step (D), the formula is as follows:
Δy(k)＝kp(ek-ek-1)+kIek+kD(ek-2ek-1+ek-2)
Figure FDA0003351609990000037
wherein ekFor the measured voltage ykAnd predicting terminal voltage
Figure FDA0003351609990000038
Difference of (a) y(k) Is the product of a gain factor K and an innovation e, KPIs a proportionality coefficient, KIIntegral coefficient, KDIs a differential coefficient.
7. The fuzzy PID-UKF based power battery SOC estimation method of claim 1, wherein the three parameters of PID in step (D) are realized by fuzzy control, the realization steps are as follows:
1) determining input and output variables; the input variable being the measured voltage ykAnd predicting terminal voltage
Figure FDA0003351609990000039
Difference e and kalman gain kk，kP、kI、kDTo output, e includes ek-ek-1、ek、ek-2ek-1+ek-2；
2) Domain discourse and membership degree of each variable; e.g. of the typek-ek-1、ek、ek-2ek-1+ek-2Respectively of [ -0.01, 0.01]、[-0.02，0.02]、[-0.01，0.01]Output quantity kP、kI、kDHas a discourse field of [ -0.06, respectively]、[-0.06，0.06]、[-0.02，0.02]The fuzzy languages are { NB (negative big), NM (negative middle), NS (negative small), Z0 (zero), PS (positive small), PM (middle big), NB (positive big) }, kkHas a discourse field of [0, 1]The fuzzy language set is { Z0 (zero), PS (positive and small), PM (positive and large), PB (positive and large) }, and membership function corresponding to all fuzzy languages is a triangular membership function;
3) establishing a fuzzy rule; and (3) forming a control rule by a plurality of if-then conditional statements of the fuzzy control: ife and kk，then kP、kI、kDThe method is realized by utilizing a fuzzy control tool box in Matlab;
4) and carrying out fuzzy operation, and finally carrying out sharpening treatment by adopting a weighted average method.
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