CN111812530A - Lithium battery state of charge estimation method - Google Patents

Lithium battery state of charge estimation method Download PDF

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CN111812530A
CN111812530A CN202010571493.XA CN202010571493A CN111812530A CN 111812530 A CN111812530 A CN 111812530A CN 202010571493 A CN202010571493 A CN 202010571493A CN 111812530 A CN111812530 A CN 111812530A
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lithium battery
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丁洁
凤良
林金星
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Nanjing University of Posts and Telecommunications
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables

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Abstract

The invention discloses a lithium battery state of charge estimation method, which comprises the following steps: establishing a second-order RC equivalent circuit model of the lithium battery to describe the internal dynamic characteristic change of the lithium battery, and establishing a state space equation by utilizing an ampere-hour integral method and electrical knowledge; identifying the model parameters by a least square algorithm with forgetting factors, and improving the identification precision of the model; establishing a functional relation between OCV and SOC by a constant current charge-discharge experiment; the participation of historical data in the EKF is considered, and the importance of innovation at different moments in the filtering process is calculated by utilizing the thought of calculating the weight of the particles; calculating weights of the innovation at different moments by considering different importance degrees of the innovation, and distributing the weights; the discrete sliding mode observer is introduced into the WI-EKF, the jitter problem caused by the sliding mode observer is considered, the saturated gain function is introduced to reduce the jitter, and the SOC estimation precision is improved.

Description

Lithium battery state of charge estimation method
Technical Field
The invention relates to a battery state measuring method, in particular to a lithium battery state of charge estimating method.
Background
In order to cope with the continuously worsening environment and the shortage of petroleum resources, the new energy industry has been rapidly developed worldwide. As an important part of the new energy industry, research on pure electric vehicles is supported by many companies. As a key component of electric vehicles, the research on lithium ion power batteries is of great significance to electric vehicles. The SOC may be used to directly reflect the remaining capacity of the battery and accurately estimate the state of charge (SOC) of the lithium battery, which may prevent over-discharge or over-charge of the battery, help protect the battery from explosion or fire, and improve the performance of the battery.
Since SOC cannot be measured directly during operation of the electric vehicle, and high non-linearity exhibited during use of the battery pack makes accurate estimation of SOC more difficult. With the development and popularization of the electric vehicle industry, how to accurately estimate the SOC has become a hot research focus in recent years. At present, the main SOC estimation methods mainly comprise an open-circuit voltage method, an ampere-hour integration method, a neural network method and an extended Kalman filtering algorithm.
The open circuit voltage method can simply and directly show the relationship between the OCV and the SOC, but the test is required to be carried out in a battery standing state, the method is not suitable for real-time online test of the electric automobile, and the relationship between the OCV and the SOC changes along with the change of the ambient temperature, the aging degree and the chemical property of the lithium battery, so that the accurate estimation of the SOC is influenced. The ampere-hour integration method is an integration algorithm, is simple and practical, but in the practical application process, the SOC estimation result is inaccurate due to the inaccuracy of the initial value of the SOC and the accumulated error of the current along with the time. The neural network method requires a large amount of data for training, and the training data and the training method have a large influence on the estimation accuracy of the SOC. The extended Kalman filtering algorithm needs to establish a battery equivalent circuit model, establish a nonlinear discrete state space model of the lithium battery and estimate the SOC by combining a recursion algorithm, and the method is simple and easy to implement, but the precision of the method is greatly influenced by the model.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a high-precision lithium battery state-of-charge (SOC) estimation method, and particularly relates to a lithium battery state-of-charge (SOC) estimation method combining an improved Discrete Sliding Mode Observer (DSMO) and a weighted multi-innovation extended Kalman filter (WI-EKF).
The technical scheme is as follows: the invention provides a lithium battery state of charge estimation method, which comprises the following steps:
(1) establishing a second-order RC equivalent circuit model of the lithium battery to describe the internal dynamic characteristic change of the lithium battery, and establishing a state space equation by utilizing an ampere-hour integral method and electrical knowledge;
(2) identifying the model parameters by a least square algorithm with forgetting factors, and improving the identification precision of the model;
(3) establishing a functional relation between OCV and SOC by a constant current charge-discharge experiment;
(4) the participation of historical data in the EKF is considered, and the importance of innovation at different moments in the filtering process is calculated by utilizing the thought of calculating the weight of the particles;
(5) calculating weights of the innovation at different moments by considering different importance degrees of the innovation, and reasonably distributing the weights;
(6) the discrete sliding mode observer is introduced into the WI-EKF, the jitter problem caused by the sliding mode observer is considered, the saturated gain function is introduced to reduce the jitter, and the SOC estimation precision is improved.
Further, the electrical characteristic expression of the equivalent circuit model in the step (1) is as follows:
UL＝Uoc-Ua-Ub-IL·R0
Figure BDA0002550039280000021
Figure BDA0002550039280000022
wherein, UL＝Uoc-Ua-Ub-IL·R0Representing the terminal voltage of the second order RC equivalent circuit model, wherein UocOpen circuit voltage, U, representing a second order RC equivalent circuit modelLIs a terminal voltage, R, representing a second order RC equivalent circuit model0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbRespectively represent electrochemical polarization capacitance and concentration polarization capacitance,
obtaining an SOC expression of the lithium battery by an ampere-hour integration method:
Figure BDA0002550039280000023
and combining the electrical knowledge with an ampere-hour integral method to obtain a discrete state space equation of the equivalent circuit model:
Figure BDA0002550039280000024
wherein x (k) ═ Ua(k) Ub(k) SOC(k)]T，u(k)＝I(k)，y(k)＝UL(k)，
Figure BDA0002550039280000025
D＝-R0
τa＝Ra·Ca，τb＝Rb·CbAnd T denotes a sampling period.
Further, a discrete recursive expression is obtained by the electrical characteristic expression as follows:
ΔU(k)＝θ1ΔU(k-1)+θ2ΔU(k-2)+θ3I(k)+θ4I(k-1)+θ5I(k-2)
wherein Δ U (k) ═ UL(k)-Uoc(k) By measurement, θi(i ═ 1, 2, 3, 4, 5) are the model parameters to be identified,
the recursive expression can then be expressed as:
Figure BDA0002550039280000032
wherein
Figure BDA0002550039280000033
Introducing a forgetting factor lambda to correct the accumulated error of time-varying old data and converging to a true value, wherein the least square algorithm with the forgetting factor comprises the following steps:
Figure BDA0002550039280000034
Figure BDA0002550039280000035
Figure BDA0002550039280000036
wherein the content of the first and second substances,
Figure BDA0002550039280000037
represents an estimate of the model parameters at time k, L (k) is an innovation vector,
Figure BDA0002550039280000038
is a covariance matrix.
Further, the function relationship between the OCV and the SOC in step (3) is:
Figure BDA0002550039280000039
further, the step (4) takes the property of the gaussian function as an idea to obtain the importance of each innovation in the EKF process as follows:
Figure BDA00025500392800000310
Figure BDA00025500392800000311
wherein σ represents the measurement noise of the second order RC equivalent circuit model.
Further, the importance is normalized in the step (5):
Figure BDA00025500392800000312
calculating the weight:
Figure BDA00025500392800000313
constructing a weight of the corresponding innovation vector:
Figure BDA00025500392800000314
further, in the step (6), a discrete sliding-mode observer is introduced into the WI-EKF,
Figure BDA00025500392800000315
wherein the content of the first and second substances,
Figure BDA0002550039280000041
is an observed value estimated at the moment k, H is a gain matrix, J is a saturation gain function, sign (phi) is a symbolic function, phi is a boundary layer, in order to reduce the jitter problem introduced by the sliding-mode observer, sat (phi) function is introduced to replace the symbolic function,
Figure BDA0002550039280000042
and (3) mixing the improved discrete sliding-mode observer and the weighted multi-innovation extended Kalman filtering estimation SOC.
Firstly, establishing a second-order RC equivalent circuit model of the lithium battery to describe the internal dynamic characteristic change of the lithium battery, and establishing a state space equation by utilizing an ampere-hour integral method and electrical knowledge; identifying the model parameters by a least square algorithm with forgetting factors, and improving the identification precision of the model; then, establishing a functional relation between the OCV and the SOC through a constant-current charge-discharge experiment; then, the participation of historical data in the EKF is considered, and the importance of the innovation at different moments in the filtering process is calculated by utilizing the thought of calculating the weight of the particles; then, considering the difference of importance degrees of the innovation, calculating the weight of the innovation at different moments, and reasonably distributing the weight; and finally, introducing the discrete sliding mode observer into the WI-EKF, and introducing a saturation gain function to reduce the jitter and improve the SOC estimation precision in consideration of the jitter problem caused by the sliding mode observer.
Has the advantages that: according to the method, for the state estimation of the lithium battery at the set moment, the participation of historical data in EKF filtering data is considered, the innovation weights at different moments are reasonably calculated and distributed through the particle weight calculation idea, the discrete sliding mode observer is introduced, in order to reduce the jitter problem caused by the discrete sliding mode observer, a saturated gain function is introduced to replace a sign function, the jitter is reduced, and the SOC estimation precision is improved. The invention utilizes the data of the moment before the set moment and reasonably distributes the innovation weights of different moments, introduces a discrete sliding mode observer to further improve the SOC estimation precision, and introduces a function to replace a symbolic function to reduce the jitter caused by the discrete sliding mode observer. By combining the discrete sliding-mode observer and the weighted multi-innovation extended Kalman filtering, the SOC state estimation precision is improved, and the method is simple and easy to realize.
Drawings
FIG. 1 is a flow diagram illustration of an example method;
FIG. 2 is a schematic diagram of the second order RC equivalent circuit in the embodiment;
FIG. 3 is a graph of OCV versus SOC as described in the examples;
FIG. 4 is a diagram showing SOC estimation results in an intermittent discharge experiment according to the method of the embodiment;
fig. 5 is a diagram illustrating SOC estimation error results in an intermittent discharge experiment according to the exemplary method.
Detailed Description
Referring to fig. 1, the lithium battery state of charge estimation method based on the hybrid improved discrete sliding-mode observer and the weighted multi-innovation extended kalman filter of the embodiment specifically includes the following steps:
firstly, an equivalent circuit model of the lithium battery is a second-order RC equivalent circuit model, and the internal dynamic characteristics of the lithium battery are described by the second-order RC equivalent circuit model; in order to better describe the internal dynamic characteristics of the lithium battery, two RC rings exist in the second-order RC circuit model, the two RC rings effectively isolate the concentration polarization resistance and the electrochemical polarization resistance of the lithium battery, and the model precision is improved.
The electrical characteristic expression of the equivalent circuit model is as follows:
UL＝Uoc-Ua-Ub-IL·R0
Figure BDA0002550039280000051
Figure BDA0002550039280000052
wherein, UL＝Uoc-Ua-Ub-IL·R0Representing the terminal voltage of the second order RC equivalent circuit model, wherein UocOpen circuit voltage, U, representing a second order RC equivalent circuit modelLIs a terminal voltage, R, representing a second order RC equivalent circuit model0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbElectrochemical polarization capacitance and concentration polarization capacitance are respectively represented.
Obtaining an SOC expression of the lithium battery by an ampere-hour integration method:
Figure BDA0002550039280000053
and combining the electrical knowledge with an ampere-hour integral method to obtain a discrete state space equation of the equivalent circuit model:
Figure BDA0002550039280000054
wherein x (k) ═ Ua(k) Ub(k) SOC(k)]T，u(k)＝I(k)，y(k)＝UL(k)，
Figure BDA0002550039280000055
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbAnd T denotes a sampling period.
Secondly, model parameter identification is carried out on the second-order RC equivalent circuit model through a least square method with forgetting factors, and identification accuracy of the model is improved.
Deriving a discrete recursive expression from the electrical expression as:
ΔU(k)＝θ1ΔU(k-1)+θ2ΔU(k-2)+θ3I(k)+θ4I(k-1)+θ5I(k-2)
wherein Δ U (k) ═ UL(k)-Uoc(k) As can be obtained by means of the measurements,
Figure BDA0002550039280000057
are the model parameters to be identified.
The recursive expression can then be expressed as:
Figure BDA0002550039280000061
wherein
Figure BDA0002550039280000062
And introducing a forgetting factor lambda to correct the accumulated error of the time-varying old data and quickly converge to a true value. The least squares algorithm with forgetting factor is as follows:
Figure BDA0002550039280000063
Figure BDA0002550039280000064
Figure BDA0002550039280000065
wherein the content of the first and second substances,
Figure BDA0002550039280000066
represents an estimate of the model parameters at time k, L (k) is an innovation vector,
Figure BDA0002550039280000067
is a covariance matrix.
Obtaining an OCV-SOC function expression through a constant current charge and discharge experiment:
Figure BDA0002550039280000068
discharge OCV-SOC function expression:
Uocd＝1813.4*SOC9-8629.9*SOC8+17470*SOC7-19595*SOC6
+13285*SOC5-5570.7*SOC4+1419.9*SOC3-208.1*SOC2+15.953 SOC +2.7228 charging OCV-SOC function expression
Uocv＝3060.5*SOC9-13713*SOC8+25909*SOC7-26862*SOC6
+16655*SOC5-6310.9*SOC4+1434.4*SOC3-185.1*SOC2+12.471*SOC+2.9002
Fourthly, calculating the importance of the information corresponding to different moments in the multi-information extended Kalman filter based on the thought of calculating the weight of the particles in the particle filter algorithm; in the invention, each innovation is regarded as a particle in the particle filter algorithm, and the importance of each innovation is calculated by utilizing a method for calculating the weight of the particle in the particle filter algorithm. In the particle filter estimation process, particles closer to an observed value have higher weight, namely, the particle filter estimation has better estimation effect through the latest data; meanwhile, the particles that are not very close to the observed value have relatively small weights, i.e., the particle filter estimation is an estimation operation process based on all data; in a gaussian function, the closer to the peak of the gaussian function, the greater the weight. Therefore, the invention constructs a gaussian function for this:
Figure BDA0002550039280000069
as can be seen from the above formula, if x and μ are expressed by innovation, f (x) represents the importance of the innovation; it is clear that x can be represented by a new message, and μ ═ 0, so the importance of each new message is that each importance can be obtained as:
Figure BDA0002550039280000071
Figure BDA0002550039280000072
wherein, sigma represents the measurement noise of the second-order Thevenin equivalent circuit model.
Calculating the weight of each importance corresponding to the innovation according to each importance, and reasonably distributing the weight of each innovation in the multi-innovation extended Kalman; specifically, since the sum of all innovation weights is the length of the innovation, based on the importance of each innovation obtained above, the process of obtaining the weight corresponding to each innovation is as follows: importance is first normalized:
Figure BDA0002550039280000073
the weights are then calculated:
Figure BDA0002550039280000074
finally, the innovation vector corresponding to the weight can be constructed as follows:
Figure BDA0002550039280000075
and sixthly, introducing the discrete sliding mode observer into a state space equation.
Figure BDA0002550039280000076
Wherein the content of the first and second substances,
Figure BDA0002550039280000077
is the observed value estimated at time k, H is the gain matrix, J is the saturation gain function, sign (·) is the sign function, and Φ is the boundary layer. To reduce the jitter problem introduced by the sliding-mode observer, the sat (-) function is introducedIn place of the sign function.
Figure BDA0002550039280000078
A hybrid improved discrete sliding-mode observer and a weighted multi-innovation extended Kalman filter are used for estimating the SOC, an estimated value is compared with an actual value, and the accuracy of the algorithm is verified; specifically, an intermittent discharge experiment is adopted for verification, in the experimental process, the external conditions for controlling the experimental simulation are consistent, the initial value of the SOC is set to be 1, and the process noise is set to be 10-7The measurement noise is set to 0.1; and from an analysis of the stability of the system,
Figure BDA0002550039280000079
H＝[0.000015；0.000015；0.000015]，J＝[0.000015；0.000015；0.000015]. The SOC of the lithium battery is estimated by respectively using the extended Kalman filtering algorithm, the mixed improved discrete sliding-mode observer and the weighted multi-innovation extended Kalman filtering algorithm, the experimental result can be seen in fig. 4 and 5, and the SOC accuracy estimated by using the mixed improved discrete sliding-mode observer and the weighted multi-innovation extended Kalman filtering algorithm is greatly improved compared with that estimated by using the traditional extended Kalman filtering method, and the error of the SOC estimated by using the method disclosed by the invention is controlled within 0.5% as can be seen from fig. 5, while the error of the SOC estimated by using the extended Kalman filtering algorithm is much larger; compared with the prior art, the method has better accuracy on SOC estimation, thereby achieving the effects of improving the use reliability of the battery, improving the utilization rate of the energy of the battery and prolonging the service life of the battery.

Claims (7)

1. A lithium battery state of charge estimation method is characterized in that: the method comprises the following steps:
(1) establishing a second-order RC equivalent circuit model of the lithium battery to describe the internal dynamic characteristic change of the lithium battery, and establishing a state space equation by utilizing an ampere-hour integral method and electrical knowledge;
(2) identifying the model parameters by a least square algorithm with forgetting factors, and improving the identification precision of the model;
(3) establishing a functional relation between OCV and SOC by a constant current charge-discharge experiment;
(4) the participation of historical data in the EKF is considered, and the importance of innovation at different moments in the filtering process is calculated by utilizing the thought of calculating the weight of the particles;
(5) calculating weights of the innovation at different moments by considering different importance degrees of the innovation, and distributing the weights;
(6) and introducing a discrete sliding mode observer into the WI-EKF, and introducing a saturation gain function to reduce jitter and perform SOC estimation by considering the jitter problem brought by the sliding mode observer.
2. The lithium battery state of charge estimation method of claim 1, wherein: the electrical characteristic expression of the equivalent circuit model in the step (1) is as follows:
UL＝Uoc-Uo-Ub-IL·R0
Figure FDA0002550039270000011
Figure FDA0002550039270000012
wherein, UL＝Uoc-Ua-Ub-IL·R0Representing the terminal voltage of the second order RC equivalent circuit model, wherein UocOpen circuit voltage, U, representing a second order RC equivalent circuit modelLIs a terminal voltage, R, representing a second order RC equivalent circuit model0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbRespectively represent electrochemical polarization capacitance and concentration polarization capacitance,
obtaining an SOC expression of the lithium battery by an ampere-hour integration method:
Figure FDA0002550039270000013
and combining the electrical knowledge with an ampere-hour integral method to obtain a discrete state space equation of the equivalent circuit model:
Figure FDA0002550039270000014
wherein x (k) ═ Ua(k) Ub(k) SOC(k)]T，u(k)＝I(k)，y(k)＝UL(k)，
Figure FDA0002550039270000021
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbAnd T denotes a sampling period.
3. The lithium battery state of charge estimation method of claim 2, wherein: obtaining a discrete recursive expression by the electrical characteristic expression as follows:
Figure FDA0002550039270000022
wherein Δ U (k) ═ UL(k)-Uoc(k) As can be obtained by means of the measurements,
Figure FDA0002550039270000023
is the parameter of the model to be identified,
the recursive expression can then be expressed as:
Figure FDA0002550039270000024
wherein
Figure FDA0002550039270000025
Introducing a forgetting factor lambda to correct the accumulated error of time-varying old data and converging to a true value, wherein the least square algorithm with the forgetting factor comprises the following steps:
Figure FDA0002550039270000026
Figure FDA0002550039270000027
Figure FDA0002550039270000028
wherein the content of the first and second substances,
Figure FDA0002550039270000029
represents an estimate of the model parameters at time k, L (k) is an innovation vector,
Figure FDA00025500392700000210
is a covariance matrix.
4. The lithium battery state of charge estimation method of claim 1, wherein: the function relationship between the OCV and the SOC in the step (3) is as follows:
Figure FDA00025500392700000211
5. the lithium battery state of charge estimation method of claim 1, wherein: the step (4) takes the property of the Gaussian function as an idea to obtain the importance of each innovation in the EKF process, and comprises the following steps:
Figure FDA00025500392700000212
Figure FDA00025500392700000213
wherein σ represents the measurement noise of the second order RC equivalent circuit model.
6. The lithium battery state of charge estimation method of claim 1, wherein: normalizing said importance in said step (5):
Figure FDA0002550039270000031
calculating the weight:
Figure FDA0002550039270000032
constructing a weight of the corresponding innovation vector:
Figure FDA0002550039270000033
7. the lithium battery state of charge estimation method of claim 1, wherein: in the step (6), a discrete sliding-mode observer is introduced into the WI-EKF,
Figure FDA0002550039270000034
wherein the content of the first and second substances,
Figure FDA0002550039270000035
is an observed value estimated at the moment k, H is a gain matrix, J is a saturation gain function, sign (phi) is a symbolic function, phi is a boundary layer, in order to reduce the jitter problem introduced by the sliding-mode observer, sat (phi) function is introduced to replace the symbolic function,
Figure FDA0002550039270000036
and (3) mixing the improved discrete sliding-mode observer and the weighted multi-innovation extended Kalman filtering estimation SOC.
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CN112946480A (en) * 2021-01-28 2021-06-11 中国矿业大学 Lithium battery circuit model simplification method for improving SOC estimation real-time performance
CN112946481A (en) * 2021-01-29 2021-06-11 南京邮电大学 Based on federation H∞Filtering sliding-mode observer lithium ion battery SOC estimation method and battery management system
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CN114114021A (en) * 2021-11-12 2022-03-01 山东大学 Lithium ion battery model considering nonlinear solid phase diffusion and parameter identification method
CN114114021B (en) * 2021-11-12 2022-09-09 山东大学 Lithium ion battery model considering nonlinear solid phase diffusion and parameter identification method
CN115015767A (en) * 2022-08-04 2022-09-06 华南理工大学 Lithium battery SOC estimation method based on multi-innovation unscented Kalman filtering algorithm fusion
CN116224099A (en) * 2023-05-06 2023-06-06 力高(山东)新能源技术股份有限公司 Method for dynamically and adaptively estimating battery SOC

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