CN112946481A - Based on federation H∞Filtering sliding-mode observer lithium ion battery SOC estimation method and battery management system - Google Patents

Based on federation H∞Filtering sliding-mode observer lithium ion battery SOC estimation method and battery management system Download PDF

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CN112946481A
CN112946481A CN202110134380.8A CN202110134380A CN112946481A CN 112946481 A CN112946481 A CN 112946481A CN 202110134380 A CN202110134380 A CN 202110134380A CN 112946481 A CN112946481 A CN 112946481A
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丁洁
姚建鑫
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]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • 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

Abstract

The invention discloses a method based on joint H∞The filtering sliding-mode observer lithium ion battery SOC estimation method and the battery management system comprise the steps of S1, using a second-order Thevenin equivalent circuit model as an equivalent circuit model of a lithium ion battery; s2, establishing an electrical characteristic expression of the second-order Thevenin equivalent circuit model through kirchhoff' S law; s3, establishing a state space equation of the second-order Thevenin equivalent circuit model according to an ampere-hour integration method and an electrical characteristic expression, and discretizing the state space equation; s4, identifying parameters of the second-order Thevenin equivalent circuit model through an intermittent discharge experiment, and establishing a functional relation between the open-circuit voltage and the SOC; s5, fitting sliding-mode observer and H∞The filter combination realizes the filtering of the signal with noise, reduces the jitter problem of the discrete sliding mode observer, and provides a more accurate estimation value for the estimation state of the sliding mode observer. The invention can improve the accuracy of SOC estimation, and is simple and easy to realize.

Description

Based on federation H∞Filtering sliding-mode observer lithium ion battery SOC estimation method and battery management system
Technical Field
The invention relates to a lithium ion battery state evaluation method, in particular to a joint H-based lithium ion battery state evaluation method∞A filtering sliding-mode observer lithium ion battery SOC estimation method and a battery management system are provided.
Background
With the increasing energy crisis and environmental pollution, the traditional energy has the problems of pollution, non-regeneration and the like, and the social demand for new energy is higher and higher. Therefore, in recent years, new energy electric vehicles have been the focus of research in various countries for sustainable development of the environment. The lithium ion battery has the characteristics of large energy density, long cycle life, low self-discharge rate, low environmental pollution and the like, and gradually replaces the traditional lead-acid battery and nickel-cadmium battery to become the first choice of the power battery of the electric automobile. In order to realize the management and control of the grouped energy storage batteries and ensure that the energy storage equipment safely and efficiently operates, the electric automobile needs to be correspondingly managed through a battery management system. The technology for observing the residual electric quantity of the battery, namely the charge state of the battery, is a core technology of a battery management system, acquires the real-time value of the residual electric quantity of the battery by combining online acquired external parameters of the battery with a corresponding algorithm, and has important significance for maintaining safe and efficient operation of battery system equipment, prolonging the life cycle of the battery, improving the safety and reliability of the battery, improving the utilization rate of an energy battery and prolonging the service life.
The using process of the lithium ion battery is an electrochemical change process, and the process is extremely complex and mainly shows multivariable, nonlinear and complex electrochemistry. The state of charge cannot be directly measured under dynamic operating conditions, and the main methods of the current main SOC estimation method include a direct measurement method, a data driving method and a model-based direct measurement method. Model-based direct measurement methods include coulometry and open circuit voltage methods. The coulomb counting method is accurate in estimating the SOC, but is very sensitive to initial value errors of the SOC and accumulated errors in an iteration process. The open-circuit voltage rule is based on a relationship between an open-circuit voltage (OCV) and an SOC, which may be affected by an external environment and a lifespan, thereby causing inaccuracy in SOC estimation. Data-driven methods include neural network methods and fuzzy logic methods. These methods require measuring large amounts of data that are accurately detected by sophisticated hardware devices and are affected by different data sets. Model-based methods are mainly closed-loop estimation methods that estimate SOC by measuring real-time parameters of the battery and using load current and terminal voltage as inputs to an equivalent model. The internal dynamic characteristics of the battery are usually described by electrochemical models and equivalent circuit models, and the SOC is estimated by combining with a filtering algorithm. A common Extended Kalman Filter (EKF) solves the nonlinear problem of the battery by using taylor's formula, but its accuracy is greatly affected by the model.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a method based on joint H∞The filtering sliding-mode observer lithium ion battery SOC estimation method and the battery management system mainly solve the problems of poor robustness and inaccurate precision of conventional filtering and improve the precision of lithium ion battery SOC estimation.
The technical scheme is as follows: the technical scheme adopted by the invention is based on joint H∞The SOC estimation method of the lithium ion battery of the sliding mode observer comprises the following steps:
s1, establishing a second-order Thevenin equivalent circuit model as an equivalent circuit model of the lithium ion battery;
s2, establishing an electrical characteristic expression of the second-order Thevenin equivalent circuit model;
s3, establishing a state space equation of a second-order Thevenin equivalent circuit model according to an ampere-hour integration method and the electrical characteristic expression, and discretizing the state space equation; the resulting discretized state space equation is:
Figure BDA0002922891600000021
wherein x (k) ═ SOC (k) Ua(k)Ub(k)]T，u(k)＝IL(k)，y(k)＝UL(k)，
Figure BDA0002922891600000022
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbT represents sampling period, eta represents battery charging and discharging coulombic efficiency, and QnTo representMaximum available capacity under the current conditions, where ULRepresenting the terminal voltage, U, of the second order Thevenin equivalent circuit modelocRepresents the open-circuit voltage, U, of the second-order Thevenin equivalent circuit modelaAnd UbRepresents the polarization voltage of the cell, ILRepresents the current, R0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbElectrochemical polarization capacitance and concentration polarization capacitance are respectively represented.
S4, obtaining a standard form of the discrete state sliding-mode observer under the condition that the discrete state space equation can observe the full rank of the matrix; the standard form of the discrete state sliding mode observer is as follows:
Figure BDA0002922891600000023
in the formula:
Figure BDA0002922891600000024
as an estimate of the state variable:
Figure BDA0002922891600000025
an estimate value output by the system; l is a gain matrix of the state observer; sat (-) is a saturation function, M is a saturation gain function;
Figure BDA0002922891600000026
is a boundary layer; the specific expression of sat (. cndot.) is as follows:
Figure BDA0002922891600000027
where sgn (·) is a sign function.
S5, identifying and calculating the parameters of the second-order Thevenin equivalent circuit model through a recursive least square algorithm, and establishing a functional relation between the open-circuit voltage and the SOC, wherein the specific process is as follows:
using a z-plane based transfer function:
Figure BDA0002922891600000028
wherein theta is1、θ2、θ3、θ4And theta5For the coefficients related to the model parameters, each parameter can be specifically calculated by the following formula:
Figure BDA0002922891600000031
wherein T represents a sampling period;
let E (k) be UL(k)-UoAnd c, (k) discretizing to obtain a discrete recurrence equation of a second-order Thevenin model as follows:
y(k)＝θ(k)Tφ(k)
wherein y (k) ═ e (k), θ (k) ═ θ1θ2θ3θ4θ5]T，φ(k)＝[E(k-1)E(k-2)I(k)I(k-1)I(k-2)]T, theta (k) is calculated by a recursive least square algorithm to obtain an estimated value of the corresponding time
Figure BDA0002922891600000032
Thereby obtaining a, b, c, d, e with respect to
Figure BDA0002922891600000033
The expression of (a) is as follows:
Figure BDA0002922891600000034
the parameters of the second-order Thevenin equivalent circuit model can be obtained as follows and are iteratively updated through a recursive least square algorithm:
Figure BDA0002922891600000035
s6 discrete slideModel observer and H∞Filter combination, using sliding-mode observer to estimate system state vector as H∞Filtering the prior value by H∞And filtering out process noise and observation noise in the estimation process to obtain system output including the SOC of the battery. The specific process is as follows:
first, a cost function is defined as follows:
Figure BDA0002922891600000041
w (k), v (k) are process noise and observation noise, respectively, and δ is H∞The performance bound of the filtering, N represents the total time of system sampling, P (0) is the initial error covariance matrix, x (0) is the initial state value,
Figure BDA00029228916000000412
is an initial state estimate, x (k) and
Figure BDA00029228916000000411
respectively representing the true value and the estimated value of the k moment; s (k) is a third order matrix designed according to the degree of importance for each state, Q (k) and R (k) being the process noise and observed noise covariance matrices, respectively;
then recursion filtering process:
and (3) state estimation:
Figure BDA0002922891600000042
Figure BDA0002922891600000043
error covariance matrix:
Figure BDA0002922891600000044
gain matrix:
Figure BDA0002922891600000045
and (3) updating the state:
Figure BDA0002922891600000046
error covariance update:
Figure BDA0002922891600000047
in order to ensure that a solution exists, each iteration in the state estimation process meets the following conditions:
Figure BDA0002922891600000048
wherein
Figure BDA0002922891600000049
And Pk/k-1For the third order prediction state matrix and the third order prediction covariance matrix,
Figure BDA00029228916000000410
and Pk/kRespectively a third order update state matrix and a third order update covariance matrix, HkAdjusting the previous state estimate, S, as a conditional factor to a three-dimensional filter gain vectorkIs a third order matrix designed according to the degree of importance for each state, QkAnd RkProcess noise and observed noise covariance matrices, respectively.
Based on the above method, the present invention further provides a battery management system, which includes a processor and a memory, wherein the processor executes the following steps:
s1, establishing a discretization state space equation of a second-order Thevenin equivalent circuit model;
s2, obtaining a standard form of the discrete state sliding-mode observer under the condition that the discrete state space equation can observe the full rank of the matrix;
s3, identifying and calculating parameters of the second-order Thevenin equivalent circuit model through a recursive least square algorithm, and establishing a functional relation between the open-circuit voltage and the SOC;
s4, discrete sliding-mode observer and H∞Filter combination, using sliding-mode observer to estimate system state vector as H∞Filtering the prior value by H∞And filtering out process noise and observation noise in the estimation process to obtain system output including the SOC of the battery. The specific calculation processing procedure of each step is as described in the foregoing lithium ion battery SOC estimation method.
Has the advantages that: compared with the prior art, the invention has the following advantages: the invention is based on union H∞Firstly, describing the internal dynamic characteristics of the lithium ion battery by using a second-order Thevenin equivalent circuit model as an equivalent circuit model of the lithium ion battery; then establishing an electrical characteristic expression of a second-order Thevenin equivalent circuit model through kirchhoff's law; then establishing a state space equation of a second-order Thevenin equivalent circuit model according to an ampere-hour integration method and an electrical characteristic expression, and discretizing the state space equation; identifying parameters of a second-order Thevenin equivalent circuit model by using a recursive least square identification method through an intermittent discharge experiment, and establishing a functional relation between OCV and SOC through a constant-current charge-discharge experiment; sliding-mode observer and H∞The filter combination realizes the filtering of the signal with noise, reduces the jitter problem of the discrete sliding mode observer and provides a more accurate estimation value for the estimation state of the sliding mode observer; the invention can improve the accuracy of SOC estimation, and is simple and easy to realize.
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FIG. 1 shows a scheme for the association based on H according to the invention∞A flow block diagram of a filtering sliding-mode observer lithium ion battery SOC estimation method;
FIG. 2 is a second order Thevenin equivalent circuit diagram according to the present invention;
FIG. 3 is a graph of OCV-SOC curves obtained from a constant current charge and discharge test;
FIG. 4 shows a scheme of the present invention based on union H∞The SOC estimation method of the lithium ion battery of the filtering sliding-mode observer is an SOC estimation result graph in an intermittent discharge experiment;
FIG. 5 shows a federation-based H scheme according to the present invention∞FilteringThe SOC estimation error result chart of the sliding-mode observer lithium ion battery SOC estimation method in the intermittent discharge experiment is shown.
Detailed Description
In order to make the technical solutions of the present invention better understood, 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. It is to be understood that the described embodiments are merely illustrative of some, but not all, of the embodiments of the invention, and that the preferred embodiments of the invention are shown in the drawings. This invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as broadly as the present disclosure is set forth in order to provide a more thorough understanding thereof. 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.
Referring to FIG. 1, in the embodiment of the present invention, the combination H is∞A combined H is provided for a core component by a sliding-mode observer of filtering∞The lithium ion battery state of charge estimation method of the filter sliding mode observer comprises the following steps:
s1: selecting a second-order Thevenin equivalent circuit model as an equivalent circuit model of the lithium ion battery to describe the internal dynamic characteristics of the lithium ion battery;
in order to accurately estimate the SOC of the lithium ion battery, an equivalent circuit model with higher accuracy needs to be established, for example, a second-order model is selected to describe the internal dynamic characteristics of the lithium ion battery in fig. 2, and two RC rings are used to effectively separate the concentration polarization internal resistance and the electrochemical polarization internal resistance of the lithium ion battery, so that the model accuracy is improved.
S2: establishing an electrical characteristic expression of a second-order Thevenin equivalent circuit model through kirchhoff's law;
in the second-order Thevenin equivalent circuit model of FIG. 2, the electrical characteristic expression can be obtained according to kirchhoff's law as follows:
UL＝Uoc-Ua-Ub-IL·R0
Figure BDA0002922891600000061
Figure BDA0002922891600000062
wherein, ULRepresents the terminal voltage of the battery, UocRepresents the open circuit voltage, UaAnd UbRepresents the polarization voltage of the cell, ILIndicating current, discharge current in positive direction, R0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbRespectively representing electrochemical polarization capacitance and concentration polarization capacitance, and t represents time.
S3, establishing a state space equation of the equivalent circuit model according to an ampere-hour integral method and a circuit characteristic expression, and discretizing the equation, wherein the concrete process is as follows:
from t by ampere-hour integration0To t1The SOC expression of the lithium ion battery in the time period is as follows:
Figure BDA0002922891600000063
wherein eta represents the charge-discharge coulombic efficiency of the battery, QnRepresents the maximum available capacity of the current battery; and combining the SOC expression with the electrical characteristic expression to obtain a continuous state space equation of the second-order Thevenin equivalent circuit model:
Figure BDA0002922891600000064
wherein x (t) ([ SOC (t)) Ua(t)UB(t)]T，u(t)＝IL(t)，y(t)＝UL(t)，
Figure BDA0002922891600000065
Discretizing the continuous state space equation yields:
Figure BDA0002922891600000066
wherein x (k) ═ soc (k) Ua(k)Ub(k)]T，u(k)＝I(k)，y(k)＝UL(k)，
Figure BDA0002922891600000067
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbAnd T denotes a sampling period.
S4, stabilizing the system, observing the full rank of the matrix, and obtaining the standard form of the designed sliding mode state observer:
Figure BDA0002922891600000071
in the formula:
Figure BDA0002922891600000072
as an estimate of the state variable:
Figure BDA0002922891600000073
an estimate value output by the system; l is a gain matrix of the state observer; sat (-) is a saturation function, M is a saturation gain function;
Figure BDA0002922891600000074
is a boundary layer; the specific expression of sat (. cndot.) is as follows, where sgn (. cndot.) is a symbolic function.
Figure BDA0002922891600000075
S5, identifying the model parameters by using a recursive least square algorithm, and establishing a function relation between the OCV and the SOC through a constant-current charge-discharge test, wherein the specific process is as follows:
the z-plane based transfer function is as follows:
Figure BDA0002922891600000076
wherein theta is1、θ2、θ3、θ4And theta5For the coefficients relating to the model parameters, the parameters can be calculated specifically by the following formula.
Figure BDA0002922891600000077
Let E (k) be UL(k)-Uoc(k) And discretizing to obtain a discrete recurrence equation of a second-order Thevenin model as follows:
E(k)＝θ1E(k-1)+θ2E(k-2)+θ3I(k)+θ4I(k-1)+θ5I(k-2)
converting the above equation into a matrix form to obtain:
y(k)＝θ(k)Tφ(k)
wherein y (k) ═ e (k), θ (k) ═ θ1θ2θ3θ4θ5]T，φ(k)＝[E(k-1)E(k-2)I(k)I(k-1)I(k-2)]T. Theta (k) can be calculated by a recursive least square algorithm to obtain an estimated value of the corresponding time
Figure BDA0002922891600000078
To obtain
Figure BDA0002922891600000079
Then, a, b, c, d, e can be obtained
Figure BDA00029228916000000710
The expression of (a) is as follows:
Figure BDA0002922891600000081
therefore, the resistance-capacitance parameters of the model can be obtained and are updated iteratively through a recursive least square algorithm:
Figure BDA0002922891600000082
as shown in fig. 3, SOC of the lithium ion battery is directly related to OCV, and in order to obtain a functional relationship between OCV and SOC, a mixed pulse power characteristic discharge test experiment is performed to obtain an OCV-SOC curve and fit the obtained functional relationship:
Figure BDA0002922891600000083
wherein k isnAre fitting coefficients.
S6, Standard H∞The filtering satisfies a cost function J defined by and minimized by the estimate to obtain an optimal estimate, while the goal is to select the appropriate process and observation noise to the maximum extent that the estimation error is continuously large. The cost function is as follows:
Figure BDA0002922891600000084
wherein N represents the total time of system sampling, N-1 is the time of N-1, P (0) is the initial error covariance matrix, x (0) is the initial state value,
Figure BDA0002922891600000085
is an initial state estimate, x (k) and
Figure BDA0002922891600000086
respectively representing the true and estimated values at time k. ω (k) is formed as R3And v (k) is the process noise and the observation noise, respectively, during the sampling time there are:
Figure BDA0002922891600000087
in practical applications, it is difficult to directly minimize, and therefore, a performance boundary δ satisfying the equation is set. Rearranging to obtain:
Figure BDA0002922891600000091
in combination with H∞Iterative estimation of the filtering sliding-mode observer lithium ion battery SOC estimation method:
and (3) state estimation:
Figure BDA0002922891600000092
Figure BDA0002922891600000093
error covariance matrix:
Figure BDA0002922891600000094
gain matrix:
Figure BDA0002922891600000095
and (3) updating the state:
Figure BDA0002922891600000096
error covariance update:
Figure BDA0002922891600000097
in order to make the result have a solution, the iteration process should satisfy the following conditions at each moment:
Figure BDA0002922891600000098
wherein
Figure BDA0002922891600000099
And Pk/k-1For the third order prediction state matrix and the third order prediction covariance matrix,
Figure BDA00029228916000000910
and Pk/kIs a third order update state matrix and a third order update covariance matrix, HkThe previous state estimate is adjusted as a conditional factor to a three-dimensional filter gain vector. SkIs a third order matrix designed according to the degree of importance for each state, and is set as a third order unit matrix in the present embodiment. The estimated value is compared with the actual value to verify the accuracy of the algorithm, and the result graph and the error graph are shown in fig. 4 and fig. 5. QkAnd RkCovariance matrices of process noise and observation noise, respectively, delta is H∞Performance bounds of filtering.
The invention is based on the association H∞Firstly, a second-order Thevenin equivalent circuit model is used as an equivalent circuit model of the lithium ion battery; then establishing an electrical characteristic expression of a second-order Thevenin equivalent circuit model through kirchhoff's law; then establishing a state space equation of a second-order Thevenin equivalent circuit model according to an ampere-hour integration method and an electrical characteristic expression, and discretizing the state space equation; secondly, identifying parameters of a second-order Thevenin equivalent circuit model through an intermittent discharge experiment, and establishing a functional relation between OCV and SOC through a constant-current charge-discharge experiment; then the sliding-mode observer is connected with the H∞The filter is combined to realize filtering of a signal with noise, so that the jitter problem of the discrete sliding mode observer is reduced, and a more accurate estimation value is provided for the estimation state of the sliding mode observer. The invention is applied to the battery management system, and the processor executes the steps to complete the SOC estimation, thereby improving the estimation precision of the battery management system on the SOC of the managed lithium battery, and being simple and easy to realize. The method comprises the following steps: s1, establishing a discretization state space equation of a second-order Thevenin equivalent circuit model; s2, obtaining a standard form of the discrete state sliding-mode observer under the condition that the discrete state space equation can observe the full rank of the matrix; s3, least squares by recursionThe algorithm identifies and calculates the parameters of the second-order Thevenin equivalent circuit model, and establishes the functional relation between the open-circuit voltage and the SOC; s4, combining the discrete sliding mode observer and the H infinity filter, estimating the system state vector by using the sliding mode observer to be used as the H∞Filtering the prior value by H∞And filtering out process noise and observation noise in the estimation process to obtain system output including the SOC of the battery. Wherein, the model, the equation and the like are established in each step, the model and the equation are stored in the memory in a data form, and when the processor executes the establishment of the model or the equation, the data of the model or the equation are actually called directly from the memory.
Finally, it should be noted that: the above examples are intended only to illustrate the technical solution of the present invention and not to limit it, and although the present invention is explained in detail with reference to the above examples, it should be understood that: all methods or products formed by modification or replacement of the described embodiments of the invention without creative effort by those skilled in the art shall be covered by the protection scope of the claims of the present invention.

Claims (10)

1. Based on unite H∞The SOC estimation method of the lithium ion battery of the sliding mode observer is characterized by comprising the following steps:
s1, establishing a second-order Thevenin equivalent circuit model as an equivalent circuit model of the lithium ion battery;
s2, establishing an electrical characteristic expression of the second-order Thevenin equivalent circuit model;
s3, establishing a state space equation of a second-order Thevenin equivalent circuit model according to an ampere-hour integration method and the electrical characteristic expression, and discretizing the state space equation;
s4, obtaining a standard form of the discrete state sliding-mode observer under the condition that the discrete state space equation can observe the full rank of the matrix;
s5, identifying and calculating parameters of the second-order Thevenin equivalent circuit model through a recursive least square algorithm, and establishing a functional relation between the open-circuit voltage and the SOC;
s6, discrete sliding-mode observer and H∞Filter combination, using sliding-mode observer to estimate system state vector as H∞Filtering the prior value by H∞And filtering out process noise and observation noise in the estimation process to obtain system output including the SOC of the battery.
2. Joint H-based according to claim 1∞The filtering sliding-mode observer lithium ion battery SOC estimation method is characterized in that the discretization state space equation obtained in the step S3 is as follows:
Figure FDA0002922891590000011
wherein x (k) ═ SOC (k) Ua(k) Ub(k)]T，u(k)＝IL(k)，y(k)＝UL(k)，
Figure FDA0002922891590000012
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbT represents sampling period, eta represents battery charging and discharging coulombic efficiency, and QnRepresents the maximum available capacity under the current conditions, where ULRepresenting the terminal voltage, U, of the second order Thevenin equivalent circuit modelocRepresents the open-circuit voltage, U, of the second-order Thevenin equivalent circuit modelaAnd UbRepresents the polarization voltage of the cell, ILRepresents the current, R0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbElectrochemical polarization capacitance and concentration polarization capacitance are respectively represented.
3. Joint H-based according to claim 1∞The filtering sliding-mode observer lithium ion battery SOC estimation method is characterized in that in the step S4, the standard form of the discrete state sliding-mode observer is adoptedComprises the following steps:
Figure FDA0002922891590000013
in the formula:
Figure FDA0002922891590000014
is an estimate of the state variable and,
Figure FDA0002922891590000015
a, B, C, D is the state parameter in the discretization state space equation which is the estimated value of the system output; l is a gain matrix of the state observer; sat (-) is a saturation function, M is a saturation gain function;
Figure FDA0002922891590000016
is a boundary layer; the specific expression of sat (. cndot.) is as follows:
Figure FDA0002922891590000021
where sgn (·) is a sign function.
4. Joint H-based according to claim 1∞The filtering sliding-mode observer lithium ion battery SOC estimation method is characterized in that parameters of the second-order Thevenin equivalent circuit model are subjected to fitting calculation through a recursive least square algorithm in the step S5, and the specific process is as follows:
using a z-plane based transfer function:
Figure FDA0002922891590000022
wherein theta is1、θ2、θ3、θ4And theta5For the coefficients relating to the model parameters, the parameters can be calculated in particular by the following formulaTo obtain:
Figure FDA0002922891590000023
wherein T represents a sampling period;
let E (k) be UL(k)-Uoc(k) And discretizing to obtain a discrete recurrence equation of the second-order Winan wearing model as follows:
y(k)＝θ(k)Tφ(k)
wherein y (k) ═ e (k), θ (k) ═ θ1 θ2 θ3 θ4 θ5]T，φ(k)＝[E(k-1) E(k-2) I(k) I(k-1) I(k-2)]TAnd theta (k) is calculated by a recursive least square algorithm to obtain an estimated value of the corresponding time
Figure FDA0002922891590000024
Thereby obtaining a, b, c, d, e with respect to
Figure FDA0002922891590000025
The expression of (a) is as follows:
Figure FDA0002922891590000031
parameters of the second-order Thevenin equivalent circuit model can be obtained and are updated iteratively through a recursive least square algorithm:
Figure FDA0002922891590000032
5. joint H-based according to claim 1∞The method for estimating the SOC of the lithium ion battery by using the filtering sliding mode observer is characterized in that the specific process of the step S6 is as follows:
first, a cost function is defined as follows:
Figure FDA0002922891590000033
w (k), v (k) are respectively process noise and observation noise at the time k, and delta is H∞The performance bound of the filtering, N represents the total time of system sampling, P (0) is the initial error covariance matrix, x (0) is the initial state value,
Figure FDA0002922891590000034
is an initial state estimate, x (k) and
Figure FDA0002922891590000035
respectively representing the true value and the estimated value of the k moment; s (k) is a third order matrix designed according to the degree of importance for each state, Q (k) and R (k) being the process noise and observed noise covariance matrices, respectively;
then recursion filtering process:
and (3) state estimation:
Figure FDA0002922891590000036
Figure FDA0002922891590000037
error covariance matrix:
Figure FDA0002922891590000038
gain matrix:
Figure FDA0002922891590000039
and (3) updating the state:
Figure FDA0002922891590000041
error covariance update:
Figure FDA0002922891590000042
in order to ensure that a solution exists, each iteration in the state estimation process meets the following conditions:
Figure FDA0002922891590000043
wherein
Figure FDA0002922891590000044
And Pk/k-1Respectively a third-order prediction state matrix and a third-order prediction covariance matrix,
Figure FDA0002922891590000045
and Pk/kRespectively a third order update state matrix and a third order update covariance matrix, HkAdjusting the previous state estimate, S, as a conditional factor to a three-dimensional filter gain vectorkIs a third order matrix designed according to the degree of importance to each state, QkAnd RkRespectively, process noise and observation noise covariance matrix, and I is a unit matrix.
6. A battery management system comprising a processor and a memory, wherein the processor performs the steps of:
s1, establishing a discretization state space equation of a second-order Thevenin equivalent circuit model;
s2, obtaining a standard form of the discrete state sliding-mode observer under the condition that the discrete state space equation can observe the full rank of the matrix;
s3, identifying and calculating parameters of the second-order Thevenin equivalent circuit model through a recursive least square algorithm, and establishing a functional relation between the open-circuit voltage and the SOC;
s4, discrete sliding-mode observer and H∞Filter combination, using sliding-mode observer to estimate system state vector as H∞Filtering the prior value by H∞In filter filtering estimationProcess noise and observation noise, and system output including battery SOC is obtained.
7. The battery management system of claim 6, wherein the discretized state space equation is:
Figure FDA0002922891590000046
wherein x (k) ═ SOC (k) Ua(k) Ub(k)]T，u(k)＝IL(k)，y(k)＝UL(k)，
Figure FDA0002922891590000047
D＝-R0，τa＝Ra·Ca，τb＝Rb·CbT represents sampling period, eta represents battery charging and discharging coulombic efficiency, and QnRepresents the maximum available capacity under the current conditions, where ULRepresenting the terminal voltage, U, of the second order Thevenin equivalent circuit modelocRepresents the open-circuit voltage, U, of the second-order Thevenin equivalent circuit modelaAnd UbRepresents the polarization voltage of the cell, ILRepresents the current, R0Represents an ohmic resistance; ra、RbRespectively representing electrochemical polarization resistance and concentration polarization resistance, Ca、CbElectrochemical polarization capacitance and concentration polarization capacitance are respectively represented.
8. The battery management system of claim 6, wherein the discrete state sliding-mode observer is in the standard form:
Figure FDA0002922891590000051
in the formula:
Figure FDA0002922891590000052
is an estimate of the state variable and,
Figure FDA0002922891590000053
a, B, C, D is the state parameter in the discretization state space equation which is the estimated value of the system output; l is a gain matrix of the state observer; sat (-) is a saturation function, M is a saturation gain function;
Figure FDA0002922891590000054
is a boundary layer; the specific expression of sat (. cndot.) is as follows:
Figure FDA0002922891590000055
where sgn (·) is a sign function.
9. The battery management system according to claim 6, wherein the parameters of the second-order Thevenin equivalent circuit model are fit-calculated by a recursive least square algorithm, and the specific process is as follows:
using a z-plane based transfer function:
Figure FDA0002922891590000056
wherein theta is1、θ2、θ3、θ4And theta5For the coefficients related to the model parameters, each parameter can be specifically calculated by the following formula:
Figure FDA0002922891590000057
wherein T represents a sampling period;
let E (k) be UL(k)-Uoc(k)，Discretizing to obtain a discrete recurrence equation of the second-order Wien model as follows:
y(k)＝θ(k)Tφ(k)
wherein y (k) ═ e (k), θ (k) ═ θ1 θ2 θ3 θ4 θ5]T，φ(k)＝[E(k-1) E(k-2) I(k) I(k-1) I(k-2)]TAnd theta (k) is calculated by a recursive least square algorithm to obtain an estimated value of the corresponding time
Figure FDA0002922891590000058
Thereby obtaining a, b, c, d, e with respect to
Figure FDA0002922891590000059
The expression of (a) is as follows:
Figure FDA0002922891590000061
parameters of the second-order Thevenin equivalent circuit model can be obtained and are updated iteratively through a recursive least square algorithm:
Figure FDA0002922891590000062
10. the battery management system according to claim 6, wherein the specific process of step S4 is as follows:
(1) defining a cost function:
Figure FDA0002922891590000063
w (k), v (k) are process noise and observation noise, respectively, and δ is H∞The performance bound of the filtering, N represents the total time of system sampling, P (0) is the initial error covariance matrix, x (0) is the initial state value,
Figure FDA0002922891590000064
is an initial state estimate, x (k) and
Figure FDA0002922891590000065
respectively representing the true value and the estimated value of the k moment; s (k) is a third order matrix designed according to the degree of importance for each state, Q (k) and R (k) being the process noise and observed noise covariance matrices, respectively;
(2) the filtering process is recurred, and the recursion equation is as follows:
and (3) state estimation:
Figure FDA0002922891590000066
Figure FDA0002922891590000067
error covariance matrix:
Figure FDA0002922891590000068
gain matrix:
Figure FDA0002922891590000069
and (3) updating the state:
Figure FDA0002922891590000071
error covariance update:
Figure FDA0002922891590000072
in order to ensure that a solution exists, each iteration in the state estimation process meets the following conditions:
Figure FDA0002922891590000073
wherein
Figure FDA0002922891590000074
And Pk/k-1Respectively a third-order prediction state matrix and a third-order prediction covariance matrix,
Figure FDA0002922891590000075
and Pk/kRespectively a third order update state matrix and a third order update covariance matrix, HkAdjusting the previous state estimate, S, as a conditional factor to a three-dimensional filter gain vectorkIs a third order matrix designed according to the degree of importance to each state, QkAnd RkRespectively, process noise and observation noise covariance matrix, and I is a unit matrix.
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