阅读说明：本技术 考虑循环次数影响的锂电池soc及soh协同估算方法 (Lithium battery SOC and SOH collaborative estimation method considering influence of cycle number ) 是由 庞辉 牟联晶 武龙星 郭龙 晋佳敏 于 2020-04-17 设计创作，主要内容包括：考虑循环次数影响的锂电池SOC及SOH协同估算方法,包括以下步骤：步骤1,构建考虑循环次数的锂电池等效电路模型；步骤2,模型参数的辨识；步骤3,将步骤1建立的模型进行仿真验证；步骤4,SOC/SOH协同估算器构建。本发明方法能够最终实现锂电池全寿命范围内的电池荷电状态(State-of-charge,SOC)和健康状态(State-of-health,SOH)估计,对电动车辆电池管理系统的状态估算和能量管理具有重大意义,解决了在不同寿命循环引起的模型不准确而导致的状态估算误差较大等问题,有效提高了动力电池组的利用效率、保证了电池组的使用寿命。(The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number comprises the following steps: step 1, constructing a lithium battery equivalent circuit model considering cycle times; step 2, identifying model parameters; step 3, carrying out simulation verification on the model established in the step 1; and step 4, constructing an SOC/SOH collaborative estimator. The method can finally realize the estimation of the State-of-charge (SOC) and the State-of-health (SOH) of the battery in the full life range of the lithium battery, has great significance for the State estimation and the energy management of the battery management system of the electric vehicle, solves the problems of large State estimation error and the like caused by inaccurate models in different life cycles, effectively improves the utilization efficiency of the power battery pack, and ensures the service life of the battery pack.)

1. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number is characterized by comprising the following steps of:

step 1, constructing a lithium battery equivalent circuit model considering cycle times;

step 2, identifying model parameters by adopting a recursive least square method;

step 3, carrying out simulation verification on the lithium battery equivalent circuit model established in the step 1 under a constant current working condition;

and 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery.

2. The lithium battery SOC and SOH collaborative estimation method considering influence of cycle times according to claim 1, wherein a mathematical relation of the lithium battery equivalent circuit model constructed in the step 1 is as follows:

formula (1)) In, U_tIs the battery terminal voltage; u shape_OC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r₀Ohmic internal resistance; r₁And C₁Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r₂And C₂Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be₀(Cyc),R₁(Cyc),C₁(Cyc),R₂(Cyc),C₂(Cyc) is written as R₀,R₁,C₁,R₂And C₂，I_tRepresents the operating current; u shape₁And U₂Electrochemical polarization voltage and concentration polarization voltage are respectively represented.

3. The lithium battery SOC and SOH collaborative estimation method considering cycle frequency influence according to claim 1, wherein the model parameters are identified in step 2 by using a recursive least square method to obtain model parameters under different cycle frequencies, and the specific formula comprises:

the terminal voltage is subjected to laplace transform:

it is provided that,

E＝U_t-U_OC(3)

the model transfer function is:

the method is simplified as follows:

the Tustin transform maps the s-plane based system equation to the z-plane:

the discrete transfer function based on the z-plane is:

G(z^-1)＝[a₃+a₄z^-1+a₅z^-2]/[1-a₁z^-1-a₂z^-2](7)

the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:

E(l)＝a₁E(l-1)+a₂E(l-2)+a₃I(l)+a₄I(l-1)+a₅I(l-2) (8)

defining a data variable Ψ for a system_lAnd a parameter variable theta_lComprises the following steps:

the time domain difference equation (8) can be rewritten as:

z_l＝Ψ_lθ_l+e_Ls,l(10)

the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:

the parameter variables and error covariance are initialized as:

inverse transformation using equation (6)

Then, equation (7) can be rewritten as:

comparing equation (7) and equation (14), we can obtain:

in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is₁＝R₁C₁，τ₂＝R₂C₂(ii) a T is the sampling interval time of the system; a is₁,a₂,a₃,a₄And a₅Unknown parameters related to model parameters; Ψ_lRepresenting system data variables; theta_lRepresenting a parameter variable; in the formula z_lAn output variable representing the system; e.g. of the type_Ls,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 10⁶And I represents an identity matrix.

4. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number according to claim 1, wherein the simulation verification is performed on the lithium battery equivalent circuit model in the step 3, and specifically comprises the following steps:

under MATLAB/Simulink environment, build the lithium cell equivalent circuit model that considers the cycle number influence, wherein the input is: current, cycle number, output as voltage; the test is carried out under seven different circulation times by using a constant-current working condition test respectively [301002003006008001000 ].

5. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle times as claimed in claim 1, wherein the step 4 is to construct a collaborative estimator considering the cycle times to estimate the SOC and the SOH of the lithium battery, specifically:

step 4.1, establishing a discrete state space model of the lithium battery system:

according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the lithium battery are calculated₁Concentration polarization voltage U₂Ohmic internal resistance R₀And reciprocal 1/C of capacity_capSelecting measurable battery terminal voltage U as state variable_tAs observed quantity, a state prediction equation and an observation equation (16) are established,

first, a system state matrix x is defined_kDefining the system output y_kAnd system input u_k：

The algorithm formula is as follows:

in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. the_k-1Is a system matrix; b is_k-1Is a control matrix; c_kOutputting a matrix for the system; u. of_kInputting for the system; t is_SFor a sampling period, P^-And P⁺Respectively state estimation covariance prior estimation and posterior estimation, K is cardThe Lrman gain, e is the innovation matrix, I is the identity matrix, η is the coulombic efficiency and assumes a value of 1 at charge and 0.98 at discharge, C_cap,kThe maximum available capacity of the battery under the current cycle; c_freshThe maximum available capacity of the battery when leaving the factory; r_freshInternal resistance for the first cycle of the battery; r_eolIndicating the internal resistance of the battery at the end of its life; r_0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,

step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the SOC and SOH collaborative estimation of the lithium battery is carried out by using a self-adaptive extended Kalman filter:

1) initialization:

at t₀At time, i.e., when k is 0, an initial value x of the state observer is set₀,P₀,Q₀,R₀；

2) A priori estimate-predict: time update [ State Slave time (k-1)⁺Arrival time (k)^-Is calculated by]

For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)⁺Reckoning to the current time (k)^-The time update equation of the adaptive extended kalman filter is expressed as follows:

and (3) system state estimation:

estimating error covariance:

wherein, f (x)_k-1,u_k-1) Representing the system stateA program function;

3) a posteriori estimation-correction: measurement update [ State Slave time (k)^-Arrival time (k)⁺Is calculated by]

This step uses the measured value y at the time k_kCorrecting state estimation and covariance estimation, the estimation results being used separatelyAndexpressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:

an innovation matrix:

kalman gain matrix:

adaptive noise covariance matching:

and (3) correcting the system state:

error covariance correction:

4) time scale update

Time of day (k)⁺The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.

Technical Field

The invention belongs to the technical field of power battery management systems, and particularly relates to a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times.

Background

With the vigorous development of the electric automobile market, the lithium battery is widely used as a power source of the electric automobile. In order to ensure safe and reliable operation of the Battery pack, good monitoring, control, and management by a Battery Management System (BMS) are required. For battery management systems, the core function is to provide accurate estimation of the State-of-charge (SOC) and State-of-health (SOH) of the battery, which is a huge challenge. Since the existing vehicle-mounted sensor cannot observe these two states, it is necessary to develop a feasible state estimation algorithm.

The state of charge is a key factor of the residual capacity of the battery system, and is helpful for predicting the residual driving mileage and the endurance time of the electric automobile. At present, research on SOC estimation algorithms is abundant, and common algorithms include coulomb counting method, model-based open circuit voltage method, neural network method and kalman filtering method. The Kalman filtering is a comprehensive algorithm comprising a coulomb counting method and an OCV prediction method based on a model, has the advantages of high precision, strong robustness and the like, and is widely applied in recent years.

State of health describes the degree of battery aging, which can be generally reflected by a loss of capacity or an increase in resistance. The existing estimation method mainly comprises the following steps: direct measurement, voltage trajectory, compatibilization analysis, differential voltage analysis, kalman filtering, particle filtering, neural network, vector machine, genetic algorithms, and artificial intelligence algorithms.

However, as the battery is cycled, the battery parameters, including capacity and impedance, may change as the battery degrades, thereby affecting the accuracy of the algorithm's estimation of the battery SOC and SOH. Therefore, in order to improve the estimation performance of SOC and SOH, it is necessary to consider the cycle aging of the lithium battery and propose a cooperative estimator that monitors the state of charge and the state of health of the battery at the same time.

In summary, a combined state estimation scheme capable of estimating SOC and SOH simultaneously is an urgent problem to be solved in the technical field of power battery management systems at present. The method has great significance for protecting the battery system, improving the performance of the whole vehicle and improving the economy.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention aims to provide a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, overcomes the limitation that the traditional equivalent circuit model is only suitable for a certain life cycle range, and greatly improves the applicability of BMS state calculation and energy management in the whole life cycle.

In order to achieve the purpose, the invention adopts the technical scheme that: the lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number comprises the following steps:

step 1, constructing a lithium battery equivalent circuit model considering cycle times;

step 2, identifying model parameters by adopting a recursive least square method;

step 3, carrying out simulation verification on the lithium battery equivalent circuit model established in the step 1 under a constant current working condition;

and 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery.

The lithium battery equivalent circuit model constructed in the step 1 has a mathematical relation as follows:

in the formula (1), U_tIs the battery terminal voltage; u shape_OC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r₀Ohmic internal resistance; r₁And C₁Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r₂And C₂Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be₀(Cyc),R₁(Cyc),C₁(Cyc),R₂(Cyc),C₂(Cyc) is written as R₀,R₁,C₁,R₂And C₂，I_tRepresents the operating current; u shape₁And U₂Electrochemical polarization voltage and concentration polarization voltage are respectively represented.

And 2, identifying the parameters of the model in the step 2 by adopting a Recursive least square method (RLS) to obtain the model parameters under different cycle times, wherein the specific formula comprises the following steps:

the terminal voltage is subjected to laplace transform:

it is provided that,

E＝U_t-U_OC(3)

the model transfer function is:

the method is simplified as follows:

the Tustin transform maps the s-plane based system equation to the z-plane:

the discrete transfer function based on the z-plane is:

G(z^-1)＝[a₃+a₄z^-1+a₅z^-2]/[1-a₁z^-1-a₂z^-2](7)

the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:

E(l)＝a₁E(l-1)+a₂E(l-2)+a₃I(l)+a₄I(l-1)+a₅I(l-2) (8)

defining a data variable Ψ for a system_lAnd parametersVariable theta_lComprises the following steps:

the time domain difference equation (8) can be rewritten as:

z_l＝Ψ_lθ_l+e_Ls,l(10)

the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:

the parameter variables and error covariance are initialized as:

inverse transformation using equation (6)

Then, equation (7) can be rewritten as:

comparing equation (7) and equation (14), we can obtain:

in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is₁＝R₁C₁，τ₂＝R₂C₂(ii) a T is the sampling interval time of the system; a is₁,a₂,a₃,a₄And a₅Unknown parameters related to model parameters; Ψ_lRepresenting system data variables; theta_lRepresenting a parameter variable; in the formula z_lAn output variable representing the system; e.g. of the type_Ls,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 10⁶And I represents an identity matrix.

And 3, performing simulation verification on the lithium battery equivalent circuit model, specifically:

under MATLAB/Simulink environment, build the lithium cell equivalent circuit model that considers the cycle number influence, wherein the input is: current, cycle number, output as voltage; the verification is carried out under seven different circulation times of [301002003006008001000] respectively by using a Constant current condition test (CCC).

In step 4, a cooperative estimator considering the cycle number is constructed to estimate the SOC and the SOH of the lithium battery, and the method specifically comprises the following steps:

step 4.1, establishing a discrete state space model of the lithium battery system:

according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the lithium battery are calculated₁Concentration polarization voltage U₂Ohmic internal resistance R₀And reciprocal 1/C of capacity_capSelecting measurable battery terminal voltage U as state variable_tAs observed quantity, a state prediction equation and an observation equation (16) are established,

first, a system state matrix x is defined_kDefining the system output y_kAnd system input u_k：

The algorithm formula is as follows:

in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. the_k-1Is a system matrix; b is_k-1Is a control matrix; c_kOutputting a matrix for the system; u. of_kInputting for the system; t is_SFor a sampling period, P^-And P⁺Respectively state estimation covariance prior estimation and posterior estimation, K is Kalman gain, e is innovation matrix, I is unit matrix, η is Coulomb efficiency, and assuming 1 during charging and 0.98 during discharging, C_cap,kThe maximum available capacity of the battery under the current cycle; c_freshThe maximum available capacity of the battery when leaving the factory; r_freshInternal resistance for the first cycle of the battery; r_eolIndicating the internal resistance of the battery at the end of its life; r_0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,

step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the SOC and SOH collaborative estimation of the lithium battery is carried out by using a self-adaptive extended Kalman filter:

1) initialization:

at t₀At time, i.e., when k is 0, an initial value x of the state observer is set₀,P₀,Q₀,R₀；

2) A priori estimate-predict: time update [ State Slave time (k-1)⁺Arrival time (k)^-Is calculated by]

For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)⁺Reckoning to the current time (k)^-The time update equation of the adaptive extended kalman filter is expressed as follows:

and (3) system state estimation:

estimating error covariance:

wherein, f (x)_k-1,u_k-1) Representing a system equation of state function;

3) a posteriori estimation-correction: measurement update [ State Slave time (k)^-Arrival time (k)⁺Is calculated by]

This step uses the measured value y at the time k_kCorrecting state estimation and covariance estimation, the estimation results being used separatelyAndexpressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:

an innovation matrix:

kalman gain matrix:

adaptive noise covariance matching:

and (3) correcting the system state:

error covariance correction:

4) time scale update

Time of day (k)⁺The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.

Compared with the prior art, the invention can obtain the following technical effects:

the invention provides a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, overcomes the limitation that the traditional model is only suitable for a certain specific cycle range, and greatly improves the applicability of a Battery Management System (BMS) in the full life cycle range in state calculation and energy management. The estimator constructed by the invention can more accurately describe the external characteristics of the power battery, and has positive significance for improving state calculation and energy management in the BMS and subsequent battery thermal management and safety management. Therefore, the lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle number has good practicability and application value in BMS and engineering.

The method can finally realize the estimation of the state of charge and the state of health of the battery in the whole life cycle range, has great significance for the state estimation and the energy management of the battery management system of the electric vehicle, solves the problems of large SOC/SOH estimation error and the like caused by inaccurate models due to different cycle times, and effectively improves the utilization efficiency of the power battery pack and the real-time monitoring of the service life of the battery. In an electric automobile, the protection of a battery system, the improvement of the performance of the whole automobile and the improvement of the economical efficiency are all significant.

Drawings

FIG. 1 is a schematic diagram of SOC and SOH estimation process according to the present invention.

Fig. 2 is a schematic diagram of a battery model according to the present invention.

FIG. 3 is a schematic diagram of the OCV-SOC curves for different cycles of the present invention.

Fig. 4 is a schematic diagram of the variation of the battery voltage under the constant current discharge condition of the invention.

FIG. 5 is a graph showing a comparison curve between a measured voltage and a simulated voltage in model verification according to the present invention.

FIG. 6 is a schematic diagram of an error curve of the measured voltage and the simulated voltage according to the present invention.

Fig. 7 is a diagram illustrating the maximum available capacity at different cycles of the present invention.

FIG. 8 is a schematic diagram of a SOC and SOH co-estimation process according to the present invention.

FIG. 9 is a diagram illustrating a comparison curve between the experimental SOC and the estimated SOC under the CCC condition according to the present invention.

FIG. 10 is a schematic diagram of an experimental SOC versus estimated SOC error curve according to the present invention.

FIG. 11 is a graphical representation of measured versus estimated capacity curves for the CCC condition of the present invention.

FIG. 12 is a graph illustrating measured capacity versus estimated capacity error curves in accordance with the present invention.

FIG. 13 is a schematic diagram of capacity and SOH estimation according to the present invention.

FIG. 14 is a graphical illustration of a comparison of the identified internal resistance to the estimated internal resistance for the CCC condition of the present invention.

FIG. 15 is a schematic diagram of an error curve of identifying the internal resistance and estimating the internal resistance according to the present invention.

FIG. 16 is a schematic diagram of the internal resistance and SOH estimation of the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.

The invention discloses a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, the realization process is shown in figure 1, and the method specifically comprises the following steps:

step 1, constructing a lithium battery equivalent circuit model considering cycle times;

the universal second-order RC equivalent circuit model has the advantages of high calculation efficiency, easiness in engineering realization, good battery dynamic behavior simulation and the like, and is widely applied to power battery modeling and state estimation. However, as the battery is recycled, especially after hundreds of cycles of charge and discharge, the battery capacity is attenuated, the internal resistance is increased, and the accuracy of the battery model is reduced, the invention provides an improved second-order RC circuit model considering different cycles on the basis of the second-order RC model, as shown in FIG. 2, wherein the model parameter R₀(Cyc),R₁(Cyc),C₁(Cyc),R₂(Cyc),C₂(Cyc) is a function of the Cycle number, and for the sake of brevity, the parameters are each written as R₀,R₁,C₁,R₂,C₂(ii) a In addition, the difference of the OCV-SOC relationship under different Cycle times is considered, the consideration on the OCV-SOC is increased, the OCV-SOC-Cycle relationship is established, as shown in FIG. 3, according to kirchhoff's law, the mathematical relationship is shown as formula (1),

in the formula (1), U_tIs the battery terminal voltage; u shape_OC(SOC, Cyc) represents open circuit voltage as a function of battery SOC and Cycle number Cycle; r₀Ohmic internal resistance; r₁And C₁Electrochemical polarization resistance and electrochemical polarization fractional order capacitance respectively; r₂And C₂Respectively a concentration polarization resistor and a concentration polarization fractional order capacitor; for simplicity, the parameter R will be₀(Cyc),R₁(Cyc),C₁(Cyc),R₂(Cyc),C₂(Cyc) is written as R₀,R₁,C₁,R₂And C₂，I_tRepresents the operating current; u shape₁And U₂Electrochemical polarization voltage and concentration polarization voltage are respectively represented.

Step 2, identifying model parameters by adopting a recursive least square method;

in the step 2 of the invention, model parameters are identified by using a Recursive least square method (RLS), and model parameters under different cycle times are respectively obtained by using constant current discharge working conditions (shown in figure 4) under different cycles [301002003006008001000], wherein the specific formula is as follows:

the terminal voltage is subjected to laplace transform:

it is provided that,

E＝U_t-U_OC(3)

the model transfer function is:

the method is simplified as follows:

the Tustin transform maps the s-plane based system equation to the z-plane:

the discrete transfer function based on the z-plane is:

G(z^-1)＝[a₃+a₄z^-1+a₅z^-2]/[1-a₁z^-1-a₂z^-2](7)

the discrete transfer function of equation (7) is converted into a time domain difference equation, and the result is:

E(l)＝a₁E(l-1)+a₂E(l-2)+a₃I(l)+a₄I(l-1)+a₅I(l-2) (8)

defining a data variable Ψ for a system_lAnd a parameter variable theta_lComprises the following steps:

the time domain difference equation (8) can be rewritten as:

z_l＝Ψ_lθ_l+e_Ls,l(10)

the system shown in the formula (10) has the following specific flow of the recursive least square algorithm:

the parameter variables and error covariance are initialized as:

inverse transformation using equation (6)

Then, equation (7) can be rewritten as:

comparing equation (7) and equation (14), we can obtain:

in the above equations (2) to (15), E is a difference between the terminal voltage and the open circuit voltage; τ ═ RC denotes a time constant, where τ is₁＝R₁C₁，τ₂＝R₂C₂(ii) a T is the sampling interval time of the system; a is₁,a₂,a₃,a₄And a₅Unknown parameters related to model parameters; Ψ_lRepresenting system data variables; theta_lRepresenting a parameter variable; in the formula z_lAn output variable representing the system; e.g. of the type_Ls,lRepresenting stable zero mean white noise, and an angle mark l representing that the data value is the ith sampling moment; g represents an algorithm gain; f is an error covariance matrix of the state estimation value; where p represents a large number, which can be empirically derived, the present invention has p of 10⁶And I represents an identity matrix.

And 3, carrying out simulation verification on the model established in the step 1 under the constant-current working condition, specifically:

the parameters R under different cycles can be obtained through the parameter identification in the step 2₀、R₁、C₁、R₂、C₂Numerical value of (1). Then, under the MATLAB/Simulink environment, a lithium ion battery equivalent circuit model considering the influence of different cycle times is built, wherein the input is as follows: current, cycle number, output is terminal voltage. The Constant Current Condition (CCC) is respectively tested at [301002003006008001000]]Performing simulation under seven different Cycle times, taking Cycle30 as an example, as shown in fig. 5, comparing the measured voltage with the simulated voltage, and obtaining a corresponding error of 0.019 as shown in fig. 6; other cycles [ 1002003006008001000]The lower errors are respectively [ 0.0190.0180.0160.0210.0220.019]；

Step 4, constructing a cooperative estimator considering the cycle number to estimate the SOC and the SOH of the lithium battery, specifically:

step 4.1, establishing a discrete state space model of the lithium battery system:

according to the mathematical expression of the model, the state of charge SOC and the electrochemical polarization voltage U of the battery are calculated₁Concentration polarization voltage U₂Ohmic internal resistance R₀And reciprocal 1/C of capacity_capSelecting measurable battery terminal voltage U as state variable_tAs observed quantity, a state prediction equation and an observation equation (16) are established,

first, a system state matrix x is defined_kDefining the system output y_kAnd system input u_k：

The SOH is defined in terms of the remaining capacity of the battery, which can be measured directly after the battery has been used for a certain period of time. The invention is provided with C_freshIs the maximum available capacity, C, of the battery when leaving the factory_cap,kFor the current maximum available capacity of the battery, the change at different cycles is shown in FIG. 7, and then the SOH_[Ccap]Is defined as:

since the battery SOH is attenuated as the internal resistance of the battery gradually increases, the battery SOH may be defined according to this relationship, wherein R is_freshInternal resistance for the first cycle of the battery; r_eolIndicating the internal resistance of the battery at the end of its life; r_0,kThe internal resistance of the battery in the current state is the battery SOH_[R0]Is defined as:

the algorithm formula of the self-adaptive extended Kalman filter is as follows:

in the above formulas (16) to (21), ω is system white noise, the mean is 0, the covariance is Q, and ν is measurement white noise, the mean is 0, and the covariance is V; a. the_k-1Is a system matrix; b is_k-1Is a control matrix; c_kOutputting a matrix for the system; u. of_kInputting for the system; t is_SFor a sampling period, P^-And P⁺Respectively state estimation covariance prior estimation and posterior estimation, K is Kalman gain, e is innovation matrix, I is unit matrix, η is Coulomb efficiency, and assuming 1 during charging and 0.98 during discharging, C_cap,kThe maximum available capacity of the battery under the current cycle; c_freshThe maximum available capacity of the battery when leaving the factory; r_freshInternal resistance for the first cycle of the battery; r_eolIndicating the internal resistance of the battery at the end of its life; r_0,kThe internal resistance of the battery in the current state is obtained; m represents a windowing size; h denotes an innovation real-time estimated covariance function derived from the windowing estimation principle,

step 4.2, aiming at the model constructed in step 4.1, a specific process shown in fig. 8 is implemented for the cooperative estimation implementation flow of the SOC and SOH of the lithium battery by using an Adaptive Extended Kalman Filter (AEKF):

1) initialization:

at t₀At time, i.e., when k is 0, the initial value of the state observer is set: x is the number of₀,P₀,Q₀,R₀；

2) A priori estimate-predict: time update [ State Slave time (k-1)⁺Arrival time (k)^-Is calculated by]

For k 1,2, a priori estimation (time update) operation is performed, estimating the state and covariance from the previous time (k-1)⁺Reckoning to the current time (k)^-The time update equation of the adaptive extended kalman filter is expressed as follows:

and (3) system state estimation:

estimating error covariance:

wherein, f (x)_k-1,u_k-1) Representing a system equation of state function;

3) a posteriori estimation-correction: measurement update [ State Slave time (k)^-Arrival time (k)⁺Is calculated by]

This step uses the measured value y at the time k_kCorrecting state estimation and covariance estimation, the estimation results being used separatelyAndexpressed, the measurement update equation of the adaptive extended kalman filter is expressed as follows:

an innovation matrix:

kalman gain matrix:

adaptive noise covariance matching:

and (3) correcting the system state:

error covariance correction:

4) time scale update

Time of day (k)⁺The state and covariance matrix of (c) are prepared as outputs, and the state estimate at time (k +1) is prepared.

In order to verify the accuracy of the constructed SOC and SOH collaborative estimator, a second-order RC equivalent circuit model considering the influence of different cycle times is firstly established in an MATLAB/Simulink environment, and a measured constant-current working condition experimental curve is compared with a model simulation curve by identifying model parameters and simulating the accuracy of a verification model. Finally, constructing a SOC and SOH co-estimator, wherein the SOH estimation comprises estimating the SOH as a representation of the maximum available capacity of the battery_[Ccap]And estimating SOH for battery internal resistance characterization_[R0]. For simplicity, a cyclic Cycle30 is used as an example, wherein the comparison curve of the experimental SOC and the estimated SOC is shown in FIG. 9, and the average absolute error is 0.26% as shown in FIG. 10. In addition, the average absolute error under constant current working condition in other cycles [ 1002003006008001000]]Respectively, the content of the components is [ 0.24%, 0.22%, 0.20%, 0.86%, 1.14%, 1.36%]. A graph of measured versus estimated capacity under cyclic 30 conditions is shown in FIG. 11, with an average absolute error of 0.018Ah as shown in FIG. 12. In addition, other cycles [ 1002003006008001000] may also be obtained]The lower errors are respectively [ 0.0160.0190.0200.0190.0210.022]Ah. Wherein, according to equation (19), a SOH estimation diagram characterized by capacity can be obtained, as shown in fig. 13. A graph of the comparison curve of the identified internal resistance and the estimated internal resistance under the condition of the cyclic 30 is shown in FIG. 14, and the error of the comparison curve is 0.00142 Ω shown in FIG. 15. In addition, other cycles [ 1002003006008001000] may also be obtained]The lower errors are respectively [ 0.001330.001500.001560.001580.001670.00187]Omega. Wherein, according to equation (20), a SOH estimation diagram characterized by internal resistance can be obtained, as shown in fig. 16. As can be seen from the error range, the estimator of the invention has long application period and has great significance for BMS state estimation and energy management.

The simulation and estimation data show that the estimation method provided by the invention can be controlled within a smaller error range in SOC estimation, capacity and resistance estimation, so that the effectiveness and the accuracy of the estimation method are verified, the application of the electric vehicle in the whole life cycle range is improved, the problems of larger state estimation error and the like caused by inaccurate models due to different life cycles are solved, and the method has great significance for state estimation and energy management of a battery management system of the electric vehicle; the method plays an important role in the utilization efficiency, the service life and the performance of the whole power battery pack.

While the foregoing specification illustrates and describes several preferred embodiments of the invention, it is to be understood, as noted above, that the invention is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.