CN111581904B - Lithium battery SOC and SOH collaborative estimation method considering cycle number influence - Google Patents
Lithium battery SOC and SOH collaborative estimation method considering cycle number influence Download PDFInfo
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Abstract
The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle times comprises the following steps: step 1, constructing a lithium battery equivalent circuit model considering cycle times; step 2, identifying model parameters; step 3, performing simulation verification on the model established in the step 1; and 4, constructing the SOC/SOH cooperative estimator. The method can finally realize the State-of-charge (SOC) and State-of-health (SOH) estimation of the lithium battery in the whole life range, has great significance for the State estimation and 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 caused by different life cycles, effectively improves the utilization efficiency of the power battery pack and ensures the service life of the battery pack.
Description
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, a 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 (Battery management system, BMS) is required. For battery management systems, the core function is to provide accurate estimation of State-of-charge (SOC) and State-of-health (SOH) of the battery, which is a great challenge. Since the existing vehicle-mounted sensor cannot observe the 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 range and the endurance time of the electric automobile. At present, many researches on an SOC estimation algorithm are carried out, and a coulomb counting method, a model-based open circuit voltage method, a neural network method and a kalman filtering method are commonly used. 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.
The state of health describes the extent of battery aging, which can generally be reflected by a loss of capacity or an increase in resistance. The existing estimation method mainly comprises the following steps: direct measurement, voltage trace, compatibilizer analysis, differential voltage analysis, kalman filtering, particle filtering, neural network, vector machine, genetic algorithm and artificial intelligence algorithm.
However, as the battery is cycled, 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 estimation performance of SOC and SOH, it is necessary to consider cyclic aging of a lithium battery and to propose a cooperative estimator for simultaneously monitoring the state of charge and state of health of the battery.
In summary, providing a combined state estimation scheme capable of simultaneously estimating SOC and SOH is a problem that needs to be solved in the technical field of the current power battery management system. The method has great significance for protecting a 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 the collaborative estimation method of the SOC and the SOH of the lithium battery considering the influence of the cycle times, overcome the limitation that the traditional equivalent circuit model is only suitable for a certain life cycle range, and greatly improve the applicability of BMS state calculation and energy management in the whole life cycle.
In order to achieve the above purpose, the invention adopts the following technical scheme: the lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle times 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, performing simulation verification on the lithium battery equivalent circuit model established in the step 1 under the constant current working condition;
and 4, constructing a cooperative estimator considering the cycle times to estimate the SOC and the SOH of the lithium battery.
The mathematical relation of the equivalent circuit model of the lithium battery constructed in the step 1 is as follows:
in the formula (1), U t Is the battery terminal voltage; u (U) OC (SOC, cyc) represents the open circuit voltage, which is a function of the battery SOC and Cycle number; r is R 0 Is ohmic internal resistance; r is R 1 And C 1 The electrochemical polarization resistor and the electrochemical polarization fractional capacitor are respectively arranged; r is R 2 And C 2 Respectively a concentration polarization resistor and a concentration polarization fractional capacitor; for the sake of brevity, the parameter R is 0 (Cyc),R 1 (Cyc),C 1 (Cyc),R 2 (Cyc),C 2 (Cyc) is written as R 0 ,R 1 ,C 1 ,R 2 And C 2 ，I t Representing the operating current; u (U) 1 And U 2 Respectively representing electrochemical polarization voltage and concentration polarization voltage.
And 2, identifying the parameters of the model in the step 2, and identifying the parameters of the model by adopting a recursive least square (Recursive least square, RLS) method to obtain the parameters of the model under different cycle times, wherein the specific formula comprises:
the terminal voltage performs laplace transform:
it is provided that the device comprises a first storage device and a second storage device,
E＝U t -U OC (3)
the model transfer function is:
the simplification is as follows:
tustin transforms map s-plane based system equations to the z-plane:
the discrete transfer function based on the z-plane is:
G(z -1 )＝[a 3 +a 4 z -1 +a 5 z -2 ]/[1-a 1 z -1 -a 2 z -2 ] (7)
the discrete transfer function of equation (7) is converted into a time domain differential equation, resulting in:
E(l)＝a 1 E(l-1)+a 2 E(l-2)+a 3 I(l)+a 4 I(l-1)+a 5 I(l-2) (8)
defining a data variable ψ of a system l And parameter variable theta l The method comprises the following steps:
the time domain difference equation (8) can be rewritten as:
z l ＝Ψ l θ l +e Ls,l (10)
the specific flow of the recursive least squares algorithm for the system shown in equation (10) is as follows:
initialization of parameter variables and error covariance is:
inverse transformation using (6)
Then equation (7) can be rewritten as:
by comparing formula (7) with formula (14), we can obtain:
in the above formulas (2) to (15), E is the difference between the terminal voltage and the open circuit voltage; τ=rc represents a time constant, where τ 1 ＝R 1 C 1 ，τ 2 ＝R 2 C 2 The method comprises the steps of carrying out a first treatment on the surface of the T is the sampling interval time of the system; a, a 1 ,a 2 ,a 3 ,a 4 And a 5 Is an unknown parameter related to the model parameter; psi l Representing system data variables; θ l Representing the parameter variables; z in l An output variable representing the system; e, e Ls,l The white noise of the stable zero mean value is represented, and the angle mark l represents the data value as the first sampling moment; g represents the algorithm gain; f is an error covariance matrix of the state estimation value; where ρ represents a large number, which can be obtained empirically, the present invention gives ρ of 10 6 I represents an identity matrix.
In the step 3, simulation verification is carried out on the equivalent circuit model of the lithium battery, and the method specifically comprises the following steps:
under MATLAB/Simulink environment, building a lithium battery equivalent circuit model considering the influence of cycle times, wherein the input is as follows: current and cycle number, and output as voltage; constant current operating mode tests (Constant current condition, CCC) were used to verify at [301002003006008001000] seven different cycles, respectively.
In step 4, constructing a cooperative estimator considering the cycle times to estimate the SOC and 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 electrochemical polarization voltage U of the lithium battery are calculated 1 Concentration polarization voltage U 2 Ohmic internal resistance R 0 Reciprocal of capacity 1/C cap As a state variable, a measurable battery terminal voltage U is selected t As observed quantity, a state prediction equation and an observation equation (16) are established,
first, a system state matrix x is defined k Define the system output y k And system input u k ：
The algorithm formula:
in the above formulas (16) to (21), ω is a system white noise, the mean value is 0, the covariance is Q, V is a measurement white noise, the mean value is 0, and the covariance is V; a is that k-1 Is a system matrix; b (B) k-1 Is a control matrix; c (C) k Outputting a matrix for the system; u (u) k Is a system input; t (T) S For sampling period, P - And P + The state estimation covariance prior estimation and the posterior estimation are respectively carried out, K is Kalman gain, e is an innovation matrix, I is an identity matrix, eta is coulomb efficiency, and the state estimation covariance prior estimation and the posterior estimation are respectively carried out, and are assumed to be 1 in charging, 0.98 in discharging and C in discharging cap,k Maximum available capacity of the battery under the current cycle; c (C) fresh Maximum available capacity at battery delivery; r is R fresh Is the internal resistance of the battery in the first cycle; r is R eol Representing the internal resistance of the battery at the end of the battery life; r is R 0,k The internal resistance of the battery in the current state is obtained; m represents the size of the window; h denotes the innovation real-time estimation covariance function obtained by the windowing estimation principle,
step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the lithium battery SOC and SOH cooperative estimation is carried out by using an adaptive extended Kalman filter:
1) Initializing:
at t 0 When time, i.e. k=0, the initial value x of the state observer is set 0 ,P 0 ,Q 0 ,R 0 ；
2) A priori estimation-prediction: time update [ state slave time (k-1) + Time of arrival (k) - Is calculated by (a)]
For k=1, 2, ·, the following a priori estimation (time update) operation is completed, estimating the state and covariance from the previous time (k-1) + The current time (k) is calculated - The time update equation for the adaptive extended kalman filter is expressed as follows:
estimating the system state:
error covariance estimation:
wherein f (x) k-1 ,u k-1 ) Representing a system state equation function;
3) Posterior estimation-correction: measurement update [ state slave time (k) - Time of arrival (k) + Is calculated by (a)]
This step uses the measurement y at time k k Correcting state estimation and covariance estimation, and using estimation results respectivelyAnd->The measurement update equation for the adaptive extended kalman filter is expressed as follows:
information matrix:
kalman gain matrix:
adaptive noise covariance matching:
correcting the system state:
error covariance correction:
4) Time scale update
Will time (k) + As outputs, state estimation 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 (Battery management system, BMS) in the whole life cycle range in state calculation and energy management. The estimator constructed by the invention can describe the external characteristics of the power battery more accurately, 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 times has good practicability and application value in BMS and engineering.
The method can finally realize the battery state of charge and the state of health estimation within 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 method has great significance in protecting a battery system, improving the whole automobile performance and improving the economy.
Drawings
FIG. 1 is a schematic diagram of the SOC and SOH estimation process according to the present invention.
Fig. 2 is a schematic view of a battery model according to the present invention.
FIG. 3 is a graph showing the OCV-SOC curves at different cycles according to the present invention.
Fig. 4 is a schematic diagram of the change of the battery voltage under the constant current discharging condition of the present invention.
FIG. 5 is a graph showing the comparison of measured voltage and simulated voltage in the model verification of the present invention.
FIG. 6 is a graph showing the error between the measured voltage and the simulated voltage according to the present invention.
Fig. 7 is a schematic diagram of the maximum available capacity at different cycles of the present invention.
FIG. 8 is a schematic diagram of a cooperative estimation flow of SOC and SOH according to the present invention.
FIG. 9 is a graph showing experimental SOC versus estimated SOC under CCC conditions of the present invention.
FIG. 10 is a graph showing the experimental SOC versus estimated SOC error for the present invention.
FIG. 11 is a graph showing the measured capacity versus estimated capacity for the CCC of the present invention.
FIG. 12 is a graph showing the error between measured capacity and estimated capacity according to the present invention.
Fig. 13 is a schematic diagram of capacity and SOH estimation according to the present invention.
FIG. 14 is a graph of the internal resistance identified versus estimated internal resistance for the CCC operating conditions of the present invention.
Fig. 15 is a schematic diagram of the present invention for identifying internal resistance and estimating an internal resistance error.
Fig. 16 is a schematic diagram of the internal resistance and SOH estimation according to the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and detailed description. It should be understood that the detailed description is intended to illustrate the invention, and not to limit the invention.
The invention discloses a lithium battery SOC and SOH collaborative estimation method considering the influence of cycle times, the implementation flow 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 general second-order RC equivalent circuit model has the advantages of high calculation efficiency, easy engineering realization, good simulation of the dynamic behavior of the battery and the like, and is widely applied to power battery modeling and state estimation. However, as the battery is recycled, particularly after several hundred cycles of charge and discharge, the battery capacity decays and the internal resistance increases, resulting in reduced accuracy of the battery model, the present invention proposes an improved second-order RC circuit model taking different cycles into account based on the second-order RC model, as shown in FIG. 2, wherein the model parameters R 0 (Cyc),R 1 (Cyc),C 1 (Cyc),R 2 (Cyc),C 2 (Cyc) is a function of the number of cycles, and for brevity, the parameters are written as R 0 ,R 1 ,C 1 ,R 2 ,C 2 The method comprises the steps of carrying out a first treatment on the surface of the In addition, the difference of the OCV-SOC relationship under different Cycle times is considered, the consideration of the OCV-SOC is increased, the OCV-SOC-Cycle relationship is established, as shown in figure 3, the mathematical relationship formula is shown in formula (1) according to kirchhoff's law,
in the formula (1), U t Is the battery terminal voltage; u (U) OC (SOC, cyc) represents the open circuit voltage, which is a function of the battery SOC and Cycle number; r is R 0 Is ohmic internal resistance; r is R 1 And C 1 The electrochemical polarization resistor and the electrochemical polarization fractional capacitor are respectively arranged; r is R 2 And C 2 Respectively a concentration polarization resistor and a concentration polarization fractional capacitor; for the sake of brevity, the parameter R is 0 (Cyc),R 1 (Cyc),C 1 (Cyc),R 2 (Cyc),C 2 (Cyc) is written as R 0 ,R 1 ,C 1 ,R 2 And C 2 ，I t Representing the operating current; u (U) 1 And U 2 Respectively representing electrochemical polarization voltage and concentration polarization voltage.
Step 2, identifying model parameters by adopting a recursive least square method;
in the step 2 of the invention, the model parameters are identified by adopting a recursive least square method (Recursive least square, RLS), and model parameters under different circulation times are respectively obtained by adopting constant current discharge working conditions (shown in figure 4) under different circulation [301002003006008001000], and the specific formulas are as follows:
the terminal voltage performs laplace transform:
it is provided that the device comprises a first storage device and a second storage device,
E＝U t -U OC (3)
the model transfer function is:
the simplification is as follows:
tustin transforms map s-plane based system equations to the z-plane:
the discrete transfer function based on the z-plane is:
G(z -1 )＝[a 3 +a 4 z -1 +a 5 z -2 ]/[1-a 1 z -1 -a 2 z -2 ] (7)
the discrete transfer function of equation (7) is converted into a time domain differential equation, resulting in:
E(l)＝a 1 E(l-1)+a 2 E(l-2)+a 3 I(l)+a 4 I(l-1)+a 5 I(l-2) (8)
defining a data variable ψ of a system l And parameter variable theta l The method comprises the following steps:
the time domain difference equation (8) can be rewritten as:
z l ＝Ψ l θ l +e Ls,l (10)
the specific flow of the recursive least squares algorithm for the system shown in equation (10) is as follows:
initialization of parameter variables and error covariance is:
inverse transformation using (6)
Then equation (7) can be rewritten as:
by comparing formula (7) with formula (14), we can obtain:
in the above formulas (2) to (15), E is the difference between the terminal voltage and the open circuit voltage; τ=rc represents a time constant, where τ 1 ＝R 1 C 1 ，τ 2 ＝R 2 C 2 The method comprises the steps of carrying out a first treatment on the surface of the T is the sampling interval time of the system; a, a 1 ,a 2 ,a 3 ,a 4 And a 5 Is an unknown parameter related to the model parameter; psi l Representing system data variables; θ l Representing the parameter variables; z in l An output variable representing the system; e, e Ls,l The white noise of the stable zero mean value is represented, and the angle mark l represents the data value as the first sampling moment; g represents the algorithm gain; f is an error covariance matrix of the state estimation value; where ρ represents a large number, which can be obtained empirically, the present invention gives ρ of 10 6 I represents an identity matrix.
Step 3, performing simulation verification on the model established in the step 1 under the constant current working condition, wherein the simulation verification comprises the following steps:
the parameters R under different cycles can be obtained respectively through the parameter identification in the step 2 0 、R 1 、C 1 、R 2 、C 2 And numerical values. Then, under the MATLAB/Simulink environment, building a lithium ion battery equivalent circuit model considering the influence of different cycle times, wherein the input is as follows: the current and the cycle times are output as terminal voltage. Using constant current operating conditions (Constant current condition, CCC) in [301002003006008001000]]Simulation is carried out under seven different Cycle times, taking Cycle30 as an example, as shown in fig. 5, comparing the measured voltage with the simulation voltage, and obtaining corresponding error of 0.019, as shown in fig. 6; other cycles [100 2003006008001000]]Lower errors are respectively [0.019 0.018 0.016 0.021 0.022 0.019 ]]；
Step 4, constructing a cooperative estimator considering the cycle times to estimate the SOC and 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 of the battery and the electrochemical polarization voltage U 1 Concentration polarization voltage U 2 Ohmic internal resistance R 0 Reciprocal of capacity 1/C cap As a state variable, a measurable battery terminal voltage U is selected t As observed quantity, a state prediction equation and an observation equation (16) are established,
first, a system state matrix x is defined k Define the system output y k And system input u k ：
SOH is defined in terms of the remaining capacity of the battery, which can be measured directly after a period of use. The invention is provided with C fresh For maximum usable capacity of battery at leaving factory, C cap,k For the current maximum available capacity of the battery, the SOH is changed under different cycles as shown in FIG. 7 [Ccap] The definition is as follows:
since the battery SOH decays with increasing internal resistance of the battery, the battery SOH can be defined according to this relationship, where R fresh Is the internal resistance of the battery in the first cycle; r is R eol Representing the internal resistance of the battery at the end of the battery life; r is R 0,k Then the internal resistance of the battery in the current state is the SOH of the battery [R0] The definition is as follows:
the algorithm formula of the adaptive extended Kalman filter is as follows:
in the above formulas (16) to (21), ω is a system white noise, the average value is 0,covariance is Q, V is measurement white noise, mean value is 0, covariance is V; a is that k-1 Is a system matrix; b (B) k-1 Is a control matrix; c (C) k Outputting a matrix for the system; u (u) k Is a system input; t (T) S For sampling period, P - And P + The state estimation covariance prior estimation and the posterior estimation are respectively carried out, K is Kalman gain, e is an innovation matrix, I is an identity matrix, eta is coulomb efficiency, and the state estimation covariance prior estimation and the posterior estimation are respectively carried out, and are assumed to be 1 in charging, 0.98 in discharging and C in discharging cap,k Maximum available capacity of the battery under the current cycle; c (C) fresh Maximum available capacity at battery delivery; r is R fresh Is the internal resistance of the battery in the first cycle; r is R eol Representing the internal resistance of the battery at the end of the battery life; r is R 0,k The internal resistance of the battery in the current state is obtained; m represents the size of the window; h denotes the innovation real-time estimation covariance function obtained by the windowing estimation principle,
step 4.2, aiming at the model constructed in step 4.1, using an adaptive extended kalman filter (Adaptive extended Kalman filter, AEKF) to implement a specific process of flow chart shown in fig. 8 for the SOC and SOH collaborative estimation of the lithium battery:
1) Initializing:
at t 0 At the time instant, i.e., when k=0, the initial value of the state observer is set: x is x 0 ,P 0 ,Q 0 ,R 0 ；
2) A priori estimation-prediction: time update [ state slave time (k-1) + Time of arrival (k) - Is calculated by (a)]
For k=1, 2, ·, the following a priori estimation (time update) operation is completed, estimating the state and covariance from the previous time (k-1) + The current time (k) is calculated - The time update equation for the adaptive extended kalman filter is expressed as follows:
estimating the system state:
error covariance estimation:
wherein f (x) k-1 ,u k-1 ) Representing a system state equation function;
3) Posterior estimation-correction: measurement update [ state slave time (k) - Time of arrival (k) + Is calculated by (a)]
This step uses the measurement y at time k k Correcting state estimation and covariance estimation, and using estimation results respectivelyAnd->The measurement update equation for the adaptive extended kalman filter is expressed as follows:
information matrix:
kalman gain matrix:
adaptive noise covariance matching:
correcting the system state:
error covariance correction:
4) Time scale update
Will time (k) + As outputs, state estimation 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 a MATLAB/Simulink environment, and the accuracy of the model is verified through model parameter identification and simulation, and a measured constant current working condition experimental curve is compared with a model simulation curve. Finally, a SOC and SOH co-estimator is constructed, wherein the SOH estimation includes estimating the SOH of the battery maximum available capacity representation [Ccap] And estimating SOH of the internal resistance representation of the battery [R0] . For brevity, the Cycle30 is taken 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 can be obtained in other cycles [100 2003006008001000]]The following are [0.24% 0.22% 0.20% 0.86% 1.14% 1.36%]. The graph of the measured capacity versus estimated capacity for the cyclic Cycle30 is shown in fig. 11, and the average absolute error is shown in fig. 12 as 0.018Ah. In addition, other cycles [100 2003006008001000] can be obtained]Lower errors are respectively [0.016 0.019 0.020 0.019 0.021 0.022 ]]Ah. Wherein a schematic representation of SOH estimation characterized by capacity can be obtained according to equation (19), as shown in FIG. 13. The graph of the comparison of the internal resistance identified under the cyclic Cycle30 condition and the estimated internal resistance is shown in fig. 14, and the error is 0.00142 Ω as shown in fig. 15. In addition, other cycles [100 2003006008001000] can be obtained]Lower errors are respectively [0.00133 0.00150 0.00156 0.00158 0.00167 0.00187 ]]Omega. Wherein a SOH estimation schematic characterized by internal resistance can be obtained according to equation (20), as shown in FIG. 16. From the error range, the estimation of the present inventionThe calculator has long application period and has great significance in BMS state estimation and energy management.
The simulation and estimated data show that the estimation method provided by the invention can be controlled in a smaller error range in SOC estimation, capacity and resistance estimation, so that the effectiveness and 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 estimation method has great significance in state estimation and energy management of a battery management system of the electric vehicle; the method plays a great role in the utilization efficiency and the service life of the power battery pack and the whole vehicle performance.
While the foregoing description illustrates and describes several preferred embodiments of the invention, it is to be understood that the invention is not limited to the forms disclosed herein, but is not to be construed as limited to other embodiments, and is capable of use in various other combinations, modifications and environments and is capable of changes or modifications within the spirit of the invention described herein, either as a result of the foregoing teachings or as a result of the knowledge or skill of the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (2)
1. The lithium battery SOC and SOH collaborative estimation method considering the influence of the cycle times is characterized by comprising the following steps:
step 1, constructing a lithium battery equivalent circuit model considering cycle times;
the mathematical relation of the equivalent circuit model of the lithium battery constructed in the step 1 is as follows:
in the formula (1), U t Is the battery terminal voltage; u (U) OC (SOC, cyc) represents the open circuit voltage, which is a function of the battery SOC and Cycle number; r is R 0 Is ohmic internal resistance; r is R 1 And C 1 The electrochemical polarization resistor and the electrochemical polarization fractional capacitor are respectively arranged; r is R 2 And C 2 Respectively a concentration polarization resistor and a concentration polarization fractional capacitor; for the sake of brevity, the parameter R is 0 (Cyc),R 1 (Cyc),C 1 (Cyc),R 2 (Cyc),C 2 (Cyc) is written as R 0 ,R 1 ,C 1 ,R 2 And C 2 ，I t Representing the operating current; u (U) 1 And U 2 Respectively representing electrochemical polarization voltage and concentration polarization voltage;
step 2, identifying model parameters by adopting a recursive least square method;
and 2, identifying parameters of the model in the step 2, and identifying the parameters of the model by adopting a recursive least square method to obtain the parameters of the model under different cycle times, wherein the specific formula comprises:
the terminal voltage performs laplace transform:
it is provided that the device comprises a first storage device and a second storage device,
E＝U t -U OC (3)
the model transfer function is:
the simplification is as follows:
tustin transforms map s-plane based system equations to the z-plane:
the discrete transfer function based on the z-plane is:
G(z -1 )＝[a 3 +a 4 z -1 +a 5 z -2 ]/[1-a 1 z -1 -a 2 z -2 ] (7)
the discrete transfer function of equation (7) is converted into a time domain differential equation, resulting in:
E(l)＝a 1 E(l-1)+a 2 E(l-2)+a 3 I(l)+a 4 I(l-1)+a 5 I(l-2) (8)
defining a data variable ψ of a system l And parameter variable theta l The method comprises the following steps:
then the time domain difference equation (8) is rewritten as:
z l ＝Ψ l θ l +e Ls,l (10)
the specific flow of the recursive least squares algorithm for the system shown in equation (10) is as follows:
initialization of parameter variables and error covariance is:
inverse transformation using (6)
Then, equation (7) is rewritten as:
by comparing formula (7) with formula (14), we can obtain:
in the above formulas (2) to (15), E is the difference between the terminal voltage and the open circuit voltage; τ=rc represents a time constant, where τ 1 ＝R 1 C 1 ，τ 2 ＝R 2 C 2 The method comprises the steps of carrying out a first treatment on the surface of the T is the sampling interval time of the system; a, a 1 ,a 2 ,a 3 ,a 4 And a 5 Is an unknown parameter related to the model parameter; psi l Representing system data variables; θ l Representing the parameter variables; z in l An output variable representing the system; e, e Ls,l The white noise of the stable zero mean value is represented, and the angle mark l represents the data value as the first sampling moment; g represents the algorithm gain; f is an error covariance matrix of the state estimation value; where ρ represents a large number, which can be obtained empirically, let ρ be 10 6 I represents an identity matrix;
step 3, performing simulation verification on the lithium battery equivalent circuit model established in the step 1 under the constant current working condition;
step 4, constructing a cooperative estimator considering the cycle times to estimate the SOC and SOH of the lithium battery,
in step 4, constructing a cooperative estimator considering the cycle times to estimate the SOC and 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 electrochemical polarization voltage U of the lithium battery are calculated 1 Concentration polarization voltage U 2 Ohmic internal resistance R 0 Reciprocal of capacity 1/C cap As a state variable, a measurable battery terminal voltage U is selected t As observed quantity, a state prediction equation and an observation equation (16) are established,
first, a system state matrix x is defined k Define the system output y k And system input u k ：
The algorithm formula:
in the above formulas (16) to (21), ω is a system white noise, the mean value is 0, the covariance is Q, V is a measurement white noise, the mean value is 0, and the covariance is V; a is that k-1 Is a system matrix; b (B) k-1 Is a control matrix; c (C) k Outputting a matrix for the system; u (u) k Is a system input; t (T) S For sampling period, P - And P + The state estimation covariance prior estimation and the posterior estimation are respectively carried out, K is Kalman gain, e is an innovation matrix, I is an identity matrix, eta is coulomb efficiency, and the state estimation covariance prior estimation and the posterior estimation are respectively carried out, and are assumed to be 1 in charging, 0.98 in discharging and C in discharging cap,k Maximum available capacity of the battery under the current cycle; c (C) fresh Maximum available capacity at battery delivery; r is R fresh For the first cycle of the batteryResistance; r is R eol Representing the internal resistance of the battery at the end of the battery life; r is R 0,k The internal resistance of the battery in the current state is obtained; m represents the size of the window; h denotes the innovation real-time estimation covariance function obtained by the windowing estimation principle,
step 4.2, aiming at the model constructed in the step 4.1, a specific estimation process of the lithium battery SOC and SOH cooperative estimation is carried out by using an adaptive extended Kalman filter:
1) Initializing:
at t 0 When time, i.e. k=0, the initial value x of the state observer is set 0 ,P 0 ,Q 0 ,R 0 ；
2) A priori estimation-prediction: time update [ state slave time (k-1) + Time of arrival (k) - Is calculated by (a)]
For k=1, 2, …, the following a priori estimation (time update) operation is completed, the state and covariance estimates are estimated from the previous time (k-1) + The current time (k) is calculated - The time update equation for the adaptive extended kalman filter is expressed as follows:
estimating the system state:
error covariance estimation:
wherein f (x) k-1 ,u k-1 ) Representing a system state equation function;
3) Posterior estimation-correction: measurement update [ state slave time (k) - Time of arrival (k) + Is calculated by (a)]
This step uses the time kMeasurement value y k Correcting state estimation and covariance estimation, and using estimation results respectivelyAnd->The measurement update equation for the adaptive extended kalman filter is expressed as follows:
information matrix:
kalman gain matrix:
adaptive noise covariance matching:
correcting the system state:
error covariance correction:
4) Time scale update
Will time (k) + As outputs, state estimation at time (k+1) is prepared.
2. The method for collaborative estimation of SOC and SOH of a lithium battery with consideration of cycle number effects according to claim 1, wherein the simulation verification of the equivalent circuit model of the lithium battery in step 3 is specifically:
under MATLAB/Simulink environment, building a lithium battery equivalent circuit model considering the influence of cycle times, wherein the input is as follows: current and cycle number, and output as voltage; the constant current working condition test is used for verification under the seven different cycle times of [301002003006008001000] respectively.
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