CN110261779B - Online collaborative estimation method for state of charge and state of health of ternary lithium battery - Google Patents

Online collaborative estimation method for state of charge and state of health of ternary lithium battery Download PDF

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CN110261779B
CN110261779B CN201910555791.7A CN201910555791A CN110261779B CN 110261779 B CN110261779 B CN 110261779B CN 201910555791 A CN201910555791 A CN 201910555791A CN 110261779 B CN110261779 B CN 110261779B
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lithium battery
ternary lithium
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刘熹
李琳
刘海龙
陈威冲
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Xian Shiyou University
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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]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
    • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract

The invention discloses an online collaborative estimation method for the state of charge and the state of health of a ternary lithium battery, which improves a Thevenin equivalent circuit model, obtains a state space equation of the improved Thevenin equivalent circuit model according to a circuit relation, further obtains a mapping relation between OCV and SOC, obtains specific numerical values of polarization resistance, polarization capacitance and internal resistance at each sampling point by acquiring external voltage and current values through an FFRLS algorithm and updates parameter values of the Thevenin equivalent circuit model in real time according to the running state of the BMS before calculating the SOC and the SOH each time, ensures that the prediction of the BMS on the SOC and the SOH is more accurate, has simple external circuit when realizing high-precision estimation of the SOC and the SOH of the ternary lithium battery, only needs the conventional BMS to acquire voltage, current and time numerical values, has strong convergence, has strong robustness on an error initial value and still adopts an iterative cycle calculation method, the sampling accuracy requirement for the BMS can be appropriately reduced.

Description

Online collaborative estimation method for state of charge and state of health of ternary lithium battery
Technical Field
The invention relates to a method for estimating the state of charge and the state of health of a battery, in particular to a method for estimating the state of charge and the state of health of a ternary lithium battery in an online collaborative manner, and belongs to the technical field of battery management.
Background
With the change of human energy consumption structure, renewable clean energy is receiving much attention. Among them, the ternary lithium battery has started to be widely applied to the fields of pure electric vehicles, large-scale energy storage and the like because of the advantages of high energy density, long cycle life, safe use, low self-discharge rate and the like. In this process, the battery can operate in an excellent state only by implementing good management of the battery, and the service life of the battery is prolonged at the same time. Therefore, how to quickly and accurately determine the operating state (remaining capacity) and the service life of the battery is one of the key technologies of a Battery Management System (BMS), and the quality of the BMS directly affects the operation quality of the power equipment.
Ternary lithium battery states mainly include two most important aspects — State of Charge (SOC) and State of Health (SOH).
The SOC reflects the current residual electric quantity of the battery, is an important premise for realizing the energy balance technology of the ternary lithium battery pack, and is one of the most important parameters in BMS monitoring.
The SOH reflects the current service life of the battery, also called the aging degree of the battery, and the SOH value generally directly determines whether the equipment needs to be replaced by the ternary lithium battery.
At present, most of the commonly used lithium battery SOC and SOH estimation methods are used for independently estimating two state variables.
The existing lithium battery SOC estimation method comprises the following steps: ampere-hour integration method, internal resistance measurement method, open circuit voltage method, etc.
The existing lithium battery SOH estimation method comprises the following steps: capacity ratio method, internal resistance measurement method, electrochemical model estimation method, etc.
Although there are many methods for estimating the SOC and SOH of the lithium battery at present, the BMS needs to design the SOC and SOH estimation system and estimation algorithm separately according to the type and model of the battery, the configuration of the battery pack, the operating condition, the operating environment, and other factors. Once the power lithium battery is replaced, the original SOC and SOH estimation system and estimation method are redesigned, so that the overall operation and use efficiency of the BMS is low, and the universality and stability of different lithium batteries are poor.
Chinese patent "a self-adaptive estimation method of power battery pack SOC and SOH" (CN201710141906), reads the battery core material and factory property test data of the power battery through a battery ID property data input module, completes the initial calculation of the power battery SOC and SOH and carries out state estimation by using recent power battery historical data through a self-adaptive SOC and SOH estimation system. Since the adaptive SOC and SOH estimation system needs to continuously store newer data as an initial value for the next estimation, the complexity of the BMS is increased, the development cost of the BMS is increased, and an algorithm may not converge or an estimation failure may occur when the algorithm is used due to a mismatch between the read initial value and the actual state of the current BMS.
Chinese patent "a lithium ion battery SOC and SOH joint estimation method" (CN201710308354) constructs a lithium ion battery offline equivalent circuit model, identifies parameters of the established model by using an offline least square method, updates model parameters in a certain range based on a rolling time domain of offline data, and completes joint estimation of SOC and SOH. Although the method can complete the joint estimation of the SOC and the SOH of the lithium battery, the model parameters are obtained based on the specific working condition under the offline condition, and when the operating working condition and the environment change, the model parameters cannot be updated in real time, so that the method has low applicability to different operating working conditions and environments and large errors.
Disclosure of Invention
In order to solve the defects of the prior art, the invention aims to provide a combined algorithm, which realizes the cooperative online estimation of the SOC and the SOH of the ternary lithium battery under the condition that a battery model is known but model parameters are unknown, further improves the online estimation precision of the SOC and the SOH of the lithium battery, and enhances the universality and the stability of the BMS on different types of lithium batteries.
In order to achieve the above object, the present invention adopts the following technical solutions:
the online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized by realizing online collaborative estimation for the state of charge and the state of health of the ternary lithium battery based on an FFRLS algorithm and an improved EKF algorithm, and specifically comprises the following steps:
step 1: a concentration polarization network is added on the basis of a traditional Thevenin equivalent circuit model, and a continuously-changed mathematical expression is obtained according to the established improved Thevenin equivalent circuit model, which is concretely as follows:
Uo(t)＝E(t)-U1(t)-U2(t)-i×R0 (1)
Figure BDA0002106841600000031
Figure BDA0002106841600000032
wherein E represents a battery electromotive force, RCAnd REAre all polarization resistances, CCAnd CEThen the corresponding polarization capacitance, i is the actual current flowing through the load, R0Is the ohmic internal resistance, U, of the batteryoIs the terminal voltage of the battery, U1And U2Terminal voltages, τ, of two RC networks, respectively1And τ2Time constants of the two RC networks are respectively;
step 2: establishing SOC and current i of the ternary lithium battery, coulombic efficiency eta and temperature compensation coefficient KTRated capacity QNAnd the time t are in a mathematical relation as follows:
Figure BDA0002106841600000041
and step 3: establishing SOH of ternary lithium battery and current internal resistance R of battery0Internal resistance R at the end of battery lifeovInternal resistance R of new batteryneThe mathematical relationship between the two is as follows:
Figure BDA0002106841600000042
and 4, step 4: deducing a discretized state space equation of the ternary lithium battery according to the formulas (1) to (4)
Figure BDA0002106841600000043
And
Figure BDA0002106841600000044
the method comprises the following specific steps:
Figure BDA0002106841600000045
Uo(k)＝E[SOC(k)]-U1(k)-U2(k)-i(k)×R0 (7)
Figure BDA0002106841600000046
Figure BDA0002106841600000047
wherein T is the sampling period, E [ SOC (k)]Is the mapping relation between the SOC of the battery and the open-circuit voltage, lambda (k) and gamma (k) are BMS noise and measurement noise respectively, and covariance is QrkAnd Rrk；
And 5: drawing an OCV-SOC fitting curve graph;
step 6: deducing a transfer function of the improved Thevenin equivalent circuit model, and mapping the ternary lithium battery model to a z plane from an s plane by using a bilinear transformation method to enable
Figure BDA0002106841600000051
Obtaining:
Figure BDA0002106841600000052
wherein, ci(i ═ 1,2,3,4,5) is a constant coefficient related to a ternary lithium battery model, and discretization can obtain:
y(k)＝c1y(k-1)+c2y(k-2)+c3I(k)+c4I(k-1)+a5I(k-2) (12)
the FFRLS algorithm is utilized to design a ternary lithium battery model as follows:
Figure BDA0002106841600000053
wherein the content of the first and second substances,
Figure BDA0002106841600000054
inputting and outputting matrix vectors for the ternary lithium battery model;
Figure BDA0002106841600000055
to include constant coefficients associated with a ternary lithium battery model
Figure BDA0002106841600000056
e0(k) Is the sampling error of the BMS;
the parameters of the ternary lithium battery model are obtained by the equal coefficients as follows:
Figure BDA0002106841600000057
obtaining R, C parameters of the ternary lithium battery model through the above formula;
and 7: and (3) substituting R, C parameters of the ternary lithium battery model with the identification finished at the point k in the step (6) into the discretized ternary lithium battery state space equation in the step (4), and setting initial values of state variables as follows:
Figure BDA0002106841600000061
Qrk＝0.001，Rrk＝0.5；
Figure BDA0002106841600000062
Qk＝0.005E(3)，Rk＝1000；
in the above formula, the first and second carbon atoms are,
Figure BDA0002106841600000063
a state vector describing the change of the internal resistance of the battery;
Figure BDA0002106841600000064
an error covariance matrix of the internal resistance of the battery;Qrkand QkRepresenting the system noise covariance; rrkAnd RkRepresenting the measurement noise covariance;
Figure BDA0002106841600000065
is a state vector describing the change in SOC; pxIs the error covariance matrix for the SOC;
and 8: the ternary lithium battery model state equation system matrix, the input matrix and the measurement matrix are respectively as follows:
Figure BDA0002106841600000066
giving initial values to a ternary lithium battery model state equation system matrix, an input matrix and a measurement matrix, wherein the initial values are respectively as follows:
Figure BDA0002106841600000067
and step 9: establishing a discretization time iteration equation and a discretization state iteration equation according to a Kalman filtering formula, wherein the discretization time iteration equation is specifically as follows:
Figure BDA0002106841600000068
Figure BDA0002106841600000071
calculating an estimation value of the current moment according to the ternary lithium battery model and the parameter value by using a time iteration equation, and calculating an estimation error value;
the discretization state iteration equation is concretely as follows:
Figure BDA0002106841600000072
Figure BDA0002106841600000073
firstly, a state iteration equation calculates Kalman filtering gain KkThe error is solved according to the minimum error principle, and then the open-circuit voltage y at the moment k is calculatedkObtaining the optimal estimation value of the current time by using the gain and the predicted value of the current time according to the difference value of the observed quantity h, and finally calculating an error matrix so as to obtain state variables SOC and R of the current time0The optimal estimated value of (a).
The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized in that in step 2, K isT＝[1+0.008×(T0-25)]，T0Is ambient temperature.
The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized in that in step 4, Q isrkAnd RrkIs usually determined by the state of the actual BMS, usually QrkThe value of (A) is in the range of 0.0001-0.01, RrkThe value of (a) is in the range of 0.5-1.
The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized in that in step 5, before an OCV-SOC fitting curve graph is drawn, a hybrid power pulse capability characteristic experiment is performed on the ternary lithium battery, and the steps are as follows:
(1) charging the ternary lithium battery to full charge, standing for 30min, measuring an open-circuit voltage value, and calibrating the SOC to be 1;
(2) setting a constant current discharge current of a programmable electronic load according to the measured capacity of the ternary lithium battery, and acquiring voltage and current data at a frequency of 10Hz during discharge;
(3) setting discharge time, stopping discharge when the discharge time is up, standing for 5min, and still acquiring voltage and current data at a frequency of 10Hz during standing;
(4) and (4) repeating the steps (2) to (3) until the SOC is 0.
The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized in that after a hybrid power pulse capability characteristic experiment is finished, a data set with the SOC descending gradient of every 5% is selected for recording, and then an OCV (open circuit voltage) -SOC (state of charge) graph is fitted with the SOC to obtain an OCV-SOC (open circuit voltage-state of charge) graph.
The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized in that in step 9, state variables SOC and R at the current moment are obtained0And after the optimal estimation value is obtained, the optimal estimation value at the current moment is combined with the voltage and current value identification of the next sampling point to obtain the Thevenin equivalent circuit model parameter value at the next moment, the model parameter value at the current moment is updated, then the algorithm sequentially and circularly calculates a time iteration equation and a state iteration equation in an alternating mode, and the steps are repeated in a reciprocating mode.
The invention has the advantages that:
(1) according to the online collaborative estimation method for the SOC and the SOH of the ternary lithium battery, a Thevenin equivalent circuit model is improved, a state space equation of the improved Thevenin equivalent circuit model is obtained according to a circuit relation, a mapping relation between Open Circuit Voltage (OCV) and the SOC is further obtained, specific numerical values of polarization resistance, polarization capacitance and internal resistance at each sampling point are obtained by acquiring external voltage and current values through an FFRLS algorithm in a real-time identification mode, parameter values of the Thevenin equivalent circuit model are updated in real time according to the running state of a BMS at the moment before the SOC and the SOH are calculated each time, and the SOC and the SOH are predicted more accurately by the BMS;
(2) according to the online collaborative estimation method for the SOC and the SOH of the ternary lithium battery, provided by the invention, when the high-precision estimation of the SOC and the SOH of the ternary lithium battery is realized, an external circuit is simple, and only a conventional BMS is used for collecting voltage, current and time values, so that the complexity of a peripheral circuit of the BMS is greatly simplified; meanwhile, the improved EKF algorithm still adopts an iterative loop calculation method for estimating SOC and SOH, and has strong convergence and strong robustness to an error initial value, so that the sampling precision requirement on the BMS can be properly reduced, the hardware cost of the BMS is further reduced, the development period of the BMS is shortened, and the BMS is convenient to maintain in a later period;
(3) according to the online collaborative estimation method for SOC and SOH of the ternary lithium battery, due to the fact that the FFRLS algorithm is adopted to identify the discrete Thevenin equivalent circuit model parameters, the identification result fully considers the influence of the running state and the surrounding environment of the current BMS, the average error obtained after the identified parameter values are brought into the Thevenin equivalent circuit model is less than 0.5%, and the relative error between the SOC value and the SOH value obtained by the identification parameters through the improved EKF algorithm and the theoretical value is less than 1.5%;
(4) according to the online collaborative estimation method for the SOC and the SOH of the ternary lithium battery, the internal resistance value of the battery is used as the characteristic quantity of the SOH (actual capacity), the internal resistance value of the ternary lithium battery can be updated iteratively in real time when the BMS runs, the actual capacity value of the battery is continuously corrected, and the accuracy and the reliability of the calculation result of the algorithm are improved to a certain extent;
(5) the online collaborative estimation method for SOC and SOH of the ternary lithium battery is suitable for lithium batteries of all models, can complete collaborative online estimation of SOC and SOH of the lithium battery under various BMSs and all actual operation conditions, greatly improves compatibility, universality and stability of the BMSs, and effectively solves the problems of SOC and SOH estimation failure and the like caused by phenomena of sudden change of external environment, uncertain operation conditions, self aging of the battery, self discharge of the battery and the like while improving estimation accuracy of the SOC and the SOH.
Drawings
Fig. 1 is a modified Thevenin equivalent circuit model;
FIG. 2 is a graph of an OCV-SOC fit;
FIG. 3 is a flow chart of online parameter identification based on FFRLS algorithm;
FIG. 4 is a graph of response voltage versus measured device voltage for a battery model based on the FFRLS algorithm;
FIG. 5 is a graph of battery model relative error based on the FFRLS algorithm;
FIG. 6 is a flow chart of SOC and SOH online collaborative estimation based on the FFRLS algorithm and the modified EKF algorithm;
FIG. 7 is a graph of SOC estimation experiment results;
FIG. 8 is a graph of relative percentage error of SOC estimates;
FIG. 9 is a graph of the results of an SOH estimation experiment;
FIG. 10 is a graph of SOH estimate relative error percentage;
FIG. 11 is a graph of the algorithm convergence verification results at the initial error value.
Detailed Description
The invention is described in detail below with reference to the figures and the embodiments.
The invention provides an online collaborative estimation method for the state of charge and the state of health of a ternary lithium battery, which is used for realizing online collaborative estimation of the state of charge and the state of health of the ternary lithium battery based on an FFRLS algorithm and an improved EKF algorithm and specifically comprises the following steps:
step 1: improved Thevenin equivalent circuit model
On the basis of a traditional Thevenin equivalent circuit model, a concentration polarization network (RC network) is added, and the improved Thevenin equivalent circuit model consists of three parts: the battery comprises a voltage source, an ohmic internal resistance and an RC network, wherein the RC network comprises two parts, one part is used for simulating the electrochemical polarization phenomenon of the battery, and the other part is used for simulating the concentration polarization phenomenon of the battery.
Referring to fig. 1, in the modified Thevenin equivalent circuit model, E represents a battery electromotive force, RCAnd REAre all polarization resistances, CCAnd CEThen the corresponding polarization capacitance, i is the actual current flowing through the load, R0Is the ohmic internal resistance, U, of the batteryoIs the battery terminal voltage.
For the first RC network (the one on the left), the terminal voltage of this RC network is U1Time constant of τ1Wherein, τ1Is used to describe the electrochemical polarization process, which proceeds slowly, so τ1And is typically large.
For the second RC-network (the one on the right), the terminal voltage of this RC-network is U2Time constant of τ2Wherein, τ2Is used to describe the charge variation process in the double-layer part during the operation of the cell, which proceeds rapidly, so τ2And is typically small.
According to the established improved Thevenin equivalent circuit model, we can obtain a continuously-changing mathematical expression of the improved Thevenin equivalent circuit model, which is specifically as follows:
Uo(t)＝E(t)-U1(t)-U2(t)-i×R0 (1)
Figure BDA0002106841600000121
Figure BDA0002106841600000122
step 2: establishing a mathematical relation between the SOC of the ternary lithium battery and related influence parameters
Establishing SOC and current i of the ternary lithium battery, coulombic efficiency eta and temperature compensation coefficient KTRated capacity QNAnd the time t are in a mathematical relation as follows:
Figure BDA0002106841600000123
wherein, KT＝[1+0.008×(T0-25)]，T0Is ambient temperature.
And step 3: establishing mathematical relation between SOH and resistance parameter of ternary lithium battery
Establishing SOH of ternary lithium battery and current internal resistance R of battery0Internal resistance R at the end of battery lifeovInternal resistance R of new batteryneThe mathematical relationship between the two is as follows:
Figure BDA0002106841600000124
and 4, step 4: deducing a discretized state space equation of the ternary lithium battery
Deducing the discretized ternary lithium battery according to the formulas (1) to (4)Pool state space equation
Figure BDA0002106841600000125
And
Figure BDA0002106841600000126
the method comprises the following specific steps:
Figure BDA0002106841600000127
Uo(k)＝E[SOC(k)]-U1(k)-U2(k)-i(k)×R0 (7)
where T is a sampling period, and E [ SOC (k) ] is a mapping relationship between the battery SOC and an Open Circuit Voltage (OCV).
Figure BDA0002106841600000131
Figure BDA0002106841600000132
Wherein λ (k) and γ (k) are BMS noise and measurement noise, respectively, and covariance is QrkAnd Rrk，QrkAnd RrkIs usually determined by the state of the actual BMS, usually QrkThe value of (A) is in the range of 0.0001-0.01, RrkThe value of (a) is in the range of 0.5-1.
And 5: plotting OCV-SOC fitting curve chart
The parameters of the experimental ternary lithium battery are shown in table 1.
TABLE 1 ternary lithium cell parameters for experiments
Figure BDA0002106841600000133
A Hybrid pulse power performance Characteristic experiment (HPPC) is carried out on a ternary lithium battery, and the steps are as follows:
(1) charging the ternary lithium battery to full charge, standing for 30min, measuring an open-circuit voltage value, and calibrating the SOC to be 1;
(2) setting a constant current discharge current (8.3A) of the programmable electronic load according to the actually measured capacity (8.3Ah) of the ternary lithium battery, and collecting voltage and current data at the frequency of 10Hz during discharge;
(3) setting discharge time (3min, according to the time calculated when the SOC is reduced by 5%), stopping discharging when the discharge time is up, standing for 5min, and still acquiring voltage and current data at the frequency of 10Hz during the standing period;
(4) and (4) repeating the steps (2) to (3) until the SOC is 0.
Next, screening experimental data, specifically, selecting a data set with SOC decrease gradient of every 5% for recording, and recording the results as shown in table 2.
TABLE 2 ternary lithium battery OCV-SOC corresponding relation table
Figure BDA0002106841600000141
Finally, the OCV is fitted to the SOC to obtain an OCV-SOC curve, see fig. 2.
Step 6: identifying model parameters using FFRLS algorithm
Deriving the transfer function of the improved Thevenin equivalent circuit model according to the established improved Thevenin equivalent circuit model as follows:
Figure BDA0002106841600000142
mapping the ternary lithium battery model from the s plane to the z plane by using a bilinear transformation method, so that
Figure BDA0002106841600000143
Obtaining:
Figure BDA0002106841600000144
in formula (11), ci(i ═ 1,2,3,4,5) is a constant coefficient related to a ternary lithium battery model, and discretization can obtain:
y(k)＝c1y(k-1)+c2y(k-2)+c3I(k)+c4I(k-1)+a5I(k-2) (12)
the FFRLS algorithm is utilized to design a ternary lithium battery model as follows:
Figure BDA0002106841600000151
wherein the content of the first and second substances,
Figure BDA0002106841600000152
inputting and outputting matrix vectors for the ternary lithium battery model;
Figure BDA0002106841600000153
to include constant coefficients associated with a ternary lithium battery model
Figure BDA0002106841600000154
e0(k) Is the sampling error of the BMS.
The process of performing online parameter identification based on the FFRLS algorithm is shown in FIG. 3.
In the algorithm shown in FIG. 3, K (k) is the gain factor; f. offA forgetting factor (the value is 0.96-1); p (k) is an error covariance matrix of the estimated values;
Figure BDA0002106841600000155
the initial value of the constant coefficient is generally any value;
Figure BDA0002106841600000156
the initial value of the error covariance matrix is large, and 10000I is generally taken, wherein I is a 5-dimensional unit matrix. The parameters of the ternary lithium battery model are obtained by the equal coefficients as follows:
Figure BDA0002106841600000157
r, C parameters of the ternary lithium battery model are obtained through the above formula, and real-time dynamic measurement and updating of the parameters of the ternary lithium battery model under any working conditions are realized.
After R, C parameters of the ternary lithium battery model identified by the FFRLS algorithm are substituted into the ternary lithium battery model under a hybrid power pulse capability characteristic test, a curve of response voltage of the ternary lithium battery model and measured voltage of equipment under excitation of the same pulse current is shown in fig. 4, and a relative error curve of the ternary lithium battery model based on the FFRLS algorithm is shown in fig. 5.
As can be seen from the analysis of fig. 4 and 5, the ternary lithium battery model identified based on the FFRLS algorithm has very high accuracy, and the average error is 0.4974%, which is better than the current identification result of the common offline fixed parameter.
And 7: state variable initialization
And (3) substituting R, C parameters of the ternary lithium battery model with the identification finished at the point k in the step (6) into the discretized ternary lithium battery state space equation in the step (4), and setting initial values of state variables as follows:
Figure BDA0002106841600000161
Qrk＝0.001，Rrk＝0.5；
Figure BDA0002106841600000162
Qk＝0.005E(3)，Rk＝1000；
in the above formula, the first and second carbon atoms are,
Figure BDA0002106841600000163
a state vector describing the change of the internal resistance of the battery;
Figure BDA0002106841600000164
an error covariance matrix of the internal resistance of the battery; qrkAnd QkRepresenting the system noise covariance; rrkAnd RkRepresenting the measurement noise covariance;
Figure BDA0002106841600000165
is a state vector describing the change in SOC; pxIs the error covariance matrix for the SOC.
And 8: giving initial value to state space equation coefficient matrix
The ternary lithium battery model state equation system matrix, the input matrix and the measurement matrix are respectively as follows:
Figure BDA0002106841600000166
giving initial values to a ternary lithium battery model state equation system matrix, an input matrix and a measurement matrix, wherein the initial values are respectively as follows:
Figure BDA0002106841600000171
and step 9: establishing a discretization time iteration equation and a state iteration equation
Establishing a discretization time iterative equation according to a Kalman filtering formula, wherein the discretization time iterative equation comprises the following specific steps:
Figure BDA0002106841600000172
Figure BDA0002106841600000173
and calculating an estimation value of the current moment according to the ternary lithium battery model and the parameter value by using the time iteration equation, and calculating an estimation error value.
Establishing a discretization state iterative equation according to a Kalman filtering formula, wherein the discretization state iterative equation specifically comprises the following steps:
Figure BDA0002106841600000174
Figure BDA0002106841600000175
firstly, a state iteration equation calculates Kalman filtering gain KkThe error is solved according to the minimum error principle, and then the open-circuit voltage y at the moment k is calculatedkObtaining the optimal estimation value of the current time by using the gain and the predicted value of the current time according to the difference value of the observed quantity h, and finally calculating an error matrix so as to obtain state variables SOC and R of the current time0The optimal estimated value of (a). Finally, the optimal estimated value of the current moment is combined with the voltage and current value identification of the next sampling point to obtain the Thevenin equivalent circuit model parameter value of the next moment to update the model parameter value of the current moment, then the algorithm can circularly and alternately calculate a time iteration equation and a state iteration equation in sequence, and the time iteration equation and the state iteration equation are circularly and repeatedly circulated, so that the state variables SOC and R of the battery can be obtained0And dynamically updating the optimal estimation value at each sampling point.
FIG. 6 is a flow chart of SOC and SOH online collaborative estimation based on the FFRLS algorithm and the modified EKF algorithm.
Referring to FIG. 6, utilizing SOC and internal resistance R0The constructed state equation and the measurement equation are combined with the improved extended Kalman filtering algorithm, and the last moment R is utilized0In combination with the Kalman filter 1, to calculate the state variable x at the current timekThen the estimated value of the state variable is used as a known quantity, and a Kalman filter 2 is used for estimating the internal resistance R0Finally, the parameter value of the ternary lithium battery model at the current moment is updated by combining the optimal estimated value at the current moment and acquiring the voltage and current value identification of the next sampling point to obtain the parameter value of the ternary lithium battery model at the next moment, and the steps are repeated in such a way, so that the battery state variable SOC and the internal resistance R can be obtained0And (4) dynamically updating the optimal estimation value at each sampling point, and obtaining the SOH predicted value by using the formula (5).
In the modified extended Kalman Filter Algorithm, filteringThe wave filter 1 completes the estimation of the state variable SOC of the battery, and the wave filter 2 completes the internal resistance R of the state variable of the battery0To estimate the optimum. Writing a program according to an FFRLS algorithm and an improved EKF algorithm to perform a Dynamic Stress Test condition experiment (DST) on the ternary lithium battery, wherein the SOC estimation experiment result is shown in FIG. 7, and the relative experiment error is shown in FIG. 8; the results of the SOH estimation experiment are shown in fig. 9, and the experimental relative error is shown in fig. 10.
As can be seen from fig. 7, 8, 9 and 10, the combination of the FFRLS algorithm and the improved EKF algorithm can not only complete the cooperative online prediction of SOC and SOH of the ternary lithium battery, but also achieve very high accuracy of the prediction result, with the average error percentage of SOC estimation being 0.945% and the average error percentage of SOH estimation being 0.471%.
The convergence verification result of the algorithm at the initial error value is shown in fig. 11.
As can be seen from fig. 11, under the condition that the error between the initial value of the algorithm and the actual measurement value is large, the convergence speed of the improved algorithm is obviously increased, and the algorithm can converge to the vicinity of the theoretical value within 100s, which indicates that the robustness of the improved algorithm is strong.
It should be noted that the above-mentioned embodiments do not limit the present invention in any way, and all technical solutions obtained by using equivalent alternatives or equivalent variations fall within the protection scope of the present invention.

Claims (6)

1. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery is characterized by realizing online collaborative estimation for the state of charge and the state of health of the ternary lithium battery based on an FFRLS algorithm and an improved EKF algorithm, and specifically comprises the following steps:
step 1: a concentration polarization network is added on the basis of a traditional Thevenin equivalent circuit model, and a continuously-changed mathematical expression is obtained according to the established improved Thevenin equivalent circuit model, which is concretely as follows:
Uo(t)＝E(t)-U1(t)-U2(t)-i×R0 (1)
Figure RE-FDA0003114232300000011
Figure RE-FDA0003114232300000012
wherein E represents a battery electromotive force, RCAnd REAre all polarization resistances, CCAnd CEThen the corresponding polarization capacitance, i is the actual current flowing through the load, R0Is the ohmic internal resistance, U, of the batteryoIs the terminal voltage of the battery, U1And U2The terminal voltages of the two RC networks are respectively;
step 2: establishing SOC and current i of the ternary lithium battery, coulombic efficiency eta and temperature compensation coefficient KTRated capacity QNAnd the time t are in a mathematical relation as follows:
Figure RE-FDA0003114232300000013
and step 3: establishing SOH of ternary lithium battery and current internal resistance R of battery0Internal resistance R at the end of battery lifeovInternal resistance R of new batteryneThe mathematical relationship between the two is as follows:
Figure RE-FDA0003114232300000014
and 4, step 4: deducing a discretized state space equation of the ternary lithium battery according to the formulas (1) to (4)
Figure RE-FDA0003114232300000015
And
Figure RE-FDA0003114232300000016
the method comprises the following specific steps:
Figure RE-FDA0003114232300000021
Uo(k)＝E[SOC(k)]-U1(k)-U2(k)-i(k)×R0 (7)
Figure RE-FDA0003114232300000022
Figure RE-FDA0003114232300000023
wherein, tau1And τ2Time constants of two RC networks, T is sampling period, E [ SOC (k)]Is a mapping relation between the battery SOC and the open-circuit voltage, and lambda (k) and gamma (k) are respectively system noise and measurement noise;
and 5: drawing an OCV-SOC fitting curve graph;
step 6: deducing a transfer function of the improved Thevenin equivalent circuit model, and mapping the ternary lithium battery model to a z plane from an s plane by using a bilinear transformation method to enable
Figure RE-FDA0003114232300000024
Obtaining:
Figure RE-FDA0003114232300000025
wherein, ci(i ═ 1,2,3,4,5) is a constant coefficient related to a ternary lithium battery model, and discretization can obtain:
y(k)＝c1y(k-1)+c2y(k-2)+c3I(k)+c4I(k-1)+c5I(k-2) (12)
the FFRLS algorithm is utilized to design a ternary lithium battery model as follows:
Figure RE-FDA0003114232300000026
wherein the content of the first and second substances,
Figure RE-FDA0003114232300000027
inputting and outputting matrix vectors for the ternary lithium battery model;
Figure RE-FDA0003114232300000028
to include constant coefficients associated with a ternary lithium battery model
Figure RE-FDA0003114232300000029
e0(k) Is the sampling error of the BMS;
the parameters of the ternary lithium battery model are obtained by the equal coefficients as follows:
Figure RE-FDA0003114232300000031
obtaining R, C parameters of the ternary lithium battery model through the above formula;
and 7: and (3) substituting R, C parameters of the ternary lithium battery model with the identification finished at the point k in the step (6) into the discretized ternary lithium battery state space equation in the step (4), and setting initial values of state variables as follows:
Figure RE-FDA0003114232300000032
Qrk＝0.001，Rrk＝0.5；
Figure RE-FDA0003114232300000033
Qk＝0.005E(3)，Rk＝1000；
in the above formula, the first and second carbon atoms are,
Figure RE-FDA0003114232300000034
to describe the state of change of internal resistance of the batteryAn amount;
Figure RE-FDA0003114232300000035
an error covariance matrix of the internal resistance of the battery; qrkAnd QkRepresenting the system noise covariance; rrkAnd RkRepresenting the measurement noise covariance;
Figure RE-FDA0003114232300000036
is a state vector describing the change in SOC; pxIs the error covariance matrix for the SOC;
and 8: the ternary lithium battery model state equation system matrix, the input matrix and the measurement matrix are respectively as follows:
Figure RE-FDA00031142323000000410
giving initial values to a ternary lithium battery model state equation system matrix, an input matrix and a measurement matrix, wherein the initial values are respectively as follows:
Figure RE-FDA00031142323000000411
and step 9: establishing a discretization time iteration equation and a discretization state iteration equation according to a Kalman filtering formula, wherein the discretization time iteration equation is specifically as follows:
Figure RE-FDA0003114232300000047
Figure RE-FDA0003114232300000048
calculating an estimation value of the current moment according to the ternary lithium battery model and the parameter value by using a time iteration equation, and calculating an estimation error value;
the discretization state iteration equation is concretely as follows:
Figure RE-FDA0003114232300000049
Figure RE-FDA0003114232300000051
firstly, a state iteration equation calculates Kalman filtering gain KkThe error is solved according to the minimum error principle, and then the open-circuit voltage y at the moment k is calculatedkObtaining the optimal estimation value of the current time by using the gain and the predicted value of the current time according to the difference value of the observed quantity h, and finally calculating an error matrix so as to obtain state variables SOC and R of the current time0The optimal estimated value of (a).
2. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery according to claim 1, wherein in step 2, K isT＝[1+0.008×(T0-25)]，T0Is ambient temperature.
3. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery according to claim 1, wherein in step 4, Q isrkAnd RrkIs determined by the state of the actual BMS, QrkThe value of (A) is in the range of 0.0001-0.01, RrkThe value of (a) is in the range of 0.5-1.
4. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery according to claim 1, characterized in that in step 5, before drawing an OCV-SOC fitting curve graph, a hybrid pulse capability characteristic experiment is performed on the ternary lithium battery, and the steps are specifically as follows:
(1) charging the ternary lithium battery to full charge, standing for 30min, measuring an open-circuit voltage value, and calibrating the SOC to be 1;
(2) setting a constant current discharge current of a programmable electronic load according to the measured capacity of the ternary lithium battery, and acquiring voltage and current data at a frequency of 10Hz during discharge;
(3) setting discharge time, stopping discharge when the discharge time is up, standing for 5min, and still acquiring voltage and current data at a frequency of 10Hz during standing;
(4) and (4) repeating the steps (2) to (3) until the SOC is 0.
5. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery according to claim 4, characterized in that after a hybrid pulse capability characteristic experiment is finished, a data set with an SOC decline gradient of every 5% is selected for recording, and then an OCV-SOC curve graph is obtained by fitting an OCV with an SOC.
6. The online collaborative estimation method for the state of charge and the state of health of the ternary lithium battery according to claim 1, characterized in that in step 9, state variables SOC and R at the current time are obtained0And after the optimal estimation value is obtained, the optimal estimation value at the current moment is combined with the voltage and current value identification of the next sampling point to obtain the Thevenin equivalent circuit model parameter value at the next moment, the model parameter value at the current moment is updated, then the algorithm sequentially and circularly calculates a time iteration equation and a state iteration equation in an alternating mode, and the steps are repeated in a reciprocating mode.
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