CN109143097A - It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method - Google Patents
It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 43
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 title claims abstract description 12
- 229910001416 lithium ion Inorganic materials 0.000 title claims abstract description 12
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 claims abstract description 24
- 229910052744 lithium Inorganic materials 0.000 claims abstract description 24
- 238000002474 experimental method Methods 0.000 claims abstract description 14
- 230000010354 integration Effects 0.000 claims abstract description 5
- 125000004122 cyclic group Chemical group 0.000 claims description 16
- 230000010287 polarization Effects 0.000 claims description 14
- 238000007599 discharging Methods 0.000 claims description 4
- 230000004913 activation Effects 0.000 claims description 3
- 230000036755 cellular response Effects 0.000 claims description 3
- 230000007613 environmental effect Effects 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
- 238000011056 performance test Methods 0.000 claims description 3
- 230000008569 process Effects 0.000 claims description 3
- 230000004044 response Effects 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
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- 238000005259 measurement Methods 0.000 description 3
- 230000032683 aging Effects 0.000 description 2
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- 238000010586 diagram Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 229910018487 Ni—Cr Inorganic materials 0.000 description 1
- 239000002253 acid Substances 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- VNNRSPGTAMTISX-UHFFFAOYSA-N chromium nickel Chemical compound [Cr].[Ni] VNNRSPGTAMTISX-UHFFFAOYSA-N 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
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Abstract
The invention discloses a kind of meter and the lithium ion battery SOC estimation methods of temperature and cycle-index, comprising steps of (1) establishes lithium battery model, including battery model, temperature model and circulation loss model；(2) experiment of lithium battery constant-current discharge is done, lithium battery model parameter is identified；(3) using current integration method as state equation, lithium battery model as observational equation；(4) SOC estimation is carried out using EKF algorithm.The factor for the influence battery SOC that the present invention considers is more, that is, increases and consider temperature and cycle-index, while the complexity of temperature model is effectively reduced, the precision of cycle-index model gets a promotion；Have the characteristics that the precision of SOC estimation is high, the difficulty of model and parameters identification is low, the complexity of calculating is low, model applicability is good.
Description
Technical Field
The invention relates to the field of lithium ion battery SOC prediction, in particular to a lithium ion battery SOC estimation method.
Background
Lithium ion batteries, which have higher energy and power densities, higher efficiencies and lower self-discharge rates than other (e.g., nickel-chromium and lead-acid) batteries, are favored as power sources for Electric Vehicles (EVs). A key requirement of EVs is to estimate the state of charge (SOC) of the battery, and direct measurements (such as ampere-hour integration) are open-loop methods that are easy to implement, but sensitive to current and voltage measurement errors. Model-based SOC estimation methods are closed-loop methods, insensitive to measurement errors, but they rely on an accurate battery model. Therefore, establishing an accurate battery model is the key to improving the accuracy of SOC estimation.
For lithium ion batteries, battery temperature not only affects open circuit voltage, internal resistance and available capacity, but can also lead to rapid aging of the battery and even thermal runaway if operated above specified temperature limits. Electrochemical/physical based models involve complex or multidimensional differential equations and have been shown to be able to represent thermal effects with greater accuracy. However, they require a number of in-depth and proprietary parameters (e.g., electrode porosity, electrolyte thickness, etc.). Some electrical and thermal coupling models for SOC estimation fully take into account the heat generation and dissipation mechanisms of the battery, but the establishment of their thermal models requires a thermal test chamber and a thermocouple, and it is difficult for a cylindrical battery to obtain its internal temperature. Some methods of estimating SOC, such as Neural Network (NN), avoid the use of thermal test chambers and thermocouples, and although these models reflect thermal effects, the parameter identification process is also subject to complexity and sensitive to the amount of available battery data (training data). In addition, these models neglect the effect of accurate battery cycle number (aging) factors on predicting available battery capacity and internal resistance.
Disclosure of Invention
The invention aims to solve the defects of the prior art, provides the lithium ion battery SOC estimation method which couples a simplified temperature model and accurate cycle loss, and improves the SOC estimation precision.
The invention is realized by the following technical scheme:
a lithium ion battery SOC estimation method considering temperature and cycle number comprises the following steps:
(1) establishing a lithium battery model, which comprises a battery model, a temperature model and a cyclic loss model;
(2) performing a lithium battery constant current discharge experiment, and identifying lithium battery model parameters;
(3) an ampere-hour integration method is used as a state equation, and a lithium battery model is used as an observation equation;
(4) SOC estimation was performed using EKF algorithm.
In the step (1), the lithium battery model is divided into three parts, which are respectively:
1) a battery model:
wherein, VbattIs the terminal voltage of the battery, E0Is the constant voltage (V) of the battery, K is the polarization constant V/(Ah), C is the available capacity (Ah) of the battery, it ═ integral [ idt ] is the actual electric quantity (Ah) of the battery, i ═ integral [ idt ] is the actual electric quantity (Ah) of the battery*Is the filtered battery current (A), AbIs the amplitude (V) of the exponential region, B is the inverse time constant (Ah) of the exponential region-1D is polarization voltage slope V/(Ah), R is the ohmic internal resistance (omega) of the battery, and i is the current (A) of the battery.
2) Temperature model:
wherein T is the battery temperature (K), TrefIs a battery reference temperature (K), TaIs the temperature of the environment and the temperature of the environment,α and β are Arrhenius constants for open circuit voltage temperature coefficient (V/K),is the battery capacity temperature coefficient (Ah/K).
3) Cyclic loss model:
R＝Rinitial+Rcycle(6)
C＝Cinitial-Ccycle(7)
wherein R isinitial、RcycleRespectively the internal resistance of a new battery or a zero-cycle battery, the internal resistance (omega) of the battery cycle, Cinitial、CcycleFresh or zero cycle battery capacity (equal to nominal capacity at nominal temperature), battery cycle fade capacity (Ah), respectively.
In the battery model in the step (1), the polarization internal resistance and the filtering current are established as follows:
1) polarized in the charging and discharging processResistor (R)pol) Respectively, as follows:
2) introduction of a filter current i for describing the dynamic characteristics of a lithium battery*Which is given by the formula:
wherein I(s) is the Laplace transform (A), t of the battery currentdIs the cell response time(s) and can be measured experimentally.
In the cyclic loss model in the step (1), the cyclic internal resistance and the cyclic attenuation capacity are established as follows:
Rcycle＝kcycle(N)1/2(11)
Ccycle＝Cinitial·ζ (12)
wherein N is the cycle number of the battery, kcycleIs a defined coefficient (Ω/cycle)1/2) ζ is the capacity loss coefficient (%), Lcalendar(%) is the calendar life loss, Lcycle(%) cycle number loss, A is constant, EaIs the activation energy (J/mol) of the battery, RgIs a gas constant (J)K/mol), T is the cell temperature (K) and z is a power factor.
In the step (2), the constant current discharge experiment is as follows:
based on two constant-current discharge experiment curves at different environmental temperatures, four points are taken on each curve, and the information of each point comprises the voltage V at the end of the batteryi jUsed electric quantityAnd battery temperature Ti j. Where i represents the ith curve and j represents the jth point. If the battery manufacturer provides the battery data table, the experimental conditions of one of the curves can be set as the conditions of the data table.
In the step (2), the model parameter identification step is as follows:
1) the polarization voltage slope D is calculated by:
2) coefficient kcycleCan be calculated from the following formula:
kcycle＝(8×10-6)T+1.3×10-3(16)
3) the parameters A,And z is different according to the types of lithium batteries and is determined experimentally.
4) Battery response time tdIt is found from the performance test that the period of time from when the current is interrupted during the charge/discharge of the battery to when the battery voltage reaches a steady state.
5) Parameter(s)Can be according to formula (5) andand (5) obtaining the compound through solution.
6) Parameter(s)α、β is solved as follows:
defining model errors:
wherein,
order:
f(x)＝eT(x)*e(x)＝0 (18)
the 6 data obtained by substituting the discharge experiment can be used for solving the objective function f (x) and the optimal solution x of the nonlinear least square method problem by a Levenberg-Marquardt (L-M) method.
In the step (3), a state equation and an observation equation of SOC estimation are established:
the state equation is:
xk+1＝f(xk,uk)+wk(19)
the observation equation is:
yk+1＝g(xk,uk)+vk(20)
wherein,
xkis a state variable, yk+1For observing variables, wk、vkIs independent of white Gaussian noise, tsIs the sampling period.
In addition, the system inputs solve the equation as:
uk＝ik(23)
in the step (5), the step of estimating the SOC of the battery by using the EKF algorithm comprises the following steps:
1) defining the covariance:
E(wkwk T)＝MkE(vkvk T)＝Hk
2) computing
3) Initialization
4)for k＝1,2,3,…
a) And (3) prediction:
predicting the state variable:
and (3) covariance prediction:
P- k+1＝Ak*Pk*Ak T+Mk
b) correcting;
prediction error:
gain:
Kg＝P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1
updating:
Pk+1＝(I-Kg*Ck+1)*P- k+1。
the invention has the advantages that more factors influencing the SOC of the battery are considered, namely, the temperature and the cycle number are considered, meanwhile, the complexity of the temperature model is effectively reduced, and the precision of the cycle number model is improved; the method has the characteristics of high SOC estimation precision, low difficulty in model parameter identification, low calculation complexity, good model applicability and the like.
Drawings
FIG. 1 is a schematic diagram of a lithium battery model.
Fig. 2 is a schematic curve of constant current discharge during parameter identification.
Fig. 3 is a flow chart of SOC estimation.
Detailed Description
The invention is further illustrated with reference to the figures and examples.
A lithium ion battery SOC estimation method considering temperature and cycle number comprises the following steps:
(1) establishing a lithium battery model, which comprises a battery model, a temperature model and a cyclic loss model;
(2) performing a lithium battery constant current discharge experiment, and identifying lithium battery model parameters;
(3) an ampere-hour integration method is used as a state equation, and a lithium battery model is used as an observation equation;
(4) SOC estimation was performed using EKF algorithm.
The lithium ion battery model diagram of fig. 1 can be divided into three parts by formula expression, which are respectively:
1) a battery model:
wherein, VbattIs the terminal voltage of the battery, E0Is the constant voltage (V) of the battery, K is the polarization constant V/(Ah), C is the available capacity (Ah) of the battery, it ═ integral [ idt ] is the actual electric quantity (Ah) of the battery, i ═ integral [ idt ] is the actual electric quantity (Ah) of the battery*Is the filtered battery current (A), AbIs the amplitude (V) of the exponential region, B is the inverse time constant (Ah) of the exponential region-1D is polarization voltage slope V/(Ah), R is ohmic internal resistance (omega) of the battery, and i is battery electricityStream (A).
2) Temperature model:
wherein T is the battery temperature (K), TrefIs a battery reference temperature (K), TaIs the temperature of the environment and the temperature of the environment,α and β are Arrhenius constants for open circuit voltage temperature coefficient (V/K),is the battery capacity temperature coefficient (Ah/K).
3) Cyclic loss model:
R＝Rinitial+Rcycle(6)
C＝Cinitial-Ccycle(7)
wherein R isinitial、RcycleRespectively the internal resistance of a new battery or a zero-cycle battery, the internal resistance (omega) of the battery cycle, Cinitial、CcycleFresh or zero cycle battery capacity (equal to nominal capacity at nominal temperature), battery cycle fade capacity (Ah), respectively.
In the battery model in the step (1), the polarization internal resistance and the filtering current are established as follows:
1) polarization internal resistance (R) in charging and discharging processpol) Respectively, as follows:
2) introduction of a filter current i for describing the dynamic characteristics of a lithium battery*Which is given by the formula:
wherein I(s) is the Laplace transform (A), t of the battery currentdIs the cell response time(s) and can be measured experimentally.
In the cyclic loss model in the step (1), the cyclic internal resistance and the cyclic attenuation capacity are established as follows:
Rcycle＝kcycle(N)1/2(11)
Ccycle＝Cinitial·ζ (12)
wherein N is the cycle number of the battery, kcycleIs a defined coefficient (Ω/cycle)1/2) ζ is the capacity loss coefficient (%), Lcalendar(%) is the calendar life loss,Lcycle(%) cycle number loss, A is constant, EaIs the activation energy (J/mol) of the battery, RgIs the gas constant (J/K/mol), T is the cell temperature (K), and z is a power factor.
In the step (2), the constant current discharge experiment is as follows:
based on two constant-current discharge experiment curves at different environmental temperatures, four points are taken on each curve, and the information of each point comprises the voltage V at the end of the batteryi jUsed electric quantityAnd battery temperature Ti j. Where i represents the ith curve and j represents the jth point. If the battery manufacturer provides the battery data table, the experimental conditions of one of the curves can be set as the conditions of the data table.
In the step (2), the model parameter identification step is as follows:
1) the polarization voltage slope D is calculated by:
2) coefficient kcycleCan be calculated from the following formula:
kcycle＝(8×10-6)T+1.3×10-3(16)
3) the parameters A,And z is different according to the types of lithium batteries and is determined experimentally.
The next step 4)5)6) is calculated in conjunction with fig. 2:
4) battery response time tdIt is found by performance test that the period of time from when the current is interrupted during the charge/discharge of the battery to when the battery voltage reaches a steady state。
5) Parameter(s)Can be according to formula (5) andand (5) obtaining the compound through solution.
6) Parameter(s)α、β is solved as follows:
defining model errors:
wherein,
order:
f(x)＝eT(x)*e(x)＝0 (18)
the 6 data obtained by substituting the discharge experiment can be used for solving the objective function f (x) and the optimal solution x of the nonlinear least square method problem by a Levenberg-Marquardt (L-M) method. Here, the OptimizationToolbox toolset in MATLAB software has a function lsqnolin that is specially used for solving the objective function f (x) by the solution, and an optimal solution can be obtained conveniently.
In the step (3), a state equation and an observation equation of SOC estimation are established:
the state equation is:
xk+1＝f(xk,uk)+wk(19)
the observation equation is:
yk+1＝g(xk,uk)+vk(20)
wherein,
xkis a state variable, yk+1For observing variables, wk、vkIs independent of white Gaussian noise, tsIs the sampling period.
In addition, the system inputs solve the equation as:
uk＝ik(23)
in the step (5), the step of estimating the SOC of the battery by using the EKF algorithm comprises the following steps: fig. 3 shows a flow chart of this process:
1) defining the covariance:
E(wkwk T)＝MkE(vkvk T)＝Hk
2) computing
3) Initialization
4)for k＝1,2,3,…
c) And (3) prediction:
predicting the state variable:
and (3) covariance prediction:
P- k+1＝Ak*Pk*Ak T+Mk
d) correcting;
prediction error:
gain:
Kg＝P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1updating:
Pk+1＝(I-Kg*Ck+1)*P- k+1。
Claims (8)
1. A lithium ion battery SOC estimation method considering temperature and cycle number is characterized in that: the method comprises the following steps:
(1) establishing a lithium battery model, which comprises a battery model, a temperature model and a cyclic loss model;
(2) performing a lithium battery constant current discharge experiment, and identifying lithium battery model parameters;
(3) an ampere-hour integration method is used as a state equation, and a lithium battery model is used as an observation equation;
(4) SOC estimation was performed using EKF algorithm.
2. The method of claim 1, wherein the method comprises the steps of: the three parts of the lithium battery model in the step (1) are specifically as follows:
1) a battery model:
wherein, VbattIs the terminal voltage of the battery, E0Is the constant voltage of the battery, K is the polarization constant, C is the available capacity of the battery, it ═ idt is the actual electric quantity of the battery, i ═ idt*For the filtered battery current, AbThe amplitude of the exponential region, B, D, R, i and I are respectively the ohmic internal resistance of the battery; rpolIs the polarization internal resistance.
2) Temperature model:
where T is the battery temperature, TrefFor the cell reference temperature, TaIs the temperature of the environment and the temperature of the environment,α and β are Arrhenius constants for open circuit voltage temperature coefficient,is the battery capacity temperature coefficient;
3) cyclic loss model:
R＝Rinitial+Rcycle(6)
C＝Cinitial-Ccycle(7)
wherein R isinitial、RcycleRespectively the internal resistance of a new battery or a zero-cycle battery, the internal resistance of a battery cycle, Cinitial、CcycleThe capacity of the new battery or the zero-cycle battery and the cyclic attenuation capacity of the battery are respectively.
3. The method of claim 2, wherein the method comprises the steps of: in the battery model, the polarization internal resistance and the filtering current of the battery model are established as follows:
1) polarization internal resistance R in charging and discharging processpolRespectively, as follows:
2) introduction of a filter current i for describing the dynamic characteristics of a lithium battery*Which is given by the formula:
wherein I(s) is the Laplace transform of the battery current, tdIs the cell response time, measured by experiment.
4. The method of claim 3, wherein the method comprises the steps of: in the cyclic loss model in the step (1), the cyclic internal resistance and the cyclic attenuation capacity are established as follows:
Rcycle＝kcycle(N)1/2(11)
Ccycle＝Cinitial·ζ (12)
wherein N is the cycle number of the battery, kcycleIs a defined coefficient, ζ is the capacity loss coefficient, LcalendarFor calendar life loss, LcycleLoss of cycle number, A is constant, EaFor activation energy of battery, RgIs the gas constant, T is the cell temperature, and z is a power factor.
5. The method of claim 4, wherein the method comprises the steps of: the constant current discharge experiment in the step (2) is as follows:
based on two constant-current discharge experiment curves at different environmental temperatures, four points are taken on each curve, and the information of each point comprises the voltage V at the end of the batteryi jUsed electric quantityAnd battery temperature Ti jWhere i represents the ith curve and j represents the jth point.
6. The method of claim 5, wherein the method comprises the steps of: the model parameter identification step in the step (2) is as follows:
1) the polarization voltage slope D is calculated by:
2) coefficient kcycleCalculated from the following formula:
kcycle＝(8×10-6)T+1.3×10-3(16)；
3) the parameters A,And z is determined experimentally;
4) battery response time tdThe performance test shows that the time from the time when the current is interrupted in the battery charging/discharging process to the time when the battery voltage reaches a stable state;
5) parameter(s)According to formula (5) andobtaining the solution;
6) parameter(s)β is solved as follows;
defining model errors:
wherein,
order:
f(x)＝eT(x)*e(x)＝0 (18)
and substituting 6 data obtained in the discharge experiment, and solving an objective function f (x) of the nonlinear least square method problem and an optimal solution x by a Levenberg-Marquardt (L-M) method.
7. The method of claim 6, wherein the method comprises the steps of: establishing a state equation and an observation equation of SOC estimation in the step (3):
the state equation is:
xk+1＝f(xk,uk)+wk(19)
the observation equation is:
yk+1＝g(xk,uk)+vk(20)
wherein,
xkis a state variable, yk+1For observing variables, wk、vkIs independent of white Gaussian noise, tsIs a sampling period;
the system inputs solving equations as:
uk＝ik(23)。
8. the method of claim 7, wherein the method comprises the steps of: the step of estimating the SOC of the battery by using the EKF algorithm in the step (4) is as follows:
1) defining the covariance:
E(wkwk T)＝MkE(vkvk T)＝Hk
2) computing
3) Initialization
4)for k＝1,2,3,…
a) And (3) prediction:
predicting the state variable:
and (3) covariance prediction:
P- k+1＝Ak*Pk*Ak T+Mk
b) correcting;
prediction error:
gain:
Kg＝P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1
updating:
Pk+1＝(I-Kg*Ck+1)*P- k+1。
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