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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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
Invention design lithium ion battery SOC predicts field, especially a kind of lithium ion battery SOC estimation method, this method
The estimation of progress SOC is influenced by the temperature and cycle-index of meter and lithium ion battery.
Background technique
Compared with other (such as nickel chromium triangle and plumbic acid) batteries, lithium ion battery has higher energy and power density, higher
Efficiency and lower self-discharge rate, be electric car (EV) favor power source.The key request of EV is the lotus for estimating battery
Electricity condition (SOC), the direct method of measurement (such as current integration method) is open-loop method, they are easily achieved, but is surveyed to electric current and voltage
Measure error sensitive.SOC estimation method based on model is closed-loop policy, insensitive to measurement error, but they are depended on accurately
Battery model.Therefore, establishing accurately battery model is the key that improve SOC estimation precision.
For lithium ion battery, battery temperature not only will affect open-circuit voltage, internal resistance and active volume, and if advising
Fixed temperature limiting operates above, it is also possible to lead to battery quick aging even thermal runaway.It is related to based on electrochemistry/physics model
And the complicated or multidimensional differential equation, and having been demonstrated can be with higher accuracy representing fuel factor.However, they are needed largely
Go deep into and proprietary parameter (such as electrode porosity, electrolyte thickness etc.).Some electrical and thermal coupling moldings for SOC estimation
Type, has fully considered heat production and the cooling mechanism of battery, but the foundation of its thermal model needs Thermal test room and thermocouple, and for
It is difficult to obtain its internal temperature for cylindrical battery.The estimation method (such as neural network (NN)) of some SOC is avoided that use
Thermal test room and thermocouple, although these models can reflect that fuel factor, parameter identification process are also influenced by complexity, and
And available battery data (training data) is measured sensitive.In addition, these models have ignored accurate circulating battery number (always
Change) influence of the factor for prediction available battery capacity and internal resistance.
Summary of the invention
The object of the invention be exactly in order to solve the deficiencies in the prior art, provide it is a kind of coupled simplify temperature model and
The lithium ion battery SOC estimation method of accurate circulation loss, improves the precision of SOC estimation.
The present invention is achieved by the following technical solutions:
It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method, comprising steps of
(1) lithium battery model, including battery model, temperature model and circulation loss model are established；
(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 step (1), lithium battery model are divided into three parts, are respectively as follows:
1) battery model:
Wherein, VbattFor battery terminal voltage, E0It is polarization constant V/ (Ah) for battery constant pressure (V), K, C is that battery can use appearance
It measures (Ah), it=∫ idt is the practical electricity of battery (Ah), i*For filtered battery current (A), AbFor exponential region amplitude (V), B
It is inverse (Ah) for exponential region time constant-1, D is polarizing voltage slope V/ (Ah), and R is respectively battery ohmic internal resistance (Ω), and i is battery
Electric current (A).
2) temperature model:
Wherein, T is battery temperature (K), TrefFor battery reference temperature (K), TaIt is environment temperature,For open-circuit voltage temperature
It spending coefficient (V/K), α and β are Arrhenius constants,It is battery capacity temperature coefficient (Ah/K).
3) circulation loss model:
R=Rinitial+Rcycle (6)
C=Cinitial-Ccycle (7)
Wherein Rinitial、RcycleRespectively new battery or zero cycle battery internal resistance, circulating battery internal resistance (Ω), Cinitial、
CcycleRespectively new battery or zero cycle battery capacity (being equal to nominal capacity at nominal temperature), circulating battery decaying capacity
(Ah)。
In the battery model of the step (1), polarization resistance and filtered circuit are established as follows:
1) charge and discharge process polarization resistance (Rpol) respectively indicate it is as follows:
2) it describes lithium battery dynamic characteristic and introduces filtered circuit i*, given below:
Wherein, I (s) is the Laplace transform (A) of battery current, tdIt is the battery response time (s), survey can be tested
?.
In the circulation loss model of the step (1), recycles internal resistance and loop attenuation capacity is established as follows:
Rcycle=kcycle(N)1/2 (11)
Ccycle=Cinitial·ζ (12)
Wherein, N is circulating battery number, kcycleIt is coefficient (Ω/cycle of definition1/2), ζ is capacitance loss coefficient
(%), Lcalendar(%) is calendar life loss, LcycleThe loss of (%) cycle-index, A is constant, EaIt can (J/ for cell activation
Mol), RgFor gas constant (J/K/mol), T is battery temperature (K), and z is power factor.
The step (2), constant-current discharge experiment are as follows:
Based on the constant-current discharge empirical curve at a temperature of two varying environments, four points are taken on every curve, each point
Information includes battery terminal voltage Vi j, used electricityWith battery temperature Ti j.Wherein i indicates that i-th curve, j indicate j-th
Point.If battery business men provides battery data table, then wherein the experiment condition of a curve may be set to the item where the tables of data
Part.
The step (2), model and parameters identification step are as follows:
1) polarizing voltage slope D is calculate by the following formula:
2) coefficient kcycleIt can be calculated by following formula:
kcycle=(8 × 10-6)T+1.3×10-3 (16)
3) parameter A,And difference different according to lithium battery type with z, measuring.
4) battery response time tdPassage capacity test obtains, i.e., during battery charging/discharging when interruptive current,
Reach this period of stable state to cell voltage.
5) parameterCan according to formula (5) andIt solves.
6) parameterα、β is solved as follows:
Definition Model error:
Wherein,
It enables:
F (x)=eT(x) * e (x)=0 (18)
6 data for substituting into discharge test acquisition can be non-linear by the solution of Levenberg-Marquardt (L-M) method
The objective function f (x) and optimal solution x of Least Square Solution.
The step (3) establishes the state equation and observational equation of SOC estimation:
State equation are as follows:
xk+1=f (xk,uk)+wk (19)
Observational equation are as follows:
yk+1=g (xk,uk)+vk (20)
Wherein,
xkFor state variable, yk+1For observational variable, wk、vkFor mutually independent white Gaussian noise, tsFor the sampling period.
In addition, system input solves equation are as follows:
uk=ik (23)
The step (5), with EKF algorithm estimation battery SOC, steps are as follows:
1) covariance is defined:
E(wkwk T)=Mk E(vkvk T)=Hk
2) it calculates
3) it initializes
4) for k=1,2,3 ...
A) it predicts:
State variable prediction:
Covariance prediction:
P- k+1=Ak*Pk*Ak T+Mk
B) it corrects；
Predict error:
Gain:
Kg=P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1
It updates:
Pk+1=(I-Kg*Ck+1)*P- k+1。
The invention has the advantages that the factor for the influence battery SOC that the present invention considers is more, that is, increases and consider temperature and circulation
Number, while the complexity of temperature model is effectively reduced, the precision of cycle-index model gets a promotion；Essence with SOC estimation
The features such as complexity that degree is high, the difficulty of model and parameters identification is low, calculates is low, model applicability is good.
Detailed description of the invention
Fig. 1 is lithium battery illustraton of model.
Fig. 2 is constant-current discharge profile when parameter identifies.
Fig. 3 is that SOC estimates flow chart.
Specific embodiment
The present invention will be further described with example with reference to the accompanying drawing.
It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method, comprising steps of
(1) lithium battery model, including battery model, temperature model and circulation loss model are established；
(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 position Fig. 1 Li-ion battery model figure can be divided into three parts with formula expression, be respectively as follows:
1) battery model:
Wherein, VbattFor battery terminal voltage, E0It is polarization constant V/ (Ah) for battery constant pressure (V), K, C is that battery can use appearance
It measures (Ah), it=∫ idt is the practical electricity of battery (Ah), i*For filtered battery current (A), AbFor exponential region amplitude (V), B
It is inverse (Ah) for exponential region time constant-1, D is polarizing voltage slope V/ (Ah), and R is respectively battery ohmic internal resistance (Ω), and i is battery
Electric current (A).
2) temperature model:
Wherein, T is battery temperature (K), TrefFor battery reference temperature (K), TaIt is environment temperature,For open-circuit voltage temperature
It spending coefficient (V/K), α and β are Arrhenius constants,It is battery capacity temperature coefficient (Ah/K).
3) circulation loss model:
R=Rinitial+Rcycle (6)
C=Cinitial-Ccycle (7)
Wherein Rinitial、RcycleRespectively new battery or zero cycle battery internal resistance, circulating battery internal resistance (Ω), Cinitial、
CcycleRespectively new battery or zero cycle battery capacity (being equal to nominal capacity at nominal temperature), circulating battery decaying capacity
(Ah)。
In the battery model of the step (1), polarization resistance and filtered circuit are established as follows:
1) charge and discharge process polarization resistance (Rpol) respectively indicate it is as follows:
2) it describes lithium battery dynamic characteristic and introduces filtered circuit i*, given below:
Wherein, I (s) is the Laplace transform (A) of battery current, tdIt is the battery response time (s), survey can be tested
?.
In the circulation loss model of the step (1), recycles internal resistance and loop attenuation capacity is established as follows:
Rcycle=kcycle(N)1/2 (11)
Ccycle=Cinitial·ζ (12)
Wherein, N is circulating battery number, kcycleIt is coefficient (Ω/cycle of definition1/2), ζ is capacitance loss coefficient
(%), Lcalendar(%) is calendar life loss, LcycleThe loss of (%) cycle-index, A is constant, EaIt can (J/ for cell activation
Mol), RgFor gas constant (J/K/mol), T is battery temperature (K), and z is power factor.
The step (2), constant-current discharge experiment are as follows:
Based on the constant-current discharge empirical curve at a temperature of two varying environments, four points are taken on every curve, each point
Information includes battery terminal voltage Vi j, used electricityWith battery temperature Ti j.Wherein i indicates that i-th curve, j indicate j-th
Point.If battery business men provides battery data table, then wherein the experiment condition of a curve may be set to the item where the tables of data
Part.
The step (2), model and parameters identification step are as follows:
1) polarizing voltage slope D is calculate by the following formula:
2) coefficient kcycleIt can be calculated by following formula:
kcycle=(8 × 10-6)T+1.3×10-3 (16)
3) parameter A,And difference different according to lithium battery type with z, measuring.
Following step 4) 5) 6) cooperate Fig. 2 to calculate:
4) battery response time tdPassage capacity test obtains, i.e., during battery charging/discharging when interruptive current,
Reach this period of stable state to cell voltage.
5) parameterCan according to formula (5) andIt solves.
6) parameterα、β is solved as follows:
Definition Model error:
Wherein,
It enables:
F (x)=eT(x) * e (x)=0 (18)
6 data for substituting into discharge test acquisition can be non-linear by the solution of Levenberg-Marquardt (L-M) method
The objective function f (x) and optimal solution x of Least Square Solution.Here, the Optimization in MATLAB software
Toolbox tool set, which has, specially solves the function lsqnonlin that objective function is f (x) with above-mentioned solution, very convenient can obtain
Optimal solution out.
The step (3) establishes the state equation and observational equation of SOC estimation:
State equation are as follows:
xk+1=f (xk,uk)+wk (19)
Observational equation are as follows:
yk+1=g (xk,uk)+vk (20)
Wherein,
xkFor state variable, yk+1For observational variable, wk、vkFor mutually independent white Gaussian noise, tsFor the sampling period.
In addition, system input solves equation are as follows:
uk=ik (23)
The step (5), with EKF algorithm estimation battery SOC, steps are as follows: Fig. 3 illustrates this process flow diagram flow chart:
1) covariance is defined:
E(wkwk T)=Mk E(vkvk T)=Hk
2) it calculates
3) it initializes
4) for k=1,2,3 ...
C) it predicts:
State variable prediction:
Covariance prediction:
P- k+1=Ak*Pk*Ak T+Mk
D) it corrects；
Predict error:
Gain:
Kg=P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1It updates:
Pk+1=(I-Kg*Ck+1)*P- k+1 。
Claims (8)
1. the lithium ion battery SOC estimation method of a kind of meter and temperature and cycle-index, it is characterised in that: the following steps are included:
(1) lithium battery model, including battery model, temperature model and circulation loss model are established；
(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.
2. the lithium ion battery SOC estimation method of a kind of meter according to claim 1 and temperature and cycle-index, feature
It is: three parts of lithium battery model described in step (1), specifically:
1) battery model:
Wherein, VbattFor battery terminal voltage, E0For battery constant pressure, K is polarization constant, and C is battery active volume, and it=∫ idt is
The practical electricity of battery, i*For filtered battery current, AbFor exponential region amplitude, B is that exponential region time constant is inverse, and D is polarization electricity
Slope is pressed, R is respectively battery ohmic internal resistance, and i is battery current；RpolFor polarization resistance.
2) temperature model:
Wherein, T is battery temperature, TrefFor battery reference temperature, TaIt is environment temperature,For open-circuit voltage temperature coefficient, α and β
It is Arrhenius constant,It is battery capacity temperature coefficient；
3) circulation loss model:
R=Rinitial+Rcycle (6)
C=Cinitial-Ccycle (7)
Wherein Rinitial、RcycleRespectively new battery or zero cycle battery internal resistance, circulating battery internal resistance, Cinitial、CcycleRespectively
For new battery or zero cycle battery capacity, circulating battery decaying capacity.
3. the lithium ion battery SOC estimation method of a kind of meter according to claim 2 and temperature and cycle-index, feature
Be: in the battery model, the polarization resistance and filtered circuit of battery model are established as follows:
1) charge and discharge process polarization resistance RpolIt respectively indicates as follows:
2) it describes lithium battery dynamic characteristic and introduces filtered circuit i*, given below:
Wherein, I (s) is the Laplace transform of battery current, tdIt is the battery response time, is measured by experiment.
4. the lithium ion battery SOC estimation method of a kind of meter according to claim 3 and temperature and cycle-index, feature
It is: in circulation loss model described in step (1), recycles internal resistance and loop attenuation capacity is established as follows:
Rcycle=kcycle(N)1/2 (11)
Ccycle=Cinitial·ζ (12)
Wherein, N is circulating battery number, kcycleIt is the coefficient of definition, ζ is capacitance loss coefficient, LcalendarFor calendar life damage
It loses, LcycleCycle-index loss, A is constant, EaFor cell activation energy, RgFor gas constant, T is battery temperature, z be power because
Son.
5. the lithium ion battery SOC estimation method of a kind of meter according to claim 4 and temperature and cycle-index, feature
It is: the experiment of constant-current discharge described in step (2) are as follows:
Based on the constant-current discharge empirical curve at a temperature of two varying environments, four points, the information of each point are taken on every curve
Including battery terminal voltage Vi j, used electricityWith battery temperature Ti j, wherein i indicates that i-th curve, j indicate at j-th point.
6. the lithium ion battery SOC estimation method of a kind of meter according to claim 5 and temperature and cycle-index, feature
It is: model and parameters identification step described in step (2) are as follows:
1) polarizing voltage slope D is calculate by the following formula:
2) coefficient kcycleIt is calculated by following formula:
kcycle=(8 × 10-6)T+1.3×10-3(16)；
3) parameter A,With z by measuring；
4) battery response time tdPassage capacity test obtains, i.e., during battery charging/discharging when interruptive current, to electricity
Cell voltage reaches this period of stable state；
5) parameterAccording to formula (5) andIt solves；
6) parameterβ is solved as follows；
Definition Model error:
Wherein,
It enables:
F (x)=eT(x) * e (x)=0 (18)
6 data that discharge test obtains are substituted into, solve non-linear minimum two by Levenberg-Marquardt (L-M) method
The objective function f (x) and optimal solution x of multiplication problem.
7. the lithium ion battery SOC estimation method of a kind of meter according to claim 6 and temperature and cycle-index, feature
It is: establishes the state equation and observational equation of SOC estimation described in step (3):
State equation are as follows:
xk+1=f (xk,uk)+wk (19)
Observational equation are as follows:
yk+1=g (xk,uk)+vk (20)
Wherein,
xkFor state variable, yk+1For observational variable, wk、vkFor mutually independent white Gaussian noise, tsFor the sampling period；
System input solves equation are as follows:
uk=ik (23)。
8. the lithium ion battery SOC estimation method of a kind of meter according to claim 7 and temperature and cycle-index, feature
Be: with EKF algorithm estimation battery SOC, steps are as follows described in step (4):
1) covariance is defined:
E(wkwk T)=Mk E(vkvk T)=Hk
2) it calculates
3) it initializes
4) for k=1,2,3 ...
A) it predicts:
State variable prediction:
Covariance prediction:
P- k+1=Ak*Pk*Ak T+Mk
B) it corrects；
Predict error:
Gain:
Kg=P- k+1*Ck+1 T*(Ck+1*Pk+1*CT k+1+Hk)-1
It updates:
Pk+1=(I-Kg*Ck+1)*P- k+1。
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| CN111581904A (en) * | 2020-04-17 | 2020-08-25 | 西安理工大学 | Lithium battery SOC and SOH collaborative estimation method considering influence of cycle number |
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| CN116298991A (en) * | 2023-05-25 | 2023-06-23 | 湖南锂汇通新能源科技有限责任公司 | Method and system for rapidly detecting and evaluating capacity of retired battery |
| CN116298991B (en) * | 2023-05-25 | 2023-09-12 | 湖南锂汇通新能源科技有限责任公司 | Method and system for rapidly detecting and evaluating capacity of retired battery |
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