CN109143097A - It is a kind of meter and temperature and cycle-index lithium ion battery SOC estimation method - Google Patents

Abstract

The invention discloses a method for estimating the SOC of a lithium ion battery considering temperature and cycle times, which includes the steps of: (1) establishing a lithium battery model, including a battery model, a temperature model and a cycle loss model; In the discharge experiment, the parameters of the lithium battery model were identified; (3) the ampere-hour integration method was used as the state equation, and the lithium battery model was used as the observation equation; (4) the EKF algorithm was used to estimate the SOC. The present invention considers more factors affecting the SOC of the battery, that is, the consideration of temperature and cycle times is increased, the complexity of the temperature model is effectively reduced, and the accuracy of the cycle times model is improved; the SOC estimation accuracy is high, and the difficulty of model parameter identification is low. , low computational complexity and good model applicability.

Description

A SOC estimation method for lithium-ion batteries considering temperature and cycle times

technical field

The invention relates to the field of lithium-ion battery SOC prediction, in particular to a lithium-ion battery SOC estimation method, which estimates the SOC by taking into account the influence of the temperature and cycle times of the lithium-ion battery.

Background technique

Compared with other batteries such as nickel-chromium and lead-acid, lithium-ion batteries have higher energy and power densities, higher efficiency and lower self-discharge rates, making them a favored power source for electric vehicles (EVs). A key requirement for EVs is to estimate the state of charge (SOC) of the battery, and direct measurement methods 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 that are not sensitive to measurement errors, but they rely on accurate battery models. Therefore, establishing an accurate battery model is the key to improving the accuracy of SOC estimation.

For Li-ion batteries, battery temperature not only affects open circuit voltage, internal resistance, and usable capacity, but can also cause rapid battery aging and even thermal runaway if operated above specified temperature limits. Electrochemical/physics-based models involve complex or multidimensional differential equations and have been shown to represent thermal effects with greater accuracy. However, they require a lot of in-depth and proprietary parameters (such as electrode porosity, electrolyte thickness, etc.). Some electrical and thermal coupled models for SOC estimation fully consider the heat generation and heat dissipation mechanisms of the battery, but the establishment of the thermal model requires a thermal test chamber and thermocouples, and it is difficult to obtain its internal temperature for cylindrical batteries. Some SOC estimation methods, such as neural network methods (NN), can avoid the use of thermal test chambers and thermocouples. Although these models can reflect thermal effects, the parameter identification process is also affected by complexity, and the available battery data (training). data) is sensitive to the amount of data. Furthermore, these models ignore the influence of accurate battery cycle times (aging) factors in predicting usable battery capacity and internal resistance.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the deficiencies of the prior art, to provide a method for estimating the SOC of a lithium ion battery coupled with a simplified temperature model and an accurate cycle loss, so as to improve the accuracy of SOC estimation.

The present invention is achieved through the following technical solutions:

A method for estimating the SOC of a lithium-ion battery considering temperature and cycle times, comprising the steps of:

(1) Establish a lithium battery model, including battery model, temperature model and cycle loss model;

(2) Do the lithium battery constant current discharge experiment to identify the model parameters of the lithium battery;

(3) The ampere-hour integration method is used as the state equation, and the lithium battery model is used as the observation equation;

(4) Using the EKF algorithm to estimate the SOC.

In the step (1), the lithium battery model is divided into three parts, which are:

1) Battery model:

Among them, V _batt is the battery terminal voltage, E ₀ is the battery constant voltage (V), K is the polarization constant V/(Ah), C is the battery available capacity (Ah), it=∫idt is the actual battery power (Ah) , i ^* is the filtered battery current (A), A _b is the exponential region amplitude (V), B is the exponential region time constant inverse (Ah) ^-1 , D is the polarization voltage slope V/(Ah), and R are respectively is the ohmic internal resistance (Ω) of the battery, and i is the battery current (A).

2) Temperature model:

where T is the battery temperature (K), T _ref is the battery reference temperature (K), T _a is the ambient temperature, is the temperature coefficient of open circuit voltage (V/K), α and β are Arrhenius constants, is the temperature coefficient of battery capacity (Ah/K).

3) Cycle loss model:

R=R _initial +R _cycle (6)

C=C _initial -C _cycle (7)

Among them, R _initial and R _cycle are the internal resistance of the new battery or zero-cycle battery, and the battery cycle internal resistance (Ω), respectively, and C _initial and C _cycle are the capacity of the new battery or zero-cycle battery (equal to the nominal capacity at the nominal temperature) , Battery cycle decay capacity (Ah).

In the battery model of the step (1), the polarization internal resistance and the filter current are established as follows:

1) The polarization internal resistance (R _pol ) during charging and discharging is expressed as follows:

2) The filter current i ^* is introduced to describe the dynamic characteristics of the lithium battery, which is given in the following formula:

Among them, I(s) is the Laplace transform of the battery current (A), and t _d is the battery response time (s), which can be measured experimentally.

In the cycle loss model of step (1), the cycle internal resistance and cycle decay capacity are established as follows:

R _cycle = k _cycle (N) ^1/2 (11)

C _cycle =C _initial ·ζ (12)

Among them, N is the number of battery cycles, k _cycle is the defined coefficient (Ω/cycle ^1/2 ), ζ is the capacity loss coefficient (%), L _calendar (%) is the calendar life loss, and L _cycle (%) The cycle number loss , A is a constant, E _a is the battery activation energy (J/mol), R _g is the gas constant (J/K/mol), T is the battery temperature (K), and z is a power factor.

Described step (2), constant current discharge experiment is:

Based on the constant current discharge experimental curves at two different ambient temperatures, four points are taken on each curve, and the information of each point includes the battery terminal voltage V _i ^j , the used power and battery temperature T _i ^j . where i represents the ith curve and j represents the jth point. If the battery manufacturer provides a battery data sheet, the experimental conditions for one of the curves can be set to the conditions in which the data sheet is located.

Described step (2), the model parameter identification step is:

1) The polarization voltage slope D is calculated by the following formula:

2) The coefficient k _cycle can be calculated by the following formula:

k _cycle = (8×10 ^-6 )T+1.3×10 ^-3 (16)

3) Parameter A, and z vary according to the type of lithium battery, and are determined experimentally.

4) The battery response time t _d is obtained through the performance test, that is, the period from when the current is interrupted during the battery charging/discharging process until the battery voltage reaches a stable state.

5) Parameters According to formula (5) and Solutions have to.

6) Parameters α, β is solved as follows:

Define model error:

in,

make:

f(x)=e ^T (x)*e(x)=0 (18)

Substitute the six data obtained from the discharge experiment to solve the objective function f(x) of the nonlinear least squares problem and the optimal solution x by the Levenberg-Marquardt (L-M) method.

In the step (3), the state equation and the observation equation for SOC estimation are established:

The equation of state is:

x _k+1 = f(x _k , u _k )+w _k (19)

The observation equation is:

y _k+1 =g(x _k ,u _k )+v _k (20)

in,

x _k is the state variable, y _k+1 is the observation variable, w _k and v _k are independent Gaussian white noises, and t _s is the sampling period.

In addition, the system input solution equation is:

u _k = i _k (23)

In the step (5), the steps of estimating the battery SOC with the EKF algorithm are as follows:

1) Define the covariance:

E(w _k w _k ^T )=M _k E(v _k v _k ^T )=H _k

2) Calculate

3) Initialize

4) for k=1,2,3,…

a) Predict:

State variable prediction:

Covariance prediction:

P ⁻ _k+1 =A _k *P _k *A _k ^T +M _k

b) amend;

Forecast error:

Gain:

K _g =P ^- _k+1 *C _k+1 ^T *(C _k+1 *P _k+1 *C ^T _k+1 +H _k ) ^-1

renew:

P _k+1 =(IK _g *C _k+1 )*P ⁻ _k+1 .

The advantages of the present invention are: the present invention considers more factors affecting the SOC of the battery, that is, the temperature and the number of cycles are increased, the complexity of the temperature model is effectively reduced, and the accuracy of the cycle number model is improved; It has the characteristics of low difficulty in model parameter identification, low computational complexity, and good model applicability.

Description of drawings

Figure 1 is a model diagram of a lithium battery.

Figure 2 is a schematic diagram of constant current discharge during parameter identification.

FIG. 3 is a flowchart of SOC estimation.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and examples.

A method for estimating the SOC of a lithium-ion battery considering temperature and cycle times, comprising the steps of:

(1) Establish a lithium battery model, including battery model, temperature model and cycle loss model;

(2) Do the lithium battery constant current discharge experiment to identify the model parameters of the lithium battery;

(3) The ampere-hour integration method is used as the state equation, and the lithium battery model is used as the observation equation;

(4) Using the EKF algorithm to estimate the SOC.

Figure 1 is a lithium-ion battery model diagram, which can be divided into three parts by formula, which are:

1) Battery model:

Among them, V _batt is the battery terminal voltage, E ₀ is the battery constant voltage (V), K is the polarization constant V/(Ah), C is the battery available capacity (Ah), it=∫idt is the actual battery power (Ah) , i ^* is the filtered battery current (A), A _b is the exponential region amplitude (V), B is the exponential region time constant inverse (Ah) ^-1 , D is the polarization voltage slope V/(Ah), and R are respectively is the ohmic internal resistance (Ω) of the battery, and i is the battery current (A).

2) Temperature model:

where T is the battery temperature (K), T _ref is the battery reference temperature (K), T _a is the ambient temperature, is the temperature coefficient of open circuit voltage (V/K), α and β are Arrhenius constants, is the temperature coefficient of battery capacity (Ah/K).

3) Cycle loss model:

R=R _initial +R _cycle (6)

C=C _initial -C _cycle (7)

Among them, R _initial and R _cycle are the internal resistance of the new battery or zero-cycle battery, and the battery cycle internal resistance (Ω), respectively, and C _initial and C _cycle are the capacity of the new battery or zero-cycle battery (equal to the nominal capacity at the nominal temperature) , Battery cycle decay capacity (Ah).

In the battery model of the step (1), the polarization internal resistance and the filter current are established as follows:

1) The polarization internal resistance (R _pol ) during charging and discharging is expressed as follows:

2) The filter current i ^* is introduced to describe the dynamic characteristics of the lithium battery, which is given in the following formula:

Among them, I(s) is the Laplace transform of the battery current (A), and t _d is the battery response time (s), which can be measured experimentally.

In the cycle loss model of step (1), the cycle internal resistance and cycle decay capacity are established as follows:

R _cycle = k _cycle (N) ^1/2 (11)

C _cycle =C _initial ·ζ (12)

Among them, N is the number of battery cycles, k _cycle is the defined coefficient (Ω/cycle ^1/2 ), ζ is the capacity loss coefficient (%), L _calendar (%) is the calendar life loss, and L _cycle (%) The cycle number loss , A is a constant, E _a is the battery activation energy (J/mol), R _g is the gas constant (J/K/mol), T is the battery temperature (K), and z is a power factor.

Described step (2), constant current discharge experiment is:

Based on the constant current discharge experimental curves at two different ambient temperatures, four points are taken on each curve, and the information of each point includes the battery terminal voltage V _i ^j , the used power and battery temperature T _i ^j . where i represents the ith curve and j represents the jth point. If the battery manufacturer provides a battery data sheet, the experimental conditions for one of the curves can be set to the conditions in which the data sheet is located.

Described step (2), the model parameter identification step is:

1) The polarization voltage slope D is calculated by the following formula:

2) The coefficient k _cycle can be calculated by the following formula:

k _cycle = (8×10 ^-6 )T+1.3×10 ^-3 (16)

3) Parameter A, and z vary according to the type of lithium battery, and are determined experimentally.

The next steps 4) 5) 6) are calculated according to Figure 2:

4) The battery response time t _d is obtained through the performance test, that is, the period from when the current is interrupted during the battery charging/discharging process until the battery voltage reaches a stable state.

5) Parameters According to formula (5) and Solutions have to.

6) Parameters α, β is solved as follows:

Define model error:

in,

make:

f(x)=e ^T (x)*e(x)=0 (18)

Substitute the six data obtained from the discharge experiment to solve the objective function f(x) of the nonlinear least squares problem and the optimal solution x by the Levenberg-Marquardt (L-M) method. Here, the OptimizationToolbox toolset in the MATLAB software specifically uses the above solution to solve the function lsqnonlin whose objective function is f(x), which can easily obtain the optimal solution.

In the step (3), the state equation and the observation equation for SOC estimation are established:

The equation of state is:

x _k+1 = f(x _k , u _k )+w _k (19)

The observation equation is:

y _k+1 =g(x _k ,u _k )+v _k (20)

in,

x _k is the state variable, y _k+1 is the observation variable, w _k and v _k are independent Gaussian white noises, and t _s is the sampling period.

In addition, the system input solution equation is:

u _k = i _k (23)

In the step (5), the steps of estimating the battery SOC with the EKF algorithm are as follows: Figure 3 shows the flow chart of this process:

1) Define the covariance:

E(w _k w _k ^T )=M _k E(v _k v _k ^T )=H _k

2) Calculate

3) Initialize

4) for k=1,2,3,…

c) Predict:

State variable prediction:

Covariance prediction:

P ⁻ _k+1 =A _k *P _k *A _k ^T +M _k

d) amendment;

Forecast error:

Gain:

K _g =P ^- _k+1 *C _k+1 ^T *(C _k+1 *P _k+1 *C ^T _k+1 +H _k ) ^-1 update:

P _k+1 =(IK _g *C _k+1 )*P ⁻ _k+1 .

Claims (8)

1. A lithium-ion battery SOC estimation method considering temperature and cycle times, is characterized in that: comprise the following steps: (1) Establish a lithium battery model, including battery model, temperature model and cycle loss model; (2) Do the lithium battery constant current discharge experiment to identify the model parameters of the lithium battery; (3) The ampere-hour integration method is used as the state equation, and the lithium battery model is used as the observation equation; (4) Using the EKF algorithm to estimate the SOC. 2. A lithium-ion battery SOC estimation method considering temperature and cycle times according to claim 1, characterized in that: the three parts of the lithium battery model described in the step (1) are specifically: 1) Battery model: Among them, V _batt is the terminal voltage of the battery, E ₀ is the constant voltage of the battery, K is the polarization constant, C is the available capacity of the battery, it=∫idt is the actual battery power, i ^* is the filtered battery current, and A _b is the index zone amplitude, B is the time constant inverse of the exponential zone, D is the polarization voltage slope, R is the ohmic internal resistance of the battery, i is the battery current; R _pol is the polarization internal resistance. 2) Temperature model: where T is the battery temperature, T _ref is the battery reference temperature, T _a is the ambient temperature, is the temperature coefficient of open circuit voltage, α and β are Arrhenius constants, is the temperature coefficient of battery capacity; 3) Cycle loss model: R=R _initial +R _cycle (6) C=C _initial -C _cycle (7) Among them, R _initial and R _cycle are the internal resistance of the new battery or zero-cycle battery, and the internal resistance of the battery cycle, respectively, and C _initial and C _cycle are the capacity of the new battery or zero-cycle battery and the battery cycle decay capacity, respectively. 3. a kind of lithium ion battery SOC estimation method considering temperature and cycle number according to claim 2, is characterized in that: in described battery model, the polarization internal resistance and filter current of battery model are established as follows: 1) The polarization internal resistance R _pol during charging and discharging is expressed as follows: 2) The filter current i ^* is introduced to describe the dynamic characteristics of the lithium battery, which is given in the following formula: Among them, I(s) is the Laplace transform of the battery current, and t _d is the battery response time, which is measured experimentally. 4. A lithium-ion battery SOC estimation method according to claim 3, characterized in that: in the cycle loss model described in step (1), the cycle internal resistance and cycle decay capacity are as follows Establish: R _cycle = k _cycle (N) ^1/2 (11) C _cycle =C _initial ·ζ (12) Among them, N is the number of battery cycles, k _cycle is the defined coefficient, ζ is the capacity loss coefficient, L _calendar is the calendar life loss, L _cycle cycle number loss, A is a constant, E _a is the battery activation energy, and R _g is the gas constant , T is the battery temperature, and z is the power factor. 5. A lithium-ion battery SOC estimation method considering temperature and cycle times according to claim 4, characterized in that: the constant current discharge experiment described in step (2) is: Based on the constant current discharge experimental curves under two different ambient temperatures, four points are taken on each curve, and the information of each point includes the battery terminal voltage V _i ^j , the used power and the battery temperature T _i ^j , where i represents the ith curve and j represents the jth point. 6. A lithium-ion battery SOC estimation method considering temperature and cycle times according to claim 5, characterized in that: the model parameter identification step described in step (2) is: 1) The polarization voltage slope D is calculated by the following formula: 2) The coefficient k _cycle is calculated by the following formula: k _cycle = (8×10 ⁻⁶ )T+1.3×10 ⁻³ (16); 3) Parameter A, and z are determined experimentally; 4) The battery response time t _d is obtained through the performance test, that is, it starts when the current is interrupted during the charging/discharging process of the battery, and the time until the battery voltage reaches a stable state; 5) Parameters According to formula (5) and Solutions have to; 6) Parameters β is solved as follows; Define model error: in, make: f(x)=e ^T (x)*e(x)=0 (18) Substitute the six data obtained from the discharge experiment, and solve the objective function f(x) of the nonlinear least squares problem and the optimal solution x by the Levenberg-Marquardt (L-M) method. 7. A lithium-ion battery SOC estimation method considering temperature and cycle number according to claim 6, characterized in that: establishing the state equation and observation equation for SOC estimation described in step (3): The equation of state is: x _k+1 = f(x _k , u _k )+w _k (19) The observation equation is: y _k+1 =g(x _k ,u _k )+v _k (20) in, x _k is the state variable, y _k+1 is the observation variable, w _k and v _k are independent Gaussian white noises, and t _s is the sampling period; The system input solution equation is: u _k = i _k (23). 8. a lithium-ion battery SOC estimation method considering temperature and cycle number according to claim 7, is characterized in that: the step of estimating battery SOC with EKF algorithm described in step (4) is as follows: 1) Define the covariance: E(w _k w _k ^T )=M _k E(v _k v _k ^T )=H _k 2) Calculate 3) Initialize 4) for k=1,2,3,… a) Predict: State variable prediction: Covariance prediction: P ⁻ _k+1 =A _k *P _k *A _k ^T +M _k b) amend; Forecast error: Gain: K _g =P ^- _k+1 *C _k+1 ^T *(C _k+1 *P _k+1 *C ^T _k+1 +H _k ) ^-1 renew: P _k+1 =(IK _g *C _k+1 )*P ⁻ _k+1 .