CN115877232A - Lithium ion battery internal temperature estimation method based on Kalman filtering - Google Patents
Lithium ion battery internal temperature estimation method based on Kalman filtering Download PDFInfo
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- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 title claims abstract description 87
- 229910001416 lithium ion Inorganic materials 0.000 title claims abstract description 87
- 238000000034 method Methods 0.000 title claims abstract description 41
- 238000001914 filtration Methods 0.000 title claims abstract description 22
- 238000012360 testing method Methods 0.000 claims abstract description 40
- 230000008878 coupling Effects 0.000 claims abstract description 21
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- 238000005485 electric heating Methods 0.000 claims description 4
- 230000020169 heat generation Effects 0.000 claims description 4
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- TYJJADVDDVDEDZ-UHFFFAOYSA-M potassium hydrogencarbonate Chemical compound [K+].OC([O-])=O TYJJADVDDVDEDZ-UHFFFAOYSA-M 0.000 claims description 2
- 238000012546 transfer Methods 0.000 claims description 2
- 238000004364 calculation method Methods 0.000 abstract description 3
- 230000036541 health Effects 0.000 abstract description 3
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical group [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention relates to a lithium ion battery internal temperature estimation method based on Kalman filtering, which comprises the following steps of establishing an electrothermal coupling model of a lithium ion battery; step two, testing the working condition of the battery to obtain battery test data: current, voltage, surface temperature and internal temperature; thirdly, performing parameter identification on the battery circuit model and the thermal model; and step four, estimating the internal temperature of the battery by utilizing Kalman filtering based on the established electric-thermal coupling model. The invention carries out good thermal management on the battery in practical application, and ensures the health state of the battery in practical work; meanwhile, the calculation amount is small, and the method is suitable for online application under actual working conditions.
Description
Technical Field
The invention provides a Kalman filtering-based lithium ion battery internal temperature estimation method, and belongs to the technical field of lithium ion battery fire prevention and control.
Background
The conventional methods for monitoring the temperature inside the lithium ion battery can be generally divided into three types. The first method is to arrange a temperature sensor directly inside the lithium ion battery for measurement, and the most significant disadvantages of this method are that the internal structure of the battery is damaged, the normal operation of the battery is influenced to some extent, and the arrangement cost is high, which is not suitable in practical engineering application. The second method is to monitor the internal temperature of the battery based on an electrochemical-thermal coupling model. The method has higher measurement accuracy, but needs to solve a plurality of complex nonlinear differential equations, has large calculation amount and is difficult to realize in the BMS. The third monitoring method is based on an electrothermal coupling model. The electrical-thermal coupling model combines an equivalent circuit model and a thermal model, and the method has the advantages of simple process and low cost, and is very suitable for practical BMS application.
In order to well represent the internal temperature of the lithium ion battery, lin et al establishes an electrothermal model of a cylindrical single battery, and can effectively obtain the state of charge (SOC), terminal voltage, surface temperature and core temperature of the battery. Dai et al propose an adaptive temperature estimation method based on kalman filtering and equivalent time-varying electrothermal models to estimate the internal temperature of the battery. Zhang et al, based on a thermoelectric coupling model, utilize extended Kalman filtering to achieve internal temperature estimation of the battery. Xiong et al use dual extended kalman filtering for on-line estimation of the internal temperature of a lithium ion power cell.
Most researchers select an online identification method when identifying parameters of a battery model in the estimation of the internal temperature of the battery. Although the online parameter identification method can omit a large number of early experiments and solve the time-varying problem of the battery parameters to a great extent, the online parameter identification method is not suitable for practical application in consideration of the limitation of computing power and the stability of application.
Lithium ion batteries are very sensitive to operating temperature, and both excessively low and excessively low operating temperatures increase the insecurity of the lithium ion batteries. Low temperature may cause battery capacity fade, increased heat generation, reduced rate performance, and the like. High temperature accelerates battery aging, and when the ambient temperature is excessively high, thermal runaway of the battery may be caused. It is therefore desirable to control the temperature of the battery within a reasonable operating range. Accurate temperature monitoring of the battery is required in order to achieve temperature control of the battery.
In practical application, the conventional battery temperature monitoring method generally includes that a temperature sensor is arranged on the outer surface of a battery to monitor the surface temperature of the battery, the real-time monitoring of the internal temperature of the battery cannot be realized, and the internal temperature of the battery can better represent the real temperature state of the battery. If the temperature inside the battery is monitored, a sensor needs to be arranged inside the battery, and certain damage is necessarily caused to the battery body.
Therefore, in order to provide good thermal management for the battery in practical applications (such as an on-board BMS), it is necessary to provide a method capable of performing lossless real-time estimation on the internal temperature of the lithium ion battery to ensure the health of the battery in actual operation. Currently, in the research of the estimation of the internal temperature of the battery, no relevant literature is comprehensively considered: the influence of the ambient temperature on the battery, (2) the interaction of the electrical and thermal characteristics of the battery, and (3) the hardware computing power and the computing stability in practical application.
Disclosure of Invention
The invention solves the problems: the method overcomes the defects of the prior art, provides a Kalman filtering-based lithium ion battery internal temperature estimation method, and performs good thermal management on the battery in practical application to ensure the health state of the battery in practical work; meanwhile, the calculation amount is small, and the method is suitable for online application of actual working conditions.
The technical scheme of the invention is as follows: a lithium ion battery internal temperature estimation method based on Kalman filtering specifically comprises the following steps:
the method comprises the steps that firstly, an electric heating coupling model of the lithium ion battery is established according to a lithium ion battery circuit model and a two-state thermal model, wherein the lithium ion battery circuit model adopts a second-order equivalent circuit model based on temperature and state of charge (SOC), and the two states refer to the internal temperature and the shell temperature of the lithium ion battery;
performing capacity test, open-circuit voltage test, hybrid power pulse characteristic test (HPPC test) and symmetric pulse test on the lithium ion battery, acquiring test data of current, voltage, shell temperature and internal temperature of the lithium ion battery under the four test conditions, and recording environment temperature;
step three, according to the test data of the step two, performing parameter identification on the electrothermal coupling model of the lithium ion battery established in the step one to obtain a parameter identification result; the parameters refer to the capacity, open-circuit voltage, resistance, capacitance, thermal resistance and thermal capacity of the battery, and the utilized parameter identification algorithm is a least square method to obtain the value of each parameter in the electric-thermal coupling model;
and step four, estimating the internal temperature of the lithium ion battery by utilizing Kalman filtering based on the electric-thermal coupling model established in the step one and the parameter identification result in the step three, and finally obtaining the internal temperature of the lithium ion battery.
The first step specifically comprises:
the circuit model of the lithium ion battery is selected as a second-order equivalent circuit model:
wherein R is 1 And R 2 Electrochemical polarization resistance and concentration polarization resistance of the lithium ion battery are respectively; c 1 And C 2 Respectively the electrochemical polarization capacitance and concentration polarization capacitance, R, of the lithium ion battery 0 Is ohmic internal resistance, U, of a lithium ion battery 1 And U 2 Are each R 1 And R 2 Voltage across, U t Terminal voltage, U, of lithium ion battery ocv Is the open circuit voltage of the lithium ion battery, and I is the load current; r 0 、R 1 、R 2 、C 1 、C 2 And U ocv Are both functions of the lithium ion battery temperature T and the lithium ion battery SOC;
calculating heat production rate of lithium ion battery by using Bernardi heat production model
The load current I is positive during discharging and negative during charging;
the established heat transfer model of the lithium ion battery is a two-state thermal model, and comprises the following steps:
wherein R is i 、R o Internal thermal resistance and external thermal resistance of lithium ion battery, C c 、C s Internal and external thermal capacities, T, of the lithium ion battery, respectively i 、T s 、T a The lithium ion battery internal temperature, the shell temperature and the ambient temperature are respectively.
Further, in the second step, a hybrid power pulse characteristic test (HPPC test) at different temperatures, an open-circuit voltage test at different temperatures, a capacity test at different temperatures, and a symmetrical periodic current pulse test are performed on the lithium ion battery, so as to obtain test data of the battery under the above test conditions: current, voltage, surface temperature and internal temperature, while recording ambient temperature; the different temperatures are 0,10,20,30 and 40 ℃.
Further, the fourth step specifically includes:
the heat generation rate at the present time is obtained from equation (2):
carrying out forward Euler dispersion on the electric heating coupling model of the lithium ion battery to obtain:
the formula (4) is further simplified to obtain:
wherein Δ t is the sampling time;
the state space equation and the observation equation for describing the temperature of the lithium ion battery are as follows:
taking a state variable X (k) = [ T% i (k),T s (k)] T Observed quantity Y (k) = T s (k) Control quantity of
T a (k) The ambient temperature at the moment k is the discrete time and is directly measured by a temperature sensor;
wherein A is a state transition matrix, B is a control matrix, C is an observation matrix, W and V are uncorrelated white noises with a mean value of zero and variance matrices of Q and R, respectively;
the matrices A, B and C are derived from equation (5) as follows:
estimating the internal temperature of the lithium ion battery according to Kalman filtering algorithm formulas (9) to (13):
and (3) state prediction:
error covariance prediction:
P(k+1|k)＝AP(k|k)A T +Q (10)
kalman gain:
K(k+1)＝P(k+1|k)C T [CP(k+1|k)C T +R] -1 (11)
and (3) updating the state:
error covariance update:
P(k+1|k+1)＝[I-K(k+1)C]P(k+1|k) (13)
u (k) is a process control quantity at the moment k;
p (k | k) and P (k + 1) are posterior estimated covariance at time k and time k +1, respectively;
p (k +1 purple k) is the prior estimated covariance at the moment k;
q is a process noise covariance matrix;
r is a measurement noise covariance matrix;
y (k + 1) is the measured value at the time of k + 1;
k (K + 1) is the Kalman gain;
a is a state transition matrix;
b is a control matrix;
c is an observation matrix;
and I is an identity matrix.
Compared with the prior art, the invention has the advantages that:
(1) According to the method, the electric-thermal coupling model of the lithium ion battery is established according to the second-order equivalent circuit model and the two-state thermal model, the real-time estimation of the internal temperature of the lithium ion battery is realized by utilizing the Kalman filtering algorithm based on the established model and the measured value of the surface temperature of the battery, and the problem that the battery structure is damaged by the conventional measurement of the internal temperature of the battery is solved.
(2) The invention considers the influence of temperature on the battery performance and improves the environmental adaptability of the electric-thermal coupling model of the lithium ion battery.
(3) The invention provides a method for estimating the internal temperature of the lithium ion battery in real time by using a Kalman filtering algorithm, and solves the problem that the battery structure is damaged by the conventional measurement of the internal temperature of the battery. Compared with the traditional finite element simulation method, the solution provided by the invention has small calculated amount and is suitable for online application of actual working conditions.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a comparison of measured and estimated temperatures inside a battery;
fig. 3 is an error value of the internal temperature estimate, wherein (a) absolute error and (b) relative error.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, in the method of the present invention, an electrical-thermal coupling model is first established according to the type of a target lithium ion battery, and then corresponding working condition tests are performed and test data are collected for parameter identification of the model. And after the parameter identification is completed, estimating the internal temperature of the battery in real time according to a Kalman filtering algorithm based on the established lithium ion battery electric-thermal coupling model.
The embodiment of the invention takes the estimation of the internal temperature of a cylindrical lithium ion battery as an example for explanation:
the method comprises the following steps: and establishing an electric-thermal coupling model of the lithium ion battery.
Firstly, establishing a second-order equivalent circuit model of the lithium ion battery for describing the dynamic characteristics of the battery:
wherein R is 1 And R 2 Electrochemical polarization resistance and concentration polarization resistance of the lithium ion battery are respectively; c 1 And C 2 Respectively the electrochemical polarization capacitance and the concentration polarization capacitance of the lithium ion battery. R 0 Ohmic internal resistance of the lithium ion battery. U shape 1 And U 2 Are each R 1 And R 2 Voltage across, U t Terminal voltage, U, of lithium ion battery ocv Is lithium ionThe open circuit voltage of the subcell, I is the load current. R 0 、R 1 、R 2 、C 1 、C 2 And U ocv Both as a function of battery temperature T and battery SOC.
Then calculating the heat production rate of the battery by using the Bernardi heat production model
The load current I is positive during discharging and negative during charging.
The established two-state thermal model of the lithium ion battery is as follows:
wherein R is i 、R o Internal thermal resistance and external thermal resistance of lithium ion battery, C c 、C s Internal and external thermal capacities, T, of the lithium ion battery, respectively i 、T s 、T a Respectively, the battery internal temperature, the battery case temperature, and the ambient temperature.
Step two: in order to carry out parameter identification on the model parameters, a hybrid power pulse characteristic test (HPPC test), an open-circuit voltage test, a capacity test and a symmetrical periodic current pulse test are carried out on the tested battery at different temperatures, and test data are recorded.
Step three: parameters such as battery resistance, capacitance, thermal resistance and thermal capacity are estimated by using a Parameter Estimator tool box of Matlab/Simulink, and a Parameter estimation algorithm is set as a least square method based on a confidence domain.
Step four: calculating the heat generation rate at the current moment:
the two-state thermal model described by equation (16) is further subjected to Euler discretization to obtain:
the internal temperature T of the lithium ion battery can be obtained by the formula (4) i And shell temperature T s Expression of (a):
where Δ t is the sampling time.
The state space equation and the observation equation of the battery temperature are as follows:
taking a state variable X (k) = [ T ] i (k),T s (k)] T Observed quantity Y (k) = T s (k) Control amount of
Where A is the state transition matrix, B is the control matrix, C is the observation matrix, W and V are uncorrelated white noise with a mean value of zero and variance matrices of Q and R, respectively.
The matrices A, B and C are derived from equation (5) as follows:
according to the Kalman filtering algorithm, a required initial value is given firstly:
p (0 equals 0), Q and R.
Wherein,
P(0|0)＝E[(X(0)-μ 0 )(X(0)-μ 0 ) T ]。
and then according to the formulas (8) - (12), system state prediction and error covariance prediction are carried out, after Kalman gain is calculated, the difference between the measured battery surface temperature and the surface temperature output by the model is used for continuous correction, so that the estimation of the internal temperature of the battery is realized:
and (3) state prediction:
error covariance prediction:
P(k+1|k)＝AP(k|k)A T +Q (23)
kalman gain:
K(k+1)＝P(k+1|k)C T [CP(k+1|k)C T +R] -1 (24)
and (3) state updating:
error covariance update:
P(k+1|k+1)＝[I-K(k+1)C]P(k+1|k) (26)
u (k) is a process control quantity at the time k;
p (k | k) and P (k + 1) are posterior estimated covariance at time k and time k +1, respectively;
p (k +1 k) is the prior estimation covariance at the moment k;
q is a process noise covariance matrix;
r is a measurement noise covariance matrix;
y (k + 1) is the measured value at the time of k + 1;
k (K + 1) is the Kalman gain;
a is a state transition matrix;
b is a control matrix;
c is an observation matrix;
and I is an identity matrix.
As shown in fig. 2, fig. 3 shows absolute errors and relative errors of the internal temperature estimation for the estimation result of the internal temperature of the battery.
As can be seen from fig. 2, the internal estimated temperature can converge to a close measurement value quickly, with good estimation results.
As can be seen from fig. 3, except for the initial rapid convergence phase, the absolute error is 1.77 ℃ at the maximum and the relative error is 4.05% at the maximum during the entire internal temperature estimation process. The absolute error is basically within 0.8 ℃ in the whole view, the relative error is basically within 2 percent, and the errors are all within an acceptable range.
The above examples are provided for the purpose of describing the present invention only and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be included within the scope of the invention.
Claims (4)
1. A method for estimating the internal temperature of a lithium ion battery based on Kalman filtering is characterized by comprising the following steps:
the method comprises the steps that firstly, an electric heating coupling model of the lithium ion battery is established according to a lithium ion battery circuit model and a two-state thermal model, wherein the lithium ion battery circuit model adopts a second-order equivalent circuit model based on temperature and state of charge (SOC), and the two states refer to the internal temperature and the shell temperature of the lithium ion battery;
performing a capacity test, an open-circuit voltage test, a hybrid power pulse characteristic test (HPPC test) and a symmetrical pulse test on the lithium ion battery, acquiring test data of current, voltage, shell temperature and internal temperature of the lithium ion battery under the four test conditions, and simultaneously recording the environmental temperature;
step three, according to the test data of the step two, performing parameter identification on the electrothermal coupling model of the lithium ion battery established in the step one to obtain a parameter identification result; the parameters refer to the capacity, open-circuit voltage, resistance, capacitance, thermal resistance and thermal capacity of the battery, and the utilized parameter identification algorithm is a least square method to obtain the value of each parameter in the electric-thermal coupling model;
and step four, estimating the internal temperature of the lithium ion battery by utilizing Kalman filtering based on the electric-thermal coupling model established in the step one and the parameter identification result in the step three, and finally obtaining the internal temperature of the lithium ion battery.
2. The Kalman filtering-based lithium ion battery internal temperature estimation method according to claim 1, characterized in that: the first step specifically comprises:
the circuit model of the lithium ion battery is selected as a second-order equivalent circuit model:
wherein R is 1 And R 2 Electrochemical polarization resistance and concentration polarization resistance of the lithium ion battery are respectively; c 1 And C 2 Respectively the electrochemical polarization capacitance and concentration polarization capacitance, R, of the lithium ion battery 0 Ohmic internal resistance, U, of lithium ion batteries 1 And U 2 Are each R 1 And R 2 Voltage across, U t Terminal voltage, U, of lithium ion battery ocv Is the open circuit voltage of a lithium ion battery, I isA load current; r is 0 、R 1 、R 2 、C 1 、C 2 And U ocv Are both functions of the temperature T and SOC of the lithium ion battery;
calculating heat production rate of lithium ion battery by using Bernardi heat production model
The load current I is positive during discharging and negative during charging;
the established heat transfer model of the lithium ion battery is a two-state thermal model, and comprises the following steps:
wherein R is i 、R o Internal thermal resistance and external thermal resistance of lithium ion battery, C c 、C s Internal and external thermal capacities, T, of the lithium ion battery, respectively i 、T s 、T a The lithium ion battery internal temperature, the shell temperature and the ambient temperature are respectively.
3. The Kalman filtering based lithium ion battery internal temperature estimation method according to claim 1, characterized in that: in the second step, hybrid power pulse characteristic tests (HPPC tests) at different temperatures, open-circuit voltage tests at different temperatures, capacity tests at different temperatures and symmetrical periodic current pulse tests are carried out on the lithium ion battery to obtain test data of the battery under the test conditions: current, voltage, surface temperature and internal temperature, while recording ambient temperature; the different temperatures are 0,10,20,30 and 40 ℃.
4. The Kalman filtering based lithium ion battery internal temperature estimation method according to claim 1, characterized in that: the fourth step specifically comprises:
the heat generation rate at the present time is obtained from equation (2):
carrying out forward Euler dispersion on the electric heating coupling model of the lithium ion battery to obtain:
the formula (4) is further simplified to obtain:
wherein Δ t is the sampling time;
the state space equation and the observation equation for describing the temperature of the lithium ion battery are as follows:
taking a state variable X (k) = [ T ] i (k),T s (k)] T Observed quantity Y (k) = T s (k) Control quantity of
T a (k) The ambient temperature at discrete time and k moment is directly measured by a temperature sensor;
wherein A is a state transition matrix, B is a control matrix, C is an observation matrix, W and V are uncorrelated white noises with a mean value of zero and variance matrices of Q and R, respectively;
the matrices A, B and C are derived from equation (5) as follows:
estimating the internal temperature of the lithium ion battery according to Kalman filtering algorithm formulas (9) to (13):
and (3) state prediction:
error covariance prediction:
P(k+1|k)＝AP(k|k)A T +Q (10)
kalman gain:
K(k+1)＝P(k+1|k)C T [CP(k+1|k)C T +R] -1 (11)
and (3) state updating:
error covariance update:
P(k+1|k+1)＝[I-K(k+1)C]P(k+1|k) (13)
u (k) is a process control quantity at the moment k;
p (k | k) and P (k + 1) are posterior estimated covariance at time k and time k +1, respectively;
p (k +1 purple k) is the prior estimated covariance at the moment k;
q is a process noise covariance matrix;
r is a measurement noise covariance matrix;
y (k + 1) is the measured value at the time of k + 1;
k (K + 1) is the Kalman gain;
a is a state transition matrix;
b is a control matrix;
c is an observation matrix;
and I is an identity matrix.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116643193A (en) * | 2023-06-14 | 2023-08-25 | 北京智芯微电子科技有限公司 | Battery data estimation method and device, storage medium and electronic equipment |
| CN116680938A (en) * | 2023-08-04 | 2023-09-01 | 通达电磁能股份有限公司 | Modeling method and system for lithium battery electric heating coupling model |
| CN117630684A (en) * | 2024-01-26 | 2024-03-01 | 昆明理工大学 | Lithium ion battery internal temperature online estimation method based on electrothermal coupling model |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116643193A (en) * | 2023-06-14 | 2023-08-25 | 北京智芯微电子科技有限公司 | Battery data estimation method and device, storage medium and electronic equipment |
| CN116680938A (en) * | 2023-08-04 | 2023-09-01 | 通达电磁能股份有限公司 | Modeling method and system for lithium battery electric heating coupling model |
| CN116680938B (en) * | 2023-08-04 | 2023-10-20 | 通达电磁能股份有限公司 | Modeling method and system for lithium battery electric heating coupling model |
| CN117630684A (en) * | 2024-01-26 | 2024-03-01 | 昆明理工大学 | Lithium ion battery internal temperature online estimation method based on electrothermal coupling model |
| CN117630684B (en) * | 2024-01-26 | 2024-05-10 | 昆明理工大学 | Lithium ion battery internal temperature online estimation method based on electrothermal coupling model |
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