CN111929581A - Method for predicting internal and external temperatures of power lithium battery - Google Patents

Method for predicting internal and external temperatures of power lithium battery Download PDF

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CN111929581A
CN111929581A CN202010505249.3A CN202010505249A CN111929581A CN 111929581 A CN111929581 A CN 111929581A CN 202010505249 A CN202010505249 A CN 202010505249A CN 111929581 A CN111929581 A CN 111929581A
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CN111929581B (en
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庞辉
郭龙
武龙星
牟联晶
晋佳敏
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Xian University of Technology
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    • G01—MEASURING; TESTING
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    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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    • G—PHYSICS
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    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
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Abstract

The invention provides a method for predicting internal and external temperatures of a power lithium battery, which comprises the following steps of firstly, constructing a lithium ion battery electric-thermal coupling model considering environmental temperature; identifying the parameters of the model by a forgetting factor least square method to respectively obtain model parameters under different environments; then, carrying out simulation layer verification on the lithium ion battery electrical thermal coupling model established by the parameter identification result in combination with dynamic working condition test data; and finally, constructing a state observer considering the environment temperature to carry out application level verification on the model. The invention solves the problems of large state estimation error and the like caused by inaccurate models caused by different environmental temperatures, and plays an important role in the utilization efficiency, the service life and the whole vehicle performance of the power battery pack.

Description

Method for predicting internal and external temperatures of power lithium battery
Technical Field
The invention belongs to the technical field of lithium ion batteries, and particularly relates to a method for predicting internal and external temperatures of a power lithium battery.
Background
In recent years, lithium ion batteries have been widely used in the field of electric vehicles due to their high specific energy, high specific power, no memory effect, and long cycle life. The lithium ion power battery is a main energy supplier of a New energy automobile (NEV), has the advantages of light weight, low discharge rate, high energy density and the like, and is widely applied to the NEV. While a Battery Management System (BMS) is critical to the safe and efficient operation of lithium batteries (at a suitable voltage, operating temperature range) in electric vehicle applications, the System is usually connected to hundreds of Battery cells in a series/parallel configuration to meet the high power and high voltage requirements of the vehicle. In addition, thermal management is a key part of the BMS, and improper control of the temperature of the battery is a real threat to the traveling safety of the new energy automobile. Therefore, accurate modeling of lithium batteries is one of the most challenging tasks and difficulties to develop efficient battery management systems.
For this reason, many researchers at home and abroad have conducted a great deal of research on the mathematical model of the lithium ion battery. The method mainly comprises an electrochemical model and an equivalent circuit model. The equivalent circuit model has the characteristics of few parameters, convenient modeling and simple calculation in the aspect of calculating the external characteristics of the battery, so the equivalent circuit model is widely applied. As the internal and external temperatures of the lithium battery are difficult to measure directly, a scholars puts forward an electric-thermal coupling model for estimating the internal and external temperatures of the lithium battery and estimating the voltage, and the electric heating model has more parameters and needs to consider the influence of the environmental temperature on modeling.
It is noted that this section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
Disclosure of Invention
The invention aims to provide a method for predicting the internal and external temperatures of a power lithium battery, which solves the problems of large state estimation error and the like caused by inaccurate models due to different environmental temperatures in the prior art, and the provided modeling method can be controlled within a small error range in the estimation of the output internal and external temperatures.
In order to achieve the purpose, the invention adopts the following technical scheme:
the method for predicting the internal and external temperatures of the power lithium battery comprises the following steps:
s1: constructing an electric-thermal coupling model of the lithium ion battery considering the environmental temperature;
s2: identifying parameters of the lithium ion battery electrical thermal coupling model in the step S1 through a forgetting factor least square method to respectively obtain model parameters under different environments;
s3: carrying out simulation layer verification on the lithium ion battery electrical-thermal coupling model established by the parameter identification result in combination with dynamic working condition test data;
s4: and comparing the measured dynamic working condition experimental data with terminal voltage simulation data obtained by model simulation, performing application level verification on the model established in the step S1, and obtaining prediction of the internal and external temperatures of the lithium battery based on an Extended Kalman Filtering (EKF) method.
Further, the mathematical relationship of the electrical characteristic part of the lithium ion battery electrical thermal coupling model in step S1 is as follows:
Figure BDA0002526301830000021
wherein, UtIs the battery terminal voltage; u shapeOCRepresents an open circuit voltage; r is ohmic internal resistance; r1(Tamb) and C1(Tamb) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature TambA function of (a); r2(Tamb) And C2(Tamb) Concentration polarization resistance and concentration polarization fractional order capacitance respectively and is ambient temperature TambA function of (a); i represents a load current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
Further, the mathematical relationship of the thermal characteristics of the lithium ion battery electrical thermal coupling model in step S1 is as follows:
Figure BDA0002526301830000031
Figure BDA0002526301830000032
Q＝(UOC-Ut)I (4)
definition of
Tis＝Tin-Tamb (5)
TSs＝TS-Tamb (6)
The above equations (2) and (3) are modified as follows:
Figure BDA0002526301830000033
Figure BDA0002526301830000034
the above equations (7) and (8) are modified as follows:
Figure BDA0002526301830000035
Figure BDA0002526301830000036
wherein, CCIs the cell core heat capacity; cSIs the thermal capacity of the housing; t isSIs the cell surface temperature; t isinIs the battery core temperature; q represents a calorific value; riAnd RoRespectively, representing equivalent internal and external thermal resistances.
Further, the application level verification in step S4 is specifically:
discretization of equation (1) can yield:
Figure BDA0002526301830000041
discretization can be done for equation (9), where Δ t represents the sampling time:
Figure BDA0002526301830000042
discretization of equation (4) can yield:
Q(k)＝I(k)(UOC(k)-UL(k)) (13)
formula (13) may be substituted for formula (12):
Figure BDA0002526301830000043
discretization of equation (10) can yield:
Figure BDA0002526301830000044
namely, it is
Figure BDA0002526301830000045
Definition of x (k) ═ soc (k), U1(k),U2(k),Tis(k),TSs(k)]TAs a state variable of the system, y (k) is an output voltage of the system, i.e., a terminal voltage; the state space equation of the system is set as follows:
Figure BDA0002526301830000046
wherein
g(X(k))＝fOCV(SOC(k))-U1(k)-U2(k)-I(k)fR(Tamb)(k) (18)
From equations (11), (14), (16), the matrix A, B is:
Figure BDA0002526301830000051
definition of
X(k+1)＝F(X(k),I(k),ω) (19)
Combining the model with an EKF algorithm, the method comprises the following specific steps:
step 1, initializing;
state initialization X0＝E[X0]
Covariance initialization P0＝E[(X0-E(X0))(X0-E(X0))T]
Noise initialization Q and R (both omega and nu are Gaussian noise)
Step 2, predicting the state;
the state estimation value at the moment k can be calculated from the state value at the moment k-1:
Figure BDA0002526301830000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002526301830000053
represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Yk＝g(Xk)+Rk (21)
the covariance estimate at time k is:
Pk/k-1＝Ak-1Pk-1Ak-1 T+Qk-1 (22)
step 3, updating and correcting;
according to the actual observed voltage y (k), updating the state value and covariance of the system as follows:
(1) computing matrix HkI.e. jacobian matrix
Figure BDA0002526301830000061
Wherein the content of the first and second substances,
Figure BDA0002526301830000062
the derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) kalman gain calculation
Kk＝Pk/k-1Hk T(HkPk/k-1Hk T+Rk)-1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
Figure BDA0002526301830000063
the error covariance update equation at time k is:
Pk/k＝Pk/k-1-KkHkPk/k-1 (26)
the invention has the beneficial effects that:
1) the modeling method provided by the invention can be controlled within a smaller error range in the estimation of the output internal temperature and the output external temperature, so that the effectiveness and the accuracy of the parameter identification method are verified, the application of the electric vehicle in a wide temperature range is improved, and the problems of larger state estimation error and the like caused by inaccurate models due to different environmental temperatures are solved;
2) the method has great significance for state estimation and energy management applied to the battery management system of the electric vehicle; the method plays an important role in the utilization efficiency, the service life and the performance of the whole power battery pack.
Drawings
FIG. 1 is a schematic diagram of the principles of the present invention;
FIG. 2 is a schematic diagram of the coupling mode of the electro-thermal coupling model of the present invention;
FIG. 3 is a schematic diagram of a thermal model in an electrothermal coupling model according to the present invention;
FIG. 4 is a diagram illustrating the relationship of OCV-SOC-Tamb according to the present invention at different ambient temperatures;
FIG. 5 is a schematic diagram showing the relationship between the discharge capacity and the ambient temperature at different ambient temperatures according to the present invention;
FIG. 6 is a diagram illustrating the variation of the input current of the battery under the DST & US06 condition according to the present invention;
FIG. 7 is a schematic diagram of the voltage variation of the battery terminal under the DST & US06 working condition of the present invention;
FIG. 8 is a schematic diagram of errors between a terminal voltage test value and a simulation value under the working condition of US06 at the ambient temperature of-10 ℃;
FIG. 9 is a schematic diagram showing the comparison between the terminal voltage test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ according to the present invention;
FIG. 10 is a schematic diagram of errors between a terminal voltage test value and a simulation value under the working condition of US06 at an ambient temperature of 50 ℃ according to the present invention;
FIG. 11 is a schematic flow chart of the forgetting factor least square method in the present invention;
FIG. 12 is a schematic diagram showing comparison between the external temperature test value and the simulation value under the working condition of US06 at the temperature of-10 ℃ in the environment of the present invention;
FIG. 13 is a schematic diagram showing the error of the comparison between the external temperature test value and the simulation value under the working condition of US06 at the ambient temperature of-10 ℃;
FIG. 14 is a schematic diagram of the comparison between the external temperature test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ according to the present invention;
FIG. 15 is a schematic diagram showing the error of the comparison between the external temperature test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ according to the present invention;
FIG. 16 is a schematic diagram showing comparison between the internal temperature test value and the simulation value under the working condition of US06 at the temperature of-10 ℃ under the environment of the present invention;
FIG. 17 is a schematic diagram showing the comparison error between the internal temperature test value and the simulation value under the working condition of US06 at the ambient temperature of-10 deg.C;
FIG. 18 is a schematic diagram showing comparison between the internal temperature test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ according to the present invention;
FIG. 19 is a graph showing the error of the comparison between the test value and the simulated value of the internal temperature under the working condition of US06 at the ambient temperature of 50 ℃ in accordance with the present invention.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features or characteristics may be combined in any suitable manner in one or more embodiments.
As shown in FIG. 1, the invention discloses a method for predicting the internal and external temperatures of a power lithium battery, which specifically comprises the following steps:
step 1, constructing an electric-thermal coupling model of the lithium ion battery considering the environmental temperature;
step 2, identifying parameters of the battery electro-thermal coupling model; specifically, a least Forgetting factor method (FFLS) is adopted to identify model parameters, and model parameters under charging and discharging conditions at different environmental temperatures are obtained respectively;
step 3, carrying out simulation layer verification on the model established in the step 1 by combining with dynamic working condition test data;
and 4, comparing the measured dynamic working condition experimental data with terminal voltage simulation data obtained by model simulation, verifying the application level of the model established in the step S1, and predicting the internal and external temperatures of the lithium battery based on an EKF method.
The battery electro-thermal coupling model constructed in the step 1, wherein the mathematical relation of the electrical characteristic part is as follows:
Figure BDA0002526301830000081
wherein, UtIs the battery terminal voltage; u shapeOCRepresents an open circuit voltage; r is ohmic internal resistance; r1(Tamb) and C1(Tamb) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature TambA function of (a); r2(Tamb) And C2(Tamb) A concentration polarization resistance and a concentration polarization fractional order capacitance respectively and is a ringAmbient temperature TambA function of (a); i represents a load current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
Wherein, the mathematical relation of the thermal characteristic part is as follows: :
Figure BDA0002526301830000091
Figure BDA0002526301830000092
Q＝(UOC-Ut)I (4)
definition of
Tis＝Tin-Tamb (5)
TSs＝TS-Tamb (6)
The above equations (2) and (3) are modified as follows:
Figure BDA0002526301830000093
Figure BDA0002526301830000094
the above equations (7) and (8) are modified as follows:
Figure BDA0002526301830000095
Figure BDA0002526301830000096
wherein, CCIs the cell core heat capacity; cSIs the thermal capacity of the housing; t isSIs the cell surface temperature; t isinIs the battery core temperature; q represents a calorific value; riAnd RoRespectively representing equivalent inside and outsideAnd (4) partial thermal resistance.
The application level verification in step S4 specifically includes:
discretization of equation (1) can yield:
Figure BDA0002526301830000097
discretization can be done for equation (9), where Δ t represents the sampling time:
Figure BDA0002526301830000101
discretization of equation (4) can yield:
Q(k)＝I(k)(UOC(k)-UL(k)) (13)
formula (13) may be substituted for formula (12):
Figure BDA0002526301830000102
discretization of equation (10) can yield:
Figure BDA0002526301830000103
namely, it is
Figure BDA0002526301830000104
Definition of x (k) ═ soc (k), U1(k),U2(k),Tis(k),TSs(k)]TAs a state variable of the system, y (k) is an output voltage of the system, i.e., a terminal voltage; the state space equation of the system is set as follows:
Figure BDA0002526301830000105
wherein
g(X(k))＝fOCV(SOC(k))-U1(k)-U2(k)-I(k)fR(Tamb)(k) (18)
From equations (11), (14), (16), the matrix A, B is:
Figure BDA0002526301830000111
definition of
X(k+1)＝F(X(k),I(k),ω) (19)
Combining the model with an EKF algorithm, the method comprises the following specific steps:
step 1, initializing;
state initialization X0＝E[X0]
Covariance initialization P0＝E[(X0-E(X0))(X0-E(X0))T]
Noise initialization Q and R (both omega and nu are Gaussian noise)
Step 2, predicting the state;
the state estimation value at the moment k can be calculated from the state value at the moment k-1:
Figure BDA0002526301830000112
in the formula (I), the compound is shown in the specification,
Figure BDA0002526301830000113
represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Yk＝g(Xk)+Rk (21)
the covariance estimate at time k is:
Pk/k-1＝Ak-1Pk-1Ak-1 T+Qk-1 (22)
step 3, updating and correcting;
according to the actual observed voltage y (k), updating the state value and covariance of the system as follows:
(1) computing matrix HkI.e. jacobian matrix
Figure BDA0002526301830000121
Wherein the content of the first and second substances,
Figure BDA0002526301830000122
the derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) kalman gain calculation
Kk＝Pk/k-1Hk T(HkPk/k-1Hk T+Rk)-1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
Figure BDA0002526301830000123
the error covariance update equation at time k is:
Pk/k＝Pk/k-1-KkHkPk/k-1 (26)
in order to verify the accuracy of the estimation of the internal and external temperatures of the battery electrical-thermal coupling model established by the parameter identification result, firstly, an electrothermal coupling equivalent circuit model considering the influence of the environmental temperature is established in the MATLAB/Simulink environment. Secondly, model parameters are identified through an FFLS algorithm, a battery electrical thermal coupling model established by parameter identification results is verified through a US06 working condition (Standard US06 Driving Cycle, US06), and experimental data of US06 dynamic working condition obtained through experimental measurement is compared with terminal voltage simulation data obtained through model simulation, wherein the experimental data are shown in figures 7, 8, 10 and 12 respectively, and errors of the experimental data are shown in figures 9, 11 and 13. And finally, obtaining the estimation of the internal and external temperatures of the lithium battery based on an EKF method, and comparing the estimation with experimental data.
Through the experiment, the estimated root mean square errors of the terminal voltage under the working conditions of different environmental temperatures US06 can be obtained, wherein the estimated root mean square errors are 0.096 at minus 10 ℃, 0.128 at 20 ℃ and 0.067 at 50 ℃, and in addition, the estimated root mean square errors of the internal temperature and the external temperature are respectively 0.127 and 0.079 at minus 10 ℃; the internal and external temperature estimation errors at 20 ℃ were 0.121, 0.075, respectively; the error in the estimation of the internal and external temperatures at 50 ℃ was 0.063, 0.039, respectively.
The data of simulation and application level show that the modeling method provided by the invention can be controlled in a smaller error range in the output internal and external temperature estimation, the effectiveness and the accuracy of the parameter identification method of the invention are verified, the application of the electric vehicle in a wide temperature range is improved, the problems of larger state estimation error and the like caused by inaccurate model due to different environmental temperatures are solved, and the method has great significance for the state estimation and the energy management of a battery management system of the electric vehicle; the method plays an important role in the utilization efficiency, the service life and the performance of the whole power battery pack.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims (4)

1. A method for predicting the internal and external temperatures of a power lithium battery is characterized by comprising the following steps:
s1: constructing an electric-thermal coupling model of the lithium ion battery considering the environmental temperature;
s2: identifying parameters of the lithium ion battery electrical thermal coupling model in the step S1 through a forgetting factor least square method to respectively obtain model parameters under different environments;
s3: carrying out simulation layer verification on the lithium ion battery electrical-thermal coupling model established by the parameter identification result in combination with dynamic working condition test data;
s4: and comparing the measured dynamic working condition experimental data with terminal voltage simulation data obtained by model simulation, performing application level verification on the model established in the step S1, and obtaining prediction of the internal and external temperatures of the lithium battery based on an extended Kalman filtering method.
2. The method for predicting the internal and external temperatures of a lithium ion battery according to claim 1, wherein the mathematical relationship of the electrical characteristics of the lithium ion battery electrical thermal coupling model in step S1 is as follows:
Figure FDA0002526301820000011
wherein, UtIs the battery terminal voltage; u shapeOCRepresents an open circuit voltage; r is ohmic internal resistance; r1(Tamb) and C1(Tamb) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature TambA function of (a); r2(Tamb) And C2(Tamb) Concentration polarization resistance and concentration polarization fractional order capacitance respectively and is ambient temperature TambA function of (a); i represents a load current; u shape1And U2Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
3. The method for predicting the internal and external temperatures of a lithium ion battery according to claim 1 or 2, wherein the mathematical relationship of the thermal characteristics of the lithium ion battery electrical thermal coupling model in the step S1 is as follows:
Figure FDA0002526301820000012
Figure FDA0002526301820000021
Q＝(UOC-Ut)I (4)
definition of
Tis＝Tin-Tamb (5)
TSs＝TS-Tamb (6)
The above equations (2) and (3) are modified as follows:
Figure FDA0002526301820000022
Figure FDA0002526301820000023
the above equations (7) and (8) are modified as follows:
Figure FDA0002526301820000024
Figure FDA0002526301820000025
wherein, CCIs the cell core heat capacity; cSIs the thermal capacity of the housing; t isSIs the cell surface temperature; t isinIs the battery core temperature; q represents a calorific value; riAnd RoRespectively, representing equivalent internal and external thermal resistances.
4. The method for predicting the internal and external temperatures of a lithium battery according to claim 1, wherein the application level verification in the step S4 specifically comprises:
discretization of equation (1) can yield:
Figure FDA0002526301820000026
discretization can be done for equation (9), where Δ t represents the sampling time:
Figure FDA0002526301820000031
discretization of equation (4) can yield:
Q(k)＝I(k)(UOC(k)-UL(k)) (13)
formula (13) may be substituted for formula (12):
Figure FDA0002526301820000032
discretization of equation (10) can yield:
Figure FDA0002526301820000033
namely, it is
Figure FDA0002526301820000034
Definition of x (k) ═ soc (k), U1(k),U2(k),Tis(k),TSs(k)]TAs a state variable of the system, y (k) is an output voltage of the system, i.e., a terminal voltage; the state space equation of the system is set as follows:
Figure FDA0002526301820000035
wherein
g(X(k))＝fOCV(SOC(k))-U1(k)-U2(k)-I(k)fR(Tamb)(k) (18)
From equations (11), (14), (16), the matrix A, B is:
Figure FDA0002526301820000036
definition of
X(k+1)＝F(X(k),I(k),ω) (19)
Combining the model with an EKF algorithm, the method comprises the following specific steps:
step 1, initializing;
state initialization X0＝E[X0]
Covariance initialization P0＝E[(X0-E(X0))(X0-E(X0))T]
Noise initialization Q and R (both omega and nu are Gaussian noise)
Step 2, predicting the state;
the state estimation value at the moment k can be calculated from the state value at the moment k-1:
Figure FDA0002526301820000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002526301820000042
represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Yk＝g(Xk)+Rk (21)
the covariance estimate at time k is:
Pk/k-1＝Ak-1Pk-1Ak-1 T+Qk-1 (22)
step 3, updating and correcting;
according to the actual observed voltage y (k), updating the state value and covariance of the system as follows:
(1) computing matrix HkI.e. jacobian matrix
Figure FDA0002526301820000043
Wherein the content of the first and second substances,
Figure FDA0002526301820000044
the derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) kalman gain calculation
Kk＝Pk/k-1Hk T(HkPk/k-1Hk T+Rk)-1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
Figure FDA0002526301820000051
the error covariance update equation at time k is:
Pk/k＝Pk/k-1-KkHkPk/k-1 (26)。
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CN113420471A (en) * 2021-06-01 2021-09-21 上海交通大学 Power lithium battery thermal model construction and establishment method and system based on electrochemical mechanism
CN113722926A (en) * 2021-09-07 2021-11-30 重庆大学 Square lithium battery electric-thermal coupling modeling error source analysis method
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