CN111929581B - 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 PDFInfo
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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 by combining 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 due to 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
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 a plurality of 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 directly measure, the electric-thermal coupling model is proposed by scholars 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 by 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 characteristics of the lithium ion battery electrical thermal coupling model in step S1 is as follows:
wherein, U t Is the battery terminal voltage; u shape OC Represents an open circuit voltage; r is ohmic internal resistance; r 1 (Tamb) and C 1 (T amb ) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature T amb A function of (a); r is 2 (T amb ) And C 2 (T amb ) Concentration polarization resistance and concentration polarization fractional order capacitance respectively and is ambient temperature T amb A function of (a); i represents a load current; u shape 1 And U 2 Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
Further, the mathematical relationship of the thermal characteristics of the lithium ion battery electrical and thermal coupling model in step S1 is as follows:
Q=(U OC -U t )I (4)
definition of
T is =T in -T amb (5)
T Ss =T S -T amb (6)
The above equations (2) and (3) are modified as follows:
the above equations (7) and (8) are modified as follows:
wherein, C C Is the cell core heat capacity; c S Is the thermal capacity of the housing; t is a unit of S Is the cell surface temperature; t is a unit of in Is the battery core temperature; q represents a calorific value; r is i And R o Respectively representing equivalent internal and external thermal resistances;
further, the application level verification in step S4 specifically includes:
discretization of equation (1) can yield:
discretization can be done for equation (9), where Δ t represents the sampling time:
discretization of equation (4) can yield:
Q(k)=I(k)(U OC (k)-U t (k)) (13)
formula (13) may be substituted for formula (12):
discretization of equation (10) can yield:
namely that
Definition of X (k) = [ SOC (k), U) 1 (k),U 2 (k),T is (k),T Ss (k)] T As 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:
wherein
g(X(k))=f OCV (SOC(k))-U 1 (k)-U 2 (k)-I(k)f R (T amb )(k) (18)
From the formulae (11), (14) and (16), the matrices A and B are:
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:
state initialization X 0 =E[X 0 ]
Covariance initialization P 0 =E[(X 0 -E(X 0 ))(X 0 -E(X 0 )) T ]
Noise initialization Q and R (omega and v are both Gaussian noise)
the state estimation value at the moment k can be calculated from the state value at the moment k-1:
in the formula (I), the compound is shown in the specification,represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Y k =g(X k )+R k (21)
the covariance estimate at time k is:
P k/k-1 =A k-1 P k-1 A k-1 T +Q k-1 (22)
according to the actual observed voltage y (k), updating the state value and covariance of the system, specifically as follows:
(1) Computing matrix H k I.e. jacobian matrix
Wherein the content of the first and second substances,the derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) Kalman gain calculation
K k =P k/k-1 H k T (H k P k/k-1 H k T +R k ) -1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
the error covariance update equation at time k is:
P k/k =P k/k-1 -K k H k P k/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 present invention;
FIG. 2 is a schematic diagram of an electro-thermal coupling model according to 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 between 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 schematic diagram of the variation of the input current of the battery under the DST & US06 condition of 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 a US06 working condition at an ambient temperature of-10 ℃ according to the present invention;
FIG. 9 is a schematic diagram showing a comparison between a terminal voltage test value and a simulation value under a US06 working condition at an ambient temperature of 50 ℃ in accordance with the present invention;
FIG. 10 is a schematic diagram of errors between a terminal voltage test value and a simulation value under US06 condition at an ambient temperature of 50 deg.C;
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 the comparison between the external temperature test value and the simulation value under the working condition of US06 at the ambient temperature of-10 ℃ according to 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 deg.C;
FIG. 14 is a schematic diagram showing comparison between the external temperature test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ in accordance with 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 ℃ in accordance with the present invention;
FIG. 16 is a schematic diagram showing the comparison between the internal temperature test value and the simulation value under the working condition of US06 at the ambient temperature of-10 ℃ according to 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 the comparison between the internal temperature test value and the simulation value under the working condition of US06 at the ambient temperature of 50 ℃ in accordance with the present invention;
FIG. 19 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 50 ℃.
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:
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 1, 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:
wherein, U t Is the battery terminal voltage; u shape OC Represents an open circuit voltage; r is ohmic internal resistance; r 1 (Tamb) and C 1 (T amb ) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature T amb Function of (2);R 2 (T amb ) And C 2 (T amb ) Concentration polarization resistance and concentration polarization fractional order capacitance respectively and is ambient temperature T amb A function of (a); i represents a load current; u shape 1 And U 2 Electrochemical polarization voltage and concentration polarization voltage are respectively represented.
Wherein, the mathematical relation of the thermal characteristic part is as follows: :
Q=(U OC -U t )I (4)
definition of
T is =T in -T amb (5)
T Ss =T S -T amb (6)
The above equations (2) and (3) are modified as follows:
the above equations (7) and (8) are modified as follows:
wherein, C C Is the cell core heat capacity; c S Is the thermal capacity of the housing; t is S Is the cell surface temperature; t is in Is the battery core temperature; q represents a calorific value; r i And R o Respectively, representing equivalent internal and external thermal resistances.
The application layer verification in the step S4 specifically includes:
discretization of equation (1) can yield:
discretization can be done for equation (9), where Δ t represents the sampling time:
discretization of equation (4) can yield:
Q(k)=I(k)(U OC (k)-U t (k)) (13)
formula (13) may be substituted for formula (12):
discretization of equation (10) can yield:
namely, it is
Definition of X (k) = [ SOC (k), U) 1 (k),U 2 (k),T is (k),T Ss (k)] T As 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:
wherein
g(X(k))=f OCV (SOC(k))-U 1 (k)-U 2 (k)-I(k)f R (T amb )(k) (18)
From the formulae (11), (14) and (16), the matrices A and B are:
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:
state initialization X 0 =E[X 0 ]
Covariance initialization P 0 =E[(X 0 -E(X 0 ))(X 0 -E(X 0 )) T ]
Noise initialization Q and R (both omega and nu are Gaussian noise)
the state estimation value at the moment k can be calculated from the state value at the moment k-1:
in the formula (I), the compound is shown in the specification,represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Y k =g(X k )+R k (21)
the covariance estimate at time k is:
P k/k-1 =A k-1 P k-1 A k-1 T +Q k-1 (22)
according to the actual observed voltage y (k), updating the state value and covariance of the system, specifically as follows:
(1) Computing matrix H k I.e. jacobi matrix
Wherein, the first and the second end of the pipe are connected with each other,the derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) Kalman gain calculation
K k =P k/k-1 H k T (H k P k/k-1 H k T +R k ) -1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
the error covariance update equation at time k is:
P k/k =P k/k-1 -K k H k P k/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, identifying model parameters through an FFLS algorithm, verifying a simulation layer of the battery electrical and thermal coupling model established by the parameter identification result through a US06 working condition (US 06) and comparing US06 dynamic working condition experimental data obtained by experimental measurement with terminal voltage simulation data obtained by model simulation, wherein the results are respectively shown in a figure 7, a figure 8, a figure 10 and a figure 12, and errors are shown in a figure 9, a figure 11 and a figure 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 0.127,0.079 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 c 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 device plays an important role in the utilization efficiency, the service life and the performance of the whole vehicle of the 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 (1)
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 by 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: 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;
the mathematical relation of the electrical characteristic part of the lithium ion battery electrical thermal coupling model in the step S1 is as follows:
wherein, U t Is the battery terminal voltage; u shape OC Represents an open circuit voltage; r is ohmic internal resistance; r 1 (Tamb) and C 1 (T amb ) Electrochemical polarization resistance and electrochemical polarization fractional order capacitance, respectively, and is the ambient temperature T amb A function of (a); r is 2 (T amb ) And C 2 (T amb ) Concentration polarization resistance and concentration polarization fractional order capacitance respectively and is ambient temperature T amb A function of (a); i represents a load current; u shape 1 And U 2 Respectively representing electrochemical polarization voltage and concentration polarization voltage;
the mathematical relation of the thermal characteristic part of the lithium ion battery electrical thermal coupling model in the step S1 is as follows:
Q=(U OC -U t )I (4)
definition of
T is =T in -T amb (5)
T Ss =T S -T amb (6)
The above equations (2) and (3) are modified as follows:
the above equations (7) and (8) are modified as follows:
wherein, C C Is the cell core heat capacity; c S Is the thermal capacity of the housing; t is a unit of S Is the cell surface temperature; t is in Is the battery core temperature; q represents a calorific value; r i And R o Respectively representing equivalent internal and external thermal resistances;
the application level verification in the step S4 specifically includes:
discretization of equation (1) can yield:
discretization can be done for equation (9), where Δ t represents the sampling time:
discretization of equation (4) can yield:
Q(k)=I(k)(U OC (k)-U t (k)) (13)
formula (13) may be substituted for formula (12):
discretization of equation (10) can yield:
namely, it is
Define X (k) = [ SOC (k), U) 1 (k),U 2 (k),T is (k),T Ss (k)] T As 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:
wherein
g(X(k))=f OCV (SOC(k))-U 1 (k)-U 2 (k)-I(k)f R (T amb )(k) (18)
From the formulae (11), (14) and (16), the matrices a and B are:
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 X 0 =E[X 0 ]
Covariance initialization P 0 =E[(X 0 -E(X 0 ))(X 0 -E(X 0 )) T ]
Noise initialization, wherein Q and R, omega and v are Gaussian noise
Step 2, predicting the state;
the state estimated value at the time k can be calculated from the state value at the time k-1:
in the formula (I), the compound is shown in the specification,represents the prediction result at the time k;
the estimated value of the terminal voltage at the moment k is as follows:
Y k =g(X k )+R k (21)
the covariance estimate at time k is:
P k/k-1 =A k-1 P k-1 A k-1 T +Q k-1 (22)
step 3, updating and correcting;
according to the actual observed voltage y (k), updating the state value and covariance of the system, specifically as follows:
(1) Calculating the matrix H k I.e. jacobian matrix
Wherein the content of the first and second substances,a derivative of the second order Taylor expansion of equation (4) with respect to SOC;
(2) Kalman gain calculation
K k =P k/k-1 H k T (H k P k/k-1 H k T +R k ) -1 (24)
(3) Measurement update
The state correction equation at the moment k is as follows:
the error covariance update equation at time k is:
P k/k =P k/k-1 -K k H k P k/k-1 (26)。
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