CN116449208A - Lithium battery internal temperature online estimation method based on SRCKF at full temperature - Google Patents
Lithium battery internal temperature online estimation method based on SRCKF at full temperature Download PDFInfo
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Abstract
The invention relates to an on-line estimation method of internal temperature of a lithium battery based on SRCKF at full temperature, which is characterized by comprising the following steps: step 1: collecting data; step 2: establishing a second-order RC equivalent circuit model and a thermal model; step 3: identifying parameters of a second-order RC equivalent circuit model and a two-state centralized parameter thermal model respectively; step 4: giving an SRC KF algorithm to perform online estimation of the internal and external temperatures of the battery; step 5: coupling of the equivalent circuit model with the two-state centralized parameter thermal model. The thermoelectric coupling model adopts a second-order RC equivalent circuit model, so that the internal resistance-capacitance characteristic of the battery can be described more accurately, the adopted dual-state thermal model can fully embody the huge difference of internal and external temperatures of the battery, and meanwhile, the heat generation equation of the battery is reasonably simplified, the complexity of the model is greatly reduced, and the calculation efficiency is improved.
Description
Technical Field
The invention belongs to the technical field of lithium ion batteries, and particularly relates to an online estimation method of internal temperature of a lithium battery based on SRCKF at full temperature.
Background
Lithium batteries are used as key power components for energy storage and power sources of electric automobiles, and the use performance and safety of the lithium batteries are of great concern. The battery temperature is used as one of the key state parameters in the lithium ion battery, and accurate estimation of the internal temperature is important to ensure the safe use of the battery. Meanwhile, the internal temperature state is also an important parameter affecting lithium battery state of charge estimation and thermal management.
However, the internal temperature of the battery is difficult to acquire in real time under the actual vehicle-mounted working condition, and the existing method still has difficulty in realizing online prediction at the full temperature and ensuring the estimation precision. The method mainly used for estimating the internal temperature of the lithium battery at the present stage based on the electrothermal coupling model comprises the electrothermal coupling model based on partial differential equation, the electrothermal coupling model with concentrated parameters and the mixed electrothermal coupling model. The electrothermal coupling model based on partial differential equations adopts a large number of solutions of partial differential equations to greatly increase BMS (Battery management system) operation load, so that the application of the electrothermal coupling model in real-time control is limited. The difficulty of the centralized parameter electrothermal coupling model is how to establish the correlation between the parameters of the electrical model and the temperature. The difficulty with the hybrid electrothermal coupling model is how to establish a correlation between electrochemical parameters and temperature, which typically requires a large number of experiments to calibrate the electrochemical parameters. Therefore, the external environment in which the battery is located has a significant impact on the accuracy of its internal temperature estimation. However, the research on a battery temperature accurate coupling model under the condition of the actual working condition of the battery and the influence of the full working temperature environment is still relatively few in the present stage. Therefore, in order to solve the problem of on-line estimation of the temperature of the vehicle-mounted power battery under the full-temperature condition, it is critical to establish a thermoelectric coupling model which can meet the actual working condition of the battery, has higher accuracy of the battery temperature estimation under the full-temperature working range and is convenient for on-line application.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides an on-line estimation method for the internal temperature of a lithium battery based on SRCKF at full temperature, which is realized by the following technical scheme:
the lithium battery internal temperature online estimation method based on SRCKF at full temperature is characterized by comprising the following steps:
step 1: and (3) data acquisition: acquiring charging and discharging data of a lithium ion single battery: performing charge and discharge test on the lithium ion battery under the full temperature condition of-20 ℃ to 60 ℃ and collecting the charge and discharge data of the lithium ion battery monomer;
step 2: establishing a second-order RC equivalent circuit model and a thermal model: establishing a second-order RC equivalent circuit model, wherein the thermal model comprises a heat generation model and a heat transfer model, a simplified Bernardi equation is adopted as the heat generation model, a dual-state centralized parameter thermal model is adopted as the heat transfer model to simulate heat transfer in the battery, and the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model are expressed in a discretization mode to respectively obtain a system state space equation and a measurement equation;
step 3: identifying parameters of a second-order RC equivalent circuit model and a two-state centralized parameter thermal model respectively: under the condition of full temperature, based on the battery charge and discharge data obtained in the step 1, carrying out parameter identification on the second-order RC equivalent circuit model established in the step 2 by using a genetic algorithm, and carrying out on-line identification on the double-state centralized parameter thermal model by using a recursive least square algorithm;
step 4: giving an SRC KF algorithm to perform online estimation of the internal and external temperatures of the battery: based on the system state space equation and the measurement equation in the step 2, the SRCKF algorithm is fused into the lithium ion battery temperature estimation, the terminal voltage and the open-circuit voltage output by the second-order RC equivalent circuit model are taken as the heat generation equation of the brought Bernardi to calculate the battery heat generation power, and then the estimation of the internal and external temperatures of the battery is realized by combining the SRCKF algorithm according to the dual-state concentrated parameter heat model;
step 5: coupling of equivalent circuit model and dual-state centralized parameter thermal model: and (3) using the battery temperature obtained in the step (4) for updating the parameters of the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, realizing the coupling between the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, and then using the updated battery electrothermal parameter for estimating the battery temperature at the next moment to realize the on-line estimation of the battery temperature based on the thermoelectric coupling model.
Further, the lithium ion battery cell charge and discharge data collected in the step 1 include voltage, current, surface temperature and tab temperature data.
Further, the second-order RC equivalent circuit model established in the step 2 is as follows:
U(t)＝U 1 (t)+U 2 (t)+U OCV (t)+R 0 I(t)
the discrete expression formula of the second-order RC equivalent circuit model is as follows:
wherein I represents a current, U represents a battery terminal voltage, U 1 And U 2 Respectively represent the voltage drop of the corresponding RC network, R 0 Represents ohmic internal resistance, R 1 、R 2 And C 1 、C 2 Respectively represent polarization resistance and capacitance, the value of which is related to temperature, E oc Represents an open circuit voltage;
in the thermal model established in the step 2, the discretization expression of the Bernardi heat generation equation is as follows:
the discrete expression of the double-state centralized parameter thermal model solving equation is as follows:
wherein Q is c Generating heat power for a unit volume of the battery; c (C) c The heat capacity of the battery is obtained; r is R c Is the thermal resistance between the interior and the surface of the battery; c (C) air The heat capacity of the battery surface shell; r is R air Is the thermal resistance between the surface of the battery and the external environment; t (T) c 、T s And T air The temperature at the core of the battery, the surface of the battery and the ambient temperature around the battery are respectively;
based on the discretization expression of the second-order RC equivalent circuit model and the thermal model, a battery internal and external temperature estimation model is established, and a system state space equation and a measurement equation are obtained:
wherein: x is X k Is the kth step state vector; a is a state transition matrix; b is a system control matrix; u (u) k The control quantity is the k-th step; z is Z k+1 Is a measurement state vector; v (V) k To have a measurement noise matrix R k Covariance white gaussian measurement noise.
Further, in the step 3, the process of performing on-line identification on the two-state centralized parameter thermal model by adopting a recursive least square algorithm is as follows:
let the model parameter vector be θ= [ αβγγ ]] T
The observation vector is:
the recursive cyclic formula is:
wherein K is a gain matrix; p is covariance matrix; Δt is the sampling time interval 1s;
internal heat generation power Q of battery c The heat capacity C of the aluminum plastic film on the surface of the battery can be estimated according to Bernardi equation air Can be obtained according to the data provided by the battery manufacturer, the value is a fixed value,
from the above parameters C c 、R c 、R air 。
Further, in the step 4, the online estimation process of the internal and external temperatures of the battery based on the srkf algorithm is as follows:
(1) Initialization of
Initializing state vectors separatelyError covariance matrix P k Process noise matrix Q k And measuring a noise matrix R k ；
(2) Prediction process
Calculating state volume points and corresponding weights thereof:
S k ＝chol(P k )
wherein: p (P) k Square root S by Cholesky decomposition k ；ξ j Is the j-th volume point; n is the dimension of the system state vector; [1]Is an identity matrix, and the weight of each volume point is
Propagation volume point:
wherein: f (X) j,k+1 ,u k ) Is a system process function;a predicted value corresponding to each volume point;
calculating a system state quantity predicted value:
calculating a state quantity error covariance matrix square root predicted value:
wherein: tria () represents an orthogonal triangular (QR) decomposition of the state quantity predictor matrix; s is S Q,k Is the square root of the covariance matrix of the process noise,is a state vector deviation matrix;
(3) Correction procedure
Performing measurement update and calculating a measurement predicted value:
wherein: x is X j,k+1 Reconstructing a state vector corresponding to the volume point for the correction stage;
calculating the volume point propagated through the measurement equation:
Z j,k+1 ＝h(X j,k+1 ,u k+1 )
calculating a predicted value of the measurement state:
calculating the square root of the innovation measurement error covariance:
S R,k ＝chol(R k )
S zz,k+1 ＝Tria([γ k+1 S R,k ])
wherein: s is S zz,k+1 For the square root of the innovation measure error covariance, S R,k To measure the square root of the covariance matrix of noise, γ k+1 A bias matrix for the measurement vector;
calculating a cross covariance matrix:
updating the Kalman gain:
updating state quantity:
updating the square root of the state quantity error covariance matrix:
S k+1 ＝Tria([x k+1 K k+1 γ k+1 K k+1 S zz,k+1 ])。
further, in the step 5, coupling between the second-order RC equivalent circuit model and the two-state centralized parameter thermal model is performed: under the excitation of current, the temperature of the battery changes, so that the parameters of a circuit model of the battery are changed, the change of the circuit parameters also causes the change of the heat-generating power of the battery, the circuit model transmits the current I, the voltage U, SOC and the resistance-capacitance parameters to the heat-generating model, the heat-generating model is helped to finish the calculation of the heat-generating power, the heat-generating model is combined with the heat-transferring model of the battery to realize the estimation of the temperature of the battery, and the feedback of the temperature T is returned to the circuit model to change the resistance-capacitance parameters, so that the two parameters are coupled.
The simplified battery thermal model is as follows:
1) Regarding the interior of the battery as a uniform heat source, and uniformly distributing the temperature of the battery along the axial direction;
2) Heat is transferred outwards only by radial direction;
3) Part of heat generated in the battery is absorbed by the battery to raise the temperature of the battery, and the other part of heat is transferred to the surface of the battery to exchange heat with the outside;
compared with the prior art, the invention has the beneficial effects that:
(1) The thermoelectric coupling model adopts a second-order RC equivalent circuit model, so that the internal resistance-capacitance characteristic of the battery can be described more accurately, the adopted dual-state thermal model can fully embody the huge difference of internal and external temperatures of the battery, and meanwhile, the heat generation equation of the battery is reasonably simplified, the complexity of the model is greatly reduced, and the calculation efficiency is improved.
(2) The influence of the external working environment temperature of the battery on the parameters of the circuit model is considered, and the terminal voltage and the open-circuit voltage are calculated by adopting the circuit parameters matched with the internal temperature of the battery.
(3) The influence of environmental temperature factors is considered, a thermoelectric coupling model under the full temperature is built, and meanwhile, the thermal parameters are updated on line, so that the battery internal temperature estimation error caused by environmental temperature interference can be well adapted;
(4) The SRCKF is introduced into temperature calculation of the thermoelectric coupling model, so that the problem that the Taylor expansion accuracy is low in the extended Kalman filtering process can be solved, and the more accurate internal temperature of the battery can be obtained.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of an online estimation method of the internal temperature of a lithium battery based on SRCKF at full temperature.
FIG. 2 is a graph showing the results of estimating the internal temperature of the battery at a temperature of 0 ℃, 20 ℃, 40 ℃ in accordance with the present invention when 2C is discharged.
Fig. 3 is a graph showing the results of estimating the internal temperature of the battery at 0.5C, 1C, 2C discharge at 20C ambient temperature according to the present invention.
FIG. 4 is a graph showing the result of estimating the internal temperature of the battery under the dynamic conditions of FUDS-UDDS of the present invention.
Detailed Description
In order to better understand the aspects of the present invention, the following description is provided with reference to the accompanying drawings and the specific embodiments.
The method can be applied to terminal equipment such as an electric automobile battery management system, and the internal temperature estimation flow of the lithium ion battery provided by the embodiment is shown in a figure 1, and specifically comprises the following steps:
step 1: and (3) data acquisition: performing charge and discharge test on the lithium ion battery under the full temperature condition of-20 ℃ to 60 ℃ and collecting the charge and discharge data of the lithium ion battery monomer; the charge and discharge data comprise charge and discharge current, voltage, surface temperature and tab temperature data of the battery. In this embodiment, lithium ions are tested for charge and discharge under different discharge rates and dynamic conditions, and specific recording results of the 2C discharge test at 20 ℃ in this embodiment are shown in table 1.
TABLE 1
Step 2: establishing a second-order RC equivalent circuit model and a thermal model: establishing a second-order RC equivalent circuit model, wherein the thermal model comprises a heat generation model and a heat transfer model, a simplified Bernardi equation is adopted as the heat generation model, a dual-state centralized parameter thermal model is adopted as the heat transfer model to simulate heat transfer in the battery, and the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model are expressed in a discretization mode to respectively obtain a system state space equation and a measurement equation.
The established second-order RC equivalent circuit model is as follows:
U(t)＝U 1 (t)+U 2 (t)+U OCV (t)+R 0 I(t)
the discrete expression formula of the second-order RC equivalent circuit model is as follows:
wherein I represents a current, U represents a battery terminal voltage, U 1 And U 2 Respectively represent the voltage drop of the corresponding RC network, R 0 Represents ohmic internal resistance, R 1 、R 2 And C 1 、C 2 Respectively represent polarization resistance and capacitance, the value of which is related to temperature, E oc Represents an open circuit voltage;
in the thermal model established in the step 2, the discretization expression of the Bernardi heat generation equation is as follows:
the discrete expression of the double-state centralized parameter thermal model solving equation is as follows:
wherein Q is c Generating heat power for a unit volume of the battery; c (C) c The heat capacity of the battery is obtained; r is R c Is the thermal resistance between the interior and the surface of the battery; c (C) air The heat capacity of the battery surface shell; r is R air Is the thermal resistance between the surface of the battery and the external environment; t (T) c 、T s And T air The temperature at the core of the battery, the surface of the battery and the ambient temperature around the battery are respectively;
based on the discretization expression of the second-order RC equivalent circuit model and the thermal model, a battery internal and external temperature estimation model is established, and a system state space equation and a measurement equation are obtained:
wherein: x is X k Is the kth step state vector; a is a state transition matrix; b is a system control matrix; u (u) k The control quantity is the k-th step; z is Z k+1 Is a measurement state vector; v (V) k To have a measurement noise matrix R k Covariance white gaussian measurement noise.
Wherein:
wherein: x is X k Is the kth step state vector; a is a state transition matrix; b is a system control matrix; u (u) k The control quantity is the k-th step; z is Z k+1 Is a measurement state vector; v (V) k To have a measured noise momentArray R k Covariance white gaussian measurement noise.
Step 3: identifying parameters of a second-order RC equivalent circuit model and a two-state centralized parameter thermal model respectively: and (3) under the full-temperature condition, based on the battery charge and discharge data obtained in the step (1), carrying out parameter identification on the second-order RC equivalent circuit model established in the step (2) by using a genetic algorithm, and carrying out on-line identification on the double-state centralized parameter thermal model by using a recursive least square algorithm.
The process of carrying out on-line identification on the two-state centralized parameter thermal model by adopting a recursive least square algorithm is as follows:
let the model parameter vector be θ= [ αβγγ ]] T
The observation vector is:
the recursive cyclic formula is:
wherein K is a gain matrix; p is covariance matrix; Δt is the sampling time interval 1s;
internal heat generation power Q of battery c The heat capacity C of the aluminum plastic film on the surface of the battery can be estimated according to Bernardi equation air Can be obtained according to the data provided by the battery manufacturer, the value is a fixed value,
from the above parameters C c 、R c 、R air 。
C in thermal model air The heat capacity of the aluminum plastic film of the battery shell is hardly changed in the whole life cycle of the lithium ion battery, C c ，R c The heat capacities at the core and core-to-surface areas inside the battery are shown to be unchanged, respectively, in a short time, but change as the battery ages. R is R air The battery heat dissipation characterization parameters related to the external environment are related to the environment where the battery is located, and are required to be identified in real time.
The recursive least square method only needs to correct the parameter estimation value of the previous moment according to the observed value of the current moment, and the actual parameter value is finally approximated along with superposition of iteration times, so that the calculated amount of the algorithm can be effectively reduced.
Step 4, giving an SRCKF algorithm to perform online estimation of the internal and external temperatures of the battery: based on the system state space equation and the measurement equation in the step 2, the SRCKF algorithm is fused into the lithium ion battery temperature estimation, the terminal voltage and the open-circuit voltage output by the second-order RC equivalent circuit model are taken as the heat generation equation of the brought Bernardi to calculate the battery heat generation power, and then the estimation of the internal and external temperatures of the battery is realized by combining the SRCKF algorithm according to the dual-state concentrated parameter heat model;
the online estimation process of the internal and external temperatures of the battery based on square root volume Kalman filtering is as follows:
(1) Initialization of
Initializing state vectors separatelyError covariance matrix P k Process noise matrix Q k And measuring a noise matrix R k ；
(2) Prediction process
Calculating state volume points and corresponding weights thereof:
S k ＝chol(P k )
wherein: p (P) k Square root S by Cholesky decomposition k ；ξ j Is the j-th volume point; n is the dimension of the system state vector; [1]Is an identity matrix, and the weight of each volume point is
Propagation volume point:
wherein: f (X) j,k+1 ,u k ) Is a system process function;a predicted value corresponding to each volume point;
calculating a system state quantity predicted value:
calculating a state quantity error covariance matrix square root predicted value:
wherein: tria () represents an orthogonal triangular (QR) decomposition of the state quantity predictor matrix; s is S Q,k Is the square root of the covariance matrix of the process noise,is a state vector deviation matrix;
(3) Correction procedure
Performing measurement update and calculating a measurement predicted value:
wherein: x is X j,k+1 Reconstructing a state vector corresponding to the volume point for the correction stage;
calculating the volume point propagated through the measurement equation:
Z j,k+1 ＝h(X j,k+1 ,u k+1 )
calculating a predicted value of the measurement state:
calculating the square root of the innovation measurement error covariance:
S R,k ＝chol(R k )
S zz,k+1 ＝Tria([γ k+1 S R,k ])
wherein: s is S zz,k+1 For the square root of the innovation measure error covariance, S R,k To measure the square root of the covariance matrix of noise, γ k+1 A bias matrix for the measurement vector;
calculating a cross covariance matrix:
updating the Kalman gain:
updating state quantity:
updating the square root of the state quantity error covariance matrix:
S k+1 ＝Tria([x k+1 K k+1 γ k+1 K k+1 S zz,k+1 ])。
based on the above estimation procedure, the internal temperature estimation result of the lithium ion battery obtained in the present embodiment at the time of 2C discharge at the ambient temperature of 0 ℃, 20 ℃, 40 ℃ is shown in fig. 2; the estimation results of the internal temperature of the battery when 0.5C, 1C and 2C are discharged at the ambient temperature of 20 ℃ are shown in a figure 3, and in the figure 3, the higher the multiplying power is, the faster the corresponding temperature rises; the internal temperature estimation result of the battery under the FUDS-UDDS dynamic working condition is shown in fig. 4, and the internal temperature estimation method of the lithium ion battery provided by the invention can realize accurate temperature estimation under different environment temperatures, different current multiplying powers and complex working conditions, and has the advantages of better adaptability and higher precision.
Step 5: coupling of equivalent circuit model and dual-state centralized parameter thermal model: and (3) using the battery temperature obtained in the step (4) for updating the parameters of the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, realizing the coupling between the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, and then using the updated battery electrothermal parameter for estimating the battery temperature at the next moment to realize the on-line estimation of the battery temperature based on the thermoelectric coupling model.
Under the excitation of current, the battery generates heat from the inside and exchanges energy with the outside through heat transfer, and the heat exchange changes the temperature of the battery, so that the parameters of a battery circuit model are changed. Changes in circuit parameters also result in changes in heat generation power. The circuit model transmits current I, voltage U, SOC and resistance-capacitance parameters to the heat-generating model, so that the heat-generating model is assisted in completing calculation of heat-generating power, the heat-generating model is combined with the battery heat-transmitting model to realize estimation of the internal temperature of the battery, and the estimated temperature T is fed back to the circuit model to change the resistance-capacitance parameters, so that coupling of the two is realized.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (6)
1. The lithium battery internal temperature online estimation method based on SRCKF at full temperature is characterized by comprising the following steps:
step 1: and (3) data acquisition: acquiring charging and discharging data of a lithium ion single battery: performing charge and discharge test on the lithium ion battery under the full temperature condition of-20 ℃ to 60 ℃ and collecting the charge and discharge data of the lithium ion battery monomer;
step 2: establishing a second-order RC equivalent circuit model and a thermal model: establishing a second-order RC equivalent circuit model, wherein the thermal model comprises a heat generation model and a heat transfer model, a simplified Bernardi equation is adopted as the heat generation model, a dual-state centralized parameter thermal model is adopted as the heat transfer model to simulate heat transfer in the battery, and the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model are expressed in a discretization mode to respectively obtain a system state space equation and a measurement equation;
step 3: identifying parameters of a second-order RC equivalent circuit model and a two-state centralized parameter thermal model respectively: under the condition of full temperature, based on the battery charge and discharge data obtained in the step 1, carrying out parameter identification on the second-order RC equivalent circuit model established in the step 2 by using a genetic algorithm, and carrying out on-line identification on the double-state centralized parameter thermal model by using a recursive least square algorithm;
step 4: giving an SRC KF algorithm to perform online estimation of the internal and external temperatures of the battery: based on the system state space equation and the measurement equation in the step 2, the SRCKF algorithm is fused into the lithium ion battery temperature estimation, the terminal voltage and the open-circuit voltage output by the second-order RC equivalent circuit model are taken as the heat generation equation of the brought Bernardi to calculate the battery heat generation power, and then the estimation of the internal and external temperatures of the battery is realized by combining the SRCKF algorithm according to the dual-state concentrated parameter heat model;
step 5: coupling of equivalent circuit model and dual-state centralized parameter thermal model: and (3) using the battery temperature obtained in the step (4) for updating the parameters of the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, realizing the coupling between the second-order RC equivalent circuit model and the dual-state centralized parameter thermal model, and then using the updated battery electrothermal parameter for estimating the battery temperature at the next moment to realize the on-line estimation of the battery temperature based on the thermoelectric coupling model.
2. The method for online estimation of the internal temperature of the lithium battery based on SRCKF at the full temperature according to claim 1, wherein the charge and discharge data of the lithium ion battery monomer collected in the step 1 comprises voltage, current, surface temperature and tab temperature data.
3. The method for online estimation of the internal temperature of the lithium battery based on SRCKF at the full temperature according to claim 1, wherein the second-order RC equivalent circuit model established in the step 2 is as follows:
U(t)＝U 1 (t)+U 2 (t)+U OCV (t)+R 0 I(t)
the discrete expression formula of the second-order RC equivalent circuit model is as follows:
wherein I represents a current, U represents a battery terminal voltage, U 1 And U 2 Respectively represent the voltage drop of the corresponding RC network, R 0 Represents ohmic internal resistance, R 1 、R 2 And C 1 、C 2 Respectively represent polarization resistance and capacitance, the value of which is related to temperature, E oc Represents an open circuit voltage;
in the thermal model established in the step 2, the discretization expression of the Bernardi heat generation equation is as follows:
the discrete expression of the double-state centralized parameter thermal model solving equation is as follows:
wherein Q is c Generating heat power for a unit volume of the battery; c (C) c The heat capacity of the battery is obtained; r is R c Is the thermal resistance between the interior and the surface of the battery; c (C) air The heat capacity of the battery surface shell; r is R air Is the thermal resistance between the surface of the battery and the external environment; t (T) c 、T s And T air The temperature at the core of the battery, the surface of the battery and the ambient temperature around the battery are respectively;
based on the discretization expression of the second-order RC equivalent circuit model and the thermal model, a battery internal and external temperature estimation model is established, and a system state space equation and a measurement equation are obtained:
wherein: x is X k Is the kth step state vector; a is a state transition matrix; b is a system control matrix; u (u) k The control quantity is the k-th step; z is Z k+1 Is a measurement state vector; v (V) k To have a measurement noise matrix R k Covariance white gaussian measurement noise.
4. The method for online estimation of internal temperature of lithium battery based on srkf at full temperature according to claim 1, wherein the process of online identification of the two-state centralized parameter thermal model by using the recursive least square algorithm in step 3 is as follows:
let the model parameter vector be θ= [ αβγγ ]] T
The observation vector is:
the recursive cyclic formula is:
wherein K is a gain matrix; p is covariance matrix; Δt is the sampling time interval 1s;
internal heat generation power Q of battery c The heat capacity C of the aluminum plastic film on the surface of the battery can be estimated according to Bernardi equation air Can be obtained according to the data provided by the battery manufacturer, the value is a fixed value,
from the above parameters C c 、R c 、R air 。
5. The method for online estimation of the internal temperature of a lithium battery based on the srkf at the full temperature according to claim 1, wherein the online estimation process of the internal and external temperatures of the battery based on the srkf algorithm in the step 4 is:
(1) Initialization of
Initializing state vectors separatelyError covariance matrix P k Process noise matrix Q k And measuring a noise matrix R k ；
(2) Prediction process
Calculating state volume points and corresponding weights thereof:
S k ＝chol(P k )
wherein: p (P) k Square root S by Cholesky decomposition k ；ξ j Is the j-th volume point; n is the dimension of the system state vector; [1]Is an identity matrix, and the weight of each volume point is
Propagation volume point:
wherein: f (X) j,k+1 ,u k ) Is a system process function;a predicted value corresponding to each volume point;
calculating a system state quantity predicted value:
calculating a state quantity error covariance matrix square root predicted value:
wherein: tria () represents an orthogonal triangular (QR) decomposition of the state quantity predictor matrix; s is S Q,k Is the square root of the covariance matrix of the process noise,is a state vector deviation matrix;
(3) Correction procedure
Performing measurement update and calculating a measurement predicted value:
wherein: x is X j,k+1 Reconstructing a state vector corresponding to the volume point for the correction stage;
calculating the volume point propagated through the measurement equation:
Z j,k+1 ＝h(X j,k+1 ,u k+1 )
calculating a predicted value of the measurement state:
calculating the square root of the innovation measurement error covariance:
S R,k ＝chol(R k )
S zz,k+1 ＝Tria([γ k+1 S R,k ])
wherein: s is S zz,k+1 For the square root of the innovation measure error covariance, S R,k To measure the square root of the covariance matrix of noise, γ k+1 A bias matrix for the measurement vector;
calculating a cross covariance matrix:
updating the Kalman gain:
updating state quantity:
updating the square root of the state quantity error covariance matrix:
S k+1 ＝Tria([x k+1 K k+1 γ k+1 K k+1 S zz,k+1 ])。
6. the method for online estimation of internal temperature of lithium battery based on srkf at full temperature according to claim 1, wherein in step 5, the second-order RC equivalent circuit model is coupled with the two-state centralized parameter thermal model: under the excitation of current, the temperature of the battery changes, so that the parameters of a circuit model of the battery are changed, the change of the circuit parameters also causes the change of the heat-generating power of the battery, the circuit model transmits the current I, the voltage U, SOC and the resistance-capacitance parameters to the heat-generating model, the heat-generating model is helped to finish the calculation of the heat-generating power, the heat-generating model is combined with the heat-transferring model of the battery to realize the estimation of the temperature of the battery, and the feedback of the temperature T is returned to the circuit model to change the resistance-capacitance parameters, so that the two parameters are coupled.
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| 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 |
| CN117728082A (en) * | 2024-02-04 | 2024-03-19 | 江苏林洋亿纬储能科技有限公司 | Control method, device, system and storage medium for energy storage system |
| CN117728082B (en) * | 2024-02-04 | 2024-06-04 | 江苏林洋储能技术有限公司 | Control method, device, system and storage medium for energy storage system |
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| 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 |
| CN117728082A (en) * | 2024-02-04 | 2024-03-19 | 江苏林洋亿纬储能科技有限公司 | Control method, device, system and storage medium for energy storage system |
| CN117728082B (en) * | 2024-02-04 | 2024-06-04 | 江苏林洋储能技术有限公司 | Control method, device, system and storage medium for energy storage system |
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