CN117630684B - Lithium ion battery internal temperature online estimation method based on electrothermal coupling model - Google Patents
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- 229910001416 lithium ion Inorganic materials 0.000 title claims abstract description 118
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 title claims abstract description 116
- 238000000034 method Methods 0.000 title claims abstract description 54
- 230000008878 coupling Effects 0.000 title claims abstract description 34
- 238000010168 coupling process Methods 0.000 title claims abstract description 34
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 34
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 45
- 238000005259 measurement Methods 0.000 claims abstract description 43
- 230000032683 aging Effects 0.000 claims abstract description 11
- 239000007790 solid phase Substances 0.000 claims description 53
- 239000011159 matrix material Substances 0.000 claims description 51
- 239000002245 particle Substances 0.000 claims description 39
- 238000009792 diffusion process Methods 0.000 claims description 31
- 239000013598 vector Substances 0.000 claims description 30
- 239000007791 liquid phase Substances 0.000 claims description 28
- 230000020169 heat generation Effects 0.000 claims description 24
- 239000007787 solid Substances 0.000 claims description 23
- 230000008569 process Effects 0.000 claims description 20
- 238000012546 transfer Methods 0.000 claims description 12
- 230000002068 genetic effect Effects 0.000 claims description 7
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- 238000000354 decomposition reaction Methods 0.000 claims description 6
- 239000007774 positive electrode material Substances 0.000 claims description 6
- 230000000644 propagated effect Effects 0.000 claims description 6
- 239000000178 monomer Substances 0.000 claims description 4
- 238000012360 testing method Methods 0.000 claims description 4
- 150000001450 anions Chemical class 0.000 claims description 3
- 239000007772 electrode material Substances 0.000 claims description 3
- 239000003792 electrolyte Substances 0.000 claims description 3
- 238000011156 evaluation Methods 0.000 claims description 3
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- 125000004122 cyclic group Chemical group 0.000 claims description 2
- 238000006243 chemical reaction Methods 0.000 claims 1
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 abstract description 7
- 229910052744 lithium Inorganic materials 0.000 abstract description 7
- 210000004027 cell Anatomy 0.000 description 12
- 230000000875 corresponding effect Effects 0.000 description 12
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- 230000001276 controlling effect Effects 0.000 description 4
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Abstract
The invention discloses an on-line estimation method for internal temperature of a lithium ion battery based on an electrothermal coupling model, and belongs to the technical field of lithium ion batteries. The method comprises the steps of constructing an electrochemical model and a thermal model of the lithium ion battery; carrying out parameter identification on the coupling model under the condition of full temperature and full service life, and constructing an electrochemical-thermal coupling model of the lithium battery; discretizing the internal and external temperatures of the lithium battery to obtain a system state space equation and a measurement equation; estimating the internal and external temperatures of the lithium ion battery by adopting an SRCKF algorithm; and introducing the estimated battery temperature into an electrochemical model to realize closed-loop updating of battery parameters. The invention considers the influence of wide-range environment temperature and different aging degrees on the internal parameters of the battery, simplifies the P2D electrochemical model, builds the electrochemical-thermal coupling model of the battery under the full temperature and full service life, integrates the SRCKF algorithm into temperature estimation, improves the operation efficiency, and solves the problem of poor estimation precision of the internal and surface temperatures of the lithium battery caused by the working environment temperature and aging.
Description
Technical Field
The invention belongs to the technical field of lithium ion batteries, and particularly relates to an on-line estimation method for internal temperature of a lithium ion battery based on an electrothermal coupling model.
Background
The lithium battery is used as a key power component of an energy storage and electric automobile power source, the service performance and safety of the lithium battery are of great concern, the accurate modeling and state estimation of the battery are of great importance to the safety of the battery and the driving mileage of the automobile, and the internal state is influenced by temperature, such as the cycle life, peak power and the like of the battery, and the battery has a very strong coupling relation with the temperature of the battery. In order to fully reveal the coupling relation to accurately simulate the dynamic characteristics of the battery and more accurately estimate the temperature state (state of temperature, SOT) of the lithium battery, development and establishment of the electrothermal coupling model have great scientific and engineering application values.
At present, a model-based method is mainly adopted to estimate the internal temperature of a lithium ion battery, a model based on an electrochemical mechanism needs a large amount of calculation amount when solving a partial differential equation, an equivalent circuit model does not consider the actual mechanism of the battery, and a machine learning model lacks generalization capability due to the data-driven property of the model. These problems present challenges in ensuring the effectiveness of the model under wide temperature, high current conditions. In addition, the internal temperature of the battery is difficult to acquire in real time under the actual vehicle-mounted working condition, and the online prediction of the internal temperature of the lithium ion battery under the full-temperature full-life cycle is still difficult to realize by the existing method, so that the estimation accuracy of the internal temperature of the lithium ion battery is ensured. The electrothermal coupling model mainly adopted in the internal temperature estimation of the lithium battery at the present stage comprises an electrothermal coupling model based on partial differential equation, an electrothermal coupling model with concentrated parameters and a mixed electrothermal coupling model. The electrothermal coupling model based on the partial differential equation adopts an electrochemical mechanism model as an electrical characteristic model, and is simultaneously coupled with a thermal model based on the thermal equation. Therefore, the model is fully described by partial differential equations, and the Battery voltage and temperature response characteristics can be accurately revealed, but the solution of a large number of partial differential equations greatly increases the running load of the BMS (Battery MANAGEMENT SYSTEM), so that the application of the model in real-time control is limited. The electrothermal coupling model for concentrating parameters adopts an equivalent circuit model as an electrical characteristic model and is coupled with a thermal model. The model has moderate complexity and is suitable for the condition of higher calculation efficiency requirement. How to establish the correlation between the electrical model parameters and temperature is a difficulty, which directly affects the model accuracy. The hybrid electrothermal coupling model adopts an electrochemical model to describe the electrical characteristics of the battery, and simultaneously couples the concentrated parameter thermal model, and the complexity of the model is positioned between the two models. Because the mechanism model is adopted to describe the electrical characteristics, the physical meaning of the model parameters is obvious, the accuracy is generally higher than that of the centralized parameter model, but how to establish the correlation between the electrochemical parameters and the temperature is a difficulty. However, the research on battery temperature state estimation methods which comprehensively consider the actual working condition of the battery and are suitable for the whole service period is still relatively few. Therefore, in order to meet the actual use requirements of the electric automobile, it is important to establish an accurate battery model and solve the problem of on-line estimation of the temperature state of the vehicle-mounted power battery in the whole service period.
Disclosure of Invention
The method aims at solving the problems of poor adaptability, low calculation efficiency, low estimation precision and the like of the existing battery temperature state estimation method. The invention provides an on-line estimation method for the internal temperature of a lithium ion battery based on an electrothermal coupling model by considering the temperature and ageing influence of the battery.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the lithium ion battery internal temperature on-line estimation method based on the electrothermal coupling model comprises the following steps:
(1) Acquiring electrochemical parameters and physical parameters of a lithium ion battery and charge and discharge data of a lithium ion single battery;
(2) Establishing an extremely simple electrochemical model based on the average electrode model, and establishing a single battery thermal model;
(3) Discretizing and expressing the extremely simple electrochemical model and the thermal model of the single battery to obtain a system state space equation and a measurement equation;
(4) Based on the charge and discharge data of the lithium ion single battery, carrying out parameter identification on the established extremely simple electrochemical model by using a genetic algorithm, and carrying out on-line parameter identification on the double-state centralized parameter thermal model by using a recursive least square algorithm;
(5) Based on a system state space equation and a measurement equation, estimating the internal temperature of the lithium ion battery by adopting an SRCKF algorithm, and then estimating the obtained battery temperature And feeding back the electrochemical model, updating electrochemical parameters of the lithium ion battery, and realizing the coupling of the electrochemical model and the thermal model of the single battery.
The invention estimates the temperature of the batteryAnd the temperature is fed back to the electrochemical model, so that the electrochemical parameters can be updated because the temperature can influence the electrical parameters, and a new temperature estimation result can be obtained by adopting the new electrochemical parameters, so that the electrochemical model and the thermal model of the single battery are mutually influenced and mutually coupled to jointly realize online accurate estimation of the internal temperature of the lithium ion battery.
As a preferred embodiment of the present invention, the electrochemical parameters of the lithium ion battery include the maximum lithium ion concentration of the solid phase and the liquid phase, the lithium ion diffusion coefficient of the solid phase and the liquid phase, and the conductivity of the solid phase and the liquid phase; the physical parameters include battery size parameters, electrode thickness, specific heat capacity.
As a preferred embodiment of the present invention, the lithium ion battery cell charge and discharge data includes voltage, current, surface temperature, and tab temperature data.
As a preferred embodiment of the present invention, the construction of the extremely simple electrochemical model specifically includes:
S2-1: the solid-phase lithium ion diffusion equation deduced from the average electrode model is:
；
Representing the cross section of the battery Axial directionThe solid-phase lithium ion concentration at the moment,The radial dimensions of the particles are indicated,The active diffusion coefficient of solid-phase lithium ions;
end voltage expression of the average electrode model:
；
；
Is the anion transfer coefficient of the polymer, Is a gas constant which is a function of the gas,The temperature of the unit cell is indicated,、、Is the thickness of the diaphragm, the positive electrode and the negative electrode,For the effective conductivity of the converted electrolyte ions,AndRespectively represent the internal resistance and the area of the current collecting plate,The concentration of lithium ions is represented by the formula,、Respectively the positive and negative electrode potentials,、The average value of the current density products of the positive electrode and the negative electrode respectively,Is the specific surface area of the electrode active material,、The lithium ion concentrations of the positive electrode and the negative electrode respectively,In the event of a current flow,To exchange current density;
S2-2: the radius equidistant dividing uniform discrete is adopted for simplifying the solid-phase lithium ion diffusion equation: independent variable of solid-phase lithium ion diffusion equation Divided intoThe equal spacing of the solid particles isThenWherein, the method comprises the steps of, wherein,Is the radius of the particles of the positive and negative electrode materials,Is the radial dimension of the solid particles, whereinI represents the i-th solid particle; then willThe difference quotient is processed and the difference quotient is processed,Represent the firstThe lithium ion concentration in the solid particles is obtained, and a simplified solid-phase lithium ion diffusion equation is obtained:
；；
Wherein, Is the concentration of the solid-phase lithium ions,Represent the firstThe concentration of lithium ions in the individual solid particles,Represent the firstThe concentration of lithium ions in the individual solid particles,Is the specific surface area of the positive electrode active material,Is the effective diffusion coefficient of positive lithium ions,Is a function of the faraday constant,Represents the concentration of lithium ions in the center of the solid phase particles,Representing an equivalent spacing from the center of the solid phase particles ofLithium ion concentration in the solid particles of (a);
s2-3: simplifying the sum of the positive and negative overpotential and the liquid phase potential of the simplified average electrode model into seven-degree polynomials: parameters of the extremely simple electrochemical model are obtained through a parameter identification method, and then polynomial fitting is carried out on the parameters to obtain the extremely simple electrochemical model:
；
Wherein the method comprises the steps of Is the coefficient of the polynomial,，Is the sum of the positive and negative electrode overpotential and the liquid phase potential,Is the temperature of the unit cell.
As a preferred embodiment of the present invention, the thermal model of the unit cell includes a heat generation model and a heat transfer model, the heat generation model adopts Bernardi heat generation equation expression:
；
the heat transfer model adopts a double-state centralized parameter thermal model expression:
；
Wherein, Generating heat power for a unit volume of the battery; The heat capacity of the battery is obtained; is the thermal resistance between the interior and the surface of the battery; the heat capacity of the battery surface shell; Is the thermal resistance between the surface of the battery and the external environment; 、 And The internal temperature of the battery, the surface of the battery and the ambient temperature of the battery, respectively; For the battery terminal voltage to be the same, Is the battery open circuit voltage.
As a preferred embodiment of the invention, the specific process of discretizing the extremely simple electrochemical model comprises the following steps:
S3-1: in order to simplify the terminal voltage expression form based on the average electrode model, a more simplified electrode model is obtained, and the terminal voltage expression of the average electrode model is simplified into the terminal voltage expression of the electrode electrochemical model; the terminal voltage equation of the extremely simple electrochemical model is:
；
Represents the terminal voltage of the extremely simple electrochemical model, Is the sum of the positive and negative electrode overpotential and the liquid phase potential;
S3-2: since the overpotential, the liquid phase potential difference and the ohmic voltage are all independent of the lithium ion concentration on the solid phase surface in the terminal voltage equation and are functions of the working current of the battery, the method can be adopted Describing, according to a terminal voltage equation of the polar-simple electrochemical model, a measurement equation is expressed as follows:
；
The sum of the positive and negative overpotential and the liquid phase potential of the simplified average electrode model is obtained;
S3-3: the solid-phase lithium ion diffusion equation of the extremely simple electrochemical model is as follows:
；
Discretizing a solid phase diffusion equation based on an extremely simple electrochemical model to obtain a state variable in the system Sum coefficient matrix：
；
；
；
；
Is the concentration of the solid-phase lithium ions,Is the solid-phase diffusion coefficient of the positive electrode,Is the radius of the positive electrode solid-phase lithium ion particles,Is the sum of the liquid phase potential difference and the overpotential,As a result of the ohmic voltage,Is thatThe sum of the liquid phase potential difference and the overpotential at the moment,Is thatOhmic voltage at moment, SOC is battery state of charge.
As a preferred embodiment of the invention, bernardi heat generation equation discretization expression is:
；
Wherein, For the heat generation power inside the battery,Is the firstGenerating heat power inside the battery; in the event of a current flow, Is the firstStep current; For the battery terminal voltage to be the same, Is the firstStep battery terminal voltage; for the open-circuit voltage of the battery, Is the firstStep battery open circuit voltage; As the internal temperature of the battery, Is the firstInternal temperature of the step cell.
The discretized expression of the two-state centralized parameter thermal model is as follows:
；
Wherein, Generating heat power for a unit volume of the battery; The heat capacity of the battery is obtained; is the thermal resistance between the interior and the surface of the battery; the heat capacity of the battery surface shell; Is the thermal resistance between the surface of the battery and the external environment; 、 And The internal temperature of the battery, the surface of the battery and the ambient temperature of the battery,Is the firstThe surface temperature of the step battery is equal to the surface temperature of the step battery,Is the firstThe internal temperature of the step battery is equal to the temperature of the battery,Is the firstThe heat generation power inside the step battery,Is the firstThe temperature of the environment outside the step is,Is thatIs the inverse of the number of (a),Is thatIs the inverse of (c).
As a preferred embodiment of the present invention, the system state space equation and the measurement equation are:
；
Wherein:
；
；
；
；
Wherein: Is the first Step state vector; a is a state transition matrix; b is a system control matrix; Is the first Controlling the amount of steps; Is the first Step measurement state vector; in order to have a measurement noise matrix, Is the firstA state vector of the step; Is the first And observing the surface temperature of the battery.
As a preferred embodiment of the invention, the process of parameter identification of the established extremely simple electrochemical model by using a genetic algorithm is as follows: is provided withAndRespectively representing a terminal voltage simulation value and an experimental value of a polar electrochemical model, wherein the evaluation index of the genetic algorithm individual is thatError function of (2)The expression is:；
The process of carrying out on-line parameter identification on the two-state centralized parameter thermal model by adopting a recursive least square algorithm is as follows:
The parameter vector of the dual-state centralized parameter thermal model is ；
The observation vector is:；
；
Then ，
Wherein,For the heat generation power inside the battery,In order to be at the temperature of the environment,In order to be the surface temperature of the battery,For the heat capacity of the battery,Is the heat capacity of the battery surface shell,To provide thermal resistance between the interior and the surface of the cell,To provide thermal resistance between the cell surface and the external environment,Is the firstThe output of the surface temperature of the step battery,Is the firstThe temperature output quantity of the internal part of the step battery,Is the firstThe surface temperature of the step battery is equal to the surface temperature of the step battery,In time steps.
As a preferred embodiment of the present invention, the step of estimating the internal temperature of the lithium ion battery by the srkf algorithm includes: and taking the terminal voltage and the open-circuit voltage output by the polar electrochemical model as the input of a single battery thermal model, calculating the internal heat generation power of the battery by adopting Bernardi heat generation equation, and then combining the battery heat transfer model with the SRCKF algorithm to estimate the internal temperature of the battery.
As a preferred embodiment of the present invention, estimating the internal temperature of the lithium ion battery using the srkf algorithm specifically includes:
S5-1: initializing: initializing state vectors separately Error covariance matrix/>Process noise matrix/>And measuring noise matrix/>；
S5-2: the prediction process comprises the following steps: calculating state volume pointsAnd the corresponding weight thereof:
；
；
；
Wherein: by/> Decomposition to square root/>；/>Is the square root of the error covariance matrix; for/> Step, system state quantity corresponding to each volume point; /(I)For/>A plurality of volume points; /(I)Is the dimension of the system state vector; /(I)Is an identity matrix, and the weight of each volume point is/>；
Propagation volume point:
；
Wherein: Is a system process function; /(I) Predicting a state quantity corresponding to each volume point;
Calculating a state quantity predictor for a system ：
；
Calculating state quantity error covariance matrix square root predicted value：
；
；
Wherein: Orthogonal triangular decomposition is carried out on the state quantity predicted value matrix; /(I) Is the square root of the covariance matrix of the process noise,/>Is a state vector deviation matrix;
S5-3: the correction process comprises the following steps:
Performing measurement update and calculating a measurement predicted value:
；
Wherein: reconstructing a state vector corresponding to the volume point for the correction stage;
Calculating the volume point propagated through the measurement equation ：
；
Wherein,For/>Controlling the amount of steps; /(I)For/>Volume point propagated by measurement equation corresponding to each volume point,/>；
Calculating a predicted value of the measured state：
；
Calculating the square root of the innovation measurement error covariance:
；
；
；
Wherein: for the square root of the innovation measure error covariance,/> For measuring covariance matrix square root of noise,/>A bias matrix for the measurement vector; /(I)For/>Volume point propagated by measurement equation corresponding to each volume point,/>；
Calculating a cross covariance matrix：
；
State variablesFirst/>State variables of the steps;
updating Kalman gain ：
；
Updating state quantity：
；
Represents the/>Measuring the observed value of the state quantity step by step;
updating the square root of the state quantity error covariance matrix:
。
Compared with the prior art, the invention has the beneficial effects that: according to the invention, the correlation between the parameters of the electrochemical model and the temperature is realized by establishing the simplified electrochemical thermal coupling model, meanwhile, the parameters of the battery model influenced by the environment and the aging are accurately identified, and the temperature of the battery is estimated by combining with the SRCKF algorithm. The method improves the adaptability of the battery temperature estimation model under different environments and aging degrees, and effectively reduces the calculated amount of the model on the premise of ensuring the estimation accuracy of the battery temperature estimation model, so that the battery temperature estimation model meets the accurate estimation of the actual vehicle-mounted power battery temperature state.
Drawings
Fig. 1 is a flowchart of the lithium ion battery internal temperature online estimation method based on the electrothermal coupling model.
Fig. 2 is a graph showing the results of estimating the internal temperature of the battery under BJDST conditions at different aging levels, wherein the SOH is 100% from top to bottom, and the SOH is 90%.
Fig. 3 is a graph showing the results of estimating the internal temperature of the battery at different ambient temperatures, wherein the graph shows the results of-20 deg.c, 0 deg.c, 20 deg.c and 40 deg.c from top to bottom.
In fig. 2 and 3, the Experimental Tc is the actual Experimental battery internal temperature, the formulation Tc is the battery internal temperature estimated value, the temperature is the temperature, and the Time is the Time.
FIG. 4 is a graph showing the results of estimating the internal temperature of a battery by using three different algorithms, EKF, SRCKF and PF; the error comparison graphs of the temperature Tc estimated data of the battery with three different algorithms of EKF, SRCKF and PF and the actual experimental battery with three different algorithms of EKF, SRCKF and PF are respectively from top to bottom;
In the figure, EKF is an extended kalman filter algorithm (extended KALMAN FILTER), srkf is an srkf algorithm, PF is a particle filter algorithm (PARTICLE FILTER), and Experimental data is actual experimental battery internal temperature data.
Detailed Description
For a better description of the objects, technical solutions and advantages of the present invention, the present invention will be further described with reference to the following specific examples.
Example 1
The method for estimating the internal temperature of the lithium ion battery on line based on the electrothermal coupling model can be applied to terminal equipment such as an electric automobile battery management system, and the flow of estimating the internal temperature of the lithium ion battery provided by the embodiment is shown in fig. 1, and specifically comprises the following steps:
(1) S1-1: obtaining electrochemical parameters and physical parameters of a lithium ion battery; the electrochemical parameters of the lithium ion battery comprise solid phase and liquid phase maximum lithium ion concentration, solid phase and liquid phase lithium ion diffusion coefficients and solid phase and liquid phase conductivities; the physical parameters include battery size parameters, electrode thickness, specific heat capacity.
S1-2: acquiring charging and discharging data of a lithium ion single battery: performing charge and discharge test and cyclic aging test on the lithium ion battery at the full temperature of-20 ℃ to 40 ℃ and collecting charge and discharge data of the lithium ion battery monomer, wherein the charge and discharge data are shown in table 1; the lithium ion battery monomer charge and discharge data comprise voltage, current, surface temperature and tab temperature data.
Table 1 experimental recorded data
| Current (A) | Voltage (V) | Surface temperature (. Degree. C.) | Tab temperature (. Degree. C.) |
| 5.9970 | 3.4886 | 20.0 | 20.0 |
| 5.9995 | 3.5745 | 20.0 | 20.0 |
| 5.9995 | 3.5918 | 20.0 | 20.0 |
| 5.9995 | 3.6015 | 20.0 | 20.0 |
| 5.9995 | 3.6089 | 20.0 | 20.0 |
| …… | …… | …… | …… |
| 5.8816 | 3.7648 | 22.5 | 22.1 |
| 5.8816 | 3.7651 | 22.3 | 22.1 |
| 5.8816 | 3.7651 | 22.5 | 22.1 |
| 5.8804 | 3.7655 | 22.5 | 22.1 |
| 5.8779 | 3.7655 | 22.5 | 21.1 |
| …… | …… | …… | …… |
| 5.5431 | 3.9273 | 23.5 | 24.7 |
| 5.5431 | 3.9276 | 23.3 | 24.9 |
| 5.5419 | 3.9279 | 23.3 | 24.7 |
| 5.5406 | 3.9282 | 23.5 | 24.7 |
| 5.5394 | 3.9282 | 23.5 | 24.7 |
(2) Extremely simple electrochemical model and single battery thermal model: on the basis of an average electrode model, only the part of open-circuit voltage is reserved, a complex equation of positive and negative electrode overpotential and liquid phase potential is simplified into a polynomial equation, and an extremely simple electrochemical model is reconstructed; the established single battery thermal model comprises a heat generation model and a heat transfer model, wherein a simplified Bernardi equation is adopted as the heat generation model, and a double-state centralized parameter heat model is adopted as the heat transfer model;
S2-1: the solid-phase lithium ion diffusion equation deduced based on the average electrode model is:
；
Representing the cross section of the battery Axial directionThe solid-phase lithium ion concentration at the moment,The radial dimensions of the particles are indicated,The active diffusion coefficient of solid-phase lithium ions;
end voltage expression of the average electrode model:
；；
Is the anion transfer coefficient of the polymer, Is a gas constant which is a function of the gas,The temperature of the unit cell is indicated,、、Is the thickness of the diaphragm, the positive electrode and the negative electrode,For the effective conductivity of the converted electrolyte ions,AndRespectively represent the internal resistance and the area of the current collecting plate,The concentration of lithium ions is represented by the formula,、Respectively the positive and negative electrode potentials,、The average value of the current density products of the positive electrode and the negative electrode respectively,Is the specific surface area of the electrode active material,、The lithium ion concentrations of the positive electrode and the negative electrode respectively,In the event of a current flow,To exchange current density;
S2-2: the radius equidistant dividing uniform discrete is adopted for simplifying the solid-phase lithium ion diffusion equation: independent variable of solid-phase lithium ion diffusion equation Divided intoThe equal spacing of the solid particles isThenWherein, the method comprises the steps of, wherein,Is the radius of the particles of the positive and negative electrode materials,Is the radial dimension of the solid particles, whereinI represents the i-th solid particle; then willThe difference quotient is processed and the difference quotient is processed,Represent the firstThe lithium ion concentration in the solid particles is obtained, and a simplified solid-phase lithium ion diffusion equation is obtained:
，；
Wherein, Is the concentration of the solid-phase lithium ions,Representing the first distance from the center of the solid phase particleThe concentration of lithium ions in the individual solid particles,Represent the firstThe concentration of lithium ions in the individual solid particles,Is the specific surface area of the positive electrode active material,Is the effective diffusion coefficient of positive lithium ions,Is a function of the faraday constant,Represents the concentration of lithium ions in the center of the solid phase spherical particles,Representing an equivalent spacing from the center of the solid phase particles ofLithium ion concentration in the solid particles of (a);
S2-3: simplifying the sum of the positive and negative overpotential and the liquid phase potential of the simplified average electrode model into seven-degree polynomials: parameters of the extremely simple electrochemical model are obtained through a parameter identification method, polynomial fitting is carried out on the parameters, polynomial coefficients are obtained, and the extremely simple electrochemical model is obtained:
；
Wherein the method comprises the steps of Is the coefficient of the polynomial,，Is the sum of the positive and negative electrode overpotential and the liquid phase potential,Is the temperature of the unit cell.
S2-4: in the established single battery thermal model, bernardi heat generation equation expression is as follows:
；
The expression of the dual-state centralized parameter thermal model is as follows:
；
Wherein, Generating heat power for a unit volume of the battery; The heat capacity of the battery is obtained; is the thermal resistance between the interior and the surface of the battery; the heat capacity of the battery surface shell; Is the thermal resistance between the surface of the battery and the external environment; 、 And The internal temperature of the battery, the surface of the battery and the ambient temperature of the battery, respectively; For the battery terminal voltage to be the same, Is the battery open circuit voltage.
(3) Based on the extremely simple electrochemical model and the single battery thermal model obtained in the step (2), discretizing and expressing a solid-phase lithium ion diffusion equation of the extremely simple electrochemical model and the single battery thermal model to obtain a system state space equation and a measurement equation:
step one: the specific process of discretizing the extremely simple electrochemical model comprises the following steps:
s3-1: the terminal voltage equation of the extremely simple electrochemical model is:
Represents the terminal voltage of the extremely simple electrochemical model, Is the sum of the positive and negative electrode overpotential and the liquid phase potential;
S3-2: since the overpotential, the liquid phase potential difference and the ohmic voltage are all independent of the lithium ion concentration on the solid phase surface in the terminal voltage equation and are functions of the working current of the battery, the measurement equation is expressed as follows according to the terminal voltage equation of the polar electrochemical model by adopting the description of y:
；
The sum of the positive and negative overpotential and the liquid phase potential of the simplified average electrode model is obtained;
S3-3: the solid-phase lithium ion diffusion equation of the extremely simple electrochemical model is as follows:
；
Discretizing a solid phase diffusion equation based on an extremely simple electrochemical model to obtain a state variable in the system Sum coefficient matrix：
；
；
；
；
Is the concentration of the solid-phase lithium ions,Is the solid-phase diffusion coefficient of the positive electrode,Is the radius of the positive electrode solid-phase lithium ion particles,Is the sum of the liquid phase potential difference and the overpotential,As a result of the ohmic voltage,Is thatThe sum of the liquid phase potential difference and the overpotential at the moment,Is thatOhmic voltage at time.
Step two: in the established single battery thermal model, the Bernardi heat generation equation discretization expression is:
；
Wherein, Is the firstGenerating heat power inside the battery; in the event of a current flow, Is the firstStep current; Is the first Step battery terminal voltage; Is the first Step battery open circuit voltage; As the internal temperature of the battery, Is the firstInternal temperature of the step cell.
The discretized expression of the two-state centralized parameter thermal model is as follows:
；
Wherein, The heat capacity of the battery is obtained; is the thermal resistance between the interior and the surface of the battery; the heat capacity of the battery surface shell; Is the thermal resistance between the surface of the battery and the external environment; 、 And The internal temperature of the battery, the surface of the battery and the ambient temperature of the battery,Is the firstThe surface temperature of the step battery is equal to the surface temperature of the step battery,Is the firstThe internal temperature of the step battery is equal to the temperature of the battery,Is the firstThe heat generation power inside the step battery,Is the firstThe temperature of the environment outside the step is,Is thatIs the inverse of the number of (a),Is thatIs the inverse of (c). .
Step three: the system state space equation and the measurement equation are:
；
Wherein:
；
；
；
；
Wherein: Is the first Step state vector; a is a state transition matrix; b is a system control matrix; Is the first Controlling the amount of steps; Is the first +1 Step measurement state vector; in order to have a measurement noise matrix, Is the firstA state vector of the step; Is the first And observing the surface temperature of the battery.
S4-1: the online identification process of the extremely simple electrochemical model by adopting a genetic algorithm is as follows:
Is provided with AndRespectively representing a terminal voltage simulation value and an experimental value of a polar electrochemical model, wherein the evaluation index of the genetic algorithm individual is thatError function of (2)The expression is:；
S4-2: the process of carrying out on-line parameter identification on the two-state centralized parameter thermal model by adopting a recursive least square algorithm is as follows:
The parameter vector of the dual-state centralized parameter thermal model is ；
The observation vector is:；
；
Then ，
Wherein,For the heat capacity of the battery,Is the heat capacity of the battery surface shell,To provide thermal resistance between the interior and the surface of the cell,To provide thermal resistance between the cell surface and the external environment,Is the firstThe output of the surface temperature of the step battery,Is the firstThe temperature output quantity of the internal part of the step battery,Is the firstThe surface temperature of the step battery is equal to the surface temperature of the step battery,In time steps.
The parameters of the established extremely simple electrochemical model and the two-state centralized parameter thermal model are identified, and a plurality of unknown parameters in the model are obtained so as to solve the model.
(5) Based on the system state space equation and the measurement equation in the step (3), the SRCKF algorithm is integrated into the lithium ion battery temperature estimation: and taking the terminal voltage and the open-circuit voltage output by the polar electrochemical model as the input of a single battery thermal model, adopting Bernardi heat generation equation to realize the calculation of the internal heat generation power of the battery, realizing the estimation of the internal and external temperature of the battery based on the battery heat transfer model and the SRCKF algorithm, feeding back the estimated internal temperature of the battery to the polar electrochemical model, updating the electrochemical parameters of the lithium ion battery, and realizing the coupling of the terminal voltage and the open-circuit voltage.
The step of integrating the SRCKF algorithm into the temperature estimation of the lithium ion battery is as follows:
s5-1: initializing: initializing state vectors separately Error covariance matrix/>Process noise matrix/>And measuring noise matrix/>；
S5-2: the prediction process comprises the following steps: calculating state volume pointsAnd the corresponding weight thereof:
；
；
；
Wherein: by/> Decomposition to square root/>；/>Is the square root of the error covariance matrix; for/> Step, system state quantity corresponding to each volume point; /(I)For/>A plurality of volume points; /(I)Is the dimension of the system state vector; /(I)Is an identity matrix, and the weight of each volume point is/>；
Propagation volume point:
；
Wherein: Is a system process function; /(I) Predicting a state quantity corresponding to each volume point;
Calculating a state quantity predictor for a system ：
；
Calculating state quantity error covariance matrix square root predicted value：/>
；
；
Wherein: Orthogonal triangular decomposition is carried out on the state quantity predicted value matrix; /(I) Is the square root of the covariance matrix of the process noise,/>Is a state vector deviation matrix;
S5-3: the correction process comprises the following steps:
Performing measurement update and calculating a measurement predicted value:
；
Wherein: reconstructing a state vector corresponding to the volume point for the correction stage;
Calculating the volume point propagated through the measurement equation ：
；
Wherein,For/>Controlling the amount of steps; /(I)For/>Volume point propagated by measurement equation corresponding to each volume point,/>；
Calculating a predicted value of the measured state：
；
Calculating the square root of the innovation measurement error covariance:
；
；
；
Wherein: for the square root of the innovation measure error covariance,/> For measuring covariance matrix square root of noise,/>A bias matrix for the measurement vector; /(I)For/>The corresponding measurement equation of the volume points propagates the volume points,；
Calculating a cross covariance matrix：
；
State variablesFirst/>State variables of the steps; /(I)
Updating Kalman gain：
；
Updating state quantity：
；
Represents the/>Measuring the observed value of the state quantity step by step;
updating the square root of the state quantity error covariance matrix:
。
Based on the above-mentioned process of integrating the srkf algorithm into the temperature estimation flow of the lithium ion battery, the internal temperature estimation results of the lithium ion battery obtained in this embodiment under different aging degrees are shown in fig. 2, the battery internal temperature estimation results under different environmental temperatures are shown in fig. 3, and it can be seen from fig. 2 and 3 that the internal temperature estimation method of the lithium ion battery provided by the invention can realize accurate temperature estimation under different environmental temperatures, different aging degrees and complex working conditions, and the error is within 1 ℃, so that the adaptability is better and the precision is higher.
The internal temperature change of the battery is highly nonlinear, and comparison of estimation results obtained by the on-line estimation method of the internal temperature of the lithium ion battery based on the electrothermal coupling model, which are different in algorithm only (EKF algorithm, PF algorithm and SRCKF algorithm), can be known, because the EKF algorithm is suitable for the nonlinear problem of partial linearization, the estimation performance is worst although the calculation efficiency of the EKF algorithm is highest. And the estimation precision of the SRCKF algorithm and the PF algorithm is good, wherein the estimation precision of the SRCKF algorithm is highest. So that for highly nonlinear systems, the error becomes easily large. The PF algorithm can more effectively deal with the non-linearity problem, and its estimation error is highly correlated with the number of particles, thereby possibly increasing the computational complexity. The SRCKF algorithm can adapt to certain degree of nonlinearity and has higher numerical stability. Meanwhile, compared with the PF algorithm, the calculation load of the system can be remarkably reduced. In conclusion, the lithium ion battery internal temperature online estimation method based on the electrothermal coupling model improves the adaptability of the battery temperature estimation model under different environments and aging degrees, and effectively reduces the calculated amount of the model on the premise of ensuring the estimation accuracy of the battery temperature estimation model, so that the battery temperature online estimation method based on the electrothermal coupling model meets the accurate estimation of the actual vehicle-mounted power battery temperature state.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the scope of the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted equally without departing from the spirit and scope of the technical solution of the present invention.
Claims (6)
1. The lithium ion battery internal temperature online estimation method based on the electrothermal coupling model is characterized by comprising the following steps of:
(1) The electrochemical parameters and physical parameters of the lithium ion battery are obtained, the lithium ion battery is subjected to charge and discharge test and cyclic aging test under the condition of the full temperature of minus 20 ℃ to 40 ℃, and the charge and discharge data of the lithium ion battery monomer are collected; the physical parameters comprise battery size parameters, electrode thickness and specific heat capacity; the electrochemical parameters of the lithium ion battery comprise the maximum lithium ion concentration of a solid phase and a liquid phase, the lithium ion diffusion coefficient of the solid phase and the liquid phase, and the conductivity of the solid phase and the liquid phase;
the lithium ion battery monomer charge and discharge data comprise voltage, current, surface temperature and tab temperature data;
(2) Based on the average electrode model, only a part of the open-circuit voltage is reserved on the basis of the average electrode model to construct an extremely simple electrochemical model, and a single battery thermal model is built;
The construction of the extremely simple electrochemical model specifically comprises the following steps:
S2-1: the solid-phase lithium ion diffusion equation deduced from the average electrode model is:
c s (x, r, t) represents the solid-phase lithium ion concentration at the time t in the x-axis direction on the cross section of the battery, r represents the radial dimension of the particles, and D s is the effective diffusion coefficient of the solid-phase lithium ions;
end voltage expression of the average electrode model:
Alpha a is an anion transfer coefficient, R is a gas constant, T is the temperature of a single battery, delta sep、δp、δn is the thickness of a diaphragm, a positive electrode and a negative electrode, k eff is the effective conductivity of electrolyte ions after conversion, R f and M respectively represent the internal resistance and the area of a current collecting plate, Represents the concentration of lithium ions, U p、Un is the potential of the positive electrode and the negative electrode respectively,/>The average value of the current density products of the positive electrode and the negative electrode respectively, a s is the specific surface area of the electrode active material,/>The lithium ion concentration of the anode and the cathode respectively, I is current, and j 0 is exchange current density;
S2-2: the solid-phase lithium ion diffusion equation in S2-1 is simplified by equally dividing and uniformly dispersing the radius: dividing an argument R of a solid-phase lithium ion diffusion equation into M r solid particles, wherein an equal space is Δr=r s/Mr, then R i =i×Δr, wherein R s is a positive and negative electrode material particle radius, and R i is a radial dimension of the solid particles, wherein i=1, 2,3,..; c s (i) is then subjected to a difference quotient treatment, c s (i) represents the lithium ion concentration in the ith solid particle, resulting in a simplified solid phase lithium ion diffusion equation:
wherein c ss is the solid-phase lithium ion concentration, Represents the concentration of lithium ions in the M r th solid particle from the center of the solid particle,/>The concentration of lithium ions in the M r -1 solid particles is represented, a s,p is the specific surface area of the positive electrode active material, D s,p is the effective diffusion coefficient of positive electrode lithium ions, F is Faraday constant, c s (0) represents the concentration of lithium ions in the center of the solid particles, and c s (1) represents the concentration of lithium ions in the solid particles with an equal distance delta r from the center of the solid particles;
S2-3: simplifying the sum of the positive and negative overpotential and the liquid phase potential of the simplified average electrode model into seven-degree polynomials: parameters of the extremely simple electrochemical model are obtained through a parameter identification method, polynomial fitting is carried out on the parameters, polynomial coefficients are obtained, and the extremely simple electrochemical model is obtained:
y＝k1*T7+k2*T6+k3*T5+k4*T4+k5*T3+k6*T2+k7*T+k8；
where kN is a polynomial coefficient, n=1, 2,3,..8, y is the sum of positive and negative overpotential and liquidus potential, and T is the temperature of the cell;
the single battery thermal model comprises a heat generation model and a heat transfer model, wherein the heat generation model adopts Bernardi heat generation equation expression:
the heat transfer model adopts a double-state centralized parameter thermal model expression:
Wherein I is current; t is the internal temperature of the battery; q c is the heat-generating power of the unit volume of the battery; c c is the heat capacity of the battery; r c is the thermal resistance between the interior and the surface of the battery; c air is the heat capacity of the battery surface case; r air is the thermal resistance between the surface of the battery and the external environment; t c、Ts and T air are the internal temperature of the battery, the surface of the battery and the ambient temperature of the battery, respectively; u is the battery terminal voltage, E oc is the battery open circuit voltage;
(3) Discretizing and expressing the extremely simple electrochemical model and the thermal model of the single battery to obtain a system state space equation and a measurement equation;
Discretizing expression of a very simple electrochemical model, which specifically comprises the following steps:
s3-1: the terminal voltage equation of the extremely simple electrochemical model is:
U(t)＝Up-Un+y；
u (t) represents the terminal voltage of the polar electrochemical model, and y is the sum of the positive and negative electrode overpotential and the liquid phase potential;
S3-2: according to a terminal voltage equation of the polar-simple electrochemical model, the obtained measurement equation is expressed as:
U(t)＝Up-Un+y；
S3-3: the solid-phase lithium ion diffusion equation of the extremely simple electrochemical model is as follows:
Discretizing a solid phase diffusion equation based on a polar electrochemical model to obtain a state variable x k and a coefficient matrix A k in the system:
C s is solid-phase lithium ion concentration, D s,p is positive solid-phase diffusion coefficient, R p is radius of positive solid-phase lithium ion particles, SOC is battery charge state, y 1,p is sum of liquid-phase potential difference and overpotential, y 2,p is ohmic voltage, y 1,p (t) is sum of liquid-phase potential difference and overpotential at time t, and y 2,p (t) is ohmic voltage at time t;
(4) Based on the charge and discharge data of the lithium ion single battery, carrying out parameter identification on the established extremely simple electrochemical model by using a genetic algorithm: let U sim and U exp respectively represent the simulation value and experimental value of terminal voltage of the extremely simple electrochemical model, the individual evaluation index of the genetic algorithm is the error function error (i) of U, and the expression is: error (i) =abs (U sim-Uexp);
Performing on-line parameter identification on the double-state centralized parameter thermal model by adopting a recursive least square algorithm;
(5) Based on a system state space equation and a measurement equation, estimating the internal temperature of the lithium ion battery by adopting an SRCKF algorithm, and then feeding back the estimated internal temperature of the battery to the electrochemical model, updating the electrochemical parameters of the electrochemical model, so as to realize the coupling of the electrochemical model and the thermal model of the single battery.
2. The method for online estimation of internal temperature of a lithium ion battery based on an electrothermal coupling model according to claim 1, wherein the Bernardi heat generation equation discretization expression is:
Wherein Q c (k) is the internal heat generation power of the kth battery; i (k) is the kth step current; u (k) is the voltage of the battery terminal of the kth step; e oc is the battery open circuit voltage, E oc (k) is the k-th battery open circuit voltage; t is the internal temperature of the battery, and T (k) is the internal temperature of the battery in the kth step;
the discretized expression of the two-state centralized parameter thermal model is as follows:
Wherein C c is the heat capacity of the battery; r c is the thermal resistance between the interior and the surface of the battery; c air is the heat capacity of the battery surface case; r air is the thermal resistance between the surface of the battery and the external environment; t s (k) is the surface temperature of the kth cell, T c (k) is the internal temperature of the kth cell, Q c (k) is the internal heat generation power of the kth cell, T air (k) is the external ambient temperature of the kth cell, Is the reciprocal of T c (k),Is the inverse of T s (k).
3. The method for online estimation of internal temperature of lithium ion battery based on electrothermal coupling model according to claim 2, wherein the system state space equation and the measurement equation are:
Wherein:
Wherein: x k is the kth step state vector; a is a state transition matrix; b is a system control matrix; u k is the control amount of the kth step; z k+1 is the k+1st measurement state vector; v k is a state vector with a measurement noise matrix, X k+1 is the (k+1) th step; t s,k is the observed quantity of the surface temperature of the battery in the k step.
4. The method for online estimation of internal temperature of lithium ion battery based on electrothermal coupling model according to claim 2, wherein the process of online parameter identification of the two-state centralized parameter thermal model by adopting a recursive least square algorithm is as follows:
the parameter vector of the two-state centralized parameter thermal model is theta= [ alpha beta gamma ] T;
the observation vector is
Then
Wherein, C C is the heat capacity of the battery, C air is the heat capacity of the shell of the surface of the battery, R C is the heat resistance between the inside and the surface of the battery, R air is the heat resistance between the surface of the battery and the external environment, T s (k) is the output of the temperature of the surface of the battery at the kth step, T s (k+1) is the temperature of the surface of the battery at the kth+1 step, and Deltat is the time step.
5. The method for online estimation of internal temperature of a lithium ion battery based on an electrothermal coupling model according to claim 1, wherein the step of estimating the internal temperature of the lithium ion battery by using an srkf algorithm comprises: and taking the terminal voltage and the open-circuit voltage output by the polar electrochemical model as the input of a single battery thermal model, calculating the internal heat generation power of the battery by adopting Bernardi heat generation equation, and then combining the battery heat transfer model with the SRCKF algorithm to estimate the internal temperature of the battery.
6. The method for estimating the internal temperature of the lithium ion battery on line based on the electrothermal coupling model according to claim 3, wherein estimating the internal temperature of the lithium ion battery by using the SRCKF algorithm specifically comprises:
s5-1: initializing: initializing state vectors separately An error covariance matrix P k, a process noise matrix Q k, and a measurement noise matrix R k;
S5-2: the prediction process comprises the following steps: calculate state volume point X j,k and its corresponding weight:
Wherein: p k obtains the square root S k;Sk as the square root of the error covariance matrix through Cholesky decomposition; x j,k is the system state quantity corresponding to each volume point in the kth step; ζ 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,uk) is a system procedure function; predicting a state quantity corresponding to each volume point;
Calculating a state quantity predictor for a system
Calculating state quantity error covariance matrix square root predicted value
Wherein: tria () represents an orthogonal triangular decomposition of the state quantity predictor matrix; s Q,k is the square root of the covariance matrix of the process noise,Is a state vector deviation matrix;
S5-3: the correction process comprises the following steps:
Performing measurement update and calculating a measurement predicted value:
wherein: x j,k+1 is the corresponding state vector of the reconstructed volume point in the correction stage;
The volume point Z j,k+1 propagated through the measurement equation is calculated:
Zj,k+1＝h(Xj,k+1,uk+1)；
Wherein u k+1 is the control quantity of the (k+1) th step; z j,k+1 is the volume point that the measurement equation corresponding to the j-th volume point propagates, j=1, 2,..2 n;
Calculating a predicted value of the measured state
Calculating the square root of the innovation measurement error covariance:
SR,k＝chol(Rk)；
Szz,k+1＝Tria([γk+1SR,k])；
Wherein: s zz,k+1 is the square root of the covariance of the innovation measurement error, S R,k is the square root of the covariance matrix of the measurement noise, and gamma k+1 is the deviation matrix of the measurement vector; z j,k+1 is the volume point that the measurement equation corresponding to the j-th volume point propagates, j=1, 2,..2 n;
Calculating a cross covariance matrix P xz,k+1:
x k+1 is the state variable of step k+1;
updating Kalman gain K k+1:
Updating state quantity
Z k+1 represents the observation of the state quantity measured at step k+1;
updating the square root of the state quantity error covariance matrix:
Sk+1＝Tria([xk+1γk+1γk+1 Kk+1Szz,k+1])。
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