CN115856644A - Energy storage battery modeling method - Google Patents
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Abstract
The invention provides a modeling method of an energy storage battery, which comprises the following steps: acquiring electrochemical impedance spectrums of the energy storage battery at different internal temperatures; establishing a first energy storage battery model and a second energy storage battery model according to electrochemical impedance spectrums of the energy storage battery at different internal temperatures; the first energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a first temperature range; the second energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a second temperature range, and the first temperature range is different from the second temperature range. According to the invention, under the condition that the internal temperatures of the energy storage batteries are different, energy storage battery models with different structures can be constructed, and the estimation precision of the SOC and the SOH of the energy storage batteries can be improved.
Description
Technical Field
The invention relates to the technical field of battery testing, in particular to a modeling method of an energy storage battery.
Background
The energy storage battery may comprise one single battery or a plurality of single batteries. In order to accurately estimate the operating states of the energy storage battery, such as the state of charge (SOC) and the state of health (SOH), of the energy storage battery, an accurate energy storage battery model needs to be established first. In the process of modeling the energy storage battery, different models are different in the aspects of characteristic description, identification method, estimation accuracy and the like, and generally, the models of the energy storage battery include three types, which are respectively: an electrochemical model, a black box model, and an equivalent circuit model.
In the working state, the energy storage battery is influenced by factors such as the operating environment, the charging and discharging state, the functional aging and the like, and therefore the factors need to be considered in the process of establishing the model of the energy storage battery. For example, the battery characteristics under different temperature conditions are different, and the capacity of any single battery in the energy storage battery is reduced nonlinearly with the reduction of the temperature. When the energy storage battery is under the working condition of temperature below 0 ℃, the diffusion rate of lithium ions is seriously reduced, so that the concentration polarization voltage is increased. Meanwhile, the precipitation of lithium ions on the surface of the negative electrode increases the resistance of a Solid Electrolyte Interface (SEI) film and decreases the ion transport capacity in the electrolyte, resulting in an increase in ohmic polarization voltage. Along with the increase of the internal temperature of the energy storage battery, the charge and discharge power of the battery is also reduced, the battery capacity of the energy storage battery is rapidly attenuated when the energy storage battery works in a high-temperature environment (for example, higher than 50 ℃) for a long time, and the cycle life of the energy storage battery is about 1/2 of that of the energy storage battery at normal temperature. Furthermore, the coulombic efficiency of the slave energy storage battery shows a non-linear change with the change of the temperature. Moreover, at different temperatures, the arrangement of lithium ions in the crystal lattice can be affected, which changes the entropy change coefficient of the energy storage cell, and further causes the open-circuit voltage to change.
The above-mentioned characteristics of the energy storage battery varying with temperature will cause that the existing SOC algorithm cannot accurately estimate the SOC of the energy storage battery under different temperature conditions. That is, if the same model is used for estimating the SOC and SOH of the energy storage battery under different temperature conditions, the accuracy of the estimation result is likely to be low.
Moreover, the internal temperature of the energy storage battery is different from the ambient temperature, so that the energy storage battery generates certain heat when working, the internal temperature of the energy storage battery is often higher than the ambient temperature at the moment, and the state and the characteristics of the energy storage battery cannot be truly reflected on the basis of an energy storage battery model established based on the ambient temperature.
Disclosure of Invention
The invention aims to provide a modeling method of an energy storage battery, which can construct energy storage battery models with different structures under the condition that the internal temperatures of the energy storage battery are different, and can improve the estimation precision of the SOC and the SOH of the energy storage battery.
A method of modeling an energy storage battery, comprising:
acquiring electrochemical impedance spectrums of the energy storage battery at different internal temperatures;
establishing a first energy storage battery model and a second energy storage battery model according to electrochemical impedance spectrums of the energy storage battery at different internal temperatures; the first energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a first temperature range, and the first energy storage battery model is a first equivalent circuit model; the second energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a second temperature range, the second energy storage battery model comprises an electrochemical model and a thermal model, and the first temperature range and the second temperature range are different;
the step of establishing a second energy storage battery model comprises the following steps:
taking a quasi-two-dimensional model of the energy storage battery established based on a porous electrode theory and a concentrated solution theory as an electrochemical model;
establishing a three-dimensional thermal model capable of reflecting the internal temperature distribution condition of the energy storage battery;
and constructing the second energy storage battery model based on the quasi two-dimensional model and the three-dimensional thermal model.
The modeling method of the energy storage battery further comprises the following steps: determining the first temperature range and the second temperature range according to electrochemical impedance spectrums of the energy storage battery at different internal temperatures.
The modeling method of the energy storage battery is characterized in that the first temperature range is a temperature range of [0 ℃,50 ℃).
The modeling method of the energy storage battery comprises the following steps of:
determining a plurality of candidate equivalent circuit models according to the electrochemical impedance spectrum of the internal temperature of the energy storage battery in the first temperature range;
acquiring impedance data of the energy storage battery, and acquiring electrochemical impedance spectrums of the candidate equivalent circuit models according to the impedance data of the energy storage battery;
and determining the first energy storage battery model according to the electrochemical impedance spectrums of the candidate equivalent circuit models and the electrochemical impedance spectrums of the internal temperature of the energy storage battery in the first temperature range.
The modeling method of the energy storage battery, wherein the step of determining the first energy storage battery model according to the electrochemical impedance spectrums of the candidate equivalent circuit models and the electrochemical impedance spectrums of the internal temperature of the energy storage battery within the first temperature range specifically includes:
and determining the first energy storage battery model according to the parameter fitting errors and the overall fitting error values of the candidate equivalent circuit models.
The modeling method of the energy storage battery includes that a parameter fitting error of the first equivalent circuit model is lower than 100%, and an overall fitting error value of the first equivalent circuit model is smaller than 1%.
The modeling method of the energy storage battery is characterized in that the second temperature range is a temperature range lower than 0 ℃ or a temperature range greater than or equal to 50 ℃.
The modeling method of the energy storage battery comprises the following steps of obtaining electrochemical impedance spectrums of the energy storage battery at different internal temperatures:
charging and discharging the energy storage battery to a first SOC value;
placing the energy storage battery in a constant temperature box, and measuring the electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder;
and (4) drawing electrochemical impedance spectrums of the energy storage battery at different internal temperatures based on the measured data.
According to the modeling method of the energy storage battery, provided by the invention, the first energy storage battery model and the second energy storage battery model are constructed according to the internal temperature of the energy storage battery, and the state and the characteristic of the energy storage battery can be truly reflected, considering that the energy storage battery can generate certain heat when working and the internal temperature of the energy storage battery is always higher than the ambient temperature at the moment. The first energy storage battery model or the second energy storage battery model is selected according to the internal temperature of the energy storage battery to estimate the SOC and the SOH of the energy storage battery, so that the accuracy of the estimation result can be improved.
Drawings
FIG. 1 is a flow chart of a method of modeling an energy storage battery according to an embodiment;
FIG. 2 is a detailed flowchart of step 101 in FIG. 1;
FIG. 3 is an EIS diagram of the internal temperature of the energy storage battery at-10 ℃ according to an embodiment;
FIG. 4 is an EIS diagram of an energy storage battery with an internal temperature of 25 ℃ according to an embodiment;
FIG. 5 is an EIS diagram of an energy storage battery with an internal temperature of 50 ℃ according to an embodiment;
FIG. 6 is a diagram illustrating a comparison of ChSq values of a first order RC circuit model, a second order RC circuit model, and a third order RC circuit model according to an embodiment;
FIG. 7 is a block diagram of a second order RC circuit model according to one embodiment;
FIG. 8 is a schematic diagram illustrating a comparison between a calculated value of the real part of the impedance in the calculated second-order RC model and an actual value of the real part of the impedance of the energy storage battery obtained according to the actually measured EIS in an embodiment;
FIG. 9 is a schematic diagram illustrating a comparison between a calculated value of the negative imaginary part of the impedance in the calculated second-order RC model and an actual value of the negative imaginary part of the impedance of the energy storage battery obtained according to the actually measured EIS in one embodiment;
FIG. 10 is a flowchart of a second method for modeling a second energy storage battery according to an embodiment;
FIG. 11 is a graph illustrating a comparison of an experimental discharge curve and a simulated discharge curve for a second temperature range of less than 0 degrees Celsius for one embodiment;
fig. 12 is a graph showing a comparison between an experimental discharge curve and a simulated discharge curve in a case where the second temperature range is a temperature range equal to or higher than 50 ℃.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a modeling method of an energy storage battery, and the energy storage battery can comprise a single battery or a plurality of single batteries. The following embodiments are exemplified by an example in which the energy storage battery includes a plurality of unit batteries.
The energy storage battery comprises a plurality of single batteries, and is a lithium iron phosphate battery pack used for power grid energy storage under the energy storage working condition. As shown in fig. 1, the modeling method of the energy storage battery of the present embodiment includes steps 101 to 102.
In some embodiments of the present invention, the,electrochemical Impedance Spectroscopy (EIS) can be used to characterize the behavior of energy storage cells as a function of internal temperature. The method for obtaining EIS is also called as alternating current impedance method, and is a frequency domain measurement method. The principle is that the energy storage battery is regarded as a black box system, disturbance signals under different frequencies are input into the black box system, a unique response corresponding to the frequency excitation signal can be obtained, and the relation between the excitation signal and the response signal is represented by a transfer function. Setting the excitation signal of the energy storage battery as the current
In response to the signal being voltage>
The transfer function is then impedance->
. Wherein the current->
The sinusoidal signal with smaller amplitude is adopted, so that the oxidation reaction and the reduction reaction can be alternately carried out in the energy storage battery, and the polarization phenomenon of the energy storage battery is prevented from continuously developing. The mathematical expression is shown as formula (1):
from equation (1), the EIS is actually a graph of impedance data at different frequencies for an energy storage battery.
In some embodiments, obtaining electrochemical impedance spectra of the energy storage cell at different internal temperatures comprises: charging and discharging the energy storage battery to a first SOC value; placing the energy storage battery in a constant temperature box, and measuring the electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder; and drawing electrochemical impedance spectrums of the energy storage battery at different internal temperatures based on the measured data. Illustratively, as shown in fig. 2, step 101 may include steps 201 to 206.
And 203, placing the energy storage battery in a constant temperature box for standing for 5 hours so that the internal temperature of the energy storage battery is equal to the ambient temperature.
And step 204, measuring the electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder.
And step 206, deriving all EIS test data, and drawing electrochemical impedance spectrums of the energy storage battery at different internal temperatures according to all EIS test data.
In some embodiments, the electrochemical impedance spectrum of the energy storage cell may be represented using a Nyquist plot (as shown in FIGS. 3-5), which is a frequency plot that may represent the transfer function versus angular frequencyωA change in (c). For energy storage cells, the transfer function is an impedance function. In the present embodiment, the real part of impedance is used
On the horizontal axis of the Nyquist plot, the negative imaginary part of the impedance->
The vertical axis of the Nyquist diagram. For example, according to the experimental data obtained in steps 201 to 206, an electrochemical impedance spectrum of the energy storage battery at a temperature of-10 ℃ to 70 ℃ can be obtained. Illustratively, the first SOC value is 40% SOC, and when the energy storage cell is discharged to 40% SOC, the EIS with an internal temperature of the energy storage cell of-10 ℃ is obtained as shown in fig. 3, the EIS with an internal temperature of the energy storage cell of 25 ℃ is obtained as shown in fig. 4, and the EIS with an internal temperature of the energy storage cell of 50 ℃ is obtained as shown in fig. 5.
The electrochemical impedance spectrum of the battery at the temperature of-10 ℃ to 70 ℃ is analyzed, and under the condition that the internal temperature of the energy storage battery is in the temperature range of [0 ℃ and 50 ℃), the electrochemical impedance spectrum of the energy storage battery has obvious capacitive reactance arc (refer to figure 4), and the electrochemical impedance spectrum presents continuous distribution in the whole complex impedance plane diagram, and the equivalent circuit model characteristic is obvious. The electrochemical impedance spectrum morphology of the energy storage cell has completely lost its regularity when the internal temperature of the energy storage cell is below 0 ℃ and equal to or above 50 ℃ (see fig. 3 and 5, respectively).
In addition, in the case where the internal temperature of the energy storage battery is lower than 0 ℃, the diffusion rate of lithium ions is seriously decreased, so that the concentration resistance and the polarization resistance are increased. Also, the negative electrode has lithium ion precipitation to increase the SEI film resistance. And the lithium ion transport rate in the electrolyte decreases, so that the ohmic polarization resistance increases. Therefore, when the energy storage battery is discharged to the first SOC value, the lower the internal temperature of the battery, the greater its impedance. Therefore, under the condition that the internal temperatures of the energy storage batteries are different, different energy storage battery models need to be established.
102, establishing a first energy storage battery model and a second energy storage battery model according to electrochemical impedance spectrums of the energy storage batteries at different internal temperatures.
In some embodiments, the first energy storage battery model is an energy storage battery model in which the internal temperature of the energy storage battery is within a first temperature range. The second energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a second temperature range.
In some embodiments, the first temperature range and the second temperature range may be determined from electrochemical impedance spectra of the energy storage cell at different internal temperatures. For example, in some embodiments, the first temperature range may include a temperature range of [0 ℃,50 ℃ C.), based on the analysis described above. The second temperature range may be a temperature range lower than 0 ℃ or a temperature range equal to or higher than 50 ℃, and the following examples exemplify the second temperature range as a temperature range lower than 0 ℃ or a temperature range equal to or higher than 50 ℃.
If the internal temperature of the energy storage battery is within the first temperature range, the EIS morphology of the energy storage battery has stronger capacitive reactance and has prominent equivalent alternating current impedance characteristics, so that an equivalent alternating current impedance model can be used as an energy storage battery model at normal temperature, and the equivalent alternating current impedance model can be understood to be also called an equivalent circuit model.
The equivalent circuit model of the energy storage battery is established to meet three conditions. The first condition is: the EIS morphology of the equivalent circuit model needs to be similar to that of the EIS obtained through actual measurement, namely the overall fitting error between the EIS of the equivalent circuit model and the EIS obtained through actual measurement cannot be too large and cannot deviate from the EIS obtained through actual measurement. The second condition is: the equivalent circuit model has applicability in a first temperature range. The third condition is: the equivalent circuit model cannot be too complex, if the established impedance model is complex, more parameters to be identified can be generated, the calculated amount can be increased, errors can be accumulated in subsequent parameter identification, and therefore the equivalent circuit model with low complexity needs to be selected on the premise of meeting the accuracy requirement.
In this case, in step 201, the method for establishing the first energy storage battery model may include steps 401 to 403.
Step 401, determining a plurality of candidate equivalent circuit models according to an electrochemical impedance spectrum of which the internal temperature of the energy storage battery is within a first temperature range.
For example, a plurality of candidate equivalent circuit models, which may be a Rint model, a Thevenin model, a second order RC model, a third order RC model, a PNGV model, and a GNL model, respectively, may be determined for the morphology of the electrochemical impedance spectrum in the first temperature range according to the internal temperature of the energy storage battery. Generally, the number of parallel-connected RCs determines the number of arcs and inflection points of the EIS, and if the EIS has a portion smaller than 0, it is considered to add an inductance element.
And 402, acquiring impedance data of the energy storage battery, and acquiring electrochemical impedance spectrums of a plurality of candidate equivalent circuit models according to the impedance data of the energy storage battery.
For example, the actually measured impedance data of the energy storage battery and the candidate equivalent circuit models may be imported into impedance spectrum fitting software to obtain electrochemical impedance spectra of the candidate equivalent circuit models. For example, the impedance spectrum fitting software may be a ZSimpWin software commonly used in the electrochemical field, and the ZSimpWin software may fit a parameter value and an EIS of a selected equivalent circuit model according to input impedance data of the energy storage battery obtained through actual measurement and the selected equivalent circuit model, and obtain a chi squared (ChSq) value and a parameter fitting error of the EIS.
The ChSq value of the EIS is the fitting deviation of fitting data and actual data calculated by ZsimWin software by using a nonlinear least square method, the deviation degree of the EIS of the equivalent alternating current impedance model and the actually measured EIS is represented, and the smaller the ChSq value is, the better the overall fitting effect is. The parameter fitting error is expressed by Rel.std.error in ZsimWin software, and can be interpreted as relative standard error, the parameter fitting error indicates whether the model has research significance, and when the parameter fitting error is large, such as the parameter fitting error exceeds 100%, the model loses the applicability. Therefore, an equivalent circuit with the ChSq value less than 1% and the parameter fitting error not more than 100% can be selected as the alternating current impedance model of the energy storage battery at normal temperature.
And 403, determining a first energy storage battery model according to the electrochemical impedance spectrums of the candidate equivalent circuit models and the electrochemical impedance spectrums with the internal temperature of the energy storage battery within a first temperature range.
For example, a plurality of candidate equivalent circuit models EIS fitted by the ZSimpWin software may be compared with the actually measured EIS to determine the first energy storage battery model.
In some embodiments, overall fitting error values and parameter fitting errors of the candidate equivalent circuit models may be obtained according to a fitting result of the ZSimpWin software, and the first energy storage battery model may be determined according to the overall fitting error values and parameter fitting errors of the candidate equivalent circuit models. For example, the first energy storage battery model is a first equivalent circuit model, a parameter fitting error of the first equivalent circuit model is lower than 100%, and an overall fitting error value of the first equivalent circuit model is smaller than 1%.
The following examples are exemplified by the case where the energy storage battery is discharged to 40% SOC with an internal temperature of 25 ℃ and the case where the energy storage battery is constructed with an equivalent circuit model in the case where the energy storage battery has a 40% SOC and an internal temperature of 25 ℃.
According to step 401, the EIS profile of the energy storage cell is analyzed, and as shown in fig. 4, the EIS of the energy storage cell has no portion less than 0 in the case of 40% soc and an internal temperature of 25 ℃, so the equivalent circuit model considers only the circuit composed of the capacitor C and the resistor R without adding an inductance element. Although the EIS shown in fig. 4 shows only one inflection point and one arc, the first-order RC circuit, the second-order RC circuit, and the third-order RC circuit may be selected as a plurality of candidate equivalent circuit models in consideration of the accuracy of the finally determined equivalent circuit model.
According to step 402, EIS measured data of the energy storage battery at 40% SOC and an internal temperature of 25 ℃ is introduced into ZsimWin software, and a first-order RC circuit, a second-order RC circuit and a third-order RC circuit are selected and fitted. The ChSq values of the three circuit models are shown in fig. 6, and it can be known that the overall fitting error value of the first-order RC circuit is higher than that of the second-order RC circuit and the third-order RC circuit, and the ChSq values of the second-order RC circuit and the third-order RC circuit are different, which indicates that the second-order RC circuit and the third-order RC circuit have better fitting effect.
And finally, considering the parameter fitting error and the integral fitting error, and selecting a reasonable equivalent circuit model. For example, a second-order RC circuit is selected as the first energy storage battery model according to consideration of the parameter fitting error and the overall fitting error. For example, the second-order RC equivalent circuit model can be shown in fig. 7, OCV is open-circuit voltage, R0 is ohmic internal resistance of the battery, I is discharge current, U is terminal voltage, R1 and C1 are polarization resistance and capacitance, respectively, R2 and C2 are concentration resistance and capacitance, respectively, and T is battery temperature. The second-order RC equivalent circuit comprises a first RC loop and a second RC loop, and the first RC loop and the second RC loop are connected in series. The first RC loop comprises a polarization resistor R1 (T) and a polarization capacitor C1 (T), and the polarization resistor R1 (T) is connected with the polarization capacitor C1 (T) in parallel. The second RC loop comprises a concentration resistor R2 (T) and a concentration capacitor C2 (T), and the concentration resistor R2 (T) and the concentration capacitor C2 (T) are connected in parallel.
The following examples, which take the example of the energy storage cell being discharged to 50% SOC and the internal temperature being 40 ℃, verify the second order RC circuit model of the energy storage cell at 50% SOC and the internal temperature being 40 ℃.
Firstly, obtaining a real part expression and a negative imaginary part expression of a second-order RC circuit model, wherein the expression is shown as a formula (2).
In the formula (2), the reaction mixture is,
and &>
Real part and negative imaginary part of the impedance in a second order RC circuit model, respectively>
Is the angular frequency, R 0 Resistance value of ohmic internal resistance, R 1 Is the resistance value of the polarization resistor, C 1 Is the capacitance value of the polarization capacitor, R 2 Is the resistance value of the concentration resistor, C 2 Is the capacitance value of the concentration capacitor.
Then, substituting the parameter values fitted by ZsimPn software under the condition that the internal temperature of the energy storage battery is 40 ℃ and the SOC is 50 percent into the expressions of the real part and the negative imaginary part of the impedance to obtain the calculated values of the real part and the negative imaginary part of the second-order RC model. And meanwhile, the real part and the negative imaginary part of the impedance of the energy storage battery are obtained according to the EIS obtained by actual measurement.
Comparing the calculated values of the real part and the negative imaginary part of the impedance in the second-order RC model with the actual values of the real part and the negative imaginary part of the impedance of the energy storage battery obtained according to the actually measured EIS, the results are shown in fig. 8 and 9. It can be known that the calculated values of the real part and the negative imaginary part of the impedance in the calculated second-order RC model are substantially consistent with the actual values of the real part and the negative imaginary part of the impedance of the energy storage battery obtained according to the actually measured EIS. Therefore, in the first temperature range, the second-order RC model is closer to the real condition of the energy storage battery, so that the accuracy can be higher.
And under the condition that the internal temperature of the energy storage battery is in the second temperature range, the electrochemical impedance spectrum appearance of the energy storage battery completely loses the regularity thereof, and the characteristics of the equivalent circuit model do not appear. Based on this, in some embodiments, an electrochemical model which can better reflect the real characteristics inside the energy storage battery, can accurately describe the electrochemical reaction inside the energy storage battery at the extreme temperature can be adopted, and a model of coupling the electrochemical model and the thermal model can be established in consideration of the influence of the temperature on the characteristics of the energy storage battery. It is understood that the second energy storage cell model includes an electrochemical model and a thermal model. The electrochemical model and the thermal model are explained below.
The electrochemical model can analyze the chemical characteristics of the energy storage battery based on the chemical reaction mechanism in the energy storage battery, so as to establish partial differential equations of the electrode and the electrolyte of the energy storage battery, further accurately measure the voltage and the current of the battery, and highly reduce and simulate the distribution conditions of physical quantities in the battery (such as the electrochemical reaction rate, the liquid phase potential, the solid phase potential, the liquid phase lithium ion concentration and the solid phase lithium ion concentration).
The thermal model can analyze the heat generation, heat dissipation rate and temperature characteristics of lithium ions based on the heat generation mechanism and the heat transfer theory of the lithium ion battery, and establish a temperature field inside the lithium ion battery. The thermal model may be divided into a lumped mass model, a one-dimensional model, a two-dimensional model, and a three-dimensional model according to the degree of dimension. The lumped mass model may consider the battery as a particle and analyze the average temperature inside the battery. The one-dimensional model can reflect the distribution of the internal temperature of the battery in one direction. The two-dimensional model can reflect the distribution of the internal temperature of the battery on the cross section of the battery. The three-dimensional model can consider the influence of the shape, the size and the external design of the battery on the internal temperature field of the battery, and further reflect the distribution condition of the internal temperature of the battery along with the whole battery. Based on the inside temperature distribution condition of energy storage battery, energy storage battery's size, shape are great, the uneven characteristics of the inside heat production heat dissipation of battery, this application uses the thermal model that adopts three-dimensional model as energy storage battery as the example, carries out the demonstration to second energy storage battery model.
In this case, as shown in fig. 10, the method for establishing the second energy storage battery model in step 102 may include steps 701 to 703:
And step 702, establishing a three-dimensional thermal model capable of reflecting the distribution condition of the internal temperature of the energy storage battery along with the whole distribution.
And 703, constructing a second energy storage battery model based on the quasi two-dimensional model and the three-dimensional thermal model.
Wherein the second energy storage cell model is constructed mainly based on heat transfer and heat generation mechanisms in the electrochemical model and the thermal model.
In step 701, equations required for constructing an electrochemical model of the energy storage battery include an electrochemical reaction rate equation, a liquid-phase lithium ion concentration equation, a solid-phase lithium ion concentration equation, a liquid-phase potential equation, and a solid-phase potential equation.
The electrochemical reaction rate equation is shown in formula (3).
In the formula (3), the reaction mixture is,
is the lithium ion reaction current density; i.e. i 0 Exchanging current density for electrode reactions; />
、/>
Respectively the anode and cathode electrode reaction conversion coefficients; r is a gas constant, and F is a Faraday constant; t is the temperature; />
Is an overvoltage.
In the formula (4), the reaction mixture is,
is at a solid phase potential->
Is liquid phase potential, U d Is the electrode steady state open circuit voltage.
The liquid-phase lithium ion concentration equation is shown in formula (5).
In the formula (5), the reaction mixture is,
is counted by the liquid phase volume and is combined with the blood pressure value>
Is the liquid phase average volume concentration; />
Is the effective diffusion coefficient of the lithium ion liquid phase; />
Is the lithium ion transport number; t is time; x is the width from the cathode.
The boundary condition of formula (5) is shown in formula (6).
In the formula (6), L is the sum of the widths of the positive electrode, the negative electrode and the separator.
The solid-phase lithium ion concentration equation is shown in formula (7).
In the formula (7), the reaction mixture is,
is the solid phase average volume concentration; />
Is the solid phase diffusion coefficient; r is the active material radial direction.
The boundary condition of formula (7) is shown in formula (8).
In the formula (8), the reaction mixture is,
is the effective reaction area of the unit volume of the electrode; />
Is the active material radial radius.
The liquid phase potential equation is shown in formula (9).
In the formula (9), the reaction mixture is,
effective ionic conductivity for the electrolyte; />
The conductivity is effectively diffused for lithium ions.
The boundary condition of formula (9) is shown in formula (10).
The solid phase potential equation is shown in formula (11).
In the formula (11), the reaction mixture is,
is the effective conductivity of the solid phase of the electrode active material.
The boundary condition of formula (11) is shown in formula (12).
In the formula (12), the reaction mixture is,
the working current of the battery; a is the electrode area; />
、/>
The effective conductivity of the solid phase of the active materials of the negative electrode and the positive electrode respectively.
In the formula (13), the reaction mixture is,
is the width of the positive electrode; />
Is the cathode width.
In step 702, the calculation formulas required for constructing the three-dimensional thermal model of the energy storage battery comprise an energy conservation equation and a unit area reversible heat q rev Formula for calculating (a) and irreversible heat per unit area (q) irrev Calculating formula, heat generation rate q of energy storage batteryCalculation formula and heat generation quantity q of heat release process Al,Cu The calculation formula of (2).
The energy conservation equation is shown in equation (14).
In the formula (14), the compound represented by the formula (I),
is the density of the energy storage cell; c p The specific heat of the energy storage battery; lambda [ alpha ] x 、λ y 、λ z The thermal conductivity coefficients of the energy storage battery in the x direction, the y direction and the z direction are respectively; and q is the heat generation rate of the energy storage battery.
Reversible heat per unit area q rev The formula (2) is shown in formula (15).
Irreversible heat per unit area q irrev The formula (2) is shown in equation (16).
The calculation formula of the heat generation rate q of the energy storage battery is as shown in formula (17).
Heat generation quantity q in exothermic process Al,Cu Is represented by equation (18).
In the formula (18), the reaction mixture,
the heat productivity of the tab is ensured; />
Is the volume of the tab; />
Is the resistance of the tab.
The boundary condition of the lithium ion thermal model is equation (19).
In the formula (19), the compound represented by the formula (I),
is the temperature of the fluid surrounding the energy storage cell; />
The surface temperature of the energy storage battery; n is the normal direction; h is the heat transfer coefficient between the surface of the energy storage cell and the surrounding fluid.
As such, the second energy storage cell model may include an electrochemical model and a thermal model in view of the heat generating and transferring mechanism between the electrochemical model and the three-dimensional thermal model. The second energy storage battery model is verified below.
Combining the formulas (3) to (19), inputting the calculated temperature of the energy storage battery into an electrochemical model in real time, and calculating the heat generation rate of the energy storage battery based on the calculated solid-phase potential, liquid-phase potential and lithium ion reaction current density in the electrochemical model and the calculated irreversible heat and reversible heat in the thermal model, thereby achieving the purpose of realizing the coupling of the electrochemical model and the thermal model.
The second energy storage battery model is verified as follows, and the verifying step includes: adopting a variable current discharge working condition as an experimental working condition of the power grid energy storage battery; measuring terminal voltage data of the energy storage battery under the variable current discharge working condition, and acquiring an experimental discharge curve according to the measured terminal voltage data; acquiring terminal voltage data of the energy storage battery under the variable voltage discharging condition, which is obtained by calculation according to the second energy storage battery model, and acquiring a simulated discharging curve according to the calculated terminal voltage data; and comparing the experimental discharge curve with the simulated discharge curve.
According to the above verification procedure, the results of comparing the experimental discharge curve and the simulated discharge curve in the case where the second temperature range is the temperature range lower than 0 ℃ are shown in fig. 11. In the case where the second temperature range is a temperature range equal to or higher than 50 deg.c, the results of comparing the experimental discharge curve with the simulated discharge curve are shown in fig. 12. According to fig. 11 and 12, it can be known that the measured value of the terminal voltage of the energy storage battery substantially matches the predicted value. The second energy storage battery model is established under the condition that the internal temperature of the energy storage battery is within the second temperature range, and the second energy storage battery model is suitable for the energy storage working condition of a power grid and has high accuracy.
In summary, according to the modeling method of the energy storage battery provided by the invention, considering that the energy storage battery generates certain heat when working, so that the internal temperature of the energy storage battery is always higher than the current environmental temperature, the first energy storage battery model and the second energy storage battery model are constructed according to the internal temperature of the energy storage battery, and the state and the characteristic of the energy storage battery can be truly reflected. The first energy storage battery model or the second energy storage battery model is selected according to the internal temperature of the energy storage battery to estimate the SOC and the SOH of the energy storage battery, and the accuracy of an estimation result can be improved.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (8)
1. A modeling method for an energy storage battery, comprising:
acquiring electrochemical impedance spectrums of the energy storage battery at different internal temperatures;
establishing a first energy storage battery model and a second energy storage battery model according to electrochemical impedance spectrums of the energy storage battery at different internal temperatures; the first energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a first temperature range, and the first energy storage battery model is a first equivalent circuit model; the second energy storage battery model is an energy storage battery model with the internal temperature of the energy storage battery within a second temperature range, the second energy storage battery model comprises an electrochemical model and a thermal model, and the first temperature range and the second temperature range are different;
the step of establishing the second energy storage battery model comprises the following steps:
taking a quasi-two-dimensional model of the energy storage battery established based on a porous electrode theory and a concentrated solution theory as an electrochemical model;
establishing a three-dimensional thermal model capable of reflecting the internal temperature distribution condition of the energy storage battery;
and constructing the second energy storage battery model based on the quasi two-dimensional model and the three-dimensional thermal model.
2. The modeling method of an energy storage battery according to claim 1, further comprising: determining the first temperature range and the second temperature range according to electrochemical impedance spectrums of the energy storage battery at different internal temperatures.
3. Method for modelling an energy storage cell according to claim 1 or 2, characterized in that said first temperature range is a temperature range of [0 ℃,50 ℃).
4. The modeling method of an energy storage battery according to claim 3, wherein the step of establishing a first energy storage battery model comprises:
determining a plurality of candidate equivalent circuit models according to the electrochemical impedance spectrum of the internal temperature of the energy storage battery in the first temperature range;
acquiring impedance data of the energy storage battery, and acquiring electrochemical impedance spectrums of the candidate equivalent circuit models according to the impedance data of the energy storage battery;
determining the first energy storage battery model according to the electrochemical impedance spectrums of the candidate equivalent circuit models and the electrochemical impedance spectrums of the internal temperature of the energy storage battery in the first temperature range.
5. The method for modeling an energy storage cell according to claim 4, wherein the step of determining the first energy storage cell model based on the electrochemical impedance spectra of the candidate equivalent circuit models and the electrochemical impedance spectra of the internal temperature of the energy storage cell within the first temperature range specifically comprises:
and determining the first energy storage battery model according to the parameter fitting errors and the overall fitting error values of the candidate equivalent circuit models.
6. The method of claim 5, wherein the parameter fitting error of the first equivalent circuit model is less than 100%, and the overall fitting error of the first equivalent circuit model is less than 1%.
7. The method of modeling an energy storage cell according to claim 2, wherein the second temperature range is a temperature range below 0 ℃ or a temperature range equal to or greater than 50 ℃.
8. The method for modeling an energy storage cell according to claim 1, wherein the step of obtaining electrochemical impedance spectra of the energy storage cell at different internal temperatures comprises:
charging and discharging the energy storage battery to a first SOC value;
placing the energy storage battery in a constant temperature box, and measuring the electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder;
and drawing electrochemical impedance spectrums of the energy storage battery at different internal temperatures based on the measured data.
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