CN115856644B - Modeling method of energy storage battery - Google Patents
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- CN115856644B CN115856644B CN202310173175.1A CN202310173175A CN115856644B CN 115856644 B CN115856644 B CN 115856644B CN 202310173175 A CN202310173175 A CN 202310173175A CN 115856644 B CN115856644 B CN 115856644B
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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 batteries 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 being in a second temperature range, and the first temperature range and the second temperature range are different. According to the invention, under the condition that the internal temperatures of the energy storage batteries are different, the energy storage battery models with different structures can be constructed, and the estimation accuracy of the SOC and 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 include one single battery or a plurality of single batteries. In order to accurately estimate the running states of the energy storage battery, such as the state of charge (SOC) and the state of health (SOH), 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 aspects of characteristic description, identification method, estimation precision and the like, and generally, the models of the energy storage battery comprise three types, namely: electrochemical models, black box models, and equivalent circuit models.
In the working state, the energy storage battery is affected by factors such as the operating environment, the charge and discharge state, and the functional aging, so that the factors are also required to be considered in the process of constructing the model of the energy storage battery. For example, the battery characteristics under different temperature conditions are different, and as the temperature decreases, the capacity of any one of the battery cells of the energy storage battery may decrease in a nonlinear manner. When the energy storage battery is in a temperature working condition below 0 ℃, the diffusion rate of lithium ions is seriously reduced, so that the concentration polarization voltage is increased. Meanwhile, precipitation of lithium ions on the surface of the negative electrode increases the impedance of the solid electrolyte interface film (solid electrolyteinterface, SEI), and the ion transport capacity in the electrolyte decreases, 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 can be reduced, the battery capacity of the energy storage battery can be rapidly attenuated when the battery is operated in a high-temperature environment (such as higher than 50 ℃), and the cycle life of the battery is about 1/2 of that of the battery at normal temperature. In addition, the coulombic efficiency from the energy storage cell may exhibit a non-linear change with a change in temperature. Moreover, at different temperatures, the arrangement of lithium ions in the crystal lattice is affected, which changes the entropy coefficient of the energy storage battery, thereby causing a change in the open circuit voltage.
The above-mentioned temperature-dependent characteristics of the energy storage battery will result in 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 to estimate the SOC and SOH of the energy storage battery under different temperature conditions, the accuracy of the estimation result is likely to be low.
Furthermore, the internal temperature and the ambient temperature of the energy storage battery also have certain difference, and certain heat is generated when the energy storage battery works, so that the internal temperature of the energy storage battery is always higher than the ambient temperature at the moment, and the state and the characteristics of the energy storage battery cannot be truly reflected based on the energy storage battery model established by 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 of different internal temperatures of the energy storage battery and can improve the estimation accuracy of the SOC and 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 batteries 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 being in 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.
The modeling method of the energy storage battery further comprises the following steps: the first temperature range and the second temperature range are determined from electrochemical impedance spectra of the energy storage cell at different internal temperatures.
The modeling method of the energy storage battery, wherein the first temperature range is a temperature range of [0 ℃ and 50 ℃).
The modeling method of the energy storage battery, wherein the step of establishing the first energy storage battery model comprises the following steps:
determining a plurality of candidate equivalent circuit models according to electrochemical impedance spectrums 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 within the first temperature range.
The modeling method of the energy storage battery, wherein the step of determining the first energy storage battery model 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.
According to the modeling method of the energy storage battery, the parameter fitting error of the first equivalent circuit model is lower than 100%, and the integral fitting error value of the first equivalent circuit model is lower than 1%.
The modeling method of the energy storage battery, wherein the second temperature range is a temperature range lower than 0 ℃ or a temperature range higher than or equal to 50 ℃.
The modeling method of the energy storage battery, wherein the step of obtaining the electrochemical impedance spectrums of the energy storage battery at different internal temperatures comprises the following steps:
charging and discharging the energy storage battery to a first SOC value;
placing the energy storage battery in an incubator, and measuring electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder;
electrochemical impedance spectra of the energy storage cells at different internal temperatures are plotted based on the measured data.
According to the modeling method of the energy storage battery, provided by the invention, the internal temperature of the energy storage battery is always higher than the environment temperature at the moment by considering that certain heat is generated when the energy storage battery works, and 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, so that the state and the characteristics of the energy storage battery can be truly reflected. And selecting the first energy storage battery model or the second energy storage battery model according to the internal temperature of the energy storage battery to estimate the SOC and SOH of the energy storage battery, so that the accuracy of an estimation result can be improved.
Drawings
FIG. 1 is a flow chart of a modeling method of an energy storage battery according to an embodiment;
FIG. 2 is a detailed flow chart of step 101 of FIG. 1;
FIG. 3 is an EIS diagram of an embodiment of an energy storage cell with an internal temperature of-10 ℃;
FIG. 4 is an EIS diagram of an embodiment of an energy storage cell with an internal temperature of 25 ℃;
FIG. 5 is an EIS diagram of an embodiment of an energy storage cell with an internal temperature of 50 ℃;
FIG. 6 is a schematic diagram showing 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 of an embodiment;
FIG. 8 is a schematic diagram showing a comparison of a calculated value of the real part of the impedance in the second-order RC model calculated in one embodiment with an actual value of the real part of the impedance of the energy storage battery obtained from an actually measured EIS;
FIG. 9 is a schematic diagram showing a comparison between a calculated value of a negative imaginary part of an impedance in a second order RC model and an actual value of the negative imaginary part of the impedance of an energy storage battery obtained according to an actually measured EIS;
FIG. 10 is a flowchart of a method for creating a second energy storage battery model according to an embodiment;
FIG. 11 is a schematic diagram showing a comparison of an experimental discharge curve and a simulated discharge curve in a case where the second temperature range is a temperature range lower than 0 ℃ in an embodiment;
FIG. 12 is a schematic diagram showing a comparison of an experimental discharge curve and a simulated discharge curve in the case where the second temperature range is equal to or higher than 50℃in an embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Embodiments of the present invention provide a method of modeling an energy storage battery that may include a single cell or a plurality of single cells. The following embodiments are exemplified by an example in which the energy storage battery includes a plurality of unit cells.
The energy storage battery comprises a plurality of single batteries, namely a lithium iron phosphate battery pack used for power grid energy storage under an 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, electrochemical impedance spectroscopy (electrochemical impedancespectroscopy, EIS) may be employed to characterize the change in characteristics of the energy storage cell with internal temperature. The method for acquiring EIS is also called ac 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 with different frequencies are input into the black box system, only one 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 excitation signal of energy storage battery as current
The response signal is voltage +.>
The transfer function is the impedance +.>
. Wherein the current->
Sinusoidal signals with smaller amplitude are adopted, so that oxidation reaction and 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 the formula (1):
as can be seen from equation (1), the EIS is actually a graph of impedance data at different frequencies for an energy storage cell.
In some embodiments, obtaining electrochemical impedance spectra of an energy storage cell at different internal temperatures includes: charging and discharging the energy storage battery to a first SOC value; placing an energy storage battery in an incubator, and measuring electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder; electrochemical impedance spectra of the energy storage cells at different internal temperatures are plotted based on the measured data. Illustratively, as shown in FIG. 2, step 101 may include steps 201 through 206.
And 203, placing the energy storage battery in an incubator for standing for 5 hours so that the internal temperature of the energy storage battery is equal to the ambient temperature.
And 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 by a Nyquist plot (as shown in fig. 3-5), which is a frequency characteristic plot that may represent the transfer function versus angular frequencyωIs a variation of (c). For an energy storage cell, the transfer function is an impedance function. In the present embodiment, the real part of impedance is used
The negative imaginary part of the impedance +.>
As the vertical axis of the Nyquist plot. For example, from the experimental data obtained in steps 201 to 206, an electrochemical impedance spectrum of the energy storage cell at a temperature between-10 ℃ and 70 ℃ can be obtained. Exemplary, the first SOC value is 40% SOC, and when the energy storage battery is discharged to 40% SOC, the acquired EIS with the internal temperature of the energy storage battery of-10 ℃ is shown in FIG. 3, the acquired EIS with the internal temperature of the energy storage battery of 25 ℃ is shown in FIG. 4, and the acquired internal temperature of the energy storage battery isEIS at 50℃is shown in FIG. 5.
The electrochemical impedance spectrum of the battery is obtained by analysis at the temperature of between-10 ℃ and 70 ℃, 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 is continuously distributed in the whole complex impedance plane graph, and the equivalent circuit model characteristics are obvious. The electrochemical impedance spectroscopy 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 higher than 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 severely reduced, so that the concentration difference resistance and polarization resistance are increased. And, the negative electrode has lithium ion precipitation to increase SEI film resistance. And the lithium ion transfer 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 battery internal temperature, the greater the impedance thereof. Thus, in case that the internal temperatures of the energy storage batteries are different, it is necessary to build different energy storage battery models.
In some embodiments, the first energy storage cell model is an energy storage cell model in which an internal temperature of the energy storage cell 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 in 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 ℃) according to the analysis described above. The second temperature range may be a temperature range of less than 0 ℃ or a temperature range of 50 ℃ or more, and the following examples exemplify a temperature range of less than 0 ℃ or a temperature range of 50 ℃ or more.
If the internal temperature of the energy storage battery is in the first temperature range, the EIS morphology of the energy storage battery has stronger capacity resistance and prominent equivalent alternating current impedance characteristics, so that an equivalent alternating current impedance model can be adopted as an energy storage battery model at normal temperature, and it can be understood that the equivalent alternating current impedance model can also be 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 the EIS morphology obtained by actual measurement, namely the integral fitting error between the EIS of the equivalent circuit model and the EIS obtained by actual measurement cannot be too large to deviate from the EIS obtained by 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 complex, if the established impedance model is complex, more parameters to be identified are generated, the calculated amount is increased, errors are accumulated in the subsequent parameter identification, and therefore the equivalent circuit model with smaller complexity is selected on the premise of meeting the accuracy requirement.
In this case, in step 201, the method of establishing the first energy storage battery model may include steps 401 to 403.
And 401, determining a plurality of candidate equivalent circuit models according to the electrochemical impedance spectrum of the internal temperature of the energy storage battery within a first temperature range.
For example, a plurality of candidate equivalent circuit models may be determined according to the internal temperature of the energy storage battery as the morphology of the electrochemical impedance spectrum in the first temperature range, and the plurality of candidate equivalent circuit models may be respectively a Rint model, a Thevenin model, a second-order RC model, a third-order RC model, a PNGV model, and a GNL model. In general, the number of parallel connection of RC determines the number of arc and inflection points of EIS, and if a portion smaller than 0 occurs in EIS, it is considered to add an inductance element.
Step 402, obtaining impedance data of the energy storage battery, and obtaining 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 plurality of candidate equivalent circuit models may be imported into impedance spectrum fitting software to obtain electrochemical impedance spectrums of the plurality of candidate equivalent circuit models. For example, the impedance spectrum fitting software may be ZSimpWin software commonly used in the electrochemical field, where the ZSimpWin software may fit the parameter value and EIS of the selected equivalent circuit model according to the input impedance data of the energy storage battery obtained by actual measurement and the selected equivalent circuit model, and obtain an integral fitting error (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 the ZSimpWin software by using a nonlinear least square method, the deviation degree of the EIS of the equivalent alternating current impedance model and the measured EIS is represented, and the smaller the ChSq value is, the better the integral fitting effect is shown. The parameter fitting error is represented by rel.std.error in zsampwin software, which can be interpreted as a relative standard error, and the parameter fitting error indicates whether the model has research significance, and when the parameter fitting error is large, for example, the parameter fitting error exceeds 100%, the model loses its applicability. Therefore, an equivalent circuit with the ChSq value smaller than 1% and the parameter fitting error not exceeding 100% can be selected as an alternating current impedance model of the energy storage battery at normal temperature.
Step 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 of the energy storage battery with the internal temperature of the energy storage battery being in the first temperature range.
For example, the 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, the overall fit error value and the parameter fit error of the plurality of candidate equivalent circuit models may be obtained according to the fit result of the zsimwin software, and the first energy storage battery model may be determined according to the overall fit error value and the parameter fit error of the plurality of candidate equivalent circuit models. For example, the first energy storage battery model is a first equivalent circuit model, 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%.
The following examples exemplify the construction of an equivalent circuit model of an energy storage battery at 40% soc with an internal temperature of 25 ℃ by taking the discharge of the energy storage battery to 40% soc as an example.
According to step 401, the EIS profile of the energy storage battery is analyzed, and as shown in fig. 4, the EIS of the energy storage battery has no part smaller than 0 at 40% soc and an internal temperature of 25 ℃, so that the equivalent circuit model does not consider adding an inductive element, but only considers a circuit composed of a capacitor C and a resistor R. Although the EIS shown in fig. 4 shows only one inflection point and one circular arc, a first-order RC circuit, a second-order RC circuit, and a 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 models.
According to step 402, EIS measured data of the energy storage battery at 40% soc and an internal temperature of 25 ℃ is imported into zsompwin software, and a first-order RC circuit, a second-order RC circuit and a third-order RC circuit are respectively selected for fitting. As shown in FIG. 6, the ChSq values of the three circuit models show 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, so that the second-order RC circuit and the third-order RC circuit have good fitting effects.
And finally, taking the parameter fitting error and the overall fitting error into consideration, and selecting a reasonable equivalent circuit model. For example, a second order RC circuit is selected as the first energy storage battery model based on consideration of the parameter fitting error and the overall fitting error. For example, the second-order RC equivalent circuit model may be as shown in fig. 7, where in fig. 7, OCV is an open circuit voltage, R0 is an ohmic internal resistance of the battery, I is a discharge current, U is a terminal voltage, R1 and C1 are respectively a polarization resistance and a capacitance, R2 and C2 are respectively a concentration difference resistance and a capacitance, and T is a 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) and the polarization capacitor C1 (T) are connected in parallel. The second RC loop comprises a concentration difference resistor R2 (T) and a concentration difference capacitor C2 (T), and the concentration difference resistor R2 (T) and the concentration difference capacitor C2 (T) are connected in parallel.
The following examples take the example of discharging an energy storage battery to 50% soc and an internal temperature of 40 ℃ as an example, validating a second order RC circuit model for an energy storage battery at 50% soc and an internal temperature of 40 ℃.
First, the real and negative imaginary expressions of the second-order RC circuit model are obtained as shown in equation (2).
In the formula (2), the amino acid sequence of the compound,
and->
The real part and the negative imaginary part of the impedance in the second-order RC circuit model are respectively +.>
Is of angular frequency, R 0 Resistance value of ohm internal resistance, R 1 C is the resistance of the polarization resistor 1 For the capacitance value of the polarized capacitor, R 2 Is the resistance value of the concentration difference resistor, C 2 Is the capacitance value of the concentration difference capacitor.
Then, substituting the parameter values fitted by the ZsimpWin software of the energy storage battery under the conditions of 50% SOC and the internal temperature of 40 ℃ 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. Meanwhile, the real part and the negative imaginary part of the impedance of the energy storage battery are obtained according to the EIS obtained through actual measurement.
The calculated values of the real part and the negative imaginary part of the impedance in the calculated second-order RC model are compared 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, and 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 identical to 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 close to the real situation of the energy storage battery, so that higher accuracy can be achieved, and the first energy storage battery model can be the second-order RC model.
Under the condition that the internal temperature of the energy storage battery is in the second temperature range, the electrochemical impedance spectrum morphology of the energy storage battery completely loses the rule, and the characteristic of an equivalent circuit model does not appear. Based on this, in some embodiments, an electrochemical model that more reflects the true characteristics of the interior of the energy storage battery, can accurately describe the electrochemical reaction of the interior of the energy storage battery at extreme temperatures, and a model that couples the electrochemical model to the thermal model can be established in view of the temperature effects 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 be based on a chemical reaction mechanism in the energy storage battery to analyze the chemical characteristics of the energy storage battery, so that partial differential equations of electrodes and electrolyte of the energy storage battery are established, voltage and current of the battery can be accurately measured, and distribution conditions (such as electrochemical reaction rate, liquid phase potential, solid phase potential, liquid phase lithium ion concentration and solid phase lithium ion concentration) of physical quantities in the battery can be highly reduced and simulated.
The thermal model can analyze the heat generation, the heat dissipation rate and the temperature characteristics of lithium ions based on the principle of the heat generation mechanism and the heat transfer theory of the lithium ion battery, and establish the internal temperature field of the lithium ion battery. The thermal model can be classified into a centralized mass model, a one-dimensional model, a two-dimensional model, and a three-dimensional model according to dimension division. The centralized quality model may treat the battery as a mass point 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 may reflect the distribution of the internal temperature of the battery over the battery cross-section. 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, so as to reflect the distribution condition of the internal temperature of the battery along with the whole battery. Based on the internal temperature distribution condition of the energy storage battery, the size and the shape of the energy storage battery are larger, and the internal heat generation and heat dissipation of the battery are uneven.
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 701, establishing a quasi two-dimensional model of the energy storage battery based on the porous electrode theory and the concentrated solution theory as an electrochemical model.
Step 703, constructing a second energy storage battery model based on the quasi two-dimensional model and the three-dimensional thermal model.
The second energy storage battery model is mainly constructed based on a heat transfer and generation mechanism in an electrochemical model and a thermal model.
In step 701, equations required to construct an electrochemical model of an energy storage cell 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 amino acid sequence of the compound,
the current density is lithium ion reaction; i.e 0 Exchanging current density for the electrode reaction; />
、/>
Respectively the reaction conversion coefficients of the anode and the cathode electrodes; r is a gas constant, F is a Faraday constant; t is the temperature; />
Is an overvoltage.
In the formula (4), the amino acid sequence of the compound,
for solid phase potential->
Is of liquid phase potential, U d Is the steady state open circuit voltage of the electrode.
The liquid-phase lithium ion concentration equation is shown in formula (5).
In the formula (5), the amino acid sequence of the compound,
for the volume fraction of the liquid phase>
Is the average volume concentration of the liquid phase; />
Is the effective diffusion coefficient of lithium ion liquid phase; />
Is the migration quantity of lithium ions; t is time; x is the width from the negative electrode.
The boundary condition of the formula (5) is shown as the formula (6).
In 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 amino acid sequence of the compound,
is the average volume concentration of the solid phase; />
Is the solid phase diffusion coefficient; r is the active material radial direction.
The boundary condition of the formula (7) is shown in the formula (8).
In the formula (8), the amino acid sequence of the compound,
an effective reaction area per unit volume of the electrode; />
Is the radial radius of the active material.
The liquid phase potential equation is shown in formula (9).
In the formula (9), the amino acid sequence of the compound,
effective ionic conductivity for the electrolyte; />
Is effective diffusion conductivity of lithium ions.
The boundary condition of the formula (9) is shown as the formula (10).
The solid phase potential equation is shown in formula (11).
In the formula (11), the amino acid sequence of the compound,
is the effective conductivity of the electrode active material solid phase.
The boundary condition of the expression (11) is shown in the expression (12).
In the formula (12), the amino acid sequence of the compound,
operating current for the battery; a is the electrode area; />
、/>
The solid phase effective conductivities of the active materials of the negative electrode and the positive electrode respectively.
In the formula (13), the amino acid sequence of the compound,
the width of the positive electrode; />
Is the width of the negative electrode.
In step 702, the calculation formula required for constructing the three-dimensional thermal model of the energy storage battery includes an energy conservation equation and reversible heat q per unit area rev Is calculated by the formula of (1) and the irreversible heat q per unit area irrev Calculation formula, calculation formula of heat generation rate q of energy storage battery and heat generation quantity q of heat release process Al,Cu Is a calculation formula of (2).
The energy conservation equation is shown in formula (14).
In the formula (14), the amino acid sequence of the compound,
is the density of the energy storage battery; c (C) p Specific heat for the energy storage cell; lambda (lambda) x 、λ y 、λ z The heat conductivity coefficients of the energy storage battery in the x, y and z directions are respectively; q is the rate of heat generation of the energy storage cell.
Reversible heat per unit area q rev The calculation formula of (2) is shown as formula (15).
Irreversible heat q per unit area irrev The calculation formula of (2) is shown as formula (16).
The calculation formula of the heat generation rate q of the energy storage battery is shown as formula (17).
Heat generation q in exothermic process Al,Cu The calculation formula of (2) is shown as formula (18).
In the formula (18), the amino acid sequence of the compound,
the heating value of the tab; />
The volume of the lug; />
Is the resistance of the tab.
The boundary condition of the lithium ion thermal model is formula (19).
In the formula (19), the amino acid sequence of the compound,
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 a mechanism of heat generation and transfer between the electrochemical model and the three-dimensional thermal model. The second energy storage cell model is verified as follows.
And (3) combining the formulas (3) to (19), inputting the calculated temperature of the energy storage battery into an electrochemical model in real time, and simultaneously 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 a thermal model, so as to achieve the aim of coupling the electrochemical model and the thermal model.
The second energy storage battery model is verified, and the verification step comprises the following steps: the method comprises the steps of adopting a variable current discharging working condition as an experimental working condition of an energy storage battery of a power grid; measuring terminal voltage data of the energy storage battery under the current discharge condition, and acquiring an experimental discharge curve according to the measured terminal voltage data; acquiring terminal voltage data of the energy storage battery under a variable voltage discharge working condition calculated according to the second energy storage battery model, and acquiring a simulated discharge curve according to the calculated terminal voltage data; and comparing the experimental discharge curve with the simulated discharge curve.
According to the above verification step, in the case where the second temperature range is a temperature range lower than 0 ℃, the results of comparing the experimental discharge curve and the simulated discharge curve are shown in fig. 11. In the case where the second temperature range is a temperature range equal to or higher than 50 ℃, the results of comparing the experimental discharge curve and the simulated discharge curve are shown in fig. 12. From fig. 11 and 12, it can be seen that the measured terminal voltage value 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 in the second temperature range, and is suitable for the energy storage working condition of the power grid and high in accuracy.
In summary, according to the modeling method of the energy storage battery, provided by the invention, the internal temperature of the energy storage battery is always higher than the environment temperature at the moment by considering that certain heat is generated when the energy storage battery works, and 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, so that the state and the characteristics of the energy storage battery can be truly reflected. And selecting the first energy storage battery model or the second energy storage battery model according to the internal temperature of the energy storage battery to estimate the SOC and SOH of the energy storage battery, so that the accuracy of an estimation result can be improved.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means 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 present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. 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 present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
Claims (5)
1. 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 batteries 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 being in 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;
constructing a second energy storage battery model based on the quasi two-dimensional model and the three-dimensional thermal model;
the modeling method further includes: 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 step of establishing a first energy storage battery model comprises the following steps:
determining a plurality of candidate equivalent circuit models according to electrochemical impedance spectrums 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 electrochemical impedance spectrums of the candidate equivalent circuit models and electrochemical impedance spectrums of the internal temperature of the energy storage battery within the first temperature range;
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 an incubator, and measuring electrochemical impedance spectrum of the energy storage battery by adopting a battery comprehensive tester and a multi-path data recorder;
electrochemical impedance spectra of the energy storage cells at different internal temperatures are plotted based on the measured data.
2. The method of modeling an energy storage cell as claimed in claim 1, wherein the first temperature range is a temperature range of [0 ℃,50 ℃).
3. The method of modeling an energy storage cell according to claim 1, wherein the step of determining the first energy storage cell model based on the electrochemical impedance spectra of the plurality of 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.
4. A method of modeling an energy storage battery according to claim 3, 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%.
5. The modeling method of an energy storage battery according to claim 1, wherein the second temperature range is a temperature range lower than 0 ℃ or a temperature range equal to or higher than 50 ℃.
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