CN111177992B - Battery model based on electrochemical theory and equivalent circuit model and construction method thereof - Google Patents
Battery model based on electrochemical theory and equivalent circuit model and construction method thereof Download PDFInfo
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 claims description 11
- RTAQQCXQSZGOHL-UHFFFAOYSA-N Titanium Chemical compound [Ti] RTAQQCXQSZGOHL-UHFFFAOYSA-N 0.000 claims description 11
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- XGZVUEUWXADBQD-UHFFFAOYSA-L lithium carbonate Chemical compound [Li+].[Li+].[O-]C([O-])=O XGZVUEUWXADBQD-UHFFFAOYSA-L 0.000 description 2
- 229910052808 lithium carbonate Inorganic materials 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 description 1
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Abstract
The embodiment of the invention provides a battery model based on an electrochemical theory and an equivalent circuit model and a construction method thereof, wherein the method comprises the following steps: adopting a first-order RC equivalent circuit model as the topology of a battery model; the improved and simplified Nernst equation, arrhenius equation and Bulter-Volmer equation are used to describe the effect of temperature on the controlled voltage source in the topology, the effect of temperature on the second resistance, and the effect of temperature and multiplying power on the polarization resistance, respectively. The embodiment of the invention obtains the battery model applicable to a wide temperature range and a wide multiplying power range; the method solves the problem that the traditional equivalent circuit model lacks theoretical basis for describing temperature sensitivity and multiplying power sensitivity of parameters, so that model errors are large when the temperature and the multiplying power are changed, provides basis for application of the battery in environments with multiple temperature and multiplying power, and can adapt to the temperature and the multiplying power changes and also give consideration to model precision and model calculation cost.
Description
Technical Field
The invention relates to the technical field of battery modeling, in particular to a battery model based on an electrochemical theory and an equivalent circuit model and a construction method thereof.
Background
In order to cope with the problems of environmental pollution and energy exhaustion, new energy automobiles and new energy rail transit vehicles are being greatly popularized in China. In recent years, lithium ion batteries have become the first choice for vehicle power systems by virtue of their high energy density and long cycle life. Among them, the lithium titanate battery using the lithium titanate material as the negative electrode has more excellent safety, high-rate and low-temperature resistance and ultra-long cycle life than other batteries.
Therefore, for some special application fields, such as the rail traffic field with high requirements on safety and multiplying power characteristics, the lithium titanate battery becomes the best choice.
The battery model serves as a bridge between the internal state of the battery and the output voltage, and is indispensable for battery system development and battery state evaluation. There are two general classes of battery models currently in use: electrochemical models and equivalent circuit models. The electrochemical model explains the chemical reaction inside the battery from the electrochemical mechanism, so that very high model precision can be obtained, but too many model parameters and partial parameters cannot be directly obtained, and the model solving requires very large calculation cost; the equivalent circuit model has the advantages that the model is simple in structure and low in calculation cost, but due to the lack of electrochemical theoretical basis, the influence of temperature and multiplying power on model parameters cannot be accurately described, and therefore the error is large when the temperature and the multiplying power are changed.
Considering that the operation conditions of lithium titanate batteries are often harsh, the method is mainly characterized in that the working environment is changeable in temperature and large in working current, and secondly, the method is considered to be practical, and limited computing resources are considered, therefore, an improved model which can adapt to temperature and multiplying power changes and can also give consideration to model precision and model computing expense is necessary for batteries such as lithium titanate batteries.
Disclosure of Invention
In order to solve the problems in the prior art, the embodiment of the invention provides a battery model based on an electrochemical theory and an equivalent circuit model and a construction method thereof.
In a first aspect, an embodiment of the present invention provides a battery model based on electrochemical theory and an equivalent circuit model, including: adopting a first-order RC equivalent circuit model as the topology of a battery model; the first-order RC equivalent circuit model comprises a controlled voltage source, a second resistor and a resistor-capacitor parallel network formed by a first resistor and a first capacitor which are connected in series; the controlled voltage source represents an Open Circuit Voltage (OCV) determined by a battery SOC, the second resistor represents ohmic internal resistance inside the battery, the first resistor represents polarized internal resistance of the battery, and the first capacitor represents polarized capacitance of the battery; the effect of temperature on the controlled voltage source is described using an improved, simplified Nernst equation, the effect of temperature on the second resistance is described using an improved, simplified Arrhenius equation, and the effect of temperature and multiplying power on the polarization resistance is described using an improved, simplified buter-Volmer equation.
Further, the expression of the modified and simplified Nernst equation is:
U OCV ＝k 1 T+k 2 (2)
wherein U is OCV Represents a controlled voltage source, T represents absolute temperature, k 1 And k 2 Representing the improved and simplified coefficients of the Nernst equation;
the expression of the improved and simplified Arrhenius equation is as follows:
wherein R is 0 Representing the second resistance, p 1 、p 2 And p 3 Representing the improved and simplified coefficients of the Arrhenius equation, T representing absolute temperature;
the expression of the improved and simplified Bulter-Volmer equation is as follows:
wherein R is 1 Representing the internal resistance of polarization, f 1 、f 2 、f 3 And f 4 The modified and simplified coefficient of the Bulter-Volmer equation is represented, T represents absolute temperature, and I represents current.
Further, the product of the polarized internal resistance and the polarized capacitance is a preset time constant.
Further, the method further comprises: respectively acquiring values of the controlled voltage source, the second resistor and the first resistor under a preset typical condition through a preset parameter identification experiment; and respectively utilizing least square fitting to obtain improved and simplified coefficients of the Nernst equation, improved and simplified coefficients of the Arrhenius equation and improved and simplified coefficients of the Bulter-Volmer equation according to values of the controlled voltage source, the second resistor and the first resistor under preset typical conditions.
Further, the obtaining the values of the controlled voltage source, the second resistor and the first resistor under the preset typical conditions through the preset parameter identification experiment respectively includes:
acquiring the value of the controlled voltage source of each typical SOC point by carrying out charge and discharge pulse tests at preset fixed multiplying power, preset SOC intervals and different preset typical temperatures;
calculating the value of the second resistance for each of the representative SOC points according to equation (16):
wherein V is 0 For the battery terminal voltage at the last sampling instant before pulse generation, V 1 The voltage of the battery terminal at the first sampling moment after pulse generation is delta I, and delta I is the magnitude of pulse current;
recording the battery terminal voltage of each typical SOC point by respectively carrying out constant current charge and discharge experiments under a plurality of preset multiplying powers at the preset typical temperature, and calculating the value of the first resistor of each typical SOC point by using the obtained controlled voltage source and the second resistor under the corresponding conditions and using the formula (17):
wherein U is t Representing the battery terminal voltage, and I representing the current.
Further, the obtaining the improved and simplified coefficient of the Nernst equation, the improved and simplified coefficient of the Arrhenius equation, and the improved and simplified coefficient of the buter-Volmer equation by least squares fitting according to the values of the controlled voltage source, the second resistor, and the first resistor under the preset typical conditions respectively includes: obtaining improved and simplified coefficients of the Nernst equation at each typical SOC point through least square fitting according to the value of the controlled voltage source of each typical SOC point at the preset typical temperature; acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in a charging process through least square fitting according to the value of the second resistor at the charging state of each typical SOC point at the preset typical temperature; acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in a discharging process through least square fitting according to the value of the second resistor in the discharging state of each typical SOC point at the preset typical temperature; obtaining improved and simplified coefficients of the Bulter-Volmer equation at each typical SOC point in a charging process through least square fitting according to the values of the first resistor at the charging state of each typical SOC point at the preset typical temperature and at the preset multiplying powers; and obtaining improved and simplified coefficients of the Bulter-Volmer equation under each typical SOC point in the discharging process through least square fitting according to the values of the first resistor under the discharging state of each typical SOC point under the preset typical temperature and the preset multiplying power.
Further, the method further comprises: obtaining the improved and simplified coefficient of the Nernst equation at any SOC point through interpolation operation according to the improved and simplified coefficient of the Nernst equation at each typical SOC point; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the charging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the charging process; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the discharging process; according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the charging process, obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the charging process through interpolation operation; and obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the discharging process.
Further, in performing the pulse test, each pulse test includes 20 of the charge pulses and 20 of the discharge pulses, and a rest time between pulses is 2 hours.
In a second aspect, an embodiment of the present invention provides a battery model based on an electrochemical theory and an equivalent circuit model, where the battery model is constructed by using any one of the above construction methods for a battery model based on an electrochemical theory and an equivalent circuit model.
Further, the battery model includes a lithium titanate battery model.
According to the battery model based on the electrochemical theory and the equivalent circuit model and the construction method thereof, provided by the embodiment of the invention, three electrochemical equations are combined with the equivalent circuit model, and the parameters of the equivalent circuit model under different temperatures and multiplying powers are described by the electrochemical equations; finally, a battery model suitable for a wide temperature range and a wide multiplying power range is obtained; the method solves the problem that the traditional equivalent circuit model lacks theoretical basis for describing temperature sensitivity and multiplying power sensitivity of parameters, so that model errors are large when the temperature and the multiplying power are changed, provides basis for application of the battery in environments with multiple temperature and multiplying power, and can adapt to the temperature and the multiplying power changes and also give consideration to model precision and model calculation cost.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for constructing a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 3 is a diagram showing the accuracy of the improved Nernst equation versus the OCV-temperature relationship in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the accuracy of the improved Arrhenius equation of the present invention versus the R0-temperature relationship;
FIG. 5 is a diagram showing the accuracy of the description of the R1-temperature relationship by the improved Butler-Volmer equation in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 6 is a diagram of the accuracy of the description of the R1-rate relationship by the improved Butler-Volmer equation in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 7 is a schematic diagram showing comparison results of predicted voltage and measured voltage of an FUDS test model at 5 ℃ for a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention;
FIG. 8 is a schematic diagram showing comparison results of predicted voltage and measured voltage of an FUDS test model at 35 ℃ for a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention.
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.
Fig. 1 is a flowchart of a battery model construction method based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention. As shown in fig. 1, the method includes:
Step 101, adopting a first-order RC equivalent circuit model as the topology of a battery model; the first-order RC equivalent circuit model comprises a controlled voltage source, a second resistor and a resistor-capacitor parallel network formed by a first resistor and a first capacitor which are connected in series; the controlled voltage source represents an open circuit voltage OCV determined by the battery SOC, the second resistance represents an ohmic internal resistance inside the battery, the first resistance represents a polarized internal resistance of the battery, and the first capacitance represents a polarized capacitance of the battery.
The topology of the traditional first-order RC equivalent circuit model is adopted, and an electrochemical formula is used for improving the topology to obtain a battery model. The controlled voltage source U transmits a first-order RC equivalent circuit model OCV A second resistor R 0 Resistor-capacitor parallel network R 1 C 1 (the first resistor is connected with the first capacitor in parallel); controlled voltage source U OCV Represents an open circuit voltage OCV determined by the battery SOC; second resistor R 0 The ohmic internal resistance of the battery is shown, and the ohmic internal resistance is shown by lumped expression of the contact impedance of the positive electrode material, the negative electrode material, the diaphragm, the current collector and each part of the battery; resistor-capacitor parallel network R 1 C 1 The method is used for describing the dynamic change of the polarization voltage of the battery in the charge and discharge processes; the polarization voltage is the voltage at two ends of the resistor-capacitor parallel network; controlled voltage source U OCV And a second resistor R 0 Is affected by temperature, polarized internal resistance R 1 And is affected by temperature and magnification.
Step 102, using an improved, simplified Nernst equation to describe the effect of temperature on the controlled voltage source, using an improved, simplified Arrhenius equation to describe the effect of temperature on the second resistance, and using an improved, simplified buter-Volmer equation to describe the effect of temperature and multiplying power on the polarization resistance.
The improved, simplified Nernst equation, the improved, simplified Arrhenius equation and the improved, simplified Bulter-Volmer equation are obtained by simplifying equation variables and the like; the effect of temperature on the controlled voltage source is described using an improved, simplified Nernst equation, the effect of temperature on the second resistance is described using an improved, simplified Arrhenius equation, and the effect of temperature and multiplying power on the polarization resistance is described using an improved, simplified buter-Volmer equation.
The battery model construction method based on the electrochemical theory and the equivalent circuit model provided by the embodiment of the invention is suitable for construction of various battery models, and is especially suitable for construction of battery models with wide multiplying power and wide temperature change application characteristics such as lithium carbonate.
According to the embodiment of the invention, three electrochemical equations are combined with the equivalent circuit model, and the parameters of the equivalent circuit model under different temperatures and multiplying powers are described by the electrochemical equations; finally, a battery model suitable for a wide temperature range and a wide multiplying power range is obtained; the method solves the problem that the traditional equivalent circuit model lacks theoretical basis for describing temperature sensitivity and multiplying power sensitivity of parameters, so that model errors are large when the temperature and the multiplying power are changed, provides basis for application of the battery in environments with multiple temperature and multiplying power, and can adapt to the temperature and the multiplying power changes and also give consideration to model precision and model calculation cost.
Further, based on the above embodiment, the expression of the modified and simplified Nernst equation is:
U OCV ＝k 1 T+k 2 (2)
wherein U is OCV Represents a controlled voltage source, T represents absolute temperature, k 1 And k 2 Representing the improved and simplified coefficients of the Nernst equation;
the expression of the improved and simplified Arrhenius equation is as follows:
wherein R is 0 Representing the second resistance, p 1 、p 2 And p 3 Representing the improved and simplified coefficients of the Arrhenius equation, T representing absolute temperature;
the expression of the improved and simplified Bulter-Volmer equation is as follows:
wherein R is 1 Representing the internal resistance of polarization, f 1 、f 2 、f 3 And f 4 The modified and simplified coefficient of the Bulter-Volmer equation is represented, T represents absolute temperature, and I represents current.
Improved and simplified Nernst equation, arrhenius equation and Bulter-Volmer equation are introduced on the basis of a first-order RC equivalent circuit model and are respectively used for describing the temperature pair U OCV Influence of temperature on R 0 Impact of (2) on R and temperature and magnification 1 Is a function of (a) and (b).
Introduction of Nernst equation to describe temperature versus U OCV Nernst equation original form writing:
in equation (1), at a certain SOC point, the temperature T is constant, and therefore can be simplified as:
U OCV ＝k 1 T+k 2 (2)
introduction of Arrhenius equation to describe temperature versus R 0 Is written as:
in the formula (3), at a certain SOC point, all the other parts are constant except the temperature T, and the simultaneous logarithm taking of the two sides of the formula (3) can be simplified into:
considering the limitations of the Arrhenius equation over a wide temperature range, ln (R 0 ) Andnot absolutelyLinear, therefore, the equation (4) is modified using a quadratic polynomial:
describing temperature and multiplying power pair polarized internal resistance R by introducing Bulter-Volmer equation 1 The Bulter-Volmer equation original form writing:
j in (6) 0 Temperature-affected, to decouple it from temperature, one can write:
in formula (7)Still subject to temperature, their respective expansions may be further written as:
The current density j in equation (6) can be expressed as:
substitution of formula (7) -formula (10) into formula (6) yields:
equation (11) is not solvable for the transcendental equation, however, since α≡0.5, under this approximation, equation (11) can be solved as follows
In the formula (12), at a certain SOC point, the temperature T and the current I are constant, so the formula (12) can be further simplified as:
thus polarization internal resistance R 1 Can be calculated by the following formula:
the meanings of the parameters in the formulae (1) to (14) are shown in Table 1.
Meaning of parameters in the formula of Table 1
On the basis of the embodiment, the Nernst equation described by the formula (2), the Arrhenius equation described by the formula (5) and the Bulter-Volmer equation described by the formula (14) are greatly simplified compared with the original equation, and the method is presented in a concise and parameter solving manner on the basis of retaining the constraint relation of an electrochemical formula on temperature and/or multiplying power, so that the calculation cost can be greatly saved, and the model precision is improved.
Further, based on the above embodiment, the product of the polarized internal resistance and the polarized capacitance is a preset time constant.
Polarization capacitor C in first-order RC equivalent circuit model 1 The influence on the model precision is small, the identification is difficult, the time constant tau of the RC parallel circuit is assumed to be a fixed value (tau takes 15s in the embodiment of the invention), and then the time constant tau is determined by a formula (15):
Wherein τ is the preset time constant, and can be obtained by back-pushing through multiple experiments, and may have different values for different batteries.
Based on the embodiment, the embodiment of the invention obtains the value of the first capacitor according to the first resistor by taking the product of the polarized internal resistance and the polarized capacitor as a preset time constant, thereby improving the model precision.
Further, based on the above embodiment, the method further includes: respectively acquiring values of the controlled voltage source, the second resistor and the first resistor under a preset typical condition through a preset parameter identification experiment; and respectively utilizing least square fitting to obtain improved and simplified coefficients of the Nernst equation, improved and simplified coefficients of the Arrhenius equation and improved and simplified coefficients of the Bulter-Volmer equation according to values of the controlled voltage source, the second resistor and the first resistor under preset typical conditions.
The controlled voltage source may be represented by equation (2), the second resistance may be represented by equation (5), and the first resistance may be represented by equation (14). Wherein the expression (2) has a coefficient k after modification and simplification of Nernst equation 1 And k 2 The method comprises the steps of carrying out a first treatment on the surface of the The Arrhenius equation in the formula (5) is improved and simplified to obtain a coefficient p 1 、p 2 And p 3 The method comprises the steps of carrying out a first treatment on the surface of the In the formula (14), the improved and simplified coefficient f of the Bulter-Volmer equation is shown 1 、f 2 、f 3 And f 4 。
Coefficient k after modification and simplification of Nernst equation acquisition 1 And k 2 Improved and simplified Arrhenius equation coefficient p 1 、p 2 And p 3 Improved and simplified coefficient f of Bulter-Volmer equation 1 、f 2 、f 3 And f 4 When in use, corresponding typical values of model parameters (controlled voltage source, second resistor and first resistor) can be obtained based on preset typical conditions, and then expressions of the model parameters can be obtained by least square fittingCoefficients. Wherein the least squares fitting may be performed by a least squares fitting tool.
The corresponding preset typical conditions in the coefficient acquisition process of the three equations are not required to be identical. However, since the controlled voltage source, the second resistor and the first resistor have a circuit constraint relationship, the preset typical conditions are also required to have a correlation.
Based on the embodiment, the model accuracy is further improved by obtaining the model parameters under the preset typical conditions and then obtaining the coefficients of each electrochemical equation through least square fitting.
Further, based on the foregoing embodiment, the obtaining, by a preset parameter identification experiment, the values of the controlled voltage source, the second resistor, and the first resistor under a preset typical condition includes:
Acquiring the value of the controlled voltage source of each typical SOC point by carrying out charge and discharge pulse tests at preset fixed multiplying power, preset SOC intervals and different preset typical temperatures;
calculating the value of the second resistance for each of the representative SOC points according to equation (16):
wherein V is 0 For the battery terminal voltage at the last sampling instant before pulse generation, V 1 The voltage of the battery terminal at the first sampling moment after pulse generation is delta I, and delta I is the magnitude of pulse current;
recording the battery terminal voltage of each typical SOC point by respectively carrying out constant current charge and discharge experiments under a plurality of preset multiplying powers at the preset typical temperature, and calculating the value of the first resistor of each typical SOC point by using the obtained controlled voltage source and the second resistor under the corresponding conditions and using the formula (17):
wherein U is t Representing the battery terminal voltage, and I representing the current.
And obtaining the value of the controlled voltage source of each typical SOC point by performing pulse test at a preset fixed multiplying power, a preset SOC interval and different preset typical temperatures. The value of the controlled voltage source is related to the temperature, so that after the typical value at the preset typical temperature is obtained, the expression of the controlled voltage source can be obtained through fitting. The preset typical temperature includes 5 ℃,15 ℃,25 ℃ and 45 ℃ for example. Because the controlled voltage source is not affected by the multiplying power, the experiment is performed under a preset fixed multiplying power, for example, the multiplying power is 1C. The controlled voltage source can be tested for value at a typical SOC point by pulse testing. The typical SOC point may be determined according to a preset SOC interval, for example, at 5% intervals, and values of the controlled voltage sources corresponding to the SOCs of 0%, 5%, …% and 100% may be obtained respectively. In the case of determining the battery capacity, the multiplying power and the current have a determined relationship, for example, in the case of a battery with 25Ah capacity, if the battery is charged and discharged at the multiplying power of 1C, the charging and discharging current is 25A, that is, the charging and discharging are completed in 1 hour. If the charge and discharge are performed at the rate of 2C, the charge and discharge current is 12.5A, i.e., the charge is completed or the discharge is completed by 2 hours, and so on.
Therefore, if the 1C magnification is set, it is necessary to fully charge or discharge the battery within 1 hour. If the above 5% is used as the interval of SOC, then a pulse duration of 3 minutes is required to perform 5% charge or discharge, i.e., 180s is required for each pulse. In order to bring the voltage of the controlled voltage source to a steady state after each pulse is applied, it is necessary to set the time interval of each pulse, i.e., the rest time, for example, the rest time of 1 to 2 hours. Depending on the set SOC interval, the number of pulses applied during the pulse test may also be obtained, for example, if 5% is used as the interval between typical SOCs, 20 charge pulses and 20 discharge pulses are required for the test. I.e. 20 charge pulses and 20 discharge pulses are required for one test. Multiple pulse tests can be set, and the obtained result is used for subsequent fitting operation.
Pulse testing is carried out at preset fixed multiplying power, preset SOC intervals and different preset typical temperatures to obtain the value of the controlled voltage source of each typical SOC point, and the value can be obtained through a charging process and a discharging process. The charging process is to charge from 0% to 100% of the SOC, and the discharging process is to discharge from 100% to 0%. For each representative SOC point, the corresponding controlled voltage source takes the value of the average of the results at charge and discharge.
Since the voltage of the controlled voltage source cannot be suddenly changed, the ohmic internal resistance R can be calculated according to the formula (16) by using the voltage difference of 1s before and after the pulse generation 0 Namely a second resistance:
wherein V is 0 For the battery terminal voltage at the last sampling instant before pulse generation, V 1 The voltage of the battery terminal at the first sampling moment after pulse generation is delta I, and delta I is the magnitude of pulse current;
the reason for 1s before and after the generation of the pulse is that the sampling time is usually 1s, and if the sampling time is another value, the value can be appropriately adjusted. In addition, V 0 For the battery terminal voltage at the last sampling instant before pulse generation, V 1 For the battery terminal voltage at the first sampling instant after pulse generation to avoid the influence of the controlled voltage source to the greatest possible extent, it is understood that V 0 And V 1 The corresponding time can also be adjusted appropriately. Based on the pulse test, the value of the second resistor in the charging process and the value of the second resistor in the discharging process can be obtained according to the formula (16).
The first resistor is related to temperature and multiplying power, and as can be seen by the formula (17), the value of the first resistor needs to be obtained based on the calculated controlled voltage source and the value of the second resistor. Therefore, it is necessary to perform the related test of the first resistor at the same preset typical temperature and at the same SOC interval to calculate the value of the first resistor by using the second resistor and the controlled voltage source under the same temperature and SOC conditions. The first resistor is provided with a first resistor, and the first resistor is provided with a first resistor, wherein the first resistor is provided with a first resistor, the first resistor is provided with a second resistor, and the first resistor is provided with a first resistor, and the second resistor is provided with a second resistor.
By performing constant current charge and discharge experiments under a plurality of preset multiplying powers at the preset typical temperature, for example, performing constant current charge and discharge experiments with multiplying powers of 1C, 2C, 3C and 4C, recording the battery terminal voltage of each typical SOC point, in the embodiment of the present invention, recording the battery terminal voltage of each 5% SOC point, calculating the value of the first resistor of each typical SOC point by using the obtained controlled voltage source and the second resistor under the corresponding conditions, and using the formula (17):
wherein U is t Representing the battery terminal voltage, and I representing the current.
According to the battery terminal voltage of the typical SOC point recorded by the constant current charging experiment and the formula (17), the value of the first resistor of the typical SOC point in the charging process can be obtained, and according to the battery terminal voltage of the typical SOC point recorded by the constant current discharging experiment and the formula (17), the value of the first resistor of the typical SOC point in the discharging process can be obtained.
Based on the embodiment, the embodiment of the invention obtains the model parameters corresponding to different typical SOC points respectively based on the preset typical temperature and multiplying power through the preset SOC interval, thereby further improving the model precision.
Further, based on the above embodiment, the obtaining the improved and simplified coefficients of the Nernst equation, the improved and simplified coefficients of the Arrhenius equation, and the improved and simplified coefficients of the buter-Volmer equation according to the values of the controlled voltage source, the second resistor, and the first resistor under the preset typical conditions respectively using least squares fitting includes: obtaining improved and simplified coefficients of the Nernst equation at each typical SOC point through least square fitting according to the value of the controlled voltage source of each typical SOC point at the preset typical temperature; acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in a charging process through least square fitting according to the value of the second resistor at the charging state of each typical SOC point at the preset typical temperature; acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in a discharging process through least square fitting according to the value of the second resistor in the discharging state of each typical SOC point at the preset typical temperature; obtaining improved and simplified coefficients of the Bulter-Volmer equation at each typical SOC point in a charging process through least square fitting according to the values of the first resistor at the charging state of each typical SOC point at the preset typical temperature and at the preset multiplying powers; and obtaining improved and simplified coefficients of the Bulter-Volmer equation under each typical SOC point in the discharging process through least square fitting according to the values of the first resistor under the discharging state of each typical SOC point under the preset typical temperature and the preset multiplying power.
The three electrochemical equations described above have different coefficients corresponding to different SOC points, and thus, it can be said that the three electrochemical equations described above correspond to SOC points. According to the preset SOC interval set as above, model parameters of different typical SOC points can be obtained, and then, for each of the equation expressions of the typical SOC points, the equation expression can be obtained by fitting, so that correlation coefficients can be obtained. Using the least squares fitting tool to fit U at all typical temperatures at a typical SOC point with the equations (3), (5) and (17) as objective functions OCV R at all typical temperatures 0 R at all typical temperatures and rates 1 Fitting to obtain coefficients k of three equations 1 ,k 2 ,p 1 ,p 2 ,p 3 ,f 1 ,f 2 ,f 3 ,f 4 。
And because the value of the controlled voltage source is related to the temperature, the improved and simplified coefficient of the Nernst equation at each typical SOC point is obtained through least square fitting according to the value of the controlled voltage source at each typical SOC point at the preset typical temperature.
Because the value of the first resistor is related to the temperature and the charging and discharging process, the improved and simplified coefficient of the Arrhenius equation at each typical SOC point in the charging process is obtained through least square fitting according to the value of the second resistor at the charging state of each typical SOC point at the preset typical temperature; and acquiring the improved and simplified coefficient of the Arrhenius equation at each typical SOC point in the discharging process through least square fitting according to the value of the second resistor in the discharging state of each typical SOC point at the preset typical temperature.
Because the value of the second resistor is related to the temperature, the multiplying power and the charging and discharging process, the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the charging process is obtained through least square fitting according to the value of the first resistor at the charging state of each typical SOC point at the preset typical temperature and the preset multiplying powers; and obtaining improved and simplified coefficients of the Bulter-Volmer equation under each typical SOC point in the discharging process through least square fitting according to the values of the first resistor under the discharging state of each typical SOC point under the preset typical temperature and the preset multiplying power.
Based on the embodiment, the embodiment of the invention respectively carries out fitting operation based on different conditions according to different influence factors of model parameters, thereby obtaining the correlation coefficient and further improving the model precision.
Further, based on the above embodiment, the method further includes: obtaining the improved and simplified coefficient of the Nernst equation at any SOC point through interpolation operation according to the improved and simplified coefficient of the Nernst equation at each typical SOC point; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the charging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the charging process; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the discharging process; according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the charging process, obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the charging process through interpolation operation; and obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the discharging process.
All parameters of the equivalent circuit model are affected by the SOC, and k is a certain SOC point 1 ,k 2 ,p 1 ,p 2 ,p 3 ,f 1 ,f 2 ,f 3 ,f 4 Are obtained by linear interpolation of values at typical SOC. Therefore, according to the improved and simplified coefficient of the Nernst equation at each typical SOC point, the improved and simplified coefficient of the Nernst equation at any SOC point is obtained through interpolation operation. Obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the charging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the charging process; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the discharging process; according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the charging process, obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the charging process through interpolation operation; and obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the discharging process.
Based on the embodiment, the embodiment of the invention obtains the equation coefficient under any SOC point through interpolation operation, thereby perfecting the circuit model.
Fig. 2 is a schematic structural diagram of a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention. As shown in fig. 2, the battery model adopts a first-order RC equivalent circuit model as the topology of the battery model; the first-order RC equivalent circuit model comprises a controlled voltage source, a second resistor and a resistor-capacitor parallel network formed by a first resistor and a first capacitor which are connected in series; the controlled voltage source represents an Open Circuit Voltage (OCV) determined by a battery SOC, the second resistor represents ohmic internal resistance inside the battery, the first resistor represents polarized internal resistance of the battery, and the first capacitor represents polarized capacitance of the battery; and in the battery model, the effect of temperature on the controlled voltage source is described using an improved, simplified Nernst equation, the effect of temperature on the second resistance is described using an improved, simplified Arrhenius equation, and the effect of temperature and multiplying power on the polarization resistance is described using an improved, simplified buter-Volmer equation.
The battery model is applicable to a battery model of lithium carbonate with wide temperature and wide multiplying power application background, and can also be applicable to other models.
According to the embodiment of the invention, three electrochemical equations are combined with the equivalent circuit model, and the parameters of the equivalent circuit model under different temperatures and multiplying powers are described by the electrochemical equations; finally, a battery model suitable for a wide temperature range and a wide multiplying power range is obtained; the method solves the problem that the traditional equivalent circuit model lacks theoretical basis for describing temperature sensitivity and multiplying power sensitivity of parameters, so that model errors are large when the temperature and the multiplying power are changed, provides basis for application of the battery in environments with multiple temperature and multiplying power, and can adapt to the temperature and the multiplying power changes and also give consideration to model precision and model calculation cost.
The high-end and low-end parameters of the SOC can not be obtained under the conditions of low temperature and high multiplying power under the constraint of the upper limit and the lower limit of the voltage, so that the model provided by the embodiment of the invention can only discuss the SOC epsilon [0.1,0.8] in the charging process and only discuss the SOC epsilon [0.2,0.9] in the discharging process.
According to the embodiment of the invention, the electrochemical theory and the first-order RC equivalent circuit model are combined, the influence of temperature and multiplying power on equivalent circuit model parameters is described for the first time from the electrochemical theory, the advantages of low calculation cost and accurate electrochemical model of the equivalent circuit model are combined, the model precision in temperature and multiplying power change is improved, and a basis is provided for the application of the lithium titanate battery in the environment with multiple temperature and multiplying power changes.
The embodiment of the invention relates to a lithium titanate battery improved model based on combination of an electrochemical theory and an equivalent circuit model, wherein the model adopts topology of a traditional first-order RC equivalent circuit model, and an electrochemical equation is used for describing the temperature and the multiplying power sensitivity of model parameters. The specific implementation steps are as follows: 1) Improving and simplifying Nernst equation, arrhenius equation and Bulter-Volmer equation, and reducing equation variables; 2) Model parameters under typical conditions, namely OCV, ohmic internal resistance and polarization internal resistance, are obtained through parameter identification experiments designed under typical temperature and typical multiplying power; 3) Obtaining three electrochemical equation parameters by using the identified model parameters under the typical conditions and a least squares fitting tool; 4) Combining the three electrochemical equations with the equivalent circuit model, and describing parameters of the equivalent circuit model under different temperatures and multiplying powers by using the electrochemical equations; finally, the lithium titanate battery model applicable to a wide temperature range and a wide multiplying power range is obtained. The embodiment of the invention solves the problem that the traditional equivalent circuit model lacks theoretical basis for describing the temperature sensitivity and the multiplying power sensitivity of parameters, so that the model error is larger when the temperature and the multiplying power are changed, and provides a basis for the application of the lithium titanate battery in the environment with multiple temperature and multiplying power.
FIG. 3 is a diagram showing the accuracy of the improved Nernst equation versus the OCV-temperature relationship in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention; FIG. 4 is a schematic diagram of the accuracy of the improved Arrhenius equation of the present invention versus the R0-temperature relationship; FIG. 5 is a diagram showing the accuracy of the description of the R1-temperature relationship by the improved Butler-Volmer equation in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention; FIG. 6 is a diagram of the accuracy of the description of the R1-rate relationship by the improved Butler-Volmer equation in a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention; FIG. 7 is a schematic diagram showing comparison results of predicted voltage and measured voltage of an FUDS test model at 5 ℃ for a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention; FIG. 8 is a schematic diagram showing comparison results of predicted voltage and measured voltage of an FUDS test model at 35 ℃ for a battery model based on electrochemical theory and an equivalent circuit model according to an embodiment of the present invention.
The embodiment of the invention performs detailed verification on the proposed battery model. In order to verify the accuracy of the model under the conditions of variable temperature and multiplying power, FUDS dynamic working condition experiments with maximum multiplying power as high as 8C are respectively carried out at 5 ℃ and 35 ℃. From fig. 7 and 8, it can be seen that the embodiment of the present invention proposes that the model can obtain higher accuracy in the application of high-magnification dynamic working conditions at two temperatures, the model error at 5 ℃ is within [ -4%,1.7% ], and the model error at 35 ℃ is within [ -0.7%,0.3% ]. As shown in fig. 3 to 6, under the condition that the temperature and the multiplying power vary widely, the accuracy of the model provided by the embodiment of the invention is obviously improved compared with that of the traditional first-order RC equivalent circuit model.
The battery model provided by the embodiment of the invention is based on the method, and specific functions can refer to the flow of the method, and are not repeated here.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. The battery model construction method based on the electrochemical theory and the equivalent circuit model is characterized by comprising the following steps:
adopting a first-order RC equivalent circuit model as the topology of a battery model; the first-order RC equivalent circuit model comprises a controlled voltage source, a second resistor and a resistor-capacitor parallel network formed by a first resistor and a first capacitor which are connected in series; the controlled voltage source represents an Open Circuit Voltage (OCV) determined by a battery SOC, the second resistor represents ohmic internal resistance inside the battery, the first resistor represents polarized internal resistance of the battery, and the first capacitor represents polarized capacitance of the battery;
describing the effect of temperature on the controlled voltage source using an improved, simplified Nernst equation, describing the effect of temperature on the second resistance using an improved, simplified Arrhenius equation, and describing the effect of temperature and multiplying power on the polarization resistance using an improved, simplified buter-Volmer equation;
The expression of the improved and simplified Nernst equation is as follows:
U OCV ＝k 1 T+k 2 (2)
wherein U is OCV Represents a controlled voltage source, T represents absolute temperature, k 1 And k 2 Representing the improved and simplified coefficients of the Nernst equation;
the expression of the improved and simplified Arrhenius equation is as follows:
wherein R is 0 Representing the second resistance, p 1 、p 2 And p 3 Representing the improved and simplified coefficients of the Arrhenius equation, T representing absolute temperature;
the expression of the improved and simplified Bulter-Volmer equation is as follows:
wherein R is 1 Representing the internal resistance of polarization, f 1 、f 2 、f 3 And f 4 The improved and simplified coefficient of the Bulter-Volmer equation is represented, T represents absolute temperature, and I represents current;
the product of the polarized internal resistance and the polarized capacitance is a preset time constant;
respectively acquiring values of the controlled voltage source, the second resistor and the first resistor under a preset typical condition through a preset parameter identification experiment;
obtaining improved and simplified coefficients of the Nernst equation, the improved and simplified coefficients of the Arrhenius equation and the improved and simplified coefficients of the Bulter-Volmer equation by least square fitting according to values of the controlled voltage source, the second resistor and the first resistor under preset typical conditions;
The obtaining the values of the controlled voltage source, the second resistor and the first resistor under the preset typical conditions through the preset parameter identification experiment respectively comprises the following steps:
acquiring the value of the controlled voltage source of each typical SOC point by carrying out charge and discharge pulse tests at preset fixed multiplying power, preset SOC intervals and different preset typical temperatures;
calculating the value of the second resistance for each of the representative SOC points according to equation (16):
wherein V is 0 For the battery terminal voltage at the last sampling instant before pulse generation, V 1 The voltage of the battery terminal at the first sampling moment after pulse generation is delta I, and delta I is the magnitude of pulse current;
recording the battery terminal voltage of each typical SOC point by respectively carrying out constant current charge and discharge experiments under a plurality of preset multiplying powers at the preset typical temperature, and calculating the value of the first resistor of each typical SOC point by using the obtained controlled voltage source and the second resistor under the corresponding conditions and using the formula (17):
wherein U is t Representing the battery terminal voltage, I representing the current;
the obtaining the improved and simplified coefficient of the Nernst equation, the improved and simplified coefficient of the Arrhenius equation, and the improved and simplified coefficient of the buter-Volmer equation by least square fitting according to the values of the controlled voltage source, the second resistor and the first resistor under the preset typical conditions respectively comprises:
Obtaining improved and simplified coefficients of the Nernst equation at each typical SOC point through least square fitting according to the value of the controlled voltage source of each typical SOC point at the preset typical temperature;
acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in the charging process through least square fitting according to the value of the second resistor at the charging state of each typical SOC point at the preset typical temperature; acquiring an improved and simplified coefficient of the Arrhenius equation at each typical SOC point in a discharging process through least square fitting according to the value of the second resistor in the discharging state of each typical SOC point at the preset typical temperature;
obtaining improved and simplified coefficients of the Bulter-Volmer equation under each typical SOC point in a charging process through least square fitting according to the value of the first resistor under the charging state of each typical SOC point under the preset typical temperature and the preset multiplying power; obtaining improved and simplified coefficients of the Bulter-Volmer equation at each typical SOC point in a discharging process through least square fitting according to the values of the first resistor in the discharging state of each typical SOC point at the preset typical temperature and at the preset multiplying powers;
Obtaining the improved and simplified coefficient of the Nernst equation at any SOC point through interpolation operation according to the improved and simplified coefficient of the Nernst equation at each typical SOC point;
obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the charging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the charging process; obtaining the improved and simplified coefficients of the Arrhenius equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficients of the Arrhenius equation at each typical SOC point in the discharging process;
according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the charging process, obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the charging process through interpolation operation; and obtaining the improved and simplified coefficient of the Bulter-Volmer equation at any SOC point in the discharging process through interpolation operation according to the improved and simplified coefficient of the Bulter-Volmer equation at each typical SOC point in the discharging process.
2. The method for constructing a battery model based on electrochemical theory and an equivalent circuit model according to claim 1, wherein each pulse test comprises 20 of the charge pulses and 20 of the discharge pulses, and the rest time between pulses is 2 hours when the pulse test is performed.
3. A battery model based on electrochemical theory and an equivalent circuit model, characterized in that the battery model is constructed by the construction method of the battery model based on electrochemical theory and an equivalent circuit model according to claim 1 or 2.
4. A battery model based on electrochemical theory and equivalent circuit model according to claim 3, characterized in that the battery model comprises a lithium titanate battery model.
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