CN106461728A - Equivalent circuit model of battery - Google Patents

Equivalent circuit model of battery Download PDF

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Publication number
CN106461728A
CN106461728A CN201480002253.0A CN201480002253A CN106461728A CN 106461728 A CN106461728 A CN 106461728A CN 201480002253 A CN201480002253 A CN 201480002253A CN 106461728 A CN106461728 A CN 106461728A
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equivalent circuit
battery
circuit model
inductive
capacitive
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吴正斌
翁荣成
孙嘉遥
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Qianhai Chinese Academy Of Sciences Cooperation Integrity Cooperation Technology Shenzhen Co ltd
Shenzhen Institute of Advanced Technology of CAS
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Qianhai Chinese Academy Of Sciences Cooperation Integrity Cooperation Technology Shenzhen Co ltd
Shenzhen Institute of Advanced Technology of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/389—Measuring internal impedance, internal conductance or related variables

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  • General Physics & Mathematics (AREA)
  • Tests Of Electric Status Of Batteries (AREA)
  • Secondary Cells (AREA)

Abstract

Provided is an equivalent circuit model of a battery, which is used for simulating an electrochemical impedance spectrum and dynamic charge and discharge characteristics of a battery. The equivalent circuit model comprises an electrical element having a complex parameter. The imaginary part of the complex parameter indicates loss characteristics related to frequency. An inductance element and a capacitor element have complex parameters. The result of the electrochemical impedance spectrum and the dynamic charge and discharge characteristics of a lithium iron phosphate battery that are calculated by using the equivalent circuit model have high accuracy with the error rate less than 5%.

Description

Battery equivalent circuit model Technical Field
The invention relates to the technical field of batteries represented by lithium ion batteries, in particular to a battery equivalent circuit model.
Background
Lithium ion batteries are increasingly in demand for new energy vehicles, grid energy storage systems, and consumer electronics because of their long service life, high energy density, and safety. In practical applications, it is very important to obtain accurate dynamic characteristics of lithium ion batteries. On the one hand, an accurate dynamic battery model is very necessary for monitoring, diagnosing and managing the battery under different actual conditions (working loads) and working environments. On the other hand, the operation strategy and the structure optimization in the complex electrical system depend on the simulation of the dynamic performance of the battery. Equivalent circuit models for batteries tend to be more computationally efficient than electrochemical models, as electrochemical models require a thorough understanding and description of complex electrochemical processes and features, which are sometimes not entirely feasible. And the equivalent circuit model is implanted into a battery management system and a network, and is practical and feasible for the application of battery system products.
Measuring Electrochemical Impedance (EI) spectra is considered to be an effective method for detecting different processes and characteristics within a cell over a wide frequency range without destroying the cell. The method is crucial to research the electrochemical impedance characteristics of the lithium ion battery by adopting a properly developed equivalent circuit model, and can be used for researching different characteristics of each part and an interface in the lithium ion battery. The most typical equivalent circuit model includes direct current internal resistance, RC cell (constant phase element or capacitor in parallel with resistor), and Warburg element, which respectively represent ohmic resistance, effect of electric double layer structure, and effect by lithium ion diffusion in the intercalation electrode. Some equivalent circuit models have additional inductive elements for characterizing the connection between the wire and the electrode. More RC cell circuits may also be used to characterize the different effects of the different parts in more detail and accurately. In the models that have been reported so far, Constant Phase Elements (CPEs), which are non-electrical elements, are commonly used to calculate electrochemical impedance spectra to obtain more accurate results. However, this can result in an inability to clearly explain its physical nature and impact on the overall performance of the cell. Meanwhile, in the existing equivalent circuit model, the frequency-dependent electrical loss and the influence of the electrical loss on the electrochemical impedance and the charge-discharge characteristics of the lithium ion battery are not considered.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the battery equivalent circuit model is a battery represented by a lithium ion battery, and solves the problems that the physical substance of a non-electric element cannot be accurately explained, the influence of the non-electric element on the overall performance of the battery cannot be represented, the frequency-related electric loss and the influence of the frequency-related electric loss on the electrochemical impedance and the charging and discharging characteristics of the battery cannot be considered, and the like.
The technical scheme for solving the problems is as follows: an equivalent circuit model of a battery is provided, which is used for simulating electrochemical impedance spectrum and dynamic charge and discharge characteristics of the battery and is characterized by comprising an electric element with a plurality of parameters, wherein an imaginary part in the plurality of parameters represents loss characteristics related to frequency, and the electric element with the plurality of parameters comprises a capacitance element.
Preferably, in the equivalent circuit model provided by the invention, the capacitor element is contained in a capacitor unit, and the equivalent circuit model comprises at least one capacitor unit, wherein the capacitor element represents an electric double layer effect formed by a battery electrode/electrolyte interface. The imaginary part of the complex parameter of the capacitive element in each of said capacitive units represents its corresponding loss.
Preferably, in the equivalent circuit model provided by the invention, when the number of the capacitor units is more than one, the capacitor units are connected in series or in parallel; at least one of the capacitive units further comprises a first resistive element connected in parallel therewith, representing a self-discharge effect of the battery, the first resistive element having a real number parameter.
Preferably, in the equivalent circuit model provided by the present invention, the first resistance element is a resistor.
Preferably, the equivalent circuit model provided by the invention further comprises a second resistor, wherein the second resistor has a real number parameter and represents the direct current internal resistance of the battery, which does not change along with the frequency change.
Preferably, in the equivalent circuit model provided by the present invention, the electrical component having a complex parameter further includes an inductive component.
Preferably, in the equivalent circuit model provided by the present invention, the inductance element is included in an inductance unit, and the equivalent circuit model includes at least one inductance unit, and the inductance unit is connected in series or in parallel with the capacitance unit.
Preferably, in the equivalent circuit model provided by the present invention, the inductance element in the inductance unit represents the effect of the connection between the lead and the electrode in the battery, and the imaginary part of the complex parameter represents the corresponding loss.
Preferably, in the equivalent circuit model provided by the present invention, when the number of the inductance units is greater than one, each of the inductance units is connected in series or in parallel; at least one of the inductive units further includes a third resistive element connected in parallel or series with the inductive unit, the third resistive element having a real number parameter.
Preferably, in the equivalent circuit model provided by the present invention, the third resistor is a resistor.
The implementation of the invention has the following beneficial effects: the equivalent circuit model of the present invention includes inductive and capacitive elements having complex parameters whose corresponding imaginary components represent frequency-dependent loss characteristics of the electrical components in the battery model. The equivalent circuit model does not include a Warburg element or a Constant Phase Element (CPE), all electrical elements having physical significance; simulating the electrochemical impedance spectrum of the lithium ion battery through the proposed model, wherein the error of the impedance is less than 2m omega within the range of the frequency from 0.01Hz to 10 kHz; the parameters of the electric elements of the proposed model are calculated and analyzed, and the parameters of the complex elements are obtained through fitting calculation, so that the dynamic charge and discharge performance of the lithium ion battery can be simulated through the proposed equivalent circuit model, and the simulation precision is high.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 shows a battery equivalent circuit model of a first preferred embodiment of the present invention;
FIG. 2 shows a battery equivalent circuit model according to a second preferred embodiment of the present invention;
FIG. 3 shows a battery equivalent circuit model according to a third preferred embodiment of the present invention;
FIG. 4 shows a battery equivalent circuit model according to a fourth preferred embodiment of the present invention;
FIG. 5 shows a battery equivalent circuit model according to a fifth preferred embodiment of the present invention;
FIG. 6 shows a battery equivalent circuit model simulating the electrochemical impedance characteristics of a 5.5Ah lithium iron phosphate/graphite battery at 50% state of charge according to a third preferred embodiment of the present invention;
fig. 7 shows the magnitude and phase of the electrochemical impedance of a 5.5Ah lithium iron phosphate/graphite cell simulated by the equivalent circuit model of the cell according to the third preferred embodiment of the present invention at 50% state of charge;
fig. 8 shows simulated and measured voltage curves of a 5.5Ah lithium iron phosphate/graphite battery during which the battery equivalent circuit model of the third preferred embodiment of the present invention simulates 10s of discharge from a 50% state of charge under a current condition of 5.5A;
fig. 9(a) shows a comparison between the results of terminal voltage simulation and measurement in the equivalent circuit model simulation process according to the third preferred embodiment of the present invention;
fig. 9(b) shows an absolute error value | Δ V | of a simulated voltage of a 5.5Ah lithium iron phosphate/graphite battery under the condition of the Federal Urban Driving Schedule in the battery equivalent circuit model simulation process according to the third preferred embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The existing equivalent circuit model comprises a Warburg Element or a Constant Phase Element (CPE), cannot accurately explain the physical nature of the non-electrical Element, cannot characterize the influence of the non-electrical Element on the overall performance of the battery, and does not consider the frequency-dependent electrical loss and the influence thereof on the electrochemical impedance and the charging and discharging characteristics of the battery. The main innovation points of the invention are as follows: providing a battery equivalent circuit model, wherein the inductive element and the capacitive element have a plurality of parameters and can reflect the consumption characteristics of the electrical element related to the frequency; the parameters of all the elements of the equivalent circuit model can be calculated by fitting the measured electrochemical impedance characteristics to analyze their different effects in different frequency ranges. The simulation result of the electrochemical impedance spectrum and the dynamic charge-discharge characteristic precision are high through the equivalent circuit model, and all errors are less than 5%.
Hereinafter, the battery equivalent circuit model of the present invention will be described in detail using a lithium ion battery as a representative. Of course, the battery equivalent circuit model of the invention is also completely suitable for nickel-cadmium batteries, nickel-hydrogen batteries, lead-acid batteries and other battery types.
FIG. 1 shows a battery equivalent circuit model according to a first preferred embodiment of the present invention, as shown in FIG. 1, in this embodiment, the electrical component with plural parameters is a capacitor CeIn the present invention, all of the plural variables are labeled with. Wherein, the capacitor CeThe imaginary part of a represents the frequency dependent loss characteristic of the cell.
In bookIn the embodiment, the capacitor CeContained in a capacitor cell, capacitor CeAnd a resistor RtThe capacitors are connected in parallel to form a capacitor unit. In the existing equivalent circuit model, the constant phase element is usually connected in parallel with an ohmic resistor, or the ohmic resistor is connected in series with the walbau element and then connected in parallel with the constant phase element to form an RC unit for simulating the actual condition of the battery. As the equivalent circuit model of the invention can completely not comprise the Valley element or the constant phase element, only the capacitance C needs to be endowedeWith a plurality of parameters, all the electrical components can be made to have physical significance. Similar to the existing equivalent circuit model, in order to improve the simulation precision, the capacitor CeConnected in parallel with a first resistive element, i.e. resistor R in this embodiment, to form a capacitive unittWith real number parameters. It can also be understood that the first resistance element is an unnecessary element, and on the premise that the requirement on the simulation accuracy is not high, the equivalent circuit model of this embodiment may not include the first resistance element, and may include the capacitor CeConstitute the capacitive cell alone.
FIG. 2 shows a battery equivalent circuit model according to a second preferred embodiment of the present invention, and as shown in FIG. 2, the electrical component with plural parameters further includes an inductive component, an inductance L and a capacitance CeThe imaginary parts of the x collectively represent the frequency dependent loss characteristics of the cell. The inductor L has a plural-parameter inductance value which is generated by the connection of the lead and the electrode.
In the present embodiment, the inductor L alone constitutes the inductor unit. In the existing equivalent circuit model, an inductance with real parameters is used in series with the RC unit for characterizing the connection between the wire and the electrode. But the inductance of the real parameter cannot represent the effect of frequency variation on its loss characteristics. Capacitor CeAnd a resistor RtThe parallel connection of the inductor and the capacitor is connected with the inductor L in series, and the inductor element and the capacitor with complex parameters can accurately represent the physical meaning of the electric element.
Fig. 3 shows a battery equivalent circuit model according to a third preferred embodiment of the present invention, and as shown in fig. 3, the equivalent circuit model includes at least one capacitor unit. I.e. the number of capacitor cells is notThe imaginary part of the complex parameter of the capacitive element in each capacitive unit may represent the loss characteristic of the corresponding element changing with the frequency change. The inductance L represents the connection effect of the lead and the electrode, and mainly affects the electrochemical impedance characteristics in a high frequency range; capacitor CeAnd a resistor RtThe parallel connection of (a), mainly affects the electrochemical impedance characteristics in the medium frequency range; capacitor C0Mainly affects the electrochemical impedance characteristics in the low frequency range.
In the present embodiment, when the number of the capacitor units is more than one, the respective capacitor units are connected in series or in parallel to accommodate a complicated battery configuration situation. Similar to the above, each capacitor unit connected in series or in parallel may be composed of only a capacitor element having a plurality of parameters, on the premise that the requirement for the simulation accuracy is not high. At least one of the capacitive units further comprises a first resistive element connected in parallel with the capacitive element for improving the simulation accuracy. All the capacitor units may include the first resistance element, or only partially include the first resistance element, or none of them, and each capacitor unit represents different electrochemical impedance characteristics, for example, electrochemical impedance characteristics in different frequency ranges.
Fig. 4 shows a battery equivalent circuit model according to a fourth preferred embodiment of the present invention, and as shown in fig. 4, the equivalent circuit model includes at least one of the inductance units. That is, the number of the inductance units may be not only one as shown in fig. 2 or fig. 3, but also a plurality of inductance units, and the imaginary part of the complex parameter of the inductance element in each inductance unit represents the loss of the connection effect of the lead and the electrode.
In this embodiment, the inductance element is included in the inductance unit, L0And a resistor Rt' parallel connection constitutes an inductive unit. Similar to the existing equivalent circuit model, in order to improve the simulation precision, the inductor L0Connected in parallel with a third resistive element, i.e. resistor R in this embodiment, to form an inductive unitt', with real parameters. Of course, the inductance L0May also be connected to a third resistive elementThe series connection constitutes an inductance unit.
It is also to be understood that the third resistive element is an optional element in the inductive unit, and that the inductive unit may not comprise the first resistive element in case the circuit is not complex, such as the inductance L, which alone constitutes the inductive unit. When the number of the inductance units is greater than one, the inductance units are connected in series or in parallel, all the inductance units may include the third resistance element, or only partially include the third resistance element, or of course, none of the inductance units may include the third resistance element, and each of the inductance units represents a different electrochemical impedance characteristic, for example, represents an electrochemical impedance characteristic in a different frequency range.
In this embodiment, two capacitor units connected in series are included, but the number of capacitor units may also be multiple. In one of the capacitor units, the capacitor CeAnd a resistor Rt1After being connected in series with the resistor Rt2And the batteries are connected in parallel to adapt to the complicated battery construction situation under the requirement of simulation precision. That is, one capacitor unit may have a plurality of first resistance elements, and a capacitor element may be connected in series with one of the first resistance elements and then connected in parallel with the other of the first resistance elements. Similarly, the inductance unit may have a structure in which a plurality of third resistance elements are provided inside one inductance unit, and the inductance element is connected in series with one part of the third resistance elements and then connected in parallel with another part of the third resistance elements.
Fig. 5 shows an equivalent circuit model of a battery according to a fifth preferred embodiment of the present invention, and as shown in fig. 5, the equivalent circuit model includes two inductance units and two capacitance units, and the composition of each inductance unit or each capacitance unit is the same as that in fig. 4. The difference lies in that an inductance unit is connected in parallel with an inductance unit, the inductance unit is composed of an inductance L, and the capacitance unit is composed of a capacitance C0Sum resistance Rt3Are connected in parallel. In the equivalent circuit model of this embodiment, other inductance units and capacitance units are connected in series in sequence. Similarly, when a plurality of inductance units or a plurality of capacitance units are included in an equivalent circuit model, part of the inductance units are connected in parallelAfter being connected, the inductor unit is connected with other inductor units and capacitor units in series; or after being connected in parallel, part of the capacitor units are connected in series with other inductor units and capacitor units so as to respectively adapt to the complicated battery construction situation.
In this embodiment, the third resistor is composed of a resistor Rt' composition, L0And a resistor Rt' parallel connection constitutes an inductive unit. The resistor Rt' denotes a resistance value after a plurality of resistors are connected in series and/or in parallel.
The following will take the equivalent circuit model of the third preferred embodiment of the lithium ion battery of the present invention as an example to illustrate the working principle of the equivalent circuit model.
In the equivalent circuit model of the third preferred embodiment of the lithium ion battery of the present invention, L, CeA and C0May be represented by the following formulas (1), (2), (3):
L*＝L+i·L' (1)
Ce*＝Ce+i·Ce' (2)
C0*＝C0+i·C0' (3)
wherein, L, CeAnd C0Are respectively L, CeA and C0And the real part of the inductance and the capacitance respectively represent the real inductance and the capacitance. L' and Ce' and C0' is a corresponding imaginary part and represents loss of the corresponding element, respectively. Alternatively, L, CeA and C0May also be represented by the following formulas (4), (5), (6):
L*＝L·(1+i·tanθL) (4)
Ce*＝Ce·(1+i·tanθCe) (5)
C0*＝C0·(1+i·tanθC0) (6)
wherein, thetaL、θCeAnd thetaC0Are respectively L, CeA and C0Phase angle of x.
ZL*、ZCeA andZC0denotes L, CeA and C0Complex impedance, and can be represented by equations (7), (8), (9):
ZL*＝i·2πf·L*＝-2πfL'+i·2πfL (7)
wherein f is the frequency. As can be seen from equations (7), (8), (9), L' and f determine the resistance of the inductor L; and a capacitor CeSum capacitance C0The value of electrical impedance is capacitance CeSum capacitance C0Real, imaginary and f.
According to FIG. 3, the overall complex electrochemical impedance Z of the lithium-ion batteryBMay be expressed as:
ZBmay be calculated by substituting equations (7), (8) and (9) into equation (10). Compared with the equivalent circuit model reported previously, for illustrating ZBAll variables of the are obviously important and have physical significance.
Based on such equivalent circuit models, all electrical component parameters can be identified more clearly by fitting the simulated electrochemical impedance characteristics to the measured data, and the influence of these electrical component parameters on the performance of the lithium ion battery can be recognized.
To characterize the difference between the simulated and measured values, an error function E is introduced herein, see formula (11):
here, N is the total number of data. XtAnd XsMeasured data and simulated data, respectively. Is XtAverage value of (a). The error function E is a difference function between the simulation data and the measurement data, and the range of E is 0-1. In this context, the error function is used not only to characterize the accuracy of the electrochemical impedance characteristics based on the proposed equivalent circuit model fitting, but also to characterize the consistency between the simulated dynamic performance of the lithium ion battery and the test results. Wherein the simulated dynamic performance is predicted by fitting element parameters of the equivalent circuit model.
Experiment:
in this example, a cylindrical LiFePO having a rated capacity of 5.5Ah was used4The battery commodity is a research object (32650, Shenzhen Wauterma Electricity)Pool, Ltd (Shenzhen OptimumNano Energy co., Ltd), Shenzhen, china). The electrochemical impedance spectra of this lithium ion cell at 50% state of charge (SOC) was measured by an electrochemical workstation (model 600, from Gamry Instruments, Wominster, USA) at an open circuit voltage (AC) of 5mV and a frequency range of 0.01Hz to 10 kHz. Performing electrochemical impedance measurements at low frequencies below 0.01Hz will consume more time and sometimes measurements with actual battery charge and discharge currents are not feasible. Therefore, the effect on battery performance under low frequency conditions below 0.01Hz is not considered herein. Therefore, for lithium iron phosphate batteries, the diffusion process below 2mHz is negligible. Nor are the corresponding Warburg elements investigated herein, as well as the effect of these elements in the proposed equivalent circuit model.
The dynamic charge and discharge performance of the battery was actually tested by a battery test system (CT-4001-5V500A, new will ltd, shenzhen, china). The state of charge of the battery was maintained at 50% prior to each test. The cell was charged to 3.65V at a charge rate (C-rate) of 0.2, and then the charging voltage was maintained at 3.65V until the charging current was below 55mA (0.01 charge rate). After waiting for 15min, the battery was discharged at a discharge rate of 0.2 with a discharge capacity of 2.75 Ah. Before each test was started, 3 hours were waited to achieve a 50% state of charge. All preparation and testing steps were carried out at ambient temperature of 25 ℃.
And (4) analyzing results:
by the equivalent circuit model provided by the embodiment, the theoretical electrochemical impedance spectrum of the lithium iron phosphate battery can be obtained by fitting the measured data through a simulated annealing optimization algorithm. Fig. 6 shows a comparison between the fitted electrochemical impedance spectrum and the measured electrochemical impedance spectrum, as shown in fig. 6, the fitted impedance visually matches the measured values very well over the frequency range studied (from 0.01Hz to 10 kHz). In order to investigate the accuracy of the fitting results, fig. 7 shows the comparison of the magnitude and phase of the fitted electrochemical impedance spectrum and the measured electrochemical impedance spectrum characteristic over a certain frequency range, and as shown in fig. 7, at a frequency of 0.01Hz, the magnitude and phase difference between the two reach maximum values, 2m Ω and 3.28 °, respectively. As can be calculated by equation (11), the error functions E of magnitude and phase are 4.87% and 1.51%, respectively. This demonstrates the high electrochemical impedance simulation accuracy of the proposed equivalent circuit model.
The fitting element parameters of the equivalent circuit model shown in fig. 3 are shown in table 1. R0The pure ohmic resistance of (2) is 32.82m omega, which is not affected by the frequency. The value of L' is-48.01 nH, indicating the inductive losses due to the battery current collector and cable. L has an inductance value of 321.1nH, primarily for making ZBThe imaginary part of the + is positive and the electrochemical impedance approaches 0.01 Ω as the frequency increases. C0Affects the electrochemical impedance mainly in the frequency range below 1 Hz; the C is0Value 1321F, is Ce(1.241F) one thousand times or more. Wherein C iseThe electrochemical impedance is mainly influenced in the mid-frequency range above 1 Hz. C0An absolute value of' C063.9% of; and CeThe absolute value of the imaginary part is 59.5% of its real part. These two percentages reflect the loss characteristics with respect to frequency, mainly due to electrochemical reactions and electrode interface capacitance.
TABLE 1 fitting parameters for equivalent circuit model elements for lithium ion phosphoric acid/graphite batteries
The dynamic charge and discharge performance in the time domain of the battery under study was also studied by this model. Fig. 8 shows simulated and measured terminal voltage (terminal voltage) of a battery discharged for 10s under a condition of 5.5A current (discharge rate of 1), and as shown in fig. 8, the voltage curve predicted by the proposed model has good agreement with the measured curve during and after the discharge process. The error function E of the pulse discharge performance of the battery was 1.44%. The dynamic performance of the lithium iron phosphate battery under study is further studied according to the Federal city Driving schedule (FUDS). As a typical duty cycle, the FUDS lasts 1372s, often used to verify the accuracy of the battery model. And generating a real-time charge and discharge signal through a battery test system according to the preset power of the FUDS driving cycle, and applying the real-time charge and discharge signal to the battery. From the current data recorded in the time domain, the equivalent circuit model can calculate the terminal voltage curve of the battery. Fig. 9 shows the comparison of the terminal voltages of the analog and measured values throughout the dynamic process, with the maximum voltage difference of 0.0357V as shown in fig. 9. The error of the terminal voltage of the FUDS cycle is calculated to be 3.32% by equation (11). The results further verify that the proposed model has excellent dynamic prediction accuracy.
Compared with the prior model, all the electric elements in the model have physical significance because the equivalent circuit model of the lithium ion battery comprises inductance and capacitance elements and has complex parameters. For LiFePO4The parameters of all the elements of the proposed equivalent circuit model of the cell are calculated by fitting the measured electrochemical impedance characteristics to analyze their different effects in different frequency ranges. The simulation result of the electrochemical impedance spectrum and the dynamic charge-discharge characteristic have high precision through the model, and all errors are less than 5%.

Claims (8)

  1. A battery equivalent circuit model is used for simulating electrochemical impedance spectrum and dynamic charge and discharge characteristics of a battery, and is characterized by comprising an electric element with a plurality of parameters, wherein an imaginary part in the plurality of parameters represents loss characteristics related to frequency, and the electric element with the plurality of parameters comprises a capacitance element.
  2. The battery equivalent circuit model of claim 1, wherein the capacitive element is contained in a capacitive cell, the equivalent circuit model including at least one of the capacitive cells, wherein the capacitive element represents an electric double layer effect formed at a battery electrode/electrolyte interface, and an imaginary component of a complex parameter of the capacitive element in each of the capacitive cells represents its corresponding loss.
  3. The battery equivalent circuit model according to claim 2, wherein when the number of the capacitor units is more than one, each of the capacitor units is connected in series or in parallel; at least one of the capacitive units further comprises a first resistive element connected in parallel therewith, representing a self-discharge effect of the battery, the first resistive element having a real number parameter.
  4. The battery equivalent circuit model according to claim 3, further comprising a second resistor having a real number parameter representing the DC internal resistance of the lithium ion battery that does not change with frequency changes.
  5. The battery equivalent circuit model according to any one of claims 1 to 4, wherein the electrical element having a complex parameter further comprises an inductive element.
  6. The battery equivalent circuit model according to claim 5, wherein the inductive element is contained in an inductive cell, the equivalent circuit model comprising at least one of the inductive cells, the inductive cell being connected in series or in parallel with the capacitive cell.
  7. The battery equivalent circuit model according to claim 6, wherein the inductive element in the inductive unit represents the effect of the wire and electrode connection in the battery, and the imaginary part of its complex parameter represents its corresponding loss.
  8. The battery equivalent circuit model according to claim 7, wherein when the number of the inductance units is more than one, each of the inductance units is connected in series or in parallel; at least one of the inductive units further includes a third resistive element connected in parallel or series with the inductive unit, the third resistive element having a real number parameter.
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