WO2016106501A1 - 一种电池等效电路模型 - Google Patents

一种电池等效电路模型 Download PDF

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WO2016106501A1
WO2016106501A1 PCT/CN2014/095317 CN2014095317W WO2016106501A1 WO 2016106501 A1 WO2016106501 A1 WO 2016106501A1 CN 2014095317 W CN2014095317 W CN 2014095317W WO 2016106501 A1 WO2016106501 A1 WO 2016106501A1
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battery
equivalent circuit
circuit model
inductance
capacitor
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PCT/CN2014/095317
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English (en)
French (fr)
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吴正斌
翁荣成
孙嘉遥
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中国科学院深圳先进技术研究院
前海中科协德科技(深圳)有限公司
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Priority to PCT/CN2014/095317 priority Critical patent/WO2016106501A1/zh
Priority to CN201480002253.0A priority patent/CN106461728A/zh
Publication of WO2016106501A1 publication Critical patent/WO2016106501A1/zh

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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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  • the invention relates to the field of battery technology represented by a lithium ion battery, and more particularly to a battery equivalent circuit model.
  • EI electrochemical impedance
  • More RC unit circuits can also be used to characterize the different effects of different parts in more detail and accurately.
  • CPE constant phase elements
  • electrochemical impedance spectroscopy To obtain more accurate results.
  • this can lead to confusion Explain its physical essence and its impact on the overall performance of the battery.
  • the frequency-dependent electrical loss and the influence of electrical wear on the electrochemical impedance and the charge and discharge characteristics of the lithium ion battery are not considered.
  • the technical problem to be solved by the present invention is to provide a battery equivalent circuit model, which is represented by a lithium ion battery, which solves the problem that the existing battery equivalent circuit model cannot accurately explain the physical essence of non-electric components and cannot represent non-characteristics.
  • the influence of electrical components on the overall performance of the battery does not take into account the frequency-related electrical losses and their effects on the electrochemical impedance and the charge and discharge characteristics of the battery.
  • the technical solution of the present invention to solve the above problems lies in: providing an equivalent circuit model of a battery for simulating an electrochemical impedance spectrum and a dynamic charge and discharge characteristic of a battery, characterized in that it comprises an electrical component having a plurality of parameters, and a plurality of parameters
  • the imaginary part represents a frequency dependent loss characteristic, wherein the electrical component having a complex parameter comprises a capacitive element.
  • the capacitive element is included in a capacitor unit, and the equivalent circuit model includes at least one of the capacitor units, wherein the capacitor element represents a battery electrode/electrolyte interface formed Double layer effect.
  • the imaginary part of the complex parameter of the capacitive element in each of the capacitive units represents its corresponding loss.
  • each of the capacitor units when the number of the capacitor units is greater than one, each of the capacitor units is connected in series or in parallel; at least one of the capacitor units further includes a parallel connection therewith
  • the first resistive element represents a self-discharge effect of the battery, and the first resistive element has a real number parameter.
  • the first resistive element is a resistor
  • a second resistor is further included, and the second resistor has a real parameter indicating a direct current internal resistance of the battery that does not change with frequency.
  • the electrical component having a plurality of parameters further includes an inductance component.
  • the inductance element is included in an inductance unit, and the equivalent circuit model includes at least one of the inductance units, and the inductance unit is connected in series or in parallel with the capacitance unit. connection.
  • the inductance component in the inductance unit represents an effect of a wire and an electrode connection in the battery, and an imaginary part of the complex parameter indicates a corresponding loss.
  • each of the inductive units when the number of the inductive units is greater than one, each of the inductive units is connected in series or in parallel; at least one of the inductive units further includes a third in parallel or in series A resistive element having a real number parameter.
  • the third resistor is a resistor.
  • the equivalent circuit model of the present invention includes an inductance element and a capacitance element having complex parameters, and the imaginary part corresponding to the complex parameter represents the frequency-dependent loss characteristic of the electrical component in the battery model.
  • the equivalent circuit model does not include Warburg components or constant phase components (CPE), all electrical components have physical meaning;
  • the electrochemical impedance spectroscopy of lithium-ion batteries is simulated by the proposed model, at frequencies from 0.01 Hz to In the range of 10 kHz, the impedance error is less than 2 m ⁇ ;
  • the electrical component parameters of the proposed model are calculated and analyzed, and the complex component parameters are calculated by fitting, so that the dynamic charging of the lithium ion battery can be performed by the proposed equivalent circuit model.
  • the discharge performance was simulated and the simulation accuracy was high.
  • 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 of a second preferred embodiment of the present invention
  • FIG. 3 shows a battery equivalent circuit model of a third preferred embodiment of the present invention
  • Figure 5 is a diagram showing a battery equivalent circuit model of a fifth preferred embodiment of the present invention.
  • FIG. 6 shows a battery equivalent circuit model of a third preferred embodiment of the present invention simulating an electrochemical impedance characteristic of a lithium iron phosphate/graphite battery of 5.5 Ah at 50% state of charge;
  • FIG. 7 is a diagram showing the battery equivalent circuit model of the third preferred embodiment of the present invention simulating the magnitude and phase of the electrochemical impedance of a lithium iron phosphate/graphite battery of 5.5 Ah in a 50% state of charge;
  • FIG. 8 is a diagram showing the simulation and measurement voltage of a 5.5 Ah lithium iron phosphate/graphite battery in a process of discharging a battery from a 50% state of charge for 10 s at a current of 5.5 A under the current equivalent circuit model of the third preferred embodiment of the present invention. curve;
  • 9(a) is a view showing a comparison between a simulation of a terminal voltage and a measurement result in an equivalent circuit model simulation process of a third preferred embodiment of the present invention.
  • Fig. 9(b) is a view showing a 5.5Ah lithium iron phosphate/graphite battery in a federal urban driving schedule under the simulation of a battery equivalent circuit model in accordance with a third preferred embodiment of the present invention.
  • the existing equivalent circuit model includes a Warburg component or a Constant Phase Element (CPE), which cannot accurately explain the physical essence of the non-electric component and cannot characterize the influence of the non-electric component on the overall performance of the battery.
  • the existing equivalent circuit model does not take into account frequency-dependent electrical losses and their effects on electrochemical impedance and charge and discharge characteristics of the battery.
  • the main innovation of the present invention is to provide a battery equivalent circuit model.
  • the inductance component and the capacitor component have complex parameters, which can reflect the power consumption characteristics of the electrical component; the parameters of all components of the equivalent circuit model, Both can be calculated by fitting the measured electrochemical impedance characteristics to analyze their different effects in different frequency ranges.
  • the equivalent circuit model of the invention the simulation results of the electrochemical impedance spectroscopy and the dynamic charge and discharge characteristics are high, and all errors are less than 5%.
  • the battery equivalent circuit model of the present invention will be described in detail with a lithium ion battery as a representative.
  • the battery equivalent circuit model of the present invention is also fully applicable to other battery types such as nickel-cadmium batteries, nickel-hydrogen batteries, and lead-acid batteries.
  • FIG. 1 shows a battery equivalent circuit model of a first preferred embodiment of the present invention.
  • an electrical component having a plurality of parameters in this embodiment is a capacitor C e *.
  • all complex variables are Mark with *.
  • the imaginary part of the capacitance C e * represents the frequency-dependent loss characteristic of the battery.
  • the capacitor C e * is included in the capacitor unit, and the capacitor C e * is connected in parallel with the resistor R t to form a capacitor unit.
  • the constant phase component is usually connected in parallel with the ohmic resistor, or the ohmic resistor is connected in series with the Warburg component and the constant phase component is connected in parallel to form an RC unit for simulating the actual condition of the battery. Since the equivalent circuit model of the present invention may completely exclude the Warburg or constant phase components, it is only necessary to give the capacitance C e * a plurality of parameters, so that all the electrical components have physical meaning.
  • the capacitor C e * is connected in parallel with the first resistive element to form a capacitor unit, and the first resistor element, that is, the resistor R t in the present embodiment, has a real parameter. It can also be understood that the first resistive element is a non-essential element. Under the premise that the simulation precision is not high, the equivalent circuit model of the embodiment may not include the first resistive element, and the capacitor C e * separately constitutes the capacitor unit.
  • the electrical component having a plurality of parameters further includes an inductance component, and the imaginary components of the inductance L* and the capacitance C e * are collectively represented. Battery frequency dependent loss characteristics.
  • the inductance L* has an inductance value of a complex parameter which is generated by the connection of the wire and the electrode.
  • the inductance L* alone constitutes an inductance unit.
  • an inductor with a real parameter is used in series with the RC unit to characterize the connection between the wire and the electrode.
  • the inductance of the real parameter cannot indicate the effect of the frequency change on its loss characteristics.
  • the capacitor C e * is connected in parallel with the resistor R t and connected in series with the inductor L*.
  • the inductor element and the capacitor element having a plurality of parameters can accurately represent the physical meaning of the electrical component.
  • the equivalent circuit model includes at least one capacitor unit. That is, the number of the capacitance units may be not only one as shown in Fig. 1, but also a plurality of, and the complex parameter corresponding to the imaginary part of the capacitance element in each of the capacitance units indicates the loss characteristic of the corresponding element which changes with frequency.
  • Inductance L* indicates the connection effect between the wire and the electrode, mainly affecting the electrochemical impedance characteristics in the high frequency range; the parallel connection of the capacitance C e * and the resistance R t mainly affects the electrochemical impedance characteristics in the intermediate frequency range; the capacitance C 0 * It mainly affects the electrochemical impedance characteristics of the low frequency range.
  • the respective capacitor units when the number of capacitor units is greater than one, are connected in series or in parallel to accommodate a complicated battery construction situation. Similar to the foregoing, in the premise that the accuracy of the simulation is not high, the capacitor units connected in series or in parallel may be composed only of capacitor elements having a plurality of parameters. At least one of the capacitor units further includes a first resistor element in parallel with the capacitor element for improving analog accuracy. All of the capacitor units may include the first resistor element, or may only partially include the first resistor element. Of course, none of the first resistor elements may be included, and each capacitor unit represents a different electrochemical impedance characteristic, for example, respectively Electrochemical impedance characteristics in different frequency ranges.
  • the equivalent circuit model includes at least one of the inductor units. That is, the number of the inductance units may be not only one as shown in FIG. 2 or FIG. 3, but also multiple, and the complex parameter of the inductance element in each of the inductance units corresponds to the imaginary part indicating the loss of the connection effect of the wire and the electrode. .
  • the inductance element is included in the inductance unit, and L 0 * is connected in parallel with the resistor R t ' to form an inductance unit.
  • the inductance L 0 * is connected in parallel with the third resistance element to constitute an inductance unit, and the third resistance element, that is, the resistor R t ' in the present embodiment, has a real parameter.
  • the inductance L 0 * can also be connected in series with the third resistance element to form an inductance unit.
  • the third resistive element is a non-essential element in the inductive unit.
  • the inductive unit may not include the first resistive element, such as the inductor L*, and the inductor unit is separately formed by the inductor L*.
  • the respective inductance units are connected in series or in parallel, and all of the inductance units may include the third resistance element, or may only partially include the third resistance element.
  • the third resistance element may not be included.
  • the inductive elements characterize different electrochemical impedance characteristics, for example, respectively representing electrochemical impedance characteristics in different frequency ranges.
  • the number of capacitor units may be plural.
  • the capacitor C e * is connected in series with the resistor R t1 and connected in parallel with the resistor R t2 to accommodate a complicated battery construction situation under analog precision requirements. That is, inside a capacitor unit, there may be a plurality of first resistor elements, and the capacitor elements are connected in series with one of the first resistor elements in parallel with the other portion of the first resistor element.
  • the inductive unit may have a structure in which a plurality of third resistive elements may be provided inside one of the inductive units, and the inductive element is connected in series with a part of the third resistive element and in parallel with the third resistive element of the other part.
  • the equivalent circuit model includes two inductor units and two capacitor units, each of which is composed of an inductor unit or a capacitor unit. Same as in Figure 4. The difference is that an inductor unit is connected in parallel with an inductor unit, which is composed of an inductor L*, which is composed of a capacitor C 0 * and a resistor R t3 in parallel. In the equivalent circuit model of this embodiment, other inductor units and capacitor units are connected in series.
  • an equivalent circuit model includes a plurality of inductor units or a plurality of capacitor units, part of the inductor units are connected in parallel, and are connected in series with other inductor units and capacitor units; or, after some capacitor units are connected in parallel, It is connected in series with other inductor units and capacitor units to adapt to complex battery construction situations.
  • the third resistor is composed of a resistor R t ', and L 0 * is connected in parallel with the resistor R t ' to form an inductor unit.
  • the resistor R t ' represents the resistance value after the plurality of resistors are connected in series and/or in parallel.
  • the equivalent circuit model of the third preferred embodiment of the lithium ion battery of the present invention will be taken as an example to illustrate the working principle of the equivalent circuit model.
  • L*, C e * and C 0 * can be expressed by the following formulas (1), (2), (3):
  • L, C e and C 0 are the real parts of L*, C e * and C 0 *, respectively, and represent the inductance and capacitance values of the real numbers, respectively.
  • L', C e ', and C 0 ' are the corresponding imaginary parts and represent the losses of the corresponding components, respectively.
  • L*, C e *, and C 0 * may also be expressed by the following formulas (4), (5), (6):
  • ⁇ L , ⁇ Ce and ⁇ C0 are phase angles of L*, C e * and C 0 *, respectively.
  • Z L *, Z Ce * and Z C0 * represent complex impedances of L*, C e * and C 0 *, and can be expressed by equations (7), (8), (9):
  • Z B * can be calculated by substituting the formulas (7), (8), and (9) into the formula (10). All of the variables used to illustrate Z B * are clearly important and physically significant compared to the previously reported equivalent circuit model.
  • N is the total number of data.
  • X t and X s are measurement data and analog data, respectively. Is the average of X t .
  • the error function E is a function of difference between the analog data and the measured data, and the range of E is 0 to 1.
  • the error function is not only used to characterize the accuracy of the electrochemical impedance characteristics based on the proposed equivalent circuit model fit, but also to characterize the consistency between the simulated dynamic performance of the lithium ion battery and the test results. Among them, the simulated dynamic performance is predicted by the fitting element parameters of the equivalent circuit model.
  • a cylindrical LiFePO 4 battery having a rated capacity of 5.5 Ah was used as a research object (32650, Shenzhen Optimum Nano Energy Co., Ltd., Shenzhen, China).
  • the electrochemical impedance spectroscopy of the lithium ion battery at 50% state of charge (SOC) was passed through an electrochemical workstation (model Reference 600, manufactured by Gamry Instruments, Warminster, USA) at an open circuit voltage (AC) of 5 mV.
  • SOC state of charge
  • AC open circuit voltage
  • the measurement is performed under the condition that the frequency range is from 0.01 Hz to 10 kHz. Conducting electrochemical impedance measurements at low frequencies below 0.01 Hz will consume more time, and sometimes measurement by actual battery charge and discharge currents is not feasible.
  • the dynamic charge and discharge performance of the battery was actually tested by a battery test system (CT-4001-5V500A, Xinwei Co., Ltd., Shenzhen, China).
  • the state of charge of the battery was maintained at 50% before each test.
  • the battery was charged to 3.65 V at a charge rate of 0.2 (C-rate), and then the charge voltage was maintained at 3.65 V until the charge current was below 55 mA (0.01 charge rate). After waiting 15 minutes, The battery was discharged at a discharge rate of 0.2, and the discharge amount was 2.75 Ah. Wait 3 hours before each test to achieve a 50% state of charge. All preparation and test procedures were carried out at an ambient temperature of 25 °C.
  • the theoretical electrochemical impedance spectroscopy of the lithium iron phosphate battery can be obtained by fitting the measurement data by the simulated annealing optimization algorithm.
  • Figure 6 shows a comparison between the fitted electrochemical impedance spectroscopy and the measured electrochemical impedance spectroscopy, as shown in Figure 6.
  • the fitted impedance is Visually matches the measured values very well.
  • Figure 7 shows the comparison of the magnitude and phase of the electrochemical impedance spectroscopy fitted in a certain frequency range and the measured electrochemical impedance spectroscopy characteristics, as shown in Figure 7, at a frequency of 0.01 Hz.
  • the fitting element parameters of the equivalent circuit model shown in Fig. 3 are shown in Table 1.
  • the pure ohmic resistance of R 0 is 32.82 m ⁇ , and the resistance value is not affected by the frequency.
  • the value of L' is -48.01nH, indicating the loss of inductance due to battery current collectors and cables.
  • the inductance value of L is 321.1nH, which is mainly used to make the imaginary part of Z B * positive, and the electrochemical impedance is close to 0.01 ⁇ as the frequency increases.
  • C 0 mainly affects the electrochemical impedance when the frequency range is lower than 1 Hz; the C 0 value is 1321 F, which is more than one thousand times the value of C e (1.241 F).
  • C e mainly affects the electrochemical impedance in the intermediate frequency range above 1 Hz.
  • Figure 8 shows the simulated and measured terminal voltage of a battery discharged for 10 s at a current of 5.5 A (discharge rate of 1), as shown in Figure 8, during and after the discharge process, The voltage curve predicted by the proposed model has good agreement with the measured curve.
  • 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 was further studied in accordance with Federal Urban Driving Schedules (FUDS). As a typical duty cycle, the FUDS lasts for 1372 s and is typically used to verify the accuracy of the battery model.
  • FUDS Federal Urban Driving Schedules
  • the real-time charge and discharge signal is generated by the battery test system according to the preset power of the FUDS exercise period, and the real-time charge and discharge signal is applied to the battery.
  • the equivalent circuit model can calculate the terminal voltage curve of the battery by the current data recorded in the time domain.
  • Figure 9 shows a comparison of the terminal voltages of the analog and measured values over the entire dynamic process. As shown in Figure 9, the maximum voltage difference is 0.0357V.
  • the error of the terminal voltage of the FUDS cycle is calculated by the formula (11) to be 3.32%. The results further verify that the proposed model has excellent prediction accuracy of dynamic characteristics.
  • the equivalent circuit model of the lithium ion battery proposed in the invention includes an inductance and a capacitance element and has a complex parameter. Compared with the existing model, since there is no Warburg element or a constant phase element, all the electrical elements in the model have physical meanings. .
  • the parameters of all the components of the proposed equivalent circuit model for the LiFePO 4 battery were calculated by fitting the measured electrochemical impedance characteristics to analyze the different effects in different frequency ranges. Through the model, the simulation results of the electrochemical impedance spectroscopy and the dynamic charge and discharge characteristics are highly accurate, and all errors are less than 5%.

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Abstract

提供一种电池等效电路模型，用于模拟电化学阻抗谱以及电池动态充放电特性，包括具有复数参数的电气元件，复数参数里的虚部表示与频率有关的损耗特性。电感元件和电容元件具有复数参数。采用所述等效电路模型计算磷酸铁锂电池电化学阻抗谱的结果以及动态充放电特性精度高，所有误差均小于5%。

Description

一种电池等效电路模型 技术领域
本发明涉及以锂离子电池为代表的电池技术领域，更具体的说，涉及一种电池等效电路模型。
背景技术
由于锂电池的使用寿命较长，并具有较高的能量密度以及安全性，因此对于新能源车辆、电网储能系统以及消费性电子产品而言，锂离子电池的需求日益增长。在实际应用中，获得锂离子电池精确的动态特性非常重要。一方面，在不同的实际工况(工作负载)和工作环境下，精确的动态电池模型对于电池的监测、诊断以及管理都是非常必要的。另一方面，复杂电气系统中的运行策略和结构优化，都取决于电池动态性能的模拟。与电化学模型相比，电池的等效电路模型的计算效率往往更高，因为电化学模型需要彻底理解和描述复杂的电化学过程和特征，而这样做有时并不完全可行。而将等效电路模型植入电池管理系统和网络中，对于电池系统产品应用则实际可行。
测量电化学阻抗(EI)谱被认为是在不破坏电池的前提下，宽频率范围内检测电池内部不同过程和特性的有效方法，。采用适当开发的等效电路模型来研究锂离子电池的电化学阻抗特性是至关重要的，可以用以研究锂离子电池中各部分及其界面的不同特性。最典型的等效电路模型包括直流内阻、RC单元(与电阻并联的恒相位元件或电容)、以及Warburg(瓦尔堡)元件，分别表示欧姆电阻、双电层结构的效应以及嵌入电极中锂离子扩散所产生的效应。一些等效电路模型具有额外的电感元件，用于表征导线和电极之间的连接。更多的RC单元电路也可以用于更详细和精确地表征不同部分的不同影响。在至今为止已经报道的模型中，作为非电气元件的恒相位元件(CPE)通常用于计算电化学阻抗谱，以获得更精确的结果。然而，这会导致无法清楚 地解释其物理实质以及对于电池整体性能的影响。同时，在现有的等效电路模型中，并未考虑到与频率相关的电气损耗、以及电气耗损对电化学阻抗和锂离子电池的充放电特性的影响。
发明内容
本发明所要解决的技术问题在于：提供一种电池等效电路模型，以锂离子电池为代表的电池，解决了现有的电池等效电路模型无法准确解释非电气元件的物理实质、无法表征非电气元件对于电池整体性能的影响、并未考虑到与频率相关的电气损耗及其对电化学阻抗和电池的充放电特性的影响等问题。
本发明解决上述问题的技术方案在于：提供一种电池的等效电路模型，用于模拟电化学阻抗谱以及电池动态充放电特性，其特征在于，包括具有复数参数的电气元件，复数参数里的虚部表示与频率有关的损耗特性，其中，所述具有复数参数的电气元件包括电容元件。
优选的，在本发明提供的等效电路模型中，所述电容元件包含在电容单元中，所述等效电路模型包括至少一个所述电容单元，其中电容元件表示电池电极/电解液界面形成的双电层效应。每个所述电容单元中电容元件的复数参数的虚部表示其对应的损耗。
优选的，在本发明提供的等效电路模型中，所述电容单元的数量大于一个时，各个所述电容单元串联或者并联连接；所述电容单元中的中的至少一个还包括与其相并联的第一电阻元件，表示电池的自放电效应，所述第一电阻元件具有实数参数。
优选的，在本发明提供的等效电路模型中，所述第一电阻元件为一个电阻。
优选的，在本发明提供的等效电路模型中，还包括第二电阻，所述第二电阻具有实数参数，表示所述电池不随频率变化而改变的直流内阻。
优选的，在本发明提供的等效电路模型中，所述具有复数参数的电气元件还包括电感元件。
优选的，在本发明提供的等效电路模型中，所述电感元件包含在电感单元中，所述等效电路模型包括至少一个所述电感单元，所述电感单元与所述电容单元串联或者并联连接。
优选的，在本发明提供的等效电路模型中，所述电感单元中电感元件表示电池中导线和电极连接等方面的效应，其复数参数的虚部表示其对应的损耗。
优选的，在本发明提供的等效电路模型中，所述电感单元的数量大于一个时，各个所述电感单元串联或者并联连接；至少一个所述电感单元还包括与其相并联或者串联的第三电阻元件，所述第三电阻元件具有实数参数。
优选的，在本发明提供的等效电路模型中，所述第三电阻为一个电阻。
实施本发明，具有如下有益效果：本发明的等效电路模型包括的电感元件和电容元件具有复数参数，这些复数参数对应的虚部表示在该电池模型中的电气元件与频率有关的损耗特性。该等效电路模型不包括Warburg(瓦尔堡)元件或恒相位元件(CPE)，所有的电气元件具有物理意义；通过所提出的模型模拟锂离子电池的电化学阻抗谱，在频率从0.01Hz到10kHz的范围内，阻抗的误差小于2mΩ；计算并分析所提出模型的电气元件参数，通过拟合计算得出的复数元件参数，使得可以通过所提出的等效电路模型对锂离子电池的动态充放电性能进行模拟，且模拟精度较高。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1示出了本发明第一较佳实施例的电池等效电路模型；
图2示出了本发明第二较佳实施例的电池等效电路模型；
图3示出了本发明第三较佳实施例的电池等效电路模型；
图4示出了本发明第四较佳实施例的电池等效电路模型；
图5示出了本发明第五较佳实施例的电池等效电路模型；
图6示出了本发明第三较佳实施例的电池等效电路模型模拟在50％的充电状态下5.5Ah的磷酸铁锂/石墨电池的电化学阻抗特性；
图7示出了本发明第三较佳实施例的电池等效电路模型模拟在50％的充电状态下5.5Ah的磷酸铁锂/石墨电池的电化学阻抗的大小和相位；
图8示出了本发明第三较佳实施例的电池等效电路模型模拟在5.5A电流条件下从50％充电状态放电10s的过程中5.5Ah的磷酸铁锂/石墨电池的模拟和测量电压曲线；
图9(a)示出了本发明第三较佳实施例的等效电路模型模拟过程中，端电压的模拟和测量结果之间的对比；
图9(b)示出了本发明第三较佳实施例的电池等效电路模型模拟过程中，5.5Ah的磷酸铁锂/石墨电池在美国联邦城市行驶工况(Federal Urban Driving Schedule)条件下的模拟电压的绝对误差值|ΔV|。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。
现有的等效电路模型包括Warburg(瓦尔堡)元件或恒相位元件(Constant Phase Element,CPE)，无法准确解释非电气元件的物理实质、无法表征非电气元件对于电池整体性能的影响，同时，现有的等效电路模型并未考虑到与频率相关的电气损耗及其对电化学阻抗和电池的充放电特性的影响等问题。本发明的主要创新点在于：提供一种电池等效电路模型，电感元件和电容元件具有复数参数，可以反映出电气元件与频率有关的耗耗特性；该等效电路模型的所有元件的参数，均可以通过拟合测量的电化学阻抗特性计算得到，以在不同频率范围内分析其不同的影响。通过本发明等效电路模型使得电化学阻抗谱的模拟结果以及动态充放电特性精度高，所有误差均小于5％。
下文将以锂离子电池为代表详细说明本发明的电池等效电路模型。当然，本发明的电池等效电路模型也完全适用于镍镉电池、镍氢电池、铅酸电池等其它电池种类。
图1示出了本发明第一较佳实施例的电池等效电路模型，如图1所示，本实施例中具有复数参数的电气元件为电容Ce*，本发明中，所有复数变量均采用*标记。其中，电容Ce*的虚部表示电池与频率有关的损耗特性。
在本实施例中，电容Ce*包含在电容单元中，电容Ce*与电阻Rt并联连接构成电容单元。在现有的等效电路模型中，恒相位元件通常与欧姆电阻并联，或者，欧姆电阻与瓦尔堡元件串联后与恒相位元件并联，形成一个RC单元，用以模拟电池实际情况。由于本发明的等效电路模型中，完全可以不包括瓦尔堡元件或恒相位元件，只需赋予电容Ce*以复数参数，即可使得所有的电气元件具有物理意义。与现有的等效电路模型类似，为了提高模拟精度，电容Ce*与第一电阻元件并联连接构成电容单元，第一电阻元件即本实施例中的电阻Rt，具有实数参数。也可以理解为，第一电阻元件为非必须元件，在模拟精度要求不高的前提下，本实施例的等效电路模型可以不包括第一电阻元件，由电容Ce*单独构成电容单元。
图2示出了本发明第二较佳实施例的电池等效电路模型，如图2所示，具有复数参数的电气元件还包括电感元件，电感L*和电容Ce*的虚部共同表示电池与频率有关的损耗特性。电感L*具有复数参数的电感值，该电感值产生于导线和电极的连接。
在本实施例中，电感L*单独构成电感单元。在现有的等效电路模型中，具有实数参数的电感用于与RC单元串联，用于表征导线和电极之间的连接。但是实数参数的电感无法表示频率变化对其损耗特性的影响。电容Ce*与电阻Rt的并联后与电感L*串联连接，具有复数参数的电感元件和电容元件能够准确的表示电气元件的物理意义。
图3示出了本发明第三较佳实施例的电池等效电路模型，如图3所示，等效电路模型包括至少一个电容单元。即，电容单元的数量不仅可以如图1中所示的一个，也可以为多个，每个所述电容单元中电容元件的复数参数对 应虚部表示对应元件随频率变化而改变的损耗特性。电感L*表示导线和电极的连接效应，主要影响高频范围内的电化学阻抗特性；电容Ce*与电阻Rt的并联连接，主要影响中频范围内的电化学阻抗特性；电容C0*主要影响低频范围的电化学阻抗特性。
在本实施例中，当电容单元的数量大于一个时，各个电容单元串联或者并联连接，以适应复杂的电池构造情形。与前文类似，在模拟精度要求不高的前提下，相串联或者并联的各个电容单元可以只由具有复数参数的电容元件构成。电容单元中的至少一个还包括与电容元件相并联的第一电阻元件，用以提高模拟精度。所有电容单元可以都包括第一电阻元件，也可以只是部分包括第一电阻元件，当然，也可以都不包括第一电阻元件，每个电容单元表征各自不同的电化学阻抗特性，例如，分别表示不同频率范围内的电化学阻抗特性。
图4示出了本发明第四较佳实施例的电池等效电路模型，如图4所示，等效电路模型包括至少一个所述电感单元。即，电感单元的数量不仅可以如图2或者图3中所示的一个，也可以为多个，每个所述电感单元中电感元件的复数参数对应虚部表示导线和电极的连接效应的损耗。
在本实施例中，电感元件包含在电感单元中，L0*与电阻Rt'并联连接构成电感单元。与现有的等效电路模型类似，为了提高模拟精度，电感L0*与第三电阻元件并联连接构成电感单元，第三电阻元件即本实施例中的电阻Rt'，具有实数参数。当然，电感L0*也可以与第三电阻元件串联连接构成电感单元。
也可以理解为，第三电阻元件在电感单元中为非必须元件，在电路情况不复杂的情形下，电感单元可以不包括第一电阻元件，如电感L*，由电感L*单独构成电感单元。电感单元的数量大于一个时，各个电感单元串联或者并联连接，所有电感单元可以都包括第三电阻元件，也可以只是部分包括第三电阻元件，当然，也可以都不包括第三电阻元件，每个电感单元表征各自不同的电化学阻抗特性，例如，分别表示不同频率范围内的电化学阻抗特性。
在本实施例中，包括有串联的两个电容单元，当然电容单元的数量也可以为多个。其中一个电容单元中，电容Ce*与电阻Rt1的串联后，与电阻Rt2 并联连接，以适应模拟精度要求下的复杂的电池构造情形。即，在一个电容单元内部，可以具有多个第一电阻元件，电容元件与其中一部分第一电阻元件串联后与另一部分的第一电阻元件并联。类似的，电感单元也可以具有此种结构，即在一个电感单元内部，可以具有多个第三电阻元件，电感元件与其中一部分第三电阻元件串联后与另一部分的第三电阻元件并联。
图5示出了本发明第五较佳实施例的电池等效电路模型，如图5所示，等效电路模型包括两个电感单元和两个电容单元，每个电感单元或者电容单元的组成与图4中相同。不同之处在于，一个电感单元与一个电感单元并联连接，该电感单元由电感L*组成，该电容单元电容C0*和电阻Rt3并联组成。在本实施例的等效电路模型中，其它的电感单元和电容单元依次串联。类似的，在一个等效电路模型中包括有多个电感单元或者多个电容单元时，部分的电感单元并联连接后，与其它电感单元、电容单元相串联；或者，部分电容单元并联连接后，与其它电感单元、电容单元相串联，以分别适应复杂的电池构造情形。
在本实施例中，第三电阻由一个电阻Rt'组成，L0*与电阻Rt'并联连接构成电感单元。该电阻Rt'表示多个电阻串联和/或并联之后的电阻值。
下文将以本发明锂离子电池第三较佳实施例的等效电路模型为例，说明等效电路模型的工作原理。
在本发明锂离子电池第三较佳实施例的等效电路模型中，L*,Ce*和C0*可以由以下公式(1)、(2)、(3)来表示：
L*＝L+i·L'               (1)
Ce*＝Ce+i·Ce'               (2)
C0*＝C0+i·C0'              (3)
其中，L、Ce和C0分别是L*、Ce*和C0*的实部，并分别表示实数的电感和电容值。L'、Ce'和C0'是对应的虚部，并分别表示相应元件的损耗。可选择地，L*、Ce*和C0*也可以由以下公式(4)、(5)、(6)来表示：
L*＝L·(1+i·tanθL)           (4)
Ce*＝Ce·(1+i·tanθCe)         (5)
C0*＝C0·(1+i·tanθC0)        (6)
其中，θL、θCe和θC0分别为L*、Ce*和C0*的相位角。
ZL*、ZCe*和ZC0*表示L*、Ce*和C0*的复数阻抗，并且可以由公式(7)、(8)、(9)来表示：
ZL*＝i·2πf·L*＝-2πfL'+i·2πfL      (7)
Figure PCTCN2014095317-appb-000001
Figure PCTCN2014095317-appb-000002
其中，f为频率。从公式(7)、(8)、(9)可以看出，L'和f决定了电感L*的电阻值；而电容Ce*和电容C0*的电阻抗值为电容Ce*和电容C0*的实部、虚部和f的函数。
根据图3，锂离子电池的整个复数电化学阻抗ZB*可以表示为：
Figure PCTCN2014095317-appb-000003
ZB*可以通过将公式(7)、(8)和(9)代入公式(10)中计算得到。与先前所报道的等效电路模型相比，用于说明ZB*的所有变量很显然都很重要，并具有物理意义。
基于这样的等效电路模型，通过将模拟的电化学阻抗特征与所测量的数据相拟合，可以更加明确地识别所有的电气元件参数，并认清这些电气元件参数对锂离子电池性能的影响。
为了表征模拟值和测量值之间的区别，在本文中引入了误差函数E，见公式(11)：
Figure PCTCN2014095317-appb-000004
这里，N是数据总数。Xt和Xs分别为测量数据和模拟数据。
Figure PCTCN2014095317-appb-000005
是Xt的平均值。误差函数E为模拟数据和测量数据之间差异函数，且E的范围为0～1。在本文中，误差函数不仅用于表征基于所提出的等效电路模型拟合的电化学阻抗特性的精度，而且用于表征锂离子电池的模拟动态性能和测试结果之间的一致性。其中，模拟动态性能通过等效电路模型的拟合元件参数来预测。
实验：
在本实施例中，以额定容量为5.5Ah的圆柱形LiFePO4电池商品为研究对象(32650，深圳市沃特玛电池有限公司(Shenzhen OptimumNano Energy Co.,Ltd)，深圳，中国)。该种锂离子电池在50％充电状态下(SOC)的电化学阻抗谱通过电化学工作站(型号为Reference 600，产自Gamry Instruments公司，沃明斯特，美国)在开路电压(交流电)为5mV、频率范围为0.01Hz～10kHz的条件下进行测量。在频率低于0.01Hz的低频下进行电化学阻抗测量将会消耗更多的时间，并且有时通过实际的电池充放电流进行测量并不可行。因此，本文并不考虑低于0.01Hz的低频条件下对电池性能产生的影响。因此，对于磷酸铁锂电池，2mHz以下的扩散过程可以忽略。本文也没有研究相应的Warburg元件以及这些元件在所提出的等效电路模型中的影响。
电池的动态充放电性能是实际上通过电池测试系统(CT-4001-5V500A，新威尔有限公司，深圳，中国)进行测试。在每次试验之前，电池的充电状态维持在50％。该电池以0.2的充电速率(C-rate)充电至3.65V，随后充电电压保持在3.65V直到充电电流低于55mA(0.01充电速率)。等待15min后， 电池以0.2的放电速率进行放电，放电量为2.75Ah。在每次试验开始前，等待3小时以实现50％的充电状态。所有的准备以及试验步骤均在25℃的环境温度下进行。
结果分析：
通过本实施例所提出的等效电路模型，通过模拟退火优化算法拟合测量数据可以获得磷酸铁锂电池的理论电化学阻抗谱。图6示出了拟合的电化学阻抗谱和测量的电化学阻抗谱之间的对比，如图6所示，在所研究的频率范围(从0.01Hz到10kHz)内，拟合的阻抗在视觉上与测量值非常好地匹配。为了研究拟合结果的精度，图7示出了一定频率范围内拟合的电化学阻抗谱和测量的电化学阻抗谱特征的大小和相位的对比，如图7所示，在频率为0.01Hz时，两者之间的大小及相位差均达到最大值，分别为2mΩ和3.28°。通过公式(11)计算可知，大小和相位的误差函数E分别为4.87％和1.51％。这证明了所提出的等效电路模型具有较高的电化学阻抗模拟精度。
图3所示的等效电路模型的拟合元件参数如表1所示。R0的纯欧姆阻值为32.82mΩ，该电阻值不受频率的影响。L'的值为-48.01nH，表明了由于电池集电器和电缆所产生的电感损耗。L的电感值为321.1nH，主要用于使得ZB*的虚部为正，并随着频率的增长，电化学阻抗接近0.01Ω。C0主要在频率范围低于1Hz时影响电化学阻抗；该C0值为1321F，是Ce(1.241F)数值的一千倍以上。其中Ce主要在高于1Hz的中频范围内影响电化学阻抗。C0'的绝对值为C0的63.9％；而Ce*的虚部绝对值为其实部的59.5％。这两个百分比反映了有关频率的损耗特性主要源于电化学反应以及电极界面电容。
表1.用于锂离子磷酸/石墨电池的等效电路模型元件的拟合参数
Figure PCTCN2014095317-appb-000006
Figure PCTCN2014095317-appb-000007
在所研究的电池的时间域内的动态充放电性能也通过这种模型进行研究。图8示出了在电流为5.5A的条件下(放电速率为1)放电10s的电池的模拟和测量的端电压(terminal voltage)，如图8所示，在放电过程中以及放电过程后，通过所提出的模型预测的电压曲线与测量所得的曲线具有良好的一致性。电池的脉冲放电性能的误差函数E为1.44％。按照联邦城市行驶工况(FUDS，Federal Urban Driving Schedules)，对所研究的磷酸铁锂电池的动态性能进行进一步的研究。作为典型的工作周期，该FUDS持续1372s，通常用于验证电池模型的精度。按照FUDS行使周期的预设功率通过电池测试系统产生实时充放电信号，并将该实时充放电信号应用在电池中。通过在时间域内所记录的电流数据，该等效电路模型可以计算出电池的终端电压曲线。图9示出了在整个动态过程中模拟值和测量值的终端电压的对比，如图9所示，最大的电压差为0.0357V。通过公式(11)计算出FUDS周期的终端电压的误差为3.32％。该结果进一步验证了所提出的模型具有极好的动态特性预测精度。
在发明提出的锂离子电池的等效电路模型包括电感和电容元件并具有复数参数，相比现有的模型，由于不具有Warburg元件或恒相位元件，在本模型中所有的电气元件具有物理意义。用于LiFePO4电池的、所提出的等效电路模型的所有元件的参数，均通过拟合测量的电化学阻抗特性计算得到，以在 不同频率范围内分析其不同的影响。通过本模型使得电化学阻抗谱的模拟结果以及动态充放电特性精度高，所有误差均小于5％。

Claims (8)

  1. 一种电池等效电路模型，用于模拟电化学阻抗谱以及电池动态充放电特性，其特征在于，包括具有复数参数的电气元件，复数参数里的虚部表示与频率有关的损耗特性，其中，所述具有复数参数的电气元件包括电容元件。
  2. 根据权利要求1所述的电池等效电路模型，其特征在于，所述电容元件包含在电容单元中，所述等效电路模型包括至少一个所述电容单元，其中所述电容元件表示电池电极/电解液界面形成的双电层效应，每个所述电容单元中电容元件的复数参数的虚部表示其对应的损耗。
  3. 根据权利要求2所述的电池等效电路模型，其特征在于，所述电容单元的数量大于一个时，各个所述电容单元串联或者并联连接；所述电容单元中的至少一个还包括与其相并联的第一电阻元件，表示电池的自放电效应，所述第一电阻元件具有实数参数。
  4. 根据权利要求3所述的电池等效电路模型，其特征在于，还包括第二电阻，所述第二电阻具有实数参数，表示所述锂离子电池不随频率变化而改变的直流内阻。
  5. 根据权利要求1～4中任一项所述的电池等效电路模型，其特征在于，所述具有复数参数的电气元件还包括电感元件。
  6. 根据权利要求5所述的电池等效电路模型，其特征在于，所述电感元件包含在电感单元中，所述等效电路模型包括至少一个所述电感单元，所述电感单元与所述电容单元串联或者并联连接。
  7. 根据权利要求6所述的电池等效电路模型，其特征在于，所述电感单元中电感元件表示电池中导线和电极连接的效应，其复数参数的虚部表示其对应的损耗。
  8. 根据权利要求7所述的电池等效电路模型，其特征在于，所述电感单元的数量大于一个时，各个所述电感单元串联或者并联连接；至少一个所述电感单元还包括与其相并联或者串联的第三电阻元件，所述第三电阻元件具有实数参数。
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