CN111722119B - Identification method for power battery fractional order equivalent circuit multi-characteristic fusion model - Google Patents

Identification method for power battery fractional order equivalent circuit multi-characteristic fusion model Download PDF

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CN111722119B
CN111722119B CN202010589756.XA CN202010589756A CN111722119B CN 111722119 B CN111722119 B CN 111722119B CN 202010589756 A CN202010589756 A CN 202010589756A CN 111722119 B CN111722119 B CN 111722119B
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张奇
张承慧
崔纳新
李岩
商云龙
段彬
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Hubei Techpow Electric Co ltd
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Abstract

The utility model discloses a power battery fractional order equivalent circuit multi-characteristic fusion model's identification method, includes: creating a power battery fractional order equivalent circuit multi-characteristic fusion model, which comprises a capacity characteristic submodel, an electrical characteristic submodel and a fractional order open-circuit voltage OCV-SOC model, wherein the capacity characteristic submodel describes the state of charge of a battery and adds self-discharge internal resistance to express the self-discharge characteristic of the battery, the electrical characteristic submodel describes the voltage-current characteristic of the battery, the capacity characteristic submodel and the electrical characteristic submodel establish a relation through the fractional order open-circuit voltage OCV-SOC model, charge-discharge current and an SOC control voltage source OCV, and a controlled voltage source OCV in the electrical characteristic submodel changes along with the change of the SOC of the capacity characteristic submodel; and carrying out a charge-discharge test on the power battery, and identifying each parameter in the power battery fractional order equivalent circuit multi-characteristic fusion model. The constructed power battery fractional order equivalent circuit multi-characteristic fusion model expresses the self-discharge characteristic of the battery.

Description

Identification method for power battery fractional order equivalent circuit multi-characteristic fusion model
Technical Field
The disclosure relates to an identification method of a power battery fractional order equivalent circuit multi-characteristic fusion model.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Due to energy conservation and environmental protection, new energy automobiles, especially electric automobiles, have become the main direction of the automobile industry in the future. The power battery is a major bottleneck restricting the scale development of the electric automobile. The battery management system BMS is crucial for the safe and reliable operation of power batteries and the efficient use of energy. The battery model has important significance for the functional design of the battery management system BMS, and is the basis for realizing accurate estimation of the battery state including the battery state of charge (SOC), the state of health (SOH) and the like.
According to the battery modeling mechanism, the battery model mainly comprises an equivalent circuit model, an electrochemical model, an analytic model, a thermal model, a neural network model and the like. The equivalent circuit model uses different circuit components according to the physical characteristics of the battery, and comprises a circuit formed by a voltage source, a current source, a resistor, a capacitor and the like to equivalently simulate the output characteristics of the power battery, particularly the voltage-current output electrical characteristics, so that the equivalent circuit model is widely applied to the fields of power electronic simulation and analysis and the like. The equivalent circuit model has the characteristics of simple and visual form and clear physical significance; the model parameters are relatively easy to identify, and the accuracy is high.
The equivalent circuit models of the power battery which have been proposed at present mainly include Rint, GNL, PNVG and the like, and although the equivalent circuit models can describe the electrical characteristics of the battery more accurately, the inventor thinks that the following common problems exist:
(1) the voltage-current electrical characteristics of the battery are only described singly, the nonlinear capacity characteristics of the battery are not considered, and therefore the actual available capacity and the residual discharge time of the battery cannot be accurately estimated;
(2) the self-discharge phenomenon of the battery cannot be quantitatively expressed;
(3) the method is limited to an integer order model, and in fact, the internal reaction process of the battery is extremely complex, including electrochemical reaction, concentration polarization effect, conductive ion transfer and the like, so that the accuracy is low when the electrical characteristics of the battery are described by adopting the integer order model;
in summary, the existing battery equivalent circuit model cannot simultaneously represent the electrical characteristics and the capacity characteristics of the power battery, and also does not consider the influence of self-discharge internal resistance, and the modeling method is limited to the traditional integer order calculus, so that the model precision is limited, the remaining discharge time of the battery cannot be accurately estimated, and the function and the benefit of the battery management system BMS are seriously influenced.
Disclosure of Invention
In order to solve the problems, the invention provides an identification method of a power battery fractional order equivalent circuit multi-characteristic fusion model, which realizes the fusion of the voltage-current electrical characteristics of a power battery and the nonlinear capacity characteristics influenced by the discharge rate; meanwhile, the self-discharge internal resistance is brought into the battery model parameters to express the self-discharge characteristic of the battery; the fractional calculus is introduced into the model, so that more degrees of freedom of model parameters are realized, the dynamic performance is better, and the model precision is higher.
In order to achieve the purpose, the following technical scheme is adopted in the disclosure:
a method for identifying a power battery fractional order equivalent circuit multi-characteristic fusion model comprises the following steps:
creating a power battery fractional order equivalent circuit multi-characteristic fusion model, which comprises a capacity characteristic submodel, an electrical characteristic submodel and a fractional order open-circuit voltage OCV-SOC model, wherein the capacity characteristic submodel describes the state of charge of a battery, self-discharge internal resistance is added to express the self-discharge characteristic of the battery, the electrical characteristic submodel describes the voltage-current characteristic of the battery, the capacity characteristic submodel and the electrical characteristic submodel establish a relation through the fractional order open-circuit voltage OCV-SOC model, charge-discharge current and an SOC control voltage source OCV, and a controlled voltage source OCV in the electrical characteristic submodel changes along with the change of the SOC of the capacity characteristic submodel;
performing a constant-current charge and discharge test on the power battery to obtain the initial capacity of the battery and the available capacity of the battery under different discharge rates, and identifying parameters in a capacity characteristic sub-model; carrying out pulse discharge test on the power battery, acquiring test data under different SOC (state of charge), and identifying parameters in the electrical characteristic sub-model; and identifying the relation between the open-circuit voltage and the SOC of the battery at different SOCs according to the parameters in the obtained electrical characteristic sub-model.
Further, capacity characteristic submodelType, comprising fractional order capacitors C connected in parallel with current control current sources, respectivelyFQ1A fractional order capacitor CFQ2And self-discharge internal resistance RdAt fractional order of capacitance CFQ2Upper series resistance RQAt a self-discharge internal resistance RdUpper series ideal current source EdBy self-discharge internal resistance RdAnd an ideal current source EdCharacterizing the self-discharge characteristics of the cell by means of a fractional order capacitance CFQ1And a fractional order capacitance CFQ2The sum of the available capacities stored above represents the SOC state of the battery, the fractional order capacity CFQ2The unavailable capacity change represents the nonlinear capacity characteristic of the battery;
the electrical characteristic sub-model comprises an SOC control voltage source, wherein the positive terminal of the SOC control voltage source is connected with the positive terminal of the battery model through a charging branch and a discharging branch, and the negative terminal of the SOC control voltage source is connected with the negative terminal of the battery model through ohmic internal resistance Ro.
Furthermore, the voltage at the two ends of the current control current source is the open-circuit voltage of the battery, and the SOC control voltage source represents the open-circuit voltage of the battery.
Further, the expression of the fractional order open-circuit voltage OCV-SOC model is as follows:
ocv＝k0+k1soc+k2soc2-k3Eα,β(-k4socα)，k0-k4is a constant.
Further, after being connected in parallel, the charging branch circuit and the discharging branch circuit are connected in series between the positive terminal of the SOC control voltage source and the positive terminal of the battery model;
the discharge branch circuit comprises diodes D connected in series in sequence1A fractional order capacitor CF1And a resistance R1Parallel connected fractional order R1-CF1Loop, fractional order capacitor CF2And a resistance R2Parallel connected fractional order R2-CF2A loop;
the charging branch comprises reverse diodes D connected in series in sequence2A fractional order capacitor CF3And a resistance R3Parallel connected fractional order R3-CF3Loop, fractional order capacitor CF4And a resistance R4Parallel connected fractional order R4-CF4And (4) a loop.
Further, constant current discharge experiments under different multiplying powers are carried out on the battery, and the initial capacity Q of the battery is obtainedFQ1And available capacity Q of the battery at different discharge ratesFQkAccording to the initial capacity QFQ1And available capacity Q of the battery at different discharge ratesFQkIdentifying the fractional order capacitor CFQ1A fractional order capacitor CFQ2Resistance RQAnd self-discharge internal resistance Rd。
Further, the fractional order capacitance C of the batteryFQ1And CFQ2Can be obtained by the following formula:
Figure BDA0002555920430000041
Uratedrated voltage calibrated for the battery to leave factory; qratedIs the rated capacity, Q, of the batteryFQ1Is the initial capacity, Q, of the batteryFQkThe available capacity of the battery under different discharge rates.
Further, the battery is subjected to a pulse discharge test, test data such as an instant drop value of the battery terminal voltage when the battery starts to discharge, an instant jump value of the battery terminal voltage after the discharge is finished, a discharge current and zero input response of the battery terminal voltage under different SOC (state of charge) are obtained, and open circuit voltage OCV and ohmic internal resistance R are identified0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3And fractional order gamma and gamma1Concentration polarization fractional order capacitor CF2And CF4And fractional orders theta and theta1。
Further, during the discharging process, the terminal voltage of the battery is:
Figure BDA0002555920430000051
in the formula，UbatIs the battery terminal voltage; r0Ohmic internal resistance; OCV is the discharge open circuit voltage; gamma and theta are fractional order capacitance CF1And CF2Order of (1) satisfies 0<γ,θ<1; i is a discharge current; tau is1,τ2Time constants of the two fractional order RC loops are respectively; u shape1(0+) and U2(0+) is the initial value of terminal voltage of two fractional order RC loops at the moment when the battery discharge is finished, and when t → ∞ is reached, the terminal voltage U of the batterybatEqual to the open circuit voltage OCV of the battery.
Further, according to the parameters and the orders in the obtained electrical characteristic submodel, the open-circuit voltage OCV and the battery ohm internal resistance R are identified based on the least square method0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3Concentration polarization fractional order capacitor CF2And CF4Electrochemical polarization fractional order capacitance fractional order gamma and gamma1Concentration polarization fractional order capacitance fractional order theta1And θ is related to the battery state of charge, SOC.
Compared with the prior art, the beneficial effect of this disclosure is:
1. according to the identification method of the power battery fractional order equivalent circuit multi-characteristic fusion model, various characteristics such as battery output electrical characteristics, discharge rate influenced nonlinear capacity characteristics and battery self-discharge characteristics are fused into the unified equivalent circuit model, and fusion modeling of the internal and external characteristics of the power battery is achieved.
2. The identification method for the power battery fractional order equivalent circuit multi-characteristic fusion model is based on the fractional order calculus theory, effectively solves the strong nonlinear dynamic behavior of the power battery expressed by internal materials, electrochemical reaction and the like, and embodies the essential characteristics of the battery fractional order; the fractional calculus is introduced into the model, so that more degrees of freedom of model parameters are realized, the dynamic performance is better, and the model precision is higher.
3. The identification method for the power battery fractional order equivalent circuit multi-characteristic fusion model disclosed by the invention is used for incorporating the self-discharge internal resistance into the battery model parameter and representing the self-discharge characteristic of the power battery.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
Fig. 1 is a schematic structural diagram of a power battery fractional order equivalent circuit multi-characteristic fusion model disclosed in the present disclosure.
The specific implementation mode is as follows:
the present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example 1
As introduced by the background art, the battery model in the prior art only describes the "voltage-current" electrical characteristics of the battery, and does not consider the non-linear capacity characteristics of the battery, so that the actual available capacity and the residual discharge time of the battery cannot be accurately estimated; the self-discharge phenomenon of the battery cannot be quantitatively expressed; and the method is limited to an integer order model, so that the precision of the model is not high.
In order to solve the above technical problem, in this embodiment, a method for identifying a power battery fractional order equivalent circuit multi-characteristic fusion model is provided, including,
establishing a power battery fractional order equivalent circuit multi-characteristic fusion model, which comprises a nonlinear capacity characteristic fractional order equivalent circuit sub-model, an electric characteristic fractional order equivalent circuit sub-model and a fractional order open-circuit voltage OCV-SOC model, wherein the capacity characteristic sub-model describes the state of charge and the nonlinear capacity characteristic of a battery, the electric characteristic sub-model describes the voltage-current characteristic of the battery, the capacity characteristic sub-model and the electric characteristic sub-model establish a connection through the fractional order open-circuit voltage OCV-SOC model, a charge-discharge current and an SOC control voltage source OCV, and a controlled voltage source in the electric characteristic sub-model changes along with the change of the SOC of the capacity characteristic sub-model;
performing a constant-current charge and discharge test on the power battery to obtain the initial capacity of the battery and the available capacity of the battery under different discharge rates, and identifying parameters in a capacity characteristic sub-model; carrying out pulse discharge test on the power battery, acquiring test data under different SOC (state of charge), and identifying parameters in the electrical characteristic sub-model; and identifying the relation between the open-circuit voltage and the SOC of the battery at different SOCs according to the parameters in the obtained electrical characteristic sub-model.
The nonlinear capacity characteristic fractional order equivalent circuit submodel is called capacity characteristic submodel for short, and the electric characteristic fractional order equivalent circuit submodel is called electric characteristic submodel for short.
A capacity characteristic submodel including fractional order capacitors C connected in parallel with the current control current sources, respectivelyFQ1A fractional order capacitor CFQ2And self-discharge internal resistance RdOne end of the current control current source is grounded, and the other end of the current control current source is connected with the fractional order capacitor CFQ2Upper series resistance RQAt a self-discharge internal resistance RdUpper series ideal current source EdThrough a fractional order capacitor CFQ1And a fractional order capacitance CFQ2The sum of the available capacities stored above represents the SOC state of the battery, the fractional order capacity CFQ2The unusable capacity variation above characterizes the nonlinear capacity characteristic of the battery.
Fractional order capacitor CFQ1Is of order alpha, fractional order capacitance CFQ2Of order beta, internal resistance R of self-dischargedAnd an ideal current source EdRepresents the self-discharge characteristic of the power battery, and the self-discharge internal resistance Rd is equal to or less thanThe material in the cell and the temperature environment of the cell determine, the current magnitude of the ideal current source Ed is determined by the fractional order capacitance CFQ1The voltage at both ends and the self-discharge internal resistance Rd.
Available capacity Q of batteryavailA part of which is stored in a fractional order capacitor CFQ1Another part is stored in fractional order capacitance CFQ2The above step (1); unavailable capacity Q of batteryunavailStored only in the fractional order capacitance CFQ2The above step (1); the sum of the available capacity and the unavailable capacity is called the total capacity Q of the batterytotal(ii) a Unavailable capacity Q of batteryunavailThe nonlinear capacity characteristic of the power battery can be described.
The current of the current control current source is the end current of the battery, and when the battery is charged and discharged, the load current passes through the current control current source to the fractional order capacitor CFQ1And a fractional order capacitance CFQ2Charging and discharging to change fractional order capacitance CFQ1And a fractional order capacitance CFQ2Upper stored available capacity and fractional order capacitance CFQ2On the non-usable capacity, fractional order capacitance CFQ1And a fractional order capacitance CFQ2The change of the available capacity of the upper memory represents the change of the SOC of the battery and the fractional order capacitance CFQ2The unusable capacity variation above characterizes the nonlinear capacity characteristic of the battery.
The voltage across the current-controlled current source is the battery open-circuit voltage OCV.
The electrical characteristic sub-model comprises an SOC control voltage source, wherein the positive end of the SOC control voltage source is connected with one end of a charging branch and one end of a discharging branch which are connected in parallel, the negative end of the SOC control voltage source is connected with one end of ohmic internal resistance Ro, the other ends of the charging branch and the discharging branch which are connected in parallel are connected with the positive end of the battery model, and the other end of the ohmic internal resistance Ro is connected with the negative end of the battery model.
The SOC-control voltage source describes an open-circuit voltage OCV of the battery.
The charging branch and the discharging branch are formed into the same structure and respectively comprise two groups of series-connected fractional order RC circuits which are formed by a diode D conducting in a single direction1And D2Respectively controlling, specifically:
discharge of electricityThe branch circuit comprises diodes D connected in series in sequence1A fractional order capacitor CF1And a resistance R1Parallel connected fractional order R1-CF1Loop, fractional order capacitor CF2And a resistance R2Parallel connected fractional order R2-CF2The capacitors in the loop being fractional order capacitors CF1Of order gamma and a fractional order capacitance CF2Order of θ, resistance R1Representing the internal resistance, R, of the electrochemical effect of the cell on discharge2Representing the internal resistance of concentration polarization effect during discharge.
The charging branch comprises reverse diodes D connected in series in sequence2A fractional order capacitor CF3And a resistance R3Parallel connected fractional order R3-CF3Loop, fractional order capacitor CF4And a resistance R4Parallel connected fractional order R4-CF4A loop; the capacitors in the loop being fractional order capacitors CF3Of order gamma1And a fractional order capacitance CF4Order of θ1Resistance R3Representing the internal resistance, R, of the cell during charging4Representing the internal resistance of concentration polarization effect during charging.
The fractional order open-circuit voltage OCV-SOC model is a fractional order calculus model established by the charge-discharge current SOC and the SOC control voltage source OVC; the capacity characteristic submodel and the electric characteristic submodel are linked through a fractional order open circuit voltage OCV-SOC model, and an SOC control voltage source OVC changes along with the change of the SOC of the capacity characteristic submodel.
The basic expression of the open-circuit voltage OCV-SOC model is as follows:
ocv＝k0+k1soc+k2soc2-k3Eα,β(-k4socα),(1)
wherein k is0-k4The constant is obtained by identifying experimental data based on a least square method; function Eα,β(-k4soca) Is a common Mittag-Leffler function in the field of fractional calculus, which is defined as:
Figure BDA0002555920430000101
in the nonlinear capacity characteristic fractional order equivalent circuit submodel, the total capacity, the available capacity and the unavailable capacity of the battery can be respectively expressed as:
Figure BDA0002555920430000102
wherein Q istotalIs the total capacity of the battery; qavailIs the available capacity of the battery; qunavailIs the battery unavailable capacity; qunavailThe actual running time of the power battery and the nonlinear capacity characteristics of the power battery can be accurately described in unit Ah; u shapeQ1Is a fractional order capacitor CFQ1Terminal voltage at both ends, UQ2Is a fractional order capacitor CFQ2Terminal voltage at both ends.
The specific process for identifying each parameter in the power battery fractional order equivalent circuit multi-characteristic fusion model is as follows:
selecting a power battery monomer with better consistency as a tested sample, and adopting a constant-current constant-voltage charging strategy to enable the tested power battery to recover to a fully charged state as an initial state of the tested power battery;
the power battery is subjected to a small-current constant-current discharge test at a current less than or equal to 0.1C, the battery is discharged to a discharge cut-off voltage within a long time, and the initial capacity Q of the power battery is obtainedFQ1；
Recovering the power battery to a full charge state by adopting a constant-current constant-voltage charging strategy, performing constant-current discharge experiments on the power battery under different discharge multiplying factors I, and acquiring the available capacity Q of the battery under different discharge multiplying factorsFQkThe ratio of the available capacity to the initial capacity is obtained by testing the power battery under different multiplying powers I
Figure BDA0002555920430000111
The available capacity ratio of the power battery under different discharge rates is called; the equivalent total capacitance C may be expressed approximately as C ═ Qrated/UratedFrom the above experimental data, the capacitance value parameter C of the fractional order capacitor in the fractional order model shown in formula (4) can be identifiedFQ1And CFQ2：
Figure BDA0002555920430000112
Wherein, UratedRated voltage calibrated for the power battery to leave factory; qratedThe rated capacity of the power battery; fractional order capacitor CFQ1A fractional order capacitor CFQ2Available capacity ratio Q, available capacity QFQkAre all functions of discharge multiplying power I.
Fractional order capacitor CFQ1And CFQ2Satisfies the following conditions:
Figure BDA0002555920430000113
laplace transform of equation (4)
Figure BDA0002555920430000114
Wherein, UQ1Is a fractional order capacitor CFQ1Terminal voltage at both ends, UQ2Is a fractional order capacitor CFQ2Terminal voltage at both ends, I is load current, alpha is fractional order capacitance CFQ1Beta is a fractional order capacitor CFQ2The order of (a).
According to fractional order capacitance CFQ1And CFQ2Thereby recognizing the resistance RQ。
Restoring the power battery to a fully charged state, carrying out a long-time standing test, periodically observing the open-circuit voltage of the power battery, predicting the residual self-discharge time of the battery, and obtaining the self-discharge internal resistance RdMay be approximately calculated as:
Figure BDA0002555920430000121
in the formula, Q0The initial capacity of the battery in the self-discharge test is shown; u shape0Is the initial open circuit voltage of the cell; u shapetdThe open-circuit voltage is the open-circuit voltage after the self-discharge of the battery is finished; t is tdIs the self-discharge time, in units of s.
Continuously carrying out a pulse charging test and a pulse discharging test on the power battery to obtain test data of the power battery under different SOC conditions, wherein the test data comprises an instant drop value of battery terminal voltage when the battery starts to discharge, an instant jump value of the battery terminal voltage after the discharge is finished, a discharging current, an instant jump value of the battery terminal voltage when the charging is started, an instant drop value of the battery terminal voltage after the charging is finished, a charging current and zero input response of the battery terminal voltage;
based on experimental data, the open-circuit voltage OCV and the ohmic internal resistance R of the battery at different SOC (state of charge) positions are obtained by adopting a least square method identification algorithm0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3And fractional order gamma and gamma1Concentration polarization fractional order capacitor CF2And CF4And fractional orders theta and theta1And completing the identification of the sub-model parameters of the electric characteristic fractional order equivalent circuit. The method specifically comprises the following steps:
taking the discharging process as an example, the battery terminal voltage can be expressed as:
Figure BDA0002555920430000131
wherein, UbatIs the battery terminal voltage; r0Ohmic internal resistance; OCV is the discharge open circuit voltage; gamma and theta are fractional order capacitance CF1And CF2Order of (1) satisfies 0<γ,θ<1; i is a discharge current; tau is1,τ2Time constants of the two RC loops are respectively; electrochemical polarization voltage of battery
Figure BDA0002555920430000132
Sum concentration polarization voltage
Figure BDA0002555920430000133
Will gradually decrease with time, and when t → ∞ the battery terminal voltage UbatEqual to the open circuit voltage OCV of the battery. Wherein, U1(0+) and U2(0+) is the initial value of terminal voltage of two fractional order RC loops at the moment when the battery discharge is finished, and the value can be expressed as:
Figure BDA0002555920430000134
because of the ohmic internal resistance R of the power battery0When the power battery discharges, the battery terminal voltage drops instantly, and the value is recorded as delta U1(ii) a When the power battery stops discharging, the battery terminal voltage will jump instantly, and the value is recorded as delta U2Therefore, the ohmic internal resistance R of the battery0Can be obtained by the following formula:
Figure BDA0002555920430000135
wherein I is the terminal current of the battery.
Internal resistance to electrochemical polarization R1Can be obtained by the following formula:
Figure BDA0002555920430000136
wherein, U1(0+) is the fractional order R at the moment when the battery discharge ends1-CF1The terminal voltage of the loop is initially.
Concentration polarization internal resistance R2Can be obtained by the following formula:
Figure BDA0002555920430000141
wherein, U2(0+) is the fractional order R at the moment when the battery discharge ends2-CF2The terminal voltage of the loop is initially.
Electrochemical polarization fractional order capacitance CF1Can be obtained by the following formula:
Figure BDA0002555920430000142
wherein, tau1dIs R1-CF1The time constant of the loop.
Concentration polarization fractional order capacitor CF2Can be obtained by the following formula:
Figure BDA0002555920430000143
wherein, tau2dIs R2-CF2The time constant of the loop.
Step (3) according to the battery open-circuit voltage OCV and the ohm internal resistance R obtained in the step (2)0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3And fractional order gamma and gamma1Concentration polarization fractional order capacitor CF2And CF4And fractional orders theta and theta1Identifying open-circuit voltage OCV and ohmic internal resistance R of battery based on least square method0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3Concentration polarization fractional order capacitor CF2And CF4Electrochemical polarization fractional order capacitance fractional order gamma and gamma1Concentration polarization fractional order capacitance fractional order theta1And the relationship between θ and the state of charge SOC of the battery, specifically:
the fractional order relationship between the open circuit voltage OCV and the state of charge SOC of the battery is:
ocv＝k0+k1soc+k2soc2-k3Eα,β(-k4socα),(14)
in the formula, k0-k4The constant is obtained by identifying experimental data based on a least square method; the function E α, β (-) is a Mittag-Leffler function common to the field of fractional calculus, which is defined as:
Figure BDA0002555920430000151
ohmic internal resistance R of battery0Electrochemical polarization internal resistance R1Internal resistance R of concentration polarization2The relation with the state of charge SOC of the battery can be expressed as:
Figure BDA0002555920430000152
wherein, a0-a4The constant value can be obtained by respectively identifying experimental data through a least square algorithm.
Electrochemical polarization fractional order capacitance CF1Concentration polarization fractional order capacitor CF2And the relation with the state of charge SOC of the battery can be expressed as:
Figure BDA0002555920430000153
wherein, b0-b5The constant value can be obtained by respectively identifying experimental data through a least square algorithm.
Electrochemical polarization fractional order capacitance fractional order gamma1Concentration polarization fractional order capacitance fractional order theta1The relation with the state of charge SOC of the battery can be expressed as:
Figure BDA0002555920430000154
wherein, c0-c4The constant value can be obtained by respectively identifying experimental data through a least square algorithm.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.

Claims (9)

1. A method for identifying a power battery fractional order equivalent circuit multi-characteristic fusion model is characterized by comprising the following steps:
creating a power battery fractional order equivalent circuit multi-characteristic fusion model, which comprises a capacity characteristic submodel, an electrical characteristic submodel and a fractional order open-circuit voltage OCV-SOC model, wherein the capacity characteristic submodel describes the state of charge of a battery, self-discharge internal resistance is added to express the self-discharge characteristic of the battery, the electrical characteristic submodel describes the voltage-current characteristic of the battery, the capacity characteristic submodel and the electrical characteristic submodel establish a connection through the fractional order open-circuit voltage OCV-SOC model, charge-discharge current and an SOC control voltage source OCV, and a controlled voltage source OCV in the electrical characteristic submodel changes along with the change of the SOC of the capacity characteristic submodel;
performing a constant-current charge and discharge test on the power battery to obtain the initial capacity of the battery and the available capacity of the battery under different discharge rates, and identifying parameters in a capacity characteristic sub-model; carrying out pulse discharge test on the power battery, acquiring test data under different SOC (state of charge), and identifying parameters in the electrical characteristic sub-model; identifying the relation between the open-circuit voltage and the SOC of the battery at different SOC positions according to the parameters in the obtained electrical characteristic sub-model;
a capacity characteristic submodel including fractional order capacitors C connected in parallel with the current control current sources, respectivelyFQ1A fractional order capacitor CFQ2And self-discharge internal resistance RdAt fractional order of capacitance CFQ2Upper series resistance RQAt a self-discharge internal resistance RdUpper series ideal current source EdBy self-discharge internal resistance RdAnd an ideal current source EdCharacterizing the self-discharge characteristics of the cell by means of a fractional order capacitance CFQ1And a fractional order capacitance CFQ2The sum of the available capacities stored above represents the SOC state of the battery, the fractional order capacity CFQ2The unavailable capacity change represents the nonlinear capacity characteristic of the battery;
fractional order capacitor CFQ1Is of order alpha, fractional order capacitance CFQ2Is beta;
the expression of the fractional order open-circuit voltage OCV-SOC model is as follows: ocv ═ k0+k1soc+k2soc2-k3Eα,β(-k4socα)，k0-k4Is a constant number of times, and is,
wherein the function Eα,β(-k4soca) Is the Mittag-Leffler function in the field of fractional calculus, which is defined as:
Figure FDA0003228159300000021
2. the method for identifying the multi-characteristic fusion model of the fractional order equivalent circuit of the power battery as claimed in claim 1, wherein the electrical characteristic sub-model comprises an SOC control voltage source, a positive terminal of the SOC control voltage source is connected with a positive terminal of the battery model through a charging branch and a discharging branch, and a negative terminal is connected with a negative terminal of the battery model through ohmic internal resistance Ro.
3. The identification method of the power battery fractional order equivalent circuit multi-characteristic fusion model as claimed in claim 2, wherein the voltage across the current control current source is the battery open-circuit voltage, and the SOC control voltage source represents the open-circuit voltage of the battery.
4. The method for identifying the power battery fractional order equivalent circuit multi-characteristic fusion model as claimed in claim 2, wherein the charging branch and the discharging branch are connected in parallel and then connected in series between the positive terminal of the SOC control voltage source and the positive terminal of the battery model;
the discharge branch circuit comprises diodes D connected in series in sequence1A fractional order capacitor CF1And a resistance R1Parallel connected fractional order R1-CF1Loop, fractional order capacitor CF2And a resistance R2Parallel connected fractional order R2-CF2A loop; the charging branch comprises reverse diodes D connected in series in sequence2A fractional order capacitor CF3And a resistance R3Parallel connected fractional order R3-CF3Loop, fractional order capacitor CF4And a resistance R4Parallel connected fractional order R4-CF4And (4) a loop.
5. The method for identifying the power battery fractional order equivalent circuit multi-characteristic fusion model as claimed in claim 1, wherein constant current discharge experiments under different multiplying powers are performed on the battery to obtain the initial capacity Q of the batteryFQ1And available capacity Q of the battery at different discharge ratesFQkAccording to the initial capacity QFQ1And available capacity Q of the battery at different discharge ratesFQkIdentifying the fractional order capacitor CFQ1A fractional order capacitor CFQ2Resistance RQAnd self-discharge internal resistance Rd。
6. The method as claimed in claim 5, wherein the fractional order capacitance C of the battery is the fractional order capacitance CFQ1And CFQ2Can be obtained by the following formula:
Figure FDA0003228159300000031
wherein, UratedCalibrating rated voltage for the factory of the battery; qratedIs the rated capacity, Q, of the batteryFQ1Is the initial capacity, Q, of the batteryFQkFor batteries of different discharge ratesC is the equivalent total capacitance, and the expression is C ═ Qrated/UratedAnd q is the available capacity ratio.
7. The method as claimed in claim 4, wherein the battery is subjected to pulse discharge test to obtain test data such as instantaneous drop value of battery terminal voltage when the battery starts to discharge, instantaneous jump value of battery terminal voltage after the discharge is finished, discharge current and zero input response of battery terminal voltage under different SOC, and the open circuit voltage OCV and ohmic internal resistance R in the electric characteristic electronic model are identified0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3And fractional order gamma and gamma1Concentration polarization fractional order capacitor CF2And CF4And fractional orders theta and theta1。
8. The method for identifying the power battery fractional order equivalent circuit multi-characteristic fusion model as claimed in claim 7, wherein in the discharging process, the terminal voltage of the battery is:
Figure FDA0003228159300000032
in the formula of UbatIs the battery terminal voltage; r0Ohmic internal resistance; OCV is the discharge open circuit voltage; gamma and theta are fractional order capacitance CF1And CF2Order of (1) satisfies 0<γ,θ<1; i is a discharge current; tau is1,τ2Time constants of the two fractional order RC loops are respectively; u shape1(0+) and U2(0+) is the initial value of terminal voltage of two fractional order RC loops at the moment when the battery discharge is finished, and when t → ∞ is reached, the terminal voltage U of the batterybatEqual to the open circuit voltage OCV of the battery,
Figure FDA0003228159300000041
is the Mittag-Leffler function in the field of fractional calculus, which is defined as:
Figure FDA0003228159300000042
Figure FDA0003228159300000043
is the Mittag-Leffler function in the field of fractional calculus, which is defined as:
Figure FDA0003228159300000044
9. the method for identifying the multi-characteristic fusion model of the fractional order equivalent circuit of the power battery as claimed in claim 8, wherein the open-circuit voltage OCV and the ohmic internal resistance R of the battery are identified based on the least square method according to the parameters and the order in the obtained electrical characteristic submodel0Electrochemical polarization internal resistance R1And R3Internal resistance R of concentration polarization2And R4Electrochemical polarization fractional order capacitance CF1And CF3Concentration polarization fractional order capacitor CF2And CF4Electrochemical polarization fractional order capacitance fractional order gamma and gamma1Concentration polarization fractional order capacitance fractional order theta1And θ is related to the battery state of charge, SOC.
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