CN107255786B - LOC model of lithium iron phosphate battery - Google Patents

LOC model of lithium iron phosphate battery Download PDF

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CN107255786B
CN107255786B CN201710352783.3A CN201710352783A CN107255786B CN 107255786 B CN107255786 B CN 107255786B CN 201710352783 A CN201710352783 A CN 201710352783A CN 107255786 B CN107255786 B CN 107255786B
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battery
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loc
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CN107255786A (en
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刘学鹏
周勤玲
赵冬梅
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Zhongshan Polytechnic
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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]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • 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]
    • G01R31/392—Determining battery ageing or deterioration, e.g. state of health

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Abstract

The invention discloses a lithium iron phosphate battery LOC model which comprises a battery LOC algorithm model, an equivalent circuit model, a battery capacity mathematical model and an effective SOC coefficient model, wherein the equivalent circuit model is used for estimating a state of charge (SOC) value of a battery, the battery capacity mathematical model is used for estimating the battery capacity, the effective SOC coefficient model is used for estimating the effective SOC coefficient of the battery according to the charging and discharging times of the battery, and the battery LOC is calculated according to the battery SOC value obtained by the equivalent circuit model, the battery capacity obtained by the battery capacity mathematical model and the effective SOC coefficient obtained by the effective SOC coefficient model. The invention relates to the technical field of batteries, in particular to a LOC model of a lithium iron phosphate battery.

Description

LOC model of lithium iron phosphate battery
Technical Field
The invention relates to the technical field of batteries, in particular to a LOC model of a lithium iron phosphate battery.
Background
LOC: life of charge.
SOC: state of Charge, also called the remaining Charge.
Environmental deterioration and energy crisis put double pressure on the development of conventional automobiles, so that electric automobiles have become the main direction of automobile development in the future. The power battery pack is an energy source of the electric automobile, and in order to ensure that the electric automobile can run safely, stably and efficiently, the battery needs to be managed and controlled necessarily. The service life of the battery is one of the most important parameters in the battery management system, the LOC can be accurately mastered to provide a basis for detection and diagnosis of the LOC, the health state of each single battery of the battery pack can be known in time, aged single batteries can be replaced in time, the overall service life of the battery pack is prolonged, and the power performance of the electric vehicle is further improved. Therefore, the method has very important practical significance for timely and accurately estimating the battery pack.
The battery management of the electric automobile comprises battery state estimation, balance management, heat management, safety and reliability management and the like, wherein the battery state estimation is not only the core and the foundation of the battery management, but also provides data basis for the energy management of the whole automobile.
The battery LOC represents the current available time of the battery, generally described by the available SOC of the battery versus the discharge rate of the battery. During the use of the battery, LOC of the battery is gradually reduced, and the LOC is represented by reduction of battery capacity, increase of internal impedance, reduction of specific energy and specific power and the like. How to effectively and feasibly establish the LOC model of the electric automobile battery is a difficult problem of electric automobile battery management.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a simple and practical LOC model of a lithium iron phosphate battery.
The technical scheme adopted by the invention is as follows: the LOC model of the lithium iron phosphate battery comprises a battery LOC algorithm model, an equivalent circuit model, a battery capacity mathematical model and an effective SOC coefficient model, wherein the equivalent circuit model is used for estimating the SOC of the open-circuit voltage of the battery, the battery capacity mathematical model is used for estimating the battery capacity, the effective SOC coefficient model is used for estimating the effective SOC coefficient of the battery according to the charging and discharging times, the equivalent circuit model is used for predicting the SOC of the battery, and the battery LOC is calculated according to the SOC obtained by the equivalent circuit model, the battery capacity obtained by the battery capacity mathematical model and the effective SOC coefficient obtained by the effective SOC coefficient model.
Further, the battery LOC algorithm model is as follows:
LOC＝Ct×KEV×S/RD(1)
where LOC is the single cycle life of the cell, CtIs the rated capacity of the battery, KEVIs the effective SOC coefficient, S is the SOC value of the battery, RDIs the discharge rate of the battery.
Further, the equivalent circuit model comprises polarization internal resistance of a battery, polarization capacitance of the battery, ohmic internal resistance of the battery, terminal voltage of the battery and a voltage source, wherein the polarization internal resistance of the battery and the polarization capacitance of the battery are connected in parallel to form an RC circuit, the RC circuit is connected with a positive electrode of the voltage source by serially connecting the ohmic internal resistance of the battery, the positive electrode of the terminal voltage of the battery is connected with the RC circuit, and a negative electrode of the terminal voltage of the battery is connected with a negative electrode of the voltage source; establishing a corresponding mathematical model according to the equivalent circuit model:
Figure GDA0002454998210000031
wherein S represents the SOC value of the battery, VSIs the polarization voltage, R, of the cell in the equivalent circuit modelSIs the internal polarization resistance of the cell, CSIs the polarization capacitance of the battery, i is the battery charging and discharging current, V is the battery terminal voltage, VOC(S) is the open circuit voltage of the cell at S, RiIs the ohmic internal resistance of the cell; due to the open circuit voltage V of the batteryOCHas a fixed relation with the SOC value of the battery and establishes the open-circuit voltage V of the batteryOCFitting equation to SOC of battery:
VOC(S)＝a+a1S+a2S2+a3S3(3)
wherein the value range of a is 3.45-3.55, a1The value ranges from 0.025 to 0.030, a2The value range is-0.025 to-0.020, a3The value ranges from 1.20 to 1.25;
establishing a state of charge (SOC) mathematical model of the battery:
Figure GDA0002454998210000032
wherein S (0) is the SOC value of the battery at the initial time, η is the charge-discharge efficiency of the battery, CtIs the rated capacity of the battery, CtI is the charge and discharge current of the battery, and i gradually decreases along with the aging of the battery; taking the state vector x ═ S VS]TThe system output y is equal to V, and the input u is equal to i, and the state space equation of the system is obtained as follows:
Figure GDA0002454998210000033
wherein,
Figure GDA0002454998210000034
and carrying out discretization processing on the state space equation of the system to obtain a state equation and a measurement equation.
Further, the state equation and the measurement equation are respectively:
Figure GDA0002454998210000041
wherein A isdAnd BdRespectively, a discretized transfer matrix and an input matrix:
Figure GDA0002454998210000042
k is tkTime of day, SkIs tkSOC value, V, of the battery at the momentOC,k(Sk) Is SkOpen circuit voltage of xkIs tkThe system state at the time; y iskIs tkMeasurement output of the time system; u. ofkIs tkA system input variable at the moment, namely the charging and discharging current of the battery; vs,kIs tkPolarization voltage of the battery in the time equivalent circuit model; w is akIs tkProcess noise of time of day, vkIs tkMeasurement noise at time.
Further, fitting the battery capacity attenuation data obtained by the battery cycle aging test to the battery capacity mathematical model is as follows:
Figure GDA0002454998210000043
wherein, b1Is a constant number, b1The value range is 0.96-0.99, f1Is a constant number f1The value ranges from-0.002 to 0.
Further, the effective SOC coefficient model is:
Figure GDA0002454998210000044
wherein N is the number of charge and discharge times. ROUND () represents taking an integer of the value calculated in parentheses.
The invention has the beneficial effects that:
the LOC model of the lithium iron phosphate battery is used for estimating the LOC of the lithium battery by combining the battery LOC algorithm model, the equivalent circuit model, the battery capacity mathematical model and the effective SOC coefficient model, and is simple, practical, accurate and reliable.
Drawings
The following further describes embodiments of the present invention with reference to the accompanying drawings:
fig. 1 is a schematic diagram of an equivalent circuit model of a lithium iron phosphate battery according to the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The LOC model of the lithium iron phosphate battery comprises a battery LOC algorithm model, an equivalent circuit model, a battery capacity mathematical model and an effective SOC coefficient model, wherein the equivalent circuit model is used for estimating a state of charge (SOC) value of the battery, the battery capacity mathematical model is used for estimating the capacity of the battery, the effective SOC coefficient model is used for estimating the effective SOC coefficient of the battery according to the charging and discharging times, and the LOC is calculated according to the state of charge (SOC) value of the battery obtained by the equivalent circuit model, the battery capacity obtained by the battery capacity mathematical model and the effective SOC coefficient obtained by the effective SOC coefficient model as the service life LOC of a single battery in the cycle is related to the SOC value of the battery, the rated capacity of the battery and the discharging multiplying power of the battery.
The battery LOC algorithm model of the invention is as follows:
LOC＝Ct×KEV×S/RD(1)
where LOC is the single cycle life of the cell, CtIs the rated capacity of the battery, KEVIs the effective SOC coefficient, S is the SOC value of the battery, RDIs the discharge rate of the battery.
FIG. 1 is a schematic diagram of an equivalent circuit model of a lithium iron phosphate battery according to the present invention, where the equivalent circuit model of the lithium iron phosphate battery includes polarization internal resistance R of the battery as shown in FIG. 1SPolarization capacitor C of batterySOhmic internal resistance R of the batteryiBattery terminal voltage V and voltage source VOCOhmic internal resistance R of the batteryiSimulating the energy consumed by electric loss in the process of charging and discharging the battery; internal resistance of polarization RSAnd said polarization capacitance CSThe RC circuit is formed by connecting in parallel, the polarization phenomenon in electrochemical reaction is simulated by the RC circuit, and the RC circuit is connected with ohmic internal resistance R in seriesiAnd a voltage source VOCIs connected with the positive pole of the battery terminal voltage V, the positive pole of the battery terminal voltage V is connected with the RC circuit, and the negative pole of the battery terminal voltage V is connected with the voltage source VOCThe invention defines that the battery system is positive when charging and negative when discharging; the battery terminal voltage V can be directly measured, and the voltage source VOCIs the open circuit voltage of the battery.
Establishing a corresponding mathematical model according to the equivalent circuit model:
Figure GDA0002454998210000061
wherein S represents the SOC of the battery, VSIs the polarization voltage, R, of the cell in the equivalent circuit modelSIs the internal polarization resistance of the cell, CSIs the polarization capacitance of the battery, i is the battery charging and discharging current, V is the battery terminal voltage, VOC(S) is the open circuit voltage of the cell at S, RiIs the ohmic internal resistance of the cell; due to the open circuit voltage V across the batteryOCHas a fixed relation with the SOC of the battery to establish an open-circuit voltage VOCFitting equation to SOC of battery:
VOC(S)＝a+a1S+a2S2+a3S3(3)
wherein the value range of a is 3.45-3.55, a1The value ranges from 0.025 to 0.030, a2The value range is-0.025 to-0.020, a3The value ranges from 1.20 to 1.25;
establishing a state of charge (SOC) mathematical model of the battery:
Figure GDA0002454998210000062
where S (0) is the SOC value of the battery at the initial time, and η is the battery charge/dischargeEfficiency; ctIs the rated capacity of the battery, CtI is the charge and discharge current of the battery, and i gradually decreases along with the aging of the battery; taking the state vector x ═ S VS]TThe system output y is equal to V, and the input u is equal to i, and the state space equation of the system is obtained as follows:
Figure GDA0002454998210000071
wherein,
Figure GDA0002454998210000072
and carrying out discretization processing on the state space equation of the system to obtain a state equation and a measurement equation.
Further, the state equation and the measurement equation are respectively:
Figure GDA0002454998210000073
wherein A isdAnd BdRespectively, a discretized transfer matrix and an input matrix:
Figure GDA0002454998210000074
k is tkTime of day, SkIs tkSOC value, V, of the battery at the momentOC,k(Sk) Is SkOpen circuit voltage of xkIs tkThe system state at the time; y iskIs tkMeasurement output of the time system; u. ofkIs tkA system input variable at the moment, namely the charging and discharging current of the battery; vs,kIs tkThe polarization voltage of the battery in the time equivalent circuit model; w is akIs tkProcess noise of time of day, vkIs tkMeasurement noise of time of day, wkAnd vkIs white gaussian noise with a mean value of zero, the two noises being uncorrelated.
Further, fitting the battery capacity attenuation data obtained by the battery cycle aging test to the battery capacity mathematical model is as follows:
Figure GDA0002454998210000081
wherein, b1Is a constant number, b1The value range is 0.96-0.99, f1Is a constant f1The value ranges from-0.002 to 0.
Further, fitting an effective SOC coefficient model according to data obtained from the cell life experiment is:
Figure GDA0002454998210000082
wherein N is the number of charge and discharge times. ROUND () represents taking an integer of the value calculated in parentheses.
In summary, the battery LOC is calculated according to the SOC value of the battery obtained by the equivalent circuit model, the battery capacity obtained by the battery capacity mathematical model, and the effective SOC coefficient obtained by the effective SOC coefficient model.
The LOC model of the lithium iron phosphate battery is used for estimating the LOC of the lithium battery by combining the battery LOC algorithm model, the equivalent circuit model, the battery capacity mathematical model and the effective SOC coefficient model, and is simple, practical, accurate and reliable.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. The LOC model of the lithium iron phosphate battery is characterized by comprising a battery LOC algorithm model, an equivalent circuit model, a battery capacity mathematical model and an effective SOC coefficient model, wherein the battery LOC algorithm model is as follows:
LOC＝Ct×KEV×S/RD(1)
wherein LOC is a monomerSingle cycle life of the battery, CtIs the rated capacity of the battery, KEVIs the effective SOC coefficient, S is the SOC value of the battery, RDThe equivalent circuit model comprises polarization internal resistance of the battery, polarization capacitance of the battery, ohmic internal resistance of the battery, terminal voltage of the battery and a voltage source, wherein the polarization internal resistance of the battery and the polarization capacitance of the battery are connected in parallel to form an RC circuit, the RC circuit is connected with the positive electrode of the voltage source by serially connecting the ohmic internal resistance of the battery, the positive electrode of the terminal voltage of the battery is connected with the RC circuit, and the negative electrode of the terminal voltage of the battery is connected with the negative electrode of the voltage source; establishing a corresponding mathematical model according to the equivalent circuit model:
Figure FDA0002454998200000011
wherein S represents the SOC value of the battery, VSIs the polarization voltage, R, of the cell in the equivalent circuit modelSIs the internal polarization resistance of the cell, CSIs the polarization capacitance of the battery, i is the battery charging and discharging current, V is the battery terminal voltage, VOC(S) is the open circuit voltage of the cell at S, RiIs the ohmic internal resistance of the cell;
due to the open circuit voltage V of the batteryOCHas a fixed relation with the SOC value of the battery and establishes the open-circuit voltage V of the batteryOCFitting equation to SOC of battery:
VOC(S)＝a+a1S+a2S2+a3S3(3)
wherein the value range of a is 3.45-3.55, a1The value ranges from 0.025 to 0.030, a2The value range is-0.025 to-0.020, a3The value ranges from 1.20 to 1.25; establishing a state of charge (SOC) mathematical model of the battery:
Figure FDA0002454998200000021
where S (0) is the SOC value of the battery at the initial time and η is the battery charge-discharge efficiencyRate; ctIs the rated capacity of the battery, CtI is the charge and discharge current of the battery, and i gradually decreases along with the aging of the battery; taking the state vector x ═ S VS]TThe system output y is equal to V, and the input u is equal to i, and the state space equation of the system is obtained as follows:
Figure FDA0002454998200000022
wherein,
Figure FDA0002454998200000023
discretizing the state space equation of the system to obtain a state equation and a measurement equation, wherein the state equation and the measurement equation are respectively as follows:
Figure FDA0002454998200000024
wherein A isdAnd BdRespectively, a discretized transfer matrix and an input matrix:
Figure FDA0002454998200000025
k is tkTime of day, SkIs tkSOC value, V, of the battery at the momentOC,k(Sk) Is SkOpen circuit voltage of xkIs tkThe system state at the time; y iskIs tkMeasurement output of the time system; u. ofkIs tkA system input variable at the moment, namely the charging and discharging current of the battery; vs,kIs tkPolarization voltage of the battery in the time equivalent circuit model; w is akIs tkProcess noise of time of day, vkIs tkMeasurement noise at time.
2. The LOC model of the lithium iron phosphate battery of claim 1, wherein the mathematical model of the battery capacity is fitted by the battery capacity decay data obtained by the battery cycle aging test as follows:
Figure FDA0002454998200000031
wherein, b1Is a constant number, b1The value range is 0.96-0.99, f1Is a constant number f1The value ranges from-0.002 to 0.
3. The lithium iron phosphate battery LOC model of claim 1, wherein the effective SOC coefficient model is:
Figure FDA0002454998200000032
where N is the number of charge and discharge cycles, and ROUND () represents an integer of the parenthesized value.
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