CN111426967B - Online real-time identification method for parameters of battery equivalent circuit model - Google Patents

Online real-time identification method for parameters of battery equivalent circuit model Download PDF

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CN111426967B
CN111426967B CN202010445997.7A CN202010445997A CN111426967B CN 111426967 B CN111426967 B CN 111426967B CN 202010445997 A CN202010445997 A CN 202010445997A CN 111426967 B CN111426967 B CN 111426967B
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CN111426967A (en
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王璐
那娜
王正君
张永华
李秋莹
于洋
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Zaozhuang Vocational College
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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]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • 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
    • 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]
    • G01R31/396—Acquisition or processing of data for testing or for monitoring individual cells or groups of cells within a battery
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10—Energy storage using batteries

Abstract

The invention discloses a parameter online real-time identification method of a battery equivalent model. The method can identify the second-order equivalent circuit model parameters of the battery on line in real time, and further can realize the estimation of various states of the battery, wherein the states of the battery include but are not limited to SOC, SOP (power state) and SOH (state of charge). The invention can identify the second-order equivalent circuit model parameters of any type of battery, and the types of the battery include but are not limited to disposable batteries, lead-acid batteries, lithium polymer batteries and the like.

Description

Parameter online real-time identification method of battery equivalent circuit model
Technical Field
The invention relates to the technical field of batteries, in particular to a parameter online real-time identification method of a battery equivalent circuit model.
Background
The advent of batteries has greatly promoted the spread of electronic devices as well as the practical use and weight reduction thereof. In order to analyze the characteristics of the battery under certain conditions, it is necessary to simulate and analyze the battery according to a model of the battery. The battery is a complex electrochemical-physical system and has strong non-linearity and time-varying characteristics, so that the model parameters of the battery are extremely difficult to obtain. Since the characteristics of the battery are influenced by many factors such as temperature, state of charge (SOC) of the battery, and state of life (SOH) of the battery, the off-line identification method is limited and is only suitable for specific applications. At present, no good method is available for real-time and online identification of battery model parameters under any condition and any connection mode.
Disclosure of Invention
The invention aims to solve the technical problem of providing a parameter online real-time identification method of a battery equivalent circuit model, which can identify the parameters of a battery second-order equivalent circuit model online in real time so as to realize the estimation of various states of the battery.
In order to solve the technical problem, the technical scheme adopted by the invention is as follows: the method for identifying the parameters of the battery equivalent circuit model in real time on line comprises the following steps:
s01), establishing a second-order equivalent circuit model of the battery, wherein the second-order equivalent circuit model of the battery comprises a resistor R, a first RC module and a second RC module which are connected in series, and the first RC module comprises a resistor R which is connected in parallelp1Capacitor Cp1The second RC module comprises a parallel resistor Rp2Capacitor Cp2；
S02), the second order equivalent circuit model of the battery can be represented by equations 1-3:
U＝Uo+RI+Up1+Up2 (1)，
Figure GDA0003637785540000011
Figure GDA0003637785540000012
where U is the terminal voltage of the battery, I is the current, UoIs open circuit voltage, R is ohmic internal resistance, Cpi、Rpii is 1, and 2 is polarization capacitance and polarization internal resistance respectively;
s03), converting equations 1-3 into a difference equation, one can obtain:
Figure GDA0003637785540000021
wherein:
Figure GDA0003637785540000022
u (k), U (k-1), U (k-2), U (k +1) and U (k +2) represent terminal voltages at the current time, the previous two times, the next time and the next two times, and U (k +1) represents terminal voltages at the current time, the previous two times, the next time and the next two timeso(k) Showing the open circuit voltage at the present time, I (k), I (k-1), I (k-2), I (k +1), I (k +2) showing the current at the present time, the previous two times, the next time and the next two times, TsRepresents a sampling period;
rewrite equation 4 to:
Figure GDA0003637785540000023
wherein:
Figure GDA0003637785540000031
s04), the terminal voltage of the battery is a measurable quantity, let ykU (k), the input matrix is represented as: phi is ak＝[1 U(k+2) U(k+1) U(k-1) U(k-2) I(k+2) I(k+1) I(k) I(k-1) I(k-2)]TThe coefficient matrix is: k ═ U'oa b c d g h m n w]TAnd the noise matrix is εkThen equation 6 can be rewritten as:
Figure GDA0003637785540000032
s05), identifying kappa through a parameter identification algorithm, and further obtaining parameters of a second-order equivalent circuit model of the battery.
Further, the parameter identification algorithm comprises a least square method, a neural network algorithm and a particle filter algorithm.
Further, the parameters of the second-order equivalent circuit model of the battery are identified by a recursive augmented least square method, and the specific process is as follows: a1) because of there is sampling error e in the collection system of gathering battery voltage and electric current, supposing that this sampling error is first order noise at least, this noise matrix also discerns through the recursive augmentation least squares method and obtains, consequently, input matrix expression is:
Figure GDA0003637785540000033
the coefficient matrix is represented as: k ═ U'o a b c d g h m n w q]T；
a2) Determining initial values of a coefficient matrix kappa, a covariance matrix P and an error e: let kappai＝[0]T，Pi＝σ2I，ei＝[0]I is the identity matrix, σ2≥106，i＝1，2；
a3) Sampling the voltage and the current of the battery for the jth time, wherein j is 1-5;
a4) and calculating a j-2 th gain matrix:
Figure GDA0003637785540000041
a5) calculating a j-2 th coefficient matrix:
Figure GDA0003637785540000042
a6) calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
a7) Calculating C according to formula 5piAnd Rpi，i＝1，2，
a8) Calculating error e according to equation 8jI.e. epsilon in equation 8k；
a9) And calculating a covariance matrix of the j-2 th time:
Figure GDA0003637785540000043
a10) collecting the voltage and the current of the battery for j +3 times;
a11) and repeating the steps a4) to a10) until the N times of acquisition are finished, wherein N is equal to or larger than 5.
Further, the specific process of identifying the parameters of the second-order equivalent circuit model of the battery is as follows:
b1) and sampling the voltage and the current for N times to construct a matrix:
Figure GDA0003637785540000044
Figure GDA0003637785540000045
representing the data obtained by each sampling;
b2) constructing a matrix: y ═ Y (3) Y (4) … Y (N)]TY represents a measured terminal voltage of the battery;
b3) solving the equation to obtain the value of kappa: k ═ phi (phi)TΦ)-1ΦTY；
b4) Calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
b5) Calculating C according to formula 5piAnd Rpi，i＝1，2。
The invention has the beneficial effects that: the method can identify the second-order equivalent circuit model parameters of the battery on line in real time, and further can realize the estimation of various states of the battery, wherein the states of the battery include but are not limited to SOC, SOP (power state) and SOH (state of charge). The invention can identify the second-order equivalent circuit model parameters of any type of battery, and the types of the battery include but are not limited to disposable batteries, lead-acid batteries, lithium polymer batteries and the like. The invention can realize the identification of the second-order equivalent circuit model parameters of the battery pack and/or the single battery in any connection mode, and the connection mode comprises but not limited to series connection, parallel connection, series-parallel connection and the like. The method is also suitable for identifying the second-order equivalent circuit model parameters of any type of battery and any connection form of battery pack and/or single battery.
Drawings
FIG. 1 is a second order equivalent circuit model of a battery;
FIG. 2 is a flowchart of example 1;
FIG. 3 is a diagram of a composite pulse test waveform;
FIG. 4 is a schematic diagram of a parallel form of cells;
FIG. 5 is a schematic diagram of cells in series;
fig. 6 is a schematic diagram of a series-parallel type battery.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
Example 1
The embodiment discloses a parameter online real-time identification method of a battery equivalent circuit model, which comprises the following steps:
s01), establishing a second-order equivalent circuit model of the battery, wherein the second-order equivalent circuit model of the battery comprises a resistor R, a first RC module and a second RC module which are connected in series, and the first RC module comprises a resistor R which is connected in parallelp1Capacitor Cp1The second RC module comprises a parallel resistor Rp2Capacitor Cp2；
S02), the second order equivalent circuit model of the battery can be represented by equations 1-3:
U＝Uo+RI+Up1+Up2 (1)，
Figure GDA0003637785540000051
Figure GDA0003637785540000052
where U is the terminal voltage of the battery, I is the current, UoIs open circuit voltage, R is ohmic internal resistance, Cpi、Rpii is 1,2 is polarization capacitanceAnd polarization internal resistance;
s03), converting equations 1-3 into a difference equation, one can obtain:
Figure GDA0003637785540000061
wherein:
Figure GDA0003637785540000062
u (k), U (k-1), U (k-2), U (k +1) and U (k +2) represent terminal voltages at the current time, the previous two times, the next time and the next two times, and U (k +1) represents terminal voltages at the current time, the previous two times, the next time and the next two timeso(k) Showing the open circuit voltage at the present time, I (k), I (k-1), I (k-2), I (k +1), I (k +2) showing the current at the present time, the previous two times, the next time and the next two times, TsRepresents a sampling period;
rewrite equation 4 to:
Figure GDA0003637785540000063
wherein:
Figure GDA0003637785540000071
s04), the terminal voltage of the battery is a measurable quantity, let ykU (k), the input matrix is represented as: phi is ak＝[1U(k+2)U(k+1)U(k-1)U(k-2)I(k+2)I(k+1)I(k)I(k-1)I(k-2)]TThe coefficient matrix is: k ═ U'o a b c d g h m n w]TAnd the noise matrix is εkThen equation 6 can be rewritten as:
Figure GDA0003637785540000072
s05), identifying kappa through a parameter identification algorithm, and further obtaining parameters of a second-order equivalent circuit model of the battery.
The parameter identification algorithm includes, but is not limited to, a least square method, a neural network algorithm, and a particle filter algorithm, and in this embodiment, the parameters of the second-order equivalent circuit model of the battery are identified by a recursive augmented least square method, as shown in fig. 1, the specific process is as follows:
a1) because of there is sampling error e in the collection system of gathering battery voltage and electric current, supposing that this sampling error is first order noise at least, this noise matrix also discerns through the recursive augmentation least squares method and obtains, consequently, input matrix expression is:
Figure GDA0003637785540000073
the coefficient matrix is represented as: k ═ U'o a b c d g h m n w q]T；
a2) Determining initial values of a coefficient matrix kappa, a covariance matrix P and an error e: let kappai＝[0]T，Pi＝σ2I，ei＝[0]I is the identity matrix, σ2≥106，i＝1，2；
a3) Sampling the voltage and the current of the battery for the jth time, wherein j is 1-5;
a4) and calculating a j-2 th gain matrix:
Figure GDA0003637785540000081
a5) calculating a j-2 th coefficient matrix:
Figure GDA0003637785540000082
a6) calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
a7) Calculating C according to formula 5piAnd Rpi，i＝1，2，
a8) Calculating error e according to equation 8jI.e. epsilon in equation 8k；
a9) And calculating a covariance matrix of the j-2 th time:
Figure GDA0003637785540000083
a10) collecting the voltage and current of the battery for j ═ j +3 times;
a11) and repeating the steps a4) to a10) until N times of collection are finished, wherein N is larger than or equal to 5.
The method can identify the second-order equivalent circuit model parameters of the battery on line and in real time, and further can realize the estimation of various states of the battery, wherein the states of the battery include but are not limited to SOC, SOP (power state) and SOH (state of charge). The method can be used for identifying the second-order equivalent circuit model parameters of any type of battery, wherein the type of the battery comprises but is not limited to a disposable battery, a lead-acid battery, a lithium polymer battery and the like. The identification of the second-order equivalent circuit model parameters of the battery pack and/or the single battery in any connection mode can be realized, and the connection mode includes but is not limited to series connection, parallel connection, series-parallel connection (as shown in fig. 4, 5 and 6) and the like. The method is also suitable for identifying the second-order equivalent circuit model parameters of any type of battery and any connection form of battery pack and/or single battery.
The open circuit voltage of the battery can be obtained by the battery standing for at least half an hour without current, so the open circuit voltage can be used to verify the accuracy of the algorithm.
A mixed pulse test experiment (fig. 3) was performed on two lithium iron phosphate batteries connected in series, voltage and current data of 60 seconds were collected, and model parameters of the batteries were identified by the method provided in this example. As can be seen from the identification results in the following table, the relative error of UO is about 0.2%, and then it can be confirmed that the patent realizes the identification of the high-precision battery model parameters.
Type of battery Identified Uo/V U of true valueo/V Relative error/%)
Battery pack 6.5587 6.577 -0.278
1# single battery 3.2807 3.288 -0.223
2# single battery 3.2829 3.289 -0.184
Example 2
The embodiment discloses another method for identifying kappa through parameter identification and further obtaining parameters of a second-order equivalent circuit model of a battery, which comprises the following specific processes:
b1) sampling the voltage and the current for N times, and constructing a matrix:
Figure GDA0003637785540000091
Figure GDA0003637785540000092
representing data obtained from each sample；
b2) And constructing a matrix: y ═ Y (3) Y (4) … Y (N)]TY represents the measured terminal voltage of the battery;
b3) solving the equation to obtain the value of kappa: k ═ phi (phi)TΦ)-1ΦTY；
b4) Calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
b5) Calculating C according to formula 5piAnd Rpi，i＝1，2。
The foregoing description is only for the basic principle and the preferred embodiments of the present invention, and modifications and substitutions by those skilled in the art are included in the scope of the present invention.

Claims (4)

1. The method for identifying the parameters of the battery equivalent circuit model in real time on line is characterized in that: the method comprises the following steps:
s01), establishing a second-order equivalent circuit model of the battery, wherein the second-order equivalent circuit model of the battery comprises a resistor R, a first RC module and a second RC module which are connected in series, and the first RC module comprises a resistor R which is connected in parallelp1Capacitor Cp1The second RC module comprises a parallel resistor Rp2Capacitor Cp2；
S02), the second order equivalent circuit model of the battery can be represented by equations 1-3:
U＝Uo+RI+Up1+Up2 (1)，
Figure FDA0003637785530000011
Figure FDA0003637785530000012
where U is the terminal voltage of the battery, I is the current, UoIs open circuit voltage, R is ohmic internal resistance, Cpi、Rpii 1 and 2 are polarization capacitance and polarization respectivelyInternal resistance;
s03), converting equations 1-3 into a difference equation, one can obtain:
Figure FDA0003637785530000013
wherein:
Figure FDA0003637785530000014
u (k), U (k-1), U (k-2), U (k +1) and U (k +2) represent terminal voltages at the current time, the previous two times, the next time and the next two times, and U (k +1) represents terminal voltages at the current time, the previous two times, the next time and the next two timeso(k) Showing the open circuit voltage at the present time, I (k), I (k-1), I (k-2), I (k +1), I (k +2) showing the current at the present time, the previous two times, the next time and the next two times, TsRepresents a sampling period;
rewrite equation 4 to:
Figure FDA0003637785530000021
wherein:
Figure FDA0003637785530000022
s04), the terminal voltage of the battery is a measurable quantity, let ykU (k), the input matrix is represented as: phi is ak＝[1 U(k+2) U(k+1) U(k-1) U(k-2) I(k+2) I(k+1) I(k) I(k-1) I(k-2)]TThe coefficient matrix is: k ═ U'o a b c d g h m n w]TAnd the noise matrix is εkThen equation 6 can be rewritten as:
Figure FDA0003637785530000023
s05), identifying kappa through a parameter identification algorithm, and further obtaining parameters of a second-order equivalent circuit model of the battery.
2. The method for on-line real-time identification of parameters of a battery equivalent circuit model according to claim 1, wherein: the parameter identification algorithm comprises a least square method, a neural network algorithm and a particle filter algorithm.
3. The method for on-line real-time identification of parameters of a battery equivalent circuit model according to claim 1, wherein: the parameters of the second-order equivalent circuit model of the battery are identified by a recursive augmented least square method, and the specific process is as follows: a1) because of there is sampling error e in the collection system of gathering battery voltage and electric current, supposing that this sampling error is first order noise at least, this noise matrix also discerns through the recursive augmentation least squares method and obtains, consequently, input matrix expression is:
Figure FDA0003637785530000031
the coefficient matrix is represented as: kappa-U'o a b c d g h m n w q]T；
a2) Determining initial values of a coefficient matrix kappa, a covariance matrix P and an error e: let kappai＝[0]T，Pi＝σ2I，ei＝[0]I is the identity matrix, σ2≥106，i＝1，2；
a3) Sampling the voltage and the current of the battery for the jth time, wherein j is 1-5;
a4) and calculating a j-2 th gain matrix:
Figure FDA0003637785530000032
a5) calculating a j-2 th coefficient matrix:
Figure FDA0003637785530000033
a6) calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
a7) Calculating C according to the formula 5piAnd Rpi，i＝1，2，
a8) Calculating error e according to equation 8jI.e. epsilon in equation 8k；
a9) Calculating a covariance matrix of the j-2 th time:
Figure FDA0003637785530000034
a10) collecting the voltage and current of the battery for j ═ j +3 times;
a11) and repeating the steps a4) to a10) until N times of collection are finished, wherein N is larger than or equal to 5.
4. The method for on-line real-time identification of parameters of a battery equivalent circuit model according to claim 1, wherein: the specific process of identifying the parameters of the second-order equivalent circuit model of the battery comprises the following steps:
b1) sampling the voltage and the current for N times, and constructing a matrix:
Figure FDA0003637785530000041
Figure FDA0003637785530000042
representing the data obtained by each sampling;
b2) constructing a matrix: y ═ Y (3) Y (4) … Y (N)]TY represents a measured terminal voltage of the battery;
b3) solving the equation to obtain the value of kappa: k ═ phi (phi)TΦ)-1ΦTY；
b4) Calculating U according to formula 7o、R、ai、biAnd ci，i＝1，2；
b5) Calculating C according to the formula 5piAnd Rpi，i＝1，2。
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