CN114818601A - Three-order RC equivalent circuit model parameter identification method for lithium ion battery - Google Patents

Three-order RC equivalent circuit model parameter identification method for lithium ion battery Download PDF

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CN114818601A
CN114818601A CN202210488832.7A CN202210488832A CN114818601A CN 114818601 A CN114818601 A CN 114818601A CN 202210488832 A CN202210488832 A CN 202210488832A CN 114818601 A CN114818601 A CN 114818601A
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lithium ion
ion battery
equivalent circuit
order
battery
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周娟
林加顺
杨晓全
吴乃豪
王梅鑫
原亚雷
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China University of Mining and Technology CUMT
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/39—Circuit design at the physical level
    • G06F30/398—Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM]
    • 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]
    • G01R31/385—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
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD

Abstract

The invention discloses a method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery, which comprises the following steps: establishing a three-order RC equivalent circuit model of the lithium ion battery; obtaining the open circuit voltage U of the lithium ion battery oc The relationship with SOC; testing the lithium ion battery by adopting a novel parameter identification working condition to obtain test data of the lithium ion battery; and identifying battery model parameters by using a recursive least square method based on specific constraint conditions according to the lithium ion battery test data. According to the invention, the specific constraint condition is obtained under the novel parameter identification working condition, and the third-order RC equivalent circuit model parameter is identified by using the recursive least square method based on the specific constraint condition, so that the identification difficulty can be reduced, and the accurate identification can be realizedIdentifying model parameters; compared with a second-order equivalent circuit model which is established based on HPPC test data identification by using a recursive least square method, the battery model established by the method has higher model precision.

Description

Three-order RC equivalent circuit model parameter identification method for lithium ion battery
Technical Field
The invention relates to the technical field of lithium ion batteries, in particular to a lithium ion battery three-order RC equivalent circuit model parameter identification method applied to a lithium ion battery management system.
Background
The State of charge of the battery is one of important bases for a battery management system to formulate an equalization strategy, but the electrochemical reaction inside the lithium ion battery is complex and changeable, the SOC (State of charge) of the lithium ion battery cannot be directly measured and obtained, and the SOC can only be estimated and obtained by a certain method based on the related physical quantity of the battery. The model-based method is a current common SOC estimation method, and the method obtains the SOC of the battery by matching a battery model with a proper estimation method, and the estimation precision of the SOC is directly related to the precision of the battery model.
The battery models widely used at present are mainly classified into electrochemical models and equivalent circuit models. The electrochemical model mainly utilizes knowledge in the chemical and physical fields to express the slight change in the reuse process of the lithium ion battery through a mathematical form, but the structure of the model is complex and the model can be used after being simplified in practical application. The equivalent circuit model describes the external characteristics of the battery by using a circuit network, and generally comprises circuit elements such as a voltage source, a resistor and a capacitor. Compared with an electrochemical model, the equivalent circuit model is simple in structure and convenient to calculate, and is widely applied to the research of a battery management system.
The RC equivalent circuit model is one of common models in lithium ion battery equivalent circuit models and consists of an ideal voltage source, a constant value resistor and a plurality of RC parallel links. Generally, the number of the RC links represents the order of the model, the accuracy of the model can be improved by increasing the order, but the difficulty of parameter identification of the model can also be greatly increased.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for identifying the parameters of a three-order RC equivalent circuit model of a lithium ion battery, which can reduce the identification difficulty and accurately identify the model parameters by acquiring specific constraint conditions under a novel parameter identification working condition and identifying the three-order RC equivalent circuit model parameters by using a recursive least square method based on the specific constraint conditions.
The invention discloses a method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery, which comprises the following steps:
step 1, establishing a three-order RC equivalent circuit model of the lithium ion battery;
step 2, obtaining the open circuit voltage U of the lithium ion battery oc A relation with SOC;
step 3, testing the lithium ion battery by adopting a novel parameter identification working condition to obtain test data of the lithium ion battery;
and 4, identifying battery model parameters by using a recursive least square method based on specific constraint conditions according to the lithium ion battery test data.
As a further improvement of the present invention, in said step 1,
the three-order RC equivalent circuit model of the lithium ion battery consists of a controlled voltage source, three RC links and an ohmic internal resistance R 0 Are connected in series.
As a further improvement of the present invention, the step 2 specifically includes:
step 3.1, discharging the battery in the full-charge state discontinuously at a constant multiplying power and fully standing to obtain the open-circuit voltage U of the battery oc And SOC data;
step 3.2, fitting open-circuit voltage U by adopting a least square method oc The relation with SOC to obtain the open-circuit voltage U oc And the functional relationship with the SOC.
As a further improvement of the present invention, in said step 3,
the novel parameter identification working condition comprises a part A with current change and a part B with stable and unchangeable current.
As a further improvement of the present invention, the step 4 specifically includes:
step 4.1, identifying the number of lithium ion battery tests under the working condition according to the novel parametersAccording to the method, the internal resistance and R are obtained bn And a third RC link R 3 And C 3 And a second RC link time constant e 2 As a specific constraint; wherein the content of the first and second substances,
R bn ＝R 0 +R 1 +R 2 +R 3 ；
step 4.2, based on the specific constraint condition, obtaining a three-order RC equivalent circuit model system discrete equation of the lithium ion battery:
U b (k)＝U oc (k)-U(k)-U 2 (k)-U 3 (k)
Figure BDA0003630479640000021
wherein I is the battery working current, U is the battery terminal voltage, U 2 For the voltage across the second RC link, U 3 Voltage at two ends of a third RC link, wherein k represents the number of steps of iterative computation at the current moment;
step 4.3: acquiring a parameter theta to be identified and a sample set h:
Figure BDA0003630479640000022
θ(k)＝[a(k)b(k)c(k)] T
h(k)＝[U b (k-1)I(k)I(k-1)]
and 4.4, identifying the parameters by using a recursive least square method, wherein the operation process in one recursive period is as follows:
K(k)＝P(k-1)h(k)[h T (k)P(k-1)h(k)+y(k)] -1
θ(k)＝θ(k-1)+K(k)[Z(k)-h T (k)θ(k-1)]
Figure BDA0003630479640000031
in the formula, K is a gain matrix, E is an identity matrix, P is a covariance matrix, y is a forgetting factor, theta (K) is a system unidentified parameter, and K represents the number of iterative computation steps at the current moment;
step 4.5, obtaining ohmic internal resistance R 0 And a first RC link parameter R 1 And C 1 ：
Figure BDA0003630479640000032
Figure BDA0003630479640000033
Figure BDA0003630479640000034
Figure BDA0003630479640000035
Step 4.6, solving a second RC link parameter R based on a specific constraint condition 2 And C 2 ：
R 2 (k)＝R bn (k)-R 0 (k)-R 1 (k)-R 3
Figure BDA0003630479640000036
Step 4.7, updating the voltage U at the two ends of the second RC link and the third RC link 2 And U 3 ：
Figure BDA0003630479640000037
Figure BDA0003630479640000038
And 4.8, circulating the steps 4.4 to 4.5 until the parameter identification is finished.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, specific constraint conditions are obtained under a novel parameter identification working condition, and then the parameters of a three-order RC equivalent circuit model of the lithium ion battery are identified by using a recursive least square method based on the specific constraint conditions; performing off-line simulation verification on battery voltage and current data acquired under the urban federal driving working condition, and comparing the result with a second-order RC equivalent circuit model; simulation results show that the method can accurately identify the parameters of the battery model and reduce the difficulty of parameter identification.
Drawings
Fig. 1 is a flowchart of a third-order RC equivalent circuit model parameter identification method for a lithium ion battery according to an embodiment of the present invention;
fig. 2 is a three-order RC equivalent circuit model of a lithium ion battery according to an embodiment of the present invention;
FIG. 3 is a current curve of a 25 ℃ single-cycle novel parameter identification working condition;
FIG. 4 is a voltage response curve of part B of a 25 ℃ novel parameter identification condition;
FIG. 5 is a flowchart illustrating the identification of battery model parameters using a recursive least squares method based on certain constraints, according to an embodiment of the present invention;
6-1, 6-2 are voltage responses of a third-order RC equivalent circuit model (ECM1) constructed by the invention under the condition of 25 ℃ U.S. Federal urban driving and a second-order RC equivalent circuit model (ECM2) constructed by using a recursive least square method based on HPPC test data identification parameters, respectively;
FIGS. 7-1 and 7-2 are voltage error diagrams of a third-order RC equivalent circuit model (ECM1) constructed by the method under the condition of 25 ℃ U.S. Federal urban driving and a second-order RC equivalent circuit model (ECM2) constructed by using a recursive least square method based on HPPC test data identification parameters, respectively.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The invention is described in further detail below with reference to the attached drawing figures:
as shown in fig. 1, the present invention provides a method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery, comprising:
step 1, establishing a three-order RC equivalent circuit model of the lithium ion battery; wherein the content of the first and second substances,
as shown in fig. 2, the three-order RC equivalent circuit model of the lithium ion battery comprises a controlled voltage source, three RC links and an ohmic internal resistance R 0 Series composition, controlled voltage source representing the open circuit voltage of the battery, RC link (R) 1 、C 1 、R 2 、C 2 、R 3 、C 3 ) The polarization internal resistance and the polarization content are used for simulating electrochemical polarization and concentration polarization of the battery, and the ohmic internal resistance of the battery is used for simulating an ohmic polarization process of the battery.
Step 2, obtaining the open circuit voltage U of the lithium ion battery oc The relationship with SOC;
the method specifically comprises the following steps:
step 2.1, discharging the battery in the full-charge state discontinuously at a constant multiplying power and fully standing to obtain the open-circuit voltage U of the battery oc And SOC data; e.g., at 10% SOC intervals;
step 2.2, fitting open-circuit voltage U by adopting least square method oc The relation with SOC to obtain the open-circuit voltage U oc Functional relationship with SOC; for example, fitting is performed using a 9 th order polynomial:
U oc ＝a 1 *SOC 9 +a 2 *SOC 8 +a 3 *SOC 7 +a 4 *SOC 6 +a 5 *SOC 5 +a 6 *SOC 4 +a 7 *SOC 3 +a 8 *SOC 2 +a 9 *SOC+a 10
step 3, testing the lithium ion battery by adopting a novel parameter identification working condition to obtain test data of the lithium ion battery; wherein the content of the first and second substances,
as shown in fig. 3, the current curve of the 25 ℃ single-cycle novel parameter identification working condition consists of two parts, namely a part A with rapidly changing current and a part B with the current being stable and unchangeable in a longer time.
Step 4, identifying battery model parameters by using a recursive least square method based on specific constraint conditions according to the lithium ion battery test data under the novel parameter identification working condition;
as shown in fig. 5, the method specifically includes:
step 4.1, according to the lithium ion battery test data under the novel parameter identification working condition, obtaining the internal resistance and the R bn And a third RC link R 3 And C 3 And a second RC link time constant e 2 As a specific constraint; wherein the content of the first and second substances,
as shown in fig. 4, for the voltage response curve of the part B of the 25 ℃ novel parameter identification working condition, the specific obtaining process of the specific constraint condition is as follows:
setting a time constant e for three RC links in a three-order RC equivalent circuit model 1 <e 2 <e 3 (e 1 ＝R 1 C 1 ，e 2 ＝R 2 C 2 ，e 3 ＝R 3 C 3 ) The bn segment is the voltage recovery stage, the voltage recovery speed and the time constant e 1 、e 2 、e 3 In connection with this, the voltage amplitude recovered simultaneously is determined by four internal resistances R 0 、R 1 、R 2 、R 3 Sum R bn And (6) determining. Analyzing the voltage recovery process of the third-order RC equivalent circuit model in the bn section, wherein the relationship is as follows:
Figure BDA0003630479640000051
in the formula of U oc Is the open circuit voltage of the battery, U 10 ，U 20 ，U 30 Initial voltages of three RC links in the battery model are obtained;
considering a third-order RC equivalent circuit modelMiddle first RC link time constant e 1 Generally not exceeding 5s, second RC link constant e 2 Generally, the voltage does not exceed 150s, so that the voltage across the first RC link and the second RC link is almost 0 after 500s from the point b, which can be ignored, and at this time, the following relationship exists between the third RC link and the battery terminal voltage in the battery model:
Figure BDA0003630479640000061
at two points f and h after 500s from the point b, a third RC link time constant e can be obtained according to the terminal voltages of the two points f and h 3 ：
Figure BDA0003630479640000062
Initial voltage U of third RC element 30 For polarizing steady-state voltage, it is connected with a third RC link resistor R 3 The following relationships exist:
U 30 ＝R 3 I
wherein I is the discharge current of the battery;
time constant e at known third RC link 3 Under the condition of (1), the third RC link resistor R can be obtained according to the terminal voltage of the point f 3 ：
Figure BDA0003630479640000063
The voltage at two ends of the first RC link is almost 0 after 50s from the point b, and can be ignored, and at the moment, the following relation exists between the second RC link and the battery terminal voltage in the battery model:
Figure BDA0003630479640000064
under the condition that the third RC link parameter is known, from two points c and d after the point b and 50s, the second RC link time constant e can be obtained according to the terminal voltages of the two points c and d 2 ：
Figure BDA0003630479640000065
After constant current discharge for a certain time, the three RC links are considered to reach a stable state, the voltage recovered by the battery in the standing stage is the ohmic internal resistance of the battery in the constant current discharge stage and the voltage drop of the three RC links, and the battery has a relationship:
U n -U b ＝R ab I。
step 4.2, acquiring a three-order RC equivalent circuit model system discrete equation of the lithium ion battery based on a specific constraint condition:
U b (k)＝U oc (k)-U(k)-U 2 (k)-U 3 (k)
Figure BDA0003630479640000066
wherein U is the battery terminal voltage, U 2 For the voltage across the second RC link, U 3 Voltage at two ends of a third RC link, wherein k represents the number of steps of iterative computation at the current moment;
step 4.3, obtaining a parameter theta to be identified and a sample set h:
Figure BDA0003630479640000071
θ(k)＝[a(k)b(k)c(k)] T
h(k)＝[U b (k-1)I(k)I(k-1)]
and 4.4, identifying the parameters by using a recursive least square method, wherein the operation process in one recursive period is as follows:
K(k)＝P(k-1)h(k)[h T (k)P(k-1)h(k)+y(k)] -1
θ(k)＝θ(k-1)+K(k)[Z(k)-h T (k)θ(k-1)]
Figure BDA0003630479640000072
step 4.5, obtaining ohmic internal resistance R 0 And a first RC link parameter R 1 And C 1 ：
Figure BDA0003630479640000073
Figure BDA0003630479640000074
Figure BDA0003630479640000075
Figure BDA0003630479640000076
Step 4.6, solving a second RC link parameter R based on a specific constraint condition 2 And C 2 ：
R 2 (k)＝R bn (k)-R 0 (k)-R 1 (k)-R 3
Figure BDA0003630479640000077
Step 4.7, updating the voltage U at the two ends of the second RC link and the third RC link 2 And U 3 ：
Figure BDA0003630479640000078
And 4.8, circulating the steps 4.4 to 4.5 until the parameter identification is finished.
Example (b):
the method is characterized in that an ANR26650 of a lithium iron phosphate battery with the rated capacity of 2.5Ah produced by A123 company is taken as a research object, and a third-order RC equivalent circuit model constructed by the method is compared with a second-order RC equivalent circuit model constructed by using a recursive least square method based on HPPC test data identification under the condition of 25 ℃ U.S. Federal city driving working condition. As can be seen from the reference of FIG. 6-1, FIG. 6-2, FIG. 7-1 and FIG. 7-2, the accuracy of the equivalent circuit model constructed by the present invention is higher.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery is characterized by comprising the following steps:
step 1, establishing a three-order RC equivalent circuit model of the lithium ion battery;
step 2, obtaining the open circuit voltage U of the lithium ion battery oc The relationship with SOC;
step 3, testing the lithium ion battery by adopting a novel parameter identification working condition to obtain test data of the lithium ion battery;
and 4, identifying battery model parameters by using a recursive least square method based on specific constraint conditions according to the lithium ion battery test data.
2. The method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery according to claim 1, wherein in the step 1,
the three-order RC equivalent circuit model of the lithium ion battery consists of a controlled voltage source, three RC links and an ohmic internal resistance R 0 Are connected in series.
3. The method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery according to claim 1, wherein the step 2 specifically comprises:
step 3.1, discharging the battery in the full-charge state discontinuously at a constant multiplying power and fully standing to obtain the open-circuit voltage U of the battery oc And SOC data;
step 3.2, fitting open-circuit voltage U by adopting a least square method oc The relation with SOC to obtain the open-circuit voltage U oc And the functional relationship with the SOC.
4. The method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery as claimed in claim 1, wherein in the step 3,
the novel parameter identification working condition comprises a part A with current change and a part B with stable and unchangeable current.
5. The method for identifying parameters of a three-order RC equivalent circuit model of a lithium ion battery according to claim 1, wherein the step 4 specifically comprises:
step 4.1, acquiring internal resistance and R according to the lithium ion battery test data under the novel parameter identification working condition bn And a third RC link R 3 And C 3 And a second RC link time constant e 2 As a specific constraint; wherein the content of the first and second substances,
R bn ＝R 0 +R 1 +R 2 +R 3 ；
step 4.2, based on the specific constraint condition, obtaining a three-order RC equivalent circuit model system discrete equation of the lithium ion battery:
U b (k)＝U oc (k)-U(k)-U 2 (k)-U 3 (k)
Figure FDA0003630479630000021
wherein I is the battery working current, U is the battery terminal voltage, U 2 For the voltage across the second RC link, U 3 Voltage at two ends of a third RC link, wherein k represents the number of steps of iterative computation at the current moment;
step 4.3: acquiring a parameter theta to be identified and a sample set h:
Figure FDA0003630479630000022
θ(k)＝[a(k) b(k) c(k)] T
h(k)＝[U b (k-1) I(k) I(k-1)]
and 4.4, identifying the parameters by using a recursive least square method, wherein the operation process in one recursive period is as follows:
K(k)＝P(k-1)h(k)[h T (k)P(k-1)h(k)+y(k)] -1
θ(k)＝θ(k-1)+K(k)[Z(k)-h T (k)θ(k-1)]
Figure FDA0003630479630000023
in the formula, K is a gain matrix, E is an identity matrix, P is a covariance matrix, y is a forgetting factor, theta (K) is a system unidentified parameter, and K represents the number of iterative computation steps at the current moment;
step 4.5, obtaining ohmic internal resistance R 0 And a first RC link parameter R 1 And C 1 ：
Figure FDA0003630479630000024
Figure FDA0003630479630000025
Figure FDA0003630479630000026
Figure FDA0003630479630000027
Step 4.6, solving a second RC link parameter R based on a specific constraint condition 2 And C 2 ：
R 2 (k)＝R bn (k)-R 0 (k)-R 1 (k)-R 3
Figure FDA0003630479630000028
Step 4.7, updating the voltage U at the two ends of the second RC link and the third RC link 2 And U 3 ：
Figure FDA0003630479630000029
Figure FDA00036304796300000210
And 4.8, circulating the steps 4.4 to 4.5 until the parameter identification is finished.
CN202210488832.7A 2022-05-06 2022-05-06 Three-order RC equivalent circuit model parameter identification method for lithium ion battery Pending CN114818601A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116184236A (en) * 2023-04-26 2023-05-30 宁德时代新能源科技股份有限公司 Battery calibration method, battery calibration device, electronic equipment and storage medium
CN117330965A (en) * 2023-12-01 2024-01-02 杭州高特电子设备股份有限公司 Optimization method and system for offline identification parameters of battery equivalent circuit model

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116184236A (en) * 2023-04-26 2023-05-30 宁德时代新能源科技股份有限公司 Battery calibration method, battery calibration device, electronic equipment and storage medium
CN116184236B (en) * 2023-04-26 2023-08-04 宁德时代新能源科技股份有限公司 Battery calibration method, battery calibration device, electronic equipment and storage medium
CN117330965A (en) * 2023-12-01 2024-01-02 杭州高特电子设备股份有限公司 Optimization method and system for offline identification parameters of battery equivalent circuit model

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