CN112946480A - Lithium battery circuit model simplification method for improving SOC estimation real-time performance - Google Patents

Lithium battery circuit model simplification method for improving SOC estimation real-time performance Download PDF

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CN112946480A
CN112946480A CN202110119785.4A CN202110119785A CN112946480A CN 112946480 A CN112946480 A CN 112946480A CN 202110119785 A CN202110119785 A CN 202110119785A CN 112946480 A CN112946480 A CN 112946480A
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孙天健
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China University of Mining and Technology CUMT
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    • 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
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Abstract

The invention discloses a lithium battery circuit model simplifying method for improving the real-time performance of SOC estimation, which is characterized in that the number of equivalent circuit model parameters to be identified is simplified, only 2 parameters related to polarization voltage need to be identified, and the coefficient of a system state equation matrix is equivalent to a constant when the performance of a lithium battery is stable, so that the computation of a system is greatly reduced on the premise of ensuring the requirement of parameter identification precision, the real-time performance of online identification of the equivalent circuit model parameters and online estimation of SOC is improved, the computation of a control system is greatly reduced, and the problems of overlarge computation of the control system and poor real-time performance existing in online identification of the second-order Thevenin equivalent circuit model parameters and online estimation of SOC in the prior art are solved.

Description

Lithium battery circuit model simplification method for improving SOC estimation real-time performance
Technical Field
The invention belongs to the technical field of lithium battery application, and relates to a lithium battery circuit model simplifying method for improving the real-time performance of SOC estimation.
Background
The lithium battery has the advantages of long cycle life, high energy density, low self-discharge rate, safety, reliability and the like, and is widely applied to the fields of electric automobiles, alternating current and direct current micro-grids and the like. The state of charge (SOC) is taken as the key of a battery management system, and rapid and high-precision SOC online estimation is extremely important for safe use of the lithium battery, so that unsafe accidents such as overcharge and overdischarge of the lithium battery are prevented, and the service life of the lithium battery is prolonged.
The accuracy and the rapidity of SOC online estimation depend on the accuracy and the complexity of a lithium battery equivalent circuit model and the accuracy and the rapidity of parameter identification of the lithium battery equivalent circuit model. The lithium battery equivalent circuit model mainly comprises an internal resistance model, a resistance-capacitance model, a PNGV model, a GNL model and a Withanan model. The internal resistance model is simple in structure, but dynamic characteristics of the battery under various working conditions cannot be well simulated by the internal resistance model, and application precision is low in practice. The resistance-capacitance model can well represent the battery characteristics, but the capacitance voltage is difficult to measure. The PNGV model is less practical. Although the GNL model has higher accuracy, more parameters need to be identified, which increases the computational complexity.
The existing method for identifying the parameters of the second-order Thevenin equivalent circuit model comprises a maximum likelihood method, a random gradient method, a least square method (RLS), a least square method (FRLS) containing forgetting factors, a least square method (VFFRLS) with variable forgetting factors, a neural network method and the like. The SOC estimation can be carried out on the basis of equivalent circuit model parameter identification, and common SOC estimation methods comprise an ampere-hour integration method, an open-circuit voltage method, a load voltage method, a Kalman filtering method and the like. However, whether the equivalent circuit model parameter identification method or the SOC estimation method is used, the parameter identification speed or the SOC estimation speed is increased for simplifying the calculation and improving the parameter identification speed or the SOC estimation speed on the premise of ensuring the accuracy, depending on the number of parameters and the computational complexity in the second-order thevenin equivalent circuit model. The existing second-order Thevenin equivalent circuit model has a large number of parameters, requires index calculation, and has poor real-time performance of online parameter identification or online SOC estimation.
Disclosure of Invention
The invention aims to provide a lithium battery circuit model simplifying method for improving the real-time performance of SOC estimation, and solves the problems that in the prior art, the control system has overlarge operation amount and poor real-time performance when the parameters of a second-order Thevenin equivalent circuit model of a lithium battery are identified on line and the SOC is estimated on line.
The technical scheme adopted by the invention is that the method for simplifying the lithium battery circuit model for improving the real-time performance of SOC estimation is implemented according to the following steps:
step 1, 5 parameters R identified by combining a lithium battery second-order Thevenin equivalent circuit model in the prior art0、R1、R2、C1And C2(ii) a Calculating input current and output voltage of second-order RC equivalent circuit model, e.g.Formula (1):
Figure BDA0002921589130000021
wherein R is0Indicating the ohmic internal resistance, R1And R2Respectively shows electrochemical polarization internal resistance and concentration polarization internal resistance, C1And C2Respectively representing electrochemical polarization capacitance and concentration polarization capacitance;
laplace transformation is carried out on the formula (1), and a traditional terminal voltage formula of a second-order Thevenin equivalent circuit model is represented by a formula (2):
Figure BDA0002921589130000022
step 2, through carrying out discharge or charge experiment on the lithium battery, measuring the terminal voltage U of the lithium batteryLAnd end current I, obtaining charge-discharge capacity Q according to the end current I, and calculating open-circuit voltage Uoc；
Step 3, measuring the terminal voltage U according to the step 2LTerminal current I and calculated open circuit voltage UocObtaining the internal parameter R of the battery by using parameter identification0、R1、R2、C1、C2A value of (d);
step 4, obtaining the internal parameter R of the battery in the step 31、R2、C1、C2To obtain the matrix coefficient A in the system state equation during SOC estimation1And B1；
Step 5, combining step 1, in the formula (2)
Figure BDA0002921589130000031
Obtaining a terminal voltage formula of the simplified circuit model, as shown in formula (11), and obtaining a corresponding simplified circuit model,
UL(s)＝Uoc(s)-I(s)R0-U1(s)-U2(s)＝Uoc(s)-I(s)(R0+KU1+KU2) (11)
step 6, discretizing the formula (11) to obtain a formula (12), and identifying the parameter value K by using a parameter identification algorithm RLS according to the formula (12)U1，KU2；
Uoc(k)-UL(k)＝I(k)(R0+KU1+KU2) (12)；
Step 7, identifying a parameter K under the second-order Thevenin equivalent circuit model in the step 6U1，KU2And obtaining an SOC estimation value by using an SOC online estimation method.
The invention is also characterized in that:
when the discharging or charging experiment is performed in step 2,
Figure BDA0002921589130000032
wherein T is1For the charging or discharging time, the current SOC value is obtained according to the formulas (3) and (4), and then the open-circuit voltage U is obtained according to the formula (5)oc；
Figure BDA0002921589130000033
Figure BDA0002921589130000041
Wherein QnThe rated capacity of the battery.
Uoc＝-303.47soc8+1336.5soc7-2437.8soc6+2382.9soc5-1350.9soc4+450.41soc3-86.042soc2+8.901soc+2.8591 (5)。
In step 3, a parameter identification algorithm RLS is adopted to perform offline parameter identification, so that recursive calculation of parameter identification is realized, and the following formulas (6) to (8) are shown:
Figure BDA0002921589130000042
Figure BDA0002921589130000043
Figure BDA0002921589130000044
where K (k) is the gain vector at time k; phi (k) is an information vector that can be obtained by measurement and calculation, phi (k) being [ U ]L(k-1)-Uoc(k-1)UL(k-2)-Uoc(k-2)I(k)I(k-1)I(k-2)]T；
Figure BDA0002921589130000045
Is the vector to be estimated and is,
Figure BDA0002921589130000046
p (k) is a covariance matrix; λ is a forgetting factor; y (k) is the actual measurement of the system terminal voltage.
The specific process of the step 4 is as follows:
step 4.1, matrix coefficient A in system state equation during existing SOC estimation0、B0As shown in the formula (9),
Figure BDA0002921589130000047
let A0In the matrix
Figure BDA0002921589130000048
Let B0In a matrix of
Figure BDA0002921589130000049
Obtaining a parameter R according to the step 31、R2、C1、C2Obtaining m1、m2、n1、n2；
Step 4.2, respectively obtaining parameters in the battery charging and discharging processm1、m2、n1、n2Average value of (2)
Figure BDA0002921589130000051
Figure BDA0002921589130000052
Because when the performance of the battery is stable,
Figure BDA0002921589130000053
the average value, which may be considered a constant value, is substituted into equation (9) to obtain the matrix coefficient A1、B1They are constant matrices, as shown in equation (10), as distinguished from the conventional variable matrix coefficients A0、B0. In SOC estimation, the matrix A1And B1Real-time updating is not needed;
Figure BDA0002921589130000054
in step 6, 5 parameters R needing to be identified by the original traditional second-order Thevenin equivalent circuit model0、R1、R2、C1、C2At this time, only 2 parameters K related to the polarization voltage need to be identifiedU1、KU2The simultaneous polarization voltage is calculated by a linear formula, namely electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1), concentration polarization voltage U2(k+1)＝KU2(k+1)*I(k+1)。
The state variables of the system in step 7 are: x (k) ([ SOC (k)) U1(k) U2(k)]TCombined with electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1) and concentration polarization voltage U2(k+1)＝KU2(K +1) × I (K +1), according to equations (11), (12) and the parameter K identified in step 6U1And KU2And (3) obtaining an SOC estimation value by combining a state equation formula (13) and an output equation formula (14) of the system and reusing the existing SOC online estimation method, wherein the output equation is the formula (13):
x(k+1)＝Ax(k)+BI(k) (13)；
Figure BDA0002921589130000055
the method has the advantages that the number of equivalent circuit model parameters needing to be identified is simplified, 5 resistance-capacitance parameters in the equivalent circuit model do not need to be accurately represented, the polarization voltage is calculated by adopting a linear formula, only 2 parameters related to the polarization voltage need to be identified, and meanwhile, the coefficient of a system state equation matrix is equivalent to a constant when the performance of the lithium battery is stable, so that the calculation amount of the system is greatly reduced on the premise of ensuring the requirement of parameter identification precision, the real-time performance of online identification of the equivalent circuit model parameters and online estimation of the SOC is improved, the calculation amount of a control system is greatly reduced, the execution time of the algorithm related to the online identification of the equivalent circuit model parameters and the online estimation of the SOC is reduced, and the real-time performance is improved.
Drawings
FIG. 1 is a second order Thevenin equivalent circuit model of a lithium battery in the prior art;
FIG. 2 is a simplified second order Thevenin equivalent circuit model of a lithium battery of the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A second-order Thevenin equivalent circuit model of a lithium battery in the prior art is shown in figure 1, ULTerminal voltage, I terminal current, Q charge-discharge capacity, UocIs an open circuit voltage, R0Indicating the ohmic internal resistance, R1For electrochemical polarization of internal resistance, R2For concentration polarization internal resistance, C1For electrochemical polarization of capacitance, C2Is concentration polarization capacitance, and T is system sampling time.
The invention discloses a lithium battery circuit model simplification method for improving the real-time performance of SOC estimation, which is implemented according to the following steps:
step (ii) of1. 5 parameters R identified by combining a lithium battery second-order Thevenin equivalent circuit model in the prior art0、R1、R2、C1And C2(ii) a As shown in fig. 1, the input current and the output voltage of the second-order RC equivalent circuit model are calculated, as shown in equation (1):
Figure BDA0002921589130000061
wherein R is0Indicating the ohmic internal resistance, R1And R2Respectively shows electrochemical polarization internal resistance and concentration polarization internal resistance, C1And C2Respectively representing electrochemical polarization capacitance and concentration polarization capacitance;
laplace transformation is carried out on the formula (1), and a traditional terminal voltage formula of a second-order Thevenin equivalent circuit model is represented by a formula (2):
Figure BDA0002921589130000071
step 2, through carrying out discharge or charge experiment on the lithium battery, measuring the terminal voltage U of the lithium batteryLAnd end current I, obtaining charge-discharge capacity Q according to the end current I, and calculating open-circuit voltage Uoc；
When the discharging or charging experiment is performed in step 2,
Figure BDA0002921589130000072
wherein T is1For the charging or discharging time, the current SOC value is obtained according to the formulas (3) and (4), and then the open-circuit voltage U is obtained according to the formula (5)oc；
Figure BDA0002921589130000073
Figure BDA0002921589130000074
Wherein QnThe rated capacity of the battery.
Uoc＝-303.47soc8+1336.5soc7-2437.8soc6+2382.9soc5-1350.9soc4+450.41soc3-86.042soc2+8.901soc+2.8591 (5)；
Step 3, measuring the terminal voltage U according to the step 2LTerminal current I and calculated open circuit voltage UocObtaining the internal parameter R of the battery by using parameter identification0、R1、R2、C1、C2The value of (c).
In step 3, a parameter identification algorithm RLS is adopted to perform offline parameter identification, so that recursive calculation of parameter identification is realized, and the following formulas (6) to (8) are shown:
Figure BDA0002921589130000075
Figure BDA0002921589130000076
Figure BDA0002921589130000077
where K (k) is the gain vector at time k; phi (k) is an information vector that can be obtained by measurement and calculation, phi (k) being [ U ]L(k-1)-Uoc(k-1)UL(k-2)-Uoc(k-2)I(k)I(k-1)I(k-2)]T；
Figure BDA0002921589130000081
Is the vector to be estimated and is,
Figure BDA0002921589130000082
p (k) is a covariance matrix; λ is a forgetting factor; y (k) is the actual measurement of the system terminal voltage.
Step 4, obtaining the step 3The obtained battery internal parameter R1、R2、C1、C2To obtain the matrix coefficient A in the system state equation during SOC estimation1And B1；
The specific process of the step 4 is as follows:
step 4.1, matrix coefficient A in system state equation during existing SOC estimation0、B0As shown in the formula (9),
Figure BDA0002921589130000083
let A0In the matrix
Figure BDA0002921589130000084
Let B0In a matrix of
Figure BDA0002921589130000085
Obtaining a parameter R according to the step 31、R2、C1、C2Obtaining m1、m2、n1、n2；
Step 4.2, respectively obtaining parameter m in the battery charging and discharging process1、m2、n1、n2Average value of (2)
Figure BDA0002921589130000086
Figure BDA0002921589130000087
Because when the performance of the battery is stable,
Figure BDA0002921589130000088
the average value, which may be considered a constant value, is substituted into equation (9) to obtain the matrix coefficient A1、B1They are constant matrices, as shown in equation (10), as distinguished from the conventional variable matrix coefficients A0、B0. In SOC estimation, the matrix A1And B1Real-time updating is not needed;
Figure BDA0002921589130000089
step 5, combining step 1, in the formula (2)
Figure BDA0002921589130000091
Obtaining a terminal voltage formula of the simplified circuit model, as shown in formula (11), and obtaining a corresponding simplified circuit model as shown in fig. 2;
UL(s)＝Uoc(s)-I(s)R0-U1(s)-U2(s)＝Uoc(s)-I(s)(R0+KU1+KU2) (11)
step 6, discretizing the formula (11) to obtain a formula (12), and identifying the parameter value K by using a parameter identification algorithm RLS according to the formula (12)U1，KU2；
Uoc(k)-UL(k)＝I(k)(R0+KU1+KU2) (12)；
In step 6, 5 parameters R needing to be identified by the original traditional second-order Thevenin equivalent circuit model0、R1、R2、C1、C2At this time, only 2 parameters K related to the polarization voltage need to be identifiedU1、KU2The simultaneous polarization voltage is calculated by a linear formula, namely electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1), concentration polarization voltage U2(k+1)＝KU2(k +1) × I (k +1), the computation load of the system is greatly reduced.
Step 7, identifying a parameter K under the second-order Thevenin equivalent circuit model in the step 6U1，KU2And obtaining an SOC estimation value by using an SOC online estimation method.
The state variables of the system in step 7 are: x (k) ([ SOC (k)) U1(k) U2(k)]TCombined with electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1) and concentration polarization voltage U2(k+1)＝KU2(k +1) × I (k +1) according to formula (a)11) (12) and the parameter K identified in step 6U1And KU2And (3) obtaining an SOC estimation value by combining a state equation formula (13) and an output equation formula (14) of the system and reusing the existing SOC online estimation method, wherein the output equation is the formula (13):
x(k+1)＝Ax(k)+BI(k) (13)
Figure BDA0002921589130000101
examples
The method for simplifying the lithium battery circuit model for improving the real-time performance of SOC estimation selects a lithium iron phosphate battery as a research object, and performs a discharge or charge experiment on the battery to obtain a terminal voltage ULTerminal current I, charge-discharge capacity Q and open-circuit voltage UocAnd fitting by Matlab software to obtain Uoc-an SOC curve equation; performing a comparison experiment based on a traditional second-order Thevenin equivalent circuit model and a simplified circuit model respectively; the time consumption comparison of the system under the two circuit models is shown in table 1, and the SOC estimation error comparison under the two circuit models is shown in table 2:
TABLE 1 time consuming comparison of systems under two circuit models
Figure BDA0002921589130000102
TABLE 2 SOC estimation error comparison under two circuit models
Circuit model Root mean square error Average relative error
Traditional second-order Thevenin equivalent circuit model 0.0656 0.0084
Simplified model 0.0657 0.0083
It can be seen from table 1 that the simplified model-based parameter identification and SOC estimation is much less time consuming than under the second order thevenin equivalent circuit model. Table 2 shows the comparison of the SOC estimation errors in the two models, and it can be seen that the SOC estimation results in the two models are approximately the same.
The existing lithium battery second-order Thevenin equivalent circuit model has 5 parameters R inside0、R1、R2、C1、C2Before SOC online estimation, the 5 RC parameters need to be identified online, so that the calculation amount of a control system is large, and the electrochemical polarization voltage U is large1Sum concentration polarization voltage U2The calculation also needs to perform complex exponential calculation according to the obtained 5 parameters, so that the identification error of the polarization voltage is increased, and further the error and the calculation amount of SOC estimation are influenced. The invention only needs to identify two parameters K by simplifying the number of equivalent circuit model parameters needing to be identifiedU1，KU2Calculating the polarization voltage U by using a linearization formula1And U2The calculation amount of the control system is greatly reduced, and meanwhile, the matrix coefficient of the system state equation is equivalent to a constant when the performance of the lithium battery is stable, so that the execution time of related algorithms for simplifying the online identification of circuit model parameters and the online estimation of the SOC is reduced, and the real-time performance is improved.

Claims (6)

1. A lithium battery circuit model simplification method for improving SOC estimation real-time performance is characterized by comprising the following steps:
step 1,5 parameters R identified by combining a lithium battery second-order Thevenin equivalent circuit model in the prior art0、R1、R2、C1And C2(ii) a Calculating the input current and the output voltage of a second-order RC equivalent circuit model, wherein the formula (1) is as follows:
Figure FDA0002921589120000011
wherein R is0Indicating the ohmic internal resistance, R1And R2Respectively shows electrochemical polarization internal resistance and concentration polarization internal resistance, C1And C2Respectively representing electrochemical polarization capacitance and concentration polarization capacitance;
laplace transformation is carried out on the formula (1), and a traditional terminal voltage formula of a second-order Thevenin equivalent circuit model is represented by a formula (2):
Figure FDA0002921589120000012
step 2, through carrying out discharge or charge experiment on the lithium battery, measuring the terminal voltage U of the lithium batteryLAnd end current I, obtaining charge-discharge capacity Q according to the end current I, and calculating open-circuit voltage Uoc；
Step 3, measuring the terminal voltage U according to the step 2LTerminal current I and calculated open circuit voltage UocObtaining the internal parameter R of the battery by using parameter identification0、R1、R2、C1、C2A value of (d);
step 4, obtaining the internal parameter R of the battery in the step 31、R2、C1、C2To obtain the matrix coefficient A in the system state equation during SOC estimation1And B1；
Step 5, combining step 1, in the formula (2)
Figure FDA0002921589120000013
Obtaining a simplified circuit modelThe terminal voltage formula of (2), as shown in equation (11), and its corresponding simplified circuit model, UL(s)＝Uoc(s)-I(s)R0-U1(s)-U2(s)＝Uoc(s)-I(s)(R0+KU1+KU2) (11)
Step 6, discretizing the formula (11) to obtain a formula (12), and identifying the parameter value K by using a parameter identification algorithm RLS according to the formula (12)U1，KU2；
Uoc(k)-UL(k)＝I(k)(R0+KU1+KU2) (12)；
Step 7, identifying a parameter K under the second-order Thevenin equivalent circuit model in the step 6U1，KU2And obtaining an SOC estimation value by using an SOC online estimation method.
2. The method as claimed in claim 1, wherein when performing the discharging or charging experiment in step 2,
Figure FDA0002921589120000021
wherein T is1For the charging or discharging time, the current SOC value is obtained according to the formulas (3) and (4), and then the open-circuit voltage U is obtained according to the formula (5)oc；
Figure FDA0002921589120000022
Figure FDA0002921589120000023
Wherein QnIs the rated capacity of the battery,
Uoc＝-303.47soc8+1336.5soc7-2437.8soc6+2382.9soc5-1350.9soc4+450.41soc3-86.042soc2+8.901soc+2.8591 (5)。
3. the method for simplifying the lithium battery circuit model for improving the real-time performance of SOC estimation according to claim 2, wherein the parameter identification algorithm RLS is adopted in the step 3 to perform offline parameter identification, so as to realize recursive calculation of parameter identification, as shown in the formulas (6) to (8):
Figure FDA0002921589120000024
Figure FDA0002921589120000025
Figure FDA0002921589120000031
where K (k) is the gain vector at time k; phi (k) is an information vector that can be obtained by measurement and calculation, phi (k) being [ U ]L(k-1)-Uoc(k-1) UL(k-2)-Uoc(k-2) I(k) I(k-1) I(k-2)]T；
Figure FDA0002921589120000032
Is the vector to be estimated and is,
Figure FDA0002921589120000033
p (k) is a covariance matrix; λ is a forgetting factor; y (k) is the actual measurement of the system terminal voltage.
4. The method for simplifying the lithium battery circuit model for improving the real-time performance of SOC estimation according to claim 3, wherein the specific process of the step 4 is as follows:
step 4.1, matrix coefficient A in system state equation during existing SOC estimation0、B0As shown in the formula (9),
Figure FDA0002921589120000034
let A0In the matrix
Figure FDA0002921589120000035
Let B0In a matrix of
Figure FDA0002921589120000036
Obtaining a parameter R according to the step 31、R2、C1、C2Obtaining m1、m2、n1、n2；
Step 4.2, respectively obtaining parameter m in the battery charging and discharging process1、m2、n1、n2Average value of (2)
Figure FDA0002921589120000037
Figure FDA0002921589120000038
Because when the performance of the battery is stable,
Figure FDA0002921589120000039
the average value, which may be considered a constant value, is substituted into equation (9) to obtain the matrix coefficient A1、B1They are constant matrices, as shown in equation (10), as distinguished from the conventional variable matrix coefficients A0、B0Matrix A in SOC estimation1And B1Real-time updating is not needed;
Figure FDA00029215891200000310
5. the method of claim 4, wherein the method comprises the step of simplifying a lithium battery circuit model to improve the real-time performance of SOC estimationAnd 5 parameters R required to be identified by the original traditional second-order Thevenin equivalent circuit model in the step 60、R1、R2、C1、C2At this time, only 2 parameters K related to the polarization voltage need to be identifiedU1、KU2The simultaneous polarization voltage is calculated by a linear formula, namely electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1), concentration polarization voltage U2(k+1)＝KU2(k+1)*I(k+1)。
6. The method as claimed in claim 5, wherein the state variables of the system in step 7 are: x (k) ([ SOC (k)) U1(k) U2(k)]TCombined with electrochemical polarization voltage U1(k+1)＝KU1(k +1) × I (k +1) and concentration polarization voltage U2(k+1)＝KU2(K +1) × I (K +1), according to equations (11), (12) and the parameter K identified in step 6U1And KU2And (3) obtaining an SOC estimation value by combining a state equation formula (13) and an output equation formula (14) of the system and reusing the existing SOC online estimation method, wherein the output equation is the formula (13):
x(k+1)＝Ax(k)+BI(k) (13)；
Figure FDA0002921589120000041
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