CN109991549B - Combined prediction method for state of charge and internal resistance of lithium ion battery - Google Patents

Combined prediction method for state of charge and internal resistance of lithium ion battery Download PDF

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CN109991549B
CN109991549B CN201910335214.7A CN201910335214A CN109991549B CN 109991549 B CN109991549 B CN 109991549B CN 201910335214 A CN201910335214 A CN 201910335214A CN 109991549 B CN109991549 B CN 109991549B
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李冠儒
孙立
金宇晖
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Southeast University
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Abstract

The invention discloses a method for predicting the charge state and the internal resistance of a lithium ion battery, which comprises the following steps: s1: providing an equivalent circuit model of the lithium ion battery; s2: obtaining parameters of an equivalent circuit model of the lithium ion battery through model identification; s3: designing a state observer to realize real-time tracking and prediction of the state of charge under the condition that the initial state of charge is uncertain; s4: and setting the internal resistance as an extended state quantity, designing an extended state observer, and realizing real-time tracking and prediction of the state of charge under the condition of uncertain internal resistance. The invention provides a lithium ion battery equivalent circuit model and provides a state observer capable of compensating initial state of charge uncertainty on the basis of the lithium ion battery equivalent circuit model; in addition, the internal resistance of the lithium ion battery is used as an expansion state quantity, and an expansion state observer capable of compensating the uncertainty of internal resistance change is provided on the basis, so that the internal resistance is observed and estimated, and the charge state of the lithium ion battery is accurately estimated.

Description

Combined prediction method for state of charge and internal resistance of lithium ion battery
Technical Field
The invention relates to the field of automatic control, in particular to a joint prediction method for the charge state and the internal resistance of a lithium ion battery.
Background
With the shortage of energy, the pressure in the environmental protection of the world and the increasing attention of the society to the sustainable development strategy, the research and application prospect of green energy is wide. Among them, lithium ion batteries have been widely used in portable electric appliances such as portable computers, video cameras, and mobile communications due to their unique performance advantages. The developed high-capacity lithium ion battery is tried out in the electric automobile, is expected to become one of main power sources of the electric automobile in the 21 st century, and is applied to the aspects of artificial satellites, aerospace and energy storage.
Despite the good development potential, some technical problems that have not yet been overcome still prevent the large-scale efficient and safe use of lithium ion batteries. Among them, the state of charge estimation of lithium ion batteries is closely connected with the high efficiency, reliability and safety of batteries, which is a key problem to be solved urgently. The state of charge of a lithium ion battery is defined as the ratio of the remaining capacity after a period of use or long standing to the capacity of its fully charged state, expressed in percent. The value range is 0-1, when the charge state is 0, the battery is completely discharged, and when the charge state is 1, the battery is completely charged. During the use process of the battery, the state of charge of the battery needs to be kept in a proper range, which is important for the efficient and safe operation of the battery, and simultaneously, the overcharge and over-discharge of the battery can be avoided, and the service life of the battery is prolonged.
The difficulty of the lithium ion battery state of charge estimation mainly lies in the existence of various uncertain disturbances, and two main disturbances which have the greatest influence on the state of charge estimation are determined through experiments: initial SOC uncertainty and internal resistance change. The state of charge at this time is easily uncertain when the lithium ion battery starts to operate, and the internal resistance is affected by the temperature change of the lithium ion battery along with the operation of the lithium ion battery. The two disturbances are very easy to occur in the using process of the lithium ion battery, and the two disturbances have great influence on the estimation of the state of charge, so that the accurate estimation of the state of charge is always a big problem.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a joint prediction method for the charge state and the internal resistance of a lithium ion battery, which can accurately estimate the charge state and the internal resistance of the lithium ion battery.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a joint prediction method of the charge state and the internal resistance of a lithium ion battery, which comprises the following steps:
s1: providing an equivalent circuit model of the lithium ion battery;
s2: obtaining parameters of an equivalent circuit model of the lithium ion battery through model identification;
s3: designing a state observer to realize real-time tracking and prediction of the state of charge under the condition that the initial state of charge is uncertain;
s4: and setting the internal resistance as an extended state quantity, designing an extended state observer, and realizing real-time tracking and prediction of the state of charge under the condition of uncertain internal resistance.
Further, the lithium ion battery equivalent circuit model in step S1 is obtained according to equations (1) and (2):
Figure BDA0002038936810000021
V＝VOC(Z)-V1-V2-IRs (2)
wherein V is the output voltage of the lithium ion battery, VOC(Z) represents a terminal voltage V of a lithium ion batteryOCAs a function of the state of charge Z, I being the current across the lithium ion battery, R1Is the resistor resistance, R, of the first RC loop2Is the resistor resistance of the second RC loop, C1Capacitor capacitance, C, of the first RC circuit2Capacitor capacitance of the second RC loop, Q being the lithium ion battery capacity, RsIs the internal resistance of lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure BDA0002038936810000022
is a V1The derivative of (a) of (b),
Figure BDA0002038936810000023
is a V2The derivative of (a) of (b),
Figure BDA0002038936810000024
is the derivative of Z.
Further, the step S2 specifically includes the following steps:
s21: for lithiumCarrying out small-current charge-discharge experiment on the ion battery to obtain a charge-discharge curve, and fitting the charge-discharge curve to obtain the voltage V at the end of the lithium ion batteryOCAnd state of charge Z:
Figure BDA0002038936810000025
wherein, akIs the kth coefficient;
s22: performing a large-current stage charge and discharge experiment on the lithium ion battery, and performing model identification on the voltage and the current obtained in the charge and discharge experiment through a particle swarm optimization algorithm to obtain equivalent circuit model parameters; the adaptive function IAE of the particle swarm optimization algorithm is as follows:
Figure BDA0002038936810000026
wherein y is the model output, V is the lithium ion battery output voltage, and T is the response time.
Further, the step S3 specifically includes the following steps:
s31: the state observer is designed according to equations (5) and (6):
Figure BDA0002038936810000031
Figure BDA0002038936810000032
wherein L is1、L2、L3Is the state observer parameter, y is the model output,
Figure BDA0002038936810000033
is an estimate of y, V is the output voltage of the lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure BDA0002038936810000034
is an estimate of the value of V,
Figure BDA0002038936810000035
is a V1Is estimated by the estimation of (a) a,
Figure BDA0002038936810000036
is a V2Is estimated by the estimation of (a) a,
Figure BDA0002038936810000037
for the purpose of the estimation of Z,
Figure BDA0002038936810000038
is composed of
Figure BDA0002038936810000039
The derivative of (a) of (b),
Figure BDA00020389368100000310
is composed of
Figure BDA00020389368100000311
The derivative of (a) of (b),
Figure BDA00020389368100000312
is composed of
Figure BDA00020389368100000313
Derivative of (A), R1Is the resistor resistance of the first RC loop, C1Capacitor capacitance, C, of the first RC circuit2The capacitor capacitance of the second RC loop, and Q is the lithium ion battery capacity;
Figure BDA00020389368100000314
represents the terminal voltage V of the lithium ion batteryOCAnd state of charge estimation
Figure BDA00020389368100000315
The functional relationship between the two components is that,
Figure BDA00020389368100000316
akis the kth coefficient; i is the current at both ends of the lithium ion battery, RsIs the internal resistance of the lithium ion battery;
s32: and observing the charge state Z as a state quantity, and compensating the charge state Z to realize real-time tracking and prediction of the charge state under the condition that the initial charge state is uncertain.
Further, the step S4 specifically includes the following steps:
s41: the extended state observer is designed according to equations (7) and (8):
Figure BDA00020389368100000317
Figure BDA00020389368100000318
wherein L is4In order to expand the parameters of the state observer,
Figure BDA00020389368100000319
is to RsIs estimated by the estimation of (a) a,
Figure BDA00020389368100000320
is composed of
Figure BDA00020389368100000321
A derivative of (a);
s42: and observing the internal resistance as an expansion state quantity, and compensating the internal resistance to realize the real-time tracking and prediction of the charge state under the condition of uncertain internal resistance.
Has the advantages that: the invention discloses a joint prediction method for the state of charge and the internal resistance of a lithium ion battery, which provides a lithium ion battery equivalent circuit model and a state observer capable of compensating the uncertainty of the initial state of charge on the basis of the model; in addition, the internal resistance of the lithium ion battery is used as an expansion state quantity, and an expansion state observer capable of compensating the uncertainty of internal resistance change is provided on the basis, so that the internal resistance is observed and estimated, and the charge state of the lithium ion battery is accurately estimated.
Drawings
Fig. 1 is a structural diagram of an equivalent circuit model of a lithium ion battery according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a result of a small current charge-discharge experiment in an embodiment of the present invention;
FIG. 3 is a diagram illustrating the results of a large current step-wise charging/discharging experiment according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating the fitting effect between the recognition result and the actual model according to the embodiment of the present invention;
fig. 5 is a comparison graph of the optimization effect of the equivalent circuit model and the state observer of the lithium ion battery on the state of charge estimation under the condition that the initial state of charge is uncertain in the embodiment of the present invention;
fig. 5(a) is a fitting effect diagram of the lithium ion battery equivalent circuit model on the estimated value and the actual value of the state of charge under the condition that the initial state of charge is uncertain;
FIG. 5(b) is a graph of the effect of a state observer fitting estimated and actual values of state of charge under conditions where the initial state of charge is uncertain;
fig. 6 is a comparison graph of optimization effects of the state observer and the extended state observer on the state of charge and the internal resistance estimation under the condition of uncertain internal resistance in the embodiment of the present invention;
fig. 6(a) is a fitting effect diagram of the state observer to the estimated value and the actual value of the state of charge under the condition that the internal resistance is uncertain;
FIG. 6(b) is a diagram of the fitting effect of the extended state observer on the estimated value and the actual value of the internal resistance under the condition of uncertain internal resistance;
fig. 6(c) is a graph of the effect of the extended state observer on the fit of the estimated value and the actual value of the state of charge under the condition of uncertain internal resistance.
Detailed Description
The technical solution of the present invention will be further described with reference to the following embodiments.
The specific embodiment discloses a joint prediction method for the charge state and the internal resistance of a lithium ion battery, which comprises the following steps:
s1: providing an equivalent circuit model of the lithium ion battery; for the model number of NCR18650GA, the electric quantity of 3450mAh, the maximum discharge current of 10A, the equivalent circuit model is as shown in fig. 1, an electronic load is adopted to receive current discharge and a voltage source is adopted to charge the battery, wherein the current is set to be negative when the battery is charged, and the current is set to be positive when the battery is discharged;
s2: obtaining parameters of an equivalent circuit model of the lithium ion battery through model identification;
s3: designing a state observer to realize real-time tracking and prediction of the state of charge under the condition that the initial state of charge is uncertain;
s4: and setting the internal resistance as an extended state quantity, designing an extended state observer, and realizing real-time tracking and prediction of the state of charge under the condition of uncertain internal resistance.
The lithium ion battery equivalent circuit model in step S1 is obtained according to equations (1) and (2):
Figure BDA0002038936810000051
V＝VOC(Z)-V1-V2-IRs (2)
wherein V is the output voltage of the lithium ion battery, VOC(Z) represents a terminal voltage V of a lithium ion batteryOCAs a function of the state of charge Z, I being the current across the lithium ion battery, R1Is the resistor resistance, R, of the first RC loop2Is the resistor resistance of the second RC loop, C1Capacitor capacitance, C, of the first RC circuit2Capacitor capacitance of the second RC loop, Q being the lithium ion battery capacity, RsIs the internal resistance of lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure BDA0002038936810000052
is a V1The derivative of (a) of (b),
Figure BDA0002038936810000053
is a V2The derivative of (a) of (b),
Figure BDA0002038936810000054
is the derivative of Z.
Step S2 specifically includes the following steps:
s21: carrying out a low-current charge-discharge experiment on the lithium ion battery to obtain a charge-discharge curve, and fitting the charge-discharge curve to obtain a voltage V at the terminal of the lithium ion batteryOCAnd state of charge Z:
Figure BDA0002038936810000055
wherein, akIs the kth coefficient;
s22: performing a large-current stage charge and discharge experiment on the lithium ion battery, and performing model identification on the voltage and the current obtained in the charge and discharge experiment through a particle swarm optimization algorithm to obtain equivalent circuit model parameters; the adaptive function IAE of the particle swarm optimization algorithm is as follows:
Figure BDA0002038936810000056
wherein y is the model output, V is the lithium ion battery output voltage, and T is the response time.
FIG. 2 is a graph showing the results of a small current charge/discharge experiment, wherein the charge current is-0.138A and the discharge current is 0.138A. Obtaining a fitting curve shown by a dot-dash line in the graph by fitting, wherein the fitting function is in a format of
Figure BDA0002038936810000061
Wherein the coefficient akThe values of (A) are shown in Table 1.
TABLE 1 values of fitting function coefficients
Figure BDA0002038936810000062
Fig. 3 is a graph showing the results of a large-current step-like charge/discharge experiment. By particle swarm optimization algorithm, the parameter R in the formula (1) is subjected to1、R2、C1、C2、Q、RsPerforming identification, wherein the adaptive function of the algorithm is
Figure BDA0002038936810000063
The identification gave the results shown in Table 2.
TABLE 2 identification of the values of the parameters obtained
Figure BDA0002038936810000064
Figure BDA0002038936810000071
FIG. 4 is a diagram illustrating the fitting effect between the identification result and the actual model. Obviously, the output voltage fitting effect is not good, so that it can be inferred that the state of charge obtained by the model is inaccurate, and therefore, a state observer and an extended state observer are designed to estimate the state of charge and compensate for possible uncertainty disturbance.
Step S3 specifically includes the following steps:
s31: the state observer is designed according to equations (5) and (6):
Figure BDA0002038936810000072
Figure BDA0002038936810000073
wherein L is1、L2、L3Is the state observer parameter, y is the model output,
Figure BDA0002038936810000074
is an estimate of y, V is the output voltage of the lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure BDA0002038936810000075
is an estimate of the value of V,
Figure BDA0002038936810000076
is a V1Is estimated by the estimation of (a) a,
Figure BDA0002038936810000077
is a V2Is estimated by the estimation of (a) a,
Figure BDA0002038936810000078
for the purpose of the estimation of Z,
Figure BDA0002038936810000079
is composed of
Figure BDA00020389368100000710
The derivative of (a) of (b),
Figure BDA00020389368100000711
is composed of
Figure BDA00020389368100000712
The derivative of (a) of (b),
Figure BDA00020389368100000713
is composed of
Figure BDA00020389368100000714
Derivative of (A), R1Is the resistor resistance of the first RC loop, C1Capacitor capacitance, C, of the first RC circuit2The capacitor capacitance of the second RC loop, and Q is the lithium ion battery capacity;
Figure BDA00020389368100000715
represents the terminal voltage V of the lithium ion batteryOCAnd state of charge estimation
Figure BDA00020389368100000716
The functional relationship between the two components is that,
Figure BDA00020389368100000717
akis the kth coefficient; i is the current at both ends of the lithium ion battery, RsIs the internal resistance of the lithium ion battery;
s32: and observing the charge state Z as a state quantity, and compensating the charge state Z to realize real-time tracking and prediction of the charge state under the condition that the initial charge state is uncertain.
Fig. 5(a) is a graph of the effect of the model obtained by recognition on the estimated and actual values of state of charge without uncertainty in the initial state of charge, in which the initial state of charge is set to be reduced by 15%, without designing a state observer. Obviously, although the change trends of the two values are the same, the difference between the two values is always maintained and cannot be eliminated because the difference exists at the beginning and the observer does not have compensation measures. For this phenomenon, a state observer needs to be designed to compensate and eliminate the possible differences. Therefore, the state observer expressed by equation (5) is designed. After linearization, the pole allocation method of automatic control theory is used to carry out the parameter L1、L2、L3Setting is carried out, and the setting result is as follows:
Figure BDA0002038936810000081
the state observer after parameter setting is used in the estimation of the state of charge, and the experimental result shown in fig. 5(b) is obtained. Obviously, after the state observer is adopted, even if the initial state of charge is uncertain, the difference can be made up in time, and accurate estimation of the state of charge is realized in the whole state observation process.
Fig. 6 is a comparison graph of the optimization effect of the extended state observer on the state of charge estimation. Fig. 6(a) is a graph of the effect of fitting the estimated value and the actual value of the state of charge with uncertainty in the internal resistance by the state observer when the extended state observer is not designed, in which the internal resistance is set to be 15% larger. Obviously, once the internal resistance changes, the estimated result and the actual result have a large deviation, and the deviation cannot be compensated and reduced in the whole observation process. For this phenomenon, the internal resistance needs to be set as a state variable, and then the extended state observer is designed to compensate and eliminate the possible difference.
Step S4 specifically includes the following steps:
s41: the extended state observer is designed according to equations (7) and (8):
Figure BDA0002038936810000082
Figure BDA0002038936810000083
wherein L is4In order to expand the parameters of the state observer,
Figure BDA0002038936810000084
is to RsIs estimated by the estimation of (a) a,
Figure BDA0002038936810000085
is composed of
Figure BDA0002038936810000086
A derivative of (a);
s42: and observing the internal resistance as an expansion state quantity, and compensating the internal resistance to realize the real-time tracking and prediction of the charge state under the condition of uncertain internal resistance.
Similarly, the parameter L is set by the pole allocation method of the automatic control theory1、L2、L3，L4Setting is carried out, and the setting result is as follows:
Figure BDA0002038936810000091
wherein, in order to guarantee that the observer is in a stable state, avoid the observer to appear the condition of dispersing, L4The positive and negative values of the value follow the positive and negative values of the current I.
The extended state observer after parameter setting is used for estimating the state of charge under the condition of uncertain internal resistance, and experimental results shown in fig. 6(b) and (c) are obtained. As can be seen from fig. 6(b), after the state observer is used, even if the internal resistance changes greatly, the extended state observer can compensate the difference of the internal resistance in time, and perform accurate estimation on the internal resistance, and further as can be seen from fig. 6(c), the extended state observer can realize accurate estimation on the state of charge in the whole state observation process.

Claims (3)

1. The joint prediction method for the charge state and the internal resistance of the lithium ion battery is characterized by comprising the following steps of: the method comprises the following steps:
s1: providing an equivalent circuit model of the lithium ion battery;
s2: obtaining parameters of an equivalent circuit model of the lithium ion battery through model identification;
s3: designing a state observer to realize real-time tracking and prediction of the state of charge under the condition that the initial state of charge is uncertain;
s4: setting the internal resistance as an extended state quantity, designing an extended state observer, and realizing real-time tracking and prediction of the state of charge under the condition of uncertain internal resistance;
the step S2 specifically includes the following steps:
s21: carrying out a low-current charge-discharge experiment on the lithium ion battery to obtain a charge-discharge curve, and fitting the charge-discharge curve to obtain a voltage V at the terminal of the lithium ion batteryOCAnd state of charge Z:
Figure FDA0002828688270000011
wherein, akIs the kth coefficient;
s22: performing a large-current stage charge and discharge experiment on the lithium ion battery, and performing model identification on the voltage and the current obtained in the charge and discharge experiment through a particle swarm optimization algorithm to obtain equivalent circuit model parameters; the adaptive function IAE of the particle swarm optimization algorithm is as follows:
Figure FDA0002828688270000012
wherein y is the model output, V is the output voltage of the lithium ion battery, and T is the response time;
the step S4 specifically includes the following steps:
s41: the extended state observer is designed according to equations (3) and (4):
Figure FDA0002828688270000013
Figure FDA0002828688270000014
wherein V is the output voltage of the lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure FDA0002828688270000015
is an estimate of the value of V,
Figure FDA0002828688270000016
is a V1Is estimated by the estimation of (a) a,
Figure FDA0002828688270000017
is a V2Is estimated by the estimation of (a) a,
Figure FDA0002828688270000018
for the purpose of the estimation of Z,
Figure FDA0002828688270000019
is composed of
Figure FDA00028286882700000110
The derivative of (a) of (b),
Figure FDA00028286882700000111
is composed of
Figure FDA00028286882700000112
The derivative of (a) of (b),
Figure FDA00028286882700000113
is composed of
Figure FDA00028286882700000114
Derivative of (A), RsIn order to provide the internal resistance of the lithium ion battery,
Figure FDA0002828688270000021
is to RsIs estimated by the estimation of (a) a,
Figure FDA0002828688270000022
is composed of
Figure FDA0002828688270000023
Derivative of, VOC(Z) represents a terminal voltage V of a lithium ion batteryOCAs a function of the state of charge Z, I being the current across the lithium ion battery, R1Is the resistor resistance, R, of the first RC loop2Is the resistor resistance of the second RC loop, C1Capacitor capacitance, C, of the first RC circuit2Capacitor capacitance of the second RC loop, Q is the lithium ion battery capacity, L1、L2、L3Is the state observer parameter, y is the model output,
Figure FDA0002828688270000024
is an estimate of y, L4To expand the state observer parameters;
s42: and observing the internal resistance as an expansion state quantity, and compensating the internal resistance to realize the real-time tracking and prediction of the charge state under the condition of uncertain internal resistance.
2. The joint prediction method for the state of charge and the internal resistance of the lithium ion battery according to claim 1, characterized in that: the lithium ion battery equivalent circuit model in step S1 is obtained according to equations (5) and (6):
Figure FDA0002828688270000025
V＝VOC(Z)-V1-V2-IRs (6)
wherein V is the output voltage of the lithium ion battery, VOC(Z) represents a terminal voltage V of a lithium ion batteryOCAs a function of the state of charge Z, I being the current across the lithium ion battery, R1Is the resistor resistance, R, of the first RC loop2Is the resistor resistance of the second RC loop, C1Capacitor capacitance, C, of the first RC circuit2Capacitor capacitance of the second RC loop, Q being the lithium ion battery capacity, RsIs the internal resistance of lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure FDA0002828688270000026
is a V1The derivative of (a) of (b),
Figure FDA0002828688270000027
is a V2The derivative of (a) of (b),
Figure FDA0002828688270000028
is the derivative of Z.
3. The joint prediction method for the state of charge and the internal resistance of the lithium ion battery according to claim 1, characterized in that: the step S3 specifically includes the following steps:
s31: the state observer is designed according to equations (7) and (8):
Figure FDA0002828688270000029
Figure FDA00028286882700000210
wherein L is1、L2、L3Is the state observer parameter, y is the model output,
Figure FDA0002828688270000031
is an estimate of y, V is the output voltage of the lithium ion battery, V1Is the voltage across the first RC loop, V2Is the voltage across the second RC loop, Z is the state of charge,
Figure FDA0002828688270000032
is an estimate of the value of V,
Figure FDA0002828688270000033
is a V1Is estimated by the estimation of (a) a,
Figure FDA0002828688270000034
is a V2Is estimated by the estimation of (a) a,
Figure FDA0002828688270000035
for the purpose of the estimation of Z,
Figure FDA0002828688270000036
is composed of
Figure FDA0002828688270000037
The derivative of (a) of (b),
Figure FDA0002828688270000038
is composed of
Figure FDA0002828688270000039
The derivative of (a) of (b),
Figure FDA00028286882700000310
is composed of
Figure FDA00028286882700000311
Derivative of (A), R1Is the resistor resistance, R, of the first RC loop2Is the resistor resistance of the second RC loop, C1Capacitor capacitance, C, of the first RC circuit2The capacitor capacitance of the second RC loop, and Q is the lithium ion battery capacity;
Figure FDA00028286882700000312
represents the terminal voltage V of the lithium ion batteryOCAnd state of charge estimation
Figure FDA00028286882700000313
The functional relationship between the two components is that,
Figure FDA00028286882700000314
akis the kth coefficient, I is the current at two ends of the lithium ion battery, RsIs the internal resistance of the lithium ion battery;
s32: and observing the charge state Z as a state quantity, and compensating the charge state Z to realize real-time tracking and prediction of the charge state under the condition that the initial charge state is uncertain.
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