CN112130081A - Method for rapidly realizing lead-acid battery SOC estimation - Google Patents

Method for rapidly realizing lead-acid battery SOC estimation Download PDF

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CN112130081A
CN112130081A CN202011017823.7A CN202011017823A CN112130081A CN 112130081 A CN112130081 A CN 112130081A CN 202011017823 A CN202011017823 A CN 202011017823A CN 112130081 A CN112130081 A CN 112130081A
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battery
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CN112130081B (en
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汪星一
邵振华
钟智雄
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Minjiang University
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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
    • 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]
    • G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
    • G01R31/379—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator for lead-acid batteries
    • 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]
    • G01R31/396—Acquisition or processing of data for testing or for monitoring individual cells or groups of cells within a battery

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Abstract

The invention relates to a lead-acid battery capable of realizing rapid implementationSOCAn estimation method, comprising the steps of: building an equivalent circuit model of a lead-acid storage battery charging and discharging system under a singular system framework; converting a singular system into a conventional state space model expression; taking into account disturbances inside the lead-acid battery system and measuring the output voltage, in order to influence the state of charge in the presence of disturbancesSOCCarrying out correct estimation, and rewriting the conventional state space model into the expression of a singular system; the lead-acid battery is ensured to be charged in limited time by using the finite time stability theory and the Lyapunov function methodSOCA correct estimation is made. The invention can quickly estimate the lead-acid batterySOC。

Description

Method for rapidly realizing lead-acid battery SOC estimation
Technical Field
The invention relates to the technical field of battery capacity estimation, in particular to a method for quickly realizing lead-acid battery SOC estimation.
Background
A lead-acid battery (VRLA) is a battery whose electrodes are made mainly of lead and its oxides and whose electrolyte is a sulfuric acid solution. In the discharge state of the lead-acid battery, the main component of the positive electrode is lead dioxide, and the main component of the negative electrode is lead; in a charged state, the main components of the positive electrode and the negative electrode are lead sulfate.
After a new battery is put into use, it must be periodically charged and discharged. The purpose of charging is to enable the storage battery to store electric energy and recover the capacity in time so as to meet the requirements of electric equipment. The purpose of discharging is to check the capacity parameters of the battery in time and to promote the activation reaction of the electrode active material. The electrical performance and the service life of the storage battery are directly influenced by the charging and discharging conditions of the storage battery. The ratio of the remaining capacity of a battery after a period of use or long standing without use to its capacity in its fully charged state is usually expressed as a percentage. The value range of the SOC is 0-1, when the SOC is 0, the battery is completely discharged, when the SOC is 1, the battery is completely full, the state of charge of the battery must be considered when the battery is controlled to operate, and the SOC state estimation effect of the lead-acid storage battery in the prior art is not ideal.
Disclosure of Invention
In view of this, the present invention provides a method for rapidly estimating the SOC of a lead-acid battery, which can rapidly estimate the SOC of the lead-acid battery.
The invention is realized by adopting the following scheme: a method for rapidly realizing lead-acid battery SOC estimation specifically comprises the following steps:
building an equivalent circuit model of a lead-acid storage battery charging and discharging system under a singular system framework;
converting a singular system into a conventional state space model expression;
considering the interference between the interior of the lead-acid storage battery system and the measured output voltage, in order to correctly estimate the state of charge SOC under the interference condition, the conventional state space model is rewritten into the expression of a singular system; and the SOC of the lead-acid battery is correctly estimated within a limited time by using a finite time stability theory and a Lyapunov function method.
Further, the lead-acid battery charging and discharging system comprises an AC bus, a bidirectional DC/AC module, a lead-acid battery and an SOC estimator; the lead-acid storage battery is connected to the AC bus through the bidirectional DC/AC module, and the SOC estimator is connected with the lead-acid storage battery and used for estimating the SOC of the lead-acid storage battery;
the equivalent circuit model of the lead-acid storage battery charging and discharging system comprises a resistor R1, a resistor R2, a resistor Rt, a capacitor C1 and a capacitor C2; the resistor R1 is connected with the capacitor C1 in series to serve as a first branch circuit, the resistor R2 is connected with the capacitor C2 in series to serve as a second branch circuit, and the first branch circuit and the second branch circuit are connected in parallel and then connected with the resistor Rt in series.
Further, the conversion of the singular system into the conventional state space model expression specifically includes the following steps:
step S21: according to the grid rule of the equivalent circuit of the battery, the equivalent circuit voltage of the lead-acid storage battery is expressed as shown in formula (1):
Figure BDA0002699678420000021
in the formula, I (t), I1(t) and I2(t) are each a via resistance Rt、R1And R2Current of (V)c1(t) and Vc2(t) each represents a capacitance C1And C2Voltage of Vt(t) is the total voltage of the battery circuit;
the above conditions are rewritten as:
Figure BDA0002699678420000031
substituting equation (2) into equation (1) yields:
Figure BDA0002699678420000032
the current through the capacitor is proportional to the derivative of its terminal voltage:
Figure BDA0002699678420000033
combining the formulas (3) and (4), obtaining a singular system model of the lead-acid storage battery as follows:
Figure BDA0002699678420000034
definition of x (t) ═ VC1(t) VC2(t) Vt(t)]TAnd u (t) i (t), rewriting the system (5) as a state space equation, as follows:
Figure BDA0002699678420000035
where y (t) is the system output, x (t) is the state variable, and u (t) is the control input.
Figure BDA0002699678420000041
Step S22: identifying lead-acid storage battery model parameters; measuring the internal resistance R of the battery when the battery is connected to charge; let R be1And R2Is equivalent and represents 80% of the total resistance, then:
R1＝R2,R1＝0.8R,Rt＝0.6R, (8)
capacity C1Is based on the energy E stored in the batteryc1Calculated as V, the energyOCThe function at SOC 0% and 100% represents:
Figure BDA0002699678420000042
in the formula, Voc(SoC)Is the open circuit voltage, V, of the current SOCoc(0％SoC)Open circuit voltage at SOC minimum;
EC1＝3600×t×I(t)×VOC(100％SoC)×SoC (10)；
wherein t is the time of charging and discharging the battery, and can be obtained as follows:
Figure BDA0002699678420000043
thus, capacity C2The values of (A) are:
Figure BDA0002699678420000044
wherein τ is the capacitance C2The charge-discharge coefficient of (d);
step S23: a novel model transformation method is provided for converting a singular system into a conventional state space model expression, wherein the system is influenced by unknown input and is expressed as follows:
Figure BDA0002699678420000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000052
unknown input interference, F is the output perturbation matrix parameter,
Figure BDA0002699678420000053
is x (t) derivative, D is expressed as perturbation matrix parameter of the system;
defining:
GE+HC＝In3； (14)
J(F-CHF)＝HF； (15)
JCGD-MF＝-GD； (16)
wherein G, H, J, M is a parameter matrix, In3An identity matrix of third order;
according to the relationship in equation (14), the system can be rewritten as:
Figure BDA0002699678420000054
obtaining:
Figure BDA0002699678420000055
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000056
the derivatives of the system output and disturbance, respectively; further considering the relationship in equation (15), we obtain:
Figure BDA0002699678420000061
substituting equation (17) by equation (19) yields:
Figure BDA0002699678420000062
finally, according to equation (16), the system (20) is represented as:
Figure BDA0002699678420000063
wherein the content of the first and second substances,
Figure BDA0002699678420000064
further, in order to correctly estimate the state of charge SOC in the presence of interference, the conventional state space model is rewritten again as an expression of a singular system, taking into account the interference of the interior of the lead-acid battery system with the measured output voltage; the method for ensuring the correct estimation of the SOC of the lead-acid battery in the limited time by utilizing the finite time stability theory and the Lyapunov function method specifically comprises the following steps:
step S31: considering a singular system where both the state equation and the output equation are unknown inputs, define:
Figure BDA0002699678420000065
obtaining:
Figure BDA0002699678420000066
step S32: in the definition:
Figure BDA0002699678420000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000072
to represent
Figure BDA0002699678420000073
(ii) an estimate of (d);
the following finite time observer is proposed for the singular system in equation (24):
Figure BDA0002699678420000074
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000075
representing the observer gain to be designed;
Figure BDA0002699678420000076
for the positive gain factor to be determined,
Figure BDA0002699678420000077
is a vector of the auxiliary states which,
Figure BDA0002699678420000078
quilt
Figure BDA0002699678420000079
The selection is made to be non-singular,
Figure BDA00026996784200000710
the parameters of the auxiliary matrix are represented,
Figure BDA00026996784200000711
representing adjustable scalar coefficients, yields:
Figure BDA00026996784200000712
by considering equation (23) - (26), the error system is obtained as follows:
Figure BDA00026996784200000713
step S33: based on the error system, consider the following Lyapunov function:
Figure BDA00026996784200000714
in the formula (I), the compound is shown in the specification,
Figure BDA00026996784200000715
is a positive matrix;
by solving the time derivative of the calculation v (t), we obtain:
Figure BDA0002699678420000081
further, it is obtained from formula (29):
Figure BDA0002699678420000082
further solving, obtaining:
Figure BDA0002699678420000083
if a positive definite diagonal matrix P exists, Sym represents the sum of the matrix and the matrix transposition, lambdamin(P)、λmax(P) are the minimum and maximum eigenroots of the matrix P, respectively, such that the following conditions are true:
Figure BDA0002699678420000084
wherein
Figure BDA0002699678420000085
The error system of the SoC can be gradually stabilized for a finite time by the distributed discontinuous state feedback fuzzy controller, and the time T of the finite time gradual stabilization can be estimated by the following formula:
Figure BDA0002699678420000086
in the formula, x0Denotes the zero initial value of x (t);
the observer gain matrix is expressed as follows:
Figure BDA0002699678420000091
further, the method also includes step S34: estimated open circuit voltage
Figure BDA0002699678420000092
Expressed as:
Figure BDA0002699678420000093
wherein n is the number of cells in the battery, E0Is the no-load voltage of the battery, E1Is the ultimate discharge voltage of the battery;
Figure BDA0002699678420000094
terminal capacitor C1And C2The voltage of (d) is expressed as:
Figure BDA0002699678420000095
then, the SOC is calculated using the following equation:
Figure BDA0002699678420000096
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000097
represents Vc1Is estimated by the estimation of (a) a,
Figure BDA0002699678420000098
represents Vc2Is estimated.
Compared with the prior art, the invention has the following beneficial effects: compared with the scheme in the prior art, the method can quickly and correctly estimate the SoC under the condition that the system and the measured output voltage are interfered, so that the stable and reliable operation of the SoC is ensured, and the quick and accurate SoC estimation is realized.
Drawings
Fig. 1 is an equivalent circuit diagram of a lead-acid battery according to an embodiment of the present invention.
Fig. 2 is a system diagram of a lead-acid battery according to an embodiment of the present invention.
FIG. 3 is a flow chart of a method according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 3, the present embodiment provides a method for rapidly estimating the SOC of a lead-acid battery, which specifically includes the following steps:
building an equivalent circuit model of a lead-acid storage battery charging and discharging system under a singular system framework;
converting a singular system into a conventional state space model expression;
considering the interference between the interior of the lead-acid storage battery system and the measured output voltage, in order to correctly estimate the state of charge SOC under the interference condition, the conventional state space model is rewritten into the expression of a singular system; and the SOC of the lead-acid battery is correctly estimated within a limited time by using a finite time stability theory and a Lyapunov function method.
In the present embodiment, as shown in fig. 2, the lead-acid battery charging and discharging system includes an AC bus, a bidirectional DC/AC module, a lead-acid battery, and an SOC estimator; the lead-acid storage battery is connected to the AC bus through the bidirectional DC/AC module, and the SOC estimator is connected with the lead-acid storage battery and used for estimating the SOC of the lead-acid storage battery;
as shown in fig. 1, the equivalent circuit model of the lead-acid battery charging and discharging system comprises a resistor R1, a resistor R2, a resistor Rt, a capacitor C1 and a capacitor C2; the resistor R1 is connected with the capacitor C1 in series to serve as a first branch circuit, the resistor R2 is connected with the capacitor C2 in series to serve as a second branch circuit, and the first branch circuit and the second branch circuit are connected in parallel and then connected with the resistor Rt in series.
In this embodiment, the converting the singular system into the conventional state space model expression specifically includes the following steps:
step S21: according to the grid rule of the equivalent circuit of the battery, the equivalent circuit voltage of the lead-acid storage battery is expressed as shown in formula (1):
Figure BDA0002699678420000111
in the formula, I (t), I1(t) and I2(t) are each a via resistance Rt、R1And R2Current of (V)c1(t) and Vc2(t) each represents a capacitance C1And C2Voltage of Vt(t) is the total voltage of the battery circuit;
the above conditions are rewritten as:
Figure BDA0002699678420000112
substituting equation (2) into equation (1) yields:
Figure BDA0002699678420000113
the current through the capacitor is proportional to the derivative of its terminal voltage:
Figure BDA0002699678420000121
combining the formulas (3) and (4), obtaining a singular system model of the lead-acid storage battery as follows:
Figure BDA0002699678420000122
definition of x (t) ═ VC1(t) VC2(t) Vt(t)]TAnd u (t) i (t), rewriting the system (5) as a state space equation, as follows:
Figure BDA0002699678420000123
where y (t) is the system output, x (t) is the state variable, and u (t) is the control input.
Figure BDA0002699678420000124
Step S22: identifying lead-acid storage battery model parameters; measuring the internal resistance R of the battery when the battery is connected to charge; let R be1And R2Is equivalent and represents 80% of the total resistance, then:
R1＝R2,R1＝0.8R,Rt＝0.6R, (8)
capacity C1Is based on the energy E stored in the batteryc1Calculated as V, the energyOCThe function at SOC 0% and 100% represents:
Figure BDA0002699678420000131
in the formula, Voc(SoC)Is the open circuit voltage, V, of the current SOCoc(0％SoC)Open circuit voltage at SOC minimum;
EC1＝3600×t×I(t)×VOC(100％SoC)×SoC (10)；
wherein t is the time of charging and discharging the battery, and can be obtained as follows:
Figure BDA0002699678420000132
thus, capacity C2The values of (A) are:
Figure BDA0002699678420000133
wherein τ is the capacitance C2The charge-discharge coefficient of (d);
step S23: a novel model transformation method is provided for converting a singular system into a conventional state space model expression, wherein the system is influenced by unknown input and is expressed as follows:
Figure BDA0002699678420000134
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000135
unknown input interference, F is the output perturbation matrix parameter,
Figure BDA0002699678420000136
is x (t) derivative, D is expressed as perturbation matrix parameter of the system;
defining:
GE+HC＝In3； (14)
J(F-CHF)＝HF； (15)
JCGD-MF＝-GD； (16)
wherein G, H, J, M is a parameter matrix, In3An identity matrix of third order;
according to the relationship in equation (14), the system can be rewritten as:
Figure BDA0002699678420000141
obtaining:
Figure BDA0002699678420000142
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000143
the derivatives of the system output and disturbance, respectively; consider further thatThe relationship in equation (15) yields:
Figure BDA0002699678420000144
substituting equation (17) by equation (19) yields:
Figure BDA0002699678420000145
finally, according to equation (16), the system (20) is represented as:
Figure BDA0002699678420000146
wherein the content of the first and second substances,
Figure BDA0002699678420000151
in the present embodiment, in order to correctly estimate the state of charge SOC in the presence of interference, the conventional state space model is rewritten again as an expression of a singular system, taking into account the interference of the interior of the lead-acid battery system with the measured output voltage; the method for ensuring the correct estimation of the SOC of the lead-acid battery in the limited time by utilizing the finite time stability theory and the Lyapunov function method specifically comprises the following steps:
step S31: considering a singular system where both the state equation and the output equation are unknown inputs, define:
Figure BDA0002699678420000152
obtaining:
Figure BDA0002699678420000153
step S32: in the definition:
Figure BDA0002699678420000154
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000155
to represent
Figure BDA0002699678420000156
(ii) an estimate of (d);
the following finite time observer is proposed for the singular system in equation (24):
Figure BDA0002699678420000157
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000161
representing the observer gain to be designed;
Figure BDA0002699678420000162
for the positive gain factor to be determined,
Figure BDA0002699678420000163
is a vector of the auxiliary states which,
Figure BDA0002699678420000164
quilt
Figure BDA0002699678420000165
The selection is made to be non-singular,
Figure BDA0002699678420000166
the parameters of the auxiliary matrix are represented,
Figure BDA0002699678420000167
representing adjustable scalar coefficients, yields:
Figure BDA0002699678420000168
by considering equation (23) - (26), the error system is obtained as follows:
Figure BDA0002699678420000169
step S33: based on the error system, consider the following Lyapunov function:
Figure BDA00026996784200001610
in the formula (I), the compound is shown in the specification,
Figure BDA00026996784200001611
is a positive matrix;
by solving the time derivative of the calculation v (t), we obtain:
Figure BDA00026996784200001612
further, it is obtained from formula (29):
Figure BDA00026996784200001613
further solving, obtaining:
Figure BDA00026996784200001614
if a positive definite diagonal matrix P exists, Sym represents the sum of the matrix and the matrix transposition, lambdamin(P)、λmax(P) are the minimum and maximum eigenroots of the matrix P, respectively, such that the following conditions are true:
Figure BDA0002699678420000172
wherein
Figure BDA0002699678420000173
The error system of the SoC can be gradually stabilized for a finite time by the distributed discontinuous state feedback fuzzy controller, and the time T of the finite time gradual stabilization can be estimated by the following formula:
Figure BDA0002699678420000174
in the formula, x0Denotes the zero initial value of x (t);
the observer gain matrix is expressed as follows:
Figure BDA0002699678420000175
in this embodiment, the method further includes step S34: estimated open circuit voltage
Figure BDA0002699678420000176
Expressed as:
Figure BDA0002699678420000177
wherein n is the number of cells in the battery, E0Is the no-load voltage of the battery, E1Is the ultimate discharge voltage of the battery;
Figure BDA0002699678420000178
terminal capacitor C1And C2The voltage of (d) is expressed as:
Figure BDA0002699678420000179
then, the SOC is calculated using the following equation:
Figure BDA0002699678420000181
in the formula (I), the compound is shown in the specification,
Figure BDA0002699678420000182
represents Vc1Is estimated by the estimation of (a) a,
Figure BDA0002699678420000183
represents Vc2Is estimated.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (5)

1. A method for rapidly realizing lead-acid battery SOC estimation is characterized by comprising the following steps:
building an equivalent circuit model of a lead-acid storage battery charging and discharging system under a singular system framework;
converting a singular system into a conventional state space model expression;
considering the interference between the interior of the lead-acid storage battery system and the measured output voltage, in order to correctly estimate the state of charge SOC under the interference condition, the conventional state space model is rewritten into the expression of a singular system; and the SOC of the lead-acid battery is correctly estimated within a limited time by using a finite time stability theory and a Lyapunov function method.
2. The method for rapidly estimating the SOC of the lead-acid battery according to claim 1, wherein the lead-acid battery charging and discharging system comprises an AC bus, a bidirectional DC/AC module, the lead-acid battery and an SOC estimator; the lead-acid storage battery is connected to the AC bus through the bidirectional DC/AC module, and the SOC estimator is connected with the lead-acid storage battery and used for estimating the SOC of the lead-acid storage battery;
the equivalent circuit model of the lead-acid storage battery charging and discharging system comprises a resistor R1, a resistor R2, a resistor Rt, a capacitor C1 and a capacitor C2; the resistor R1 is connected with the capacitor C1 in series to serve as a first branch circuit, the resistor R2 is connected with the capacitor C2 in series to serve as a second branch circuit, and the first branch circuit and the second branch circuit are connected in parallel and then connected with the resistor Rt in series.
3. The method for rapidly estimating the SOC of the lead-acid battery according to claim 2, wherein the step of converting the singular system into the conventional state space model expression specifically comprises the following steps:
step S21: according to the grid rule of the equivalent circuit of the battery, the equivalent circuit voltage of the lead-acid storage battery is expressed as shown in formula (1):
Figure FDA0002699678410000011
in the formula, I (t), I1(t) and I2(t) are each a via resistance Rt、R1And R2Current of (V)c1(t) and Vc2(t) each represents a capacitance C1And C2Voltage of Vt(t) is the total voltage of the battery circuit;
the above conditions are rewritten as:
Figure FDA0002699678410000021
substituting equation (2) into equation (1) yields:
Figure FDA0002699678410000022
the current through the capacitor is proportional to the derivative of its terminal voltage:
Figure FDA0002699678410000023
combining the formulas (3) and (4), obtaining a singular system model of the lead-acid storage battery as follows:
Figure FDA0002699678410000024
definition of x (t) ═ VC1(t) VC2(t) Vt(t)]TAnd u (t) i (t), rewriting the system (5) as a state space equation, as follows:
Figure FDA0002699678410000025
where y (t) is the system output, x (t) is the state variable, and u (t) is the control input.
Figure FDA0002699678410000031
Step S22: identifying lead-acid storage battery model parameters; measuring the internal resistance R of the battery when the battery is connected to charge; let R be1And R2Is equivalent and represents 80% of the total resistance, then:
R1＝R2,R1＝0.8R,Rt＝0.6R, (8)
capacity C1Is based on the energy E stored in the batteryc1Calculated as V, the energyOCThe function at SOC 0% and 100% represents:
Figure FDA0002699678410000032
in the formula, Voc(SoC)Is the open circuit voltage, V, of the current SOCoc(0％SoC)Open circuit voltage at SOC minimum;
EC1＝3600×t×I(t)×VOC(100％SoC)×SoC (10)；
wherein t is the time of charging and discharging the battery, and can be obtained as follows:
Figure FDA0002699678410000033
thus, capacity C2The values of (A) are:
Figure FDA0002699678410000034
wherein τ is the capacitance C2The charge-discharge coefficient of (d);
step S23: a novel model transformation method is provided for converting a singular system into a conventional state space model expression, wherein the system is influenced by unknown input and is expressed as follows:
Figure FDA0002699678410000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002699678410000042
unknown input interference, F is the output perturbation matrix parameter,
Figure FDA0002699678410000043
is x (t) derivative, D is expressed as perturbation matrix parameter of the system;
defining:
GE+HC＝In3； (14)
J(F-CHF)＝HF； (15)
JCGD-MF＝-GD； (16)
wherein G, H, J, M is a parameter matrix, In3An identity matrix of third order;
according to the relationship in equation (14), the system can be rewritten as:
Figure FDA0002699678410000044
obtaining:
Figure FDA0002699678410000045
in the formula (I), the compound is shown in the specification,
Figure FDA0002699678410000046
the derivatives of the system output and disturbance, respectively; further considering the relationship in equation (15), we obtain:
Figure FDA0002699678410000051
substituting equation (17) by equation (19) yields:
Figure FDA0002699678410000052
finally, according to equation (16), the system (20) is represented as:
Figure FDA0002699678410000053
wherein the content of the first and second substances,
Figure FDA0002699678410000054
4. the method for rapidly estimating the SOC of the lead-acid battery according to claim 3, wherein the conventional state space model is rewritten into the expression of a singular system again in order to correctly estimate the SOC under the interference condition in consideration of the interference between the interior of the lead-acid battery system and the measured output voltage; the method for ensuring the correct estimation of the SOC of the lead-acid battery in the limited time by utilizing the finite time stability theory and the Lyapunov function method specifically comprises the following steps:
step S31: considering a singular system where both the state equation and the output equation are unknown inputs, define:
Figure FDA0002699678410000055
obtaining:
Figure FDA0002699678410000061
step S32: in the definition:
Figure FDA0002699678410000062
in the formula (I), the compound is shown in the specification,
Figure FDA0002699678410000063
to represent
Figure FDA0002699678410000064
(ii) an estimate of (d);
the following finite time observer is proposed for the singular system in equation (24):
Figure FDA0002699678410000065
in the formula (I), the compound is shown in the specification,
Figure FDA0002699678410000066
representing the observer gain to be designed;
Figure FDA0002699678410000067
for the positive gain factor to be determined, q ∈ {1,2,3},
Figure FDA0002699678410000068
is a vector of the auxiliary states which,
Figure FDA00026996784100000614
quilt
Figure FDA00026996784100000615
The selection is made to be non-singular,
Figure FDA00026996784100000616
the parameters of the auxiliary matrix are represented,
Figure FDA0002699678410000069
representing adjustable scalar coefficients, yields:
Figure FDA00026996784100000610
by considering equation (23) - (26), the error system is obtained as follows:
Figure FDA00026996784100000611
step S33: based on the error system, consider the following Lyapunov function:
Figure FDA00026996784100000612
in the formula (I), the compound is shown in the specification,
Figure FDA00026996784100000613
is a positive matrix;
by solving the time derivative of the calculation v (t), we obtain:
Figure FDA0002699678410000071
further, it is obtained from formula (29):
Figure FDA0002699678410000072
further solving, obtaining:
Figure FDA0002699678410000073
if a positive definite diagonal matrix P exists, Sym represents the sum of the matrix and the matrix transposition, lambdamin(P)、λmax(P) are the minimum and maximum eigenroots of the matrix P, respectively, such that the following conditions are true:
Figure FDA0002699678410000074
wherein
Figure FDA0002699678410000075
The error system of the SoC can be gradually stabilized for a finite time by the distributed discontinuous state feedback fuzzy controller, and the time T of the finite time gradual stabilization can be estimated by the following formula:
Figure FDA0002699678410000076
in the formula, x0Denotes the zero initial value of x (t);
the observer gain matrix is expressed as follows:
Figure FDA0002699678410000081
5. the method for rapidly estimating the SOC of the lead-acid battery according to claim 4, further comprising the step S34: estimated open circuit voltage
Figure FDA0002699678410000082
Expressed as:
Figure FDA0002699678410000083
wherein n is the number of cells in the battery, E0Is the no-load voltage of the battery, E1Is the ultimate discharge voltage of the battery;
Figure FDA0002699678410000084
terminal capacitor C1And C2The voltage of (d) is expressed as:
Figure FDA0002699678410000085
then, the SOC is calculated using the following equation:
Figure FDA0002699678410000086
in the formula (I), the compound is shown in the specification,
Figure FDA0002699678410000087
represents Vc1Is estimated by the estimation of (a) a,
Figure FDA0002699678410000088
represents Vc2Is estimated.
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