CN110716146A - Estimation method of power battery open circuit voltage - Google Patents

Estimation method of power battery open circuit voltage Download PDF

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CN110716146A
CN110716146A CN201910941317.8A CN201910941317A CN110716146A CN 110716146 A CN110716146 A CN 110716146A CN 201910941317 A CN201910941317 A CN 201910941317A CN 110716146 A CN110716146 A CN 110716146A
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voltage
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terminal voltage
circuit voltage
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徐蒙恩
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Sophisticated Electric Polytron Technologies Inc
Jing Jin Electric Technologies Beijing Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/3644—Constructional arrangements
    • G01R31/3648—Constructional arrangements comprising digital calculation means, e.g. for performing an algorithm
    • 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

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Abstract

The application discloses an estimation method of open circuit voltage, which comprises the following steps: firstly, establishing a second-order RC equivalent circuit model; secondly, performing a pulse discharge experiment to obtain terminal voltage-time data which is kept stand in a short time; and thirdly, constructing a terminal voltage error square sum model, and calculating an extreme value of the terminal voltage error square sum model so as to estimate the open-circuit voltage. The method can estimate and obtain accurate open-circuit voltage in a short time, correct the initial value of the State of Charge (SOC) of the battery in the ampere-hour integration method more frequently, make up for the defect that the accumulated error of the ampere-hour integration method increases along with the time, and improve the robustness of the SOC estimation algorithm.

Description

Estimation method of power battery open circuit voltage
Technical Field
The application relates to the technical field of electric automobiles, in particular to a method for estimating open-circuit voltage of a power battery.
Background
The State of charge (SOC) estimation is the most basic and important part in a battery management system, and the accurate SOC estimation not only can accurately monitor the State of the battery, optimize power distribution, prolong the endurance mileage of single full charge to a certain extent, but also can prevent the battery from overcharging, overdischarging, firing and even explosion. However, the SOC of the power battery cannot be directly measured by an instrument, and can only be indirectly obtained through current and voltage data, which brings certain difficulty to accurate estimation of the SOC.
In the current research, there are the following methods for estimating the SOC of the power battery. Closed-loop estimation algorithms, such as kalman filter algorithms and non-linear observers. The closed-loop estimation algorithm can improve the estimation accuracy of the remaining power to a certain extent, but the method is complex, and the calculation amount is increased when estimating the SOC, which poses a challenge to the limited calculation capacity of the battery management system. However, the neural network method requires a large amount of data to learn, and the quality of the estimation result is usually dependent on the selected data and is generally used less frequently. And finally, estimating the SOC of the power battery by combining the open-circuit voltage with an ampere-hour method, wherein the method is simple and convenient to operate and has small calculated amount. After the battery is kept still for a long time (2 hours), the electrochemical reaction in the battery reaches an equilibrium state, the terminal voltage of the battery is equivalent to an open-circuit voltage at the moment, the SOC at the current moment is obtained by combining the relation between the open-circuit voltage and the SOC, and finally the SOC at other moments is obtained by using an ampere-hour integration method. The integration method is considered to be relatively accurate in a short time ampere-hour, but as the estimation time increases, the SOC integration error increases due to a sampling error of the current, so that it is necessary to frequently use the open circuit voltage method to correct the initial value of the SOC. However, the battery needs to be left standing for a long time to correct the initial SOC, which is often difficult to satisfy during actual driving of the electric vehicle, and especially for a vehicle requiring long-term operation, calibration of the initial SOC using an open-circuit voltage is less likely to be triggered.
Disclosure of Invention
In view of the above, the present invention proposes a method for estimating the open-circuit voltage of a power battery, so as to solve or at least partially solve the above problems.
In order to achieve the technical purpose, the technical scheme of the invention is realized as follows:
the invention provides a method for estimating open-circuit voltage of a power battery, which comprises the following steps:
step 1, establishing a second-order RC equivalent circuit model;
step 2, performing a pulse discharge experiment to obtain terminal voltage-time data which is stood in a short time;
and 3, constructing a terminal voltage error square sum model, and calculating an extreme value of the terminal voltage error square sum model so as to estimate the open-circuit voltage.
Further, the establishing a second-order RC equivalent circuit model includes:
will resistance R0、R1、R2Are sequentially connected in series with a battery pack UOCAnd the capacitor C is connected to1And a resistor R1Parallel connection, a capacitor C2And a resistor R2Parallel connection;
the state equation is as follows:
an output equation:
UT＝UOC(SOC)-R0IT-U1-U2(2)
in formulae (1) and (2): qnIs the current maximum available capacity, U, of the batteryOC(SOC) is the present open circuit voltage as a function of SOC, ITIs the total current of the battery pack, UTIs the terminal voltage of the battery, R0Is the ohmic internal resistance, U, of the battery1And U2Are respectively a capacitor C1And C2The voltage across;
based on the superposition principle, the polarization voltage U is obtained1And U2：
Figure BDA0002222957320000031
Figure BDA0002222957320000032
In formulae (3) and (4): t is time, U1(t) is the capacitance C at time t1Polarization voltage at both ends, U1(0) Is at the beginningEtching capacitor C1Polarization voltage at both ends, U2(t) is the capacitance C at time t2Polarization voltage at both ends, U2(0) Is the initial moment capacitance C2Polarization voltage across, ITIs the total current, τ, of the battery pack1Is a capacitor C1And a resistor R1Product of, τ2Is a capacitor C2And a resistor R2The product of (a);
when the current is set to 0 from the time t is 0, the polarization voltage U at the time t is obtained1And U2Can be expressed as:
Figure BDA0002222957320000034
the terminal voltage U of the batteryT(t) can be expressed as:
Figure BDA0002222957320000035
equation (7) can be expressed as:
f(a,b,c)＝ax+by+c (8)
wherein f (a, b, c) is UT(t)，
Figure BDA0002222957320000036
a＝U1(0)，b＝U2(0)，c＝UOC(SOC)。
Further, the values of x and y can be obtained from the result of the pulse measurement.
Further, the estimating the open-circuit voltage by using an off-line least square method includes:
step 301, building a terminal voltage error sum of squares model:
Figure BDA0002222957320000037
in formula (9): rs is terminal voltageSum of squares of errors, ziIs the measured terminal voltage value at time i, xiIs the value of x at time i, yiIs the value at time i, y;
step 302, solving the terminal voltage error square sum model extreme value:
performing first-order partial derivation on a, b and c in the terminal voltage error square sum model;
Figure BDA0002222957320000038
let the above first partial derivative equal zero, then:
Figure BDA0002222957320000041
order to
Figure BDA0002222957320000042
Figure BDA0002222957320000043
Equation (11) can be simplified as:
Figure BDA0002222957320000044
suppose in (a)0,b0,c0) In this regard, equation (12) holds;
performing a, b and c second-order partial derivative in the terminal voltage error square sum model;
Figure BDA0002222957320000045
from equation (13), it can be seen that the second partial derivatives are all greater than zero, again because the rss is at (a)0,b0,c0) The first partial derivative of the point for a, b, c is 0, then the rss is at (a)0,b0,c0) The point is the minimum value.
Step 303, estimating the open circuit voltage:
taking the minimum value in the rssC of (1)0The open circuit voltage is as follows:
Figure BDA0002222957320000046
namely, the value of the open circuit voltage is obtained.
The invention has the beneficial effects that:
the method is based on a second-order RC equivalent circuit model, utilizes terminal voltage-time data of a short standing time and combines a least square method, and can estimate and obtain accurate open-circuit voltage in a short time.
The foregoing description is only an overview of the technical solutions of the present application, and the present application can be implemented according to the content of the description in order to make the technical means of the present application more clearly understood, and the following detailed description of the present application is given in order to make the above and other objects, features, and advantages of the present application more clearly understandable.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the application. In the drawings:
FIG. 1 illustrates a system block diagram of the present invention providing an open circuit voltage estimation method;
FIG. 2 is a schematic diagram of a second order RC equivalent circuit model according to the present invention;
fig. 3 shows a graph of terminal voltage versus time data over a period of standing in one embodiment of the invention;
FIG. 4 illustrates a graph comparing the estimated open circuit voltage and the true open circuit voltage using the method in one embodiment of the present invention;
FIG. 5 shows an error plot of the open circuit voltage estimated using this method in one embodiment of the present invention;
FIG. 6 shows an enlarged view of the open circuit voltage error estimated using this method in one embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The embodiment of the invention discloses a method for estimating open-circuit voltage of a power battery, which comprises the following steps:
step 1, establishing a second-order RC equivalent circuit model;
step 2, performing a pulse discharge experiment to obtain terminal voltage-time data which is stood in a short time;
and 3, constructing a terminal voltage error square sum model, and calculating an extreme value of the terminal voltage error square sum model so as to estimate the open-circuit voltage.
As shown in fig. 1, in the invention, a second-order RC equivalent circuit model can well describe the dynamic characteristics of a lithium battery, model parameters are identified by using an off-line parameter identification method based on the second-order RC equivalent circuit model, and a terminal voltage equation expression is obtained according to the established model; and then, fitting the open-circuit voltage by using terminal voltage-time data of a period of time after the standing stage, so that accurate open-circuit voltage can be estimated in a short time. As can be seen from fig. 3, after the battery is left standing for a long time, the terminal voltage tends to be stable, and the terminal voltage at this time can be equivalent to an open-circuit voltage. As can be seen from fig. 4, 5, and 6, with the present invention for estimating the open circuit voltage, the estimation is achieved in a short time, and the estimated value and the true value are substantially identical.
In one embodiment, establishing the second order RC equivalent circuit model comprises:
as shown in fig. 2, the resistor R is connected to0、R1、R2Are sequentially connected in series with a battery pack UOCAnd the capacitor C is connected to1And a resistor R1Parallel connection, a capacitor C2And a resistor R2Parallel connection;
the state equation is as follows:
Figure BDA0002222957320000061
an output equation:
UT＝UOC(SOC)-R0IT-U1-U2(2)
in formulae (1) and (2): qnIs the current maximum available capacity, U, of the batteryOC(SOC) is the present open circuit voltage as a function of SOC, ITIs the total current of the battery pack, UTIs the terminal voltage of the battery, R0Is the ohmic internal resistance, U, of the battery1And U2Are respectively a capacitor C1And C2The voltage across;
based on the superposition principle, the polarization voltage U is obtained1And U2：
Figure BDA0002222957320000062
Figure BDA0002222957320000063
In formulae (3) and (4): t is time, U1(t) is the capacitance C at time t1Polarization voltage at both ends, U1(0) Is the initial moment capacitance C1Polarization voltage at both ends, U2(t) is the capacitance C at time t2Polarization voltage at both ends, U2(0) Is the initial moment capacitance C2Polarization voltage across, ITIs the total current, τ, of the battery pack1Is a capacitor C1And a resistor R1Product of, τ2Is a capacitor C2And a resistor R2The product of (a);
when the current is set to 0 from the time t is 0, the polarization voltage U at the time t is obtained1And U2Can be expressed as:
Figure BDA0002222957320000071
Figure BDA0002222957320000072
the terminal voltage U of the batteryT(t) can be expressed as:
Figure BDA0002222957320000073
equation (7) can be expressed as:
f(a,b,c)＝ax+by+c (8)
wherein f (a, b, c) is UT(t)，
Figure BDA0002222957320000074
a＝U1(0)，b＝U2(0)，c＝UOC(SOC)。
In one embodiment, each discrete x is calculated based on terminal voltage-time datai、yiThe value is obtained.
In a preferred embodiment, estimating the open circuit voltage using the terminal voltage-time data standing for a short time includes:
step 301, building a terminal voltage error sum of squares model:
Figure BDA0002222957320000075
in formula (9): rss is the sum of squared errors of terminal voltages, ziIs the measured terminal voltage value at time i, xiIs the value of x at time i, yiIs the value at time i, y;
step 302, solving a terminal voltage error square sum model extreme value:
a, b and c first-order partial derivatives in the end-to-end voltage error square sum model;
Figure BDA0002222957320000076
let the above first partial derivative equal zero, then:
Figure BDA0002222957320000077
order to
Figure BDA0002222957320000078
Figure BDA0002222957320000081
Equation (11) can be simplified as:
Figure BDA0002222957320000082
suppose in (a)0,b0,c0) In this regard, equation (12) holds;
second-order partial derivatives of a, b and c in the end-to-end voltage error square sum model;
Figure BDA0002222957320000083
from equation (13), the second partial derivatives are all greater than zero, again due to rss being in (a)0,b0,c0) The first partial derivative of the point for a, b, c is 0, then rss is at (a)0,b0,c0) The point is the minimum value.
Step 303, estimating open circuit voltage:
c when rss takes a minimum0For open circuit voltage, there are:
Figure BDA0002222957320000084
substituting the terminal voltage-time data which are kept stand in a short time to calculate the value of the open-circuit voltage.
In summary, the present invention discloses a method for estimating an open circuit voltage, the method comprising: firstly, establishing a second-order RC equivalent circuit model; secondly, performing a pulse discharge experiment to obtain terminal voltage-time data which is kept stand in a short time; and thirdly, constructing a terminal voltage error square sum model, and calculating an extreme value of the terminal voltage error square sum model so as to estimate the open-circuit voltage. The method can estimate and obtain accurate open-circuit voltage in a short time, correct the initial value of the SOC in the ampere-hour integration method more frequently, make up for the defect that the accumulated error of the ampere-hour integration method increases along with the time, and improve the robustness of the SOC estimation algorithm.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes, substitutions or improvements within the technical scope of the present invention, and all such changes, substitutions or improvements are included in the scope of the present invention.
In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the application may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

Claims (4)

1. A method for estimating open-circuit voltage of a power battery is characterized by comprising the following steps:
step 1, establishing a second-order RC equivalent circuit model;
step 2, performing a pulse discharge experiment to obtain terminal voltage-time data which is stood in a short time;
and 3, constructing a terminal voltage error square sum model, and calculating an extreme value of the terminal voltage error square sum model so as to estimate the open-circuit voltage.
2. The method for estimating the open-circuit voltage of the power battery according to claim 1, wherein the establishing of the second-order RC equivalent circuit model comprises:
will resistance R0、R1、R2Are sequentially connected in series with a battery pack UOCAnd the capacitor C is connected to1And a resistor R1Parallel connection, a capacitor C2And a resistor R2Parallel connection;
the state equation is as follows:
Figure FDA0002222957310000011
an output equation:
UT＝UOC(SOC)-R0IT-U1-U2(2)
in formulae (1) and (2): qnIs the current maximum available capacity, U, of the batteryOC(SOC) is the present open circuit voltage as a function of SOC, ITIs the total current of the battery pack, UTIs the terminal voltage of the battery, R0Is the ohmic internal resistance, U, of the battery1And U2Are respectively a capacitor C1And C2The voltage across;
based on the superposition principle, the polarization voltage U is obtained1And U2：
Figure FDA0002222957310000013
In formulae (3) and (4): t is time, U1(t) is the capacitance C at time t1Polarization voltage at both ends, U1(0) Is the initial moment capacitance C1Polarization voltage at both ends, U2(t) is the capacitance C at time t2Polarization voltage at both ends, U2(0) Is the initial moment capacitance C2Polarization voltage across, ITIs the total current, τ, of the battery pack1Is a capacitor C1And a resistor R1Product of, τ2Is a capacitor C2And a resistor R2The product of (a);
when the current is set to 0 from the time t is 0, the polarization voltage U at the time t is obtained1And U2Can be expressed as:
Figure FDA0002222957310000014
Figure FDA0002222957310000021
the terminal voltage U of the batteryT(t) can be expressed as:
Figure FDA0002222957310000022
equation (7) can be expressed as:
f(a,b,c)＝ax+by+c (8)
wherein f (a, b, c) is UT(t)，a＝U1(0)，b＝U2(0)，c＝UOC(SOC)。
3. The method for estimating the open circuit voltage of the power battery according to claim 2, wherein the step 2 further comprises:
calculating discrete x's based on said terminal voltage-time datai、yiThe value is obtained.
4. The method for estimating the open circuit voltage of the power battery according to claim 3, wherein the estimating the open circuit voltage comprises:
step 301, building a terminal voltage error sum of squares model:
Figure FDA0002222957310000024
in formula (9): rss is the sum of squared errors of terminal voltages, ziIs the measured terminal voltage value at time i, xiIs the value of x at time i, yiIs the value at time i, y;
step 302, solving the terminal voltage error square sum model extreme value:
performing first-order partial derivation on a, b and c in the terminal voltage error square sum model;
Figure FDA0002222957310000025
let the above first partial derivative equal zero, then:
order to
Figure FDA0002222957310000027
Figure FDA0002222957310000028
Equation (11) can be simplified as:
Figure FDA0002222957310000031
suppose in (a)0,b0,c0) In this regard, equation (12) holds;
performing a, b and c second-order partial derivative in the terminal voltage error square sum model;
from equation (13), it can be seen that the second partial derivatives are all greater than zero, again because the rss is at (a)0,b0,c0) The first partial derivative of the point for a, b, c is 0, then the rss is at (a)0,b0,c0) The point is the minimum value.
Step 303, estimating the open circuit voltage:
c when the rss takes a minimum0The open circuit voltage is as follows:
Figure FDA0002222957310000033
namely, the value of the open circuit voltage is obtained.
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