CN114740376A - On-line diagnosis method for battery state of charge - Google Patents

On-line diagnosis method for battery state of charge Download PDF

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CN114740376A
CN114740376A CN202210481839.6A CN202210481839A CN114740376A CN 114740376 A CN114740376 A CN 114740376A CN 202210481839 A CN202210481839 A CN 202210481839A CN 114740376 A CN114740376 A CN 114740376A
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CN114740376B (en
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刘爱华
宋欣民
王荣强
周建军
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Hangzhou Kegong Electronic Technology 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]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D21/00—Measuring or testing not otherwise provided for
    • G01D21/02—Measuring two or more variables by means not covered by a single other subclass
    • 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]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
    • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current 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]
    • G01R31/389—Measuring internal impedance, internal conductance or related variables
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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    • Y02T10/70—Energy storage systems for electromobility, e.g. batteries

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Abstract

The invention discloses a battery SOC (state of charge) online diagnosis method, which is characterized in that the SOC of a characteristic point in a battery voltage platform interval is acquired by using battery offline test data and battery voltage, current, temperature and SOC data acquired online by a BMS (battery management system) battery management system through methods of data standardization, plane curve comparison and the like, so that the online calibration of the SOC is realized, the calculation complexity is low, the dependence on the calculation power of a chip is reduced, and the accuracy of an SOC correction result is ensured while the calculation efficiency is considered.

Description

On-line diagnosis method for battery state of charge
Technical Field
The invention relates to the technical field of battery management cables, in particular to a battery state of charge online diagnosis method.
Background
State of charge (SOC) diagnostics in lithium ion battery pack management is one of the core technologies in the field. In the current commercial battery management system, a battery state of charge diagnosis method combining an open-circuit voltage method, an ampere-hour integral method and a characteristic interval correction method is generally applied. The method is simple in calculation, small in calculation amount and wide in application range, and becomes a basic method for diagnosing the state of charge of the battery. However, the open-circuit duration condition of the open-circuit voltage method is not easy to achieve, the ampere-hour integral method is greatly influenced by the accuracy of current collection of the current sensor, and the battery charge state needs to be calibrated by an interval correction method so as to meet the accuracy requirement of engineering application. The interval correction method can effectively calibrate the battery charge state only in two state intervals of the battery charge approaching full charge and the battery discharge approaching emptying, can cause the battery charge state to jump, and has low calibration precision.
In order to further improve the battery state-of-charge diagnosis precision, methods such as an experience model, a mechanism model, a neural network model and a data-driven filtering algorithm are widely researched and applied in academic circles and industrial circles at home and abroad. The empirical model and the mechanism model need to calculate the state of charge of the battery by using a clear mathematical analytic formula, and have no universality and unsatisfactory accuracy for batteries of different electrochemical systems. Data driving methods such as a neural network model and a filtering algorithm need a large amount of prior data for modeling or model training, the data processing process of battery charge state diagnosis is complex, the calculation amount is large, the requirement on the calculation capacity of a battery management system chip is high, and the method is difficult to popularize and use practically.
Disclosure of Invention
The invention provides an online diagnosis method for the state of charge of a battery, which ensures the accuracy of an SOC correction result and realizes the online diagnosis of the SOC while considering the calculation amount.
In order to achieve the purpose, the invention adopts the following technical scheme:
provided is a battery state of charge online diagnosis method, including:
step S1, acquiring first curve cluster data of voltage U and SOC at different temperatures T and different currents I for testing the battery in an off-line state;
step S2, marking each voltage U obtained in step S1Standardized processing to obtain the value falling into the numerical range [0, 1]Internal normalized voltage UsThen generate UsSecond curve cluster data with SOC;
step S3, drawing a curve (U) based on the second curve cluster data in the same plane rectangular coordinate systems～SOC)T，ISum curve (SOC-U)s)T，I；
Step S4, calculating the curve (U) in the same plane coordinate systems～SOC)T，IAnd the curve (SOC-U)s)T，IDistance d between symmetrical discrete points in (1)ijTo obtain a distance matrix { d }ij}1×nAnd i represents the curve (U)s～SOC)T，IThe ith said discrete point of (a); j represents the curve (SOC-U)s)T，IA j-th discrete point having a symmetrical relationship with the discrete point i, and n represents the curve (U)s～SOC)T，IThe number of discrete points having a symmetrical relationship;
step S5, calculating the distance matrix { d } in step S4ij}1×nEach of the distances dijAnd dijCorresponding SOC obtained in step S1 is a data point, and a curve (SOC-d) corresponding to temperature T and current I is drawnij)T，I；
Step S6, for the curves (SOC-d)ij)T，IPerforming polynomial fitting to obtain the curve (SOC-d)ij)T，ICorresponding trend lines are searched out, and all extreme points are found out from the trend lines and are marked as (SOC)m，dijm)I，2×p，SOCm、dijmRespectively representing a horizontal axis coordinate value and a vertical axis coordinate value of the mth extreme point on the trend line, wherein p represents the number of the extreme points on the trend line;
step S7, according to the (SOC) of each extreme pointm，dijm) Data pairs and corresponding voltages UsConstructing a set of SOC corrected feature space points, denoted as (U)s，m，SOCm，dijm)I，3×p，Us，mRepresents the m < th >The voltage U corresponding to the extreme points；
Step S8, obtaining battery voltage U (t), current I (t), temperature T (t) in real time at t time of charging or discharging the battery, calculating SOC (t), and calculating the distance d according to the calculation provided by steps S2-S3ijThe distance d (t) corresponding to the voltage U (t) under the current I (t) is calculated;
step S9, based on d (t-1) corresponding to the battery voltage U (t-1) at the time d (t) and t-1, and d (t-2) corresponding to the battery voltage U (t-2) at the time t-2, determining whether d (t) changes with time,
if yes, calculate d (t) and set { d }ijm}I，1×pEach of d inijmTo obtain a set { D }1×pAnd will { D }1×pMinimum value of dminCorresponding SOCminUpdating and correcting the SOC (t) as the calibration value of the SOC (t), the SOCmin∈(SOCm)I，1×p；
If not, the SOC (t) is not corrected.
Preferably, in step S2, each of the voltages U is normalized by the following formula (1):
Figure BDA0003627811790000031
in formula (1), Ucut，minRepresents a discharge lower limit voltage of the battery;
Ucut，maxrepresents a charging upper limit voltage of the battery.
Preferably, in step S4, the distance dijCalculated by the following formula (2):
Figure BDA0003627811790000032
in the formula (2), xiRepresents the curve (U)s～SOC)T，IThe coordinate value of the abscissa of the discrete point i in (1);
yjrepresents the curve (SOC-U)s)T，IAnd coordinate values of the ordinate of the discrete point j having a symmetrical relationship with the discrete point i.
Preferably, in step S6, the curves (SOC to d) are obtained by polynomial fitting using the following formula (3)ij)T，IThe corresponding trend line:
y＝k0+k1·x+k2·x2+k3·x3+k4·x4+k5·x5+k6·x6formula (3)
In the formula (3), y represents the distance dij(ii) a x represents SOC; k is a radical of0、k1、k2、k3、k4、k5、k6Representing the coefficients of the fitting equation.
Preferably, in step S6, the fitting formula coefficient k is estimated by iterative reweighted least squares of robust regression0、k1、k2、k3、k4、k5、k6The calculation steps are as follows:
step S61, establishing a minimized error function E, wherein the calculation method is shown in formula (4);
Figure BDA0003627811790000033
step S62, introducing distance weight wiSee formula (5);
Figure BDA0003627811790000041
step S63, for each coefficient k0、k1、k2、k3、k4、k5、k6Calculating a partial derivative, which is shown in a formula (6) to a formula (12);
Figure BDA0003627811790000042
Figure BDA0003627811790000043
Figure BDA0003627811790000044
Figure BDA0003627811790000045
Figure BDA0003627811790000046
Figure BDA0003627811790000047
Figure BDA0003627811790000048
step S64, transforming equations (6) to (12) into matrix form to obtain coefficient k0、k1、k2、k3、k4、k5、k6The calculation method is shown in formula (13);
Figure BDA0003627811790000049
preferably, in step S9, when d (t) > d (t-1) and d (t-1) ≦ d (t-2), or d (t) < d (t-1) and d (t-1) > d (t-2), it is determined that d (t) is changed with time.
Preferably, in step S9, d (t) and { d ] are calculated by the following formula (14)ijm}I,1×pEach of d inijmDistance D of (D):
D＝|d(t)-dijmi formula (14)
According to the method, the battery offline test data and the battery voltage, current, temperature and SOC data acquired online by the BMS battery management system are utilized, the state of charge of the characteristic point in the battery voltage platform interval is acquired by methods such as data standardization and plane curve comparison, the online calibration of the state of charge of the battery is realized, the calculation complexity is low, and the accuracy of the SOC correction result is ensured while the calculation efficiency is considered.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments of the present invention will be briefly described below. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
Fig. 1 is a diagram illustrating implementation steps of a battery state of charge online diagnosis method according to an embodiment of the present invention;
fig. 2 is a charging graph of the battery voltage U and the SOC acquired in step S1;
fig. 3 is a discharge graph of the battery voltage U and the SOC acquired in step S1;
FIG. 4 shows the voltage U normalized in step S2sA charge profile versus SOC;
FIG. 5 shows the voltage U normalized in step S2sDischarge profile versus SOC;
FIG. 6 is a schematic diagram of calculating distances between symmetrical discrete points in the charging curve shown in FIG. 4;
FIG. 7 is a schematic diagram of calculating distances between symmetrical discrete points in the discharge curve shown in FIG. 4;
fig. 8 is an exemplary diagram of the trend line fitted in step S5.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.
Wherein the showings are for the purpose of illustration only and are shown by way of illustration only and not in actual form, and are not to be construed as limiting the present patent; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "inner", "outer", etc. are used for indicating the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not indicated or implied that the referred device or element must have a specific orientation, be constructed in a specific orientation and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and are not to be construed as limitations of the present patent, and the specific meanings of the terms may be understood by those skilled in the art according to specific situations.
In the description of the present invention, unless otherwise explicitly specified or limited, the term "connected" or the like, if appearing to indicate a connection relationship between the components, is to be understood broadly, for example, as being fixed or detachable or integral; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or may be connected through one or more other components or may be in an interactive relationship with one another. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
An embodiment of the present invention provides an online battery state of charge diagnosis method, as shown in fig. 1, including:
step S1, acquiring first curve cluster data of voltage U and SOC at different temperatures T and different currents I for testing the battery in an offline state; first curve cluster data such as a battery voltage U versus SOC at 0.1C charge rate, or a battery voltage U versus SOC at 0.3C charge rate, for example, as shown in fig. 2 and 3;
step S2, normalizing each voltage U obtained in step S1 to obtain a value falling within the numerical range [0, 1]Internal normalized voltage UsThen generate UsSecond curve cluster data with SOC; corresponding to data points in a charging or discharging curve, for example as shown in fig. 4 or 5 (U)sSOC) data pair;
each voltage U is normalized by the following formula (1):
Figure BDA0003627811790000061
in formula (1), Ucut,minRepresents a discharge lower limit voltage of the battery;
Ucut,maxrepresents the upper limit charge voltage of the battery.
Step S3, in the rectangular coordinate system of the same plane (i.e. XY axis coordinate system), based on the second curve cluster data (i.e. multiple sets (U) under the same temperature T and the same current IsSOC) data pair) is plotted (U)s～SOC)T,I(denoted by reference numeral "100" in FIG. 4) and curves (SOC. about. U)s)T,I(indicated by reference numeral "200" in FIG. 4);
step S4, calculating a curve (U) in the same plane coordinate systems～SOC)T,ISum curve (SOC-U)s)T,IDistance d between symmetrical discrete points in (1)ijTo obtain a distance matrix { d }ij}1×nAnd i represents a curve (U)s～SOC)T,IThe ith discrete point in (a); j represents a curve (SOC-U)s)T，IThe j-th discrete point having a symmetrical relationship with the discrete point i, and n represents a curve (U)s～SOC)T，IThe number of discrete points having a symmetrical relationship; the symmetric relation between the discrete point i and the discrete point j refers to the X-axis coordinate value X of the discrete point iiY-axis coordinate value Y equal to discrete point jjAnd the Y-axis coordinate value Y of the discrete point iiX-axis coordinate value X equal to discrete point jj；
Calculating dijPlease refer to FIG. 6And FIG. 7, distance dijCalculated by the following formula (2):
Figure BDA0003627811790000071
in the formula (2), xiRepresents a curve (U)s～SOC)T，IThe coordinate value of the abscissa of the discrete point i;
yjexpression curve (SOC-U)s)T，IThe coordinate value of the ordinate of the discrete point j having a symmetrical relationship with the discrete point i.
Step S5, calculating the distance matrix { d } in step S4ij}1×nEach distance d ofijAnd dijCorresponding SOC obtained in step S1 is a data point, and a curve (SOC-d) corresponding to temperature T and current I is drawnij)T，IPlotted curve (SOC-d)ij)T，IFor example as indicated by reference numeral "300" in fig. 8.
Step S6, for curves (SOC-d)ij)T，IPerforming polynomial fitting to obtain a curve (SOC-d)ij)T，IThe corresponding trend line (denoted by reference numeral "400" in fig. 8) is followed by finding all extreme points from the trend line, and recording as (SOC)m，dijm)I，2×p，SOCm、dijmThe abscissa and ordinate coordinate values of the m-th extreme point on the trend line are respectively represented, and p represents the number of extreme points on the trend line, e.g., 3 extreme points d shown in FIG. 8ij1、dij2、dij3。
Preferably, the curve (SOC-d) is plotted by the following equation (3)ij)T，IPerforming polynomial fitting:
y＝k0+k1·x+k2·x2+k3·x3+k4·x4+k5·x5+k6·x6formula (3)
In the formula (3), y represents the distance dij(ii) a x represents SOC; k is a radical of0、k1、k2、k3、k4、k5、k6Representing the coefficients of the fitting equation.
More specifically, Iterative Reweighted Least Squares (IRLS) estimation of fitting formula coefficients k using robust regression0、k1、k2、k3、k4、k5、k6The calculation steps are as follows:
step S61, establishing a minimized error function E, wherein the calculation method is shown in a formula (4);
Figure BDA0003627811790000081
step S62, introducing distance weight wiSee formula (5);
Figure BDA0003627811790000082
step S63, for each coefficient k0、k1、k2、k3、k4、k5、k6Calculating the partial derivatives, which are shown in formula (6) to formula (12);
Figure BDA0003627811790000083
Figure BDA0003627811790000084
Figure BDA0003627811790000085
Figure BDA0003627811790000086
Figure BDA0003627811790000087
Figure BDA0003627811790000088
Figure BDA0003627811790000089
step S64, transforming equations (6) to (12) into matrix form to obtain coefficient k0、k1、k2、k3、k4、k5、k6The calculation method is shown in formula (13);
Figure BDA00036278117900000810
step S7, according to each extreme point dijm(SOC)m,dijm) Data pairs and corresponding voltages UsConstructing a set of SOC corrected feature space points, denoted as (U)s,m,SOCm,dijm)I,3×p,Us,mRepresenting the voltage U corresponding to the mth extremum points(ii) a Voltage U corresponding to mth extremum pointsObtained by the following steps:
according to the coordinate value of the longitudinal axis of the mth extreme point, i.e. dijmAnd formula (2) to obtain xiOr yjThen according to xiOr yjAnd voltage UsObtaining the voltage U corresponding to the mth extreme points。
Step S8, obtaining battery voltage U (t), current I (t), temperature T (t) in real time at t time of battery charging or discharging, calculating SOC (t) (such as calculating by conventional ampere-hour integration method), and calculating distance d provided by steps S2-S3ijThe method of (1), calculating the distance d (t) corresponding to the voltage U (t) at the temperature T (t) and the current I (t);
step S9, based on d (t-1) corresponding to battery voltage U (t-1) at time d (t) 1 and d (t-2) corresponding to battery voltage U (t-2) at time t-2, determining whether d (t) changes with time,
if so, d (t) and the set { d } are calculated by the following equation (14)ijm}I，1×pEach of d inijmTo obtain a set { D }1×pAnd will { D }1×pMinimum value of dminCorresponding SOCminUpdating and correcting the SOC (t) as the calibration value of the SOC (t), wherein the SOC (t)min∈(SOCm)I，1×p；
D＝|d(t)-dijmI formula (14)
The conditions for determining the transition of d (t) with time are: d (t) is more than d (t-1) and d (t-1) is less than or equal to d (t-2), or d (t) is less than d (t-1) and d (t-1) is more than or equal to d (t-2).
If not, the SOC (t) is not corrected.
In summary, the invention obtains the state of charge of the characteristic point in the battery voltage platform interval by using the battery offline test data and the battery voltage, current, temperature and SOC data acquired online by the BMS battery management system through methods of data standardization, plane curve comparison and the like, realizes online calibration of the state of charge of the battery, has low calculation complexity, and ensures the accuracy of the SOC correction result while considering the calculation efficiency.
It is to be understood that the above-described embodiments are merely preferred embodiments of the invention and that the technical principles herein may be applied. It will be understood by those skilled in the art that various modifications, equivalents, changes, and the like can be made to the present invention. However, such variations are within the scope of the invention as long as they do not depart from the spirit of the invention. In addition, certain terms used in the specification and claims of the present application are not limiting, but are used merely for convenience of description.

Claims (7)

1. A method for online diagnosis of battery state of charge, comprising:
step S1, acquiring first curve cluster data of voltage U and SOC at different temperatures T and different currents I for testing the battery in an off-line state;
step S2, normalizing each of the voltages U obtained in step S1 to obtain values falling within a numerical range [0, 1 ]]Internal normalized voltage UsThen generate UsSecond curve cluster data with SOC;
step S3, drawing a curve (U) based on the second curve cluster data in the same plane rectangular coordinate systems～SOC)T，ISum curve (SOC-U)s)T，I；
Step S4, calculating the curve (U) in the same plane coordinate systems～SOC)T，IAnd the curve (SOC-U)s)T，IDistance d between symmetrical discrete points in (1)ijTo obtain a distance matrix { d }ij}1×nI represents the curve (U)s～SOC)T，IThe ith said discrete point in (a); j represents the curve (SOC-U)s)T，IA j-th discrete point having a symmetrical relationship with the discrete point i, and n represents the curve (U)s～SOC)T，IThe number of discrete points having a symmetrical relationship;
step S5, calculating the distance matrix { d } in step S4ij}1×nEach of the distances dijAnd dijCorresponding SOC obtained in step S1 is a data point, and a curve (SOC-d) corresponding to temperature T and current I is plottedij)T，I；
Step S6, for the curves (SOC-d)ij)T，IPerforming polynomial fitting to obtain the curve (SOC-d)ij)T，ICorresponding trend lines are searched out, and all extreme points are found out from the trend lines and are marked as (SOC)m，dijm)I，2×p，SOCm、dijmRespectively representing the coordinate value of the horizontal axis and the coordinate value of the vertical axis of the mth extreme point on the trend line, wherein p represents the number of the extreme points on the trend line;
step S7, according to the (SOC) of each extreme pointm，dijm) Data pairs and corresponding voltages UsConstructing a set of SOC corrected feature space points, denoted as (U)s，m，SOCm，dijm)I，3×p，Us，mRepresents the voltage U corresponding to the mth extreme points；
Step S8, obtaining battery voltage U (t), current I (t), temperature T (t) in real time at t time of charging or discharging the battery, calculating SOC (t), and calculating the distance d according to the calculation provided by steps S2-S3ijThe distance d (t) corresponding to the voltage U (t) under the current I (t) is calculated;
step S9, based on d (t-1) corresponding to battery voltage U (t-1) at time d (t) 1 and d (t-2) corresponding to battery voltage U (t-2) at time t-2, determining whether d (t) changes with time,
if yes, d (t) and set { d { t } are calculatedijm}I，1×pEach of d inijmTo obtain a set { D }1×pAnd will { D }1×pMinimum value of dminCorresponding SOCminUpdating and correcting the SOC (t) as the calibration value of the SOC (t), the SOCmin∈(SOCm)I，1×p；
If not, the SOC (t) is not corrected.
2. The online battery state of charge diagnosis method according to claim 1, wherein in step S2, each of the voltages U is normalized by the following equation (1):
Figure FDA0003627811780000021
in formula (1), Ucut，minRepresents a discharge lower limit voltage of the battery;
Ucut，maxrepresents a charging upper limit voltage of the battery.
3. The method according to claim 1, wherein in step S4, the distance d is set toijCalculated by the following formula (2):
Figure FDA0003627811780000022
in the formula (2), xiRepresents the curve (U)s～SOC)T，IThe coordinate value of the abscissa of the discrete point i in (1);
yjrepresents the curve (SOC-U)s)T，IAnd coordinate values of the ordinate of the discrete point j having a symmetrical relationship with the discrete point i.
4. The method according to claim 1, wherein in step S6, the curve (SOC-dij) is obtained by polynomial fitting according to the following equation (3)T，IThe corresponding trend line:
y＝k0+k1·x+k2·x2+k3·x3+k4·x4+k5·x5+k6·x6formula (3)
In the formula (3), y represents the distance dij(ii) a x represents SOC; k is a radical of formula0、k1、k2、k3、k4、k5、k6Representing the coefficients of the fitting equation.
5. The method according to claim 4, wherein in step S6, the coefficient k of the fitting formula is estimated by using an iterative reweighted least squares method of robust regression0、k1、k2、k3、k4、k5、k6The calculation steps are as follows:
step S61, establishing a minimized error function E, wherein the calculation method is shown in formula (4);
Figure FDA0003627811780000031
step S62, introduce the distance weight wiSee formula (5);
Figure FDA0003627811780000032
step S63, for each coefficient k0、k1、k2、k3、k4、k5、k6Calculating a partial derivative, which is shown in a formula (6) to a formula (12);
Figure FDA0003627811780000033
Figure FDA0003627811780000034
Figure FDA0003627811780000035
Figure FDA0003627811780000036
Figure FDA0003627811780000037
Figure FDA0003627811780000038
Figure FDA0003627811780000039
in step S64, the equations (6) to (12) are converted into a matrix form to obtain the coefficient k0、k1、k2、k3、k4、k5、k6The calculation method is shown in formula (13);
Figure FDA00036278117800000310
6. the method according to claim 1, wherein in step S9, when d (t) > d (t-1) and d (t-1) ≦ d (t-2), or d (t) < d (t-1) and d (t-1) ≧ d (t-2), d (t) is determined to transition with time.
7. The method according to claim 1, wherein in step S9, d (t) and { d } are calculated by the following equation (14)ijm}I，1×pEach of d inijmDistance D of (D):
D＝|d(t)-dijmequation (14).
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