CN113219342A - Method and system for estimating battery SOC (state of charge) by using dimension reduction gas-liquid dynamic battery model - Google Patents

Method and system for estimating battery SOC (state of charge) by using dimension reduction gas-liquid dynamic battery model Download PDF

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CN113219342A
CN113219342A CN202110582487.9A CN202110582487A CN113219342A CN 113219342 A CN113219342 A CN 113219342A CN 202110582487 A CN202110582487 A CN 202110582487A CN 113219342 A CN113219342 A CN 113219342A
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soc
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CN113219342B (en
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陈彪
江浩斌
孙化阳
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Jiangsu 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]
    • G01R31/367—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
    • 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
    • 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]
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    • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements

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Abstract

The invention provides a method and a system for estimating the SOC of a battery by using a dimension-reducing gas-liquid dynamic battery model, which comprises the following steps: estimating the average temperature inside the battery so that the average temperature inside the battery is consistent with the definition of the average temperature in the gas-liquid dynamic battery model; reducing the dimension of the gas-liquid dynamic battery model, and reducing the two-dimensional gas-liquid dynamic battery model to one dimension; the one-dimensional gas-liquid dynamic battery model is coupled with the EKF algorithm, so that the calculated amount is reduced, and the robustness is improved; and verifying the SOC estimation precision of the battery. The jacobian matrix is not easy to generate ill-condition during one-dimensional data operation, and the robustness of the algorithm is obviously improved, so that the variance Q of the state equation and the equation R of the observation equation can be set to be larger values during the initialization of the algorithm so as to improve the anti-interference capability and the convergence speed of the algorithm, and the method has obvious precision advantage compared with the same type of technology.

Description

Method and system for estimating battery SOC (state of charge) by using dimension reduction gas-liquid dynamic battery model
Technical Field
The invention relates to the field of battery management systems, in particular to a method and a system for estimating the SOC of a battery by using a dimension reduction gas-liquid dynamic battery model, and particularly relates to an SOC online estimation technology of a lithium ion power battery of an electric vehicle.
Background
In the twenty-first century, human beings have made unprecedented breakthroughs in the fields of science and technology, but face the problems of energy shortage and increasingly serious environmental pollution. The transportation industry accounts for a large proportion of the whole fossil energy consumption, the lithium ion battery technology is continuously broken through, lithium ion battery products are mature day by day, electric energy can be generated by solar energy, wind energy, hydraulic power and other clean modes, the transmission cost is low, the lithium ion battery has wide application in the aspects of social production and life, most countries in the world successively make policies for developing new energy automobiles, and the new energy automobile industry is greatly supported. At present, the electric automobile accounts for more than eight percent of the whole new energy automobile, and the industry generally considers that the electromotion is one of the final development forms of the automobile. A Battery Management System (BMS) is an indispensable component of an electric vehicle and is also a core problem and a difficult problem in the current research field of electric vehicles. The main functions of the BMS include battery data acquisition and detection, battery state estimation, online fault diagnosis and early warning, battery thermal management, etc., where real-time estimation of state of charge (SOC) is one of the core issues of the BMS.
The SOC of the battery cell reflects the remaining capacity of the battery, and the SOC of the entire battery pack reflects the remaining mileage of the electric vehicle. The accurate SOC can obviously improve the management efficiency and the use safety of the battery, reduce the power consumption of hundreds of kilometers, prolong the service life of the battery and further reduce the comprehensive use cost of the electric automobile. At present, an observer method with a feedback mechanism coupled with a battery mechanism model is a research hotspot of a battery SOC estimation technology, the battery mechanism model usually selected comprises an electrochemical model, an equivalent circuit model and a pneumatic and hydraulic mechanical battery model, and an observer algorithm for designing the feedback mechanism comprises an Extended Kalman Filter (EKF) algorithm, a particle filter algorithm, a synovial membrane algorithm and the like. However, in the research process, the battery model is usually multidimensional (larger than one dimension) and the established SOC estimation method is also multidimensional, so that the estimation method is very complex and difficult to apply in a vehicle-mounted embedded system, and finally, a large number of SOC estimation methods are stopped from theoretical research.
Disclosure of Invention
Aiming at the technical problem, the invention provides an SOC estimation method and system based on a corrected gas-liquid dynamic battery model. The method estimates the average temperature inside the battery through the surface temperature of the battery, and improves the modeling precision of the gas-liquid dynamic battery model; the gas-liquid dynamic battery model is simplified into a one-dimensional state model, and a one-dimensional extended Kalman filter EKF coupled gas-liquid dynamic battery model SOC estimation method with a feedback mechanism is designed.
The invention is realized by the following technical scheme: a method for estimating the SOC of a battery by using a dimension-reduced gas-liquid dynamic battery model comprises the following steps:
step S1, estimating the internal average temperature of the battery: estimating the average temperature inside the battery through the surface temperature of the battery, so that the average temperature inside the battery is consistent with the average temperature inside the gas-liquid dynamic battery model;
step S2: dimension reduction gas-liquid dynamic battery model: reducing the two-dimensional gas-liquid dynamic battery model to a one-dimensional gas-liquid dynamic battery model;
step S3: the one-dimensional gas-liquid dynamic battery model coupling EKF algorithm: coupling the one-dimensional gas-liquid dynamic battery model with the one-dimensional EKF, and inputting the average temperature in the battery obtained in the step S1 into the EKF algorithm coupled with the one-dimensional gas-liquid dynamic battery model to obtain the SOC estimated value of the battery;
step S4: and verifying the SOC estimation precision of the battery.
In the foregoing solution, the step S1 of estimating the average temperature inside the battery includes the following steps:
the method comprises the steps of establishing a battery temperature model, and estimating the average temperature of the battery by adopting an assumed battery temperature model, wherein the first method adopts a temperature gradient calculation method when two or more temperature acquisition points are installed on the surface of the battery, and the second method adopts a Bernadi heat generation model calculation method when only one temperature acquisition point is installed on the surface of the battery.
In the above solution, the first method for calculating a temperature gradient when two or more temperature collection points are installed on a surface of a battery includes the following steps:
constructed at length and height of batteryA temperature sensor is arranged at the center of the surface and one or more temperature sensors are arranged at other positions of the surface, and the temperature sensor at the center of the battery collects the temperature as the highest central temperature T0The temperature collected by the temperature sensors at other positions is T1,T2,T3…Tn，n≥2,n∈N+The distances from the temperature sensors at other positions to the sensor at the central position are respectively d1,d2,d3…dn，n≥2,n∈N+And the battery temperature gradient GradT is obtained by calculating the formula I:
Figure BDA0003086550060000021
average temperature T of batteryaverCalculated by formula two:
Figure BDA0003086550060000022
wherein r is the pole diameter, theta is the pole angle, V is the cell volume, and b is the cell thickness.
In the foregoing solution, the second calculation method for a Bernadi heat generation model when only one temperature collection point is installed on the surface of the battery includes the following steps:
a temperature sensor is arranged at any position of the surface formed by the length and the height of the battery, and the temperature sensor acquires the temperature T1The distance from the temperature sensor to the center of the surface is d1The heat production rate of the battery is obtained by calculating according to a Bernadi formula III, the temperature gradient GradT is obtained by calculating according to a formula IV, and the highest temperature of the center of the battery is obtained by calculating according to a formula V:
Figure BDA0003086550060000031
wherein I is current, ULTerminal voltage, V battery volume, T1Collecting temperature for a temperature sensor, wherein OCV is open-circuit voltage of a battery;
Figure BDA0003086550060000032
wherein k issFor heat transfer coefficient, TbR is the temperature of the heat exchange fluid, r is the diameter of the pole, klIs the thermal conductivity of the battery in the length direction.
T0＝T1+d1XGradT formula five
Knowing the center maximum temperature T of the cell0And temperature gradient GradT, average temperature T of the cellaverThe formula II is calculated to obtain:
Figure BDA0003086550060000033
wherein b is the thickness of the battery, T0The center maximum temperature, θ is the polar angle.
In the above scheme, the dimension reduction gas-liquid dynamic battery model includes the following steps:
the charge state estimation equation of the gas-liquid dynamic battery model is a formula six, and the terminal voltage estimation equation is a formula seven:
Figure BDA0003086550060000034
therein, SOC1To pre-sample time state of charge, SOC2For the state of charge, Q, at the present sampling momentTIs the rated capacity of the battery, t1For pre-sampling time points, t2Tau is an integral variable for the current sampling time point;
Figure BDA0003086550060000035
wherein, ULTerminal voltage, OCVpresOpen circuit voltage, OCV, for the current sampling instantinitFor open circuit voltage, T, at the previous sampling instantaverIs the average temperature of the batteryI is the current, k1、k2、k3、k4Parameters of a gas-liquid dynamic battery model are obtained;
there are two state variables OCV in equation sevenpresAnd OCVinitThe state vector is a two-dimensional column vector when coupled with the EKF, which correlates the OCVinitSet as S, the OCV is assigned at the end of each estimationpresAssigning S and OCV as state variableinitAs an element of the input vector, formula seven is rewritten as formula eight:
Figure BDA0003086550060000036
wherein S is an initial open circuit voltage.
In the above scheme, the EKF algorithm coupled to the one-dimensional gas-liquid dynamic battery model includes the following steps:
in the EKF algorithm, formula nine is a state equation, formula ten is an observation equation, and the discrete equation is:
Figure BDA0003086550060000041
wherein w is the system noise, and P (w) -N (0, Q), i.e. w obeys 0 desired normal distribution, Q is the system noise variance; v is the measurement noise, and P (v) -N (0, R), i.e., v obeys 0 expected normal distribution, R is the measurement noise variance; SOCkIs the kth state of charge value, SOCk-1Is the k-1 th charge state value, QTRated capacity, I, for the batterykFor the k-th current sample value, w, of the batteryk-1Is the k-1 th noise, U of the state equationkEstimating terminal voltage, OCV, for battery kthkIs the kth open circuit voltage, T, of the batteryaver_kIs the k-th average temperature, S, of the batterykIs the k-th initial open circuit voltage, vkMeasuring noise for the kth time of an observation equation, wherein t is sampling time and delta t is time interval;
written as standard EKF format, set:
Figure BDA0003086550060000042
zk＝Uk,μk＝[Ik,Taver_k,Sk],
Figure BDA0003086550060000043
then:
Figure BDA0003086550060000044
Figure BDA0003086550060000045
if two or more temperature sensors:
Figure BDA0003086550060000046
if there is one temperature sensor:
Figure BDA0003086550060000047
T0＝T1+d1×GradT
Figure BDA0003086550060000048
wherein x iskIs the k-th state vector, xk-1Is the k-1 st state vector, zkFor the k-th observation vector, OCV (x)k) In order to obtain the k-th open-circuit voltage by looking up the OCV-SOC curve table,
Figure BDA0003086550060000049
for optimal estimation of the previous sampling instant, Ak-1Is a state equation in
Figure BDA0003086550060000051
A derivative;
Figure BDA0003086550060000052
for a priori estimation of the current sampling instant, HkFor the observation equation in
Figure BDA0003086550060000053
Derivative of (a), T0The highest temperature at the center, V the cell volume, klThe thermal conductivity coefficient in the length direction of the battery, b the thickness of the battery and theta the polar angle;
coupling EKF of a one-dimensional gas-liquid dynamic battery model:
initialization:
k,SOC0,S1,QT,P0,Q,R,k1,k2,k3,k4
and (3) cycle estimation:
Figure BDA0003086550060000054
Figure BDA0003086550060000055
Figure BDA0003086550060000056
Figure BDA0003086550060000057
Figure BDA0003086550060000058
Figure BDA0003086550060000059
where k is the sampling instant ukFor the kth equation of state input matrix, μkThe matrix is input for the k-th observation equation,
Figure BDA00030865500600000510
is the k-th prior covariance matrix, PkIs the K-th posterior covariance matrix, KkIs the k-th Kalman gain, E is the identity matrix with the same dimension as the operation matrix, P0Is an initial covariance matrix, Pk-1Is the k-1 th a posteriori covariance matrix,
Figure BDA00030865500600000511
for the k-1 st state coefficient matrix transposition,
Figure BDA00030865500600000512
for the observation equation in
Figure BDA00030865500600000513
Transposing the derivative matrix of (A), HkFor the observation equation in
Figure BDA00030865500600000514
The matrix of the derivatives of (a) and (b),
Figure BDA00030865500600000515
and performing optimal estimation on the state vector at the k time.
In the above scheme, in the estimating of the average temperature inside the battery, the battery is a square battery, a battery temperature model is established, the length of the battery is l, the height of the battery is h, and the thickness of the battery is b, the thickness of the square battery is smaller than the length and the height of the battery, and the heat transfer coefficient in the thickness direction is also smaller than the length and the height of the battery.
In the scheme, the SOC estimation accuracy of the battery is verified through the actual measurement working condition of FUDS.
A system for realizing the method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model comprises a signal acquisition module, an average temperature estimation module, an SOC estimation module, a data storage module and a display module;
the signal acquisition module is used for acquiring the terminal voltage, the surface temperature and the current of the battery, is respectively connected with the average temperature estimation module and the SOC estimation module, and transmits the acquired current, surface temperature and terminal voltage signals to the average temperature estimation module and the SOC estimation module; the average temperature estimation module is used for estimating the average temperature inside the battery so that the average temperature inside the battery is consistent with the average temperature inside the gas-liquid dynamic battery model; the SOC estimation module is used for estimating the SOC of the battery by using a one-dimensional gas-liquid dynamic battery model coupled EKF algorithm according to the current and terminal voltage data acquired by the signal acquisition module and the average temperature estimated by the average temperature estimation module; the SOC estimation module is connected with the display module and sends the battery acquisition data, the estimated average temperature and the SOC estimation value to the display module.
In the above scheme, the signal acquisition module includes voltage sensor, temperature sensor and current sensor, and voltage sensor is used for gathering the terminal voltage of battery, and temperature sensor is used for gathering the surface temperature of battery, and current sensor is used for gathering the electric current of battery. Compared with the prior art, the invention has the beneficial effects that: according to the invention, the modeling precision of the gas-liquid dynamic battery model is improved by the fact that the calculated internal average temperature of the battery is consistent with the internal average temperature defined by the gas-liquid dynamic battery model. The gas-liquid dynamic battery model is reduced to the one-dimensional model, all data operations are one-dimensional without matrix operations when the gas-liquid dynamic battery model is coupled with the EKF algorithm, and the calculation amount is greatly reduced, so that the gas-liquid dynamic battery model can be directly applied to a vehicle-mounted embedded system, and the high industrial application value is shown. The jacobian matrix is not easy to generate ill-conditioned (irregular) conditions during one-dimensional data operation, and the robustness of the algorithm is obviously improved, so that the variance Q of the state equation and the equation R of the observation equation can be set to be larger values during the initialization of the algorithm so as to improve the anti-interference capability and the convergence speed of the algorithm, and the method has obvious precision advantage compared with the same type of technology.
Drawings
FIG. 1: is an implementation flow diagram of one embodiment of the present invention;
FIG. 2: is a selected square lithium ion battery of an embodiment of the invention;
FIG. 3: the estimation result of the SOC under the FUDS working condition is obtained according to the embodiment of the invention;
FIG. 4: the local development map of the SOC estimation result of the FUDS working condition is an embodiment of the invention;
FIG. 5: is a system component of an embodiment of the present invention;
FIG. 6: an OCV-SOC curve according to an embodiment of the present invention;
FIG. 7: is an embodiment of the present invention
Figure BDA0003086550060000061
Curve line.
Detailed Description
The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
Fig. 1 shows a technical route of the method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model, which includes the following steps:
the method comprises the following steps: estimating the average temperature inside the battery to ensure that the definition of the average temperature inside the battery is consistent with that in the gas-liquid dynamic battery model, and improving the modeling precision of the gas-liquid dynamic battery model;
step two: reducing the dimension of the gas-liquid dynamic battery model, and reducing the two-dimensional gas-liquid dynamic battery model to one dimension;
step three: the one-dimensional gas-liquid dynamic battery model is coupled with the extended Kalman filter EKF algorithm, so that the calculated amount is reduced, and the robustness is improved;
step four: verifying the SOC estimation precision of the battery, and verifying the SOC estimation precision of the battery through the actual measurement working condition of FUDS;
the first step of estimating the average temperature inside the battery specifically comprises the following steps:
firstly, in order to realize application in a vehicle-mounted embedded system, an assumption needs to be made on a battery temperature model to achieve the purpose of reducing the calculation amount; according to this embodiment, preferably, taking a square packaged lithium ion battery adopting a laminated cell as an example, a battery temperature model is established, where the battery length is l, the height is h, and the thickness is b, the thickness of the square battery is usually much smaller than the length and the height, and the heat transfer coefficient in the thickness direction is also much smaller than the length and the height (in this embodiment, the measured physical parameters of the square battery are k in the length direction, the height direction, and the thickness direction, respectivelyl＝29.9W/(m·K)、kh＝29.9W/(m·K)、kd1.03W/(m · K); length, height and thickness dimensions of l 122mm, h 88mm and b 9mm, respectively), it can be assumed that the temperature distribution of the battery is uniform in the thickness direction; establishing a polar coordinate system of the battery by taking the center of the battery as a polar coordinate origin and taking a plane formed by the length direction and the height direction as a polar coordinate plane; the method comprises the following steps of adopting an assumed battery temperature model to estimate the average temperature of the battery, adopting a temperature gradient calculation method when two or more temperature acquisition points are installed on the surface of the battery in the first method, and adopting a Bernadi heat generation model calculation method when only one temperature acquisition point is installed on the surface of the battery in the second method;
the first method for calculating the temperature gradient when two or more temperature collection points are installed on the surface of a battery comprises the following steps:
a temperature sensor is arranged at the center of the surface formed by the length and the height of the battery, one or more temperature sensors are arranged at other positions of the surface, and the temperature sensor at the center of the battery collects the temperature as the highest center temperature T0The temperature collected by the temperature sensors at other positions is T1,T2,T3…Tn，n≥2,n∈N+The distances from the temperature sensors at other positions to the sensor at the central position are respectively d1,d2,d3…dn，n≥2,n∈N+Temperature ladder for batteryThe degree GradT is obtained by calculating the formula I:
Figure BDA0003086550060000071
average temperature T of batteryaverCalculated by formula two:
Figure BDA0003086550060000072
wherein r is the pole diameter, theta is the pole angle, V is the cell volume, and b is the cell thickness.
The second calculation method for the Bernadi heat generation model when only one temperature acquisition point is installed on the surface of the battery comprises the following steps:
a temperature sensor is arranged at any position of the surface formed by the length and the height of the battery, and the temperature sensor acquires the temperature T1The distance from the temperature sensor to the center of the surface is d1The heat production rate of the battery is obtained by calculating according to a Bernadi formula III, the temperature gradient GradT is obtained by calculating according to a formula IV, and the highest temperature of the center of the battery is obtained by calculating according to a formula V:
Figure BDA0003086550060000081
wherein I is current, ULThe voltage is terminal voltage, V is battery volume, T is temperature acquired by a temperature sensor, and OCV is battery open-circuit voltage;
Figure BDA0003086550060000082
wherein k issFor heat transfer coefficient, TbR is the temperature of the heat exchange fluid, r is the diameter of the pole, klIs the thermal conductivity of the battery in the length direction.
T0＝T1+d1XGradT formula five
Knowing the center maximum temperature T of the cell0And temperature gradient GradT, average temperature T of the cellaverThe formula II is calculated to obtain:
Figure BDA0003086550060000083
wherein b is the thickness of the battery, T0The center maximum temperature, θ is the polar angle.
The step two dimension reduction gas-liquid dynamic battery model comprises the following steps:
the charge state estimation equation (formula six) and the terminal voltage estimation equation (formula seven) of the gas-liquid dynamic battery model are as follows:
Figure BDA0003086550060000084
here, SOC1To pre-sample time state of charge, SOC2For the state of charge, Q, at the present sampling momentTIs the rated capacity of the battery, t1For pre-sampling time points, t2Tau is an integral variable for the current sampling time point;
Figure BDA0003086550060000085
here, ULTerminal voltage, OCVpresOpen circuit voltage, OCV, for the current sampling instantinitFor open circuit voltage, T, at the previous sampling instantaverIs the average temperature of the battery, I is the current, k1、k2、k3、k4Parameters of a gas-liquid dynamic battery model are obtained;
there are two state variables OCV in equation sevenpresAnd OCVinitThe state vector is a two-dimensional column vector when coupled with the EKF if the OCV is consideredinitSet as S, the OCV is assigned at the end of each estimationpresAssigned to S, the state variable OCV can be setinitAs an element of the input vector, formula seven can be rewritten as formula eight:
Figure BDA0003086550060000086
wherein S is an initial open circuit voltage.
The three-dimensional gas-liquid dynamic battery model coupling EKF algorithm comprises the following steps:
in the EKF algorithm, formula nine is a state equation, formula ten is an observation equation, and the discrete equation is:
Figure BDA0003086550060000091
here, w is the system noise, and P (w) N (0, Q), i.e., w follows an expected normal distribution of 0, Q being the system noise variance; v is the measurement noise, and P (v) -N (0, R), i.e., v obeys 0 expected normal distribution, R is the measurement noise variance; the subscripts of all the letters contain k or k-1 to respectively represent data at the k-th sampling moment or data at the k-1 sampling moment; SOCkIs the kth state of charge value, SOCk-1Is the k-1 th charge state value, QTRated capacity, I, for the batterykFor the k-th current sample value, w, of the batteryk-1Is the k-1 th noise, U of the state equationkEstimating terminal voltage, OCV, for battery kthkIs the kth open circuit voltage, T, of the batteryaver_kIs the k-th average temperature, S, of the batterykIs the k-th initial open circuit voltage, vkMeasuring noise for the kth time of an observation equation, wherein t is sampling time, and delta t is time interval;
written as standard EKF format, set:
Figure BDA0003086550060000092
zk＝Uk,μk＝[Ik,Taver_k,Sk],
Figure BDA0003086550060000093
then:
Figure BDA0003086550060000094
Figure BDA0003086550060000095
if two or more temperature sensors:
Figure BDA0003086550060000096
if there is one temperature sensor:
Figure BDA0003086550060000097
T0＝T1+d1×GradT
Figure BDA0003086550060000098
here, xkIs the k-th state vector, xk-1Is the k-1 st state vector, zkFor the k-th observation vector, OCV (x)k) In order to obtain the k-th open-circuit voltage by looking up the OCV-SOC curve table,
Figure BDA0003086550060000099
for optimal estimation of the previous sampling instant, Ak-1Is a state equation in
Figure BDA0003086550060000101
A derivative;
Figure BDA0003086550060000102
for a priori estimation of the current sampling instant, HkFor the observation equation in
Figure BDA0003086550060000103
Derivative of (a), T0The highest temperature at the center, V the cell volume, klThe thermal conductivity coefficient in the length direction of the battery, b the thickness of the battery and theta the polar angle;
the coupling EKF of the one-dimensional gas-liquid dynamic battery model comprises the following steps:
initialization:
k,SOC0,S1,QT,P0,Q,R,k1,k2,k3,k4
and (3) cycle estimation:
Figure BDA0003086550060000104
Figure BDA0003086550060000105
Figure BDA00030865500600001018
Figure BDA0003086550060000106
Figure BDA0003086550060000107
Figure BDA0003086550060000108
where k is the sampling instant ukFor the kth equation of state input matrix, μkThe matrix is input for the k-th observation equation,
Figure BDA0003086550060000109
is the k-th prior covariance matrix, PkIs the K-th posterior covariance matrix, KkFor the k-th kalman gain,e is an identity matrix with the same dimension as the operation matrix, P0Is an initial covariance matrix, Pk-1Is the k-1 th a posteriori covariance matrix,
Figure BDA00030865500600001010
for the k-1 st state coefficient matrix transposition,
Figure BDA00030865500600001011
for the observation equation in
Figure BDA00030865500600001012
Transposing the derivative matrix of (A), HkFor the observation equation in
Figure BDA00030865500600001013
The matrix of the derivatives of (a) and (b),
Figure BDA00030865500600001014
and performing optimal estimation on the state vector at the k time.
Wherein, the OCV-SOC curve of the selected square battery is shown in FIG. 6,
Figure BDA00030865500600001015
the curves are shown in FIG. 7;
the step four of verifying the SOC estimation precision of the battery specifically comprises the following steps:
the accuracy of the SOC estimation method is verified by selecting the FUDS actual measurement working condition data of a square battery.
The specific embodiment is as follows:
method for estimating battery SOC by using dimension-reduced gas-liquid dynamic battery model, and parameter (k) of gas-liquid dynamic battery model1＝0.4318,k2＝0.0343,k3＝0.00277,k40.000014) identification method refer to published invention patent 201910137591.
Initialization: k is 1, SOC0＝100，S1＝4.193，QT＝5.53，P0＝1(P0∈R+，R+Positive and real), Q ═ 20(Q ∈ R)+，R+Positive and real), R ═ 1(R ∈ RR+，R+Positive real number), k1＝0.4318,k2＝0.0343,k3＝0.00277,k40.000014; and (3) cycle estimation: reading the collected terminal voltage z as shown in Table 1k＝4.190，Ik＝-3.428，Tk297.45, the estimated average temperature is 297.50; computing
Figure BDA00030865500600001016
Calculating Pk -Calculate K as 21k0.326, calculate
Figure BDA00030865500600001017
Calculating PkAnd (8) 20.893, adding 1 to k, switching to the next moment, and repeating the steps to finish the online estimation of the SOC of the battery.
TABLE 1 sample data and estimation results
Figure BDA0003086550060000111
The accuracy of the SOC estimation method is verified through the actual measurement working condition data of FUDS, the estimation result is shown in fig. 3 and fig. 4, fig. 3 shows an SOC curve (black cross curve) obtained through experimental tests, an SOC curve (light gray curve) estimated by the model under the condition of no initial error, an SOC curve (gray curve) estimated by the model under the condition of 50% initial error and an SOC curve (dark gray curve) estimated by an ampere-hour integration method under the condition of 50% initial error, and the maximum estimation error of the SOC of the model under the condition of no initial error is 1.28%; FIG. 4 is an enlarged view of the first 60 second curve of FIG. 3, where the model substantially eliminates the initial error after about 25 seconds after 50% of the initial error is input, and the curve coincides with the estimated curve without the initial error, but the ampere-hour integration method is not always capable of eliminating the initial error. The jacobian matrix is not easy to generate ill-condition during one-dimensional data operation, and the robustness of the algorithm is obviously improved, so that the variance Q of the state equation and the equation R of the observation equation can be set to be larger values during the initialization of the algorithm, so that the anti-interference capability and the convergence speed of the algorithm are improved. The maximum SOC estimation error is 1.28% under the actual measurement FUDS working condition, and compared with the same type of technology, the method has the obvious precision advantage.
A system for realizing the method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model comprises a signal acquisition module, an average temperature estimation module, an SOC estimation module, a data storage module and a display module, wherein the signal acquisition module, the average temperature estimation module, the SOC estimation module, the data storage module and the display module are shown in figure 5;
the signal acquisition module comprises a voltage sensor, a temperature sensor and a current sensor which are respectively used for acquiring the terminal voltage, the surface temperature and the current of the battery, and the signal acquisition module and the average temperature estimation module are connected with the SOC estimation module and transmit the acquired current, surface temperature and terminal voltage signals to the average temperature estimation module and the SOC estimation module; the average temperature estimation module estimates the internal average temperature of the battery by using the acquired surface temperature of the battery and a Bernadi heat generation rate formula, so that the internal average temperature of the battery is consistent with the internal average temperature of the gas-liquid dynamic battery model, and the modeling precision of the gas-liquid dynamic battery model is improved; the SOC estimation module is used for estimating the SOC of the battery by using a one-dimensional gas-liquid dynamic battery model coupled EKF algorithm according to the current and terminal voltage data acquired by the signal acquisition module and the average temperature estimated by the average temperature estimation module; the SOC estimation module is connected with the display module, and is used for sending the data collected by the battery, the estimated average temperature and the SOC estimation value to the display module for the reference of a user and storing the data in the data storage module.
The average temperature estimation module and the SOC estimation module are realized by a single chip microcomputer, and the single chip microcomputer is preferably a Shekal automobile grade single chip microcomputer. The method for estimating the SOC of the battery by using the dimension reduction gas-liquid dynamic battery model is realized on hardware, and codes written by C language on a singlechip can be realized on a CodeWarrior Development Studio Development platform.
According to this embodiment, preferably, the SOC estimation module is specifically:
firstly, loading a library function file of a singlechip, configuring a singlechip register by using the library function, and compiling a clock function, a timer function, a delay function, a storage function, a data verification function, an average temperature estimation function, a main function and the like;
firstly, connecting a current sensor and a temperature sensor to a signal acquisition card, wherein the acquisition card can directly acquire the voltage of a single battery, and preferably, the voltage range of the single battery is within 0-5V;
secondly, the acquisition card is connected with a serial port of the singlechip, RS-232 is selected as a communication mode, and signals of current, voltage and surface temperature of the battery are transmitted to the singlechip;
thirdly, reading current, voltage and surface temperature signals of the battery by the main function of the single chip microcomputer, and calling an average temperature estimation function to calculate an average temperature value under current input; the master function estimates the SOC value at the current moment through the battery current, the terminal voltage, the average temperature value and the initialization data of the last sampling moment, and sends the battery current, the terminal voltage, the average temperature and the calculated SOC value to a display module of the upper computer for display;
and fourthly, circulating the steps from the first step to the third step to finish the real-time SOC estimation of the battery pack.
The upper computer is developed based on a Microsoft Visual Studio platform and is used for displaying the terminal voltage and the SOC of the battery pack, the SOC of all the series single batteries and the fitted lowest SOC of the batteries;
the singlechip includes: 2nA single-chip microcomputer, n is 1,2,3, and various arithmetic units of ARM cores;
the signal communication protocol used includes: RS-485, CAN, TCP, modbus, MPI, serial port communication and the like.
It should be understood that although the present description has been described in terms of various embodiments, not every embodiment includes only a single embodiment, and such description is for clarity purposes only, and those skilled in the art will recognize that the embodiments described herein may be combined as suitable to form other embodiments, as will be appreciated by those skilled in the art.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.

Claims (10)

1. A method for estimating the SOC of a battery by using a dimension-reduced gas-liquid dynamic battery model is characterized by comprising the following steps:
step S1, estimating the internal average temperature of the battery: estimating the average temperature inside the battery through the surface temperature of the battery, so that the average temperature inside the battery is consistent with the average temperature inside the gas-liquid dynamic battery model;
step S2: dimension reduction gas-liquid dynamic battery model: reducing the two-dimensional gas-liquid dynamic battery model to a one-dimensional gas-liquid dynamic battery model;
step S3: the one-dimensional gas-liquid dynamic battery model coupling EKF algorithm: coupling the one-dimensional gas-liquid dynamic battery model with the one-dimensional EKF, and inputting the average temperature in the battery obtained in the step S1 into the EKF algorithm coupled with the one-dimensional gas-liquid dynamic battery model to obtain the SOC estimated value of the battery;
step S4: and verifying the SOC estimation precision of the battery.
2. The method for estimating the SOC of the battery using the dimension-reduced gas-liquid dynamic battery model according to claim 1, wherein the step S1 of estimating the average temperature inside the battery comprises the steps of:
the method comprises the steps of establishing a battery temperature model, and estimating the average temperature of the battery by adopting an assumed battery temperature model, wherein the first method adopts a temperature gradient calculation method when two or more temperature acquisition points are installed on the surface of the battery, and the second method adopts a Bernadi heat generation model calculation method when only one temperature acquisition point is installed on the surface of the battery.
3. The method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model according to claim 2, wherein the first method for calculating the temperature gradient when two or more temperature collection points are installed on the surface of the battery comprises the following steps:
a temperature sensor is arranged at the center of the surface formed by the length and the height of the battery and one or more temperature sensors are arranged at other positions of the surfaceA temperature sensor at the center of the battery and collecting the highest temperature T0The temperature collected by the temperature sensors at other positions is T1,T2,T3…Tn，n≥2,n∈N+The distances from the temperature sensors at other positions to the sensor at the central position are respectively d1,d2,d3…dn，n≥2,n∈N+And the battery temperature gradient GradT is obtained by calculating the formula I:
Figure FDA0003086550050000011
average temperature T of batteryaverCalculated by formula two:
Figure FDA0003086550050000012
wherein r is the pole diameter, theta is the pole angle, V is the cell volume, and b is the cell thickness.
4. The method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model as claimed in claim 2, wherein the second calculation method for the Bernadi heat generation model when only one temperature collection point is installed on the surface of the battery comprises the following steps:
a temperature sensor is arranged at any position of the surface formed by the length and the height of the battery, and the temperature sensor acquires the temperature T1The distance from the temperature sensor to the center of the surface is d1The heat production rate of the battery is obtained by calculating according to a Bernadi formula III, the temperature gradient GradT is obtained by calculating according to a formula IV, and the highest temperature of the center of the battery is obtained by calculating according to a formula V:
Figure FDA0003086550050000021
wherein I is current, ULTerminal voltage, V battery volume, T1Collecting temperature for a temperature sensor, wherein OCV is open-circuit voltage of a battery;
Figure FDA0003086550050000022
wherein k issFor heat transfer coefficient, TbR is the temperature of the heat exchange fluid, r is the diameter of the pole, klIs the thermal conductivity of the battery in the length direction.
T0＝T1+d1XGradT formula five
Knowing the center maximum temperature T of the cell0And temperature gradient GradT, average temperature T of the cellaverThe formula II is calculated to obtain:
Figure FDA0003086550050000023
wherein b is the thickness of the battery, T0The center maximum temperature, θ is the polar angle.
5. The method for estimating the SOC of the battery using the dimension-reduced gas-liquid dynamic battery model according to claim 1, wherein the dimension-reduced gas-liquid dynamic battery model comprises the steps of:
the charge state estimation equation of the gas-liquid dynamic battery model is a formula six, and the terminal voltage estimation equation is a formula seven:
Figure FDA0003086550050000024
therein, SOC1To pre-sample time state of charge, SOC2For the state of charge, Q, at the present sampling momentTIs the rated capacity of the battery, t1For pre-sampling time points, t2Tau is an integral variable for the current sampling time point;
Figure FDA0003086550050000025
wherein, ULTerminal voltage, OCVpresOpen circuit voltage, OCV, for the current sampling instantinitFor open circuit voltage, T, at the previous sampling instantaverIs the average temperature of the battery, I is the current, k1、k2、k3、k4Parameters of a gas-liquid dynamic battery model are obtained;
there are two state variables OCV in equation sevenpresAnd OCVinitThe state vector is a two-dimensional column vector when coupled with the EKF, which correlates the OCVinitSet as S, the OCV is assigned at the end of each estimationpresAssigning S and OCV as state variableinitAs an element of the input vector, formula seven is rewritten as formula eight:
Figure FDA0003086550050000026
wherein S is an initial open circuit voltage.
6. The method for estimating the SOC of the battery according to claim 1, wherein the EKF algorithm coupled with the one-dimensional aerodynamic battery model comprises the following steps:
in the EKF algorithm, formula nine is a state equation, formula ten is an observation equation, and the discrete equation is:
Figure FDA0003086550050000031
wherein w is the system noise, and P (w) -N (0, Q), i.e. w obeys 0 desired normal distribution, Q is the system noise variance; v is the measurement noise, and P (v) -N (0, R), i.e., v obeys 0 expected normal distribution, R is the measurement noise variance; SOCkIs the kth state of charge value, SOCk-1Is the k-1 th charge state value, QTRated capacity, I, for the batterykFor the k time electricity of the batteryFlow sample value, wk-1Is the k-1 th noise, U of the state equationkEstimating terminal voltage, OCV, for battery kthkIs the kth open circuit voltage, T, of the batteryaver_kIs the k-th average temperature, S, of the batterykIs the k-th initial open circuit voltage, vkMeasuring noise for the kth time of an observation equation, wherein t is sampling time, and delta t is time interval;
written as standard EKF format, set:
Figure FDA0003086550050000032
zk＝Uk,μk＝[Ik,Taver_k,Sk],
Figure FDA0003086550050000033
then:
Figure FDA0003086550050000034
Figure FDA0003086550050000035
if two or more temperature sensors:
Figure FDA0003086550050000036
if there is one temperature sensor:
Figure FDA0003086550050000037
T0＝T1+d1×GradT
Figure FDA0003086550050000038
wherein x iskIs the k-th state vector, xk-1Is the k-1 st state vector, zkFor the k-th observation vector, OCV (x)k) In order to obtain the k-th open-circuit voltage by looking up the OCV-SOC curve table,
Figure FDA0003086550050000041
for optimal estimation of the previous sampling instant, Ak-1Is a state equation in
Figure FDA0003086550050000042
A derivative;
Figure FDA0003086550050000043
for a priori estimation of the current sampling instant, HkFor the observation equation in
Figure FDA0003086550050000044
Derivative of (a), T0The highest temperature at the center, V the cell volume, klThe thermal conductivity coefficient in the length direction of the battery, b the thickness of the battery and theta the polar angle;
coupling EKF of a one-dimensional gas-liquid dynamic battery model:
initialization:
k,SOC0,S1,QT,P0,Q,R,k1,k2,k3,k4
and (3) cycle estimation:
Figure FDA0003086550050000045
Figure FDA0003086550050000046
Figure FDA0003086550050000047
Figure FDA0003086550050000048
Figure FDA0003086550050000049
Figure FDA00030865500500000410
where k is the sampling instant ukFor the kth equation of state input matrix, μkThe matrix is input for the k-th observation equation,
Figure FDA00030865500500000411
is the k-th prior covariance matrix, PkIs the K-th posterior covariance matrix, KkIs the k-th Kalman gain, E is the identity matrix with the same dimension as the operation matrix, P0Is an initial covariance matrix, Pk-1Is the k-1 th a posteriori covariance matrix,
Figure FDA00030865500500000412
for the k-1 st state coefficient matrix transposition,
Figure FDA00030865500500000413
for the observation equation in
Figure FDA00030865500500000414
Transposing the derivative matrix of (A), HkFor the observation equation in
Figure FDA00030865500500000415
The matrix of the derivatives of (a) and (b),
Figure FDA00030865500500000416
and performing optimal estimation on the state vector at the k time.
7. The method according to claim 2, wherein in the step of estimating the average temperature inside the battery, the battery is a square battery, the battery temperature model is established, the battery length is l, the height is h, the thickness is b, the thickness of the square battery is smaller than the length and the height, the heat transfer coefficient in the thickness direction is smaller than the length and the height, and a battery polar coordinate system is established by taking the center of the battery as the origin of polar coordinates and the plane formed by the length direction and the height direction as the polar coordinate plane, assuming that the temperature of the battery in the thickness direction is uniformly distributed.
8. The method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model according to claim 1, wherein the accuracy of estimating the SOC of the battery is verified by actually measuring the working condition of FUDS.
9. A system for realizing the method for estimating the SOC of the battery by using the dimension-reduced gas-liquid dynamic battery model according to any one of claims 1-8 is characterized by comprising a signal acquisition module, an average temperature estimation module, an SOC estimation module, a data storage module and a display module;
the signal acquisition module is used for acquiring the terminal voltage, the surface temperature and the current of the battery, is respectively connected with the average temperature estimation module and the SOC estimation module, and transmits the acquired current, surface temperature and terminal voltage signals to the average temperature estimation module and the SOC estimation module; the average temperature estimation module is used for estimating the average temperature inside the battery so that the average temperature inside the battery is consistent with the average temperature inside the gas-liquid dynamic battery model; the SOC estimation module is used for estimating the SOC of the battery by using a one-dimensional gas-liquid dynamic battery model coupled EKF algorithm according to the current and terminal voltage data acquired by the signal acquisition module and the average temperature estimated by the average temperature estimation module; the SOC estimation module is connected with the display module and sends the battery acquisition data, the estimated average temperature and the SOC estimation value to the display module.
10. The system of claim 9, wherein the signal acquisition module comprises a voltage sensor, a temperature sensor and a current sensor, the voltage sensor is used for acquiring the terminal voltage of the battery, the temperature sensor is used for acquiring the surface temperature of the battery, and the current sensor is used for acquiring the current of the battery.
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