CN112578286A - Battery SOC estimation method and device - Google Patents

Battery SOC estimation method and device Download PDF

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CN112578286A
CN112578286A CN202011323313.2A CN202011323313A CN112578286A CN 112578286 A CN112578286 A CN 112578286A CN 202011323313 A CN202011323313 A CN 202011323313A CN 112578286 A CN112578286 A CN 112578286A
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soc
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高尚
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Jingwei Hengrun Tianjin Research And Development Co ltd
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Abstract

The invention provides a method and a device for estimating the SOC of a battery. The state equation and the output equation of the electrochemical cell are used as an electrochemical reduced-order model, a partial differential equation does not exist, and the electrochemical cell has high precision and can be applied to a battery management system in engineering.

Description

Battery SOC estimation method and device
Technical Field
The invention relates to the technical field of batteries, in particular to a battery SOC estimation method and device.
Background
Under the background of energy requirements and carbon emission requirements, new energy automobiles, especially electric automobiles, become an important development direction of future automobiles. The main power system of the electric automobile is a lithium ion power battery system. The lithium ion battery model can simulate the relation between the internal state of the battery and the output voltage, and has important significance for the development of a battery management system of an automobile.
Estimation of the State of charge (SOC) of a power battery is one of the important functions of a battery management system. For an electric automobile, accurate estimation of the SOC of a power battery is the basis of functions such as estimation of the remaining range of the electric automobile, capacity estimation of the power battery, and fault diagnosis.
The model estimation method of the power battery SOC is a method for obtaining the battery SOC by obtaining the voltage and the current when the battery runs based on the relation between the battery voltage, the battery current and the battery SOC given by a battery model. Model selection in a model estimation method of the power battery SOC has an important influence on the accuracy of battery SOC estimation. Common battery models include equivalent circuit models, electrochemical models, and the like.
The equivalent circuit model comprises a rint model, a first-order RC model, a second-order RC model and the like; the equivalent circuit model does not consider electrochemical mechanisms such as battery particle radial direction SOC distribution, so when the equivalent circuit model is adopted to estimate the battery SOC, the result accuracy is low. The electrochemical model comprises a quasi-two-dimensional model, a single-particle model and the like; the existing electrochemical model can describe the electrochemical mechanism in the battery, but the model parameters are too many, and a large number of partial differential equations exist, so that the application of battery SOC estimation cannot be realized in engineering.
Disclosure of Invention
In view of the above, the present invention provides a method and an apparatus for estimating battery SOC, which are intended to improve the accuracy of battery SOC estimation and reduce the computation to realize application of battery SOC estimation in engineering.
In order to achieve the above object, the following solutions are proposed:
in a first aspect, a battery SOC estimation method is provided, including:
acquiring a state equation of an electrochemical cell, wherein the electrochemical cell is a cell of an electrochemical system based on ion diffusion characteristics, and the state equation of the electrochemical cell is as follows:
Figure BDA0002793571710000021
Figure BDA0002793571710000022
wherein the content of the first and second substances,
Figure BDA0002793571710000023
is the electrochemical cell SOC at time k +1,
Figure BDA0002793571710000024
the electrochemical cell SOC at the k-th time, I (k) is the current flowing at the k-th timeCurrent value of chemical battery, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure BDA0002793571710000025
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1);
obtaining an output equation of the electrochemical cell, the output equation of the electrochemical cell being:
Figure BDA0002793571710000026
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure BDA0002793571710000027
for electrochemical cells at a particle concentration of
Figure BDA0002793571710000028
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell;
analyzing by adopting a preset filtering algorithm based on a state equation and an output equation of the electrochemical cell to obtain an estimated value of the SOC of the electrochemical cell; the preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value.
Optionally, the preset filtering algorithm is a kalman filtering algorithm;
the method for obtaining the estimated value of the SOC of the electrochemical battery by adopting a preset filtering algorithm based on the state equation and the output equation of the electrochemical battery comprises the following steps:
obtaining a predicted value of the state quantity according to a state quantity prediction equation, wherein the state quantity prediction equation is as follows:
Figure BDA0002793571710000031
Figure BDA0002793571710000032
Figure BDA0002793571710000033
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure BDA0002793571710000034
is an estimate of the electrochemical cell SOC at time k, Qi(k) ' is an estimated value of the ith state parameter of the electrochemical cell at the kth time, and A is a state transition matrix;
obtaining a predicted value of the error covariance matrix according to an error covariance matrix prediction equation, wherein the error covariance matrix prediction equation is as follows:
P(k+1)″＝A·P(k)′·AT+Q(k)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure BDA0002793571710000035
obtaining a gain matrix according to a gain matrix equation, wherein the gain matrix equation is as follows:
K(k+1)＝P(k+1)″·C(k+1)·(C(k+1)T·P(k+1)″·C(k+1)+R(k+1))-1
Figure BDA0002793571710000041
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure BDA0002793571710000042
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000043
to SOC-X＝1To pair
Figure BDA0002793571710000044
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000045
in order to provide a SOC for an electrochemical cell,
Figure BDA0002793571710000046
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiIs the ith state parameter of the electrochemical cell;
obtaining an updated terminal voltage according to a terminal voltage updating equation, wherein the terminal voltage updating equation is as follows:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and Vmeasure(k +1) is a measured value of the terminal voltage of the electrochemical cell at the (k +1) th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the (k +1) th moment calculated by using the output equation;
obtaining an estimation value of an error covariance matrix according to an error covariance matrix estimation equation, wherein the error covariance matrix estimation equation is as follows:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 moment, and Id is a unit matrix;
obtaining an estimated value of the state quantity according to a state quantity estimation equation, wherein the state quantity estimation equation is as follows:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time.
Optionally, the value of N is 4.
Optionally, a is obtained by genetic iterative algorithm in advanceiAnd bi。
Optionally, the electrochemical cell is specifically: lithium ion batteries or nickel metal hydride batteries.
In a second aspect, there is provided a battery SOC estimation device including:
the first obtaining unit is used for obtaining a state equation of an electrochemical cell, wherein the electrochemical cell is a cell of an electrochemical system based on ion diffusion characteristics, and the state equation of the electrochemical cell is as follows:
Figure BDA0002793571710000051
Figure BDA0002793571710000052
wherein the content of the first and second substances,
Figure BDA0002793571710000053
is the electrochemical cell SOC at time k +1,
Figure BDA0002793571710000054
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure BDA0002793571710000055
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1);
a second obtaining unit, configured to obtain an output equation of the electrochemical cell, where the output equation of the electrochemical cell is:
Figure BDA0002793571710000056
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure BDA0002793571710000057
for electrochemical cells at a particle concentration of
Figure BDA0002793571710000058
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0Is an ideal gas constant, T is an electrochemical cellF is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell;
the filtering unit is used for analyzing and obtaining an estimated value of the SOC of the electrochemical battery by adopting a preset filtering algorithm based on a state equation and an output equation of the electrochemical battery; the preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value.
Optionally, the preset filtering algorithm is a kalman filtering algorithm;
the filtering unit includes:
the state quantity prediction unit is used for obtaining a predicted value of the state quantity according to a state quantity prediction equation, wherein the state quantity prediction equation is as follows:
Figure BDA0002793571710000061
Figure BDA0002793571710000062
Figure BDA0002793571710000063
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure BDA0002793571710000064
is an estimate of the electrochemical cell SOC at time k, Qi(k) ' is an estimated value of the ith state parameter of the electrochemical cell at the kth time, and A is a state transition matrix;
the error covariance matrix prediction unit is used for obtaining a prediction value of the error covariance matrix according to an error covariance matrix prediction equation, wherein the error covariance matrix prediction equation is as follows:
P(k+1)″＝A·P(k)′·AT+Q(k)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure BDA0002793571710000071
the gain matrix calculation unit is used for obtaining a gain matrix according to a gain matrix equation, wherein the gain matrix equation is as follows:
K(k+1)＝P(k+1)″·C(k+1)·(C(k+1)T·P(k+1)″·C(k+1)+R(k+1))-1
Figure BDA0002793571710000072
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure BDA0002793571710000073
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000074
to SOC-X＝1To pair
Figure BDA0002793571710000075
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000081
in order to provide a SOC for an electrochemical cell,
Figure BDA0002793571710000082
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiIs the ith state parameter of the electrochemical cell;
the terminal voltage updating unit is used for obtaining an updated terminal voltage according to a terminal voltage updating equation, and the terminal voltage updating equation is as follows:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and Vmeasure(k +1) is a measured value of the terminal voltage of the electrochemical cell at the (k +1) th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the (k +1) th moment calculated by using the output equation;
the error covariance matrix estimation unit is used for obtaining an estimation value of an error covariance matrix according to an error covariance matrix estimation equation, wherein the error covariance matrix estimation equation is as follows:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 moment, and Id is a unit matrix;
the state quantity estimation unit is used for obtaining an estimation value of the state quantity according to a state quantity estimation equation, wherein the state quantity estimation equation is as follows:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time.
Optionally, the value of N is 4.
Optionally, a is obtained by genetic iterative algorithm in advanceiAnd bi。
Optionally, the electrochemical cell is specifically: lithium ion battery or nickel-hydrogen battery
Compared with the prior art, the technical scheme of the invention has the following advantages:
the method comprises the step of analyzing by adopting a preset filtering algorithm to obtain an estimated value of the SOC of the electrochemical battery based on a state equation and an output equation of the electrochemical battery. The state equation and the output equation of the electrochemical cell are used as an electrochemical reduced-order model, a partial differential equation does not exist, and the electrochemical cell has high precision and can be applied to a battery management system in engineering.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flowchart of a method for estimating a battery SOC according to an embodiment of the present invention;
FIG. 2 is a graphical illustration of the open circuit voltage as a function of SOC for an electrochemical cell according to an embodiment of the present invention;
FIG. 3 provides an input current curve for an embodiment of the present invention;
FIG. 4 is a schematic diagram of a voltage simulation result of a battery model according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating the effect of the method for estimating the SOC of the battery according to the embodiment of the present invention;
fig. 6 is a schematic diagram of a battery SOC estimation device according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The present embodiment provides a battery SOC estimation method, referring to fig. 1, including the steps of:
s11: obtaining an equation of state of the electrochemical cell, the equation of state of the electrochemical cell being:
Figure BDA0002793571710000091
Figure BDA0002793571710000092
wherein the content of the first and second substances,
Figure BDA0002793571710000093
is the electrochemical cell SOC at time k +1,
Figure BDA0002793571710000094
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure BDA0002793571710000095
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1). Electrochemical cells are cells of electrochemical systems based on ion diffusion characteristics. The electrochemical cell may be a lithium ion cell or a nickel hydride cell, but is not limited thereto.
S12: obtaining an output equation of the electrochemical cell, the output equation of the electrochemical cell being:
Figure BDA0002793571710000101
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure BDA0002793571710000102
for electrochemical cells at a particle concentration of
Figure BDA0002793571710000103
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell.
S13: and analyzing by adopting a preset filtering algorithm to obtain an estimated value of the SOC of the electrochemical battery based on the state equation and the output equation of the electrochemical battery.
The preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value. The measured value is an actually measured value; the predicted value is a value predicted according to a state equation and an output equation of the electrochemical cell.
The state equation and the output equation of the electrochemical cell adopted in the embodiment are used as an electrochemical reduced-order model, a partial differential equation does not exist, and the electrochemical cell has high precision and can be applied to a battery management system in engineering. The process of obtaining the state equation and the output equation of the electrochemical cell of the present invention is described in detail below.
The electrochemical reduction model in the present invention relates to the terminal voltage E of an electrochemical cellcellDivided into internal potentials
Figure BDA0002793571710000104
Ohmic overpotential ηohmReaction activation overpotential etaactAnd concentration overpotential ηconcAs shown in formula (1):
Figure BDA0002793571710000105
wherein the internal potential
Figure BDA0002793571710000106
Is the average concentration of particles in the electrochemical cell
Figure BDA0002793571710000107
Open circuit voltage at the lower.
Figure BDA0002793571710000108
Also referred to as electrochemical cell SOC.
Ohmic overpotential ηohmObtained by the formula (2):
ηohm＝Rohm·Icell (2)
wherein R isohmIs the ohmic internal resistance of the electrochemical cell, IcellIs the magnitude of the current flowing through the current collector of the electrochemical cell.
Reaction activation overpotential etaactObtained by the formula (3):
Figure BDA0002793571710000109
wherein R is0Is an ideal gas constant, F is the Faraday constant, I0For the exchange current density of the electrochemical cell, T is the temperature of the electrochemical cell.
Concentration overpotential etaconcCan be obtained by the formula (4):
Figure BDA0002793571710000111
wherein X is a normalized variable of the radial length of the electrochemical cell particles, and SOC is in electrochemical stateThe electrochemical cell SOC values are different when X is different, namely the X changes along the diameter direction of the particles in the chemical cell particle model; SOC-X＝1Is the SOC of the particle surface of the electrochemical cell. EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1As a function of (c).
The distribution of SOC in the diameter direction of the electrochemical cell particles satisfies equation (5), and the boundary conditions are given by equation (6), equation (7), and equation (8):
Figure BDA0002793571710000112
Figure BDA0002793571710000113
Figure BDA0002793571710000114
SOC|t＝0＝SOCcell,0 (8)
wherein ^ represents the gradient in the radial direction,. tau.is a diffusion characteristic parameter of the electrochemical cell, is determined by the characteristics of the electrochemical cell, and can be calibrated through a charge-discharge curve of the electrochemical cell, t is time, and Q iscell,0Is the standard capacity, SOC, of the electrochemical cellcell,0Is the initial SOC of the electrochemical cell.
Average concentration of particles in electrochemical cells
Figure BDA0002793571710000115
Given by equation (9):
Figure BDA0002793571710000116
equation (5) is a partial differential equation in two dimensions (i.e., time and space) for the variable SOC, which cannot be used in the controller of the battery management system due to the requirements of cost and calculation amount.In this embodiment, equation (5) is reduced to an ordinary differential equation, and is used in a battery management system. The specific order reduction method introduces variables theta and t0As shown in formulas (10) and (11):
θ＝SOC (10)
Figure BDA0002793571710000117
normalizing the formula (5) and the boundary conditions of the formula (6), the formula (7) and the formula (8), wherein the normalized formula is shown as a formula (12), and the boundary conditions are shown as a formula (13), a formula (14) and a formula (15):
Figure BDA0002793571710000121
Figure BDA0002793571710000122
Figure BDA0002793571710000123
Figure BDA0002793571710000124
introducing a variable deltasAnd thetaini。
Further, by laplace transform of formula (12), formula (16) and formula (17) can be obtained, with the boundary conditions being formula (18) and formula (19):
Figure BDA0002793571710000125
Figure BDA0002793571710000126
Figure BDA0002793571710000127
Figure BDA0002793571710000128
where β is a complex variable, "-" indicates a function obtained by laplace transform, and "avg" indicates averaging.
Solving the laplace equation of equation (17) yields:
Figure BDA0002793571710000129
and respectively calculating a function and an average function of the formula (17) when the value of X is 1 to obtain a formula (18) and a formula (19). And the two functions are subtracted, thereby obtaining equation (20):
Figure BDA00027935717100001210
Figure BDA00027935717100001211
Figure BDA00027935717100001212
in order to realize the order reduction of the partial differential equation, it is necessary to obtain an approximate transfer function G of the function G (β) in the equation (20)TF(β) represented by the formula (21):
Figure BDA0002793571710000131
theoretically, the larger the value of N is, the more accurate the approximation is; in some embodiments, N is takenThe value was 4. By using genetic iterative algorithm, the corresponding optimized parameter a can be obtainediAnd biI is 1,2,3,4, such that G (β) and GTFThe mode of the difference (β) is the smallest. The specific optimization parameter results are shown in table 1. The optimization parameter a obtained hereiAnd biI is 1,2,3,4, which is determined mainly by the formula (5), i.e. the diffusion process mechanism of the electrochemical cell, so that the parameter a is optimized for different electrochemical cellsiAnd biI is the same as 1,2,3 and 4.
TABLE 1 approximate transfer function optimization parameter results
i 1 2 3 4
ai 35058.7 1382.966 141.595 22.32279
bi -268.261 -30.9242 -7.59606 -2.59525
The approximation here is actually to
Figure BDA0002793571710000132
This complex frequency equation is equivalent to
Figure BDA0002793571710000133
A transfer function form. By using genetic iterative algorithm, the corresponding optimized parameter a can be obtainediAnd biAnd i is 1,2,3 and 4. The genetic iterative algorithm is a self-adaptive global optimization search algorithm, and the optimal solution of the problem is searched by simulating the evolution process of the natural creatures. Specifically, firstly, initializing a population, namely creating a population by a random generation mode; the population number may be 500, i.e. 500 aiAnd bi(i is 1,2,3, 4). By using
Figure BDA0002793571710000134
And
Figure BDA0002793571710000135
the modulus of the difference is used as an 'adaptive value function' of the genetic iterative algorithm to evaluate the optimization parameter aiAnd biGood or bad. Further, the fitness value of each individual in the population is calculated using a "fitness value function". And secondly, selecting the individuals with small adaptation values from the current population. Then, performing cross operation; the step adopts the modes of single-point crossing, multi-point crossing and the like to generate new crossing individuals. Further carrying out mutation operation; this step is another operation that creates a new individual; firstly, the variation points are randomly generated, and then the original genes of the variation points are inverted. This creates a new generation population. And (5) carrying out a series of operations such as adaptive value calculation again to breed the next generation of population. And when the iteration times exceed the preset times, outputting the individual with the minimum adaptive value function, namely the optimized parameter.
Will function G (. beta.) in equation (20)Using an approximate transfer function GTF(β) is approximated by the following equations (22) and (23). Further, the inverse laplace transform is performed to obtain expression (24) and its boundary condition expression (25). In the same way, expression (26) and its boundary condition expression (27) are obtained by performing inverse laplace transform on expression (19).
Figure BDA0002793571710000141
Figure BDA0002793571710000142
Figure BDA0002793571710000143
Qi(t0＝0)＝0 i＝1,2,3,4 (25)
Figure BDA0002793571710000144
θavg(t0＝0)＝θini (27)
The reduced ordinary differential equation (28), the formula (29) and the formula (30), and the boundary condition equations (31) and (32) of the formula (5) can be obtained by reducing the normalized parameters of the formula (24), the formula (25), the formula (26), and the formula (27) to the original parameters:
Figure BDA0002793571710000145
Figure BDA0002793571710000146
Figure BDA0002793571710000147
Figure BDA0002793571710000148
Qi(t＝0)＝0 i＝1,2,3,4 (32)
Qi(t), i ═ 1,2,3,4 are state parameters of the electrochemical cell.
Respectively solve for
Figure BDA0002793571710000149
Q1(t)、Q2(t)、Q3(t) and Q4An analytical solution can be obtained by ordinary differential equation of (t), see formula (33) and formula (34):
Figure BDA00027935717100001410
Figure BDA00027935717100001411
in order to perform SOC estimation using kalman filtering, it is necessary to obtain the state equation of the electrochemical cell. For the problem of estimation of SOC of an electrochemical cell, SOC is the internal state that needs to be estimated, current is the input to the system, and terminal voltage is the output of the system. In connection with the model, the state quantities of the system include
Figure BDA00027935717100001412
Q1(k)、Q2(k)、Q3(k) And Q4(k) I.e. by
Figure BDA0002793571710000151
The equation of state of the electrochemical cell can be obtained by discretizing the equations (33) and (34), see equations (35) and (36). The output equation of the electrochemical cell is equation (37):
Figure BDA0002793571710000152
Figure BDA0002793571710000153
Figure BDA0002793571710000154
wherein the content of the first and second substances,
Figure BDA0002793571710000155
is the electrochemical cell SOC at time k +1,
Figure BDA0002793571710000156
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure BDA0002793571710000157
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure BDA0002793571710000158
for electrochemical cells at a particle concentration of
Figure BDA0002793571710000159
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell.
Step S13 specifically includes the following steps:
s131: and obtaining a predicted value of the state quantity according to the state quantity prediction equation.
The state quantity prediction equation is as follows:
Figure BDA0002793571710000161
Figure BDA0002793571710000162
Figure BDA0002793571710000163
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure BDA0002793571710000164
is an estimate of the electrochemical cell SOC at time k, Qi(k) ' is an estimate of the ith state parameter of the electrochemical cell at time k, and A is a state transition matrix.
S132: and obtaining a predicted value of the error covariance matrix according to the error covariance matrix prediction equation.
The error covariance matrix prediction equation is:
P(k+1)″＝A·P(k)′·AT+Q(k) (40)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure BDA0002793571710000165
w (k) conforms to a Gaussian white noise distribution.
S133: and obtaining a gain matrix according to a gain matrix equation.
The gain matrix equation is:
K(k+1)＝P(k+1)″·C(k+1)·(C(k+1)T·P(k+1)″·C(k+1)+R(k+1))-1 (41)
Figure BDA0002793571710000171
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure BDA0002793571710000172
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000173
to SOC-X＝1To pair
Figure BDA0002793571710000174
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000175
in order to provide a SOC for an electrochemical cell,
Figure BDA0002793571710000176
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiFor the ith state parameter of the electrochemical cell, J (k) corresponds to a Gaussian white noise distribution.
S134: and obtaining the updated terminal voltage according to the terminal voltage updating equation.
The terminal voltage update equation is:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1) (43)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and VmeasureAnd (k +1) is a measured value of the terminal voltage of the electrochemical cell at the k +1 th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the k +1 th moment calculated by using an output equation of the electrochemical cell.
S135: and obtaining an estimated value of the error covariance matrix according to the error covariance matrix estimation equation.
The error covariance matrix estimation equation is:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″ (44)
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 th moment, and Id is the unit matrix.
S135: and obtaining an estimated value of the state quantity according to the state quantity estimation equation.
The state quantity estimation equation is:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1) (45)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time. x (k + 1)' comprises
Figure BDA0002793571710000181
And Qi(k + 1)', i takes the values of 1, … … and N, and N is more than or equal to 2.
Figure BDA0002793571710000182
Is the estimated value of the SOC of the electrochemical cell at the k +1 time. Qi(k + 1)' for electrochemical cellsThe estimate of the ith state parameter at time k + 1. Therefore, after obtaining the estimated value of the state quantity, the estimated value of the SOC of the electrochemical cell is also obtained.
Repeating the steps from (38) to (45) can continuously update the estimated value of the SOC of the electrochemical cell to realize SOC estimation.
For electrochemical cells, the ohmic internal resistance of the cell and the functional relationship between the open-circuit voltage and the SOC can be obtained by HPPC (Hybrid pulse power characteristics) testing. The exchange current density can be measured by linear polarization. The parameter tau can be identified by using a standard charge-discharge curve of the electrochemical cell and adopting a genetic algorithm. The genetic algorithm is a self-adaptive global optimization search algorithm, and the root mean square error between the model terminal voltage and the actually measured voltage is used as the optimization evaluation standard of the genetic algorithm. And identifying the model parameter tau by setting the population number and the iteration number and setting the upper limit and the lower limit of the variation of the parameter. The parameters of the obtained specific battery model are shown in table 3. The open circuit voltage measured by the battery as a function of SOC is shown in fig. 2, and the input current curve in the experiment is shown in fig. 3.
Parameter values in the model of Table 3
Qcell,0 12Ah Rohm 10Ω
τ 1017 I0 1.023A
SOCcell,0 0.3797
The voltage simulation result of the cell model is shown in fig. 4, and it can be seen that the model has high precision and the error is less than 5 mV. The SOC curve obtained by using this SOC estimation method is shown in fig. 5, and it can be seen that the accuracy of the SOC estimation algorithm can reach 1%.
While, for purposes of simplicity of explanation, the foregoing method embodiments have been described as a series of acts or combination of acts, it will be appreciated by those skilled in the art that the present invention is not limited by the illustrated ordering of acts, as some steps may occur in other orders or concurrently with other steps in accordance with the invention.
The following are embodiments of the apparatus of the present invention that may be used to perform embodiments of the method of the present invention. For details which are not disclosed in the embodiments of the apparatus of the present invention, reference is made to the embodiments of the method of the present invention.
Referring to fig. 6, the present embodiment provides a battery SOC estimation apparatus, which includes: a first acquisition unit 61, a second acquisition unit 62 and a kalman filtering unit 63.
A first obtaining unit 61 for obtaining the equation of state of the electrochemical cell.
The state equation for an electrochemical cell is:
Figure BDA0002793571710000191
Figure BDA0002793571710000192
wherein the content of the first and second substances,
Figure BDA0002793571710000193
is the electrochemical cell SOC at time k +1,
Figure BDA0002793571710000194
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure BDA0002793571710000195
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1). Electrochemical cells are cells of electrochemical systems based on ion diffusion characteristics. The electrochemical cell may be a lithium ion cell or a nickel hydride cell, but is not limited thereto.
A second obtaining unit 62 for obtaining an output equation of the electrochemical cell.
The output equation for an electrochemical cell is:
Figure BDA0002793571710000196
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure BDA0002793571710000197
for electrochemical cells at a particle concentration of
Figure BDA0002793571710000198
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell.
And the filtering unit 63 is configured to obtain an estimated value of the SOC of the electrochemical cell by using a preset filtering algorithm based on the state equation and the output equation of the electrochemical cell.
The preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value.
In some embodiments, the predetermined filtering algorithm is a kalman filtering algorithm. A filtering unit 63, comprising: the device comprises a state quantity prediction unit, an error covariance matrix prediction unit, a gain matrix calculation unit, a terminal voltage updating unit, an error covariance matrix estimation unit and a state quantity estimation unit.
And the state quantity prediction unit is used for obtaining the predicted value of the state quantity according to the state quantity prediction equation.
The state quantity prediction equation is as follows:
Figure BDA0002793571710000201
Figure BDA0002793571710000202
Figure BDA0002793571710000203
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure BDA0002793571710000204
is an estimate of the electrochemical cell SOC at time k, Qi(k) Is an electrochemical cellAnd the estimated value of the ith state parameter at the kth moment, wherein A is a state transition matrix.
And the error covariance matrix prediction unit is used for obtaining a prediction value of the error covariance matrix according to the error covariance matrix prediction equation.
The error covariance matrix prediction equation is:
P(k+1)″＝A·P(k)′·AT+Q(k)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure BDA0002793571710000211
and the gain matrix calculation unit is used for obtaining a gain matrix according to the gain matrix equation.
The gain matrix equation is:
K(k+1)＝P(k+1)″·C(k+1)·(C(k+1)T·P(k+1)″·C(k+1)+R(k+1))-1
Figure BDA0002793571710000212
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure BDA0002793571710000213
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000221
to SOC-X＝1To pair
Figure BDA0002793571710000222
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure BDA0002793571710000223
in order to provide a SOC for an electrochemical cell,
Figure BDA0002793571710000224
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiIs the ith state parameter of the electrochemical cell.
And the terminal voltage updating unit is used for updating an equation according to the terminal voltage to obtain an updated terminal voltage.
The terminal voltage update equation is:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and VmeasureAnd (k +1) is a measured value of the terminal voltage of the electrochemical cell at the k +1 th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the k +1 th moment calculated by using an output equation of the electrochemical cell.
And the error covariance matrix estimation unit is used for estimating an equation according to the error covariance matrix to obtain an estimation value of the error covariance matrix.
The error covariance matrix estimation equation is:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 th moment, and Id is the unit matrix.
And the state quantity estimation unit is used for obtaining the estimation value of the state quantity according to the state quantity estimation equation.
The state quantity estimation equation is:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The embodiments in the present description are mainly described as different from other embodiments, the same and similar parts in the embodiments may be referred to each other, and the features described in the embodiments in the present description may be replaced with each other or combined with each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A battery SOC estimation method, comprising:
acquiring a state equation of an electrochemical cell, wherein the electrochemical cell is a cell of an electrochemical system based on ion diffusion characteristics, and the state equation of the electrochemical cell is as follows:
Figure FDA0002793571700000011
Figure FDA0002793571700000012
wherein the content of the first and second substances,
Figure FDA0002793571700000013
is the electrochemical cell SOC at time k +1,
Figure FDA0002793571700000014
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure FDA0002793571700000015
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the ith state of the electrochemical cell at time k +1State parameter, Qi(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1);
obtaining an output equation of the electrochemical cell, the output equation of the electrochemical cell being:
Figure FDA0002793571700000016
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure FDA0002793571700000017
for electrochemical cells at a particle concentration of
Figure FDA0002793571700000018
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell;
analyzing by adopting a preset filtering algorithm based on a state equation and an output equation of the electrochemical cell to obtain an estimated value of the SOC of the electrochemical cell; the preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value.
2. The battery SOC estimation method according to claim 1, wherein the preset filter algorithm is a kalman filter algorithm;
the method for obtaining the estimated value of the SOC of the electrochemical battery by adopting a preset filtering algorithm based on the state equation and the output equation of the electrochemical battery comprises the following steps:
obtaining a predicted value of the state quantity according to a state quantity prediction equation, wherein the state quantity prediction equation is as follows:
Figure FDA0002793571700000021
Figure FDA0002793571700000022
Figure FDA0002793571700000023
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure FDA0002793571700000024
is an estimate of the electrochemical cell SOC at time k, Qi(k) ' is an estimated value of the ith state parameter of the electrochemical cell at the kth time, and A is a state transition matrix;
obtaining a predicted value of the error covariance matrix according to an error covariance matrix prediction equation, wherein the error covariance matrix prediction equation is as follows:
P(k+1)″＝AP(k)′·AT+Q(k)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure FDA0002793571700000025
obtaining a gain matrix according to a gain matrix equation, wherein the gain matrix equation is as follows:
K(k+1)＝P(k+1)″·C(k+1)·(C(k+1)T·P(k+1)″·C(k+1)+R(k+1))-1
Figure FDA0002793571700000031
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure FDA0002793571700000032
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure FDA0002793571700000033
to SOC-X＝1To pair
Figure FDA0002793571700000034
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure FDA0002793571700000035
in order to provide a SOC for an electrochemical cell,
Figure FDA0002793571700000036
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiIs the ith state parameter of the electrochemical cell;
obtaining an updated terminal voltage according to a terminal voltage updating equation, wherein the terminal voltage updating equation is as follows:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and Vmeasure(k +1) is a measured value of the terminal voltage of the electrochemical cell at the (k +1) th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the (k +1) th moment calculated by using the output equation;
obtaining an estimation value of an error covariance matrix according to an error covariance matrix estimation equation, wherein the error covariance matrix estimation equation is as follows:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 moment, and Id is a unit matrix;
obtaining an estimated value of the state quantity according to a state quantity estimation equation, wherein the state quantity estimation equation is as follows:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time.
3. The battery SOC estimation method according to claim 1, wherein the value of N is 4.
4. The battery SOC estimation method according to claim 1, wherein a is obtained by using a genetic iterative algorithm in advanceiAnd bi。
5. The method for estimating the SOC of a battery according to any one of claims 1 to 4, wherein the electrochemical cell is specifically: lithium ion batteries or nickel metal hydride batteries.
6. A battery SOC estimation device, characterized by comprising:
the first obtaining unit is used for obtaining a state equation of an electrochemical cell, wherein the electrochemical cell is a cell of an electrochemical system based on ion diffusion characteristics, and the state equation of the electrochemical cell is as follows:
Figure FDA0002793571700000041
Figure FDA0002793571700000042
wherein the content of the first and second substances,
Figure FDA0002793571700000043
is the electrochemical cell SOC at time k +1,
Figure FDA0002793571700000044
is the SOC of the electrochemical cell at time k, I (k) is the value of the current flowing through the electrochemical cell at time k, Qcell,0Δ t is the time difference between the k +1 th and the k th time, w, which is the standard capacity of the electrochemical cell1(k) Is that
Figure FDA0002793571700000045
I takes values of 1, … … and N, N is not less than 2, Qi(k +1) is the i-th state parameter, Q, of the electrochemical cell at time k +1i(k) Is the i-th state parameter, a, of the electrochemical cell at the k-th point in timeiOptimizing the parameters for the ith molecule, biOptimizing the parameter for the ith denominator, tau is the diffusion characteristic parameter of the electrochemical cell, wi+1(k) Is Qi(k) The process noise of (1);
a second obtaining unit, configured to obtain an output equation of the electrochemical cell, where the output equation of the electrochemical cell is:
Figure FDA0002793571700000046
wherein V (k +1) is the terminal voltage of the electrochemical cell at time k +1,
Figure FDA0002793571700000051
for electrochemical cells at a particle concentration of
Figure FDA0002793571700000052
Open circuit voltage of time, RohmIs the ohmic internal resistance, R, of the electrochemical cell0For an ideal gas constant, T is the temperature of the electrochemical cell, F is the Faraday constant, I0J (k) is the system measurement noise at time k, which is the exchange current density of the electrochemical cell;
the filtering unit is used for analyzing and obtaining an estimated value of the SOC of the electrochemical battery by adopting a preset filtering algorithm based on a state equation and an output equation of the electrochemical battery; the preset filtering algorithm is a filtering algorithm for obtaining an estimated value by combining the measured value and the predicted value.
7. The battery SOC estimation device according to claim 6, wherein the preset filter algorithm is a kalman filter algorithm;
the filtering unit includes:
the state quantity prediction unit is used for obtaining a predicted value of the state quantity according to a state quantity prediction equation, wherein the state quantity prediction equation is as follows:
Figure FDA0002793571700000053
Figure FDA0002793571700000054
Figure FDA0002793571700000055
wherein x (k +1) "is the predicted value of the state quantity at the k +1 th time, x (k)' is the estimated value of the state quantity at the k th time,
Figure FDA0002793571700000061
is an estimate of the electrochemical cell SOC at time k, Qi(k) ' is an estimated value of the ith state parameter of the electrochemical cell at the kth time, and A is a state transition matrix;
the error covariance matrix prediction unit is used for obtaining a prediction value of the error covariance matrix according to an error covariance matrix prediction equation, wherein the error covariance matrix prediction equation is as follows:
P(k+1)″＝A·P(k)′·AT+Q(k)
wherein P (k +1) "is the predicted value of the error covariance matrix at the k +1 th time, P (k)' is the estimated value of the error covariance matrix at the k th time, Q (k) is W (k) the covariance matrix at the k th time, ATIs the transposed matrix of A, W (k) is:
Figure FDA0002793571700000062
the gain matrix calculation unit is used for obtaining a gain matrix according to a gain matrix equation, wherein the gain matrix equation is as follows:
Figure FDA0002793571700000063
wherein K (K +1) is the gain matrix at the K +1 th moment, C (K +1) is the Jacobian matrix at the K +1 th moment, C (K +1)TIs the transposed matrix of C (k +1), R (k +1) is the covariance matrix of J (k +1), J (k +1) is the system measurement noise at the k +1 th moment, (C (k +1)T·P(k+1)″·C(k+1)+R(k+1))-1Is C (k +1)TInverse matrix of P (k + 1)'. C (k +1) + R (k +1), EOCV(SOC|X＝1) Open circuit voltage vs. SOC for electrochemical cellX＝1X is a normalized variable of the radial length of the electrochemical cell particles, SOCX＝1Is the SOC of the particle surface of the electrochemical cell, SOC (k +1) & ltY & gtX＝1The SOC of the surface of the particles of the electrochemical cell at time k +1,
Figure FDA0002793571700000071
is EOCV(SOC|X＝1) To SOC-X＝1The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure FDA0002793571700000072
to SOC-X＝1To pair
Figure FDA0002793571700000073
The partial derivative is calculated and the partial derivative value at the k +1 th time is calculated,
Figure FDA0002793571700000074
in order to provide a SOC for an electrochemical cell,
Figure FDA0002793571700000075
to SOC-X＝1To QiThe partial derivative is calculated and the partial derivative value Q at the k +1 th timeiIs the ith state parameter of the electrochemical cell;
the terminal voltage updating unit is used for obtaining an updated terminal voltage according to a terminal voltage updating equation, and the terminal voltage updating equation is as follows:
ΔV(k+1)＝Vmeasure(k+1)-V(k+1)
wherein, Δ V (k +1) is the difference between the measured value and the predicted value of the terminal voltage of the electrochemical cell at the k +1 th time, and Vmeasure(k +1) is a measured value of the terminal voltage of the electrochemical cell at the (k +1) th moment, and V (k +1) is a predicted value of the terminal voltage of the electrochemical cell at the (k +1) th moment calculated by using the output equation;
the error covariance matrix estimation unit is used for obtaining an estimation value of an error covariance matrix according to an error covariance matrix estimation equation, wherein the error covariance matrix estimation equation is as follows:
P(k+1)′＝(Id-K(k+1)·C(k+1))·P(k+1)″
wherein, P (k + 1)' is the estimated value of the error covariance matrix at the k +1 moment, and Id is a unit matrix;
the state quantity estimation unit is used for obtaining an estimation value of the state quantity according to a state quantity estimation equation, wherein the state quantity estimation equation is as follows:
x(k+1)′＝x(k+1)″+K(k+1)·ΔV(k+1)
where x (k + 1)' is an estimated value of the state quantity at the k +1 th time.
8. The battery SOC estimation device according to claim 6, wherein the value of N is 4.
9. The battery SOC estimation apparatus according to claim 6, wherein a is obtained in advance using a genetic iterative algorithmiAnd bi。
10. The battery SOC estimation device according to any one of claims 6 to 9, wherein the electrochemical cell is specifically: lithium ion batteries or nickel metal hydride batteries.
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