CN110888056A - Online SOC observer building method and system suitable for vehicle-mounted power lithium ion battery - Google Patents

Online SOC observer building method and system suitable for vehicle-mounted power lithium ion battery Download PDF

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CN110888056A
CN110888056A CN201911142644.3A CN201911142644A CN110888056A CN 110888056 A CN110888056 A CN 110888056A CN 201911142644 A CN201911142644 A CN 201911142644A CN 110888056 A CN110888056 A CN 110888056A
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张希
程麒豫
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Shanghai Jiaotong University
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    • G—PHYSICS
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    • 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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
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    • B60L58/12—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries responding to state of charge [SoC]
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    • 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
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Abstract

The invention provides a method and a system for building an online SOC observer suitable for a vehicle-mounted power lithium ion battery, wherein the method comprises the following steps: step M1: constructing an SPMe function model, and acquiring SPMe function model information; step M2: setting a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation; step M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution; step M4: the concentration of the lithium ions on the surface of the cathode is reversely solved through the output voltage and is respectively input into a cathode/anode lithium ion concentration progressive state observer; step M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information. The invention is suitable for the dynamic change of the battery characteristic, and has the advantages of high battery model precision, high convergence speed, stability and reliability.

Description

Online SOC observer building method and system suitable for vehicle-mounted power lithium ion battery
Technical Field
The invention relates to the technical field of electrolyte power, in particular to a method and a system for building an online SOC observer suitable for a vehicle-mounted power lithium ion battery.
Background
With the shift of energy consumption concept brought by greenhouse effect and energy loss to people, the automobile industry gradually shifts to automobile electromotion. BMS is very important for electric vehicles that are hot when a fire is dropped. In BMS, accurate estimation of SOC is a critical part of this. Accurate SOC estimation results can be used as important criteria for power battery pack charge and discharge control, battery equalization management, thermal management, and the like. In addition, the accuracy of SOC estimation will also directly affect the accuracy of subsequent SOH, SOP, etc. estimation, as well as the accuracy of the vehicle control strategy. Therefore, an accurate power battery SOC estimation model is built, real-time online simulation analysis is carried out, and the method plays an important role in prolonging the service life of the battery and knowing the health state of the battery in real time. However, the SOC is used as a control judgment basis for the whole electric vehicle, and no matter the internal and external factors affect the accuracy of the result, the result deviates from the actual value of the SOC to a certain extent, and the external conditions are as follows: temperature, charge and discharge rate, etc. Internal conditions such as the degree of aging of the battery, etc. Moreover, the dynamic change of the electric vehicle in different working conditions is very large, so that the SOC estimation accuracy of the battery is still difficult to guarantee until now. At present, the construction methods of power battery models at home and abroad mainly focus on two categories. One of the categories is an equivalent circuit model, which includes (1) Rint model: the model ignores the existence of polarization internal resistance, and considers the values of current and voltage as fixed in the whole working process of the battery. Therefore, the Rint model has low precision, is suitable for being applied under an ideal stable working condition, but is not suitable for a road running working condition changing in real time to carry out subsequent real-time simulation; (2) RC equivalent circuit model: the RC circuit equivalent model cannot accurately track the SOC and perform accurate response analysis, so that the RC circuit equivalent model is not suitable for SOC online estimation simulation of the lithium ion battery; (3) a PNGV equivalent circuit model; (4) thevenin equivalent circuit model. Another category is electrochemical models, which include: (1) SPM model: the model regards the interior of the battery as two spherical particles, neglects the influence of the battery electrolyte on the output voltage, provides a partial differential equation of material conservation and charge conservation of the solid-phase electrode, describes the even-sum relation of state variables by a Butler-Volume equation, and simplifies certain boundary conditions and input conditions. (2) SPMe model: on the basis of an SPM model, considering the influence of electrolyte on output voltage, and providing a partial differential equation of material conservation and charge conservation of liquid-phase electrolyte; (3) a DFN model; and (3) describing the internal dynamics of the battery by considering partial differential equations of solid-liquid phase material conservation and charge conservation without any simplification. In addition, the SOC estimation method of the power battery at home and abroad mainly comprises the following steps: (1) discharge test method: the calculation was performed after constant current discharge of the cell. The method is the simplest one of all estimation methods, but needs a large amount of standing and measuring time, and a discharge experiment method can only be used for testing under an off-line condition and cannot meet the on-line test of real-time change working conditions of the electric automobile, so that the discharge experiment method cannot be used for carrying out experiments in the process of on-line SOC estimation simulation of the electric automobile. (2) An ampere-hour integration method: the whole battery is taken as a closed system, in addition, in the whole experiment process, the electrochemical reaction in the battery monomer is ignored, and all the physical parameters are regarded as irrelevant and exist independently. And recording the capacity change of the battery within a period of time, and obtaining the residual capacity of the battery at the moment by subtracting from the initial value. However, in the whole experiment process of the ampere-hour integration method, the electrochemical reaction in the battery cell is ignored, and each physical parameter is regarded as irrelevant and exists independently, so that the battery system becomes an open-loop system, and the instantaneous value of the charging current is affected by a plurality of external factors, so that the estimation accuracy of the method is still not high enough. Therefore, in practical applications, the ampere-hour integration method is usually combined with other methods to perform experiments. (3) Open circuit voltage method: after the battery is sufficiently left, the open-circuit voltage Uoc and the SOC can be expressed by a certain functional relationship. Therefore, the SOC value corresponding to the battery in the current state can be found according to the fitted functional relation after the open-circuit voltage after the battery is kept still for a long time is collected. The open circuit voltage method is simple in principle and difficult to operate practically. However, since the whole experiment must wait until the terminal voltage of the battery is in a stable state before the measurement can be started, it takes a long time; in addition, when the electric vehicle runs under a real-time working condition, the condition that the battery pack is kept still for a long time cannot be guaranteed, and stable terminal voltage cannot be obtained, so that the method cannot perform simulation estimation on the SOC of the electric vehicle under the actual working condition, but the method can be combined with other methods for performing experiments. (4) Kalman filtering method: and continuously iterating by updating the weights of the estimated value and the observed value on line, thereby sequentially circulating and recurrently, finally combining the required result precision requirement, and interrupting the circulation timely to obtain the final required estimated value. (5) And (4) an observer method for establishing an observer to carry out online estimation on the SOC. Is the method to which this patent relates. In practical application, the existing battery SOC estimation methods have certain inconvenience and defects to different degrees, so further innovation is necessary. The observer method has better error correction capability and noise resistance capability, and the precision of the observer method obviously depends on the precision of the battery model. Therefore, the method selects the SPMe model based on high precision, reduces the calculated amount of a computer as much as possible, designs an SOC progressive observer and carries out online estimation on the SOC.
Patent document CN106918789B discloses a SOC-SOH joint online real-time estimation and online correction method, which includes: the SOC hardware pre-estimation module converts a large current signal into a low voltage signal by using a Hall current sensor, carries out noise filtering on the signal through a band-pass filter, then sends the filtered signal into an RC integrator to indirectly realize integration of the current signal, and sends an integrated signal acquired by the ADC to the MCU chip to realize correction; the lithium battery equivalent circuit parameter correction module comprises a square wave pulse switch current source and a controllable electronic load, the square wave pulse switch current source or the controllable electronic load is used for carrying out charging or discharging tests on a lithium battery pack, the ADC is used for collecting the terminal voltage of the battery pack, and parameters of a battery equivalent model in the charging or discharging process are corrected according to the input response of a charging or discharging curve. The patent is not well applicable to on-line SOC observation of the vehicle-mounted power lithium ion battery.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for building an online SOC observer suitable for a vehicle-mounted power lithium ion battery.
According to the method for building the on-line SOC observer suitable for the vehicle-mounted power lithium ion battery, the on-line identification is carried out on the internal state variable of the battery by building the SPMe electrochemical function model and designing the progressive observer based on the SPMe electrochemical function model so as to obtain the relation of the change of the concentration of the cathode lithium ions along with the time, and finally the on-line estimation is carried out on the SOC through the definition formula. The method estimates the SOC of the lithium ion battery from the level of the reaction mechanism, thereby improving the estimation precision of the SOC. The method can be widely applied to the field of electric vehicles and energy storage battery management systems. It is characterized by comprising: step M1: obtaining the simplified SPMe function model by a series of reliability assumptions and by introducing mathematical methods such as a finite difference method, a laplace transformation method and the like, and then deriving to obtain the SPMe function model information; step M2: setting a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation; step M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution; step M4: the lithium ion concentration on the surface of the cathode is reversely solved by the output voltage by using a least square method, and the lithium ion concentration is respectively input into a cathode/anode lithium ion concentration progressive state observer; step M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information.
Preferably, the step 1 comprises: step 1.1: according to the lithium ion battery P2D model (which is the most classical model), the following assumptions are made: (1) the internal state quantity of the lithium ion battery is uniformly distributed in the longitudinal direction; (2) two solid-phase poles of the lithium ion battery are considered as two spheres which are uniformly distributed, and the state quantity of the solid phase is changed only in the radial direction r of the spheres; (3) the lithium ion battery liquid phase state quantity varies along the horizontal x direction. And (3) performing finite difference method on the lithium ion battery solid Fick second law equation in the r direction, and performing laplace transformation on the liquid phase potential equation in the x direction, thereby obtaining SPMe function model information.
The solved functions of the terms are:
(1) solving a solid phase diffusion equation:
Figure BDA0002281374720000041
Figure BDA0002281374720000042
Figure BDA0002281374720000043
Figure BDA0002281374720000044
Figure BDA0002281374720000045
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
(2) Solving a liquid phase diffusion equation:
Figure BDA0002281374720000046
wherein Cen (x, s)/Jn(s), Cep (x, s)/Jp(s) are expressed as follows:
Figure BDA0002281374720000047
K＝-2Lm-Lp+Ln
Figure BDA0002281374720000048
K＝2Lm-Lp+Ln
wherein Ln, Lm, Ln and A are respectively the thickness of a negative electrode plate, the thickness of a diaphragm, the thickness of a positive electrode plate and the surface area of the electrode plate, and are obtained by the measurement of a battery disassembling experiment;
r is a gas constant and is 3.14J/molK;
f is a Faraday constant, and 96345 Coolumbs/mol is taken;
t is the experimental temperature, and 298.15K is taken;
t0+ is the ion conversion coefficient, and is 0.363;
kneffkmeffkpeff is the liquid phase conductivity, where:
ki eff＝kεei 1.5i ═ n/m/p, k is the liquid phase conductivity at the reference temperature, obtained from literature;
εe n,εe pthe liquid phase volume coefficients of the negative electrode and the positive electrode are obtained by looking up documents;
Dep eff,Den effrespectively positive and negative liquid phase diffusion coefficients, and Dei eff＝Deεei 1.5And i is n/p, and De is a standard liquid phase diffusion coefficient obtained from the literature.
Step 1.2: according to a solid phase diffusion equation simplified by a finite difference method, the design of the Roeberg observer is carried out, wherein the selection of a feedback matrix G of the Roeberg observer needs to be manually selected, the selection condition is that characteristic values of the A-GC all have negative real parts, and the output error of the A-GC gradually converges to 0.
Preferably, the step M2 includes: step M2.1: according to the observability judgment result information (the observability judgment result information comprises an observability matrix O of the solid phase diffusion equation simplified by the finite difference method, controllability judgment result information and a controllability matrix C, if the matrix O and the matrix C are of full rank, the equation is controllable and observable, and the observability matrix is [ C C AC A2C*A3...C*A(n-1)]T(ii) a The controllability matrix is: c ═ B, A, B, A2*B,A3*B...A(n-1)*B]) And obtaining feedback progressive observation result information. Step M2.2: according to the equation
Figure BDA0002281374720000051
Wherein, csIs the solid-phase lithium ion concentration, cs,surAs the concentration j of lithium ions on the solid phase surfaceLiFor the intercalation reaction rate of lithium ions, the A, B, C and D matrixes are formed by finite differenceThe simplified matrix has the expression:
Figure BDA0002281374720000052
Figure BDA0002281374720000053
Figure BDA0002281374720000061
Figure BDA0002281374720000062
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
Introducing a state feedback matrix G, and obtaining a state observer equation as follows:
Figure BDA0002281374720000063
wherein for the design of the feedback matrix G, it needs to satisfy: the eigenvalues of the a-GC all have negative real parts, then the asymptotic convergence of the observer can be guaranteed. According to the observed state quantity, the radius of the sphere is taken as Rs, the solid-phase lithium ion concentration information is obtained, and the basis is
Figure BDA0002281374720000064
Wherein R issIs the radius of the solid phase sphere of lithium ion, r is the distance (vector) of each point from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csThe solid-phase lithium ion concentration is obtained from the literature. Thereby obtaining estimation result information of the battery SOC according to the equation.
Preferably, step M1.1 comprises: step M1.1.1: according to the second law equation information of the solid phase Fick, the finite difference method is used for simplification to obtain the concentration c of the solid phase lithium ionss(r, t) information;
step M1.1.2:obtaining the concentration c of the liquid-phase lithium ions through laplace transformation according to the liquid-phase potential equation informatione(L,t)-ce(0, t) information;
preferably, the method further comprises the following steps: step M6: and estimating the temperature of the battery model by adopting a temperature estimation introduction equation.
Figure BDA0002281374720000065
Figure BDA0002281374720000066
Wherein, TambFor the outside temperature, since the battery was operated in the incubator, the constant temperature was set to 298.5K; t is the estimated battery surface temperature; q is the heat generated by the battery; v is the output voltage of the battery, and data are collected by equipment; i is battery input current, and the current operation condition is set manually; rhoaveIs the average density of lithium ion battery, CpIs the specific heat capacity, h is the heat transfer coefficient, obtained from consulting literature; u shapepsoc,Unsoc,Up,UnAs above, the open circuit voltage of the positive and negative electrodes of the battery is given by an empirical formula:
Upsocor Up＝-3.536*tanh(-3.749*x-0.9174)+3.45*exp(-3.81*x)；
UnsocOr Un＝-31.14-12.72*tanh(38.17*x+1.126)+73.05*exp(-6.108*x-5.543)+43.94；
Wherein x is the electrochemical equivalent.
Compared with the prior art, the invention has the following beneficial effects:
the method adopts the SOC observer based on the SPMe model to build, wherein the electrochemical parameters of the battery are obtained by looking up documents; estimating the concentration of the solid-phase lithium ions by adopting a progressive observer; estimating the concentration of the liquid-phase lithium ions by adopting Laplace transformation; the estimated value of the battery SOC is obtained according to a definitional expression. Compared with the traditional state off-line identification method, the estimation method and the estimation system overcome the phenomena of inaccurate initial SOC value and accumulated error in the ampere-hour integration method, are suitable for the dynamic change of the battery characteristics, and have the advantages of high battery model precision, high convergence speed, stability and reliability.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic diagram of the SPMe model of the present invention.
FIG. 2 is a flow chart of the construction of the online SOC observer of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
As shown in fig. 1 and fig. 2, according to the method for constructing the online SOC observer suitable for the vehicle-mounted power lithium ion battery provided by the invention, the internal state variable of the battery is identified online by constructing the SPMe electrochemical function model and designing the progressive observer based on the SPMe function model to obtain the relation of the change of the cathode lithium ion concentration with time, and finally, the SOC is estimated online by the definition formula. The method estimates the SOC of the lithium ion battery from the level of the reaction mechanism, thereby improving the estimation precision of the SOC. The method can be widely applied to the field of electric vehicles and energy storage battery management systems. It is characterized by comprising: step M1: obtaining the simplified SPMe function model by a series of reliability assumptions and by introducing mathematical methods such as a finite difference method, a laplace transformation method and the like, and then deriving to obtain the SPMe function model information; step M2: designing a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation; step M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution; step M4: the lithium ion concentration on the surface of the cathode is reversely solved by the output voltage by using a least square method, and the lithium ion concentration is respectively input into a cathode/anode lithium ion concentration progressive state observer; step M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information.
Preferably, the step 1 comprises: step 1.1: according to the lithium ion battery P2D model, the following assumptions were made: (1) the internal state quantity of the lithium ion battery is uniformly distributed in the longitudinal direction; (2) two solid-phase poles of the lithium ion battery are considered as two spheres which are uniformly distributed, and the state quantity of the solid phase is changed only in the radial direction r of the spheres; (3) the lithium ion battery liquid phase state quantity varies along the horizontal x direction. And (3) performing finite difference method on the solid Fick second law equation in the r direction, and performing laplace transformation on the liquid phase potential equation in the x direction to obtain SPMe function model information.
The solved functions of the terms are:
(1) solving a solid phase diffusion equation:
Figure BDA0002281374720000081
Figure BDA0002281374720000082
Figure BDA0002281374720000083
Figure BDA0002281374720000084
Figure BDA0002281374720000085
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
(2) Solving a liquid phase diffusion equation:
Figure BDA0002281374720000091
wherein Cen (x, s)/Jn(s), Cep (x, s)/Jp(s) are expressed as follows:
Figure BDA0002281374720000092
K＝-2Lm-Lp+Ln
Figure BDA0002281374720000093
K＝2Lm-Lp+Ln
wherein Ln, Lm, Ln and A are respectively the thickness of a negative electrode plate, the thickness of a diaphragm, the thickness of a positive electrode plate and the surface area of the electrode plate, and are obtained by the measurement of a battery disassembling experiment;
r is a gas constant and is 3.14J/molK;
f is a Faraday constant, and 96345 Coolumbs/mol is taken;
t is the experimental temperature, and 298.15K is taken;
t0+ is the ion conversion coefficient, and is 0.363;
kneffkmeffkpeff is the liquid phase conductivity, where:
ki eff＝kεei 1.5
i ═ n/m/p, k is the liquid phase conductivity at the reference temperature, obtained from literature;
εe n,εe pthe liquid phase volume coefficients of the negative electrode and the positive electrode are obtained by looking up documents;
Dep eff,Den effrespectively positive and negative liquid phase diffusion coefficients, and Dei eff＝Deεei 1.5And i is n/p, and De is a standard liquid phase diffusion coefficient obtained from the literature.
Step 1.2: and designing the Longbeige observer according to a solid Fick second law equation simplified by a finite difference method, wherein the selection of a feedback matrix G of the Longbeige observer needs manual selection, the selection condition is that the characteristic values of the A-GC all have negative real parts, and the output error of the A-GC gradually converges to 0.
Preferably, the step M2 includes: step M2.1: according to observability judgment result information (the observability judgment result information comprises an observability matrix O of a solid-phase Fick second law equation simplified by a finite difference method, controllability judgment result information and a controllability matrix C, if the matrix O and the matrix C are full rank, the equation is controllable and observable2CA3...CA(n-1)]T(ii) a The controllability matrix is: c ═ B, AB, A2*B,A3*B...A(n-1)*B]) And obtaining feedback progressive observation result information. Step M2.2: according to the equation
Figure BDA0002281374720000101
Wherein, csIs the solid-phase lithium ion concentration, cs,surAs the concentration j of lithium ions on the solid phase surfaceLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure BDA0002281374720000102
Figure BDA0002281374720000103
Figure BDA0002281374720000104
Figure BDA0002281374720000105
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
Introducing a state feedback matrix G to obtain a state observerThe equation is:
Figure BDA0002281374720000106
wherein for the design of the feedback matrix G, it needs to satisfy: the eigenvalues of the a-GC all have negative real parts, then the asymptotic convergence of the observer can be guaranteed. According to the observed state quantity, the radius of the sphere is taken as Rs, the solid-phase lithium ion concentration information is obtained, and the basis is
Figure BDA0002281374720000107
Wherein R issIs the radius of the solid phase sphere of lithium ion, r is the distance (vector) of each point from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csThe solid-phase lithium ion concentration is obtained from the literature. Thereby obtaining estimation result information of the battery SOC according to the equation.
Preferably, step M1.1 comprises: step M1.1.1: simplifying the equation information according to the second law of the solid phase Fick through a finite difference method to obtain the information of the concentration cs (r, t) of the solid phase lithium ions;
step M1.1.2: obtaining the concentration c of the liquid-phase lithium ions through laplace transformation according to the liquid-phase potential equation informatione(L,t)-ce(0, t) information;
preferably, the method further comprises the following steps: step M6: and estimating the temperature of the battery model by adopting a temperature estimation introduction equation.
Figure BDA0002281374720000111
Figure BDA0002281374720000112
Wherein, TambFor the outside temperature, since the battery was operated in the incubator, the constant temperature was set to 298.5K; t is the estimated battery surface temperature; q is the heat generated by the battery; v is the output voltage of the battery, and data are collected by equipment; i is battery input current, and the current operation condition is set manually; rhoaveIs the average density of lithium ion battery, CpIs the specific heat capacity, h is the heat transfer coefficient,obtained from a reference document; u shapepsoc,Unsoc,Up,UnAs above, the open circuit voltage of the positive and negative electrodes of the battery is given by an empirical formula:
Upsocor Up＝-3.536*tanh(-3.749*x-0.9174)+3.45*exp(-3.81*x)；
UnsocOr Un＝-31.14-12.72*tanh(38.17*x+1.126)+73.05*exp(-6.108*x-5.543)+43.94；
Wherein x is the electrochemical equivalent.
Referring to fig. 2, specifically, in an embodiment, an SOC online observer building method adopts an SPMe module, a solid-phase PDE progressive observer module, a liquid-phase PDE transfer function module, an output voltage inverse solution module, and an SOC estimation module. The method comprises the following specific steps:
constructing an SPMe model according to the DFN model and the introduced hypothesis;
and (3) designing a Longbeige progressive observer for a second law equation of the simple polarized solid phase Fick:
Figure BDA0002281374720000113
wherein, csIs the solid-phase lithium ion concentration of the positive electrode, cs,surIs the lithium ion concentration on the solid phase surface of the positive electrode, jLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure BDA0002281374720000114
Figure BDA0002281374720000115
Figure BDA0002281374720000121
Figure BDA0002281374720000122
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the anode of the lithium ion battery is obtained by consulting documents.
Here, our matrix G is chosen as:
Figure BDA0002281374720000123
wherein r is the radius (vector) from the coordinate point to the sphere center, Rs is the radius of the anode solid phase sphere, and gamma is an artificial set value.
Similarly, designing a feedback progressive observer for the second law equation of the cathode Fick;
Figure BDA0002281374720000124
wherein, csIs the solid-phase lithium ion concentration of the negative electrode, cs,surIs the lithium ion concentration of the solid phase surface of the negative electrode, jLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure BDA0002281374720000125
Figure BDA0002281374720000126
Figure BDA0002281374720000127
Figure BDA0002281374720000128
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery negative electrode is obtained from a reference document.
Wherein, the selection of the matrix P is:
Figure BDA0002281374720000131
wherein r is the radius (vector) from the coordinate point to the sphere center, Rs is the radius of the negative solid phase sphere, and gamma is an artificial set value.
Carrying out Laplace transformation and solving on lithium ion potential (material conservation) equations in the electrolyte in the negative electrode and diaphragm areas of the battery based on corrected boundary conditions to obtain a transfer function of the lithium ion concentration in the electrolyte to the electrochemical reaction rate, wherein the corrected boundary conditions are as follows:
Figure BDA0002281374720000132
Figure BDA0002281374720000133
the transfer function is:
Figure BDA0002281374720000134
K＝-2Lm-Lp+Ln
Figure BDA0002281374720000135
K＝2Lm-Lp+Ln
wherein Ln, Lm, Ln, A are respectively the thickness of the negative electrode plate, the thickness of the diaphragm, the thickness of the positive electrode plate, and the surface of the electrode plate
The product is obtained by measuring a battery disassembling experiment;
r is a gas constant and is 3.14J/molK;
f is a Faraday constant, and 96345 Coolumbs/mol is taken;
t is the experimental temperature, and 298.15K is taken;
t0+ is the ion conversion coefficient, and is 0.363;
kneffkmeffkpeff is the liquid phase conductivity, where:
ki eff＝kεei 1.5
i ═ n/m/p, k is the liquid phase conductivity at the reference temperature, obtained from literature;
εe n,εe pthe liquid phase volume coefficients of the negative electrode and the positive electrode are obtained by looking up documents;
Dep eff,Den effrespectively positive and negative liquid phase diffusion coefficients, and Dei eff＝Deεei 1.5And i is n/p, and De is a standard liquid phase diffusion coefficient obtained from the literature.
According to the formula of definition
Figure BDA0002281374720000141
Wherein R issIs the radius of the solid phase sphere of lithium ion, r is the distance (vector) of each point from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csThe solid-phase lithium ion concentration is obtained from the literature. Thereby obtaining estimation result information of the battery SOC according to the equation.
The method adopts an estimation strategy based on the SOC observer of the SPME electrochemical power battery, wherein a simplified electrochemical model of the battery is obtained through a series of reliability simplification according to five basic diffusion kinetic equations of the battery. The estimated value of the SOC of the battery is an SPMe electrochemical model of the battery and is estimated according to a designed progressive Longeberg observer. Compared with the traditional method for estimating the SOC on line based on the equivalent circuit model, the method has the advantages that the adopted battery model is high in precision, high in convergence speed, stable and reliable.
According to the online SOC observer building system suitable for the vehicle-mounted power lithium ion battery, the SPMe electrochemical function model is built, the progressive observer is designed based on the SPMe function model, the internal state variable of the battery is identified online, the relation of the change of the concentration of the cathode lithium ions along with time is obtained, and finally the SOC is estimated online through a definition formula. The method estimates the SOC of the lithium ion battery from the level of the reaction mechanism, thereby improving the estimation precision of the SOC. The method can be widely applied to the field of electric vehicles and energy storage battery management systems. The method comprises the following steps: module M1: obtaining the simplified SPMe function model by a series of reliability assumptions and by introducing mathematical methods such as a finite difference method, a laplace transformation method and the like, and then deriving to obtain the SPMe function model information; module M2: designing a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation; module M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution; module M4: the lithium ion concentration on the surface of the cathode is reversely solved by the output voltage by using a least square method, and the lithium ion concentration is respectively input into a cathode/anode lithium ion concentration progressive state observer; module M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information.
Preferably, the module 1 comprises: module 1.1: according to the lithium ion battery P2D model, the following assumptions were made: (1) the internal state quantity of the lithium ion battery is uniformly distributed in the longitudinal direction; (2) two solid-phase poles of the lithium ion battery are considered as two spheres which are uniformly distributed, and the state quantity of the solid phase is changed only in the radial direction r of the spheres; (3) the lithium ion battery liquid phase state quantity varies along the horizontal x direction. And (3) performing finite difference method on the solid Fick second law equation in the r direction, and performing laplace transformation on the liquid phase potential equation in the x direction to obtain SPMe function model information.
(1) Solving a solid phase diffusion equation:
Figure BDA0002281374720000151
Figure BDA0002281374720000152
Figure BDA0002281374720000153
Figure BDA0002281374720000154
Figure BDA0002281374720000155
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
(2) Solving a liquid phase diffusion equation:
Figure BDA0002281374720000156
wherein Cen (x, s)/Jn(s), Cep (x, s)/Jp(s) are expressed as follows:
Figure BDA0002281374720000157
K＝-2Lm-Lp+Ln
Figure BDA0002281374720000158
K＝2Lm-Lp+Ln
wherein Ln, Lm, Ln, A are respectively the thickness of the negative electrode plate, the thickness of the diaphragm, the thickness of the positive electrode plate, and the surface of the electrode plate
The product is obtained by measuring a battery disassembling experiment;
r is a gas constant and is 3.14J/molK;
f is a Faraday constant, and 96345 Coolumbs/mol is taken;
t is the experimental temperature, and 298.15K is taken;
t0+ is the ion conversion coefficient, and is 0.363;
kneffkmeffkpeff is the liquid phase conductivity, where:
ki eff＝kεei 1.5
i ═ n/m/p, k is the liquid phase conductivity at the reference temperature, obtained from literature;
εe n,εe pare respectively asThe liquid phase volume coefficients of the negative electrode and the positive electrode are obtained by looking up documents;
Dep eff,Den effrespectively positive and negative liquid phase diffusion coefficients, and Dei eff＝Deεei 1.5And i is n/p, and De is a standard liquid phase diffusion coefficient obtained from the literature.
Module 1.2: and designing the Longbeige observer according to a solid Fick second law equation simplified by a finite difference method, wherein the selection of a feedback matrix G of the Longbeige observer needs manual selection, the selection condition is that the characteristic values of the A-GC all have negative real parts, and the output error of the A-GC gradually converges to 0.
Preferably, said module M2 comprises: module M2.1: according to observability judgment result information (the observability judgment result information comprises an observability matrix O of a solid-phase Fick second law equation simplified by a finite difference method, controllability judgment result information and a controllability matrix C, if the matrix O and the matrix C are full rank, the equation is controllable and observable, and the observability matrix O is 0 ═ C C A C A2C*A3...C*A(n-1)]T(ii) a The controllability matrix is: c ═ B, A, B, A2*B,A3*B...A(n-1)*B]) And obtaining feedback progressive observation result information. Module M2.2: according to the equation
Figure BDA0002281374720000161
Wherein, csIs the solid-phase lithium ion concentration, cs,surAs the concentration j of lithium ions on the solid phase surfaceLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure BDA0002281374720000162
Figure BDA0002281374720000163
Figure BDA0002281374720000171
Figure BDA0002281374720000172
wherein i is 1 or 2, Nr△ r is the difference step length determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained by consulting documents.
Introducing a state feedback matrix G, and obtaining a state observer equation as follows:
Figure BDA0002281374720000173
wherein for the design of the feedback matrix G, it needs to satisfy: the eigenvalues of the a-GC all have negative real parts, then the asymptotic convergence of the observer can be guaranteed. According to the observed state quantity, the radius of the sphere is taken as Rs, the solid-phase lithium ion concentration information is obtained, and the basis is
Figure BDA0002281374720000174
Wherein R issIs the radius of the solid phase sphere of lithium ion, r is the distance (vector) of each point from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csThe solid-phase lithium ion concentration is obtained from the literature. Thereby obtaining estimation result information of the battery SOC according to the equation.
Preferably, the module M1.1 comprises: module M1.1.1: according to the second law equation information of the solid phase Fick, the finite difference method is used for simplification to obtain the concentration c of the solid phase lithium ionss(r, t) information;
module M1.1.2: obtaining the concentration c of the liquid-phase lithium ions through laplace transformation according to the liquid-phase potential equation informatione(L,t)-ce(0, t) information;
preferably, the method further comprises the following steps: module M6: and estimating the temperature of the battery model by adopting a temperature estimation introduction equation.
Figure BDA0002281374720000175
Figure BDA0002281374720000176
Wherein, TambFor the outside temperature, since the battery was operated in the incubator, the constant temperature was set to 298.5K; t is the estimated battery surface temperature; q is the heat generated by the battery; v is the output voltage of the battery, and data are collected by equipment; i is battery input current, and the current operation condition is set manually; rhoaveIs the average density of lithium ion battery, CpIs the specific heat capacity, h is the heat transfer coefficient, obtained from consulting literature; u shapepsoc,Unsoc,Up,UnAs above, the open circuit voltage of the positive and negative electrodes of the battery is given by an empirical formula:
Upsocor Up＝-3.536*tanh(-3.749*x-0.9174)+3.45*exp(-3.81*x)；
UnsocOr Un＝-31.14-12.72*tanh(38.17*x+1.126)+73.05*exp(-6.108*x-5.543)+43.94；
Wherein x is the electrochemical equivalent.
Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, units provided by the present invention as pure computer readable program code, the system and its various devices, modules, units provided by the present invention can be fully implemented by logically programming method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units included in the system for realizing various functions can also be regarded as structures in the hardware component; means, modules, units for performing the various functions may also be regarded as structures within both software modules and hardware components for performing the method.
In the description of the present application, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience in describing the present application and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present application.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (10)

1. The utility model provides a method of constructing online SOC observer suitable for on-vehicle power lithium ion battery which characterized in that includes:
step M1: constructing an SPMe function model, and acquiring SPMe function model information;
step M2: setting a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation;
step M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution;
step M4: the concentration of the lithium ions on the surface of the cathode is reversely solved through the output voltage and is respectively input into a cathode/anode lithium ion concentration progressive state observer;
step M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information.
2. The method for building the on-line SOC observer applied to the vehicle-mounted power lithium ion battery according to claim 1, wherein the step M1 comprises the following steps:
step M1.1: performing finite difference method on the solid Fick second law equation in the r direction, and performing laplace transformation on the liquid phase potential equation in the x direction to obtain SPMe function model information;
step M1.2: and designing the Longbeige observer according to a solid Fick second law equation simplified by a finite difference method, wherein the selection of a feedback matrix G of the Longbeige observer needs manual selection, the selection condition is that the characteristic values of the A-GC all have negative real parts, and the output error of the A-GC gradually converges to 0.
3. The method for building the on-line SOC observer applied to the vehicle-mounted power lithium ion battery according to claim 1, wherein the step M2 comprises the following steps:
step M2.1: obtaining feedback progressive observation result information according to the observability judgment result information;
step M2.2: according to the equation
Figure FDA0002281374710000011
Wherein, csIs the solid-phase lithium ion concentration, cs,surIs the lithium ion concentration on the solid phase surface, jLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure FDA0002281374710000021
Figure FDA0002281374710000022
Figure FDA0002281374710000023
Figure FDA0002281374710000024
wherein i is 1 or 2, Nr△ r is the difference step size, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained;
to introduce the state feedback matrix G, the equation of the state observer is obtained as:
Figure FDA0002281374710000025
wherein for the design of the feedback matrix G, it needs to satisfy: the characteristic values of the A-GC all have negative real parts, so that the progressive convergence of the observer can be ensured; thereby obtaining the radius of the sphere as R according to the observed state quantitysAnd obtaining the solid-phase lithium ion concentration information according to the following steps:
Figure FDA0002281374710000026
wherein R issThe radius of the solid phase sphere of lithium ion, the distance of each point of r from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csIs the solid phase lithium ion concentration; thereby obtaining estimation result information of the battery SOC according to the equation.
4. The method for building the on-line SOC observer applied to the vehicle-mounted power lithium ion battery according to claim 1, wherein the step M1.1 comprises:
step M1.1.1: according to the second law equation information of the solid phase Fick, the finite difference method is used for simplification to obtain the concentration c of the solid phase lithium ionss(r, t) information;
step M1.1.2: obtaining the concentration c of the liquid-phase lithium ions through laplace transformation according to the liquid-phase potential equation informatione(L,t)-ce(0, t) information.
5. The method for building the on-line SOC observer applied to the vehicle-mounted power lithium ion battery according to claim 1, further comprising:
step M6: estimating the temperature of the battery model by adopting a temperature estimation introduction equation, wherein the temperature estimation introduction equation is as follows:
Figure FDA0002281374710000031
Figure FDA0002281374710000032
wherein, TambFor the outside temperature, since the battery was operated in the incubator, the constant temperature was set to 298.5K; t is the estimated battery surface temperature; q is the heat generated by the battery; v is the output voltage of the battery, and data are collected by equipment; i is battery input current, and the current operation condition is set manually; rhoaveIs the average density of lithium ion battery, CpIs the specific heat capacity, and h is the heat transfer coefficient; u shapepsoc,UnsocThe open-circuit voltage of the anode and the cathode of the battery is given by an empirical formula:
Up＝-3.536*tanh(-3.749*x-0.9174)+3.45*exp(-3.81*x)；
Un＝-31.14-12.72*tanh(38.17*x+1.126)+73.05*exp(-6.108*x-5.543)+43.94；
wherein x is the electrochemical equivalent;
the step M6 is located between step M1 and step M2.
6. The utility model provides a system is built to online SOC observer suitable for on-vehicle power lithium ion battery which characterized in that includes:
module M1: constructing an SPMe function model, and acquiring SPMe function model information;
module M2: setting a cathode/anode lithium ion concentration progressive observer through a simplified cathode/anode Fick second law equation;
module M3: performing Laplace transformation on the simplified electrolyte potential equation and then solving the electrolyte concentration distribution;
module M4: the concentration of the lithium ions on the surface of the cathode is reversely solved through the output voltage and is respectively input into a cathode/anode lithium ion concentration progressive state observer;
module M5: and based on the SPMe function model, carrying out online estimation on the SOC according to the SOC definition formula to obtain online SOC observation result information.
7. The on-line SOC observer building system suitable for on-vehicle power lithium ion battery of claim 6, wherein the module M1 comprises:
module M1.1: performing finite difference method on the solid Fick second law equation in the r direction, and performing laplace transformation on the liquid phase potential equation in the x direction to obtain SPMe function model information;
module M1.2: and designing the Longbeige observer according to a solid Fick second law equation simplified by a finite difference method, wherein the selection of a feedback matrix G of the Longbeige observer needs manual selection, the selection condition is that the characteristic values of the A-GC all have negative real parts, and the output error of the A-GC gradually converges to 0.
8. The on-line SOC observer building system suitable for on-vehicle power lithium ion battery of claim 6, wherein the module M2 comprises:
module M2.1: obtaining feedback progressive observation result information according to the observability judgment result information;
module M2.2: according to the equation
Figure FDA0002281374710000041
Wherein, csIs the solid-phase lithium ion concentration, cs,surAs the concentration j of lithium ions on the solid phase surfaceLiFor the lithium ion intercalation reaction rate, the A, B, C and D matrixes are simplified by a finite difference method, and the expression is as follows:
Figure FDA0002281374710000042
Figure FDA0002281374710000043
Figure FDA0002281374710000044
Figure FDA0002281374710000045
wherein i is 1 or 2, NrIs the number of differential nodes△ r is the difference step size, determined by human, DsThe solid phase diffusion coefficient of the lithium ion battery is obtained;
introducing a state feedback matrix G, and obtaining a state observer equation as follows:
Figure FDA0002281374710000046
wherein for the design of the feedback matrix G, it needs to satisfy: the characteristic values of the A-GC all have negative real parts, so that the progressive convergence of the observer can be ensured; thereby obtaining the radius of the sphere as R according to the observed state quantitysObtaining the information of the concentration of the solid-phase lithium ions based on
Figure FDA0002281374710000047
Wherein R issThe radius of the solid phase sphere of lithium ion, the distance of each point of r from the center of the sphere, cs,maxIs the maximum lithium ion concentration in the solid phase, csIs the solid phase lithium ion concentration; thereby obtaining estimation result information of the battery SOC according to the equation.
9. The on-line SOC observer building system suitable for on-vehicle power lithium ion battery of claim 6, characterized in that module M1.1 includes:
module M1.1.1: according to the second law equation information of the solid phase Fick, the finite difference method is used for simplification to obtain the concentration c of the solid phase lithium ionss(r, t) information;
module M1.1.2: obtaining the concentration c of the liquid-phase lithium ions through laplace transformation according to the liquid-phase potential equation informatione(L,t)-ce(0, t) information.
10. The on-line SOC observer building system suitable for the vehicle-mounted power lithium ion battery according to claim 6, further comprising:
module M6: estimating the temperature of the battery model by adopting a temperature estimation introduction equation, wherein the temperature estimation introduction equation is as follows:
Figure FDA0002281374710000051
Figure FDA0002281374710000052
wherein, TambFor the outside temperature, since the battery was operated in the incubator, the constant temperature was set to 298.5K; t is the estimated battery surface temperature; q is the heat generated by the battery; v is the output voltage of the battery, and data are collected by equipment; i is battery input current, and the current operation condition is set manually; rhoaveIs the average density of lithium ion battery, CpIs the specific heat capacity, and h is the heat transfer coefficient; u shapepsoc,Unsoc,Up,UnThe open-circuit voltage of the anode and the cathode of the battery is given by an empirical formula:
Upsocor Up＝-3.536*tanh(-3.749*x-0.9174)+3.45*exp(-3.81*x)；
UnsocOr Un＝-31.14-12.72*tanh(38.17*x+1.126)+73.05*exp(-6.108*x-5.543)+43.94；
Wherein x is the electrochemical equivalent;
the module M6 is located between module M1 and module M2.
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