CN113176503B - Full SOC range lithium ion battery equivalent model based on electrochemical process - Google Patents

Full SOC range lithium ion battery equivalent model based on electrochemical process Download PDF

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CN113176503B
CN113176503B CN202110443302.6A CN202110443302A CN113176503B CN 113176503 B CN113176503 B CN 113176503B CN 202110443302 A CN202110443302 A CN 202110443302A CN 113176503 B CN113176503 B CN 113176503B
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battery
soc
lithium ion
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ion battery
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CN113176503A (en
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王大方
杨博文
金毅
张齐
汪井威
李旭
郝自伟
董浩崧
张毕
孙旭
陈仕钦
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Weihai Tianda Automobile Technology Co ltd
Harbin Institute of Technology Weihai
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
    • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements
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Abstract

A full SOC range lithium ion battery equivalent model based on electrochemical process relates to the field of lithium ion battery equivalent models and comprises a capacitor Ccapacity、Cds1、Cds2Resistance Rds1、Rds2Lithium ion battery real-time SOC simulation model composed of first current source and second current source and capacitor Cdl、CconcTwo, impedance ZctrVoltage source UOCVTerminal voltage UtThe terminal voltage response simulation model of the lithium ion battery is composed of two parts; u shapet＝UOCV(USOC_surf)‑IRohm‑ηctr‑ηconc(ii) a The method has high simulation precision and high calculation efficiency in the full SOC range of the lithium battery, avoids the solution of partial differential equations, and is more suitable for being applied to BMS.

Description

Full SOC range lithium ion battery equivalent model based on electrochemical process
Technical Field
The invention relates to the field of lithium ion battery equivalent models, in particular to a full SOC (state of charge) range lithium ion battery equivalent model based on an electrochemical process, which can provide higher simulation precision in a full SOC range of a battery, especially in a low SOC range
Background
It is known that as the holding capacity of electric vehicles increases, the endurance of power batteries is receiving much attention. On one hand, the research on a battery body is required to increase the energy density of the power battery; on the other hand, more efficient energy management strategies need to be developed. By virtue of the advantages of relatively high energy density, long cycle life and the like, the lithium battery becomes a main energy storage unit of the current electric automobile. In order to ensure that the vehicle-mounted energy system of the electric vehicle can operate safely and efficiently, a Battery Management System (BMS) becomes an important component of the electric vehicle. The power battery state estimation is an important function of the BMS and is generally performed based on a battery equivalent model. The external characteristics or the internal reaction mechanism of the battery are simulated by the equivalent model, so that the effect of estimating the real-time working state of the battery or predicting the future working state of the battery is achieved. The commonly used power battery model mainly comprises: electrochemical models and equivalent circuit models.
The electrochemical model describes the electrochemical process in the lithium battery in detail from the perspective of the electrochemical mechanism in the lithium battery, so as to simulate the working characteristics of the battery. Pseudo-Two-Dimensional (P2D) models built based on porous electrode theory and concentrated solution theory have long been considered as the basis for battery electrochemical models. The active materials on the electrodes are simplified into round balls with the same size in a P2D model, and the processes of participation of lithium ions in the battery are described by partial differential equations respectively: solid-phase diffusion of lithium ions in the active particles, charge transfer reactions occurring at solid-liquid interfaces, and liquid-phase diffusion of lithium ions in the electrolyte. Therefore, the P2D model can simulate the external characteristics of the battery and the process of changing the electrochemical substances inside the battery at the same time. Single Particle Model (SPM) based on the P2D Model, the electrochemical reaction is assumed to be uniformly distributed on the electrodes, so that the active material on each electrode is simplified into a Single sphere. Compared with the P2D model, the SPM ignores the liquid phase diffusion of lithium ions, and accordingly simplifies a part of the operation process. The P2D model applies a series of partial differential equations to describe the change of the electrochemical variables in the battery, and solving the partial differential equations brings huge calculation to the model, so that the model is difficult to achieve real-time performance, and cannot be applied to the BMS. Although the SPM is simplified on the basis of the P2D model, partial differential equations still need to be solved, the calculation efficiency is general, and the SPM ignores the liquid phase diffusion of lithium ions, so that the simulation accuracy of the model under high magnification is reduced. Meanwhile, the electrochemical model has more parameters and cannot realize the online identification of the parameters.
The equivalent circuit model adopts electronic elements such as a resistor, a capacitor and the like to build a circuit, and the external characteristics of the lithium ion battery are simulated. The earliest Rint model only describes the internal ohmic impedance of the battery, the Thevenin model adds an RC parallel module to describe the polarization characteristic of the battery on the basis of the Rint model, and different numbers of RC parallel modules are added to obtain a second-order RC equivalent circuit model and an n-order RC equivalent circuit model based on the Thevenin model. The accuracy and the operand of the model are integrated, and the second-order RC equivalent circuit model is widely applied. The Model based on the Running Time (RTM) simulates the working current of the battery by using a current control current source on the basis of a second-order RC Model, so that the current State of Charge (SOC) of the battery is obtained on the basis of an ampere-hour integration method, and the effect of predicting the residual running time of the battery is achieved while the terminal voltage response of the battery is estimated. In addition, an improved equivalent Circuit model established based on the electrochemical process inside the battery is provided, and the solid phase diffusion of lithium ions is considered in the updating of the Open Circuit Voltage (OCV) of the battery so as to improve the accuracy of the model in the low SOC range. The equivalent circuit model is only used to fit the external characteristics of the cell and does not illustrate the electrochemical processes inside the cell. Taking the most widely applied second-order RC equivalent circuit model as an example to analyze the error sources of the model: although the two RC modules used for simulating the internal polarization process of the battery have difference in time constant, the effects of the two RC modules on terminal voltage are parallel, the RC modules are obtained simultaneously through off-line identification and on-line identification, and the RC modules do not have obvious corresponding relation with the internal electrochemical process of the lithium ion battery. Meanwhile, the charge transfer reaction at the solid-liquid phase interface inside the lithium battery is not purely resistive, so that a second-order RC equivalent circuit model describes the process by using a resistor, and a large error is generated. In addition, the real-time OCV of the battery in a working state can be influenced by the solid-phase diffusion process of lithium ions in the lithium battery, and the OCV of the battery is determined by the macroscopic average SOC of the second-order RC equivalent circuit model, so that the simulation accuracy of the model in a low SOC range is low.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provide an electrochemical process-based full-SOC lithium ion battery equivalent model which can provide higher simulation accuracy in a full-SOC range of a battery, particularly in a low-SOC range. In consideration of the requirements of the battery model of the electric automobile BMS on the precision and the real-time performance, the invention simplifies the internal electrochemical process of the lithium battery and uses the simplified electrochemical process for improving the equivalent circuit model, thereby providing a high-precision lithium ion battery equivalent model in the full SOC range based on the electrochemical process,
the technical scheme adopted by the invention for solving the defects of the prior art is as follows:
a full SOC range lithium ion battery equivalent model based on an electrochemical process is characterized by comprising a lithium ion battery real-time SOC simulation model and a lithium ion battery terminal voltage response simulation model;
the lithium ion battery real-time SOC simulation model consists of three capacitors Ccapacity、Cds1、Cds2Two resistors Rds1、Rds2And two currents I and I respectivelydlThe control current source I and the control current source II form a circuit structure which is as follows: resistance Rds1And a capacitor Cds1Parallel connection, resistance Rds2And a capacitor Cds2The two RC modules are connected in parallel to form two RC modules respectively, and the two RC modules are connected in series, then connected with the current source II in parallel, and then connected with the current source I and the capacitor CcapacityAre connected in series to form a closed loop circuit; wherein, the capacitor CcapacityThe actual available capacity of the battery is represented, and an external current I controls a first current source to track the working current of the battery; current IdlA second current source is controlled to charge current for the double electric layer capacitor; r isds1、Rds2、Cds1And Cds2To describe the equivalent resistance and equivalent capacitance of solid phase diffusion, Rds1And Cds1、Rds2And Cds2Together forming a second-order RC module for simulating solid phase diffusion.
The lithium ion battery terminal voltage response simulation model is composed of two capacitors Cdl、CconcTwo resistors Rohm、RconcAn impedance ZctrA voltage source UOCVAnd terminal voltage UtComposition is carried out; the circuit structure is as follows: resistance RconcAnd a capacitor CconcConnected in parallel to form an RC module, impedance ZctrAnd a capacitor CdlA ZC module, an RC module, a ZC module and a resistor RohmVoltage source UOCVAnd terminal voltage UtAre sequentially connected in series to form a closed loop circuit; wherein, UOCVCharacterizing the open circuit voltage, R, of a batteryohmIs an equivalent ohmic resistance, CdlIs an electric double layer capacitor, ZctrEquivalent impedance for charge transfer reaction, CdlAnd ZctrSimulating the reactive polarization part together with the reactive polarization overpotential etactrCorresponding; rconcPolarize the equivalent electricity for concentrationResistance, CconcIs concentration polarization equivalent capacitance, CconcAnd RconcSimulating the concentration polarization part together with the concentration polarization overpotential etaconcCorresponding; u shapetIs the battery terminal voltage; lithium ion battery terminal voltage UtThe calculation formula of (A) is as follows:
Ut＝UOCV(USOC_surf)-IRohm-ηctr-ηconc。
a full SOC range lithium ion battery equivalent model based on an electrochemical process is characterized in that a model formula is as follows:
ohmic polarization effect: etaohm＝IRohm
Concentration polarization effect:
Figure GDA0003631285290000031
electrode potential taking into account solid phase diffusion:
Figure GDA0003631285290000032
charge transfer effects:
Figure GDA0003631285290000033
battery terminal voltage calculation process: u shapet＝UOCV(USOC_surf)-IRohm-ηctr-ηconc
The concentration polarization overpotential and parameter online identification and acquisition process comprises the following steps:
Figure GDA0003631285290000041
reaction polarization overpotential and parameter acquisition process:
Figure GDA0003631285290000042
an open circuit voltage acquisition process:
Figure GDA0003631285290000043
wherein, each variable of the lithium ion battery has the following meanings: rohmIs ohmic internal resistance, RconcIs an equivalent concentration polarization resistance, CconcFor equivalent concentration polarization capacitance, tauconcIs equivalent concentration polarization time constant, lambda is forgetting factor of recursion least square method, a is active particle specific surface area, L is plate thickness, S is plate area, CdlIs an electric double layer capacitor, kc0As fitting coefficient, kc1As fitting coefficient, kc2As fitting coefficient, ks,1As fitting coefficient, τds,、As fitting coefficient, ks,2As fitting coefficient, τds,As fitting coefficients, α is the transmission coefficient, T is the Kelvin temperature, F is the Faraday constant, UassIs an intermediate variable, k1Is an intermediate variable, k2Is an intermediate variable, k3Is an intermediate variable, y (k) is,
Figure GDA0003631285290000051
is an intermediate variable, θT(k) Is an intermediate variable, j0To exchange the current density, ksAs rate constant of electrochemical reaction, CeIs the lithium ion liquid phase concentration, keffThe liquid-phase conductivity of the lithium ion is,
Figure GDA0003631285290000052
is the liquid phase transfer coefficient of lithium ion, K is the combination coefficient, K1As a combination coefficient, K2Is a combination coefficient, keAs fitting coefficient, c0As fitting coefficient, kc2As fitting coefficient, kc1As fitting coefficient, kc0Are fitting coefficients.
The method is applied to the BMS, the working process and the working characteristics of the lithium battery are simulated, the real-time high-precision simulation of the terminal voltage of the lithium battery is realized, and the state estimation of the BMS on the lithium battery is facilitated to be improved, so that a more efficient management strategy is formulated, and the energy utilization rate of the battery is improved.
The first step is as follows: the actual available capacity and SOC-OCV of the battery are calibrated through a battery experiment, and a data basis is provided for establishing a model;
the second step: and carrying out online identification on a fitting coefficient introduced in the electrochemical process, and carrying out function fitting on the numerical solution of the electrochemical variable under the step current so as to calibrate the fitting coefficient.
The third step: and inputting the initial state and the real-time working current of the battery, and acquiring the surface SOC of the battery considering the solid-phase diffusion process, so as to obtain the real-time open-circuit voltage of the battery through table lookup. The description of the solid phase diffusion process is key to improving the accuracy of the model in the low SOC range.
The fourth step: submodules for simplifying and describing the processes of internal ohm simplification, reaction polarization and concentration polarization of the battery in the model respectively simulate the ohm polarization overpotential, the reaction polarization overpotential and the concentration polarization overpotential of the battery. The simplified description method mentioned in the second step enables the Butler-Volmer equation to be directly applied to an equivalent model, and the description accuracy of the model to the reactive polarization process is improved. And the real-time simulation of the terminal voltage of the battery is realized by combining the real-time open-circuit voltage of the battery.
According to the method, the internal electrochemical process of the lithium battery is simplified and then used for improving the equivalent circuit model, and based on the analysis and simplification of the internal electrochemical process of the lithium battery, the equivalent model which can realize high precision, high calculation efficiency and online parameter identification in the full SOC range of the battery is established. The method has the capability of describing the electric double layer capacitance effect, the charge transfer reaction, the liquid phase diffusion and the solid phase diffusion, provides an approximate method for describing the microcosmic electrochemical variable inside the battery by using the macroscopic electrical variable, avoids the solution of a partial differential equation, and enables the model to be more suitable for being applied to the BMS.
Drawings
Fig. 1 is a schematic diagram of the electrochemical process inside a lithium ion battery during operation.
Fig. 2 is a schematic structural diagram of a lithium ion battery real-time SOC simulation model according to the present invention.
Fig. 3 is a schematic structural diagram of a lithium ion battery terminal voltage response simulation model of the present invention.
Fig. 4 is a schematic diagram of electric double layer capacitance measurement in a current interruption experiment.
FIG. 5 is a graph comparing experimental measurements of terminal voltage response and voltage at a full SOC range HPPC for a lithium ion battery according to the invention model, RTM (run time based equivalent circuit model).
FIG. 6 is a root-mean-square-error (RMSE) plot of terminal voltage root-mean-square-error (RTM) for a full SOC range HPPC of a lithium ion battery according to the present invention.
Fig. 7 is a graph comparing terminal voltage response and experimental voltage measurements for the RTM at low SOC range HPPC of li-ion batteries according to the present invention model (corresponding to the enlarged partial view in fig. 5).
FIG. 8 is a terminal voltage root mean square error graph of RTM under low SOC range HPPC of lithium ion battery according to the present invention.
Fig. 9 is a diagram of the input current of the invention and RTM under DST.
Fig. 10 is a terminal voltage response diagram of the present invention and RTM under DST.
Fig. 11 is a graph of terminal voltage error under DST for the present invention and RTM.
Fig. 12 is a graph of terminal voltage RMSE under DST for the present invention and RTM.
Detailed Description
A full SOC range lithium ion battery equivalent model based on electrochemical process is characterized by comprising a lithium ion battery real-time SOC simulation model and a lithium ion battery terminal voltage response simulation model;
the lithium ion battery real-time SOC simulation model consists of three capacitors Ccapacity、Cds1、Cds2Two resistors Rds1、Rds2And two currents I and I respectivelydlThe control current source I and the control current source II form a circuit structure which is as follows: resistance Rds1And a capacitor Cds1Parallel connection, resistance Rds2And a capacitor Cds2The two RC modules are connected in parallel to form two RC modules respectively, the two RC modules are connected in series and then connected with a current source II in parallel, and the whole body after being connected in parallel is connected with the current source I and a capacitor CcapacityAre connected in series to form a closed loop circuit; wherein, the capacitor CcapacityCharacterization ofThe actual available capacity of the battery, and an external current I controlling a current source I for tracking the operating current of the battery due to a capacitor CcapacityThe capacitance value of (1) is equal to the actual available capacity of the battery, the voltage at two ends of the capacitor is 1V in the full charge state, and the voltage U at two ends of the capacitor is along with the progress of the discharge process of the batterySOC_avgChanging from 1V to 0, which is equivalent to average SOC calculated by an ampere-hour integration method; current IdlA second current source is controlled to charge current for the double electric layer capacitor; rds1、Rds2、Cds1And Cds2Equivalent resistance and equivalent capacitance to describe solid phase diffusion, Rds1And Cds1、Rds2And Cds2Jointly form a second-order RC module for simulating solid-phase diffusion and charging current I through an electric double-layer capacitor according to the composition condition of the current in the batterydlControlling the second current source to separate a Faraday current I from the external currentfThen simulating U generated by solid phase diffusion through a second-order RC moduleΔSOC，USOC_avgAnd UΔSOCSubtracting the two to obtain the surface SOC, U of the batterySOC_surfNamely the real-time SOC;
the lithium ion battery terminal voltage response simulation model is composed of two capacitors Cdl、CconcTwo resistors Rohm、RconcAn impedance ZctrA voltage source UOCVAnd terminal voltage UtComposition is carried out; the circuit structure is as follows: resistance RconcAnd a capacitor CconcConnected in parallel to form an RC module, impedance ZctrAnd a capacitor CdlA ZC module, an RC module, a ZC module and a resistor RohmVoltage source UOCVAnd terminal voltage UtAre sequentially connected in series to form a closed loop circuit; wherein, UOCVCharacterizing the open circuit voltage of the battery (which may be represented by U)SOC_surfObtained by looking up an SOC-OCV comparison table); rohmIs equivalent ohmic resistance to ohmic polarization overpotential etaohmCorresponding; cdlIs an electric double layer capacitor, ZctrEquivalent impedance for charge transfer reaction, CdlAnd ZctrSimulating the reactive polarization part together with the reactive polarization overpotential etactrCorresponding;Rconcis concentration polarization equivalent resistance, CconcIs concentration polarization equivalent capacitance, CconcAnd RconcSimulating concentration polarization part together with concentration polarization overpotential etaconcCorresponding; u shapetIs the battery terminal voltage; lithium ion battery terminal voltage UtThe calculation formula of (A) is as follows:
Ut＝UOCV(USOC_surf)-IRohm-ηctr-ηconc。
a full SOC range lithium ion battery equivalent model based on an electrochemical process is characterized in that a model formula is as follows:
ohmic polarization effect: etaohm＝IRohm
Concentration polarization effect:
Figure GDA0003631285290000071
electrode potential taking into account solid phase diffusion:
Figure GDA0003631285290000072
charge transfer effect:
Figure GDA0003631285290000073
battery terminal voltage calculation process: u shapet＝UOCV(USOC_surf)-IRohm-ηctr-ηconc
The concentration polarization overpotential and parameter online identification and acquisition process comprises the following steps:
Figure GDA0003631285290000081
reaction polarization battery and parameter acquisition process:
Figure GDA0003631285290000082
open circuit voltage acquisition process:
Figure GDA0003631285290000083
wherein, each variable of the lithium ion battery has the following meanings: r isohmIs ohmic internal resistance, RconcIs an equivalent concentration polarization resistance, CconcFor equivalent concentration polarization capacitance, tauconcIs equivalent concentration polarization time constant, lambda is forgetting factor of recursive least square method, a is specific surface area of active particles, L is plate thickness, S is plate area, C isdlIs an electric double layer capacitor, kc0As fitting coefficient, kc1As fitting coefficient, kc2As fitting coefficient, ks,1As fitting coefficient, τds,、As fitting coefficient, ks,2As fitting coefficient, τds,As fitting coefficients, α is the transmission coefficient, T is the Kelvin temperature, F is the Faraday constant, UassIs an intermediate variable, k1Is an intermediate variable, k2Is an intermediate variable, k3Is an intermediate variable, y (k) is,
Figure GDA0003631285290000091
is an intermediate variable, θT(k) Is an intermediate variable, j0To exchange the current density, ksAs rate constant of electrochemical reaction, CeIs the lithium ion liquid phase concentration, keffIs the liquid-phase conductivity of the lithium ions,
Figure GDA0003631285290000092
is the lithium ion liquid phase transfer coefficient, K is the combination coefficient, K1As a combination coefficient, K2Is a combination coefficient, keAs fitting coefficient, c0As fitting coefficient, kc2As fitting coefficient, kc1As fitting coefficient, kc0Are fitting coefficients.
The method is applied to the BMS, the working process and the working characteristics of the lithium battery are simulated, the real-time high-precision simulation of the terminal voltage of the lithium battery is realized, and the state estimation of the BMS on the lithium battery is facilitated to be improved, so that a more efficient management strategy is formulated, and the energy utilization rate of the battery is improved.
The first step is as follows: the actual available capacity and SOC-OCV of the battery are calibrated through a battery experiment, and a data basis is provided for establishing a model;
the second step is that: and carrying out online identification on a fitting coefficient introduced in the electrochemical process, and carrying out function fitting on the numerical solution of the electrochemical variable under the step current so as to calibrate the fitting coefficient.
The third step: and inputting the initial state and the real-time working current of the battery, and acquiring the surface SOC of the battery considering the solid-phase diffusion process, so as to obtain the real-time open-circuit voltage of the battery through table lookup. The description of the solid phase diffusion process is key to improving the accuracy of the model in the low SOC range.
The fourth step: submodules for simplifying and describing the processes of internal ohm simplification, reaction polarization and concentration polarization of the battery in the model respectively simulate the ohm polarization overpotential, the reaction polarization overpotential and the concentration polarization overpotential of the battery. The simplified description method mentioned in the second step enables the Butler-Volmer equation to be directly applied to an equivalent model, and the description precision of the model on the reactive polarization process is improved. And the real-time simulation of the terminal voltage of the battery is realized by combining the real-time open-circuit voltage of the battery.
According to the method, the internal electrochemical process of the lithium battery is simplified and then used for improving the equivalent circuit model, and based on the analysis and simplification of the internal electrochemical process of the lithium battery, the equivalent model which can realize high precision, high calculation efficiency and online parameter identification in the full SOC range of the battery is established. The method has the capability of describing the electric double layer capacitance effect, the charge transfer reaction, the liquid phase diffusion and the solid phase diffusion, provides an approximate method for describing the microcosmic electrochemical variable inside the battery by using the macroscopic electrical variable, avoids the solution of a partial differential equation, and enables the model to be more suitable for being applied to the BMS.
The theory of the invention is derived as follows:
description of the electrochemical Process
During operation, a series of electrochemical processes exist inside the lithium ion battery, and a schematic diagram is shown in fig. 1.
Taking the discharge working condition as an example, the internal electrochemical process of the lithium ion battery comprises the following steps:
1) solid-phase diffusion of lithium ions from the inside to the surface of the negative electrode active particles;
2) forming double electric layer capacitance of the solid-liquid interface of the negative electrode and transferring charge;
3) liquid phase diffusion in which lithium ions released from the negative electrode active particles reach the surface of the positive electrode active particles;
4) forming double electric layer capacitance of positive solid-liquid interface and charge transfer reaction;
5) lithium ions are solid-phase diffused from the surface of the positive electrode active particle to the inside.
Since the effects of the electrochemical processes at the positive and negative ends are superimposed on the external terminal voltage, the positive and negative polarization characteristics are considered in the present invention. The lithium ion battery internal electrochemical process described by the combined equivalent model comprises the following steps: the electric double layer capacitance effect, the charge transfer reaction at the solid-liquid interface, the solid phase diffusion of lithium ions inside the active particles, and the liquid phase diffusion of lithium ions in the electrolyte. The respective reaction processes will be described below from the mechanism level.
(1) Ohmic polarisation
Ohmic polarization is a phenomenon in which the terminal voltage is instantaneously lowered due to resistance to the transfer of electric charges occurring in an external circuit and the inside of the battery during the operation of the battery. Sources of internal ohmic impedance of the lithium battery include the impedance of a current collector and an external circuit conductor to electrons, the impedance of electrode active particles, an SEI (solid-electrolyte interface) film and electrolyte to ions, and a resistor R is used in the modelohmTo simulate, the ohmic polarization overpotential η generated by ohmic polarizationohmCan be calculated by the formula (1), wherein I is the operating current of the battery.
ηohm＝IRohm (1)
(2) Concentration polarization
In the lithium battery, concentration polarization phenomenon is generated when lithium ions move under the action of diffusion and electromigration, and the concentration polarization phenomenon can be described by Fick's second law and liquid-phase ohm's law. Combining the ohmic impedance of the lithium ion liquid phase diffusion with other ohmic impedances inside the batteryIt is contemplated that concentration polarization may then be simplified by one RC parallel module. According to kirchhoff's current law and kirchhoff's voltage law, concentration polarization overpotential η due to concentration polarizationconcCan be calculated by equation (2):
Figure GDA0003631285290000101
wherein R isconcIs an equivalent concentration polarization resistance, CconcIs an equivalent concentration polarization capacitance.
(3) Electric double layer capacitance effect
When the external circuit is switched on, the electric potential difference between the anode and the cathode of the battery drives the external circuit and the charge transfer in the battery, in the external circuit, the charge transfer is realized by the movement of electrons in a lead, and the charge transfer in the battery is completed by charged ions. Since the electrons in the external circuit move at a much higher rate than the ions inside the cell, charge build-up occurs on the active particle surface, and the accumulated charge attracts oppositely charged ions in solution, thus forming an electric double layer capacitance.
(4) Electrode potential taking into account solid phase diffusion
The real-time open-circuit voltage of the battery can be obtained by table look-up according to the SOC-OCV corresponding relation measured by experiments by the real-time SOC in a working state, and the acquisition of the real-time SOC of the battery is a key problem.
The SOC of the battery is determined by the solid-phase concentration of lithium ions inside the battery. When the lithium battery is in a balanced state, the concentration of lithium ions in the active particles is uniform; when the lithium battery is in a working state, the surface of active particles in the lithium battery is subjected to electrochemical reaction, surface lithium ions are consumed, and solid-phase diffusion of the lithium ions in the active particles is driven, so that the concentration of the lithium ions in the active particles and the concentration of the lithium ions on the surface of the active particles are different. Generally, macroscopically, the average SOC is obtained according to the external current integration, and is characterized by the average lithium ion concentration in the active particles, the definition of the average SOC is shown as formula (3), and the calculation is shown as formula (4). The electrode potential difference is actually determined by the lithium ion concentration on the surface of the active particles, so that certain error is caused by reflecting the open-circuit voltage of the battery by using the average SOC. Therefore, the invention introduces the surface SOC, as shown in formula (5), and obtains the potential difference of the battery by using the battery charge state described by the surface lithium ion concentration.
Figure GDA0003631285290000111
Figure GDA0003631285290000112
Figure GDA0003631285290000113
Wherein, USOC_avgIs an average SOC, cs,avgAs the average solid phase concentration of lithium ions within the active particles, cs,lowerIs the solid-phase concentration of lithium ions at the time of complete discharge of the lithium battery, cs,upperIs the solid-phase concentration of lithium ions in the fully charged state of the lithium ion battery, cs,maxMaximum solid phase concentration of lithium ion, SOC0Is an initial SOC, QcapacityIs the maximum available capacity, U, of the batterySOC_surfIs surface SOC, cs,surfIs the active particle surface lithium ion concentration.
Since the lithium ion concentration on the surface of the active particles can not be calculated by the external macroscopic variables of the battery, U is introduced to simplify the calculation amountΔSOCApproximately replaces the influence of lithium ion solid phase diffusion, as shown in formula (6):
Figure GDA0003631285290000114
(5) polarization of charge transfer reaction
The lithium ion flow density j participating in the electrochemical reaction is the electrochemical reaction for completing the electron transfer in the solid-liquid phase interface of the lithium ion battery electrodefAnd reaction polarization overpotential etactrThe relationship between them can be described by the reaction kinetics Butler-Volmer equation. Consider the Butler-Volmer equation descriptionIs a monopolar electrochemical reaction polarization process, and introduces a reaction polarization overpotential coefficient kctrAnd (3) calculating the total reaction polarization overpotential of the positive electrode and the negative electrode of the lithium ion battery in a combined manner, wherein the adjusted Butler-Volmer equation is shown as a formula (7):
Figure GDA0003631285290000115
wherein eta isctrPolarizing the overpotential for the reaction; j is a function offThe flux density of lithium ions participating in the reaction, also known as the faraday current density; j is a function of0Exchange current density, that is, the flow density of electrode reaction when the lithium ion battery is in an equilibrium state; α is the transmission coefficient, typically taken to be 0.5; f is a Faraday constant; t is the Kelvin temperature; r is an ideal gas constant.
Proposal of lithium ion full SOC range equivalent model capable of describing electrochemical process
Considering the requirements of the BMS on the equivalent model in terms of precision and operand, and meanwhile, the SOC estimation method commonly used in the BMS is an ampere-hour integral method, so that RTM is selected as a model structure basis. Based on the analysis and simplification of the electrochemical processes, a lithium ion full SOC range equivalent model capable of describing the electrochemical processes is established:
Ut＝UOCV(USOC_surf)-IRohm-ηctr-ηconc (8)
the circuit structure is shown in fig. 2 and 3.
The specific modules and the parameter acquisition process thereof are as follows:
(1) ohmic polarization overpotential ηohmSum concentration polarization overpotential etaoncAnd specific acquisition process of parameters thereof
Ohmic polarization overpotential ηohm＝IRohmI is the operating current of the battery, where RohmIs a parameter to be acquired, RohmThe method is obtained by performing online identification and acquisition through a recursive least square method based on forgetting factors.
From the formula (2), the concentration polarization overpotential
Figure GDA0003631285290000121
Wherein R isconcAnd CconcIs a parameter to be acquired, and can be compared with RohmThe method is obtained by carrying out online identification and acquisition through a recursive least square method based on forgetting factors, and the specific process is as follows.
And (3) parameter online identification process: the invention provides a parameter R in a battery terminal voltage response simulation module based on a recursive least square method of forgetting factorsohm、RconcAnd CconcThe online identification method can improve the adaptability of the battery terminal voltage response simulation module parameters, and is convenient for the battery to more accurately simulate the external characteristics of the battery under different SOC and dynamic working conditions.
First, formula (2) is laplace-transformed to convert formula (2) containing a real parameter t into formula (9) containing a complex parameter s, as follows:
Figure GDA0003631285290000122
then combining formula (8) and formula (9) to convert the battery terminal voltage UtConverted to a mathematical form suitable for the least squares method, as shown in equation (10):
Figure GDA0003631285290000123
let τ beconc＝RconcCconc，Uass＝UOCV-ηctrWork-up to give formula (11):
Ut(τconcs+1)＝Uass(τconcs+1)-τconcRohmIs-I(Rohm+Rconc) (11)
order to
Figure GDA0003631285290000124
Discretization treatment is carried out by substituting the formula (11), t is sampling time, and the formula (12) can be obtained by arranging:
Figure GDA0003631285290000125
order to
Figure GDA0003631285290000126
y(k)＝Ut(k)-Uass(k)，
Figure GDA0003631285290000127
θT(k)＝[k1,k2,k3]Then, formula (13):
Figure GDA0003631285290000128
the forgetting factor recursive least square method calculation process is shown as a formula (14), wherein lambda is the forgetting factor and is generally 0.95-1. P (0) ═ C · E, C is a constant and E is an identity matrix.
Figure GDA0003631285290000131
Deriving k from the identification1、k2、k3According to k1、k2、k3The expression can obtain the battery terminal voltage response simulation module parameter Rohm、RconcAnd Cconc。
(2) Overpotential η of reactive polarizationctrAnd specific acquisition process of parameters thereof
By the aforementioned
Figure GDA0003631285290000137
To solve etactr。
And introducing an auxiliary variable xi to solve the Butler-Volmer equation, wherein the equation is shown as the formula (15):
Figure GDA0003631285290000133
eta can be obtained by solving the inverse hyperbolic sine functionctrAs shown in formula (16):
Figure GDA0003631285290000134
solving the auxiliary variable xi requires first completing the faraday current density jfAnd exchange current density j0And (4) calculating. j is a function offCan be controlled by a Faraday current IfThe relevant size parameters of the lithium battery are calculated, and are shown as the formula (17):
Figure GDA0003631285290000135
wherein a is the specific surface area of the active particles, L is the thickness of the polar plate, and S is the area of the polar plate.
Therefore, the lithium ion flux density j is obtainedfFirst, a Faraday current I is obtainedfFaraday current IfThe obtaining process of (a) may be obtained in combination with an electric double layer capacitance reaction. Based on the double electric layer capacitance effect, the external current I is generated by the Faraday current I participating in the charge transfer reaction of the solid-liquid interface inside the lithium ion batteryfAnd a non-faradaic current I for charging an electric double layer capacitordlAnd (4) forming. Consider Faraday current IfAnd has a first order transient relation with the external current I, as shown in formula (18):
Figure GDA0003631285290000136
wherein, taudlIs a time constant and an electric double layer capacitance CdlAnd the equivalent impedance Z of charge transfer reactionctrIs related to the size of the cell.
The size of the electric double layer capacitance can be measured by a current cutoff experiment, the experimental principle is as shown in fig. 3, and since the electric double layer capacitance is charged with a small-amplitude pulse current before the 0 time, the liquid phase diffusion process is negligible. Wherein eta isohmIn order to respond to the internal ohmic internal resistance of the lithium battery at the moment of cutting off the current, after the current is cut offThe discharge current of the electric double layer capacitor is maximum in an extremely short time Δ t and is approximately equal to the current before time 0. Electric double layer capacitor CdlCan be determined by the variation of the terminal voltage of the battery within Δ tctrAnd (3) calculating, as shown in formula (19):
Figure GDA0003631285290000141
exchange current density j0Representing the difficulty degree of the electrode reaction, wherein the calculation process is shown as the formula (20):
j0＝ksce 0.5(cs,max-cs,surf)0.5cs,surf 0.5 (20)
wherein k issIs the rate constant of electrochemical reaction, ceIs the lithium ion liquid phase concentration.
The invention provides a new approximation method because the real-time lithium ion liquid phase concentration and the surface solid phase concentration cannot be directly obtained. The relationship between the lithium ion liquid phase concentration and the concentration polarization overpotential can be characterized by liquid phase ohm's law, as shown in equation (21):
Figure GDA0003631285290000142
wherein k iseffIs the liquid-phase conductivity of the lithium ions,
Figure GDA0003631285290000143
is the lithium ion liquid phase transfer coefficient, x is the lithium ion liquid phase diffusion direction coordinate, ieIs the liquid phase current density.
In order to express the relationship between the two more clearly, the equation (22) can be written by integrating the two sides of the equation (21) simultaneously:
Kηconc＝K1 ln ce-K2 (22)
wherein, K1And K2Are all combination coefficients.
Formula (22) can be rewritten as formula (23):
Figure GDA0003631285290000144
by using Taylor's formula to expand (23), ignoring second and higher order terms, the liquid phase lithium ion concentration can be represented by a linear function of the concentration polarization overpotential, as shown in equation (24):
ce＝keηconc+c0 (24)
wherein k ise、c0Are all fitting coefficients.
Based on surface SOC and lithium ion surface lithium insertion rate
Figure GDA0003631285290000145
Linear relationship between them, introducing a quadratic function c of the surface SOCs,solidAs shown in formula (25):
cs,solid＝(cs,max-cs,surf)cs,surf＝kc2USOC_surf 2+kc1USOC_surf+kc0 (25)
wherein k isc2、kc1And kc0Are fitting coefficients, which are related to the battery SOC. C under different SOC and constant current discharge conditions is calculated by adopting a finite difference methods,surfThe numerical solution of (a) can be used to fit these coefficients.
By this approximate simplification, the exchange current density j can be obtained without the need to calculate electrochemical microscopic variables0So as to directly calculate the reaction polarization overpotential eta by the Butler-Volmer equationctr。
(3) Battery open circuit voltage UOCV(USOC_surf) Specific acquisition procedure of
Battery open circuit voltage UOCVCan be composed of UDOC_surfFrom the examination of the SOC-OCV control table, in consideration of solid phase diffusion of the battery, formula (26) can be obtained from formulas (3), (4), (5), and (6):
USOC_surf＝USOC_avg-UΔSOC (26)
wherein, UΔSOCApproximately replacing the influence of the solid-phase diffusion of the lithium ions, approximately solving the concentration distribution of the solid-phase lithium ions in the solid-phase diffusion process by using a 4-parameter 6-order polynomial, and displaying the result that U isΔSOCAnd Faraday current IfThere is an approximate second order transient relationship between them, which can be described by equation (27).
Figure GDA0003631285290000151
Wherein k iss,1、τds,1、、ks,2、τds,2All the coefficients are fitting coefficients, and the numerical solution of the solid phase diffusion can be approximately solved by using a finite difference method and then obtained by function curve fitting.
Obtain UΔSOCThen, U can be obtainedSOC_surfFurther looking up the SOC-OCV look-up table to obtain UOCV。
The description of the specific model of the invention is summarized as follows:
Figure GDA0003631285290000152
Figure GDA0003631285290000161
the equivalent model needs to obtain some model parameters when describing the terminal voltage response, and some intermediate variables need to be used in the parameter obtaining process, and specific model parameters, obtaining modes and intermediate variables are listed as follows:
Figure GDA0003631285290000171
the method is contrastively verified based on lithium battery experiments, the RTM which is most commonly used at present is selected as a contrast object, and model precision verification is completed under a Hybrid Pulse Power Condition (HPPC) and a Dynamic Condition (DST) respectively.
As can be seen from fig. 5 and 6, RTM has good fitting effect in the middle and high SOC ranges, but the error increases significantly in the low SOC range. This is because the lithium ion battery has a strong polarization characteristic in a low SOC state, and the internal impedance changes sharply. Compared with a second-order RC equivalent circuit model, the model provided by the invention has better terminal voltage characteristics in the early stage of discharge, more importantly, the following of terminal voltage response can be completed in a low SOC range, and although the error is slightly increased, the superiority of the model in describing the voltage characteristics of the battery in the full SOC range can be still reflected.
As can be seen from fig. 7 and 8, compared with the HPPC working condition in the full SOC range, the RTM performance under the independent low SOC constant current discharge working condition is improved, but the polarization characteristics of the battery at the constant current discharge and rebound stages cannot be simulated well at the same time. The model provided by the invention can still well simulate the polarization characteristic of the battery under the low SOC state, which is mainly attributed to the description of the solid phase diffusion process inside the lithium ion battery, on one hand, U is usedΔSOCThe real-time open-circuit voltage under the working condition of the battery is corrected, and on the other hand, U is introducedSOC_surfThe description of the electrode reaction polarization process is participated, and the calculation of the reaction polarization overpotential is improved.
The adaptability of the equivalent model to dynamic working conditions is an important characteristic that the equivalent model can meet the application of a real-time system; as can be seen from fig. 9, 10, 11 and 12, compared to RTM, the model proposed by the present invention can exhibit superior simulation characteristics under DST, especially under the condition of frequent charge and discharge current changes. As the operating current varies, the internal impedance of the cell changes frequently with complex electrochemical processes, which presents challenges to RTM. The model provided by the invention can approximately describe the electrochemical process in the battery, so that a more accurate response can be made in terms of mechanism.
BMS: battery Management System, Battery Management System. The method is used for detecting the state of the power battery in the electric automobile, finishing state estimation and formulating a reasonable power battery management strategy.
P2D model: Pseudo-Two-Dimensional model. A lithium battery mechanism model is established based on a porous electrode theory and a concentrated solution theory, the internal electrochemical reaction process of the battery can be described in detail, and the change process of the external characteristics and the internal variables of the battery can be simulated.
SPM: single-particle Model, Single-particle Model. Based on the P2D model, the active materials on the electrode are simplified into single round balls, and the electrochemical model of liquid phase diffusion of lithium ions in the battery is ignored.
Equivalent circuit model: a circuit is built by adopting electronic elements such as a resistor, a capacitor and the like, and the external characteristics of the lithium ion battery are simulated.
RTM: a Runtime-based Model, equivalent circuit Model based on Runtime. A resistor is used for simulating internal ohmic impedance of the battery, two RC parallel modules are used for simulating the internal polarization process of the battery, and meanwhile, a capacitor and a current control current source are used for building an SOC estimation model (ampere-hour integral method).
OCV: open Circuit Voltage, Open Circuit Voltage of the battery. The terminal voltage when the inside of the battery is in a balanced state is used for representing the balanced potential of the battery (potential difference between the positive electrode and the negative electrode in the balanced state).
SOC: state of Charge, State of Charge of the battery. For characterizing the remaining capacity of the battery.
Average SOC: the SOC of the battery is determined by the lithium ion solid phase concentration, and the average SOC refers to the SOC characterized by the average lithium ion concentration inside the active particles.
Surface SOC: SOC characterized by the concentration of lithium ions on the surface of the active particles.
Diffusion: a phenomenon in which a certain component in different regions moves from a region with a high concentration to a region with a low concentration.
Solid phase diffusion: lithium ions move from a region of high concentration to a region of low concentration inside the active particles.
Liquid phase diffusion: lithium ions move from a region of high concentration to a region of low concentration in the electrolyte.

Claims (1)

1. A full SOC range lithium ion battery equivalent model based on an electrochemical process is characterized by comprising a lithium ion battery real-time SOC simulation model and a lithium ion battery terminal voltage response simulation model;
the lithium ion battery real-time SOC simulation model consists of three capacitors Ccapacity、Cds1、Cds2Two resistors Rds1、Rds2And two currents I and I respectivelydlThe control current source I and the control current source II form a circuit structure which is as follows: resistance Rds1And a capacitor Cds1Parallel connection, resistance Rds2And a capacitor Cds2The two RC modules are connected in parallel to form two RC modules respectively, and the two RC modules are connected in series, then connected with the current source II in parallel, and then connected with the current source I and the capacitor CcapacityAre connected in series to form a closed loop circuit; wherein, the capacitor CcapacityThe actual available capacity of the battery is represented, and an external current I controls a first current source to track the working current of the battery; current IdlCharging current for the double electric layer capacitor and controlling a second current source; rds1、Rds2、Cds1And Cds2To describe the equivalent resistance and equivalent capacitance of solid phase diffusion, Rds1And Cds1、Rds2And Cds2Together form a second-order RC module for simulating solid phase diffusion,
simulation of U generated by solid phase diffusion through second-order RC moduleΔSOC，USOC_avgAnd UΔSOCSubtracting the two to obtain the surface SOC, U of the batterySOC_surfNamely the real-time SOC;
Figure FDA0003667391220000011
wherein, USOC_avgIs an average SOC, cs,avgIs the average solid phase concentration of lithium ions in the active particles, cs,lowerIs the solid-phase concentration of lithium ions at the time of complete discharge of the lithium battery, cs,upperIs the solid-phase concentration of lithium ions in the fully charged state of the lithium ion battery, cs,maxIs the maximum solid phase concentration of lithium ions.
The terminal voltage response mode of the lithium ion batteryThe simulation model consists of two capacitors Cdl、CconcTwo resistors Rohm、RconcAn impedance ZctrA voltage source UOCVAnd terminal voltage UtForming; the circuit structure is as follows: resistance RconcAnd a capacitor CconcConnected in parallel to form an RC module, impedance ZctrAnd a capacitor CdlA ZC module, an RC module, a ZC module and a resistor RohmVoltage source UOCVAnd terminal voltage UtAre sequentially connected in series to form a closed loop circuit; wherein, UOCVCharacterizing the open circuit voltage, R, of a batteryohmIs an equivalent ohmic resistance, CdlIs an electric double layer capacitor, ZctrEquivalent impedance for charge transfer reaction, CdlAnd ZctrSimulating the polarization part of the reaction together with the overpotential η of the reaction polarizationctrCorresponding; rconcIs concentration polarization equivalent resistance, CconcIs a concentration polarization equivalent capacitance, CconcAnd RconcSimulating concentration polarization part together with concentration polarization overpotential etaconcCorresponding; u shapetIs the battery terminal voltage; terminal voltage U of lithium ion batterytThe calculation formula of (A) is as follows:
Ut＝UOCV(USOC_surf)-IRohm-ηctr-ηconc。
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