Method for simulating charge and discharge behavior of secondary battery

Abstract

The present application can provide a method for simulating charge and discharge behaviors of a secondary battery, a hardware device storing the method, and a battery management device storing the method. The present application can provide a method capable of simulating charge and discharge behaviors of a secondary battery with high consistency with actual behaviors in a relatively simple manner, and a hardware device and a battery management device storing the method.

Description

Technical Field

[0001] This application claims the benefit of priority based on Korean Patent Application No. 10-2022-0101842 filed on August 16, 2022, and all the contents disclosed in the document of the Korean Patent Application are incorporated herein by reference.

[0002] This application relates to a method for simulating charge and discharge behavior of a secondary battery, a hardware device storing the method, and a battery management device storing the method.

Background Art

[0003] A secondary battery is a rechargeable device that can store electrical energy by converting it into chemical energy and generate electricity as needed.

[0004] With the expansion of the electric vehicle market and the like, the development of secondary batteries with excellent stability and high energy density is required.

[0005] Accurately grasping the state and life of a secondary battery is important from the perspective of maximizing performance within a safe range and increasing the degree of freedom in using the secondary battery.

[0006] There are various modeling methods for secondary batteries for this purpose.

[0007] For example, an Electric Circuit Model (or equivalent model) is a method of modeling the input and output characteristics of a secondary battery through the configuration of an electric circuit, and can be realized while changing the element configuration according to the type of secondary battery. This method has the advantage of being simple and having low computational cost, but is not effective from the perspective of accuracy.

[0008] Another method is also known as the Electrochemical Model method. The Electrochemical Model method is also called the Physical Equation Model method. This method is based on the detailed composition of the chemical reactions occurring inside the secondary battery. This method is a modeling that formulates the physical movement of the internal particles of the secondary battery using partial differential equations (PDEs) and ordinary differential equations (ODEs) in space and time. Although the electrochemical modeling method is somewhat complex in calculation, it has high accuracy, and due to the development of computer hardware, the problems caused by the complexity of the calculation are also decreasing.

[0009] However, even in the electrochemical modeling method, it is necessary to supplement in order to accurately simulate the charge and discharge behavior of the secondary battery. The electrochemical modeling method has the disadvantage that the so-called hysteresis of the charge and discharge of the secondary battery is not reflected.

[0010] The hysteresis of the secondary battery means the voltage difference that occurs when the secondary battery is charged to a certain specific state of charge and when it is discharged to that state, and it is a phenomenon in which charging and discharging are different at the same state of charge.

[0011] This phenomenon is non-linear and has a great impact on the performance of the secondary battery, so it is important to accurately predict it. Summary of the Invention Problems to be Solved by the Invention

[0012] The present application aims to provide a method for simulating the charge and discharge behavior of a secondary battery, a hardware device storing the method, and a battery management device storing the method. The present application aims to provide a method capable of simulating the charge and discharge behavior of a secondary battery with high consistency with the actual behavior in a relatively simple manner, and a hardware device and a battery management device storing the method.

Means for Solving the Problems

[0013] This specification discloses a method for simulating the charge and discharge behavior of a secondary battery.

[0014] The method can include a step of simulating the charge and discharge behavior of a secondary battery through electrochemical modeling, and a step of applying hysteresis modeling to correct the simulation result obtained by the electrochemical modeling.

[0015] In the method, the step of simulating the charge and discharge behavior of a secondary battery through electrochemical modeling can be performed using DFN (Doyle-Fuller-Newman) modeling.

[0016] In the above, the step of simulating the charge and discharge behavior of a secondary battery through electrochemical modeling can be performed using one or more of the following formulas 1 to 5.

[0017] [Formula 1]

Number

[0018] In Formula 1, Cs is the concentration of lithium in the solid particle phase (unit: mol / m 3 ), r is the radius of the particle (unit: m), and Ds is the lithium diffusion coefficient (unit: cm 2 / s).

[0019] [Equation 2] [Math] In Equation 2, [Math] is the volume fraction of the electrolyte, De,eff is the diffusivity constant of the electrolyte medium (unit: cm 2 / s), and c e is the concentration of the electrolyte (unit: mol / m 3 ).

[0020] [Equation 3] [Math] In Equation 3, [Math] is the effective electrical conductivity of the solid phase (unit: S / cm), [Math] is the potential of the solid phase (unit: V), [Math] is the specific interfacial area (unit: m 2 / m 3 ), F is the Faraday's constant (96,487 C / eq), and j is the molar flux of lithium through the interface between the solid phase and the electrolyte.

[0021] [Equation 4] [Math] In Equation 4, [Number] is the effective ionic conductivity (S / cm) of the electrolyte, [Number] is the potential of the electrolyte (unit: V), c e is the concentration of the electrolyte, [Number] is the specific interfacial area (unit: m 2 / m 3 )), F is the Faraday's constant (96,487 C / eq), and j is the molar flux of lithium passing through the interface between the solid phase and the electrolyte.

[0022] [Equation 5] [Number] In Equation 5, i is the current density passing through the interface (unit: A / cm 2 ), and [Number] is the exchange current density with respect to the electrode - electrolyte interface (unit: A / cm 2 ), α a is the charge transfer coefficient of the anodic reaction, α c is the charge transfer coefficient of the cathodic reaction, η is the over potential, F is the Faraday's constant, R is the gas constant, and T is the absolute temperature (unit: K).

[0023] In the above, in the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling, all of the above formulas 1 to 5 can be used.

[0024] In the above, the step of applying hysteresis modeling to correct the simulation result by electrochemical modeling may be a step of converging the hysteresis at the time of conversion from charge to discharge and at the time of conversion from discharge to charge according to the passage of time in the simulation result by the electrochemical modeling.

[0025] In the above, the step of applying hysteresis modeling to correct the simulation result by electrochemical modeling can be performed using the following formula 6.

[0026] [Formula 6] [Number]

[0027] In formula 6, h is the voltage deviation by hysteresis, z is the state of charge (SOC) or the stoichiometry of the substance, M is the maximum voltage gap in the major hysteresis loop, and γ is the adjustment constant.

[0028] This specification also discloses a hardware device in which the above method or algorithm (the algorithm according to the above method) is stored.

[0029] This specification also discloses a battery management device or a battery management system in which the above method or algorithm (the algorithm according to the above method) is stored. [Advantages of the Invention]

[0030] According to an embodiment of the present application, it is possible to provide a method for simulating charge and discharge behavior of a secondary battery, a hardware device storing the method, and a battery management device storing the method. According to an embodiment of the present application, it is possible to provide a method for simulating charge and discharge behavior of a secondary battery with high consistency with actual behavior in a relatively simple manner, and a hardware device and a battery management device storing the method.

Brief Description of the Drawings

[0031]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Modes for Carrying Out the Invention

[0032] The present application relates to a method for simulating charge and discharge behavior of a secondary battery. In the present application, when simulating charge and discharge behavior of a secondary battery, a so-called electrochemical modeling method and a hysteresis modeling method are combined.

[0033] In particular, by appropriately controlling, selecting, and combining the electrochemical modeling method and the hysteresis modeling method, in the present application, it is possible to simulate charge and discharge behavior of a secondary battery with high consistency with actual behavior.

[0034] Figure 1 is a diagram showing the manner in which the method of the present application proceeds.

[0035] As shown in Figure 1, in the present application, after inputting experimental parameters, the charge and discharge behavior of the secondary battery is simulated by correcting the results simulated through electrochemical modeling based on the input parameters through a hysteresis model.

[0036] Accordingly, the method of the present application can include the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling and the step of correcting the simulation results of the electrochemical modeling by applying a hysteresis model.

[0037] The electrochemical modeling method is a modeling that formulates the physical movement of the internal substances of the secondary battery by partial differential equations (PDEs) and ordinary differential equations (ODEs) in time and space.

[0038] Various methods for such electrochemical modeling are known.

[0039] In the present application, an appropriate method can be selected and used from among the known battery chemical modeling methods. However, from the perspective of ensuring consistency with the actual behavior of the secondary battery after correction by hysteresis modeling, it may be advantageous to apply the so-called DFN (Doyle-Fuller-Newman) modeling method. The DFN modeling method is a method of modeling the spatio-temporal change in lithium ion concentration, potential, intercalation kinetics, and current density between the solid phase and the electrolyte phase existing in the porous electrode.

[0040] As an example, in this method, a battery cell having a shape as shown in FIG. 2 can be modeled. At this time, it is considered that lithium ions are transported one-dimensionally from one electrode to the other electrode through a separator.

[0041] In the modeling of the present application, so-called volume averaging is also applied. In such modeling, the anode structure is porous and is regarded as heterogeneous materials. In particular, the heterogeneities of the material are small and are regarded as being uniformly distributed with respect to the overall dimension of the system from a statistical point of view. The transport process and geometric structure at the microscale determine the macroscopic transport characteristics. Typically, in the said method, an RVE (Representative Volume Element) is defined whose dimension is sufficiently small compared to the system geometry and at the same time is sufficiently large to be able to include all macroscopic phenomena. In the volume averaging method, the microscopic equations are converted into macroscopic equations within the said RVE.

[0042] In one example, in the electrochemical modeling step of the present application, the following five equations can be used as governing equations.

[0043] In the present application, the said modeling can be performed using any one or two or more or all of the following equations (1) to (5).

[0044] [Equation (1)] [Number]

[0045] In Equation (1), Cs is the concentration of lithium in the solid particle phase (unit: mol / m 3) where r is the radius of the particle (unit: m), and Ds is the lithium-ion diffusion coefficient (unit: cm 2 / s).

[0046] Equation 1 is an equation obtained by applying Fick's Law on the assumption that the particles such as the electrode material have a spherical particle shape and that the diffusion coefficient does not depend on the concentration.

[0047] Equation 1 is affected by the Neumann boundary conditions in the following Equations 1 to 3 at the center of the particle (when r in Equation 1 is 0) and at the surface of the particle (when r in Equation 1 is the radius R of the particle). s

[0048] [Equation 1] [Number]

[0049] [Equation 2] [Number]

[0050] [Equation 3] [Number]

[0051] In Equations 1 to 3, Cs is the concentration of lithium in the solid particle phase (unit: mol / m 3 ), r is the radius of the particle (unit: m), Ds is the lithium-ion diffusion coefficient (unit: cm 2 / s), and [Number] ​is the initial concentration profile of the particles, and j n is the molar flux, indicating the rate of the lithium intercalation / de-intercalation reaction.

[0052] [Equation 2] [Number] In Equation 2, [Number] is the volume fraction of the electrolyte, De,eff is the diffusivity constant of the electrolyte medium (unit: cm 2 / s), and c e is the concentration of the electrolyte (unit: mol / m 3 ).

[0053] Equation 2 is an equation derived by the volume average of mass conservation on the electrolyte of the porous electrode, and can inform changes such as the concentration gradient depending on the electrolyte diffusion flux of the local volume-averaged concentration of lithium.

[0054] [Equation 3] [Number] In Equation 3, [Number] is the effective electrical conductivity of the solid phase (unit: S / cm), [Number] is the potential of the solid phase (unit: V),

Number

[0055] The left side of Equation 3 represents the current density, and Equation 3 means that the divergence of the current density in any volume in the cell is the same as the net charge reaching or existing from the given volume. In Equation 3,

Number

Number

[0056] [Mathematical formula 4]

Number

Number

Number

[0057] [Equation 4]

Number

Number

Number

Number

[0058] Equation 4 uses the volume averaging theorem for the liquid phase charge conservation equation and refers to the charge continuity equation in the electrolyte. Equation 4 means that the net charge flux existing in or entering the electrolyte volume is equal to the difference in current density and the logarithmic concentration gradient in the electrolyte.

[0059] Some of the variables in Equation 4 have the relationship of the following Mathematical Formula 5.

[0060] [Mathematical Formula 5]

Number

Number

[0061] [Equation 5] [Number]

[0062] In Equation 5, i is the current density passing through the interface (unit: A / cm 2 ), and [Number] is the exchange current density with respect to the electrode-electrolyte interface (unit: A / cm 2 ), α a is the charge transfer coefficient of the anodic reaction, α c is the charge transfer coefficient of the cathodic reaction, η is the over potential, F is the Faraday constant, R is the gas constant, and T is the absolute temperature (unit: K).

[0063] Equation 5 is the governing equation that simulates the movement of lithium ions between the solid phase and the electrolyte phase, and is derived from the Butler-Volmer equation based on the assumption that the concentration of lithium ions in the electrolyte on the electrode surface is equal to the bulk concentration.

[0064] In this application, the simulation is performed through the above battery chemical modeling method. The method of performing the simulation using each of the above governing equations and the experimental parameters applied at this time are well known.

[0065] FIG. 3 is a diagram exemplarily showing the simulation results to which the above electrochemical modeling is applied.

[0066] The results in FIG. 3 are the results of simulating the case of charging and discharging a coin half-cell to which an LFP (LiFePO4) electrode is applied as an anode at a current of 1 / 50C. At this time, the loading amount of the applied LFP electrode is about 3.55 mAh / cm 2 , the porosity is about 25.6%, and the average radius of the LFP particles is about 1.5 μm.

[0067] In the drawing, the results of the charge-discharge simulation are shown by a red line. Depending on the electrochemical modeling as shown in the drawing, a result is obtained in which the voltage changes abruptly when switching from charging to discharging or from discharging to charging. However, the behavior of an actual battery is different from this, and thus, a correction for this is required.

[0068] Accordingly, in the present application, a step of further correcting the simulation results by applying the hysteresis modeling is performed.

[0069] The hysteresis means the difference in voltage that occurs when a secondary battery is charged to a specific state of charge and reaches that state and when it is discharged and reaches that state, and it is a phenomenon in which charging and discharging are different at the same state of charge (SOC). During simulation by electrochemical modeling, the hysteresis phenomenon is not reflected in the process of switching from charging to discharging and / or the process of switching from discharging to charging, and the voltage is calculated as changing abruptly.

[0070] Therefore, in the present application, a step of correcting the simulation results by electrochemical modeling with hysteresis modeling is performed.

[0071] Specifically, the correction step can be performed in a manner that converges the hysteresis over time in the charge-discharge conversion process in the simulation results by the electrochemical modeling. In the above, the charge-discharge conversion process can be when converting from charge to discharge and / or when converting from discharge to charge.

[0072] The correction process can be performed, for example, using the following governing equation (Equation 6).

[0073] [Equation 6]

Number

[0074] In Equation 6, h is the Voltage deviation by hysteresis, z is the state of charge (SOC) or the stoichiometry of the substance, M is the maximum voltage gap in the major hysteresis loop, and γ is the adjustment constant.

[0075] In the above, the adjustment constants are M and γ, which are experimental values that change according to the State of Charge (SOC).

[0076] Equation 6 is based on the one-state model among various hysteresis models, such as the combined model, simple mode, zero-state hysteresis model, and one-state model.

[0077] When correcting the simulation results to which Equations 1 to 5 are applied, Equation 6, which is the governing equation, can obtain results that match the actual situation.

[0078] In the above formula 6, h(z, t) is the hysteresis voltage as a function of SOC (State of Charge) and time, [Number] is determined by the following mathematical formula 6.

[0079] [Mathematical formula 6] [Number] In formula 6, [Number] is a function that gives the rate-of-change of SOC (state of charge) and the maximum polarization due to hysteresis as a function of SOC. In formula 6, [Number] describes that the rate-of-change of the hysteresis voltage is proportional to the distance from the major hysteresis loop, leading to a kind of exponential decay of the voltage with respect to the main loop.

[0080] In formula 6, γ is a positive constant that adjusts the degree of the decrease, [Number] enables formula 6 to act effectively during the charging and discharging processes. As described above [Number] has +1 in the charging state and -1 in the discharging state.

[0081] When obtaining the OCV (open - circuit voltage) including hysteresis through the results obtained from Equation 6, the following Equation 7 is applied to the OCV after charging, and the following Equation 8 is applied to the OCV after discharging.

[0082] [Equation 7]

[0083] OCV after charging = Main hysteresis OCV in charging situation + h - M

[0084] [Equation 8]

[0085] OCV after discharging = Main hysteresis OCV in discharging situation - h + M

[0086] In the above Equation 7, h and M are as defined in Equation 6.

[0087] In this application, the simulation results of electrochemical modeling can be corrected by applying the above - mentioned modeling method, and accordingly, more realistic results can be obtained.

[0088] Figure 4 shows the result of correcting the result of Figure 3 by the above method.

[0089] The correction for obtaining the result of Figure 4 was performed by a method of obtaining the M value and γ according to the SOC (State of Charge) through experiments and then obtaining the OCV after charging or discharging.

[0090] Figure 5 is a diagram showing the M value confirmed as a function of the SOC (State of Charge), and Figure 6 is a diagram showing how the γ value optimized at SOC50 is applied to the actual OCV calculation.

[0091] In the corrected result as shown in the drawings, when converting from charging to discharging and when converting from discharging to charging, the voltage converges to a predetermined value at a certain rate, which corresponds to the behavior of an actual battery.

[0092] FIG. 7 shows the actual charge and discharge behavior of the battery simulated in FIG. 4. Comparing FIGS. 4 and 7, it can be seen that results consistent with the actual situation can be obtained by the method of the present application.

[0093] In the present application, by simulating the charge and discharge behavior of the secondary battery in the above manner, results consistent with the actual situation can be effectively obtained.

[0094] When simulating the charge and discharge behavior of the secondary battery through the above-described method, known software or the like can be used.

[0095] Such a method of the present application can also be provided in the hardware state or system state in which the method is stored.

[0096] Therefore, the present application also relates to a hardware device or system in which the simulation method of the charge and discharge behavior of the secondary battery is stored.

[0097] As an example, the device or system may be a so-called Battery Management Device or a Battery Management System (BMS). As is known, the Battery Management Device or the Battery Management System (BMS) measures various elements such as current, voltage, and / or temperature of a secondary battery applied to an electric vehicle or a hybrid electric vehicle through a sensor or the like, and controls the charging and / or discharging state and the remaining amount of the secondary battery. Such a device mainly performs state control of the secondary battery, separation of the battery or secondary battery in case of emergency, adjustment of imbalance in the secondary battery intermediate variables in an integrated battery module or pack, provision of charging information of the secondary battery, provision of information on the state of the secondary battery, provision of information for driver display and warning, prediction of the usable function range of the battery (such as the travelable distance), provision of an optimal charging algorithm for charging the integrated battery module or pack or the secondary battery, provision of an approach means enabling charging of individual secondary batteries, and response to changes in the vehicle driving mode.

[0098] According to the method of the present application, the simulation results for the charge and discharge behavior of the secondary battery can be effectively provided, and such results can be used in cooperation with the algorithm of the battery management device or system to provide an optimal operating environment for the secondary battery. Further, the algorithm of the battery management device or system in cooperation with the method of the present application can provide, for example, an electric and motor control system suitable for the driving mode of the vehicle, and can effectively adjust the performance of the secondary battery according to acceleration, braking, idling availability, and vehicle operation mode (electric vehicle mode, hybrid mode).

[0099] There is no particular limitation on the method of applying the method of the present application to the battery management device or system, and an appropriate known algorithm configuration method and device and system configuration method can be applied to construct the battery management device or system.

Claims

1. A method for simulating the charge and discharge behavior of a secondary battery, comprising: simulating the charge and discharge behavior of the secondary battery through electrochemical modeling; and correcting the simulation result obtained by the electrochemical modeling by applying hysteresis modeling.

2. The method according to claim 1, wherein the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling is performed using DFN modeling.

3. The method according to claim 1, wherein the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling is performed using one or more of the following formulas (1) to (5): [Formula 1] 【Number 47】 In Equation 1, Cs is the concentration of lithium in the solid particle phase (unit: mol / m ３ ), r is the radius of the particle (unit: m), and Ds is the diffusion coefficient of lithium (unit: cm ２ / s): [Formula 2] 【Number 48】 In Formula 2, 【Number 49】 is the volume fraction of the electrolyte, and De,eff is the diffusion coefficient of the electrolyte medium (unit: cm ２ / s), and c ｅ is the concentration of the electrolyte (unit: mol / m ３ ): [Formula 3] 【Number 50】 In Formula 3, 【Number 51】 is the effective electrical conductivity of the solid phase (unit: S / cm), 【Number 52】 is the potential of the solid phase (unit: V), 【Number 53】 is the non-interfacial area between solids (unit: m ２ / m ３ ), F is the Faraday constant (96,487 C / eq), and j is the molar flux of lithium passing through the interface between the solid phase and the electrolyte: [Formula 4] 【Number 54】 In Formula 4, 【Number 55】 is the effective ionic conductivity of the electrolyte (S / cm), 【Number 56】 is the potential of the electrolyte (unit: V), and c ｅ is the concentration of the electrolyte, 【Number 57】 is the non-interfacial area between solids (unit: m ２ / m ３ ), F is the Faraday constant (96,487 C / eq), and j is the molar flux of lithium passing through the interface between the solid phase and the electrolyte: [Formula 5] 【Number 58】 In Formula 5, i is the current density passing through the interface (unit: A / cm ２ ), and 【Number 59】 is the exchange current density at the electrode / electrolyte interface (unit: A / cm ２ ), α a is the charge transfer coefficient of the cathode reaction, α c is the charge transfer coefficient of the anode reaction, η is the overpotential, F is the Faraday constant, R is the gas constant, and T is the absolute temperature (unit: K).

4. The method according to claim 3, wherein in the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling, all of Formulas (1) to (5) are used.

5. The method according to claim 1, wherein the step of correcting the simulation result obtained by the electrochemical modeling by applying hysteresis modeling is a step of converging the hysteresis when converting from charge to discharge and when converting from discharge to charge over time according to the simulation result obtained by the electrochemical modeling.

6. The method according to claim 3, wherein the step of correcting the simulation result obtained by the electrochemical modeling by applying hysteresis modeling is performed using the following formula (6). [Formula 6] 【Number 60】 In Formula 6, h is the voltage deviation due to hysteresis, z is the state of charge (SOC) or the stoichiometry of the substance, M is the gap of the maximum voltage in the main hysteresis loop, and γ is an adjustment constant.

7. A hardware device storing the method according to any one of claims 1 to 6.

8. A battery management device storing the method according to any one of claims 1 to 6.

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