Method for simulating charge / discharge behavior of secondary battery

Abstract

The present application may provide a method for simulating charge / discharge behavior of a secondary battery; a hardware device storing the method; and a battery management apparatus storing the method. The present application can provide a method capable of simulating the charge / discharge behavior of a secondary battery in a relatively simple manner so as to be highly consistent with the actual behavior; the invention also provides a hardware device and a battery management device for 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, the disclosure of which is incorporated herein by reference in its entirety.

[0002] The present application relates to a method for simulating the charging and discharging behavior of a secondary battery, a hardware device storing the method, and a battery management device storing the method. Background Art

[0003] Secondary batteries are devices that can be charged and discharged, converting electrical energy in the form of chemical energy for storage and then generating electricity when needed.

[0004] With the expansion of the electric vehicle market and the like, there is a need to develop secondary batteries having high energy density and capable of achieving high energy density.

[0005] In terms of obtaining maximum performance within a safe range and increasing the degree of freedom in application of secondary batteries, it is important to accurately identify the condition and life of the secondary battery, etc.

[0006] For this reason, there are various modeling methods for secondary batteries.

[0007] For example, the circuit model (or equivalent model) is a method of modeling the input characteristics and output characteristics of a secondary battery by the configuration of the circuit, which can be achieved by changing the component configuration according to the type of the secondary battery. This method has the advantages of simplicity and low computational cost, but is not effective in terms of accuracy.

[0008] As another method, the electrochemical model method is also known. The electrochemical model method is also called the physical equation model method. The method is based on the detailed configuration of the chemical reaction occurring inside the secondary battery. The method is to model the physical movement of the internal particles of the secondary battery by equationalizing partial differential equations (partial differential equation, PDE) and space-time ordinary differential equations (space-time ordinary differential equation, ODE). The electrochemical modeling method is somewhat complicated to calculate, but the accuracy is high, and with the development of computer hardware, the problem of computational complexity is also reduced.

[0009] However, even in the electrochemical modeling method, supplementation is required to accurately simulate the charge and discharge behavior of the secondary battery. The disadvantage of the electrochemical modeling method is that it does not reflect the so-called hysteresis phenomenon of the charge and discharge of the secondary battery.

[0010] The hysteresis of a secondary battery refers to the difference between voltages occurring when the secondary battery is charged to a certain charge state to reach the state and discharged to reach the state, which is a phenomenon that charging and discharging occur differently at the same charge amount (charge state).

[0011] Since this phenomenon is nonlinear and has a significant impact on the performance of secondary batteries, it is important to accurately predict this phenomenon. Summary of the invention

[0012] Technical issues

[0013] 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 in a relatively simple manner to have a high degree of consistency with the actual behavior, as well as a hardware device storing the relevant method and a battery management device.

[0014] Technical Solution

[0015] This specification discloses a method for simulating the charge and discharge behavior of a secondary battery.

[0016] The method may include the following steps: simulating the charge and discharge behavior of the secondary battery by electrochemical modeling; and applying hysteresis modeling to correct the simulation result of the electrochemical modeling.

[0017] In the above method, the step of simulating the charge and discharge behavior of the secondary battery by electrochemical modeling may be performed using DFN (Doyle-Fuller-Newman) modeling.

[0018] Here, the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling may be performed using one or more of Equations 1 to 5 below.

[0019] [Equation 1]

[0020]

[0021] 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) (lithium ion diffusion coefficient).

[0022] [Equation 2]

[0023]

[0024] In Equation 2, εe is the volume fraction of electrolyte, D e,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 ).

[0025] [Equation 3]

[0026]

[0027] In Equation 3, σ eff is the effective conductivity of the solid phase (unit: S / cm), Φs is the potential of the solid phase (unit: V), and α s is the specific interface 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 across the boundary between the solid phase and the electrolyte.

[0028] [Equation 4]

[0029]

[0030] In Equation 4, κ eff is the effective ionic conductivity of the electrolyte (S / cm), Φ e is the potential of the electrolyte (unit: V), c e is the concentration of the electrolyte, and α s is the specific interface 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 across the boundary between the solid phase and the electrolyte.

[0031] [Equation 5]

[0032]

[0033] In Equation 5, i is the current density across the interface (unit: A / cm 2 ), ι0 is the exchange current density at the interface between the electrode and the electrolyte (unit: A / cm 2 ), α a is the charge transfer coefficient of the negative electrode reaction, α c is the charge transfer coefficient of the positive electrode reaction, η is the overpotential, F is the Faraday constant, R is the gas constant, and T is the absolute temperature (unit: K).

[0034] Here, in the step of simulating the charge and discharge behavior of the secondary battery through electrochemical modeling, all of Equation 1 to Equation 5 above may be used.

[0035] Here, the step of applying hysteresis modeling to correct the simulation result of electrochemical modeling may be a step of causing the hysteresis when switching from charge to discharge and the hysteresis when switching from discharge to charge in the simulation result of the electrochemical modeling to converge over time.

[0036] Here, the step of applying hysteresis modeling to correct the simulation results of electrochemical modeling may be performed using Equation 6 below.

[0037] [Equation 6]

[0038]

[0039] In Equation 6, h is the voltage deviation due to hysteresis, z is the stoichiometry or SOC (state of charge) of the material, and M is the maximum voltage difference in the main hysteresis loop, and γ is the regulation constant.

[0040] This specification also discloses a hardware device in which a method or an algorithm (an algorithm by which the method is implemented) is stored.

[0041] The present specification also discloses a battery management device or a battery management system, in which the method or algorithm (algorithm by the method) is stored.

[0042] Beneficial Effects

[0043] The present application may 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 may provide: a method capable of simulating the charge and discharge behavior of a secondary battery in a relatively simple manner to have a high degree of consistency with the actual behavior, and a hardware device storing the relevant method and a battery management device. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart showing the process of executing the method of the present application.

[0045] Figure 2 is a schematic diagram of the structure of a battery cell suitable for modeling.

[0046] Figure 3 is an example of simulation results using electrochemical modeling.

[0047] Figure 4 is corrected by hysteresis modeling Figure 3 An example of the results of the results.

[0048] Figure 5is a graph showing M values ​​confirmed as a function of SOC (state of charge).

[0049] Figure 6 is a graph showing how the optimized gamma value at SOC 50 is applied to the OCV calculation.

[0050] Figure 7 It is shown Figure 4 Figure 2. A diagram of the charge and discharge behavior of a simulated battery. DETAILED DESCRIPTION

[0051] The present application relates to a method for simulating the charge and discharge behavior of a secondary battery. When simulating the charge and discharge behavior of a secondary battery, the present application combines the so-called electrochemical modeling method and the hysteresis modeling method.

[0052] Specifically, by appropriately controlling, selecting, and combining electrochemical modeling methods and hysteresis modeling methods, the present application can simulate the charge and discharge behavior of a secondary battery to have a high degree of consistency with reality.

[0053] Figure 1 is a diagram showing how to perform the method of the present application.

[0054] like Figure 1 As shown, the present application simulates the charge and discharge behavior of a secondary battery by inputting experimental parameters, and then corrects the results of the electrochemical modeling simulation based on the input parameters through a hysteresis model.

[0055] Therefore, the method of the present application may include the steps of simulating the charge and discharge behavior of the secondary battery by electrochemical modeling and correcting the simulation result of the electrochemical modeling by applying hysteresis modeling.

[0056] The electrochemical modeling method is a modeling method that equationalizes the physical motion of particles inside a secondary battery by using a partial differential equation (PDE) and a time-space ordinary differential equation (ODE).

[0057] Various methods for such electrochemical modeling are known.

[0058] In the present application, an appropriate method can be selected and used in the known cell chemistry modeling methods, but in terms of ensuring consistency with the actual secondary battery behavior after correction by hysteresis modeling, it is advantageous to apply and implement the so-called DFN (Doyle-Fuller-Newman) modeling method. The DFN modeling method is a method for modeling the spatiotemporal changes of lithium ion concentration, potential, intercalation kinetics, and current density between the solid phase and the electrolyte phase in the porous electrode.

[0059] In one example, Figure 2A battery cell of the type shown in can be modeled in this approach. In this case, a one-dimensional transport of lithium ions from one electrode to the other through a separator is considered.

[0060] In the modeling of the present application, the so-called volume averaging is also applied. In this modeling, the cathode structure is considered as a porous and heterogeneous material. In particular, the material has a small heterogeneity and, from a statistical point of view, it is considered to be uniformly distributed in all dimensions of the system. Microscale transport processes and geometric structures determine the macroscopic transport properties. Generally, in this method, an RVE (representative volume element) is defined, whose size is small enough compared to the system geometry and at the same time large enough to include all macroscopic phenomena. In the volume averaging method, the microscopic equations are converted into macroscopic equations within the RVE.

[0061] In one example, the following five equations can be used as the controlling equations in the electrochemical modeling step of the present application.

[0062] In the present application, modeling may be performed using any one, two or more, or all of the following Equations 1 to 5.

[0063] [Equation 1]

[0064]

[0065] 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) (lithium ion diffusion coefficient).

[0066] The above equation 1 is an equation to which the so-called Fick's law is applied, assuming that particles such as electrode materials are in the form of spherical particles and that the diffusion coefficient is independent of concentration.

[0067] Equation 1 is affected by the following mathematical formulas 1 to 3, which are the center of the particle (if r in Equation 1 is 0) and the surface of the particle (if r in Equation 1 is the radius R of the particle) s ) at the Neumann boundary condition.

[0068] [Mathematical formula 1]

[0069]

[0070] [Mathematical formula 2]

[0071]

[0072] [Mathematical formula 3]

[0073]

[0074] In mathematical formula 1-3, 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 diffusion coefficient of lithium (Li ion diffusion coefficient) (unit: cm 2 / s), C i 0 is the initial concentration distribution of particles, and j n is the molar flux and represents the rate of lithium insertion / deinsertion reactions.

[0075] [Equation 2]

[0076]

[0077] In Equation 2, ε e is the volume fraction of electrolyte, D e,eff is the diffusion coefficient of the electrolyte medium (unit: cm 2 / s), c e is the concentration of the electrolyte (unit: mol / m 3 ).

[0078] Equation 2 is an equation derived by volume averaging of mass conservation in the electrolyte phase of the porous electrode, which can inform that the local volume average concentration of lithium depends on the change caused by the concentration gradient, etc. due to the electrolyte diffusion flux.

[0079] [Equation 3]

[0080]

[0081] In Equation 3, σ eff is the effective conductivity of the solid phase (unit: S / cm), Φ s is the potential of the solid phase (in V), and α s is the specific interface 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 through the boundary between the solid phase and the electrolyte.

[0082] The left side of Equation 3 represents the current density, and Equation 3 indicates that the difference in current density at any volume in the cell is equal to the net charge arriving or present from a given volume.

[0083] In Equation 3, σ eff and Φ s The relationship in the following mathematical formula 4 can be expressed.

[0084] [Mathematical formula 4]

[0085]

[0086] In mathematical formula 4, ε s represents the volume fraction of the solid phase, and ι s It is the current of a solid.

[0087] [Equation 4]

[0088]

[0089] In Equation 4, κ eff is the effective ionic conductivity of the electrolyte (S / cm), Φ e is the potential of the electrolyte (unit: V), c e is the concentration of the electrolyte, and α s is the specific interface 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 through the boundary between the solid phase and the electrolyte.

[0090] Equation 4 uses the volume average theorem of the liquid phase charge conservation equation, which refers to the charge continuity equation in the electrolyte. Equation 4 indicates that the net charge flux present in or into the electrolyte volume is equal to the difference between the current density and the logarithmic concentration gradient in the electrolyte.

[0091] Some variables in Equation 4 have the relationship in the following mathematical formula 5.

[0092] [Mathematical formula 5]

[0093]

[0094] In mathematical formula 5, ε e is the volume fraction of the electrolyte, and ι e It is the current of a solid.

[0095] [Equation 5]

[0096]

[0097] In Equation 5, i is the current density across the interface (unit: A / cm 2 ), ι0 is the exchange current density at the interface between the electrode and the electrolyte (unit: A / cm 2 ), α a is the charge transfer coefficient of the negative electrode reaction, α cis the charge transfer coefficient of the positive electrode reaction, η is the overpotential, F is the Faraday constant, R is the gas constant, and T is the absolute temperature (unit: K).

[0098] Equation 5 is the governing equation that models the movement of lithium ions between the solid phase and the electrolyte phase, which is derived through the Butler-Volmer equation based on the assumption that the lithium ion concentration in the electrolyte on the electrode surface is the same as the bulk concentration.

[0099] The present application performs simulations by this cell chemistry modeling method. The method of performing simulations using the corresponding control equations as described above and the experimental parameters applied at this time is well known.

[0100] Figure 3 A diagram schematically showing simulation results using electrochemical modeling.

[0101] Figure 3 The results in the figure are the results of simulating the case where a button half-cell using an LFP (LiFePO4) electrode as a positive electrode is charged and discharged at a current of 1 / 50C, wherein 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.

[0102] In the figure, the results of the charge and discharge simulation are shown in red. As shown in the figure, the electrochemical modeling obtains the result that the voltage changes rapidly when switching from charging to discharging or when switching from discharging to charging. However, the behavior of the actual battery is different, so it is necessary to correct for this.

[0103] Therefore, the present application also performs the step of applying hysteresis modeling to correct the simulation results.

[0104] Hysteresis refers to the difference between the voltage generated when a secondary battery is charged to a certain charge state to reach the state and when the secondary battery is discharged to reach the state, which is a phenomenon that charging and discharging occur differently at the same charge amount (charge state). When simulating using electrochemical modeling, the hysteresis phenomenon is not reflected in the process of switching from charging to discharging and / or switching from discharging to charging, and the voltage is calculated to change rapidly.

[0105] Therefore, the present application performs the step of correcting the simulation results of electrochemical modeling by utilizing hysteresis modeling.

[0106] Specifically, the correction step can be performed by a method that allows the hysteresis in the switching process of charging and discharging in the simulation results of electrochemical modeling to converge over time. Here, the switching process of charging and discharging can be switching from charging to discharging and / or switching from discharging to charging.

[0107] The correction process can be performed, for example, using the following control equation (Equation 6).

[0108] [Equation 6]

[0109]

[0110] In Equation 6, h is the voltage deviation due to hysteresis, z is the stoichiometry or SOC (state of charge) of the material, and M is the maximum voltage difference in the main hysteresis loop, and γ is the regulation constant.

[0111] Here, the adjustment constants are M and γ, which are experimental values ​​that vary according to SOC (State of Charge).

[0112] The above Equation 6 is based on a single-state model among various hysteresis modeling, such as a combination model, a simple mode, a zero-state hysteresis model, and a single-state model.

[0113] When the simulation results applying Equation 1 to Equation 5 are corrected, Equation 6 as a control equation can obtain a result consistent with reality.

[0114] In Equation 6, h(z,t) is the hysteresis voltage as a function of SOC (state of charge) and time, and z · Determined by the following mathematical formula 6.

[0115] [Mathematical formula 6]

[0116]

[0117] In Equation 6, M(z,z · ) is a function that gives the maximum polarization due to hysteresis as a function of the rate of change of SOC (state of charge) and SOC.

[0118] In Equation 6, M(z,z · )-h(z,t) describes that the rate of change of the hysteresis voltage is proportional to the distance from the main hysteresis loop and results in an exponential decrease in the voltage on the main loop.

[0119] In Equation 6, γ is a positive constant and adjusts the degree of degreasing, and sgn(z · ) allows Equation 6 to work effectively during the charge and discharge process. Such sgn(z · ) has +1 in the charging case and -1 in the discharging case.

[0120] When OCV (open-circuit voltage) including hysteresis is obtained through the result of Equation 6, the following Equation 7 is applied to the OCV after charge, and the following Equation 8 is applied to the OCV after discharge.

[0121] [Equation 7]

[0122] OCV after charging = main hysteresis OCV in charging condition + hM

[0123] [Equation 8]

[0124] OCV after discharge = main hysteresis OCV under discharge condition - h + M

[0125] In Equation 7, h and M are as defined in Equation 6.

[0126] The present application can correct the simulation results of electrochemical modeling by adopting such a modeling method, thereby obtaining results consistent with reality.

[0127] Figure 4 It shows that the correction in the above manner Figure 3 the result of the result.

[0128] Obtaining the M value and γ by experiment according to the SOC (state of charge) and then obtaining the OCV after charging or discharging is performed. Figure 4 Correction of the results.

[0129] Figure 5 is a graph showing the M value confirmed as a function of SOC (state of charge), and Figure 5 is a graph showing the M value confirmed as a function of SOC (state of charge), and Figure 6 is a graph showing how the optimized gamma value at SOC 50 is applied to the OCV calculation.

[0130] In the correction results in the drawing, the voltage converges to a predetermined value at a constant rate when switching from charging to discharging and when switching from discharging to charging, which corresponds to the behavior of an actual battery.

[0131] Figure 7 yes Figure 4 The actual charge and discharge behavior of the battery simulated in . Figure 4 and Figure 7 It can be seen that the method of the present application can obtain results consistent with reality.

[0132] The present application can effectively obtain results consistent with reality by simulating the charge and discharge behavior of a secondary battery in this way.

[0133] When simulating the charge and discharge behavior in the secondary battery by the above method, known software or the like can be used.

[0134] The method of the present application may also be provided to store the hardware state or system state of the method.

[0135] Therefore, the present application also relates to a hardware device or system storing a method for simulating the charge and discharge behavior of a secondary battery.

[0136] In one example, the device or system may be a so-called battery management device or battery management system (BMS). As is well known, a battery management device or battery management system (BMS) is a device and system that measures various elements such as current, voltage and / or temperature of a secondary battery applied to an electric vehicle or hybrid electric vehicle, etc., through sensors, etc., to control the charging and / or discharging state and the remaining amount of the secondary battery. Such a device mainly performs secondary battery state control, disconnection of a battery or secondary battery during an emergency, adjustment of the imbalance existing in the secondary battery parameters within an integrated battery module or battery pack, provision of charging information of the secondary battery, provision of information about the state of the secondary battery, provision of information about the driver display and alarm, prediction of the available range of the battery (mileage, etc.), provision of the best charging algorithm for charging an integrated battery module or battery pack or a secondary battery, provision of rechargeable access devices for each secondary battery, response to changes in the vehicle driving mode, etc.

[0137] According to the method of the present application, simulation results of the charge and discharge behavior of the secondary battery can be effectively provided, and by connecting these results with the algorithm of the battery management device or system, an optimal operating environment can be provided for the secondary battery. In addition, the algorithm of the battery management device or system related to the method of the present application can effectively adjust the performance of the secondary battery according to acceleration, braking, idling and vehicle operation mode (electric vehicle mode, hybrid mode) by providing, for example, an electric and motor control system suitable for the vehicle drive mode.

[0138] There is no particular limitation on the method of applying the method of the present application to a battery management device or system, and the battery management device or system can be constructed by applying appropriate known algorithm configuration methods and device and system configuration methods.

Claims

1. A method for simulating the charge and discharge behavior of a secondary battery, the method comprising the following steps: Simulating the charge and discharge behavior of the secondary battery by electrochemical modeling; The simulation results of the electrochemical modeling were corrected by applying hysteresis modeling.

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

3. The method according to claim 1, wherein: The simulation of the charge and discharge behavior of the secondary battery by the electrochemical modeling is performed by using one or more of the following Equations 1 to 5: [Equation 1] Where Cs is the lithium concentration in the solid particle phase (unit: mol / m 3 ), r is the particle radius (unit: m), and Ds is the lithium ion diffusion coefficient (unit: cm 2 / s): [Equation 2] Among them, ε e is the volume fraction of electrolyte, D e,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 ): [Equation 3] Among them, σ eff is the effective conductivity of the solid phase (unit: S / cm), Φ s is the potential of the solid phase (unit: V), α s is the specific interface 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 across the boundary between the solid phase and the electrolyte: [Equation 4] Among them, κ eff is the effective ionic conductivity of the electrolyte (S / cm), Φ e is the potential of the electrolyte (unit: V), c e is the concentration of the electrolyte, and α s is the specific interface 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 across the boundary between the solid phase and the electrolyte; [Equation 5] Where i is the current density across the interface (unit: A / cm 2 ), ι0 is the exchange current density between the electrode and the electrolyte interface (unit: A / cm 2 ), α a is the charge transfer coefficient of the negative electrode reaction, α c is the charge transfer coefficient of the positive electrode 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: When simulating the charge and discharge behavior of the secondary battery by electrochemical modeling, all of Equation 1 to Equation 5 are used.

5. The method according to claim 1, wherein: The step of correcting the simulation result of the electrochemical modeling by applying hysteresis modeling includes causing hysteresis generated when switching from charge to discharge and hysteresis generated when switching from discharge to charge in the simulation result of the electrochemical modeling to converge over time.

6. The method according to claim 3, wherein: Correction of the simulation results of the electrochemical modeling by applying hysteresis modeling was performed using the following Equation 6: [Equation 6] Where h is the voltage deviation due to hysteresis, z is the stoichiometry or SOC state of charge of the material, M is the maximum voltage difference in the main hysteresis loop, and γ is the regulation constant.

7. A hardware device, wherein the method according to any one of claims 1 to 6 is stored.

8. A battery management device, wherein the method according to any one of claims 1 to 6 is stored.

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