Accelerated battery lifetime simulations using adaptive inter-cycle extrapolation algorithm

Abstract

A method for manufacturing an electrochemical cell is disclosed, wherein the cell undergoes degradation resulting in loss of active material and cation inventory during the charge phase(s) of cell cycles. The method comprises: selecting at least one cell component from electrolytes, cathode active materials, and anode active materials; sequentially calculating cell capacities at the end of each of a plurality of cell cycles based on total cyclable cations, accessible storage sites at each electrode, and cell component(s), using a degradation model based on porous-electrode theory having degradation path(s) — cell cycles are initialized based on the rate of degradation over previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over previous cycles —; and predicting the end of the cell life based on one of the calculated cell capacities being less than a percentage of the nominal capacity.

Description

Technology Field

[0001] This application claims priority to U.S. Patent Application No. 63 / 321,402, filed on March 18, 2022.

[0002] The present invention was made with government support pursuant to Grant No. 1762247 awarded by the National Science Foundation. The U.S. government has certain rights to the present invention.

[0003] The present invention relates to methods for increasing the speed of battery life prediction systems so that manufacturers can accelerate the battery cell development process. Background Technology

[0004] As demand for electric vehicles increases, global lithium-ion battery manufacturing capacity is rapidly approaching the terawatt-hour scale. Lithium-ion batteries are used in a wide range of applications due to their low cost, reduced expenses, high energy densities, and long cycle life. Batteries for light vehicles and grid applications are typically manufactured to last and be guaranteed for 8 to 10 years. An improved understanding of battery degradation can lead to better reliability, safety, expanded battery utilization, and consequently cost savings. However, battery degradation can take approximately 10 years in the field, which is too long to understand the impact of changes in battery design parameters on lifespan.

[0005] The total testing time for predicting battery cycle life is typically reduced in the laboratory by using accelerated aging conditions and skipping breaks between cycles to degrade the battery within a few months. To further reduce time, modeling is required. In particular, physics-based electrochemical models that include degradation mechanisms are useful for evaluating the capacity and power fade of lithium-ion batteries at various duty cycles and thus predicting their lifespan, as they can directly simulate a wide range of realistic battery applications at various scales. However, physics-based simulations of total battery life generally take minutes to hours. For example, if simulating a single full charge / discharge cycle takes 1 second, simulating 1,000 cycles takes about 15 minutes. While this is much faster than experimental time scales, it is still too slow and is not ideal for rapid feedback and iterative simulations in parameter estimation routines that require multiple forward solves of the model.

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[0007] The present invention addresses the aforementioned needs by providing methods for increasing the speed of battery life prediction systems so that manufacturers can accelerate the battery cell development process.

[0008] In one embodiment, the present disclosure provides a method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations that move from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell at a state of 100% health; (c) using a degradation model based on porous-electrode theory having one or more degradation pathways, the total circulating cations ( (d) a step of sequentially calculating cell capacities at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — cell cycles are initialized based on the rate of degradation over a plurality of previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over a plurality of previous cycles —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0009] In one embodiment, the present disclosure provides a method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations that move from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of solid electrolyte interphase formation as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0010] In one embodiment, the present disclosure provides a method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations that move from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of cation plating as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0011] In one version of these methods, the model does not include algebraic equations. In another version of these methods, the step of sequentially calculating cell capacity at the end of each of multiple cell cycles is at least three times faster than a degradation model based on porosity-electrode theory that includes algebraic equations. In another version of these methods, the model [includes] surface potential difference Without including an algebraic equation to calculate, here represents the solid phase potential of the anode. represents the phase potential of the electrolyte.

[0012] In other versions of these methods, step (c) is a solid electrolyte interphase kinetic rate constant ( k SEI ), solid electrolyte interphase layer diffusivity (D SEI ), and active material particle cracking rate (β LAM The method includes the step of sequentially calculating the cell capacity at the end of each of a plurality of cell cycles based on ). In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a linear degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a self-limiting degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate an accelerated degradation path for the calculated cell capacities of the plurality of cell cycles.

[0013] One version of these methods further comprises: (e) selecting at least one different cell component; (f) sequentially calculating a second cell capacity at the end of each of a plurality of cell cycles based on at least one different cell component; (g) determining an additional predicted end of life of an electrochemical cell based on one of the calculated second cell capacities being less than a predetermined percentage of the nominal capacity; (h) comparing the predicted end of life with the additional predicted end of life and selecting a preferred cell having the greater predicted end of life between the predicted end of life and the additional predicted end of life; and (i) manufacturing the preferred cell.

[0014] In one version of these methods, cell capacity calculation uses the following relationship: Here represents the anode capacity, and represents the scaled volumed-averaged negative particle concentration at 100% charge, and It represents the scaled volume-average negative particle concentration in a 0% charge state.

[0015] In other versions of these methods, step (c) is the total circulating cations, solid electrolyte interphase thickness , solid-phase porosity of the anode , and solid-phase porosity of the cathode Based on this, it includes the step of sequentially calculating cell capacity at the end of at least some of the multiple cell cycles.

[0016] In other versions of these methods, the model is the surface potential Without including an algebraic equation to calculate, here Silver represents the solid-phase potential of the anode, and represents the phase potential of the electrolyte.

[0017] In other versions of these methods, the cations are lithium cations. In other versions of these methods, the anode comprises an anode material selected from graphite, lithium titanium oxide, hard carbon, tin / cobalt alloys, silicon / carbon, or lithium metal, the electrolyte comprises a liquid electrolyte comprising a lithium compound in an organic solvent, and the cathode comprises (i) lithium metal oxides (wherein the metal is one or more aluminum, cobalt, iron, manganese, nickel, and vanadium), (ii) lithium-containing phosphates having the general formula LiMPO4 (wherein M is one or more of cobalt, iron, manganese, and nickel), and (iii) formula LiNi x Mn y Co z It includes a cathode active material selected from materials having O2 (where x+y+z = 1 and x:y:z = 1:1:1 (NMC 111), x:y:z = 4:3:3 (NMC 433), x:y:z = 5:2:2 (NMC 522), x:y:z = 5:3:2 (NMC 532), x:y:z = 6:2:2 (NMC 622), or x:y:z = 8:1:1 (NMC 811).

[0018] In other versions of these methods, the anode comprises graphite, and the electrolyte comprises a liquid electrolyte comprising a lithium compound in an organic solvent, wherein the lithium compound is selected from LiPF6, LiBF4, LiClO4, lithium bis(fluorosulfonyl)imide (LiFSI), LiN(CF3SO2)2 (LiTFSI), and LiCF3SO3 (LiTf), and the organic solvent is selected from carbonate-based solvents, ether-based solvents, ionic liquids, and mixtures thereof, wherein the carbonate-based solvent is selected from the group consisting of dimethyl carbonate, diethyl carbonate, ethyl methyl carbonate, dipropyl carbonate, methylpropyl carbonate, ethyl propyl carbonate, methyl ethyl carbonate, ethylene carbonate, propylene carbonate, and butylene carbonate, and mixtures thereof, and the ether-based solvent is diethyl ether, dibutyl ether, monoglame, diglame, tetraglame, It is selected from the group consisting of 2-methyltetrahydrofuran, tetrahydrofuran, 1,3-dioxolane, 1,2-dimethoxyethane, and 1,4-dioxane and mixtures thereof.

[0019] In another aspect, the present disclosure provides a method for predicting the end of life of an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacities at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — cell cycles are initialized based on the rate of degradation over a plurality of previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over a plurality of previous cycles —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0020] In another aspect, the present disclosure provides a method for predicting the end of life of an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of solid electrolyte interphase formation as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0021] In another aspect, the present disclosure provides a method for predicting the end of life of an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of cation plating as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0022] In one version of these methods, the model does not include algebraic equations. In another version of these methods, the step of sequentially calculating cell capacity at the end of each of multiple cell cycles is at least three times faster than a degradation model based on porosity-electrode theory that includes algebraic equations. In another version of these methods, the model [includes] surface potential difference Without including an algebraic equation to calculate, here It represents the solid-phase potential of the anode. represents the phase potential of the electrolyte.

[0023] In other versions of these methods, step (c) is a solid electrolyte interphase kinetic rate constant ( k SEI ), solid electrolyte interphase layer diffusivity (D SEI ), and active material particle cracking rate (β LAM The method includes the step of sequentially calculating the cell capacity at the end of each of a plurality of cell cycles based on ). In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a linear degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a self-limiting degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate an accelerated degradation path for the calculated cell capacities of the plurality of cell cycles.

[0024] In other versions of these methods, cell capacity calculation uses the following relationship: Here represents the anode capacity, and represents the scaled volume-average negative particle concentration at 100% charge, and It represents the scaled volume-average negative particle concentration in a 0% charge state.

[0025] In other versions of these methods, step (c) is the total circulating cations, solid electrolyte interphase thickness , solid-phase porosity of the anode , and solid-phase porosity of the cathode Based on this, it includes the step of sequentially calculating cell capacity at the end of at least some of the multiple cell cycles.

[0026] In other versions of these methods, the model is the surface potential Without including an algebraic equation to calculate, here Silver represents the solid-phase potential of the anode, and represents the phase potential of the electrolyte.

[0027] In another aspect, the present disclosure provides a method in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of cell cycles. The method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacities at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — cell cycles are initialized based on the rate of degradation over a plurality of previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over a plurality of previous cycles —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0028] In another aspect, the present disclosure provides a method in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of cell cycles. The method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of solid electrolyte interphase formation as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0029] In another aspect, the present disclosure provides a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, and the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of cell cycles. The method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( (d) a step of sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on accessible storage sites at each electrode and at least one cell component — the model uses the current density of cation intercalation as a variable rather than the current density of cation plating as a variable —; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0030] In one version of these methods, the model does not include algebraic equations. In another version of these methods, the step of sequentially calculating cell capacity at the end of each of multiple cell cycles is at least three times faster than a degradation model based on porosity-electrode theory that includes algebraic equations. In another version of these methods, the model [includes] surface potential difference Without including an algebraic equation to calculate, here It represents the solid-phase potential of the anode. represents the phase potential of the electrolyte.

[0031] In other versions of these methods, step (c) is a solid electrolyte interphase kinetic rate constant ( k SEI ), solid electrolyte interphase layer diffusivity (D SEI ), and active material particle cracking rate (β LAMThe method includes the step of sequentially calculating the cell capacity at the end of each of a plurality of cell cycles based on ). In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a linear degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a self-limiting degradation path for the calculated cell capacities of the plurality of cell cycles. In another version of these methods, step (c) includes the step of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate an accelerated degradation path for the calculated cell capacities of the plurality of cell cycles.

[0032] In other versions of these methods, cell capacity calculation uses the following relationship: Here represents the anode capacity, and represents the scaled volume-average negative particle concentration at 100% charge, and It represents the scaled volume-average negative particle concentration in a 0% charge state.

[0033] In other versions of these methods, step (c) is the total circulating cations, solid electrolyte interphase thickness , solid-phase porosity of the anode , and solid-phase porosity of the cathode Based on this, it includes the step of sequentially calculating cell capacity at the end of at least some of the multiple cell cycles.

[0034] In other versions of these methods, the model is the surface potential Without including an algebraic equation to calculate, here Silver represents the solid-phase potential of the anode, and represents the phase potential of the electrolyte.

[0035] These and other features, embodiments, and advantages of the present invention will be better understood in consideration of the following detailed description, drawings, and appended claims. Brief explanation of the drawing

[0036] Figure 1 is a schematic diagram of a lithium-ion battery.

[0037] Figure 1a is a schematic diagram of a lithium metal battery.

[0038] Figure 1b illustrates a schematic diagram of a multi-particle electrochemical and mechanical model of a lithium-ion battery.

[0039] Figure 1c illustrates linear, self-limiting, and acceleration capacity fade trajectories versus the number of cycles using the parameters of Table 3.

[0040] Figure 2 illustrates comparisons of the ODE (ordinary differential equation) formula (8) and DAE (differential algebraic equation) formula (1c)-(1g) for the SEI (solid electrolyte interphase) equations. Both formulas are simulated using PyBaMM [Reference 27].

[0041] Figure 3 shows the root mean square percentage error between the ODE formula (8) and the DAE formula (1c)-(1g) for the SEI equations.

[0042] Figure 4 illustrates a schematic diagram of the cycle-to-cycle extrapolation algorithm. The change in SOH parameters (Δ) over one cycle y1) is assumed to remain constant during the next n cycles, resulting in a change of nΔy1 over the n cycles. Subsequently, the change in SOH over the n-th cycle is calculated and extrapolated to the 2n-th cycle, etc. Here, SOH represents the internal degradation variable of the model, for example, SEI thickness. or the volume fraction of the active material at either electrode There can be various types, such as this.

[0043] Figure 5 shows x from x0 (red line) end It illustrates that extrapolating the change up to (blue line) by n steps results in extrapolated values ​​(black line) that fall outside the physical range [0,1] for dimensionless particle concentration. Therefore, the next cycle cannot be simulated starting from the extrapolated concentration. Here, n = 30.

[0044] Figure 6 illustrates a comparison between the overall simulation and the fixed-step extrapolation algorithm. The fixed-step extrapolation algorithm is accurate for linear and accelerated cases where the underlying degradation modes are linear (see below). In the case of self-limiting where degradation is non-linear, significant errors occur in fixed-step extrapolation, and the errors are larger for larger steps.

[0045] Figure 7 illustrates the changes in degradation variables during linear degradation. The degradation modes 'Lithium Inventory Loss' (LLI) and 'Active Material Loss' (LAM) are defined below. Stoichiometric limits are the envelope of the electrode stoichiometry during cycling, which also changes as the battery degrades.

[0046] Figure 8 illustrates the changes in degradation variables during self-limiting degradation (see Figure 7 for details).

[0047] Figure 9 illustrates the changes in degradation variables while accelerating degradation (see Figure 7 for details). Specific details for implementing the invention

[0048] Before any embodiments of the present invention are described in detail, it should be understood that the present invention is not limited to the configuration details and the arrangement of components presented in the following description or illustrated in the drawings. Other embodiments of the present invention may be implemented or carried out in various possible ways. Furthermore, it should be understood that the phrases and terms used herein are for illustrative purposes only and should not be construed as limiting. The use of "including, comprising," or "having" and variations thereof in this invention is meant to encompass additional items as well as the items listed below and their equivalents.

[0049] The following discussion is presented to enable a person skilled in the art to make and use embodiments of the present invention. Various modifications to the exemplified embodiments will be obvious to those skilled in the art, and the general principles of the present invention may be applied to other embodiments and applications without departing from the embodiments of the present invention. Accordingly, the embodiments of the present invention are not intended to be limited to the embodiments shown and described, but should be given the broadest scope consistent with the principles and features disclosed herein. Those skilled in the art will recognize that the examples provided herein have many useful alternatives and fall within the scope of the embodiments of the present invention.

[0050] FIG. 1 illustrates a non-limiting example of a lithium-ion battery (110) that can be manufactured according to one embodiment of the present disclosure. The lithium-ion battery (110) comprises a first current collector (112) (e.g., aluminum) in contact with a cathode (114). A solid-state electrolyte (121) is arranged between a solid-state electrolyte interphase (117) on the cathode (114) and a solid-state electrolyte interphase (119) on the anode (118) in contact with a second current collector (122) (e.g., aluminum). The solid-state electrolyte interphase may also be within a porous structure of the cathode (114), and the solid-state electrolyte interphase may also be within a porous structure of the anode (118). The first and second current collectors (112 and 122) of the lithium-ion battery (110) may communicate electrically with an electrical component (124). The electric component (124) can place the lithium-ion battery (110) in electrical communication with an electric load that discharges the battery or a charger that charges the battery.

[0051] An active material suitable for the cathode (114) of a lithium-ion battery (110) is a lithium host material capable of storing and subsequently releasing lithium ions. An exemplary cathode active material is a lithium metal oxide, wherein the metal is one or more aluminum, cobalt, iron, manganese, nickel, and vanadium. Non-limiting exemplary lithium metal oxides include LiCoO2 (LCO), LiFeO2, LiMnO2 (LMO), LiMn2O4, LiNiO2 (LNO), and LiNi x Co y O 2, LiMn x Co y O2, LiMn x Ni y O2, LiMn x Ni y O4, LiNi x Co y Al z O2(NCA), LiNi 1 / 3 Mn1 / 3 Co 1 / 3 It is O2, etc. Other examples of cathode active materials are lithium-containing phosphates having the general formula LiMPO4, such as lithium iron phosphate (LFP) and lithium iron fluorophosphate, where M is one or more of cobalt, iron, manganese, and nickel. The cathode has the chemical formula LiNi x Mn y Co z It may include a cathode active material having O2, where x+y+z = 1 and x:y:z = 1:1:1 (NMC 111), x:y:z = 4:3:3 (NMC 433), x:y:z = 5:2:2 (NMC 522), x:y:z = 5:3:2 (NMC 532), x:y:z = 6:2:2 (NMC 622), or x:y:z = 8:1:1 (NMC 811). The cathode active material may be a mixture of any number of these cathode active materials.

[0052] In some embodiments, the cathode (114) may include a conductive additive. Many different conductive additives, for example, Co, Mn, Ni, Cr, Al, or Li, may be added to or replaced in the structure to affect electronic conductivity, alignment of layers, stability against delithiation, and cycling performance of the cathode materials. Other suitable conductive additives include graphite, carbon black, acetylene black, Ketjen black, channel black, furnace black, lamp black, thermal black, conductive fibers, metallic powders, conductive whiskers, conductive metal oxides, and mixtures thereof.

[0053] An active material suitable for the anode (118) of a lithium-ion battery (110) is a lithium host material capable of containing or subsequently releasing lithium ions, such as graphite (artificial, natural), lithium metal oxide (e.g., lithium titanium oxide), hard carbon, tin / cobalt alloy, or silicon / carbon. The anode active material may be a mixture of any number of these anode active materials. In some embodiments, the anode (118) may also include one or more conductive additives similar to those listed above for the cathode (114).

[0054] A suitable solid-state electrolyte (121) for a lithium-ion battery (110) is the chemical formula Li u Re v M w A x O y It includes an electrolyte material having, wherein Re can be any combination of elements with a nominal valence of +3, including La, Nd, Pr, Pm, Sm, Sc, Eu, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb, and Lu; M can be any combination of metals having a nominal valence of +3, +4, +5 or +6, including Zr, Ta, Nb, Sb, W, Hf, Sn, Ti, V, Bi, Ge, and Si; A can be any combination of dopant atoms having a nominal valence of +1, +2, +3, or +4, including H, Na, K, Rb, Cs, Ba, Sr, Ca, Mg, Fe, Co, Ni, Cu, Zn, Ga, Al, B, and Mn; u can vary from 3 to 7.5; v can vary from 0 to 3; w can vary from 0 to 2; x can vary from 0 to 2; and y can vary from 11 to 12.5. The electrolyte material may be undoped or doped lithium lanthanum zirconium oxide.

[0055] Other exemplary solid-state electrolytes (121) may include garnet, perovskite, NaSICON, or any combination oxide or phosphate materials having a LiSICON phase. The solid-state electrolyte (121) of the lithium-ion battery (110) may include any solid material capable of storing and transporting ions between the anode (118) and the cathode (114).

[0056] The current collector (112) and the current collector (122) may include a conductive material. For example, the current collector (112) and the current collector (122) may include molybdenum, aluminum, nickel, copper, combinations thereof and alloys, or stainless steel.

[0057] Alternatively, the separator may replace the solid-state electrolyte (121), and the electrolyte for the battery (110) may be a liquid electrolyte. An exemplary separator material for the battery (110) may be a permeable polymer such as a polyolefin. Exemplary polyolefins include polyethylene, polypropylene, and combinations thereof. The liquid electrolyte may contain a lithium compound in an organic solvent. The lithium compound may be selected from LiPF6, LiBF4, LiClO4, lithium bis(fluorosulfonyl)imide (LiFSI), LiN(CF3SO2)2 (LiTFSI), and LiCF3SO3 (LiTf). The organic solvent may be selected from carbonate-based solvents, ether-based solvents, ionic liquids, and mixtures thereof. Carbonate-based solvents may be selected from the group consisting of dimethyl carbonate, diethyl carbonate, ethyl methyl carbonate, dipropyl carbonate, methylpropyl carbonate, ethyl propyl carbonate, methyl ethyl carbonate, ethylene carbonate, propylene carbonate, and butylene carbonate; ether-based solvents are selected from the group consisting of diethyl ether, dibutyl ether, monoglame, diglame, tetraglame, 2-methyltetrahydrofuran, tetrahydrofuran, 1,3-dioxolane, 1,2-dimethoxyethane, and 1,4-dioxane.

[0058] Solid electrolyte interphases (117, 119) are formed during the first charge of the lithium-ion battery (110). To further explain the formation of the solid electrolyte interphases, a non-limiting exemplary lithium-ion battery (110) having an anode containing graphite and using a liquid electrolyte is used in this paragraph. Since lithiated carbons are not stable in air, a non-limiting example of a lithium-ion battery (110) having a graphite anode and lithiated cathode materials is assembled in its discharged state. The electrolyte solution is Li / Li +It is thermodynamically unstable at potentials lower or very high compared to. Therefore, during the first charge of a lithium-ion battery cell, the electrolyte solution begins to be reduced / degraded on the surface of the graphite anode and forms a solid electrolyte interphase (SEI). Competitive and parallel solvent and salt reduction processes occur, leading to the deposition of numerous organic and inorganic degradation products on the surface of the graphite anode. The SEI layer imparts kinetic stability to the electrolyte against further reductions in continuous cycles, thereby ensuring excellent cyclability of the electrode. It has been reported that SEI thickness varies from a few angstroms to tens or hundreds of angstroms. Studies suggest that the SEI of the graphite anode is a dense layer of inorganic components close to the carbon of the anode, followed by a porous organic or polymer layer close to the electrolyte phase.

[0059] The present invention is not limited to lithium-ion batteries. In alternative embodiments, a suitable anode may comprise magnesium, sodium, or zinc. Alternative cathode and electrolyte materials suitable for such magnesium-ion batteries, sodium-ion batteries, or zinc-ion batteries may be selected. For example, a sodium-ion battery may comprise: (i) an anode comprising sodium ions; (ii) a solid-state electrolyte comprising a metal cation-alumina (e.g., sodium-β-alumina or sodium-β"-alumina); and (iii) a cathode comprising an active material selected from the group consisting of layered metal oxides (e.g., NaFeO, NaMnO, NaTiO, NaNiO, NaCrO, NaCoO, and NaVO), metal halides, polyanionic compounds, porous carbon, and sulfur-containing materials.

[0060] FIG. 1a illustrates a non-limiting example of a lithium metal battery (210) that can be manufactured according to one embodiment of the present disclosure. The lithium metal battery (210) includes a current collector (212) in contact with a cathode (214). A solid-state electrolyte (216) is arranged between a solid electrolyte interphase (217) on the cathode (214) and a solid electrolyte interphase (218) on the anode (220) in contact with a second current collector (222) (e.g., aluminum). The current collectors (212 and 222) of the lithium metal battery (210) may communicate electrically with an electric component (224). The electric component (224) may position the lithium metal battery (210) to communicate electrically with an electric load that discharges the battery or a charger that charges the battery. The active material suitable for the cathode (214) of the lithium metal battery (210) is one or more of the lithium host materials listed above for the battery (110), porous carbon (in the case of a lithium air battery), or sulfur-containing materials (in the case of a lithium sulfur battery). The solid-state electrolyte material suitable for the solid-state electrolyte (216) of the lithium metal battery (210) is one or more of the solid-state electrolyte materials listed above for the battery (110). In one embodiment, the anode (220) of the lithium metal battery (210) comprises lithium metal. In one embodiment, the anode (220) of the lithium metal battery (210) is composed essentially of lithium metal.

[0061] Alternatively, the separator may replace the solid-state electrolyte (216), and the electrolyte of the lithium metal battery (210) may be a liquid electrolyte. An exemplary separator material for the lithium metal battery (210) is one or more of the separator materials listed above for the lithium-ion battery (110). A liquid electrolyte suitable for the lithium metal battery (210) is one or more of the liquid electrolytes listed above for the lithium-ion battery (110).

[0062] Solid electrolyte interphases (217, 218) are formed during the first charge of the lithium metal battery (210). To further illustrate the formation of the solid electrolyte interphases, a non-limiting exemplary lithium metal battery (210) having a liquid electrolyte and a lithium metal anode is used in this paragraph. The liquid electrolyte contains a lithium salt in an organic solvent. A non-limiting exemplary lithium metal battery (210), having a lithium metal anode and a lithiated amount of cathode material, is assembled in its discharged state. The reduction potential of the organic solvent is generally 1.0 V (vs. Li + It is less than / Li). Therefore, when a bare lithium anode is exposed to an electrolyte solution and a first charging current is applied, immediate reactions occur between lithium and electrolyte species. The insoluble products of parasitic reactions between lithium ions, anions, and solvents deposited on the surface of a metallic lithium anode are considered to be solid electrolyte interphases. Since SEI components depend significantly on the electrode materials, electrolyte salts, solvents, as well as the operating conditions of the cell, the same SEI layer cannot be found in two different situations. Consequently, the actual surface chemical properties of the SEI layer in a given system are generally obtained by characterization methods such as Fourier Transform Infrared Spectrometer (FTIR) and X-ray Photoelectron Spectrometer (XPS).

[0063] The present invention is not limited to lithium metal batteries. In alternative embodiments, a suitable anode may comprise magnesium metal, sodium metal, or zinc metal. Alternative cathode and electrolyte materials suitable for these magnesium metal batteries, sodium metal batteries, or zinc metal batteries may be selected.

[0064] In one embodiment of the present invention, a method for manufacturing an electrochemical cell is provided, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations that move from the cathode to the anode during the charge phase of each of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) sequentially calculating the cell capacity at the end of each of the plurality of cell cycles based on the total circulating cations, accessible storage sites at each electrode, and at least one cell component, using a degradation model based on porous-electrode theory having one or more degradation paths; and includes the step of determining the predicted end of life of an electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity. For example, end of life may be defined as 20% degradation from the nominal capacity.

[0065] In one version of this method, cell cycles are initialized based on the rate of degradation over multiple previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over multiple previous cycles. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of solid electrolyte interphase formation as a variable. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of cation plating as a variable. Another version of this method comprises: (e) selecting at least one different cell component; (f) sequentially calculating a second cell capacity at the end of each of multiple cell cycles based on at least one different cell component; (g) determining an additional predicted end of life of the electrochemical cell based on one of the calculated second cell capacities being less than a predetermined percentage of the nominal capacity; (h) a step of comparing a predicted end of life with an additional predicted end of life and selecting a preferred cell having the greater predicted end of life between the predicted end of life and the additional predicted end of life; and (i) a step of manufacturing the preferred cell further comprising

[0066] In another embodiment of the present invention, a method for predicting the end of life of an electrochemical cell is provided, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations that move from the cathode to the anode during the charge phase of each of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles. The method comprises: (a) selecting at least one cell component selected from the group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) determining a nominal discharge capacity for the cell in a 100% healthy state; (c) sequentially calculating the cell capacity at the end of each of the plurality of cell cycles based on the total circulating cations, accessible storage sites at each electrode, and at least one cell component, using a degradation model based on porous-electrode theory having one or more degradation paths; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0067] In one version of this method, cell cycles are initialized based on the degradation rate over multiple previous cycles, and the time to simulate the next cycle is selected based on the degradation rate over multiple previous cycles. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of solid electrolyte interphase formation. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of cation plating.

[0068] In another embodiment of the present invention, a method is provided in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during a charge phase of each of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of cell cycles. The method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) sequentially calculating cell capacity at the end of each of a plurality of cell cycles based on total cyclable cations, accessible storage sites at each electrode, and at least one cell component using a degradation model based on porous-electrode theory having one or more degradation paths; and (d) determining the predicted end of life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity.

[0069] In one version of this method, cell cycles are initialized based on the degradation rate over multiple previous cycles, and the time to simulate the next cycle is selected based on the degradation rate over multiple previous cycles. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of solid electrolyte interphase formation. In another version of this method, the model uses the current density of cation intercalation as a variable, rather than the current density of cation plating.

[0070] In the present disclosure, we propose non-limiting exemplary methods that include algorithms that accelerate physics-based battery life simulations by 10 to 100 times compared to state-of-the-art technology. By adaptively selecting and simulating representative cycles, these algorithms utilize the difference between the "fast" time scale of battery cycling and the "slow" time scale of battery degradation, thereby requiring fewer cycle simulations to simulate the entire lifespan. For example, simulations of a three-month lifespan that previously took three minutes can now be performed within five seconds. This enables interaction with simulations at a human time scale, opening up the possibility for much faster and more accurate model development, testing, and comparison with experimental data.

[0071] Some embodiments of the present invention provide algorithms that accelerate physics-based battery life simulations by 10 to 100 times compared to state-of-the-art technology. Some embodiments include the reconstruction of single-particle models with side reactions that reduce stiffness by eliminating algebraic equations, along with a three-fold speed improvement in simulation time (intra-cycle reformulation). Other embodiments of the present invention provide algorithms that require fewer cycle simulations to simulate full life by adaptively selecting and simulating representative cycles and skipping other cycles, thereby utilizing the difference between the 'fast' time scale of battery cycling and the 'slow' time scale of battery degradation (adaptive inter-cycle extrapolation). While this algorithm is demonstrated by specific degradation mechanisms, it can be applied to models of various aging phenomena. In the case study considered, simulations for full life are performed within 5 seconds. This opens up the possibility of much faster and more accurate model development, testing, and comparability with experimental data. yes

[0072] The following examples are provided to further illustrate the invention and are not intended to limit the invention in any way. The statements provided in the examples are presented without being bound by theory. 1. Introduction to the Example

[0073] In general, improved understanding of battery degradation can lead to better reliability, safety, extended battery utilization, and consequently cost reductions [Reference 1]. Batteries for light vehicles and grid applications are typically designed to last and be guaranteed for 8–10 years [References 2, 3]. Battery degradation in the field can take about 10 years, which is too long to understand the impact of changes in battery design parameters on lifespan. Total testing time is usually reduced in the laboratory by using accelerated aging conditions and skipping breaks between cycles to degrade the battery within a few months. To further reduce time, modeling is required. In particular, physics-based electrochemical models that include degradation mechanisms are useful for evaluating the capacity and power fade of lithium-ion batteries under various duty cycles and thus predicting lifespan, because they can directly simulate a wide range of realistic battery applications at various scales [Reference 4]. However, physics-based simulations of total battery lifespan generally take minutes to hours. For example, if simulating a single full charge / discharge cycle takes 1 second, simulating 1,000 cycles takes about 15 minutes. While this is much faster than experimental time scales, it is still too slow and is not ideal for rapid model feedback and iterative simulations in parameter estimation routines that require multiple forward solves of the model. In this example, we propose an algorithm that speeds up physics-based battery life simulations by 10 to 100 times, thereby simulating the entire battery life within seconds (Table 1). Table 1

[0074] Table 1 includes the time scales required to measure or simulate a single cycle or the entire lifespan of a battery. Typical driving patterns and industry standards for an 8-year warranty can be assumed. This can be reduced by continuously cycling the cells in the laboratory and further reduced using simulations. For example, since simulating one full cycle of the Single Particle Model (SPM) takes 0.6 seconds, simulating the entire lifespan (1,000 cycles) takes approximately 10 minutes. This can be reduced to 0.2 seconds / 3 minutes by reconfiguring the model to eliminate algebraic equations (reconfiguration within cycles, see below). Without further changing the simulation time for a single cycle, the lifespan simulation time can be further reduced to less than 5 seconds by adaptively extrapolating between cycles (extrapolation between cycles, see below).

[0075] Many modeling studies have made significant advancements in investigating single-cycle degradation and performing simulations of individual cycles (in-cycle simulations) as efficiently as possible. Smith et al. proposed a low-order dynamic model using applications in battery management [Ref. 5]. Cai et al. derived a reduced-order model using appropriate orthogonal decomposition [Ref. 6]. Northrop et al. reconstructed a model for implementation in a battery management system based on earlier work by Subramanian et al. [Ref. 8] [Ref. 7]. Barai et al. proposed a reduced-order model for mechanical degradation [Ref. 9]. Two other reduced-order models are a single-particle model [Ref. 10] and a single-particle model with an electrolyte [Ref. 11]. Various authors have used perturbation theory to derive various reduced-order 1-dimensional [References 12, 13, 14, 15, 16] and 3-dimensional [References 17, 18] models from various asymptotic constraints.

[0076] In contrast, few methods have been proposed in the literature to accelerate simulations over the entire battery life. There is an idea to use detailed micro-scale simulations to inform macro-scale simulations without explicitly deriving macro-scale equations [Refs. 19, 20]. More strictly speaking, systems with distinct time scales can be solved asymptotically using multi-scale methods [Ref. 21]. Battery simulations have fast cycling time scales and slow degradation time scales, and since the fast time scale is generally periodic when performing controlled experiments in a laboratory setting, this approach is ideally suited [Ref. 1]. However, there are generally few studies attempting to separate the cycling and degradation time scales.

[0077] One proposed method involves an algorithm that iteratively simulates a single cycle and linearly extrapolates degradation over a fixed number of cycles (inter-cycle extrapolation). This algorithm was proposed for fuel cell models by Mayur et al. as a 'time-upscaling method' [References 22, 23] and adapted for lithium-ion batteries by Kupper et al. [Reference 24]. Independently, Vora et al. [Reference 25] proposed a similar algorithm and referred to it as 'extrapolation'. This fixed-size linear extrapolation algorithm has two major drawbacks and has not been widely adopted to date. First, the 'extrapolation' hyperparameters need to be selected a priori without a systematic way to know appropriate values. Second, while this method performs fixed steps over the entire battery life, some regions may require smaller steps and others larger steps depending on the linearity of aging.

[0078] Some embodiments of the present invention provide an adaptive inter-cycle extrapolation algorithm in which the step size is automatically selected based on past and present degradation rates. This algorithm works with any degradation model based on porosity-electrode theory, but for presentation purposes, a single-particle model with SEI growth and particle cracking introduced in the example below may be used. Different degradation parameters may be used to simulate different capacity fade trajectories (linear, self-limiting, and accelerated). As can be seen below, the in-cycle model can be reconfigured to eliminate algebraic equations for a 3x rate improvement with minimal loss of accuracy. Additionally, the adaptive inter-cycle extrapolation algorithm is described below, resulting in each of the three degradation cases. In each case, an additional rate improvement of 10 to 100 times is achieved compared to the baseline. Because the rate improvement is multiplied and combined with the rate improvement in a single-cycle simulation, the entire life of the battery can advantageously be simulated in just a few seconds.

[0079] This enables interaction with simulations at a human time scale [Ref. 26], opening up the possibility for much faster and more accurate model development and comparison with experimental data. The algorithm is implemented in the open-source battery modeling package PyBaMM [Ref. 27] and can therefore be easily used to simulate any aging model implemented within that framework. Alternatively, it can be easily integrated into other simulation frameworks. The results presented below also show how the capacity fade curve changes qualitatively when different degradation mechanisms are dominant, as in Fig. 1c. In particular, we investigate the knee point around cycle (600) in the 'accelerated' capacity fade curve and show that this knee point is due to electrode saturation. Finally, several extensions and possible research directions enabled by this algorithm are discussed below. 2. Degradation Model

[0080] The algorithms introduced herein are intended to operate generally with any degradation model based on porosity-electrode theory. For demonstration purposes, numerical improvements to case study degradation models—namely, a single-particle model with SEI formation [Ref. 28] and loss of active material due to particle expansion [Ref. 31, 32] [Ref. 29, 30]—are discussed herein. Fig. 1b illustrates a schematic diagram of a multi-particle electrochemical and mechanical model of a lithium-ion battery [Ref. 32]. More complex models may also be used without modifying the algorithms introduced below. The case study degradation models are as follows: Single particle model: SEI Model [Reference 28]: Here f SEI is a function derived below. Particle mechanics assuming maximum stress at the particle surface and minimum stress of zero [References 29, 30, 31, 32] voltage: The parameter values ​​are as in [Reference 32], where additional degradation parameters are provided in Table 2. After spatial discretization (e.g., using finite volumes), the discretized state vector is as follows:

[0081] The degradation rate consists of three parameters ( k SEI , D SEI , and β LAMIt can be controlled by adjusting ). A rapid simulation algorithm is demonstrated in three scenarios with qualitatively different degradation paths: one linear, one self-limiting, and one accelerated (see FIG. 1c). The parameters resulting from these three behaviors are provided in Table 3. In each case, the total life is simulated using both standard sequential cycle simulations and adaptive cycle extrapolation, and the results are compared. Each cycle consists of 1C discharge to 3 V, 1 hour rest, followed by 1C charge to 4.2 V, and finally maintaining 4.2 V until the current drops below C / 50. Simulations are performed up to 60% capacity fade, and the capacity is defined by the equation (26) derived below. The capacity fade curves of Fig. 1c are obtained by solving the PyBaMM model (1) [Ref. 27] using the line method to semi-discretize PDEs and SUNDIALS (via CasADi) to solve the resulting system of ODEs / DAEs [Ref. 33, 34]. Each cycle is simply initialized to the final state of the previous cycle. Table 2

[0082] Table 2 illustrates the degradation parameters of the model. The other parameters are as in [Reference 32]. The three remaining degradation parameters vary depending on the case, as shown in Table 3. (†) = Parameters introduced herein. Table 3

[0083] Table 3 shows the key degradation parameters for each degradation type. The parameters were selected to show the capacity fade trajectory required to reach 60% capacity fade at approximately 1,000 cycles. 3. Reconstruction of the In-Cycle Model of Side Reactions

[0084] One way to accelerate lifetime simulations is to speed up the simulation of individual cycles through model reconstruction, reduced-order models, or more efficient numerical algorithms. Here, we propose a model reconstruction for side reactions that can eliminate algebraic equations from the model and achieve a threefold speed improvement compared to the original model. After spatial discretization, the reconstructed model is an ODE system (instead of the DAE system of the original model), which allows for the use of a wider range of algorithms from control theory.

[0085] Equations ((1c)-(1g)) are surface potential differences ( It can be reduced to a single algebraic equation for ).

[0086] If we assume a symmetric Butler-Volmer equation without side reactions and as is generally the case, the potentials can be found in a closed form by inverting the Butler-Volmer equation. If side reactions are included, since there are no closed-form solutions for the transcendental equations of form (4), (4) is an additional algebraic equation (in-particle diffusion, in the case of SPM) that must be solved along with other equations of the model. This requires more complex and slower numerical methods to solve, as it changes the model from an ODE system to a DAE system after quasi-discretionation.

[0087] To avoid this problem, the model can be reconstructed by utilizing the fact that the side reaction current density is much smaller than the intercalation current density [Ref. 29]. Systematically performing asymptotic expansion requires complete dimensionlessness, but the general idea is as follows. In some embodiments, we find that the magnitude of the SEI current is much smaller than the magnitude of the intercalation current. Some small parameters to make it so ( Note that it defines ). Also cast Defined as. Next Extend the dynamic variables to powers of. If we substitute (5) into 1c-1g, we Find the preceding order of. As the first order of, Therefore, we have an explicit approximate form for j, and Here This is given by (6a). Since the explicit form (8) can be used in the boundary conditions of the particle diffusion equation (28b), the lithium inventory loss during circulation is accounted for. Using this approach, the model is maintained as a system of ODEs; compared to the standard SPM, the only additional equation is the equation (1h) for SEI thickness growth, and there are no additional equations for current. The derivation is very similar when other side reactions, such as lithium plating, are involved. However, this approach breaks down when side reactions begin to become dominant, because asymptotic extension is no longer valid.

[0088] It may be noted that the simplification from DAE to ODE works only when the Butler-Volmer response is symmetric, as it relies on the inversion of the sinh term. For asymmetric Butler-Volmer responses, an alternative way to maintain the model as an ODE system is to introduce capacitance into the system. For example, it is of the following form, and Here C dl is a double-layer capacitance [References 36, 37].

[0089] Furthermore, the simplification from DAE to ODE is applicable only to electrode-averaged models, such as single-particle models. In the overall DFN (Doyle-Fuller-Newman) model [Reference 12], the total interfacial current (j tot ) is not simply given by (1e), but instead must be solved as an algebraic equation spatially distributed across the electrodes.

[0090] Described below is a comparison of models using the ODE formula (8) and the DAE formula ((1c)-(1g)) for the SEI equations over a representative 1C / 1C discharge / charge cycle. The relevant electrical variables are compared in FIG. 2: voltage (V), total interfacial current density of the cathode (j tot,n ), cathode intercalation current density (j int,n ), SEI overpotential( ), SEI current density(j SEI ), and loss of lithium inventory (LLI). There is no noticeable difference between the two formulas under any conditions.

[0091] Figure 3 illustrates the root mean square percentage error. In each case, the percentage error is also less than 1% in all states. The only exceptions are j in the transitions between discharge and rest, and between rest and charge. int,n This is because the two solutions reach the cutoff discharge voltage at slightly different times. This error is quickly corrected and does not cause errors in other states of interest, such as voltage and lithium inventory loss.

[0092] The simulation time using the ODE formula is three times faster than the DAE formula with a negligible error. Therefore, the ODE formula was used to report the simulation times in the following section. 4. Adaptive intercycle extrapolation

[0093] Some embodiments of the present invention provide an algorithm that accelerates battery life simulations using adaptive inter-cycle extrapolation. This can be performed in conjunction with or separately from the reconstruction discussed above. Inter-cycle extrapolation is described below. This can be improved by making the algorithm adaptive as described below.

[0094] Battery cycling is a typical example of a process that uses multiple time scales. The fast time scale is charge / discharge ('cycling'), which occurs over a period of a few hours and is characterized by the state of charge (SOC). The slow time scale is degradation, which occurs over a period of a few months and is characterized by the state of health (SOH). The state of health can be assumed to be nearly constant for a single cycle, and varies linearly over several cycles—with exceptions at the beginning and end of the lifespan, particularly after the 'inflection point' [References 28, 38].

[0095] This observation leads to a simple direct extrapolation algorithm for simulating the repeated cycles depicted in Fig. 4: execute one cycle, measure each state change between the start and end of the simulation, and extrapolate this over several cycles to initialize the next simulation after n cycles.

[0096] Such direct extrapolation algorithms were proposed for fuel cell models by Mayur et al. as a 'time-upscaling method' [References 22, 23] and adapted for lithium-ion batteries by Kupper et al. [Reference 24]. Vora et al. [Reference 25] proposed a similar algorithm at the same time and referred to it as 'extrapolation'. However, direct extrapolation algorithms are suboptimal because they require extrapolated values ​​of 'micro-scale' variables, such as particle concentration, which can change rapidly over short time scales. As illustrated in Fig. 5, small changes in the values ​​of 'micro-scale' variables can cause large changes after extrapolation. Instead, only 'coarse-scale' variables that change over longer time scales should be extrapolated [Reference 19]. These variables can be explicit states of the model or aggregated from micro-scale variables. In the case of the SPM considered here (1), coarse-scale variables can be used.

[0097] 3 scalar variables ( , , and ) are explicit states of the model, but because they change slowly over the degradation time scale (small changes over a single cycle), they can also be used as course-scale variables. However, rapidly changing particle concentrations (c s,n and c s,p ) is the total circulating lithium defined as follows ( It can be replaced with ).

[0098] Details regarding the total circulating lithium and related 'degradation modes' are described below. Given the total circulating lithium value, the particle concentrations at full charge (and full discharge) can be calculated using (25). These are then used to initialize the next simulation after extrapolation. In summary, the fixed-step extrapolation algorithm with step size (n) is as follows: 1. In order to obtain Simulating one cycle from 2. Using (13) and Calculate 3. In order to obtain (10), equivalent to extrapolate 4. Using (25) Calculate and repeat

[0099] It may be noted that when the model includes algebraic states such as transpositions, they are not included in the y vector because they must be automatically initialized by the solver in a way that satisfies algebraic equations without requiring initial conditions.

[0100] Figure 6 illustrates the results of using fixed-step cycle extrapolation compared to the full simulation for three different step sizes (25, 50, and 100). In the first and third cases, the fundamental degradation in mode-space is linear. Therefore, fixed-step extrapolation simulations perform well at any step size because the assumption that the degradation rate is constant is maintained. However, in the case of self-limiting, fixed-step extrapolation simulations have significant errors, and the errors are higher at larger steps. This is because the extrapolation simulations overestimate the degradation rate, as the degradation rate decreases rapidly at the start of the life.

[0101] The results in Fig. 6 illustrate that the cycle-to-cycle extrapolation algorithm must take small steps when the rate of degradation changes rapidly and large steps when the rate of degradation is constant. Therefore, instead of extrapolating by a fixed number of cycles each time, an adaptive algorithm can be used in which the size of the extrapolation step varies depending on how quickly the rate of degradation changes.

[0102] In general, Figure 6 compares the entire simulation to the fixed-step extrapolation algorithm. The fixed-step extrapolation algorithm is accurate in linear and accelerated cases, where the underlying degradation modes are linear. In the case of self-limiting where degradation is non-linear, significant errors occur from fixed-step extrapolation, and the errors are larger for larger steps.

[0103] The degradation system can be written as an ODE and: Here, y is defined as in (12). "Time" is the number of cycles, and is the change in y from the start to the end of a cycle, as observed by simulating a cycle. More specifically, as a function of (t and y) Each evaluation of includes the following: 1. Using (25) from Calculate 2. Simulating the entire discharge / charge cycle to obtain 3. Using (13) from Calculate 4. return

[0104] Each evaluation of is relatively expensive because it must solve the entire discharge / charge cycle. Equation (14) encodes the degradation occurring over each cycle into a continuous-time framework that can be solved by standard numerical integrators. In this context, the fixed-step 'extrapolation' method [References 22, 23, 24, 25] is a Forward Euler solution. This can be improved by using an adaptive numerical method [References 39, 40]. Although Equation (14) is not robust, since evaluating the right-hand side is expensive, a method with as few right-hand side evaluations as possible is required. 3(2) The Runge-Kutta algorithm [Reference 41] can be used as implemented in SciPy [Reference 42]. Since the development of the slow-time scale ODE is monotonic and nearly linear, low tolerances (10 for both relative and absolute tolerances) -2 ) can be used, allowing the ODE solver to perform large steps at the required accuracy.

[0105] The cycle-adaptive algorithm is implemented in the open-source battery modeling package PyBaMM [Ref. 27] and can therefore be used with any model in the library. 'Slow' degradation ODEs are solved using 3(2) Runge-Kutta in SciPy [Ref. 42]. Each 'fast' cycle simulation is solved using the line method, which first spatially discretizes the PDEs using finite volumes with 30 grid points for each particle and then solves the resulting ODE system using CVODEs from SUNDIALS via CasADi [Ref. 33, 34]. A 60% capacity termination condition is implemented as a stop condition in the 'slow' degradation ODE solver.

[0106] The results for the three cases (linear, self-limiting, and accelerated) are shown in FIGS. 7 to 9, respectively. As well as the thermodynamic capacity and stoichiometric limits calculated using (25), lithium inventory loss (LLI) and cathode (LAM) NE ) and anode (LAM PE Three degradation modes of active material loss of the electrodes are illustrated. In each case, the red solid lines represent the overall simulation, the blue dashed lines represent the adaptive cycle-to-cycle extrapolation simulation, and the blue dots indicate that cycles were selected by the adaptive ODE solver to solve the degradation ODE (14). The adaptive cycle-to-cycle extrapolation algorithm accurately captures the evolution of each variable in each case. The results are discussed in more detail below.

[0107] In the linear case (Fig. 7), the degradation rate is nearly constant, and each basic degradation mode is approximately linear with respect to the number of cycles. This leads to approximately linear variations in capacity and stoichiometric limits, and the adaptive simulation is accurate while being able to perform a small number of large steps while maintaining accuracy.

[0108] In the case of self-limiting (Fig. 8), the rate of degradation slows as the cell driven by self-limiting SEI growth (and thus self-limiting LLI) degrades. This effect is most pronounced in the first few hundred cycles. Therefore, adaptive simulation must take small steps to address the changing degradation rate at the start of life, and larger steps toward end-of-life when degradation is more linear. This example demonstrates the power of adaptive simulation in capturing changing degradation rates.

[0109] Finally, in the case of accelerated degradation (Fig. 9), there is an inflection point in the capacity fade curve around cycle (600) where the capacity fade becomes much faster. Nevertheless, adaptive simulations can perform very large steps. This is because the mode-space degradation where extrapolation occurs is nearly linear. Here, the cause of the inflection point is that the maximum anode stoichiometry reaches 1 at about 600 cycles and cannot exceed this, resulting in nonlinearity in the minimum anode stoichiometry limit and capacity (both related via (25)). This effect has already been reported in the literature [Reference 43].

[0110] In summary, for this model, capacity fade is influenced by, first, the relative rates of lithium inventory loss and active material loss, and second, whether SEI growth is reaction-limited or diffusion-limited. If lithium inventory loss due to side reactions is faster than active material loss in both electrodes, causing the utilization of each electrode to decrease with cell aging, degradation is linear or self-limiting. If active material loss is faster in one of the electrodes, leading to wider utilization, one of the electrodes eventually saturates, causing an inflection point (capacity fade 'acceleration'). Within linear and self-limiting degradation, capacity fade is approximately linear if SEI growth is reaction-limited, and slows down if SEI growth is diffusion-limited.

[0111] In Table 4, the simulation times of the full simulation and the adaptive simulation are compared. Since the adaptive simulations solve 100 times fewer cycles, they achieve nearly a 100-fold speed improvement. Therefore, the adaptive simulations can provide almost immediate feedback on the human time scale. The time required to remain small even when simulating tens of thousands of cycles is because larger steps are possible in this case. Note that the number of cycles solved by the adaptive simulation is not equal to the number of blue dots in Figures 7 through 9 (it is about 3 times larger). This is because each blue dot in Figures 7 through 9 requires three cycle evaluations for the third-order adaptive ODE solver used here. Table 4

[0112] Table 4 shows the number of cycles solved and the time taken for the full and adaptive simulations for each case. Since the adaptive simulations perform extrapolation between cycles and simulate the full battery life within about 5–10 seconds, they solve about 20–40 times fewer cycles than the full simulations. The simulations are run on an Apple M1 CPU.

[0113] Embodiments of the present invention provide the basis for an adaptive cycle-to-cycle extrapolation algorithm capable of simulating the entire lifespan of lithium-ion batteries within seconds, and illustrate an approach that works well in single-particle models with SEI formation and active material loss. The examples herein will allow researchers to study battery degradation with very rapid feedback on lifespan performance, thereby enabling a better understanding of different degradation mechanisms and their combinations. Cycle-adaptive simulations can also be used to speed up parameter estimation algorithms for determining parameters of degradation models, such as those in Table 3.

[0114] The SEI dynamics model by Yang et al. [Reference 28] is as follows. This is and Since it is a linear system for, we have the surface concentration of EC ( By removing ), you do not need to solve additional algebraic equations: In (16), the relative magnitudes of the two terms control SEI kinetics. If the first term is larger, SEI growth is reaction-limited. If the second term is larger, SEI growth is diffusion-limited.

[0115] Generally, battery degradation can occur through a number of mechanisms including (but not limited to) SEI layer growth, lithium plating, mechanical effects of particles, and electrolyte oxidation [References 44, 45, 29]. To classify these mechanisms, it is helpful to use degradation modes [References 44, 45]. The three main degradation modes are lithium inventory loss (LLI), active material loss (LAM) of the cathode, and LAM of the anode.

[0116] Loss of active material is generally caused by mechanical effects. This is the capacity of the electrodes ( C k Reduces )

[0117] The charging capacity of the electrodes (in Ah units) can be defined as follows, and Therefore, any changes in capacity are the active material volume fraction ( It is caused by changes in ). Degradation models including LAM generally do so through differential equations for the active material volume fraction or electrode capacity. Lithium inventory loss is defined as follows, and Here is the total moles of circulating lithium in the particles, and Here and is the scaled volume-averaged negative and positive particle concentrations (or 'electrode stoichiometry') defined in (29). At any time, the total current density (j) of each electrode tot ) is the intercalation density (j int ) and the total current density of side reactions (j side It must be equal to the sum of ).

[0118] We are J r,k is the domain It is defined as the total current for reaction r. This provides the relationship derived below, and Therefore, according to (19), LLI can be broken down into three parts, and Here, LLI rxn It is an LLI due to side effects and LAM liNE and LAM liPE is the loss of lithiated active material, and the loss of delithiated active material is LAM de = LAM - LAM li It is defined as. Equation (23) states that the loss of lithium inventory is due to side reactions (I side Not only the result of / F) but also the loss of active material (dC k It illustrates that it also occurs as a result of / dt).

[0119] Some degradation mechanisms, such as pore blockage, do not contribute to LLI or LAM but instead contribute to an increase in the cell's internal resistance. This is sometimes characterized as ORI (Ohmic Resistance Increase), although the term can be misleading because the increase in resistance can depend non-linearly on current (e.g., when associated with larger concentration gradients resulting from reduced torsional stress).

[0120] Degradation modes stoichiometric limits ( , , , and It is useful to relate to ), where the subscript represents SOC. Any given , , , and voltage limits ( and In the case of ), stoichiometric limits can be found using the following equations [Ref. 46]: Next, the cell capacity is provided by the following, and And that charge state is provided by the following. Equation (26) provides the capacity of the cell without the need to simulate a completely low C-rate discharge, and Equation (25) can be used to initialize the simulation at a given SOC while taking into account the balance of lithium and preserving the total lithium.

[0121] surface( ), volume( ), and surface area ( Microscopic-scale particle domains having ) ) is volume( ) macroscopic scale electrode domain( It can be considered within. The conservation of particle mass provides the following, Here, c s is the molar concentration of intercalated lithium, and N s is the lithium flux within the particles, and R s is the particle radius, and j is the intercalation current.

[0122] Electrode stoichiometry is particle domain ( ) and electrode domain( It can be defined as the particle concentration averaged over both and can be normalized by the electrode volume and particle volume: Differentiate time and substitute (28a) to provide the following, By applying the divergence theorem and substituting (28b), we obtain the following: because, and This is because it is uniform across the surface of this particle. Now, N to the electrode tot If there are particles, by definition the following is provided, and Therefore, the surface area to volume ratio is related to porosity through the following.

[0123] In the case of spherical particles, this is a well-known relationship ( Provides ). Substitute (33) into (31) to provide the following, and (22) and (18) can be replaced to obtain the following. For simplification, Is Although it can be assumed to be unrelated to, go In the case where it is a function of, the derivation can be adapted.

[0124] The rate of change of total lithium can be determined. By differentiating (20) over time and applying chain rules, the following is provided. (35) provides the following by replacing it. Now, integrate (21) over the entire electrode to provide the following, Therefore, the total side reaction current ( Defines ). Therefore, it is as follows.

[0125] List of symbols and abbreviations Abbreviations: EC = Ethylene carbonate LAM = Loss of active material LLI = Lithium inventory loss SEI = Solid Electrolyte Interphase Variables: C = Capacity; Unit = Ah I = Current; Unit = A J = Current; Unit = A N = molar flux; unit = mol m -2 s -1 V = Voltage; Unit = V a = surface area to volume ratio; unit = m -1 c = concentration; unit = mol m -3 i = current density; unit = A m -2 j = interfacial current density; unit = A m -2 n Li = Lithium Inventory; Unit = Moles r = radial coordinates t = time = thickness; unit = m = Active material volume fraction = Overpotential; Unit = V = Potential; Unit = V = Stoichiometry = Stress; Unit = Pa Parameters: See also Table 2 and Table 3. F = Faraday constant; unit = mol m -3 L = Electrode thickness; Unit = m R = Ideal gas constant; unit = J mol -1 K -1 R film = SEI film resistivity; Unit = m R k = Particle radius; Unit = m U = Open-circuit potential; Unit = V i0 = Intercalation exchange - current density; unit = A m -2 Subscripts: e = Electrolyte phase int = intercalation k = electrode k(n or p) n = cathode p = positive electrode s = solid phase tot = total Superscripts: surf = on the surface (of a particle) 0 = precedence-order of asymptotic expansion 1 = 1st order of asymptotic expansion

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[0127] Although the present invention has been described in considerable detail with reference to specific embodiments, a person skilled in the art will understand that the invention may be practiced by embodiments other than those described, which are presented for illustrative purposes rather than limitation. Therefore, the scope of the appended claims should not be limited to the description of the embodiments included herein.

Claims

Claim 1 A method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during a charge phase of each of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, wherein the method is performed by a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor, and wherein the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell at a state of 100% health; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( A method comprising: (d) a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the cell capacity at the end of each of the plurality of cell cycles, wherein the cell cycles are initialized based on the rate of degradation over the plurality of previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over the plurality of previous cycles; and (d) a step of determining the predicted end of the life of the electrochemical cell based on the fact that one of the calculated cell capacities is less than a predetermined percentage of the nominal capacity. Claim 2 A method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, wherein the method is performed by a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor, and wherein the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths to determine the total circulating cations ( A method comprising: (d) a step of sequentially calculating a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the current density of cation intercalation as a variable, rather than the current density of solid electrolyte interphase formation as a variable; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity. Claim 3 A method for manufacturing an electrochemical cell, wherein the electrochemical cell comprises an anode, an electrolyte, and a cathode comprising cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, wherein the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, wherein the method is performed by a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor, and wherein the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths to determine the total circulating cations ( A method comprising: (d) a step of sequentially calculating a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the current density of cation intercalation as a variable, rather than the current density of cation plating as a variable; and (d) a step of determining the predicted end of the life of the electrochemical cell based on the fact that one of the calculated cell capacities is less than a predetermined percentage of the nominal capacity. Claim 4 A method according to any one of claims 1 to 3, wherein the model does not include an algebraic equation. Claim 5 A method according to any one of claims 1 to 3, wherein the step of sequentially calculating the cell capacity at the end of each of the plurality of cell cycles is at least three times faster than a degradation model based on porosity-electrode theory including algebraic equations. Claim 6 In any one of paragraphs 1 to 3, the model is a surface potential difference Without including an algebraic equation to calculate, represents the solid phase potential of the above anode, and A method representing the phase potential of the above electrolyte. Claim 7 In any one of claims 1 to 3, step (c) is a solid electrolyte interphase kinetic rate constant ( k SEI ), solid electrolyte interphase layer diffusivity (D SEI ), and active material particle cracking rate (β LAM A method comprising the step of sequentially calculating the cell capacity at the end of each of the plurality of cell cycles based on ). Claim 8 A method according to claim 7, wherein step (c) comprises adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a linear degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 9 A method according to claim 7, wherein step (c) comprises adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a self-limiting degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 10 A method according to claim 7, wherein step (c) comprises adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate an accelerated degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 11 A method according to any one of claims 1 to 3, further comprising: (e) receiving a selection of at least one different cell component; (f) sequentially calculating a second cell capacity at the end of each of the plurality of cell cycles based on the at least one different cell component; (g) determining an additional predicted end of life of the electrochemical cell based on one of the calculated second cell capacities being less than a predetermined percentage of the nominal capacity; and (h) comparing the predicted end of life with the additional predicted end of life and selecting a preferred cell having the greater of the predicted end of life and the additional predicted end of life. Claim 12 In any one of paragraphs 1 to 3, the step of calculating the cell capacity uses the following relationship: , represents the capacity of the above anode, and represents the scaled volumed-averaged negative particle concentration at 100% charge, and A method representing the volume-average negative particle concentration scaled at 0% charge. Claim 13 In any one of claims 1 to 3, step (c) is the total circulating cations, solid electrolyte interphase thickness , solid-phase porous of the above anode , and the solid-phase porous structure of the cathode A method comprising the step of sequentially calculating the cell capacity at the end of at least some of the plurality of cell cycles based on Claim 14 A method according to any one of claims 1 to 3, wherein the cations are lithium cations. Claim 15 In any one of claims 1 to 3, the anode comprises an anode material selected from graphite, lithium titanium oxide, hard carbon, tin / cobalt alloys, silicon / carbon, or lithium metal, the electrolyte comprises a liquid electrolyte comprising a lithium compound in an organic solvent, and the cathode comprises (i) lithium metal oxides — the metal is one or more of aluminum, cobalt, iron, manganese, nickel, and vanadium —, (ii) lithium-containing phosphates having the general formula LiMPO4 — M is one or more of cobalt, iron, manganese, and nickel —, and (iii) formula LiNi x Mn y Co z Materials containing O2 — x+y+z = 1 and x:y:z = 1:1:1 (NMC 111), x:y:z = 4:3:3 (NMC 433), x:y:z = 5:2:2 (NMC 522), x:y:z = 5:3:2 (NMC 532), x:y:z = 6:2:2 (NMC 622), or x:y:z = 8:1:1 (NMC 811) — A method comprising a cathode active material selected from Claim 16 In any one of claims 1 to 3, the anode comprises graphite, and the electrolyte comprises a liquid electrolyte comprising a lithium compound in an organic solvent, wherein the lithium compound is selected from LiPF6, LiBF4, LiClO4, lithium bis(fluorosulfonyl)imide (LiFSI), LiN(CF3SO2)2 (LiTFSI), and LiCF3SO3 (LiTf), and the organic solvent is selected from carbonate-based solvents, ether-based solvents, ionic liquids, and mixtures thereof, and the carbonate-based solvent is selected from the group consisting of dimethyl carbonate, diethyl carbonate, ethyl methyl carbonate, dipropyl carbonate, methylpropyl carbonate, ethyl propyl carbonate, methyl ethyl carbonate, ethylene carbonate, propylene carbonate, and butylene carbonate, and mixtures thereof, and the ether-based solvent is diethyl ether, dibutyl ether, monoglycerin, A method selected from the group consisting of deglaim, tetraglaim, 2-methyltetrahydrofuran, tetrahydrofuran, 1,3-dioxolane, 1,2-dimethoxyethane, and 1,4-dioxane and mixtures thereof. Claim 17 A method in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, and the electrochemical cell comprises a cathode comprising an anode, an electrolyte, and cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, and the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths, the total circulating cations ( A method comprising: (d) a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the cell capacity at the end of each of the plurality of cell cycles, wherein the cell cycles are initialized based on the rate of degradation over the plurality of previous cycles, and the time to simulate the next cycle is selected based on the rate of degradation over the plurality of previous cycles; and (d) a step of determining the predicted end of the life of the electrochemical cell based on the fact that one of the calculated cell capacities is less than a predetermined percentage of the nominal capacity. Claim 18 A method in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, and the electrochemical cell comprises a cathode comprising an anode, an electrolyte, and cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, and the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths to determine the total circulating cations ( A method comprising: (d) a step of sequentially calculating a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the current density of cation intercalation as a variable, rather than the current density of solid electrolyte interphase formation as a variable; and (d) a step of determining the predicted end of the life of the electrochemical cell based on one of the calculated cell capacities being less than a predetermined percentage of the nominal capacity. Claim 19 A method in a data processing system comprising at least one processor and at least one memory, wherein the at least one memory comprises instructions executed by the at least one processor to implement an electrochemical cell end-of-life prediction system, and the electrochemical cell comprises a cathode comprising an anode, an electrolyte, and cations moving from the cathode to the anode during each of the charge phases of a plurality of cell cycles, and the cell undergoes degradation resulting in loss of active material and loss of cation inventory during one or more charge phases of the cell cycles, and the method comprises: (a) receiving a selection of at least one cell component selected from a group consisting of electrolytes, cathode active materials, and anode active materials — said at least one cell component causes degradation of the cell —; (b) receiving a nominal discharge capacity for the cell in a 100% healthy state; (c) using a degradation model based on porous-electrode theory having one or more degradation paths to determine the total circulating cations ( A method comprising: (d) a step of sequentially calculating a cell capacity at the end of each of the plurality of cell cycles based on the at least one cell component, accessible storage sites at each electrode, and the current density of cation intercalation as a variable, rather than the current density of cation plating as a variable; and (d) a step of determining the predicted end of the life of the electrochemical cell based on the fact that one of the calculated cell capacities is less than a predetermined percentage of the nominal capacity. Claim 20 A method according to any one of claims 17 to 19, wherein the model does not include an algebraic equation. Claim 21 A method according to any one of claims 17 to 19, wherein the step of sequentially calculating the cell capacity at the end of each of the plurality of cell cycles is at least three times faster than a degradation model based on porosity-electrode theory including algebraic equations. Claim 22 In any one of paragraphs 17 to 19, the model is a surface potential difference Without including an algebraic equation to calculate, represents the solid-phase potential of the above anode, and A method representing the phase potential of the above electrolyte. Claim 23 In any one of claims 17 to 19, step (c) is a solid electrolyte interphase kinetic rate constant ( k SEI ), solid electrolyte interphase layer diffusivity (D SEI ), and active material particle cracking rate (β LAM A method comprising the step of sequentially calculating the cell capacity at the end of each of the plurality of cell cycles based on ). Claim 24 In claim 23, the method comprises the step (c) of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a linear degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 25 A method according to claim 23, wherein step (c) comprises adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to generate a self-limiting degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 26 In claim 23, the method comprises the step (c) of adjusting the solid electrolyte interphase kinetic rate constant, the solid electrolyte interphase layer diffusivity, and the active material particle cracking rate to create an accelerated degradation path for the calculated cell capacities of the plurality of cell cycles. Claim 27 In any one of paragraphs 17 through 19, the step of calculating the cell capacity uses the following relationship: , represents the capacity of the above anode, and represents the scaled volume-average negative particle concentration at 100% charge, and A method representing the volume-average negative particle concentration scaled at 0% charge. Claim 28 In any one of claims 17 to 19, step (c) is the total circulating cations, solid electrolyte interphase thickness , solid-phase porous of the above anode , and the solid-phase porous structure of the cathode A method comprising the step of sequentially calculating the cell capacity at the end of at least some of the plurality of cell cycles based on Claim 29 delete Claim 30 delete Claim 31 delete Claim 32 delete Claim 33 delete

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