US-12625186-B2 - Method and system for target-based electric field decoupling for electrochemical model

US12625186B2US 12625186 B2US12625186 B2US 12625186B2US-12625186-B2

Abstract

The invention discloses method and system for target-based electric field decoupling for an electrochemical model. The method includes selecting one endpoint of a negative/positive electrode region as a starting point and the other endpoint as an end point; providing a trial solution of solid-phase and liquid-phase potentials of the starting point empirically, obtaining solid-phase/liquid-phase current of the end point according to the trial solution; obtaining a tentative solution that satisfies boundary value conditions by iterative approximation; designating the tentative solution satisfying the boundary value conditions as a deterministic solution of the solid phase potential and the liquid phase potential of the starting point; and obtaining the microscopic physical quantity of any spatial point in the positive electrode region/negative electrode region in the electric field based on the deterministic solution of the solid phase/liquid phase current, the solid phase and liquid phase potentials at the starting point.

Inventors

Danfei Gu
Siyuan Chen
Mingchen Jiang
Xiao Yan
Enhai Zhao

Assignees

Makesense Energy Technology Co., Limited.

Dates

Publication Date: 20260512
Application Date: 20230612
Priority Date: 20220629

Claims (9)

1 . A method for target-based electric field decoupling for an electrochemical model of a lithium ion battery, comprising: selecting a negative electrode region or a positive electrode region of the electrochemical model of the lithium ion battery as a calculation region, and marking one endpoint of the calculation region as a starting point and the other endpoint as an end point; selecting a solid phase current or a liquid phase current as an observed quantity; acquiring the observed quantity of the starting point at a present time; initializing a solid-phase potential and a liquid-phase potential of the starting point at the present time by using a trial solution; based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time, obtaining the observed quantity of the end point at the present time according to an electrochemical reaction process of the electrochemical model; determining whether an error between the observed quantity of the end point at the present time and a target value of the end point is within an error range; when the error is not within the error range, updating the trial solution according to a preset rule, initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time using another trial solution, obtaining the observed quantity of the end point at the present time according to said another trial solution, determining whether the error between the observed quantity of the end point at the present time and the target value of the observed quantity is within the error range, and repeating the process until the error is within the error range; when the error is within the error range, using the trial solution as a deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time; and obtaining microscopic physical quantities of each spatial point in the calculation region at the present time according to the observed quantity of the starting point at the present time and the deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time, wherein said initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using the trial solution comprises: initializing the solid-phase potential of the starting point at the present time to the deterministic solution of the solid-phase potential of the starting point at a previous time, and initializing the liquid-phase potential of the starting point at the present time to the deterministic solution of the liquid-phase potential of the starting point at the previous time.
2 . The method of claim 1 , when the starting point is an endpoint proximal to a current collector, the solid-phase current of the starting point at the present time is equal to an external current at the present time, and the target value of the solid-phase current of the end point at the present time is 0; when the starting point is an endpoint distal to the current collector, the solid phase current of the starting point at the present time is equal to 0, and the target value of the solid phase current of the end point at the present time is the external current at the present time.
3 . The method of claim 1 , wherein said obtaining the observed quantity of the end point at the present time based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time comprises: based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time, calculating the observed quantity, the solid-phase potential and the liquid-phase potential of a next spatial point at the present time along the x axis at a preset pace; and calculating the observed quantity, the solid-phase potential and the liquid-phase potential of another next spatial point at the present time according to the observed quantity, the solid-phase potential and the liquid-phase potential of the next spatial point at the present time, and repeating the processes until the observed quantity, the solid-phase potential and the liquid-phase potential of the end point at the present time are obtained.
4 . The method of claim 3 , wherein said calculating the observed quantity, the solid-phase potential and the liquid-phase potential of the next spatial point at the present time based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point comprises: based on the solid phase potential and the liquid phase potential of the starting point at the present time, obtaining an overpotential of the starting point at the present time by a formula of: η( x,t )=φ s ( x,t )−φ e ( x,t )−ocv( x,t ); wherein η is the overpotential, φ s is the solid phase potential, φ e is the liquid phase potential, ocv is an electrode steady state open circuit voltage related to a lithium ion concentration on surfaces of solid phase particles; based on the overpotential of the starting point at the present time, obtaining an exchange current density of the starting point at the present time by a formula of: j n ( x , t ) = 1 F ⁢ j 0 ( x , t ) [ exp ⁡ ( α + ⁢ F R ⁢ T ⁢ η ⁡ ( x , t ) ) - exp ⁡ ( - α - ⁢ F R ⁢ T ⁢ η ⁡ ( x , t ) ) ] ; wherein α + and α − are transfer coefficients, F is a Faraday constant, R is a molar gas constant, T is an absolute temperature of the battery, and j 0 is the exchanging current density for an electrode reaction in an equilibrium state; based on the exchange current density of the starting point at the present time, calculating the observed quantity of the next spatial point at the present time by using a difference method or a Runge-Kutta method; based on the observed quantity of the starting point at the present time, obtaining a partial derivative of the solid-phase potential of the starting point at the present time by a formula of: ∂ ϕ s ∂ x ⁢ ( x , t ) = - i s ( x , t ) k wherein i s is the solid phase current, k is a solid phase conductivity; calculating the solid phase potential of the next spatial point by using the difference method or the Runge-Kutta method based on the partial derivative of the solid phase potential of the starting point at the present time; obtaining a partial derivative of the liquid phase potential of the starting point at the present time according to a formula of: ∂ ϕ e ∂ x ⁢ ( x , t ) = - i e ( x , t ) σ * ε b ⁢ r ⁢ u ⁢ g + 2 ⁢ R ⁢ T F ⁢ ( 1 - t c ) ⁢ ∂ ln ⁢ c e ∂ x ⁢ ( x , t ) wherein i e is the liquid phase current, t c is the point mobility, c e is a liquid phase lithium ion concentration, σ is a liquid phase conductivity, ε is a liquid phase volume fraction, brug is a porous media coefficient; and calculating the liquid phase potential of the next spatial point by using the difference method or the Runge-Kutta method based on the partial derivative of the liquid phase potential of the starting point at the present time.
5 . The method of claim 1 , wherein said updating the trial solution according to the preset rule comprises: x k + 1 = x k + g - i k i k - i k - 1 ⁢ ( x k - x k - 1 ) wherein x k is the kth trial solution, i k is the observed quantity of the end point at the present time obtained by adopting the k-th trial solution, and g is the target value of the observed quantity of the end point at the present time.
6 . The method of claim 1 , wherein after said obtaining microscopic physical quantities of each spatial point in the calculation region at the present time, the method further comprises: performing an early warning diagnosis on the lithium ion battery according to the microscopic physical quantities.
7 . The method of claim 6 , wherein the microscopic physical quantities include the overpotential; and wherein said performing the early warning diagnosis on the lithium ion battery based on the microscopic physical quantities comprises: when the overpotential of at least one spatial point is smaller than a first potential threshold value, the lithium ion battery is considered to have SEI film thickening; when the overpotential of at least one spatial point is smaller than a second potential threshold, the lithium ion battery is considered to have lithium dendrite growth; and when the overpotential of at least one spatial point is higher than a third potential threshold, the lithium ion battery is considered to have electrolyte decomposition.
8 . The method of claim 6 , wherein the microscopic physical quantities include the liquid phase current; and wherein said performing the early warning diagnosis on the lithium ion battery based on the microscopic physical quantities comprises when the liquid phase current of at least one spatial point is higher than a first current threshold, the lithium ion battery is considered to have an internal short circuit.
9 . A system for target-based electric field decoupling for an electrochemical model of a lithium ion battery, wherein a negative electrode region or a positive electrode region of the electrochemical model of the lithium ion battery is selected as a calculation region, and one endpoint of the calculation region is marked as a starting point and the other endpoint is marked as an end point, and a solid phase current or a liquid phase current is selected as an observed quantity, the system comprising: an acquisition module, configured to acquire the observed quantity of the starting point at a present time; a setting module, configured to initialize a solid-phase potential and a liquid-phase potential of the starting point at the present time by using a trial solution, wherein said initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using the trial solution comprises: initializing the solid-phase potential of the starting point at the present time to the deterministic solution of the solid-phase potential of the starting point at a previous time, and initializing the liquid-phase potential of the starting point at the present time to the deterministic solution of the liquid-phase potential of the starting point at the previous time; a calculation module configured to obtain the observed quantity of the end point at the present time according to the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time and the electrochemical reaction process of the electrochemical model; determine whether an error between the observed quantity of the end point at the present time and a target value of the end point is within an error range; when the error is not within the error range, update the trial solution according to a preset rule, initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using another trial solution, obtain the observed quantity of the end point at the present time according to said another trial solution, determine whether the error between the observed quantity of the end point at the present time and the target value of the observed quantity is within the error range, and repeat the process until the error is within the error range; when the error is within the error range, the trial solution is used as a deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time; and a microscopic quantity updating module, configured to obtain the microscopic physical quantities of each spatial point in the calculation region at the present time according to the observed quantity of the starting point at the present time and the deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time.

Description

CROSS-REFERENCE TO RELATED PATENT APPLICATION This application claims priority to and the benefit of Chinese Patent Application No. 202210752376.2, filed Jun. 29, 2022, which are incorporated herein in their entireties by reference. FIELD OF THE INVENTION The invention relates generally the field of batteries, and more particularly to a method and a system for target-based electric field decoupling for an electrochemical model of a lithium ion battery. BACKGROUND OF THE INVENTION Lithium-ion batteries are a new generation of secondary batteries, with high energy density and cycle life, and are widely used in mobile communications, digital technology, electric vehicles, energy storage and other fields. By establishing electrochemical models for lithium-ion batteries, the simulated values of various microscopic physical quantities in the internal space and time of the battery can be obtained, which can more clearly understand and monitor the real-time working status of lithium-ion batteries. In the electrochemical models, the transformation of most microscopic physical quantities with time and space is described by time-domain partial differential equations. On one hand, these partial differential equations are described in both time and space, and attention needs to be paid to the separation of time and space. On the other hand, multiple partial differential equations are strongly coupled to each other, and decoupling is required when performing numerical simulations. The electrochemical pseudo-two-dimensional (P2D) coupling model is a full-order electrochemical model, and its equation describes only one dimension in the Euclidean space, and meanwhile, the radial dimension of the active material particles is wound everywhere in the one-dimensional Euclidean space. In these two spatial dimensions, multiple fields such as an electric field, a thermal field, and a stress field are coupled each other to describe various physical and chemical processes such as electrochemistry, mass transfer, heat transfer, and momentum transfer, and various phases and subphases such as particles, solids, liquids, metals, and polymers, which are very complex. In the electric field of the full-order electrochemical model, there are two kinds of carriers, lithium ions and electrons, and the internal state physical quantities include solid-phase ion concentration, liquid-phase ion concentration, solid-phase current, liquid-phase current, solid-liquid two-phase exchange current density, solid phase potential, liquid phase potential, and the likes. Each of these quantities is coupled to the other quantities. The coupling means that the change of the physical quantity X causes the change of the physical quantity Y, which in turns causes the change of the physical quantity X, until the real-time dynamic balance is reached. With respect to the solution of an electrochemical model, on the one hand, the internal state solution of the single field or single phase is relatively mature, including, but is not limited to, the single field solution of the temperature field, the solution of the solid phase or liquid phase concentration of the lithium ion concentrations. The current solution technology does not involve the solution of multi-field and multi-phase coupled physical fields. The solution is to simplify and reduce the order of the model, so that the coupling between fields and phases is weakened or eliminated, and then obtain the solution of a plurality of single fields or single phases. However, such solution inevitably has loss, and cannot simulate and reflect the real internal state of the battery. On the other hand, the mathematical systems of the temperature field and the concentration field are linear systems, and its solution difficulty is relatively low. However, the physical response of the electric field of the battery is a less suitable nonlinear system, and multi-field and multi-phase exist in the electric field, so that no good solution exists for electric field decoupling in a full-order electrochemical model. Therefore, a heretofore unaddressed need exists in the art to address the aforementioned deficiencies and inadequacies. SUMMARY OF THE INVENTION In view of the above-noted shortcomings, one of the objectives of this invention is to provide a method and a system for target-based electric field decoupling for an electrochemical model of a lithium ion battery to solve the electric field decoupling problems of the electrochemical reaction process in a lithium ion battery full-order electrochemical model in the prior art. In one aspect of the invention, the method includes selecting a negative electrode region or a positive electrode region of the electrochemical model of the lithium ion battery as a calculation region, and marking one endpoint of the calculation region as a starting point and the other endpoint as an end point; selecting a solid phase current or a liquid phase current as an observed quantity; acquiring t