Method and device for solving electric field physical quantities in electrochemical model, and storage medium

Abstract

The present invention provides a method and device for solving electric field physical quantities in an electrochemical model, and a storage medium. The method includes: selecting a negative electrode region or a positive electrode region as a calculation region, solid-phase current or liquid-phase current as an observation quantity, and solid-phase potential and liquid-phase potential as co-state variables; inserting a number of nodes between the two endpoints of the calculation region, and determining the observation quantity values of the nodes; constructing N calculation units based on the above nodes, starting with the first calculation unit, and using the converged solution obtained after each calculation unit is targeted as the initial trial solution when the next calculation unit is targeted. The N calculation units are targeted sequentially to obtain a definite solution of the co-state variable at the starting point at the current moment, and then further obtaining the electric field physical quantity at any spatial point in the calculation region. The present invention improves the targeting method. By using multiple targeting methods, the conventional targeting method avoids the high dependence on the initial trial solution, and can also ensure the convergence of the electric field decoupling of the full-order electrochemical model under extreme working conditions.

Description

Technical Field

[0001] The present invention relates to the field of batteries, and in particular to a method and device for solving electric field physical quantities in an electrochemical model, as well as a storage medium. Background Art

[0002] To more clearly understand and monitor the real-time operating status of lithium-ion batteries, the battery's electrochemical reaction processes are modeled and an electrochemical model is established to obtain various physical quantities within the battery in space and time. For example, the electrochemical pseudo-two-dimensional model (P2D model), as a full-order model, is complex and offers very accurate simulations, but it also requires a high degree of coupling between various physical quantities and a high computational load.

[0003] In the electric field of the P2D model, there are two types of carriers: lithium ions and electrons. Internal 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, etc. Each of these physical quantities is coupled with other physical quantities.

[0004] In electric field coupling, a series of boundary value problems involving partial differential equations must be solved. The shooting method is a numerical approach for solving boundary value problems. This method is simple in principle, offers high accuracy, and is highly practical. However, its greatest challenge lies in guessing the initial values of the covariates. Improper initial values can lead to overflow and non-convergence. For systems with a high degree of nonlinearity, the region of convergence can be very small.

[0005] When the target shooting method is used for electric field decoupling under high current and high temperature conditions, the control equation of the full-order electrochemical model is highly nonlinear. It is easy for the initial value to be far from the true solution, resulting in non-convergence or exceeding the expression range of the data type when calculated on hardware and PC. Summary of the Invention

[0006] The purpose of the present invention is to provide a method and device for solving electric field physical quantities in an electrochemical model, as well as a storage medium, to solve the problem that when using a conventional shooting method to perform electric field decoupling of a full-order electrochemical model of a lithium-ion battery, the electric field is highly dependent on the initial value, and inappropriate initial values may easily lead to non-convergence or data overflow.

[0007] The technical solutions provided by the present invention are as follows:

[0008] A method for solving electric field physical quantities in an electrochemical model comprises: selecting a cathode region or a cathode region of the electrochemical model as a calculation region; selecting a solid-phase current or a liquid-phase current as an observed quantity, and selecting a solid-phase potential and a liquid-phase potential as co-state variables;

[0009] Inserting (the number of spatial discrete units N-1) mutually different nodes between the two end points of the calculation area, and determining the observation target value of each node according to a preset interpolation method;

[0010] Construct N computing units, where the starting point of each computing unit is the starting point of the computing region and the end point is one of the (N-1) nodes or the end point of the computing region, wherein the spatial region of the i-th computing unit is a subset of the spatial region of the (i+1)-th computing unit, where i = 1, 2, ..., N-1;

[0011] Starting from the first calculation unit, the target shooting of N calculation units is completed in ascending order until a converged solution of the target shooting of the Nth calculation unit is obtained, and the converged solution is used as the definite solution of the co-state variable of the starting point at the current moment;

[0012] Obtaining the electric field physical quantity of each spatial point in the calculation region at the current moment based on the observed value of the starting point at the current moment and the determined solution of the co-state variable;

[0013] Among them, the targeting of each computing unit includes:

[0014] Targeting the computing unit starting from an initial trial solution of the targeting of the computing unit to obtain a converged solution of the targeting of the computing unit, wherein the converged solution is a trial solution of the covariate variable at the starting point such that the value of the observation at the end point of the computing unit converges to the target value of the observation at the corresponding point;

[0015] If the computing unit is not the first computing unit, the initial trial solution of the targeting of the computing unit is obtained according to the converged solution of the targeting of the previous computing unit.

[0016] In some embodiments, determining the target value of the observation quantity of each node according to a preset interpolation method includes:

[0017] An interpolation function is constructed according to a preset interpolation method, wherein the values of the interpolation function at the two endpoints of the calculation area are respectively equal to the boundary values of the observation quantity in the calculation area; the preset interpolation method is one of the linear interpolation method, the Lagrange interpolation method, and the Newton interpolation method; and the target value of the observation quantity of each node is calculated according to the interpolation function.

[0018] In some embodiments, if the observed quantity is solid-phase current, the observed quantity target value of the i-th node is: Among them, i external is the external current, L is the thickness of the electrode, x i is the distance between the ith node and the current collector.

[0019] In some embodiments, it further includes:

[0020] If the targeting of one computing unit overflows or fails to converge during the targeting of N computing units, the number of spatial discrete units is increased, all computing units are reconstructed according to the new number of spatial discrete units, and targeting is restarted from the first computing unit.

[0021] In some embodiments, the targeting of each computing unit further includes:

[0022] If the computing unit is the first computing unit, the initial trial solution of the computing unit's target shooting is the definite solution of the co-state variable at the starting point of the computing region at the previous moment.

[0023] In some embodiments, the step of performing target practice on the computing unit starting from an initial trial solution of the target practice of the computing unit to obtain a converged solution of the target practice of the computing unit includes:

[0024] Obtaining the value of the observation quantity of the starting point of the calculation unit at the current moment;

[0025] Setting the co-state variable of the starting point at the current moment according to the initial trial solution of the target shooting of the computing unit;

[0026] Obtaining the observation value of the end point of the calculation unit at the current moment according to the observation value and the co-state variable of the starting point at the current moment and the control equation of the electrochemical model;

[0027] Determining whether an error between an observation value of an endpoint of the calculation unit at a current moment and a target observation value is within an error range;

[0028] If the error is not within the error range, the trial solution of the co-state variable is updated according to a preset rule, the co-state variable of the starting point at the current moment is set according to the new trial solution, the observation value of the end point of the computing unit at the current moment is obtained according to the new trial solution, and whether the error between the observation value of the end point of the computing unit at the current moment and the target value of the observation value is within the error range is determined, and the above process is repeated until the error is within the error range;

[0029] If the error is within the error range, the trial solution is used as the converged solution of the target shooting of the calculation unit.

[0030] In some embodiments, obtaining the observation value of the endpoint of the calculation unit at the current moment based on the observation value and co-state variable of the starting point at the current moment and according to the control equation of the electrochemical model includes:

[0031] Starting from the starting point, based on the observation quantity and co-state variable of the current spatial point at the current moment, the observation quantity and co-state variable of the next spatial point at the current moment are calculated, and the current spatial point is updated with the next spatial point. The above process is repeated until the observation quantity and co-state variable of the end point of the calculation unit at the current moment are obtained.

[0032] In some embodiments, calculating the observation value and co-state variable of the next spatial point at the current moment based on the observation value and co-state variable of the current spatial point at the current moment includes:

[0033] According to the solid phase potential and liquid phase potential of the current spatial point at the current moment, the overpotential of the current spatial point at the current moment is obtained using the following formula:

[0034] η(x,t)=φ s (x,t)-φ e (x,t)-ocv(x,t);

[0035] Where η is the overpotential, φ s is the solid phase potential, φ e is the liquid phase potential, and ocv is the steady-state open circuit voltage of the electrode related to the lithium ion concentration on the surface of the solid particles;

[0036] According to the overpotential of the current spatial point at the current moment, the exchange current density of the current spatial point at the current moment is obtained using the following formula:

[0037]

[0038] Among them, α + , α - is the transfer coefficient, F is the Faraday constant, R is the molar gas constant, T is the absolute temperature of the battery, and j0 is the exchange current density of the electrode reaction in equilibrium;

[0039] Calculating the observed value of the next spatial point at the current moment using a difference method or a Runge-Kutta method according to the exchange current density of the current spatial point at the current moment;

[0040] According to the observed value of the current spatial point at the current moment, the partial derivative of the solid-phase potential of the current spatial point at the current moment is obtained using the following formula:

[0041]

[0042] Among them, i s is the solid phase current, k is the solid phase conductivity;

[0043] Calculating the solid-phase potential of the next spatial point using a difference method or a Runge-Kutta method according to the partial derivative of the solid-phase potential of the current spatial point at the current moment;

[0044] The partial derivative of the liquid potential at the current spatial point at the current moment is obtained according to the following formula:

[0045]

[0046] Among them, i e is the liquid phase current, t c is the point mobility, c e is the liquid lithium ion concentration, σ is the liquid conductivity, ε is the liquid volume fraction, and brug is the porous medium coefficient;

[0047] The liquid phase potential of the next spatial point is calculated using a difference method or a Runge-Kutta method according to the partial derivative of the liquid phase potential of the current spatial point at the current moment.

[0048] The present invention also provides a device for solving electric field physical quantities in an electrochemical model, comprising:

[0049] Selecting the negative electrode region or the positive electrode region of the electrochemical model as the calculation region, recording one endpoint of the calculation region as the starting point, and the other endpoint as the end point; selecting the solid phase current or the liquid phase current as the observed quantity, and the solid phase potential and the liquid phase potential as the co-state variables;

[0050] An interpolation module is used to insert (the number of spatial discrete units N-1) different nodes between the two endpoints of the calculation area and determine the target value of the observation quantity of each node according to a preset interpolation method;

[0051] a unit construction module, configured to construct N computing units, each starting point being a starting point of the computing region and an end point being one of the (N-1) nodes or an end point of the computing region, wherein the spatial region of the i-th computing unit is a subset of the spatial region of the (i+1)-th computing unit, where i = 1, 2, ..., N-1;

[0052] An improved targeting module is used to start from the first computing unit and complete the targeting of N computing units in ascending order until a converged solution of the targeting of the Nth computing unit is obtained, and use the converged solution as the definite solution of the co-state variable of the starting point at the current moment;

[0053] A physical quantity calculation module is used to obtain the electric field physical quantity of each spatial point in the calculation area at the current moment based on the observed quantity of the starting point at the current moment and the determined solution of the co-state variable;

[0054] The improved target shooting module comprises:

[0055] Targeting unit, used to complete the targeting of each computing unit;

[0056] The targeting unit is also used to target the computing unit starting from the initial trial solution of the targeting of the computing unit to obtain a converged solution of the targeting of the computing unit, wherein the converged solution is a trial solution of the covariate variable at the starting point that makes the value of the observation quantity at the end point of the computing unit converge to the observation quantity target value of the corresponding point; if the computing unit is not the first computing unit, the initial trial solution of the targeting of the computing unit is obtained based on the converged solution of the targeting of the previous computing unit.

[0057] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for solving the electric field physical quantity in the electrochemical model described in any one of the above items is implemented.

[0058] Compared with the prior art, the method and device for solving electric field physical quantities in electrochemical models, as well as the storage medium provided by the present invention, can at least bring the following beneficial effects:

[0059] The present invention avoids the high dependence of conventional shooting methods on initial trial solutions and the data overflow or non-convergence phenomenon that easily occurs during the shooting process by multiple shootings. It can also successfully achieve electric field decoupling of full-order electrochemical models under extreme working conditions such as high current and high temperature. It has the advantages of conventional shooting methods, consumes less storage resources, and has high calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The preferred embodiment will be described below in a clear and understandable manner with reference to the accompanying drawings, further illustrating the above-mentioned characteristics, technical features, advantages and implementation methods of the method and device for solving electric field physical quantities in the electrochemical model and the storage medium.

[0061] Figure 1 is a flow chart of an embodiment of a method for solving electric field physical quantities in an electrochemical model of the present invention;

[0062] Figure 2 1 is a schematic structural diagram of an embodiment of a device for solving electric field physical quantities in an electrochemical model of the present invention;

[0063] Figure 3 It is a schematic diagram of the structure of the P2D model of lithium-ion batteries;

[0064] Figure 4 It is a schematic diagram of the improved target shooting method provided by the present invention. DETAILED DESCRIPTION

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings and other embodiments can be obtained based on these drawings without inventive work.

[0066] To simplify the drawings, only the parts relevant to the present invention are schematically shown in each figure. They do not represent the actual structure of the product. Furthermore, to simplify the drawings and facilitate understanding, in some figures, only one of the components with the same structure or function is schematically depicted or labeled. As used herein, "one" not only means "only one" but also "more than one."

[0067] As mentioned previously, we can use the shooting method to solve for electric field quantities such as current and potential at various spatial points in electrochemical models. However, conventional shooting methods are highly dependent on the initial trial solution of the covariates. If the initial trial solution is not appropriate, it will lead to overflow of intermediate calculation data and non-convergence of the shooting method.

[0068] To this end, the present invention improves the shooting method, converting a single shooting with a fixed tracking length into multiple shootings with different tracking lengths, with the tracking length gradually increasing to the maximum tracking length; starting from the shooting with the smallest tracking length, even if the initial trial solution of the first shooting is not very accurate, due to the small tracking length, it can better prevent data overflow during shooting; the initial trial solution of the shooting of this calculation unit is obtained based on the converged solution of the shooting of the previous calculation unit, so that the initial trial solution used in subsequent shooting can be made closer and closer to the true value, and even if the tracking length is increased, it can still be guaranteed that the subsequent shooting will not overflow.

[0069] The following describes the solution of the present invention in detail by taking the quasi-two-dimensional (P2D) model of a lithium-ion battery as an example.

[0070] The structural diagram of the P2D model is as follows Figure 3 As shown in Figure 2, the basic components of a lithium-ion battery are a copper current collector, a negative electrode, a separator, a positive electrode, and an aluminum current collector. In terms of spatial distribution, a lithium-ion battery can be divided into the positive electrode region, the negative electrode region, and the separator region. The width of the positive electrode region is Lp, the width of the negative electrode region is Ln, and the width of the separator region is Ls.

[0071] A plane coordinate system is established for the battery, and the x-axis is established along the direction from the negative pole to the positive pole.

[0072] In one embodiment of the present invention, Figure 1 As shown in FIG, a method for solving electric field physical quantities in an electrochemical model includes:

[0073] The negative electrode region or the positive electrode region of the electrochemical model is selected as the calculation region, and one end point of the calculation region is recorded as the starting point and the other end point is recorded as the end point.

[0074] Select solid-phase current or liquid-phase current as the observed quantity, and solid-phase potential and liquid-phase potential as covariates.

[0075] The boundary values of the observations in the calculation region, that is, the values of the observations at the two endpoints of the calculation region, are certain and known, but the covariates are not certain.

[0076] If the starting point of the calculation region is the endpoint near the current collector and the end point is the endpoint far from the current collector, then the solid-phase current at the starting point at the current moment is equal to the external current at the current moment, and the liquid-phase current at the starting point at the current moment is equal to 0; the solid-phase current at the end point at the current moment is 0, and the liquid-phase current at the end point is the external current. If the starting point is the endpoint far from the current collector and the end point is the endpoint near the current collector, the conclusion is exactly the opposite.

[0077] Step S1000 inserts (N-1) distinct nodes between the two endpoints of the computational region and determines the target value of the observation value for each node using a preset interpolation method. N is the number of spatial discrete units.

[0078] Specifically, several nodes may be inserted between two end points of the calculation region at equal or unequal intervals.

[0079] Step S1100 constructs an interpolation function based on a preset interpolation method. The domain of the interpolation function is the calculation region, and the values of the interpolation function at the two endpoints of the calculation region are equal to the boundary values of the observation in the calculation region. The preset interpolation method can be one of linear interpolation, Lagrange interpolation, and Newton interpolation.

[0080] Step S1200 calculates the target value of the observation quantity of each node according to the interpolation function.

[0081] The target values of the observations at the two endpoints of the calculation area are also the boundary values of the observations in the calculation area.

[0082] In order to avoid the occurrence of extreme values of the interpolation function in the calculation area that may cause non-convergence of the target, preferably, a threshold range is set according to the boundary value of the observation quantity in the calculation area, such as the minimum value and the maximum value, to limit the value of the interpolation function at each node to not exceed this threshold range.

[0083] Step S2000 constructs N computing units.

[0084] Each computational unit has two endpoints: a starting point and an ending point. The starting point of each computational unit is the starting point of the computational region, and the ending point is one of the inserted (N-1) nodes or the ending point of the computational region. The spatial region of the i-th computational unit is a subset of the spatial region of the (i+1)-th computational unit, where i = 1, 2, ..., N-1.

[0085] Specifically, all computational units have the same starting point, which is the starting point of the computational region and is collectively referred to as the starting point. All computational units have different endpoints. Counting along the direction from the starting point to the end point of the computational region, the endpoint of the first computational unit is the first node, the endpoint of the i-th computational unit is the i-th node, and so on, until the endpoint of the N-th computational unit is the end point of the computational region.

[0086] Step S3000 starts from the first calculation unit and completes the targeting of N calculation units in ascending order until a converged solution of the targeting of the Nth calculation unit is obtained, which is used as the definite solution of the co-state variable at the starting point at the current moment.

[0087] The target shooting of each computing unit includes:

[0088] Step S3100 performs a target practice on the computation unit starting from an initial trial solution of the target practice of the computation unit to obtain a converged solution of the target practice of the computation unit, wherein the converged solution is a trial solution of the covariate variable at the starting point such that the value of the observation at the end point of the computation unit converges to the target value of the observation at the corresponding point;

[0089] In step S3200, if the computing unit is not the first computing unit, the initial trial solution of the computing unit's target practice is obtained based on the converged solution of the previous computing unit's target practice.

[0090] The converged solution of the previous calculation unit's shooting can be directly used as the initial trial solution of the current calculation unit's shooting, or the converged solution of the previous calculation unit's shooting can be slightly processed to obtain the initial trial solution of the current calculation unit's shooting.

[0091] If the computational unit is the first computational unit, the initial trial solution of the computational unit's target shooting can be obtained based on an empirical method or a reduced-order model.

[0092] The boundary values of the observation quantity in each calculation unit, that is, the target values of the observation quantity at the starting point of the calculation unit and the end point of the calculation unit, are determined in step S1000 before shooting.

[0093] Each computational unit is trained using a conventional shooting method, starting from the starting point and moving toward the end point of the computational unit. The target is the observed value at the end point of the computational unit. Starting from the initial trial solution of the computational unit, through multiple iterations, the converged solution of this shooting is obtained.

[0094] The initial trial solution is the first trial solution at the starting point of the covariate variables used in the computational unit's target practice. During the target practice, the trial solution is adjusted according to certain rules to obtain a trial solution that makes the value of the observation at the end of the computational unit converge to the target value of the observation at the corresponding point. This trial solution is considered the converged solution obtained in this target practice.

[0095] The Nth calculation unit is the calculation area, so the converged solution of the target shooting of the Nth calculation unit is actually the definite solution of the co-state variables at the starting point at the current moment.

[0096] Step S4000 obtains the electric field physical quantity of each spatial point in the calculation area at the current moment based on the value of the observation quantity of the starting point at the current moment and the determined solution of the co-state variable.

[0097] Electric field quantities include but are not limited to solid-phase current, liquid-phase current, solid-phase potential, and liquid-phase potential.

[0098] For example, Figure 4 As shown in the figure, the boundaries of the computational region are points a and b, with point a being the starting point and point b being the end point. The values of the observations at the boundaries of the computational region are predetermined, such as ɑ at point a and β at point b. Using the shooting method, we can obtain a definite solution for the covariates at point a (the starting point). The value of the observations obtained from this definite solution at point b (the end point of the computational region) converges to β (the target value of the observations at point b).

[0099] Insert two nodes t1 and t2 between points a and b. The target values of the observation quantities of the two nodes can be obtained by interpolation. Figure 4 The target value of the node's observation is obtained by linear interpolation.

[0100] Point a to point t1 constitutes the first calculation unit, point a to point t2 constitutes the second calculation unit, point a to point b constitutes the third calculation unit, and the third calculation unit is equal to the calculation area.

[0101] First, the first calculation unit is shot (i.e., the first shooting). Counting from left to right, curve 1 (FIRST SHOT) is obtained based on the trial solution 1 of the costate variable at point a (i.e., the initial trial solution of the first shooting). The value of curve 1 at point t1 (the end point of the first calculation unit) is far from the target value of the observation at point t1. After multiple iterations, the trial solution is continuously adjusted to obtain curve 4. The value of curve 4 at point t1 converges to the target value of the observation at point t1, so the trial solution of the costate variable at point a corresponding to curve 4 is the converged solution obtained by the first shooting.

[0102] The converged solution obtained from the first shooting is used as the initial trial solution for the second shooting, and the second calculation unit is shot. The value of curve 4 (SECOND SHOT) corresponding to the initial trial solution at point t2 is far away from the target value of the observation quantity at point t2. Through multiple iterations, curve 7 (THIRD SHOT) that converges to the target value of the observation quantity at point t2 is obtained, and the trial solution corresponding to curve 7 is used as the converged solution obtained from the second shooting.

[0103] Repeat the above process and perform the third shooting until curve 9 is obtained, which converges to the target value of the observation quantity at point b. The trial solution corresponding to curve 9 is taken as the converged solution obtained from the third shooting.

[0104] The third calculation unit is the calculation area, so the converged solution obtained from the third target shooting is the definite solution of the co-state variable at point a.

[0105] If we directly perform target shooting in the calculation area, starting from the trial solution 1 of the co-state variable at point a, it can be predicted from the figure that the value of curve 1 at point b is far away from β. During the target shooting process, overflow is likely to occur, resulting in the inability to continue the target shooting process. Figure 4 It can be seen that if the initial trial solution is not appropriate, the conventional shooting process is prone to overflow and the correct solution cannot be obtained.

[0106] In this embodiment, by constructing multiple computing units with different tracking lengths, targeting is started from the computing unit with the smallest tracking length. Even if the initial trial solution of the first targeting is not very accurate, the short tracking length can better prevent targeting overflow. The initial trial solution of the next computing unit is obtained based on the converged solution of the previous computing unit, which can make the initial trial solution used in subsequent targeting closer and closer to the true value, thereby ensuring that targeting does not overflow.

[0107] The solution method for the electric field physical quantities in the negative electrode region and the positive electrode region is the same. You can first perform the solution for one region, and then perform the solution for the other region using the same method, thus completing the solution of the electric field physical quantities in the entire space.

[0108] In one embodiment, step S1000 includes:

[0109] If the observed quantity is solid-phase current, the observed quantity target value of the i-th node is: Among them, i external is the external current, L is the thickness of the electrode, x i is the distance between the i-th node and the current collector, i = 1, 2, ..., N-1.

[0110] x i It can be obtained by dividing the calculation area into N equal parts. The observation target values of the above nodes are calculated based on the linear interpolation method.

[0111] In one embodiment, the method for solving the electric field physical quantity further includes:

[0112] If a computing unit overflows or fails to converge during the targeting of N computing units, the number of spatial discrete units is increased, and steps S1000 to S4000 are re-executed according to the new number of spatial discrete units.

[0113] In one embodiment, step S3000 includes:

[0114] In step S3300, if the computing unit is the first computing unit, the initial trial solution of the computing unit's target is the definite solution of the co-state variables at the starting point of the computing region at the previous moment.

[0115] The determined solution of the co-state variable starting at the previous moment is closer to the true value, and selecting it as the initial trial solution is more conducive to the convergence of the targeting algorithm.

[0116] In one embodiment, step S3100 includes:

[0117] Step S3110 obtains the value of the observation quantity of the starting point of the calculation unit at the current moment;

[0118] Step S3120 sets the co-state variables of the starting point at the current moment according to the initial trial solution of the target shooting of the computing unit;

[0119] Step S3130 obtains the observation value of the end point of the calculation unit at the current moment based on the observation value and co-state variable of the starting point at the current moment and the control equation of the electrochemical model;

[0120] Step S3140 determines whether the error between the observation value of the endpoint of the calculation unit at the current moment and the observation value target value of the endpoint is within the error range;

[0121] If the result is not within the error range in step S3150, the trial solution of the co-state variables is updated according to the preset rules, the co-state variables at the starting point at the current moment are set according to the new trial solution, and then the process jumps to step S3130;

[0122] If the result in step S3160 is within the error range, the trial solution is taken as the converged solution for this calculation unit target practice.

[0123] The error range can be set according to the accuracy requirements. If it is not within the error range, further iterations are required to adjust the current trial solution. Adjustments can be made based on the difference between the observation value obtained at the end point of the calculation unit and the target observation value. If a converged solution is obtained, the calculation unit is considered a success.

[0124] In one embodiment, step S3130 includes:

[0125] Starting from the starting point, based on the observation quantity and co-state variables of the current spatial point at the current moment, calculate the observation quantity and co-state variables of the next spatial point at the current moment, update the current spatial point with the next spatial point, and repeat the above process until the observation quantity and co-state variables of the end point of the calculation unit at the current moment are obtained.

[0126] The calculation of the observation quantity and co-state variable of the next spatial point at the current moment according to the observation quantity and co-state variable of the current spatial point at the current moment includes:

[0127] Step S3131 calculates the overpotential of the current spatial point at the current moment using the following formula based on the solid-phase potential and liquid-phase potential of the current spatial point at the current moment:

[0128] η(x,t)=φ s (x,t)-φ e (x,t)-ocv(x,t);

[0129] Where η is the overpotential, φ s is the solid phase potential, φ e is the liquid phase potential, and OCV is the steady-state open-circuit voltage of the electrode, which is related to the lithium ion concentration on the surface of the solid particles. The distribution of OCV on the x-axis can be obtained in advance before electric field decoupling.

[0130] Step S3132: Based on the overpotential of the current spatial point at the current moment, the exchange current density j of the current spatial point at the current moment can be obtained using the following formula: n :

[0131]

[0132] Among them, α + , α - is the transfer coefficient, F is the Faraday constant, R is the molar gas constant, T is the absolute temperature of the battery, and j0 is the exchange current density of the electrode reaction in equilibrium.

[0133] Step S3133 calculates the observation value of the next spatial point at the current moment using the difference method or the Runge-Kutta method based on the observation value and exchange current density of the current spatial point at the current moment.

[0134] The next spatial point is equal to the current spatial point plus the preset step. The exchange current density reflects both the change in lithium-ion current per unit area and the change in electron current. The observed value is either solid-phase current or liquid-phase current. Therefore, the observed value at the current spatial point and the exchange current density can be used to determine the observed value at the next spatial point.

[0135] Step S3134 obtains the partial derivative of the solid-phase potential of the current spatial point at the current moment based on the observation value of the current spatial point at the current moment, and calculates the solid-phase potential of the next spatial point using the difference method or the Runge-Kutta method based on the partial derivative of the solid-phase potential of the current spatial point at the current moment.

[0136] If the observed quantity is solid-phase current, the partial derivative of the solid-phase potential at the current spatial point at the current moment is obtained according to the following formula: Among them, i s is the solid phase current, and k is the solid phase conductivity.

[0137] If the observed quantity is liquid phase current, then according to i s (x,t)+i e (x,t)=i external (t), i external For the external current, first obtain the solid-phase current of the current spatial point at the current moment, and then obtain the partial derivative of the solid-phase potential of the current spatial point at the current moment according to the above formula;

[0138] Using the difference method or the Runge-Kutta method, the solid-phase potential of the next spatial point can be obtained based on the solid-phase potential of the current spatial point at the current moment and the partial derivative of the solid-phase potential.

[0139] Step S3135 obtains the partial derivative of the liquid phase potential of the current spatial point at the current moment, and calculates the liquid phase potential of the next spatial point using the difference method or the Runge-Kutta method based on the partial derivative of the liquid phase potential of the current spatial point at the current moment.

[0140] Specifically, if the observed quantity is solid-phase current, then according to i s (x,t)+i e (x,t)=i external (t), get the liquid phase current of the current spatial point at the current moment;

[0141] Then, the partial derivative of the liquid potential at the current spatial point is obtained according to the following formula: Among them, i e is the liquid phase current, t c is the point mobility, c e is the liquid lithium ion concentration, σ is the liquid conductivity, ε is the liquid volume fraction, and brug is the porous medium coefficient;

[0142] The liquid potential at the next spatial point is calculated based on the liquid potential at the current spatial point and the partial derivative of the liquid potential.

[0143] In one embodiment of the present invention, Figure 2 As shown, a device for solving electric field physical quantities in an electrochemical model includes:

[0144] Select the cathode or anode region of the electrochemical model as the calculation region. The calculation region has two endpoints, one of which is the starting point and the other is the end point. Select the solid-phase current or liquid-phase current as the observed variable, and the solid-phase potential and liquid-phase potential as the covariates.

[0145] The interpolation module 100 is used to insert (the number of spatial discrete units N-1) different nodes between the two end points of the calculation area, and determine the target value of the observation quantity of each node according to a preset interpolation method.

[0146] The unit construction module 200 is used to construct N computation units. The starting point of each computation unit is the starting point of the computation region, and the end point is one of the inserted (N-1) nodes or the end point of the computation region. The spatial region of the i-th computation unit is a subset of the spatial region of the (i+1)-th computation unit, where i = 1, 2, ..., N-1.

[0147] The improved targeting module 300 is used to complete the targeting of N computing units in ascending order starting from the first computing unit until a converged solution of the targeting of the Nth computing unit is obtained, which is used as the definite solution of the co-state variable at the starting point at the current moment.

[0148] The physical quantity calculation module 400 is used to obtain the electric field physical quantity of each spatial point in the calculation area at the current moment based on the value of the observation quantity of the starting point at the current moment and the determined solution of the co-state variable.

[0149] The improved target shooting module 300 includes:

[0150] Targeting unit, used to complete the targeting of each computing unit;

[0151] The targeting unit is also used to target the computing unit starting from the initial trial solution of the targeting of the computing unit to obtain the converged solution of the targeting of the computing unit. The converged solution is a trial solution of the covariate variable at the starting point that makes the value of the observation quantity at the end point of the computing unit converge to the target value of the observation quantity at the corresponding point; if the computing unit is not the first computing unit, the initial trial solution of the targeting of the computing unit is obtained according to the converged solution of the targeting of the previous computing unit.

[0152] In some embodiments, the interpolation module is further configured to:

[0153] If the observed quantity is solid-phase current, the observed quantity target value of the i-th node is: Among them, i external is the external current, L is the thickness of the electrode, x i is the distance between the ith node and the current collector.

[0154] In some embodiments, the device for solving the electric field physical quantity further includes:

[0155] The unit number update module is used to increase the number of spatial discrete units if a computing unit overflows or fails to converge during the target shooting of N computing units;

[0156] The interpolation module and the unit construction module are adaptively updated according to the new number of spatial discrete units.

[0157] In one embodiment, the targeting unit is further used for, if the computing unit is the first computing unit, the initial trial solution of the targeting of the computing unit is the determined solution of the co-state variables at the starting point of the computing region at the previous moment.

[0158] In one embodiment, the targeting unit is also used to obtain the value of the observation quantity of the starting point of the calculation unit at the current moment; according to the initial trial solution of the targeting of the calculation unit, the costate variable of the starting point at the current moment is set; according to the observation quantity and the costate variable of the starting point at the current moment, according to the control equation of the electrochemical model, the observation quantity of the end point of the calculation unit at the current moment is obtained; it is determined whether the error between the observation quantity of the end point of the calculation unit at the current moment and the target value of the observation quantity of the end point is within the error range; if not within the error range, the trial solution of the costate variable is updated according to the preset rules, and the costate variable of the starting point at the current moment is set according to the new trial solution; if it is within the error range, the trial solution is used as the converged solution of this targeting of the calculation unit.

[0159] The target shooting unit includes:

[0160] The overpotential calculation unit is used to obtain the overpotential of the current spatial point at the current moment according to the solid phase potential and liquid phase potential of the current spatial point at the current moment.

[0161] The exchange current density calculation unit is used to obtain the exchange current density of the current spatial point at the current moment according to the overpotential of the current spatial point at the current moment.

[0162] The current calculation unit is used to calculate the observation value of the next spatial point at the current moment using the difference method or the Runge-Kutta method based on the observation value and exchange current density of the current spatial point at the current moment.

[0163] The electric potential calculation unit is used to obtain the partial derivative of the solid phase potential of the current spatial point at the current moment based on the observation value of the current spatial point at the current moment, and calculate 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 current spatial point at the current moment; obtain the partial derivative of the liquid phase potential of the current spatial point at the current moment, and calculate 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 current spatial point at the current moment.

[0164] It should be noted that the embodiments of the device for determining electric field quantities in an electrochemical model provided herein and the aforementioned embodiments of the method for determining electric field quantities in an electrochemical model are based on the same inventive concept and achieve the same technical effects. Therefore, for other specific details of the embodiments of the device for determining electric field quantities in an electrochemical model, reference can be made to the description of the aforementioned embodiments of the electric field decoupling method.

[0165] In one embodiment of the present invention, a computer-readable storage medium stores a computer program thereon, and when the computer program is executed by a processor, it can implement the method for solving the electric field physical quantity in the electrochemical model as described in the aforementioned embodiment. That is, when part or all of the technical solutions that contribute to the prior art in the aforementioned embodiment of the present invention are embodied in the form of a computer software product, the aforementioned computer software product is stored in a computer-readable storage medium. The computer-readable storage medium can be any physical device or equipment that can carry a computer program code. For example, the computer-readable storage medium can be a USB flash drive, a mobile disk, a magnetic disk, an optical disk, a computer memory, a read-only memory, a random access memory, etc.

[0166] It should be noted that the above embodiments can be freely combined as needed. The above description is only a preferred embodiment of the present invention. It should be pointed out that those skilled in the art can make several improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for solving electric field physical quantities in an electrochemical model, characterized in that: include: Select the negative electrode area or positive electrode area of the electrochemical model as the calculation area; Select solid phase current or liquid phase current as the observed variable, solid phase potential and liquid phase potential as the co-state variables; Inserting (N-1) different nodes of the spatial discrete unit between the two end points of the calculation area, and determining the observation target value of each node according to a preset interpolation method; Construct N computing units, where the starting point of each computing unit is the starting point of the computing region and the end point is one of the (N-1) nodes or the end point of the computing region, wherein the spatial region of the i-th computing unit is a subset of the spatial region of the (i+1)-th computing unit, where i = 1, 2, ..., N-1; Starting from the first calculation unit, the target shooting of N calculation units is completed in ascending order until a converged solution of the target shooting of the Nth calculation unit is obtained, and the converged solution is used as the definite solution of the co-state variable of the starting point at the current moment; Obtaining the electric field physical quantity of each spatial point in the calculation region at the current moment based on the observed value of the starting point at the current moment and the determined solution of the co-state variable; Among them, the targeting of each computing unit includes: Targeting the computing unit starting from an initial trial solution of the targeting of the computing unit to obtain a converged solution of the targeting of the computing unit, wherein the converged solution is a trial solution of the covariate variable at the starting point such that the value of the observation at the end point of the computing unit converges to the target value of the observation at the corresponding point; If the computing unit is not the first computing unit, the initial trial solution of the targeting of the computing unit is obtained according to the converged solution of the targeting of the previous computing unit.

2. The method for solving electric field physical quantities in an electrochemical model according to claim 1, characterized in that: The method of determining the target value of the observation quantity of each node according to the preset interpolation method includes: Constructing an interpolation function according to a preset interpolation method, wherein the values of the interpolation function at the two endpoints of the calculation region are respectively equal to the boundary values of the observation value in the calculation region; the preset interpolation method is one of linear interpolation, Lagrange interpolation, and Newton interpolation; The observation target value of each node is calculated according to the interpolation function.

3. The method for solving electric field physical quantities in an electrochemical model according to claim 2, characterized in that: The calculation of the observation target value of each node according to the interpolation function includes: If the observed quantity is solid-phase current, the observed quantity target value of the i-th node is: Among them, i external is the external current, L is the thickness of the electrode, x i is the distance between the ith node and the current collector.

4. The method for solving electric field physical quantities in an electrochemical model according to claim 1, characterized in that: Also includes: If the targeting of one computing unit overflows or fails to converge during the targeting of N computing units, the number of spatial discrete units is increased, all computing units are reconstructed according to the new number of spatial discrete units, and targeting is restarted from the first computing unit.

5. The method for solving electric field physical quantities in an electrochemical model according to claim 1, characterized in that: The target shooting of each computing unit also includes: If the computing unit is the first computing unit, the initial trial solution of the computing unit's target shooting is the definite solution of the co-state variable at the starting point of the computing region at the previous moment.

6. The method for solving electric field physical quantities in an electrochemical model according to claim 1, characterized in that: The step of performing target practice on the computing unit starting from an initial trial solution of the target practice of the computing unit to obtain a converged solution of the target practice of the computing unit includes: Obtaining the value of the observation quantity of the starting point of the calculation unit at the current moment; Setting the co-state variable of the starting point at the current moment according to the initial trial solution of the target shooting of the computing unit; Obtaining the observation value of the end point of the calculation unit at the current moment according to the observation value and the co-state variable of the starting point at the current moment and the control equation of the electrochemical model; Determining whether an error between an observation value of an endpoint of the calculation unit at a current moment and a target observation value is within an error range; If the error is not within the error range, the trial solution of the co-state variable is updated according to a preset rule, the co-state variable of the starting point at the current moment is set according to the new trial solution, the observation value of the end point of the computing unit at the current moment is obtained according to the new trial solution, and whether the error between the observation value of the end point of the computing unit at the current moment and the target value of the observation value is within the error range is determined, and the above process is repeated until the error is within the error range; If the error is within the error range, the trial solution is used as the converged solution of the target shooting of the calculation unit.

7. The method for solving electric field physical quantities in an electrochemical model according to claim 6, characterized in that: The method of obtaining the observation value of the end point of the calculation unit at the current moment based on the observation value and the co-state variable of the starting point at the current moment and the control equation of the electrochemical model includes: Starting from the starting point, based on the observation quantity and co-state variable of the current spatial point at the current moment, the observation quantity and co-state variable of the next spatial point at the current moment are calculated, and the current spatial point is updated with the next spatial point. The above process is repeated until the observation quantity and co-state variable of the end point of the calculation unit at the current moment are obtained.

8. The method for solving electric field physical quantities in an electrochemical model according to claim 7, characterized in that: The calculation of the observation quantity and co-state variable of the next spatial point at the current moment according to the observation quantity and co-state variable of the current spatial point at the current moment includes: Establish a plane coordinate system for the battery model, and establish the x-axis along the direction from the negative electrode to the positive electrode; According to the solid phase potential and liquid phase potential of the current spatial point at the current moment, the overpotential of the current spatial point at the current moment is obtained using the following formula: η(x,t)=φ s (x,t)-φ e (x,t)-ocv(x,t); Where η is the overpotential, φ s is the solid phase potential, φ e is the liquid phase potential, and ocv is the steady-state open circuit voltage of the electrode related to the lithium ion concentration on the surface of the solid particles; According to the overpotential of the current spatial point at the current moment, the exchange current density of the current spatial point at the current moment is obtained using the following formula: Among them, α + , α - is the transfer coefficient, F is the Faraday constant, R is the molar gas constant, T is the absolute temperature of the battery, and j0 is the exchange current density of the electrode reaction in equilibrium; Calculating the observed value of the next spatial point at the current moment using a difference method or a Runge-Kutta method according to the exchange current density of the current spatial point at the current moment; According to the observed value of the current spatial point at the current moment, the partial derivative of the solid-phase potential of the current spatial point at the current moment is obtained using the following formula: Among them, i s is the solid phase current, k is the solid phase conductivity; Calculating the solid-phase potential of the next spatial point using a difference method or a Runge-Kutta method according to the partial derivative of the solid-phase potential of the current spatial point at the current moment; The partial derivative of the liquid potential at the current spatial point at the current moment is obtained according to the following formula: Among them, i e is the liquid phase current, t c is the point mobility, c e is the liquid lithium ion concentration, σ is the liquid conductivity, ε is the liquid volume fraction, and brug is the porous medium coefficient; The liquid phase potential of the next spatial point is calculated using a difference method or a Runge-Kutta method according to the partial derivative of the liquid phase potential of the current spatial point at the current moment.

9. A device for solving electric field physical quantities in an electrochemical model, characterized in that: include: Selecting the negative electrode region or the positive electrode region of the electrochemical model as the calculation region; selecting the solid phase current or the liquid phase current as the observed quantity, and the solid phase potential and the liquid phase potential as the co-state variables; An interpolation module is used to interpolate (N-1) different nodes of the spatial discrete unit between the two end points of the calculation area, and determine the target value of the observation quantity of each node according to a preset interpolation method; a unit construction module, configured to construct N computing units, each starting point being a starting point of the computing region and an end point being one of the (N-1) nodes or an end point of the computing region, wherein the spatial region of the i-th computing unit is a subset of the spatial region of the (i+1)-th computing unit, where i = 1, 2, ..., N-1; An improved targeting module is used to start from the first computing unit and complete the targeting of N computing units in ascending order until a converged solution of the targeting of the Nth computing unit is obtained, and use the converged solution as the definite solution of the co-state variable of the starting point at the current moment; A physical quantity calculation module is used to obtain the electric field physical quantity of each spatial point in the calculation area at the current moment based on the observed quantity of the starting point at the current moment and the determined solution of the co-state variable; The improved target shooting module comprises: Targeting unit, used to complete the targeting of each computing unit; The targeting unit is also used to target the computing unit starting from the initial trial solution of the targeting of the computing unit to obtain a converged solution of the targeting of the computing unit, wherein the converged solution is a trial solution of the covariate variable at the starting point that makes the value of the observation quantity at the end point of the computing unit converge to the observation quantity target value of the corresponding point; if the computing unit is not the first computing unit, the initial trial solution of the targeting of the computing unit is obtained based on the converged solution of the targeting of the previous computing unit.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for solving electric field physical quantities in an electrochemical model according to any one of claims 1 to 8 is implemented.

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