Calibration method for a three-dimensional nodal model, computer program and associated electronic device
The calibration method for three-dimensional nodal models enhances simulation speed and accuracy by adjusting resistance values and scaling, addressing the limitations of existing nodal models in battery simulations.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- AUTOMOTIVE CELLS CO SE
- Filing Date
- 2024-12-13
- Publication Date
- 2026-06-19
AI Technical Summary
Existing three-dimensional nodal models for simulating battery behavior lack a systematic method to optimize the trade-off between simulation speed and accuracy, leading to inaccuracies compared to finite element simulations.
A calibration method for three-dimensional nodal models that involves determining equivalent resistance values between nodes, applying multiplicative coefficients to adjust predictions, and scaling the model to improve accuracy while maintaining speed, using fundamental physics laws and reference simulations.
The calibrated nodal model provides faster simulations with accuracy comparable to finite element methods by realistically modeling physical quantity transfer between nodes, ensuring precise predictions under varying conditions.
Smart Images
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Abstract
Description
Title of the invention: Method for calibrating a three-dimensional nodal model, computer program and associated electronic device
[0001] The present invention relates to a method for calibrating a three-dimensional nodal model to simulate a physical quantity related to a battery. It also relates to a computer program comprising software instructions which, when implemented by a computer, implement such a calibration method. Finally, it relates to an electronic device for generating such a three-dimensional nodal model.
[0002] During the development or diagnostics of automotive batteries, it is useful to be able to predict battery behavior, such as thermal behavior, based on usage. Such predictions make it possible, for example, to control battery behavior in many use cases without performing experimental tests, or to predict battery aging. Numerous multiphysics simulation software programs are available that allow the prediction of physical quantities, such as thermal or electrical properties, in a battery of known geometry, particularly through finite element simulation. To reduce computation time compared to the finite element method, it is also known to use a three-dimensional nodal model.
[0003] One limitation of using a nodal model is the accuracy of the simulation. Indeed, while such models are faster than finite element simulations, they are also less accurate. A calibration phase of the nodal model is therefore crucial to improving the simulation accuracy. For example, the article "Contribution to the thermal modeling of LiFePO4 battery packs for low-carbon vehicles" by Damay, N. (Doctoral dissertation, University of Technology of Compiègne, 2015) describes a thermal modeling of a battery using a three-dimensional nodal model, a parameterization of this model using the fundamental laws of physics, and a calibration of this model using experimental data acquired on the battery cells.
[0004] However, this method does not guarantee that the accuracy of the simulation obtained from the nodal model is comparable to a simulation performed using finite elements. Furthermore, the aforementioned article does not formalize a systematic method for calibrating the nodal model to obtain a model that optimizes the trade-off between speed and simulation accuracy.
[0005] The aim of the invention is then to propose a calibration method for a three-dimensional nodal model that optimizes the trade-off between speed and accuracy of simulation.
[0006] To this end, the invention relates to a method for calibrating a three-dimensional nodal model to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the method comprising a step of acquiring an initial three-dimensional nodal model of the battery, the method further comprising, for at least a portion of the initial nodal model, called the reference portion: - a step of evaluating resistances, comprising determining, for at least one pair of nodes belonging to the reference portion, an equivalent resistance value between the two nodes of the pair of nodes, the equivalent resistance value representing a resistance of the battery to a transmission of the physical quantity between the two nodes of the pair of nodes; and - a resistance calibration step, including a multiplication by a respective multiplicative coefficient of each resistance value determined during the evaluation step, each multiplicative coefficient allowing to adjust a prediction of the physical quantity by the initial three-dimensional nodal model to a prediction of the physical quantity by a reference simulation;
[0007] the method providing a calibrated nodal model, to predict battery behavior relative to the physical quantity.
[0008] Thanks to the invention, the calibrated nodal model makes it possible to perform a simulation of the physical quantity related to the battery that is faster than a finite element simulation, due to the nodal structure, while remaining faithful to predictions made by such a finite element simulation. Indeed, the determination and then calibration of resistances using the reference simulation makes it possible to model the transfer of the physical quantity between the nodes realistically. The resulting nodal model, calibrated to minimize the discrepancies in the prediction of the physical quantity by the nodal model compared to the reference simulation, can then be used to simulate the physical quantity, faster than the reference simulation, but with comparable accuracy, under conditions different from the calibration conditions.
[0009] According to other advantageous aspects of the invention, the calibration method comprises one or more of the following features, taken individually or in all technically possible combinations:
[0010] - each equivalent resistance value is determined from laws fundamentals of physics or reference simulation;
[0011] - the calibration step includes grouping, into at least one group, the values of resistances determined during the evaluation stage, and the multiplicative coefficient is identical for all resistances in the same group;
[0012] - the physical quantity is a temperature;
[0013] - two resistors belong to the same group if: • the nodes that the said resistors connect have the same primary axis of thermal conduction, the primary axis of thermal conduction of a node being an axis along which heat transfer within the node is predominant or exceeds a predetermined minimum heat transfer threshold; or • the nodes that said resistors connect belong to the same battery component, where each battery component is chosen from: a stack comprising at least one anode and one cathode, a set of electrical terminals, and an external casing of a battery cell;
[0014] - the acquisition step further includes an acquisition with a value of at least a geometric parameter for each node belonging to the reference portion from a known geometry of the battery, each geometric parameter being chosen from a group of geometric parameters including: a volume of the node, an external area of the node, and a mass of the node; the geometric parameters preferably including all the parameters of the group of geometric parameters;
[0015] - the acquisition step further includes an acquisition worth at least one material parameter for each node belonging to the reference portion from a material database, each material parameter being chosen from a group of material parameters including: a thermal conductivity of the node, a specific heat capacity of the node, and a density of the node; the material parameters preferably including all the parameters of the material parameter group;
[0016] - the method further comprises a scaling step, subsequent to the step calibration, during which the nodes not belonging to the reference portion are calibrated, either by duplication of the nodes of the calibrated reference portion, or by the same steps as those performed on the nodes of the reference portion, providing a calibrated nodal model of the battery.
[0017] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement a calibration method as defined above.
[0018] The invention also relates to an electronic device for calibrating a three-dimensional nodal model to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the calibration device comprising a module for acquiring an initial three-dimensional nodal model of the battery, the electronic calibration device further comprising: - a resistance evaluation module for at least a portion of the initial nodal model, called the reference portion, the resistance evaluation module being configured to determine, for at least one pair of nodes belonging to the reference portion, an equivalent resistance value between the two nodes of the pair of nodes, the equivalent resistance value representing a resistance of the battery to a transmission of the physical quantity between the two nodes of the pair of nodes; and - a resistance calibration module for at least one reference portion, configured to perform a multiplication by a respective multiplicative coefficient of each resistance value determined by the evaluation module, each multiplicative coefficient allowing to adjust a prediction of the physical quantity by the three-dimensional nodal model to a prediction of the physical quantity by a reference simulation;
[0019] the electronic calibration device providing a calibrated nodal model, to predict battery behavior relative to the physical quantity.
[0020] The invention will become clearer upon reading the following description, given solely by way of non-limiting example, and made with reference to the drawings in which:
[0021] [Fig-1] [Fig.1] is a schematic representation of a calibration device of a three-dimensional nodal model according to the invention;
[0022] [Fig.2] [Fig.2] is a flowchart of a calibration method for a nodal model three-dimensional according to the invention, implemented by the calibration device of [Fig. 1]; and
[0023] [Fig. 3] [Fig. 3] is a diagram of part of a three-dimensional nodal model obtained via the calibration process of [Fig.2].
[0024] Figure 1 represents an electronic device 1 for calibrating a three-dimensional nodal model. The calibration device 1 is configured to implement a method 100 for calibrating a three-dimensional nodal model, described below. The calibration method 100 provides a calibrated nodal model Mc that can simulate a physical quantity related to a battery, for example, a thermal or electrical quantity. In the example developed in this description, and without limitation, the physical quantity is a temperature of a material constituting the battery in different areas of the battery. Alternatively, the physical quantity is an electrical potential or force.
[0025] A three-dimensional nodal model is a model comprising a set of nodes, each node being characterized by a spatial position. The three-dimensional nodal model of the battery is intended to predict the battery's behavior with respect to the physical quantity. More specifically, in the example, the prediction consists of predicting a battery temperature at each node of the three-dimensional nodal model and the evolution of the temperature over time, as a function of battery operating conditions, in particular as a function of a current applied to the battery terminals.
[0026] To this end, the electronic calibration device 1 includes an acquisition module 3, an evaluation module 5 and a calibration module 7. As an optional complement, the electronic calibration device 1 also includes a scaling module 9. The role of these different modules is described in the rest of the description.
[0027] In the example of [Fig.1], the electronic calibration device 1 includes an information processing unit 11 formed for example of a memory 13 and a processor 15 associated with the memory 13.
[0028] In the example of [Fig. 1], the acquisition module 3, the evaluation module 5, and the calibration module 7, as well as the optional upscaling module 9, are each implemented as a software program, or a software component, executable by the processor 15. The memory 13 of the electronic device 1 is thus capable of storing acquisition software, evaluation software, and calibration software, as well as the optional upscaling software. The processor is then capable of executing each of the following software programs: acquisition software, evaluation software, and calibration software, as well as the optional upscaling software.
[0029] In an alternative not shown, the acquisition module 3, the evaluation module 5 and the calibration module 7, as well as the optional scaling module 9, are each implemented as a programmable logic component, such as an FPGA (Field Programmable Gate Array) or an integrated circuit, such as an ASIC (Application Specified Integrated Circuit).
[0030] When the electronic calibration device 1 is implemented in the form of one or more software programs, i.e., in the form of a computer program, also called a computer program product, it is further capable of being stored on a computer-readable medium, not shown. The computer-readable medium is, for example, a medium capable of storing electronic instructions and being connected to a bus of a computer system. For example, the readable medium is a disk. Optical, magneto-optical, ROM, RAM, any type of non-volatile memory (e.g., FLASH or NVRAM), or magnetic card. A computer program containing software instructions is then stored on the readable medium.
[0031] The calibration process of a three-dimensional nodal model 100, implemented by the electronic calibration device 1, is described in the following description with reference to [Fig.2].
[0032] The calibration method 100 is performed on a battery, not shown, whose geometry and constituent materials are known. For example, the battery is a Lithium-ion battery comprising several cells.
[0033] Prior to the calibration process 100, an initial nodal model Mi is generated using a generation process not shown. It is advantageously assumed that the number and position of the nodes of the initial nodal model Mi optimize the trade-off between accuracy and speed of the battery temperature simulation.
[0034] The objective of the calibration process 100 is to determine the calibrated three-dimensional nodal model Mc, allowing the thermal behavior of the battery to be simulated faster than a reference finite element simulation S with a precision comparable to the reference simulation S of the state of the art.
[0035] To do this, the calibration process 100 includes an acquisition step 102, an evaluation step 104 and a calibration step 106. Advantageously, the calibration process 100 further includes a scaling step 108.
[0036] Acquisition step 102 is implemented by acquisition module 3 and includes an acquisition of the initial nodal model Mi.
[0037] The evaluation steps 104 and calibration steps 106 are initially implemented for a portion, or part, of the initial nodal model Mi, called the reference portion Mi'. The reference portion Mi' advantageously corresponds to a cell of the battery, called the reference cell. Alternatively, the reference portion Mi' designates any portion of the initial nodal model Mi.
[0038] Figure 3 shows an example of a reference portion Mi' of the initial nodal model Mi corresponding to the reference cell. In this example, the reference portion Mi' comprises 18 nodes: N12, N13, N15, N21, N24, N31, N34, N51, N52, N6, N7, and N8. Node N15 corresponds to a bottom face of a housing in the reference cell, nodes N21, N24, N31, and N34 correspond to side faces of the housing in the reference cell, and node N6 corresponds to a lid of a housing in the reference cell. Nodes N1, N12, and N13 correspond respectively to a top part of a stack, a middle part of the stack, and a bottom part of the stack. The stack comprises at least one anode, one cathode, one electrolyte, and one separator. Nodes N51 and N52 correspond to internal connections of the reference cell. Nodes N7 and N8 correspond to external connections of the reference cell, or interconnections.
[0039] Advantageously, the acquisition step 102 further includes acquiring a value of at least one geometric parameter for each node belonging to the reference portion Mi'. In the example in Figure 2, the geometric parameters include a volume V of the node, an external area A of the node, and a mass m of the node. Alternatively, the external area A of the node is replaced by at least one external surface of the node. These geometric parameters are derived from the known geometry of the battery. In particular, these geometric parameters are, for example, derived from a computer-aided design (CAD) model of the battery.
[0040] Advantageously, the acquisition step 102 further includes acquiring a value for at least one material parameter for each node belonging to the reference portion Mi'. In the example in Figure 1, the material parameters include at least a thermal conductivity 2 of the node, a specific heat capacity Cp of the node, and a density P of the node. These parameters are derived from prior knowledge of the materials constituting the battery and are typically obtained from a materials database or from characterization measurements performed in the laboratory.
[0041] Thus, at the end of acquisition step 102, the reference portion Mi' of the initial nodal model Mi is enriched with geometric and material parameters for each of its nodes. In this sense, acquisition step 102 is also a parameterization step. The geometric and / or material parameters make the initial nodal model Mi more faithful to the real battery that one seeks to simulate, and therefore improve the accuracy of the temperature prediction from this model.
[0042] Evaluation step 104 is implemented by evaluation module 5 and includes determining, for at least one pair of nodes belonging to the reference portion Mi', an equivalent resistance value R11, R12, R13, R21, R22, R31, R32, R41, R42, R61, R62, R7 or R8 between the two nodes of the pair of nodes. For readability, the equivalent thermal resistances linking nodes N6, N15, N21, N24, N31 and N34 together are not shown in [Fig. 3].
[0043] Each resistance value represents the resistance of the reference cell of the battery to the transmission of the physical quantity between the two nodes of the pair of nodes. For example, the thermal resistance R61 shown in [Fig. 3] represents the resistance of the reference cell to heat transfer between nodes N51 and N6.
[0044] Each resistance value is advantageously determined from fundamental laws of physics or from a reference simulation S.
[0045] In particular, when the geometry of the battery at the considered node pair is sufficiently simple to allow the resistances to be determined by the fundamental laws governing heat transfer, the thermal resistances are determined by applying these laws (e.g., the heat equation). When the geometry is more complex, a heat flux value and a temperature gradient value are estimated by the reference simulation S, and then used to estimate the thermal resistance value, which is equal to the quotient of the temperature gradient by the heat flux.
[0046] The reference simulation S is advantageously a simulation of the temperature in the battery and the evolution of the temperature over time using physical laws governing the thermal behavior of materials (for example, the unsteady 3D heat equation, including in particular Fourier's and Newton's laws) and a finite element model of the battery. This reference simulation S is, for example, executed by multiphysics simulation software.
[0047] Alternatively, in the case of complex geometries, simplification assumptions are used to reduce to a case that can be directly calculated by physical laws, or the resistance values are derived from experimental values obtained for similar geometries.
[0048] The calibration step 106 is implemented by the calibration module 7 and includes a multiplication by a respective multiplicative coefficient of each resistance value determined during the evaluation step 104. Each multiplicative coefficient allows a temperature prediction by the three-dimensional nodal model Mi to be adjusted to a prediction of the physical quantity by the reference simulation S.
[0049] To this end, calibration step 106 includes a temperature simulation by the initial nodal model Mi at each of the two nodes of the pair of nodes connected by the thermal resistance whose multiplicative coefficient is to be calculated, as well as the acquisition of an equivalent simulated temperature value at each of the two nodes of the pair of nodes by the reference simulation S. The equivalent temperature value simulated at a given node by the reference simulation S is, for example, a volumetric average of point temperature values within the node. Then, the multiplicative coefficient to be applied to the thermal resistance connecting the two nodes considered is determined using an optimization algorithm based on the temperature simulation by the initial nodal model Mi and the equivalent temperature value from the reference simulation S.
[0050] Advantageously, the calibration step 106 further includes grouping the resistance values determined during the evaluation step 104 into at least one group G1, G2, G3, G4, or G5. The multiplication factor is then determined jointly for all the resistances in the same group. In particular, the multiplication factor is identical for all the resistances in the same group. This grouping makes the calibration procedure 100 faster.
[0051] The primary thermal conduction axis of a node is defined as an axis, or direction, along which heat transfer within the node is predominant or exceeds a predetermined minimum heat transfer threshold. Groups are defined such that two thermal resistances belong to the same group if the nodes they connect share the same primary thermal conduction axis or belong to the same battery component. Battery components include, for example, the cathode-anode stack, the external casing of the reference cell, or a set of electrical terminals. This grouping choice preserves the physical meaning of the calibration process 100, thus simplifying the interpretation of simulation results obtained with the calibrated nodal model Mc.
[0052] In the example in [Fig. 3], the resistors are grouped into 5 groups. A first group G1, comprising resistors R11, R12, and R13, a second group G2, comprising resistors R21 and R22, and a third group G3, comprising resistors R31 and R32, each group together resistors connecting nodes having the same primary axis of thermal conduction. A fourth group G4 groups together resistors R41 and R42, belonging to the same battery component, in this case, the set of electrical terminals of the reference cell. A fifth group G5 groups together resistors R61 and R62, belonging to the same battery component, in this case, the set of electrical terminals of the reference cell cover. Resistors R7 and R8 are treated separately.
[0053] At the end of calibration step 106, the reference portion Mi' is calibrated. In other words, calibration step 106 provides a calibrated reference portion Mc'.
[0054] The scaling step 108 is implemented by the scaling module 9. During this scaling step 108, the nodes of the initial nodal model Mi of the battery that do not belong to the reference portion Mi' are calibrated, either by duplicating the nodes of the calibrated reference portion Mc', or by the same steps as those performed on the nodes of the reference portion Mi'. Thus, the scaling step 108 makes it possible to go from the calibrated reference portion Mc' of a cell to a calibrated nodal model Mc of a battery module. In other words, The scaling step 108 is a generalization step, and the scaling module 9 is a generalization module.
[0055] In particular, the battery generally comprises a stack of cells all identical to the reference cell. During the scaling step 108, the nodes corresponding to each of these cells are replaced by the corresponding nodes of the calibrated reference portion Mc'. In addition, the battery includes components not belonging to any cell, for example, an external battery casing and an insulator. As an optional complement, the nodes belonging to these components are then calibrated following the same steps as the acquisition 102, evaluation 104, and calibration 106 steps.
[0056] Alternatively, the initial nodal model Mi comprises only the reference portion Mi'. The scaling step 108 then includes a generation of additional nodes, identical to the nodes of the calibrated reference portion Mc', allowing the conversion from the calibrated reference portion Mc' to the calibrated nodal model Mc of a battery module.
[0057] At the end of the scaling step 108, the entire initial nodal model Mi is calibrated. The calibrated nodal model Mc includes the geometric, material, and thermal resistance parameters necessary for a simulation of the battery temperature that is both fast and as accurate as possible to the accuracy of the reference simulation S.
[0058] Any feature described above for one example or variant can also be implemented in the other examples and variants described above. Nomenclature:
[0059] 1: electronic calibration device; 3: acquisition module; 5: module evaluation; 7: calibration module; 9: scaling module; 11: information processing unit; 13: memory; 15: processor; 100: calibration process; 102: acquisition step; 104: evaluation step; 106: calibration step; 108: scaling step; Mi: initial nodal model; Mc: calibrated nodal model; Mi': reference portion; Mc': calibrated reference portion; S: reference simulation; N11, N12, N13, N14, N15, N21, N22, N23, N24, N31, N32, N33, N34, N51, N52, N6, N7, and N8: nodes; V: node volume; A: external area of the node; m: node mass; μ2: thermal conductivity of the node; Cp: specific heat capacity of the node; P: node density; R11, R12, R31, R32, R41, R42, R61, R62, R7 and R8: equivalent thermal resistances; G1, G2, G3, G4 and G5: groups.
Claims
Demands
1. A method for calibrating (100) a three-dimensional nodal model for simulating a physical quantity relating to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the method being implemented by an electronic calibration device, the method (100) comprising an acquisition step (102) of an initial three-dimensional nodal model (Mi) of the battery, characterized in that the method (100) further comprises, for at least a portion of the initial nodal model (Mi), called the reference portion (Mi'): - a resistance evaluation step (104), comprising a determination, for at least one pair of nodes belonging to the reference portion (Mi'), of an equivalent resistance value between the two nodes of the pair of nodes,the equivalent resistance value representing the battery's resistance to the transmission of the physical quantity between the two nodes of the node pair; and - a resistance calibration step (106), comprising multiplying each resistance value determined during the evaluation step (104) by a respective multiplicative coefficient, each multiplicative coefficient allowing a prediction of the physical quantity by the initial three-dimensional nodal model (Mi) to be adjusted to a prediction of the physical quantity by a reference simulation (S); the method (100) providing a calibrated nodal model (Mc), to predict battery behavior with respect to the physical quantity, in order to control battery behavior or predict battery aging.
2. Method (100) according to claim 1, wherein each equivalent resistance value is determined from fundamental laws of physics or from the reference simulation (S).
3. A method according to any one of the preceding claims, wherein the calibration step (106) comprises a grouping, in at less one group (Gl, G2, G3, G4, G5), of resistance values determined during the evaluation step (104), and in which the multiplicative coefficient is identical for all resistances of the same group.
4. Method (100) according to any one of the preceding claims, wherein the physical quantity is a temperature.
5. A method (100) according to claims 3 and 4, wherein two resistors belong to the same group if: - the nodes that said resistors connect have the same primary thermal conduction axis, the primary thermal conduction axis of a node being an axis along which heat transmission within the node is predominant or is greater than a predetermined minimum heat transmission threshold; or - the nodes that said resistors connect belong to the same battery component, where each battery component is selected from: a stack comprising at least one anode and one cathode, a set of electrical terminals, and an external casing of a battery cell.
6. A method (100) according to any one of the preceding claims, wherein the acquisition step (102) further comprises acquiring a value of at least one geometric parameter for each node belonging to the reference portion (Mi') from a known geometry of the battery, each geometric parameter being chosen from a group of geometric parameters including: a volume (V) of the node, an external area (A) of the node, and a mass (m) of the node; the geometric parameters preferably comprising all the parameters of the group of geometric parameters.
7. A method (100) according to any one of the preceding claims taken with claim 4, wherein the acquisition step (102) further comprises acquiring a value of at least one material parameter for each node belonging to the reference portion (Mi') from a material database, each material parameter being selected from a group of material parameters including: a thermal conductivity (2) of the node, a specific heat capacity (Cp) of the node, and a density (P) of the node; the material parameters preferably including all parameters of the material parameter group.
8. A method (100) according to any one of the preceding claims, further comprising a scaling step (108), subsequent to the calibration step (106), during which the nodes not belonging to the reference portion (Mi') are calibrated, either by duplication of the nodes of the calibrated reference portion (Mc'), or by the same steps as those performed on the nodes of the reference portion (Mi'), providing a calibrated nodal model (Mc) of the battery.
9. Computer program, comprising software instructions which, when implemented by computer, implement a method (100) according to any one of the preceding claims.
10. Electronic calibration device (1) of a three-dimensional nodal model for simulating a physical quantity relating to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the calibration device (1) comprising an acquisition module (3) of an initial three-dimensional nodal model (Mi) of the battery, characterized in that the electronic calibration device (1) further comprises: - a resistance evaluation module (5) for at least a portion of the initial nodal model (Mi), referred to as the reference portion (Mi'), the resistance evaluation module (5) being configured to determine, for at least one pair of nodes belonging to the reference portion (Mi'), an equivalent resistance value between the two nodes of the pair of nodes, the equivalent resistance value representing a resistance of the battery to a transmission of the physical quantity between the two nodes of the pair of nodes; and - a resistance calibration module (7) of at least one reference portion (Mi'), configured to perform a multiplication by a respective multiplicative coefficient of each resistance value determined by the evaluation module (5), each multiplicative coefficient allowing to adjust a prediction of the physical quantity by the three-dimensional nodal model to a prediction of the physical quantity by a reference simulation (S); the electronic calibration device (1) providing a calibrated nodal model (Mc), to predict battery behavior relative to the physical quantity, in order to control battery behavior or to predict battery aging.