Simulation analysis method of fluid inside arc extinguishing chamber of SF6 circuit breaker with electromagnetic thermal effects

Abstract

The present application relates to a method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal effects, and relates to the technical field of fluid simulation analysis inside the arc extinguishing chamber of a circuit breaker. The method comprises: obtaining a target physical quantity; the target physical quantity is a physical quantity directly related to the control equation of the fluid region; the target physical quantity includes the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time; constructing a simulation model of the fluid inside the arc extinguishing chamber based on the target physical quantity; solving the simulation model of the fluid inside the arc extinguishing chamber based on the real parameter fitting interpolation method, and obtaining the simulation analysis results corresponding to the simulation model of the fluid inside the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker. The use of this method can improve modeling efficiency and simulation effects.

Description

Technical Field

[0001] The present application relates to the technical field of fluid simulation analysis in a circuit breaker arc extinguishing chamber, and in particular to a method for fluid simulation analysis in a SF6 circuit breaker arc extinguishing chamber by introducing electromagnetic thermal influences. Background Art

[0002] In power systems, high-voltage switches are critical equipment for the safe and stable operation of power grids. Their performance directly impacts the reliability, economy, and safety of power systems. With the rapid development of the power industry, the requirements for high-voltage switchgear are increasing, especially in the fields of ultra-high and ultra-high voltage transmission. The breaking capacity, stability, and lifespan of switchgear have become urgent technical challenges. The breaking operation of high-voltage switches involves complex physical processes, including transient changes in the system's near-field circuits, the generation and extinction of switching arcs, the dynamic response of the transmission mechanism, and the electromagnetic effects of the drive mechanism. The interactions and influences between these multiple physical fields constitute the core challenges of high-voltage switch design and evaluation. Among them, the simulation of the plasma inside the arc extinguishing chamber of an SF6 circuit breaker involves electromagnetic and thermal effects, and the physical properties of SF6 gas are highly nonlinear, making it a critical and most difficult step in the high-voltage switch simulation process.

[0003] Obtaining complete SF6 arc plasma physical parameters is a necessary prerequisite and foundation for arc simulation. Existing technologies typically use equilibrium composition calculation methods based on the principle of minimum Gibbs free energy to determine the equilibrium chemical composition and basic thermophysical parameters of SF6. This method makes numerous assumptions and is not suitable for areas with large temperature gradients or low electron density. It also requires a high computational effort, which is particularly time-consuming when coupled with multiple physical fields. Furthermore, its computational complexity makes it unsuitable for widespread application in engineering fields.

[0004] It can be seen that the current fluid simulation method for SF6 circuit breakers has the problems of low modeling efficiency and poor simulation effect. Summary of the Invention

[0005] Based on this, it is necessary to provide a fluid simulation analysis method, device, computer equipment, computer-readable storage medium and computer program product for the SF6 circuit breaker arc extinguishing chamber that introduces electromagnetic thermal influences to improve modeling efficiency and simulation effects in order to address the above technical problems.

[0006] In a first aspect, an embodiment of the present application provides a method for simulating and analyzing the fluid in an SF6 circuit breaker arc extinguishing chamber by introducing electromagnetic thermal effects. The method comprises:

[0007] Obtaining target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time;

[0008] A fluid simulation model in the arc extinguishing chamber is constructed based on the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid during the high-voltage switch breaking process of the SF6 circuit breaker;

[0009] The fluid simulation model of the arc extinguishing chamber is solved based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0010] In one embodiment, constructing a fluid simulation model in the arc extinguishing chamber according to the target physical quantity includes:

[0011] Determine the fluid energy conservation equation based on the Joule heat value of the high voltage current and the radiation heat value brought by the high temperature;

[0012] determining a momentum conservation equation based on the value of the Lorentz force generated by the time-varying current;

[0013] Determining a control equation of the fluid region corresponding to the fluid simulation model in the arc extinguishing chamber according to the fluid energy conservation equation and the momentum conservation equation;

[0014] The radiation heat value brought by the high temperature is determined according to the net radiation coefficient.

[0015] In one embodiment, the method further comprises:

[0016] Obtain the magnetic field force and electric field force values ​​that charged particles experience in a magnetic field;

[0017] The magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field are weightedly summed to obtain the Lorentz force value generated by the current that varies with time.

[0018] In one embodiment, the method further comprises:

[0019] Obtain current density, conductivity and potential values;

[0020] Determining the Joule heat value of the high-voltage current according to the current density value, the conductivity value, and the potential value based on a calculation rule of Joule heat and current density;

[0021] The calculation rule of the Joule heat and current density is that the Joule heat is proportional to the square of the current density.

[0022] In one embodiment, solving the arc extinguishing chamber fluid simulation model based on real parameter fitting interpolation includes:

[0023] Obtaining a pre-built built-in physical property parameter library; the built-in physical property parameter library includes thermophysical parameter values ​​corresponding to different temperature values ​​and pressure values;

[0024] Based on the built-in physical property parameter library, matching and obtaining the values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value;

[0025] Solving a fluid simulation model in the arc extinguishing chamber according to the values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value obtained by matching;

[0026] The thermophysical parameters are nonlinear parameters, and include gas density, specific heat capacity at constant pressure, dynamic viscosity coefficient, thermal conductivity, and electrical conductivity corresponding to the SF6 circuit breaker.

[0027] In one embodiment, the governing equations of the fluid region further include a continuity equation and an energy equation of the solid domain;

[0028] The continuity equation is determined according to the fluid density and fluid velocity, and the energy equation of the solid domain is determined without considering the heat source term.

[0029] In a second aspect, the present application also provides a device for simulating and analyzing fluid in an SF6 circuit breaker arc extinguishing chamber by introducing electromagnetic thermal influences. The device comprises:

[0030] A target physical quantity acquisition module is used to acquire a target physical quantity; the target physical quantity is a physical quantity directly related to the control equation of the fluid region; the target physical quantity includes the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time;

[0031] A model building module is used to construct a fluid simulation model in the arc extinguishing chamber according to the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid in the SF6 circuit breaker during the high-voltage switch breaking process;

[0032] The model solving module is used to solve the fluid simulation model in the arc extinguishing chamber based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model in the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0033] In a third aspect, the present application further provides a computer device. The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are performed:

[0034] Obtaining target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time;

[0035] A fluid simulation model in the arc extinguishing chamber is constructed based on the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid during the high-voltage switch breaking process of the SF6 circuit breaker;

[0036] The fluid simulation model of the arc extinguishing chamber is solved based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0037] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps:

[0038] Obtaining target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time;

[0039] A fluid simulation model in the arc extinguishing chamber is constructed based on the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid during the high-voltage switch breaking process of the SF6 circuit breaker;

[0040] The fluid simulation model of the arc extinguishing chamber is solved based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0041] In a fifth aspect, the present application further provides a computer program product. The computer program product includes a computer program that, when executed by a processor, implements the following steps:

[0042] Obtaining target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time;

[0043] A fluid simulation model in the arc extinguishing chamber is constructed based on the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid during the high-voltage switch breaking process of the SF6 circuit breaker;

[0044] The fluid simulation model of the arc extinguishing chamber is solved based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0045] The above-mentioned fluid simulation analysis method, device, computer equipment, storage medium and computer program product for SF6 circuit breaker arc extinguishing chamber with the introduction of electromagnetic thermal influence are used to analyze the fluid simulation in the SF6 circuit breaker arc extinguishing chamber by introducing electromagnetic thermal influence; firstly, target physical quantities related to the fluid region control equations are obtained, including the Joule heating value of the high-voltage current and the time-varying Lorentz force value, which directly affect the thermodynamic behavior of the fluid; then, a fluid simulation model of the arc extinguishing chamber is constructed based on these target physical quantities, which reflects the control equations of the fluid region, such as the continuity equation, the momentum conservation equation, and the momentum conservation equation. The model is solved by the real parameter fitting interpolation method to obtain the simulation analysis results of the fluid in the arc extinguishing chamber, so as to evaluate the performance of the SF6 circuit breaker during the high-voltage switch breaking process, and then optimize the circuit breaker design. Without introducing the basic solution of electromagnetic theory, only the influence of electromagnetic thermal characteristics on fluid characteristics is considered, which effectively simplifies the plasma simulation calculation. At the same time, the real parameter fitting interpolation method is used to simplify the calculation process of SF6 physical parameters, greatly simplifying the calculation process, improving the model construction and calculation efficiency, and improving the simulation analysis effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 This is a diagram showing the application environment of a method for simulating and analyzing fluid in an arc extinguishing chamber of an SF6 circuit breaker that introduces electromagnetic thermal effects in one embodiment;

[0048] Figure 2 A flow chart of a method for simulating and analyzing fluid in an SF6 circuit breaker arc extinguishing chamber by introducing electromagnetic thermal influences in one embodiment;

[0049] Figure 3A flow chart of a method for simulating and analyzing fluid in an SF6 circuit breaker arc extinguishing chamber in accordance with another embodiment of the present invention, which introduces electromagnetic thermal effects;

[0050] Figure 4 This is a structural block diagram of a device for simulating and analyzing fluid in an SF6 circuit breaker arc extinguishing chamber that introduces electromagnetic thermal influences in one embodiment;

[0051] Figure 5 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0053] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with the relevant laws, regulations and standards of relevant countries and regions.

[0054] The fluid simulation analysis method for the SF6 circuit breaker arc extinguishing chamber provided by the embodiment of the present application, which introduces electromagnetic thermal influence, can be applied to Figure 1 In the application environment shown, the terminal 102 communicates with the server 104 via a network.

[0055] Terminal 102 may include, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices may include smart speakers, smart TVs, smart air conditioners, and smart car devices. Portable wearable devices may include smart watches, smart bracelets, and head-mounted devices. Server 104 may be implemented as a standalone server or a server cluster consisting of multiple servers.

[0056] In one embodiment, Figure 2 As shown in the figure, a fluid simulation analysis method for the arc extinguishing chamber of SF6 circuit breaker with the introduction of electromagnetic thermal influence is provided. Figure 1 Taking the terminal 102 in FIG. 1 as an example, the method includes the following steps:

[0057] S201, obtaining target physical quantity.

[0058] The target physical quantities are physical quantities directly related to the control equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that changes with time.

[0059] S202: Construct a simulation model of the fluid in the arc extinguishing chamber according to the target physical quantity.

[0060] Among them, the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid of the SF6 circuit breaker during the high-voltage switch breaking process.

[0061] Exemplarily, the fluid simulation model in the interrupter can be embodied by the governing equations of the fluid region and their solutions. Specifically, the governing equations of the fluid region may include: the continuity equation, the momentum conservation equation, the fluid energy conservation equation, the energy equation of the solid domain, etc.

[0062] S203 , solving the fluid simulation model in the arc extinguishing chamber based on a real parameter fitting interpolation method to obtain a simulation analysis result corresponding to the fluid simulation model in the arc extinguishing chamber.

[0063] The simulation analysis results are used to evaluate the performance of SF6 circuit breakers.

[0064] For example, considering that only two physical quantities, Joule heating and Lorentz force, directly enter the fluid governing equations, these two quantities are not coupled with the NS equations for the fluid. Instead, these two terms are treated as external inputs and source terms. These two terms are calculated externally using dedicated electromagnetic analysis software and input via the universal coupling control platform.

[0065] In the above-mentioned fluid simulation analysis method for the arc extinguishing chamber of an SF6 circuit breaker that introduces electromagnetic thermal effects, the fluid simulation within the arc extinguishing chamber of the SF6 circuit breaker is analyzed by introducing electromagnetic thermal effects. First, the target physical quantities related to the fluid region control equations are obtained, including the Joule heating value of the high-voltage current and the time-varying Lorentz force value. These physical quantities directly affect the thermodynamic behavior of the fluid. Then, based on these target physical quantities, a fluid simulation model of the arc extinguishing chamber is constructed. The model reflects the control equations of the fluid region, such as the continuity equation, the momentum conservation equation, the fluid energy conservation equation, and the solid domain energy equation. Finally, the model is solved using the real parameter fitting interpolation method to obtain simulation analysis results of the fluid in the arc extinguishing chamber to evaluate the performance of the SF6 circuit breaker during the high-voltage switch breaking process, thereby optimizing the circuit breaker design. Without introducing the basic solutions of electromagnetic theory, only the influence of electromagnetic thermal characteristics on fluid characteristics is considered, effectively simplifying the plasma simulation calculation. At the same time, the real parameter fitting interpolation method is used to simplify the calculation process of the SF6 physical parameters, greatly simplifying the calculation process, improving the model construction and calculation efficiency, and improving the simulation analysis effect.

[0066] In one embodiment, a fluid simulation model within the arc extinguishing chamber is constructed based on target physical quantities, including: determining a fluid energy conservation equation based on the Joule heat value of the high-voltage current and the radiation heat value brought by the high temperature; determining a momentum conservation equation based on the Lorentz force value generated by the current that varies with time; determining a control equation for the fluid region corresponding to the fluid simulation model within the arc extinguishing chamber based on the fluid energy conservation equation and the momentum conservation equation; wherein the radiation heat value brought by the high temperature is determined based on the net radiation coefficient.

[0067] For example, the fluid energy conservation equation:

[0068]

[0069] Where h is the specific enthalpy, K is the kinetic energy, αeff is the effective thermal diffusion coefficient, εN is the net radiation coefficient, and Qjoule is the Joule heat source term. The Joule heat value of the high voltage current is The radiation heat value brought by high temperature is .

[0070] Momentum conservation equation:

[0071]

[0072] Where p is pressure, FB is Lorentz force, and τ is turbulent stress. The Lorentz force generated by the current is .

[0073] In this embodiment, first, the fluid energy conservation equation is determined based on the Joule heating value of the high-voltage current and the radiation heating value brought by the high temperature; secondly, the momentum conservation equation is determined based on the Lorentz force value generated by the current that changes with time, taking into account the effects of pressure, Lorentz force and turbulent stress; the fluid energy conservation equation and the momentum conservation equation are combined to finally form the control equation for the fluid in the arc extinguishing chamber; by accurately simulating the interaction between the arc and the fluid, the arc extinguishing performance of the SF6 circuit breaker can be effectively evaluated, thereby optimizing the design, improving the safety and reliability of the equipment, and ensuring the stable operation of the high-voltage switch in actual applications. Without introducing the basic solutions in electromagnetic theory, only the influence of electromagnetic force and thermal characteristics on fluid characteristics is considered, which effectively simplifies the plasma simulation calculation and improves the calculation efficiency.

[0074] In one embodiment, the method further includes: obtaining the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field; performing weighted summation on the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field to obtain the Lorentz force value generated by the current that changes with time.

[0075] For example, the Lorentz force is the sum of the magnetic field force and the electric field force exerted on a charged particle in a magnetic field, and is calculated using the following formula:

[0076]

[0077] Where q is the charge, E is the electric field intensity, J is the current density, and B is the magnetic induction intensity.

[0078] In this embodiment, the magnetic field force and electric field force values ​​exerted on the charged particles in the magnetic field are first obtained. Specifically, the magnetic field force is determined by the motion state of the charged particles in the magnetic field, while the electric field force is determined by the electric field strength and the charge of the particles. Then, the time-varying Lorentz force value is calculated by taking a weighted sum of these two forces. The Lorentz force value is accurately calculated to prepare for subsequent simulations, so that the fluid simulation model can more accurately simulate the dynamic changes of the fluid under the interaction between current and magnetic field, thereby improving the performance evaluation and design optimization of the arc extinguishing chamber and ensuring the reliability and safety of the high-voltage switch under complex arc conditions.

[0079] In one embodiment, the method further includes: obtaining a current density value, a conductivity value, and an electric potential value; and determining the Joule heating value of the high voltage current based on the current density value, the conductivity value, and the electric potential value based on a calculation rule of Joule heating and current density.

[0080] The calculation rule of Joule heat and current density is that Joule heat is proportional to the square of current density.

[0081] For example, Joule heating is proportional to the square of the current density:

[0082]

[0083] Where σ is the conductivity and φ is the electric potential.

[0084] In this embodiment, the current density, conductivity and potential values ​​are first obtained. Based on the calculation rule that Joule heat is proportional to the square of the current density, the obtained current density, conductivity and potential are combined to calculate the Joule heat value of the high-voltage current. By accurately quantifying the Joule heat of the high-voltage current, key data support is provided, and the influence of current density on energy conversion is considered in the fluid simulation model, thereby facilitating subsequent simulation analysis.

[0085] In one embodiment, the fluid simulation model in the arc extinguishing chamber is solved based on the real parameter fitting interpolation method, including: obtaining a pre-built built-in physical property parameter library; matching the values ​​of the thermophysical parameters corresponding to the current temperature value and pressure value based on the built-in physical property parameter library; solving the fluid simulation model in the arc extinguishing chamber according to the matched values ​​of the thermophysical parameters corresponding to the current temperature value and pressure value.

[0086] Among them, the thermophysical parameters are nonlinear parameters, and the thermophysical parameters include gas density, specific heat capacity at constant pressure, dynamic viscosity coefficient, thermal conductivity, and electrical conductivity corresponding to the SF6 circuit breaker.

[0087] The built-in physical property parameter library includes thermophysical parameter values ​​corresponding to different temperature and pressure values.

[0088] For example, in an arc extinguishing chamber filled with SF6 gas, the thermophysical parameters of the plasma exhibit nonlinear variations with temperature. To ensure accurate calculations, nonlinear thermophysical parameters must be set in the model. Assuming that the energy relaxation process of each particle in the equilibrium SF6 plasma is complete and that the electrons and heavy ions have the same temperature, the thermophysical parameters are functions of temperature and pressure. A built-in physical property parameter library is pre-implemented for realistic SF6 gas variations during the solution; users can also import external parameters that vary with temperature and pressure.

[0089] The calculation process automatically calls upon a user-specified physical property parameter library, automatically updating parameters during the solution process without requiring additional user configuration. Preset physical property parameters are loaded upon simulation initialization. Within each iteration of the calculation, after solving the pressure and energy equations, the physical properties of the SF6 fluid are updated based on the current pressure and temperature of each fluid cell. The conductivity distribution at this point is also calculated and transferred to the electromagnetic field via the coupling platform for electromagnetic calculations. This iterative cycle continues until the final calculation is complete.

[0090] In this embodiment, the system first obtains a built-in physical property parameter library, which contains thermophysical parameter values ​​under different temperature and pressure conditions, and then matches the corresponding nonlinear thermophysical parameters according to the current temperature and pressure. By accurately simulating the nonlinear thermophysical properties of SF6 gas, the calculation accuracy and real-time performance of the fluid simulation model in the arc extinguishing chamber are significantly improved. The calculation process of the SF6 physical property parameters is simplified by using real parameter fitting interpolation, which greatly simplifies the calculation process and improves the calculation efficiency.

[0091] In one embodiment, the governing equations of the fluid region further include a continuity equation and an energy equation of the solid domain; wherein the continuity equation is determined according to the fluid density and fluid velocity, and the energy equation of the solid domain is determined without considering the heat source term.

[0092] For example, the continuity equation:

[0093]

[0094] Where ρ is the fluid density, t is the time, and U is the fluid velocity vector.

[0095] The solid domain does not involve changes in flow-related physical quantities and does not consider heat source terms. Its energy equation is as follows:

[0096]

[0097] In another embodiment, Figure 3 As shown, a method for simulating and analyzing the fluid in the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal influence is provided, comprising the following steps:

[0098] S301, obtaining the magnetic field force and electric field force values ​​exerted on the charged particle in the magnetic field;

[0099] S302, performing a weighted summation of the magnetic field force and the electric field force exerted on the charged particle in the magnetic field to obtain the Lorentz force generated by the current that varies with time;

[0100] S303, obtaining current density value, conductivity value and potential value;

[0101] S304, determining the Joule heating value of the high voltage current based on the current density value, the conductivity value, and the potential value based on the calculation rules of Joule heating and current density;

[0102] S305, determining the fluid energy conservation equation based on the Joule heating value of the high voltage current and the radiation heating value caused by the high temperature;

[0103] S306, determining a momentum conservation equation based on a Lorentz force value generated by the current that varies with time;

[0104] S307, determining a control equation for a fluid region corresponding to the fluid simulation model in the arc extinguishing chamber according to the fluid energy conservation equation and momentum conservation equation;

[0105] S308 , solving the fluid simulation model in the arc extinguishing chamber based on the real parameter fitting interpolation method to obtain a simulation analysis result corresponding to the fluid simulation model in the arc extinguishing chamber.

[0106] It should be noted that the specific definitions of the above steps can be found in the specific definitions of the fluid simulation analysis method for the arc extinguishing chamber of an SF6 circuit breaker introducing electromagnetic thermal effects, which will not be repeated here.

[0107] In the existing technology, there are complex and mutually coupled electrical, thermal, and mechanical physical processes in the arc extinguishing chamber of the SF6 circuit breaker during the current breaking process. How to deal with the mutual influence between the various physical processes and the changes of various physical parameters in this process is the primary issue that needs to be considered during the plasma simulation calculation in the arc extinguishing chamber.

[0108] Existing simulation techniques are typically implemented using Ansys Fluent (computational fluid dynamics) software combined with UDFs (User Defined Functions). This approach requires users to have a solid foundation in electromagnetic theory to solve electric and magnetic fields using the UDS functionality and define material thermophysical properties using UDFs. This approach presents a steep learning curve and is difficult to use. Furthermore, due to Fluent's rigid computational workflow, users lack control over the solution process, leading to significant drawbacks during the debugging of complex cases. Furthermore, this approach requires the use of the same mesh for both fluid analysis and electromagnetic calculations. Since the governing equations in electromagnetic theory and the Navier-Stokes equations (NSEs) in fluids have different forms and properties, using the same mesh significantly limits flexibility, hindering computational accuracy and convergence. Furthermore, this approach requires a phased restart function to perform calculations before and after arc initiation, making the process relatively cumbersome and unsuitable for widespread adoption.

[0109] To address the above shortcomings, an embodiment of the present application provides a method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal effects, also known as a method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal effects in fluid calculations. This method does not solve basic parameters in electromagnetic theory such as electric field intensity and magnetic vector when performing fluid calculations, but only introduces physical quantities directly related to the fluid control equations, such as Joule heat and Lorentz force. Based on this idea, a dedicated simulation software for arc magnetofluids was developed, and changes in the thermal properties of the plasma were processed internally through interpolation, avoiding the large amount of calculations caused by the use of the local thermodynamic equilibrium assumption, improving the convergence characteristics of the fluid calculation, and increasing the simulation efficiency.

[0110] The following describes in detail a method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal effects using a specific embodiment. It is worth noting that the following description is merely an example and does not constitute a specific limitation on the application.

[0111] The method for simulating and analyzing the fluid in the arc extinguishing chamber of an SF6 circuit breaker with the introduction of electromagnetic thermal influence provided in this application specifically includes the following contents:

[0112] Due to the complex multi-physics problems such as air flow field, temperature field, electromagnetic field, etc. in the arc extinguishing chamber, the influence of electromagnetic thermal force must be considered in the analysis. During the interruption process of the SF6 circuit breaker, the electromagnetic thermal characteristics of the fluid in the arc extinguishing chamber mainly affect the plasma flow characteristics in two aspects:

[0113] First, the influence of Joule heat and Lorentz force generated by the electromagnetic properties of the fluid on the fluid velocity, pressure, temperature, etc.; second, the influence of local temperature, pressure and other parameters on the plasma physical properties during the calculation process.

[0114] The arc magnetofluid simulation during the high-voltage switch opening process can be divided into two stages based on the physical process, namely the cold air flow simulation stage and the arc magnetofluid simulation stage after arcing.

[0115] During the simulation, cold airflow simulation primarily considers changes in flow parameters and flow conditions caused by contact movement, without considering changes in electromagnetic properties. Therefore, this stage can be simulated within the confines of a single fluid physical field, eliminating the need for coupling with electromagnetic fields and circuits. Due to the relatively simple flow conditions, laminar flow is used by default for this stage to improve computational efficiency.

[0116] Arcing occurs when the moving and static contacts of a circuit breaker separate. During this process, the SF6 arc is fully ionized into an equilibrium plasma. Changes in physical parameters such as the electric field, temperature field, and flow field within the arc extinguishing chamber influence each other, resulting in a high degree of coupling. At the governing equation level, the fluid energy equation needs to account for Joule heating and radiant heating of the high-voltage current, and the momentum equation needs to account for the Lorentz force generated by the time-varying current. At this point, the governing equation for the fluid region is as follows:

[0117] Continuity equation:

[0118]

[0119] Where ρ is the fluid density, t is the time, and U is the fluid velocity vector.

[0120] Momentum conservation equation:

[0121]

[0122] Where p is pressure, FB is Lorentz force, and τ is turbulent stress.

[0123]

[0124] Where μ is the fluid viscosity and I is the unit tensor.

[0125] Fluid energy conservation equation:

[0126]

[0127] Where h is the specific enthalpy, K is the kinetic energy, αeff is the effective thermal diffusivity, εN is the net radiation coefficient, and Qjoule is the Joule heat source term. The rightmost term in the momentum equation represents the Lorentz force source term on the fluid due to the time-varying magnetic field generated by the current. The last two terms in the energy equation represent the radiation heat from the high temperature and the Joule heat from the high voltage current, respectively. The radiation heat source term is calculated from the net radiation coefficient.

[0128] The solid domain does not involve changes in flow-related physical quantities and does not consider heat source terms. Its energy equation is as follows:

[0129]

[0130] In this application, the "introduction of electromagnetic thermal effects" in the governing equations is primarily reflected in the Lorentz force term and the Joule heat term in the momentum equation. Both of these terms are related to the electromagnetic properties of the fluid. The Lorentz force is the sum of the magnetic and electric field forces on a charged particle in a magnetic field, and is calculated using the following formula:

[0131]

[0132] Where q is the charge, E is the electric field intensity, J is the current density, and B is the magnetic induction intensity.

[0133] Joule heating is proportional to the square of the current density:

[0134]

[0135] Where σ is the conductivity and φ is the electric potential.

[0136] In previous studies, the electric field intensity E and the current density J were solved in the fluid, and then the Lorentz force and Joule heat were calculated. In fact, these basic electromagnetic parameters do not directly participate in the coupled iteration of pressure-velocity-energy of the fluid. In this application, considering that there are only two physical quantities, Joule heat and Lorentz force, that directly enter the fluid control equation, these two physical quantities are not coupled with the NS equations of the fluid to solve, but the item is treated as an external input item and treated as a source item. These two items are calculated externally by dedicated electromagnetic analysis software and given via a universal coupling control platform. At the same time, the conductivity of the plasma needs to be output in the fluid calculation as an input item for the external electromagnetic calculation.

[0137] By adopting this method, it is no longer necessary to solve the basic electromagnetic parameters in the plasma solution process. Only the influence of electromagnetic thermal characteristics on fluid characteristics is considered, which can effectively simplify the plasma simulation calculation. At the same time, since the electromagnetic and fluid are not solved in the same set of grids, the electromagnetic simulation can adopt a more free grid control strategy and iterative control strategy, which is conducive to obtaining more accurate Lorentz force and Joule heat. At the same time, in the previous simulation of plasma in the arc extinguishing chamber, since the electromagnetic parameters and fluid parameters are solved together, it is inconvenient to adjust the convergence control of each and easily cause divergence. The fluid simulation analysis method for the arc extinguishing chamber of the SF6 circuit breaker that introduces the influence of electromagnetic thermal force provided in this application has a higher degree of control freedom because the fluid and electromagnetic control equations are solved separately, which is conducive to the final convergence of the calculation results.

[0138] The density of SF6 changes with increasing temperature and pressure. Under the influence of an arc, the thermal motion of gas molecules increases, potentially leading to a decrease in density. Increasing temperature typically increases gas viscosity due to increased collisions between molecules. However, increasing pressure may decrease viscosity due to enhanced interactions between molecules. Thermal conductivity is a measure of a material's ability to conduct heat. Under arc conditions, the thermal conductivity of SF6 may increase due to increased molecular thermal motion. Specific heat is the amount of heat required to raise a unit temperature per unit mass of a substance. Under high temperature conditions, the specific heat of SF6 may increase due to excitation of internal molecular energy levels. The presence of an arc causes the gas to ionize, resulting in a significant increase in conductivity. This is because the free electrons and ions produced by ionization can conduct electrical current.

[0139] Although the physical properties of real SF6 gas are highly nonlinear and subject to numerous influencing factors, the scenario simulates a fixed SF6 gas. Using traditional equilibrium composition calculation methods would result in unnecessary recalculation during repeated simulations. The arc extinguishing chamber is filled with SF6 gas, and its plasma thermophysical parameters exhibit nonlinear variations with temperature. To ensure accurate calculations, the model requires nonlinear thermophysical parameters such as SF6 gas density, specific heat capacity at constant pressure, dynamic viscosity coefficient, thermal conductivity, and electrical conductivity. Assuming that the energy relaxation process of all particles in the equilibrium SF6 plasma is complete and that electrons and heavy ions have the same temperature, the thermophysical parameters are functions of temperature and pressure. A built-in physical property parameter library is pre-populated during the solution to account for real-world SF6 gas variations. Furthermore, to expand usage scenarios, the system supports externally importing user-defined physical property parameter variations with temperature and pressure. The calculation automatically references the user-defined physical property parameter library and automatically updates the parameters during the solution, eliminating the need for additional user configuration. During simulation initialization, preset physical properties are loaded. Within each iteration of each time step, after solving the pressure and energy equations, the physical properties of the SF6 fluid, including density, viscosity, thermal conductivity, specific heat, and electrical conductivity, are updated based on the current pressure and temperature of each fluid cell. The electrical conductivity distribution at this point is also calculated and transferred to the electromagnetic field via the coupling platform for electromagnetic calculations. This iterative cycle continues until the final calculation is complete.

[0140] This application proposes a method for simulating and analyzing the fluid inside an SF6 circuit breaker arc chamber, incorporating electromagnetic and thermal influences. This method avoids solving complex Maxwell equations and does not introduce fundamental solutions from electromagnetic theory. Instead, it considers only the effects of electromagnetic and thermal characteristics on fluid properties, effectively simplifying plasma simulation calculations. Furthermore, it employs real-world parameter fitting and interpolation to simplify the calculation process for SF6 physical parameters, significantly streamlining the computational process and improving efficiency.

[0141] In the simulation of plasma inside the arc extinguishing chamber during the start-up process of an SF6 circuit breaker, there are many plasma characteristic parameters in the arc extinguishing chamber, which are dependent on and interact with each other. The present invention strives to make the fluid solution process clear and concise while considering the influence of electromagnetic thermal force. The advantages of using the fluid simulation analysis method for the arc extinguishing chamber of an SF6 circuit breaker introduced by the present application are:

[0142] (1) No redundant electromagnetic parameters are introduced in the fluid calculation. Only Joule heat and Lorentz force directly related to the fluid calculation are introduced. This can effectively simplify the plasma simulation calculation, facilitate the final calculation convergence, and improve the calculation accuracy.

[0143] (2) The interpolation method is used to deal with the changes in the thermophysical properties of plasma, which avoids the large amount of calculation caused by the local thermodynamic equilibrium assumption, improves the convergence characteristics of fluid calculations, and improves simulation efficiency.

[0144] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0145] Based on the same inventive concept, an embodiment of the present application further provides a device for simulating and analyzing the fluid within the arc extinguishing chamber of an SF6 circuit breaker with electromagnetic thermal influences, which is used to implement the aforementioned method for simulating and analyzing the fluid within the arc extinguishing chamber of an SF6 circuit breaker with electromagnetic thermal influences. The solution provided by this device is similar to the solution described in the aforementioned method. Therefore, the specific limitations of one or more embodiments of the device for simulating and analyzing the fluid within the arc extinguishing chamber of an SF6 circuit breaker with electromagnetic thermal influences provided below can be found in the above-mentioned limitations of the method for simulating and analyzing the fluid within the arc extinguishing chamber of an SF6 circuit breaker with electromagnetic thermal influences, and will not be further elaborated here.

[0146] In one embodiment, Figure 4 As shown, a fluid simulation and analysis device for an SF6 circuit breaker arc extinguishing chamber with the introduction of electromagnetic thermal influence is provided, comprising: a target physical quantity acquisition module 401, a model construction module 402, and a model solution module 403, wherein:

[0147] The target physical quantity acquisition module 401 is used to acquire target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heating value of the high-voltage current and the Lorentz force generated by the current that varies with time;

[0148] The model building module 402 is used to construct a fluid simulation model in the arc extinguishing chamber according to the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid during the high-voltage switch breaking process of the SF6 circuit breaker;

[0149] The model solving module 403 is used to solve the fluid simulation model in the arc extinguishing chamber based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model in the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker.

[0150] In one embodiment, the device is used to: determine the fluid energy conservation equation based on the Joule heating value of the high-voltage current and the radiation heating value brought by the high temperature; determine the momentum conservation equation based on the Lorentz force value generated by the current that changes with time; and determine the control equation of the fluid area corresponding to the fluid simulation model in the arc extinguishing chamber based on the fluid energy conservation equation and the momentum conservation equation.

[0151] In one embodiment, the device is used to: obtain the magnetic field force and electric field force values ​​exerted on charged particles in the magnetic field; perform weighted summation on the magnetic field force and electric field force values ​​exerted on the charged particles in the magnetic field to obtain the Lorentz force value generated by the current that changes with time.

[0152] In one embodiment, the device is used to: obtain current density value, conductivity value and potential value; based on the calculation rules of Joule heat and current density, determine the Joule heat value of the high voltage current according to the current density value, conductivity value and potential value.

[0153] In one embodiment, the device is used to: obtain a pre-built built-in physical property parameter library; the built-in physical property parameter library includes thermophysical parameter values ​​corresponding to different temperature values ​​and pressure values; based on the built-in physical property parameter library, match the values ​​of the thermophysical parameters corresponding to the current temperature value and pressure value; solve the fluid simulation model in the arc extinguishing chamber according to the matched values ​​of the thermophysical parameters corresponding to the current temperature value and pressure value.

[0154] Each module in the aforementioned device for simulating and analyzing the fluid inside the arc chamber of an SF6 circuit breaker with the introduction of electromagnetic thermal influences can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0155] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 5As shown. The computer device includes a processor, memory, an input / output interface, a communication interface, a display unit, and an input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals via wired or wireless communication, and the wireless communication can be achieved via Wi-Fi, mobile cellular networks, NFC (near-field communication), or other technologies. When executed by the processor, the computer program implements a method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic and thermal influences. The display unit of the computer device is used to produce a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the computer device casing, or an external keyboard, touchpad or mouse.

[0156] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0157] In one embodiment, a computer device includes a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0158] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0159] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0160] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic devices (PLDs), data processing logic devices based on quantum computing, and the like.

[0161] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0162] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for simulating and analyzing the fluid inside the arc extinguishing chamber of an SF6 circuit breaker by introducing electromagnetic thermal influence, characterized in that: The method comprises: Obtaining target physical quantities; the target physical quantities are physical quantities directly related to the governing equations of the fluid region; the target physical quantities include the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time; including: obtaining the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field; performing weighted summation of the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field to obtain the Lorentz force value exerted by the current that varies with time; A fluid simulation model in the arc extinguishing chamber is constructed based on the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid in the SF6 circuit breaker during the high-voltage switch opening and closing process; the model comprises: determining a fluid energy conservation equation based on the Joule heat value of the high-voltage current and the radiation heat value brought by the high temperature; determining a momentum conservation equation based on the Lorentz force value generated by the current that varies with time; determining a control equation for the fluid region corresponding to the fluid simulation model in the arc extinguishing chamber based on the fluid energy conservation equation and the momentum conservation equation; wherein the radiation heat value brought by the high temperature is determined based on the net radiation coefficient; The fluid simulation model of the arc extinguishing chamber is solved based on the real parameter fitting interpolation method to obtain the simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker; including: obtaining a pre-built built-in physical property parameter library; the built-in physical property parameter library includes thermophysical parameter values ​​corresponding to different temperature values ​​and pressure values; based on the built-in physical property parameter library, matching the values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value; solving the fluid simulation model of the arc extinguishing chamber according to the matched values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value; wherein the thermophysical parameters are nonlinear parameters, and the thermophysical parameters include gas density, specific heat capacity at constant pressure, dynamic viscosity coefficient, thermal conductivity, and electrical conductivity corresponding to the SF6 circuit breaker.

2. The method according to claim 1, characterized in that The method further comprises: Obtain current density, conductivity and potential values; Determining the Joule heat value of the high-voltage current according to the current density value, the conductivity value, and the potential value based on a calculation rule of Joule heat and current density; The calculation rule of the Joule heat and current density is that the Joule heat is proportional to the square of the current density.

3. The method according to claim 1, characterized in that The governing equations of the fluid region also include the continuity equation and the energy equation of the solid domain; The continuity equation is determined according to the fluid density and fluid velocity, and the energy equation of the solid domain is determined without considering the heat source term.

4. A fluid simulation and analysis device for an SF6 circuit breaker arc extinguishing chamber that introduces electromagnetic thermal influences, characterized in that: The device comprises: A target physical quantity acquisition module is used to acquire a target physical quantity; the target physical quantity is a physical quantity directly related to the control equation of the fluid region; the target physical quantity includes the Joule heat value of the high-voltage current and the Lorentz force value generated by the current that varies with time; The target physical quantity acquisition module is specifically used to obtain the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field; perform weighted summation on the magnetic field force value and the electric field force value exerted on the charged particle in the magnetic field to obtain the Lorentz force value generated by the current that varies with time; A model building module is used to construct a fluid simulation model in the arc extinguishing chamber according to the target physical quantity; the fluid simulation model in the arc extinguishing chamber is used to characterize the changes in the arc magnetic fluid in the SF6 circuit breaker during the high-voltage switch breaking process; The model building module is specifically used to determine the fluid energy conservation equation based on the Joule heating value of the high-voltage current and the radiation heating value brought by the high temperature; determine the momentum conservation equation based on the Lorentz force value generated by the current that varies with time; and determine the control equation of the fluid region corresponding to the fluid simulation model in the arc extinguishing chamber based on the fluid energy conservation equation and the momentum conservation equation; wherein the radiation heating value brought by the high temperature is determined based on the net radiation coefficient; A model solving module, configured to solve the fluid simulation model of the arc extinguishing chamber based on real parameter fitting and interpolation, and obtain simulation analysis results corresponding to the fluid simulation model of the arc extinguishing chamber; the simulation analysis results are used to evaluate the performance of the SF6 circuit breaker; The model solving module is specifically used to obtain a pre-built built-in physical property parameter library; the built-in physical property parameter library includes thermophysical parameter values ​​corresponding to different temperature values ​​and pressure values; based on the built-in physical property parameter library, the values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value are matched; according to the matched values ​​of the thermophysical parameters corresponding to the current temperature value and the pressure value, the fluid simulation model in the arc extinguishing chamber is solved; wherein, the thermophysical parameters are nonlinear parameters, and the thermophysical parameters include gas density, specific heat capacity at constant pressure, dynamic viscosity coefficient, thermal conductivity, and electrical conductivity corresponding to the SF6 circuit breaker.

5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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