Heat flow coupling calculation method for oil-gas two-phase gas transportation in transformer

Abstract

The invention relates to the technical field of power equipment fault diagnosis, in particular to a heat flow coupling calculation method for oil-gas two-phase gas transportation in a transformer, and the method comprises the steps: building a three-dimensional diffusion model of dissolved gas in oil in the transformer; initial conditions and boundary conditions are set; based on the initial condition and the boundary condition, solving a control equation of the three-dimensional diffusion model through an integral transformation method to obtain an instantaneous diffusion distribution concentration solution under an instantaneous gas production condition; calculating a continuous diffusion distribution concentration solution under a continuous gas production condition by performing superposition integration on a time domain based on the instantaneous diffusion distribution concentration solution; obtaining the three-dimensional concentration distribution of the gas dissolved in the oil at any moment and any position in the transformer by utilizing the continuous diffusion distribution concentration solution; according to the method, the heat flow coupling three-dimensional diffusion model is constructed, and the integral transformation and superposition integral method is utilized, so that the accurate simulation and visualization of the gas production diffusion process of the internal fault of the transformer are realized.

Description

Technical Field

[0001] This invention relates to the field of power equipment fault diagnosis technology, and in particular to a thermal flux coupling calculation method for oil-gas two-phase gas transport inside a transformer. Background Technology

[0002] Dissolved gas analysis in transformer oil is the primary technique for detecting early-stage low gas production rate faults and anomalies within transformers. However, due to the single and fixed monitoring points in online oil chromatography, the concentration changes are insufficient to reflect the occurrence and development of low gas production rate faults in transformer oil. In recent years, numerical simulation of gas transport based on computational fluid dynamics has attracted considerable attention and has made initial progress. However, current simulations do not consider the complexity of gas transport mechanisms in transformer oil and neglect the dissolution process and initial diffusion process of gas generated from the fault area.

[0003] Therefore, there is an urgent need to propose a thermal-fluid coupling calculation method for the two-phase gas transport of oil and gas inside transformers, so as to provide theoretical support for the virtual sensing of the gas transport distribution in the oil inside transformers and the source location of gas generation using DGA. Summary of the Invention

[0004] To address this issue, the present invention provides a thermal-fluid coupling calculation method for the two-phase gas transport of oil and gas inside a transformer, in order to overcome the problem of inaccurate fault simulation caused by neglecting the gas dissolution and initial diffusion process in the prior art.

[0005] To achieve the above objectives, this invention provides a method for calculating the heat-fluid coupling of oil-gas two-phase gas transport within a transformer, comprising:

[0006] Step S1: Establish a three-dimensional diffusion model of dissolved gas in the transformer oil. The model is based on computational fluid dynamics and Fick's diffusion law, and coupled with the diffusion coefficient determined by temperature and the transport velocity determined by oil flow.

[0007] Step S2: Set initial conditions and boundary conditions. The initial condition is that there is an instantaneous gas source defined by the Dirac delta function at the fault source location, and the initial gas concentration at other locations is 0. The boundary condition is the gas diffusion reflection boundary formed by the transformer tank wall.

[0008] Step S3: Based on the initial and boundary conditions, solve the control equations of the three-dimensional diffusion model using the integral transform method to obtain the instantaneous diffusion distribution concentration solution under instantaneous gas production conditions;

[0009] Step S4: Based on the instantaneous diffusion distribution concentration solution, calculate the continuous diffusion distribution concentration solution under continuous gas production conditions by superimposing and integrating in the time domain.

[0010] Step S5: Using the continuous diffusion distribution concentration solution, obtain the three-dimensional concentration distribution of dissolved gas in the oil at any time and any location inside the transformer.

[0011] Further, in step S1, establishing a three-dimensional diffusion model of dissolved gases in the transformer internal oil includes:

[0012] (1);

[0013] In the formula, C is the dissolved gas content in the oil, t is the diffusion time of the gas transport process, Dx, Dy, and Dz are the diffusion coefficients of the dissolved gas in the oil in the x, y, and z directions, respectively, and ux, uy, and uz are the transformer oil flow velocities of the dissolved gas in the oil in the x, y, and z directions, respectively.

[0014] Furthermore, in step S1, the diffusion coefficients Dx, Dy, and Dz are isotropic and have equal values.

[0015] Furthermore, in step S1, the values ​​of the diffusion coefficients Dx, Dy, and Dz are determined through experimental data and are associated with the specific temperature and gas type inside the transformer.

[0016] Furthermore, in step S2, the initial conditions of the instantaneous gas source, defined by the Dirac delta function, are as follows:

[0017] (2);

[0018] In the formula, M represents the mass of dissolved gas in the oil. , , It represents a generalized function of the unit intensive distribution quantity.

[0019] Further, in step S2, the generalized function includes:

[0020] (3);

[0021] In the formula, x0, y0, and z0 are the three-dimensional coordinates of the internal fault source of the transformer.

[0022] Furthermore, in step S2, the boundary conditions are:

[0023] (4);

[0024] Using the diffusion time t of dissolved gas transport in oil as a parameter, a Fourier transform is performed on both sides of equation (1), assuming... Then there is

[0025] (5);

[0026] In the formula, i is the imaginary unit in complex numbers.

[0027] Furthermore, in step S2, solving formula (5) yields:

[0028] (6).

[0029] Further, in step S3, an inverse Fourier transform is performed on equation (6) to obtain the instantaneous diffusion distribution concentration solution:

[0030] (7).

[0031] Furthermore, in step S3, the definite integral of equation (7) is taken to obtain the instantaneous diffusion distribution concentration solution in unbounded space:

[0032] (8).

[0033] Further, in step S3, the spatial range of the reflection boundary is defined as: -h1≤x≤h1, -h2≤y≤h2, -h3≤z≤h3.

[0034] Furthermore, in step S3, an infinite number of reflection superposition terms are introduced to correct the instantaneous diffusion distribution concentration solution, thereby obtaining the instantaneous diffusion distribution concentration solution in bounded space:

[0035] (9);

[0036] In the formula, H1=2nh1, H2=2nh2, H3=2nh3 represent the total distance of diffusion and reflection of dissolved gas in oil in the x, y and z directions, respectively, and n represents the number of reflections that occur when dissolved gas in oil is transported to the boundary.

[0037] Further, in step S4, the superposition integration in the time domain includes: discretizing the continuous gas production process into a superposition of instantaneous gas production sources with intensity Mdτ at time τ; the concentration contribution of any instantaneous source at any spatial location at observation time t is expressed as:

[0038] (10).

[0039] Furthermore, in step S4, the continuous diffusion distribution concentration solution from time 0 to time t is obtained by integrating over the concentration contributions of all instantaneous sources:

[0040] (11).

[0041] Furthermore, in step S5, obtaining the three-dimensional concentration distribution of dissolved gas in oil at any time and any location inside the transformer includes: based on the continuous diffusion distribution concentration solution, obtaining the gas concentration values ​​at different spatial locations inside the transformer at different time points through numerical calculation, and constructing a complete spatiotemporal concentration distribution field.

[0042] Furthermore, step S5 also includes fault source tracing and location, which involves comparing the calculated three-dimensional concentration distribution of dissolved gas in the oil with the actual concentration measurement data inside the transformer to determine the location coordinates of the fault source.

[0043] Compared with existing technologies, the advantages of this invention are that it directly calibrates key parameters through precise experimental data, ensuring the accuracy and physical authenticity of subsequent three-dimensional diffusion model calculations. This overcomes the simulation distortion problem caused by inaccurate parameter estimation in traditional simulations. It not only obtains discrete diffusion coefficient values ​​at specific temperatures but also establishes a universal empirical formula between diffusion coefficient and temperature through regression analysis. This allows the model to automatically adjust and select the correct diffusion coefficient based on the actual, dynamically changing temperature field inside the transformer, greatly enhancing the model's adaptability and predictive ability under different operating conditions. By repeating the experimental process for different types of fault gases (such as H2, CH4, C2H2, etc.), a diffusion coefficient database covering major fault characteristic gases and spanning major operating temperature ranges can be established, providing a solid and universal data support platform for transformer condition assessment and fault diagnosis.

[0044] Furthermore, this invention uses the Dirac delta function to describe the initial gas source. Its core advantage lies in its ability to accurately and ideally simulate a fault gas generation event that is highly localized in space and occurs instantaneously in time. By applying Fourier transform, the partial differential equation (PDE) containing convection-diffusion terms, which was originally difficult to solve directly, is transformed into an ordinary differential equation (ODE) that is easy to solve. This greatly simplifies the mathematical complexity of the solution process and bypasses the numerical difficulties of directly solving the three-dimensional transient PDE. As a result, the theoretical solution (i.e., the instantaneous diffusion distribution concentration solution) under the instantaneous gas generation scenario can be obtained efficiently and accurately. The instantaneous diffusion distribution concentration solution obtained by the above mathematical processing provides an indispensable theoretical core and mathematical tool for the final accurate calculation and visualization of the full-time and spacetime concentration distribution inside the transformer.

[0045] Furthermore, this invention successfully transforms the solution from the frequency domain back to the real physical space-time domain by performing an inverse Fourier transform on the solution after the Fourier transform. This yields an analytical expression that can directly describe the gas concentration at any location and time in the transformer oil, providing a direct mathematical tool for subsequent numerical calculations and visualization analysis. By performing definite integral processing on the solution, the instantaneous diffusion distribution concentration solution in unbounded space is finally obtained, revealing the core law that the gas concentration follows a Gaussian distribution with distance and time. By introducing an infinite reflection superposition term to correct the solution in unbounded space, the invention overcomes the idealization defect of the traditional model that treats the transformer space as infinitely large, accurately characterizing the reflection effect of the tank wall on the gas diffusion wave. This method incorporates the complex influence of finite boundaries into the analytical framework through the mathematical principle of the mirror method, enabling the final obtained bounded space instantaneous solution to realistically simulate the complex concentration distribution formed by multiple reflections and superpositions of gas in the closed oil tank of the transformer, greatly improving the prediction accuracy and reliability of the model in real physical environments.

[0046] Furthermore, by discretizing the continuous gas generation process into a superposition of a series of instantaneous gas generation sources, this invention overcomes the limitations of the idealized model that simply treats a fault as a single sudden gas generation. The resulting continuous diffusion distribution concentration solution can calculate the gas concentration value at any spatial location inside the transformer from any historical moment after the fault begins to the present and even any future moment. This provides a unique and continuous data source for realizing the full-time and space-time dynamic visualization of the gas diffusion process and concentration prediction based on virtual sensing, laying an irreplaceable and solid foundation for subsequent fault tracing and localization.

[0047] Furthermore, this invention transforms the invisible gas diffusion process hidden within the transformer's enclosed tank into a clear and intuitive three-dimensional concentration cloud map and spatiotemporal variation curve by numerically calculating the continuous concentration distribution solution on a discrete grid. This provides a virtual window for observing the dynamics inside the transformer, enabling pre-simulation of the concentration change trajectory that sensors installed at different locations can monitor. Before actual sensor installation, by comparing key indicators such as the sensitivity and response speed of the concentration signal under different layout schemes, the optimal installation point that can most effectively capture fault characteristics can be scientifically selected. This overcomes the blind reliance on experience for sensor placement in existing technologies and significantly improves the reliability of the online monitoring system. By combining measured data with inversion algorithms for fault source tracing and location, the invention can combine a limited number of sensor readings with a full-field physical model to reverse-calculate the most likely precise three-dimensional coordinates of the fault source, providing a clear target for subsequent maintenance and repair, and greatly improving the accuracy of fault diagnosis and operational efficiency. Attached Figure Description

[0048] Figure 1This is a flowchart illustrating the thermal-fluid coupling calculation method for the two-phase gas transport of oil and gas inside the transformer according to the present invention. Detailed Implementation

[0049] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0050] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0051] Please see Figure 1 As shown, Figure 1 This is a flowchart illustrating the thermal-fluid coupling calculation method for the two-phase gas transport of oil and gas inside the transformer according to the present invention.

[0052] The technical solution provided in this application includes the following steps:

[0053] Step S1: Establish a three-dimensional diffusion model of dissolved gas in the transformer oil. The model is based on computational fluid dynamics and Fick's diffusion law, and coupled with the diffusion coefficient determined by temperature and the transport velocity determined by oil flow.

[0054] Step S2: Set initial conditions and boundary conditions. The initial condition is that there is an instantaneous gas source defined by the Dirac delta function at the fault source location, and the initial gas concentration at other locations is 0. The boundary condition is the gas diffusion reflection boundary formed by the transformer tank wall.

[0055] Step S3: Based on the initial and boundary conditions, solve the control equations of the three-dimensional diffusion model using the integral transform method to obtain the instantaneous diffusion distribution concentration solution under instantaneous gas production conditions;

[0056] Step S4: Based on the instantaneous diffusion distribution concentration solution, calculate the continuous diffusion distribution concentration solution under continuous gas production conditions by superimposing and integrating in the time domain.

[0057] Step S5: Using the continuous diffusion distribution concentration solution, obtain the three-dimensional concentration distribution of dissolved gas in the oil at any time and any location inside the transformer.

[0058] Specifically, in step S1, establishing a three-dimensional diffusion model of dissolved gases in the transformer internal oil includes:

[0059] (1);

[0060] In the formula, C is the dissolved gas content in the oil, in ppm; t is the diffusion time of the gas transport process, in s; Dx, Dy, and Dz are the diffusion coefficients of the dissolved gas in the oil in the x, y, and z directions, respectively; ux, uy, and uz are the transformer oil flow velocities of the dissolved gas in the oil in the x, y, and z directions, respectively, and all velocities are constants.

[0061] Specifically, in step S1, the diffusion coefficients Dx, Dy, and Dz are isotropic and have equal values.

[0062] Specifically, in step S1, the values ​​of the diffusion coefficients Dx, Dy, and Dz are determined through experimental data and are associated with the specific temperature and gas type inside the transformer.

[0063] In this embodiment of the invention, a temperature-controlled sealed oil cup experimental system is constructed. This system includes a sealed oil cup with a constant-temperature jacket, a high-precision temperature controller, a gas path system for introducing and collecting specific fault gases, and a gas chromatograph or specific gas sensor for online monitoring of dissolved gas concentration in the oil. Fresh transformer oil, after vacuum degassing, is injected into the oil cup, and the oil temperature is controlled to be stable at a specific value T1 (e.g., 40℃, 60℃, 80℃). At the center of the bottom of the oil cup, a known mass of specific fault gas M is instantaneously injected or continuously injected at a low flow rate using a micro-bubbling device. Simultaneously with gas injection, a low-speed stirrer inside the oil cup is activated to simulate the convection effect of oil flow inside the transformer, and the initial moment is recorded. At different radial distances r1, r2, r3... from the injection point, multiple sampling points or online sensors are used to continuously monitor and record the change curve of dissolved gas concentration in the oil over time. The experimental data C(r,t) is obtained; the concentration data C(r,t) obtained from the above experiment is fitted with the simplified form of the three-dimensional diffusion model described in this invention; during the model fitting process, the oil flow velocities ux, uy, uz are taken as known quantities (converted from the stirrer speed), and the diffusion coefficient D is taken as the key parameter to be inverted; optimization algorithms such as nonlinear least squares method are used to adjust the value of the diffusion coefficient D so that the error between the concentration-time curve calculated by the model and the experimental measurement curve is minimized; through the above method, the diffusion coefficient value D of a specific gas (such as H2) in transformer oil at a specific temperature T1 is obtained; by changing the experimental temperature T and repeating steps 2 and 3, a set of diffusion coefficients D(T) at different temperatures can be obtained, for example: D(40℃), D(60℃), D(80℃)...; based on this set of data, an empirical relationship between the diffusion coefficient D and temperature T is established through regression analysis. Typically, this relationship conforms to the Arrhenius equation. By repeating the entire experimental procedure for different types of faulty gases (such as H2, CH4, C2H2, C2H4, CO, etc.), a database of diffusion coefficients or a set of empirical formulas covering different gases and temperatures can be established.

[0064] This invention directly calibrates key parameters using precise experimental data, ensuring the accuracy and physical realism of subsequent three-dimensional diffusion model calculations. It overcomes the simulation distortion problem caused by inaccurate parameter estimation in traditional simulations. It not only obtains discrete diffusion coefficient values ​​at specific temperatures but also establishes a universal empirical formula between diffusion coefficient and temperature through regression analysis. This allows the model to automatically adjust and select the correct diffusion coefficient based on the actual, dynamically changing temperature field inside the transformer, greatly enhancing the model's adaptability and predictive ability under different operating conditions. By repeating the experimental process for different types of fault gases (such as H2, CH4, C2H2, etc.), a diffusion coefficient database covering major fault characteristic gases and spanning major operating temperature ranges can be established, providing a solid and universal data support platform for transformer condition assessment and fault diagnosis.

[0065] Specifically, in step S2, the initial conditions of the instantaneous gas source, defined by the Dirac delta function, are as follows:

[0066] (2);

[0067] In the formula, M represents the mass of dissolved gas in the oil. , , It represents a generalized function of the unit intensive distribution quantity.

[0068] Specifically, in step S2, the generalized function includes:

[0069] (3);

[0070] In the formula, x0, y0, and z0 are the three-dimensional coordinates of the internal fault source of the transformer.

[0071] Specifically, in step S2, the boundary conditions are:

[0072] (4);

[0073] Using the diffusion time t of dissolved gas transport in oil as a parameter, a Fourier transform is performed on both sides of equation (1), assuming... Then there is

[0074] (5);

[0075] In the formula, i is the imaginary unit in complex numbers.

[0076] Specifically, in step S2, solving formula (5) yields:

[0077] (6).

[0078] This invention uses the Dirac delta function to describe the initial gas source. Its core advantage lies in its ability to accurately and ideally simulate a fault gas generation event that is highly localized in space and occurs instantaneously in time. By applying Fourier transform, the partial differential equation (PDE) containing convection-diffusion terms, which was originally difficult to solve directly, is transformed into an ordinary differential equation (ODE) that is easier to solve. This greatly simplifies the mathematical complexity of the solution process and bypasses the numerical difficulties of directly solving the three-dimensional transient PDE. As a result, the theoretical solution (i.e., the instantaneous diffusion distribution concentration solution) under the instantaneous gas generation scenario can be obtained efficiently and accurately. The instantaneous diffusion distribution concentration solution obtained by the above mathematical processing provides an indispensable theoretical core and mathematical tool for the final accurate calculation and visualization of the full spatiotemporal concentration distribution inside the transformer.

[0079] Specifically, in step S3, an inverse Fourier transform is performed on equation (6) to obtain the instantaneous diffusion distribution concentration solution:

[0080] (7).

[0081] Specifically, in step S3, the definite integral of equation (7) is taken to obtain the instantaneous diffusion distribution concentration solution in unbounded space:

[0082] (8).

[0083] Specifically, in step S3, the spatial range of the reflection boundary is defined as: -h1≤x≤h1, -h2≤y≤h2, -h3≤z≤h3.

[0084] Specifically, in step S3, an infinite number of reflection superposition terms are introduced to correct the instantaneous diffusion distribution concentration solution, thereby obtaining the instantaneous diffusion distribution concentration solution in bounded space:

[0085] (9);

[0086] In the formula, H1=2nh1, H2=2nh2, H3=2nh3 represent the total distance of diffusion and reflection of dissolved gas in oil in the x, y and z directions, respectively, and n represents the number of reflections that occur when dissolved gas in oil is transported to the boundary.

[0087] This invention successfully transforms the solution from the frequency domain back to the real physical space-time domain by performing an inverse Fourier transform on the solution obtained after the Fourier transform. This yields an analytical expression that can directly describe the gas concentration at any location and time in transformer oil, providing a direct mathematical tool for subsequent numerical calculations and visualization analysis. By performing definite integral processing on the solution, the instantaneous diffusion distribution concentration solution in unbounded space is finally obtained, revealing the core law that the gas concentration follows a Gaussian distribution with distance and time. By introducing an infinite reflection superposition term to correct the solution in unbounded space, the invention overcomes the idealization defect of the traditional model that treats the transformer space as infinitely large, accurately characterizing the reflection effect of the tank wall on the gas diffusion wave. This method incorporates the complex influence of finite boundaries into the analytical framework through the mathematical principle of the mirror method, enabling the final obtained bounded space instantaneous solution to realistically simulate the complex concentration distribution formed by multiple reflections and superpositions of gas in the closed oil tank of the transformer, greatly improving the prediction accuracy and reliability of the model in real physical environments.

[0088] Specifically, in step S4, the superposition integration in the time domain includes: discretizing the continuous gas production process into a superposition of instantaneous gas production sources with intensity Mdτ at time τ; the concentration contribution of any instantaneous source at any spatial location at observation time t is expressed as:

[0089] (10).

[0090] Specifically, in step S4, the continuous diffusion distribution concentration solution from time 0 to time t is obtained by integrating over the concentration contributions of all instantaneous sources:

[0091] (11).

[0092] This invention overcomes the limitations of the idealized model that simply treats a fault as a single, sudden gas generation by discretizing the continuous gas generation process into a superposition of a series of instantaneous gas generation sources. The resulting continuous diffusion distribution concentration solution can calculate the gas concentration value at any spatial location inside the transformer from any historical moment after the fault begins to the present and even any future moment. This provides a unique and continuous data source for realizing the full-time and spatial dynamic visualization of the gas diffusion process and concentration prediction based on virtual sensing, laying an irreplaceable and solid foundation for subsequent fault tracing and localization.

[0093] Specifically, in step S5, obtaining the three-dimensional concentration distribution of dissolved gas in oil at any time and any location inside the transformer includes: based on the continuous diffusion distribution concentration solution, obtaining the gas concentration values ​​at different spatial locations inside the transformer at different time points through numerical calculation, and constructing a complete spatiotemporal concentration distribution field.

[0094] In this embodiment of the invention, based on the actual tank dimensions of a transformer (e.g., 2m x 1.5m x 2m), a corresponding three-dimensional computational space is established in the computer. This space is discretized in the x, y, and z directions at intervals of 0.1m, generating a three-dimensional grid system containing thousands of grid points. A spatiotemporal query point is set: assuming it is necessary to analyze the global gas distribution inside the transformer on the 10th day after the fault (i.e., t = 864000s), and simultaneously, the historical concentration changes at a preset DGA sensor location at coordinates (1.0, 0.5, 1.5) are considered. Substituting t = 864000s and the coordinates (x, y, z) of each grid point into the continuous diffusion distribution concentration solution C(x, y, z, t), the solution is obtained through computer programming. The process involves batch calculations to determine the gas concentration C at all grid points at a specific time. The sensor location coordinates (1.0, 0.5, 1.5) are fixed, and the time t is varied from 0 to 864000 s in steps (e.g., 1 hour). Substituting these values ​​into C(x, y, z, t), the concentration value at that point is calculated for each day from the start of the fault to the 10th day. The calculated concentration values ​​at all grid points are then visualized in three-dimensional space using color mapping: for example, blue represents low-concentration areas, and red represents high-concentration areas. This results in a three-dimensional concentration cloud map that clearly shows how the gas diffuses from the fault source within the transformer on the 10th day, influenced by oil flow and boundary reflections. Simultaneously, the concentration-time variation curve at the sensor location is plotted.

[0095] Specifically, step S5 also includes fault source tracing and location, which involves comparing the calculated three-dimensional concentration distribution of dissolved gas in the oil with the actual concentration measurement data inside the transformer to determine the location coordinates of the fault source.

[0096] In this embodiment of the invention, during the operation of the transformer, the actual dissolved gas concentration in the oil is measured by multiple DGA sensors (such as sensors A, B, and C) installed at different internal locations. To locate the fault source, the following steps are implemented: First, a potential fault source location P'(x',y',z') is assumed in the three-dimensional model of the transformer and used as the gas generation point. Using the thermal-fluid coupling model established in this invention, the theoretical gas concentration values ​​at each sensor location (A, B, and C) under this assumption are calculated. The calculated theoretical concentration value is compared with the actual measured concentration value of the sensor at the same time, and the error between the two (such as root mean square error) is calculated. The coordinates of the assumed fault source P' are systematically changed throughout the entire space of the transformer using an inversion algorithm (such as grid search or optimization algorithm), and step 1 is repeated. When a specific coordinate point P(x0,y0,z0) is found, such that the overall error between the theoretical calculated concentration value and the actual measured value of all sensor locations is minimized, the point P can be determined as the most likely true fault source location.

[0097] This invention transforms the invisible gas diffusion process hidden within the transformer's enclosed tank into a clear and intuitive three-dimensional concentration cloud map and spatiotemporal variation curve by numerically calculating the continuous concentration distribution solution on a discrete grid. This provides a virtual window for observing the dynamics inside the transformer, allowing for pre-simulation of concentration change trajectories monitored by sensors installed at different locations. Before actual sensor installation, by comparing key indicators such as sensitivity and response speed of concentration signals under different layout schemes, the optimal installation point for effectively capturing fault characteristics can be scientifically selected. This overcomes the blind reliance on experience in sensor placement in existing technologies, significantly improving the reliability of the online monitoring system. By combining measured data with inversion algorithms for fault source tracing and location, it can combine a limited number of sensor readings with a full-field physical model to reverse-calculate the most likely precise three-dimensional coordinates of the fault source, providing a clear target for subsequent maintenance and repair, greatly improving the accuracy of fault diagnosis and operational efficiency.

[0098] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this application.

Claims

1. A method for heat-flow coupled calculation of oil-gas two-phase gas transport inside a transformer, characterized in that, The method comprises the following steps: Step S1, a three-dimensional diffusion model of the dissolved gas in the transformer oil is established, the model is based on the computational fluid dynamics and the Fick diffusion law, and is coupled with the diffusion coefficient determined by the temperature and the transport speed determined by the oil flow; Step S2, initial conditions and boundary conditions are set, the initial conditions are that there is a transient gas source defined by a Dirac delta function at the position of the fault source, and the initial gas concentration is 0 at the remaining positions, and the boundary conditions are that the gas diffusion reflection boundary is formed by the wall surface of the transformer oil tank; Step S3, based on the initial conditions and the boundary conditions, the control equation of the three-dimensional diffusion model is solved by the integral transform method, and a transient diffusion distribution concentration solution under the condition of transient gas production is obtained; Step S4, based on the transient diffusion distribution concentration solution, the continuous diffusion distribution concentration solution under the condition of continuous gas production is calculated by performing superposition integration in the time domain; Step S5, the three-dimensional concentration distribution of the dissolved gas in the transformer oil at any time and any position in the transformer is obtained by using the continuous diffusion distribution concentration solution.

2. The method of claim 1, wherein, In step S1, the three-dimensional diffusion model of the dissolved gas in the transformer oil comprises: （1）； In the formula, C is the content of the dissolved gas in the oil, t is the diffusion time of the gas transport process, Dx, Dy and Dz are respectively the diffusion coefficients of the dissolved gas in the oil in the x, y and z directions, and ux, uy and uz are respectively the transformer oil flow velocities of the dissolved gas in the x, y and z directions.

3. The method of claim 2, wherein, In step S1, the diffusion coefficients Dx, Dy and Dz are isotropic, and the values are equal.

4. The method of claim 3, wherein, In step S1, the values of the diffusion coefficients Dx, Dy and Dz are determined by experimental data, and are associated with the specific temperature and gas type in the transformer.

5. The method of claim 1, wherein, In step S2, the initial condition of the transient gas source defined by the Dirac delta function is: （2）； where M represents the mass of the dissolved gas in the oil, , , is a generalized function of the unit concentration distribution.

6. The method of claim 5, wherein the method is a method of calculating heat flow coupling of oil-gas two-phase gas transport inside a transformer. In step S2, the generalized function comprises: （3）； In the formula, x0, y0 and z0 are the three-dimensional coordinates of the fault source in the transformer.

7. The method of claim 5, wherein the method is a method of calculating heat flow coupling of oil-gas two-phase gas transport inside a transformer. In step S2, the boundary condition is: （4）； Taking the diffusion time t of the gas transported in the oil as a parameter, the Fourier transform is applied to both sides of equation (1), assuming then （5）； In the formula, i is the imaginary unit in the complex number.

8. The method of claim 7, wherein the method is a method of calculating heat flow coupling of oil-gas two-phase gas transport inside a transformer. In step S2, the formula (5) is solved to obtain: （6）。 9. The method of claim 8, wherein the method is a method of calculating heat flow coupling of oil-gas two-phase gas transport inside a transformer. In step S3, the inverse Fourier transform of the formula (6) is performed to obtain the transient diffusion distribution concentration solution: （7）。 10. The method of claim 9, wherein the method is a method of calculating heat flow coupling of oil-gas two-phase gas transport inside a transformer. In step S3, the definite integral of the formula (7) is solved to obtain the transient diffusion distribution concentration solution in the unbounded space: (8)。 11. The method of claim 1, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized in that, In step S3, the spatial range of the reflection boundary is defined as: -h1≤x≤h1, -h2≤y≤h2, -h3≤z≤h3.

12. The method of claim 11, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized in that, In step S3, the transient diffusion distribution concentration solution is modified by introducing infinite reflection superposition items to obtain the transient diffusion distribution concentration solution in the bounded space: (9)； In the formula, H1=2nh1, H2=2nh2 and H3=2nh3 represent the total distance of the diffusion reflection of the dissolved gas in the oil in the x, y and z directions, and n represents the number of reflections of the dissolved gas transport to the boundary.

13. The method of claim 1, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized in that, In step S4, the superposition integration in the time domain comprises: discretizing the continuous gas production process into the superposition of the transient gas source with the intensity of Mdτ at the time τ; and the concentration contribution of any transient source at the observation time t at any position in the space is represented as: (10)。 14. The method of claim 10, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized in that, In step S4, the continuous diffusion distribution concentration solution from 0 to t moment is obtained by integrating the concentration contribution of all transient sources: (11)。 15. The method of claim 1, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized in that, In step S5, obtaining the three-dimensional concentration distribution of dissolved gas in oil at any time and any position inside the transformer includes: based on the continuous diffusion distribution concentration solution, the gas concentration values at different spatial positions and different time points inside the transformer are obtained by numerical calculation, and a complete space-time concentration distribution field is constructed.

16. The method of claim 1, wherein the transformer internal oil-gas two-phase gas transport and heat flow coupling calculation method is characterized by, In step S5, it also includes fault source positioning, by comparing the calculated three-dimensional concentration distribution of dissolved gas in oil with the actual concentration measurement data inside the transformer, the position coordinates of the fault source are determined.

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