Oil-immersed power transformer temperature rise calculation method, device, equipment and medium

Abstract

The present invention discloses a method for calculating the temperature rise of an oil-immersed power transformer, which relates to the technical field of grid digitization and is used to solve the problem of low efficiency in existing temperature rise calculations. The method includes the following steps: obtaining physical property parameters, finite element node mesh data, and boundary conditions, and based on the physical property parameters, finite element node mesh data, and boundary conditions, using the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtaining an initial solution optimization equation; solving the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise. The present invention also discloses an oil-immersed power transformer temperature rise calculation device, an electronic device, and a computer storage medium. By combining the initial solution optimization algorithm with the hybrid variable step size algorithm, the present invention improves the calculation efficiency of the temperature rise.

Description

Technical Field

[0001] The present invention relates to the technical field of power grid digitization, and particularly relates to a method, device, equipment and medium for calculating the temperature rise of an oil-immersed power transformer. Background Art

[0002] Power grid digitization is an important part of the construction of a new power system. The oil-immersed power transformer is an important device in power grid digitization. The accurate calculation and analysis of the operating conditions of the oil-immersed power transformer are an inevitable requirement for power grid digitization. The overheating of the oil-immersed power transformer during operation is one of the main reasons for its failure. Therefore, it is necessary to perform digital analysis on the thermal characteristics of the winding.

[0003] In the prior art, the calculation of the thermal characteristics of the winding of an oil-immersed power transformer mainly uses the numerical calculation method. The numerical calculation method has the advantages of clear physical meaning, high calculation accuracy, strong versatility, etc. Commonly used numerical calculation methods generally include: the finite difference method, the finite volume method, and the finite element method, etc. However, the structure of a large oil-immersed power transformer is relatively complex, and the number of meshes and nodes for subdivision is too large. When using methods such as the finite element method to solve, due to the huge scale of the equations, the calculation efficiency is low, resulting in being unable to be applied to engineering actual calculations, and this problem is particularly prominent in transient calculations. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, one of the purposes of the present invention is to provide a method for calculating the temperature rise of an oil-immersed power transformer, which quickly calculates the transient temperature rise of the oil-immersed power transformer through an initial solution optimization algorithm combined with a hybrid variable step size algorithm.

[0005] One of the purposes of the present invention is achieved by adopting the following technical solutions:

[0006] A method for calculating the temperature rise of an oil-immersed power transformer includes the following steps:

[0007] Obtain physical property parameters, finite element node mesh data and boundary conditions. According to the physical property parameters, finite element node mesh data and boundary conditions, based on the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtain an initial solution optimization equation;

[0008] Solve the initial solution optimization equation through the POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise.

[0009] Further, the boundary conditions include the initial oil flow temperature and the initial winding temperature.

[0010] Further, according to the physical property parameters, finite element node grid data, and boundary conditions, based on the least squares - upwind finite element method, through an initial solution optimization algorithm, combined with the fluid - thermal coupling finite element equation, an initial solution optimization equation is obtained, including the following steps:

[0011] According to the physical property parameters and the finite element node grid data, calculate the velocity of the flow field at each moment through the LSFEM algorithm;

[0012] Import the velocity at the moment when the iterative residual is less than the set value into the temperature field calculation, and the temperature field calculation is carried out through the UFEM algorithm to obtain the calculated temperature at the moment;

[0013] According to the calculated temperature at the moment, calculate the iterative initial value of the next time step through the initial solution optimization algorithm to obtain the initial solution optimization equation.

[0014] Further, the calculation of the initial solution optimization algorithm combined with the fluid - thermal coupling finite element equation includes the following steps:

[0015] Introduce the control equation of oil flow and transform the control equation to the two - dimensional rectangular coordinate system;

[0016] Through the Backward - Euler method, numerically discretize the time term of the transformed control equation and convert it into matrix form;

[0017] Discretize the control equation in matrix form by the least squares finite element method to obtain the discrete form of the flow field control equation;

[0018] Discretize the temperature field control equation by the streamline upwind finite element method;

[0019] Through θ Discretize the time term of the temperature field control equation by the discretization method;

[0020] Combine the discrete form of the flow field control equation with the discretized temperature field control equation to obtain the initial solution optimization equation for transient temperature rise.

[0021] Further, solve the initial solution optimization equation through the POD - ATS - HTS hybrid variable - step - size algorithm to obtain the transient temperature rise, including the following steps:

[0022] Calculate the time step size, and obtain the POD orthogonal basis according to the singular value decomposition to construct a reduced - order model;

[0023] According to the reduced - order model, judge the future step - size through the ATS and HTS algorithms:

[0024] When the calculation result is a failure step, recalculate; otherwise, select the smaller time step value among the results of the ATS and HTS algorithms as the time step calculation result.

[0025] Furthermore, it also includes improving the condition number of the POD orthogonal basis, including:

[0026] Simplify the initial solution optimization equation to obtain the equation: , where K is the stiffness matrix, g is the solution vector, b represents the right-hand side term;

[0027] Based on singular value decomposition, calculate the extracted orthogonal basis;

[0028] According to the Galerkin projection method, project the space where the original system equation is located onto the subspace composed of the orthogonal basis. That is, obtain the orthogonal basis through the singular value decomposition method, and then project the physical equation onto the subspace composed of the orthogonal basis.

[0029] The second object of the present invention is to provide an oil-immersed power transformer temperature rise calculation device, which solves the initial solution optimization equation through the POD-ATS-HTS hybrid variable time step algorithm to calculate the transient temperature rise.

[0030] Furthermore, it also includes performing transient fluid-structure interaction heat transfer calculation through the POD-ATS-HTS hybrid variable time step algorithm, including:

[0031] Calculate the estimated value and the second-order accuracy estimated value according to Taylor's formula;

[0032] Calculate the truncation error according to the difference between the estimated value and the second-order accuracy estimated value;

[0033] Calculate the time step according to the truncation error.

[0034] Based on the initial solution optimization of Taylor expansion, it is added to the solution process of the transient fluid-thermal coupling finite element equation, making the equation iteration speed and solution speed faster.

[0035] The second object of the present invention is achieved by the following technical solutions:

[0036] An oil-immersed power transformer temperature rise calculation device, which includes:

[0037] An initial optimization module, used to obtain physical property parameters, finite element node grid data, and boundary conditions. According to the physical property parameters, finite element node grid data, and boundary conditions, based on the least squares-upwind finite element method, through the initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtain the initial solution optimization equation;

[0038] The temperature rise calculation module is used to solve the initial solution optimization equation through the POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise.

[0039] The third object of the present invention is to provide an electronic device for implementing one of the invention objects, which includes a processor, a storage medium, and a computer program. The computer program is stored in the storage medium, and when the computer program is executed by the processor, the above-mentioned oil-immersed power transformer temperature rise calculation method is realized.

[0040] The fourth object of the present invention is to provide a computer-readable storage medium for storing one of the invention objects, on which a computer program is stored, and when the computer program is executed by the processor, the above-mentioned oil-immersed power transformer temperature rise calculation method is realized.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] By adding the initial solution optimization algorithm to the fluid-thermal coupling equation for calculating the transformer temperature rise, the present invention can make the initial solution of each time step of the equation closer to the convergent solution, thereby effectively reducing the number of iterations for solving the equation and improving the calculation efficiency. In addition, the present invention also introduces the POD-ATS-HTS hybrid variable step size algorithm, which not only reduces the number of transient calculation steps but also improves the single-step solution efficiency, enabling the solution efficiency of the transformer transient temperature rise to be improved and applicable to the actual operations of various scale projects. Description of the Drawings

[0043] Figure 1 is the flowchart of the oil-immersed power transformer temperature rise calculation method in Embodiment 1;

[0044] Figure 2 is the flowchart of the initial solution optimization calculation in Embodiment 1;

[0045] Figure 3 is the flowchart of the hybrid variable step size calculation in Embodiment 1;

[0046] Figure 4 is the oil duct speed change comparison diagram in Embodiment 2;

[0047] Figure 5 is the solution time comparison diagram in Embodiment 2;

[0048] Figure 6 is the structural block diagram of the oil-immersed power transformer temperature rise calculation device in Embodiment 3;

[0049] Figure 7 is the structural block diagram of the electronic device in Embodiment 4. Detailed Embodiments

[0050] The present invention will be described in more detail below in conjunction with the accompanying drawings. It should be noted that the description of the present invention with reference to the accompanying drawings below is illustrative only and not restrictive. Combinations can be made between different embodiments to form other embodiments not shown in the following description.

[0051] Embodiment 1

[0052] Embodiment 1 provides an oil-immersed power transformer temperature rise calculation method, aiming to reduce the calculation time and cost through a hybrid variable step size algorithm, and at the same time solve the problems of excessive result deviation and time redundancy caused by improper step size setting.

[0053] It should be noted that the algorithms involved in this embodiment, such as UFEM, ATS, HT and other algorithms, are all existing algorithms. This embodiment does not improve the algorithms themselves. Therefore, only a brief description is given to the specific topics and processes of each algorithm in this embodiment, and no more details and detailed principles are elaborated.

[0054] Please refer to Figure 1 As shown, an oil-immersed power transformer temperature rise calculation method includes the following steps:

[0055] S1. Obtain physical property parameters, finite element node mesh data and boundary conditions, and obtain an initial solution optimization equation through an initial solution optimization algorithm in combination with the fluid-thermal coupling finite element equation according to the physical property parameters, finite element node mesh data and boundary conditions;

[0056] The above boundary conditions include the initial oil flow temperature and the initial winding temperature. Of course, the S1 mesh data also includes finite element node coordinates, element information, etc. Such data belongs to the data required conventionally, and the acquisition method thereof is not elaborated in this embodiment.

[0057] S1 calculates the transient temperature rise of the two-dimensional single-segment sub-turn winding of the oil-immersed power transformer based on the least squares-upwind finite element method, proposes an initial solution optimization scheme and applies it to the finite element calculation equation to achieve the purpose of reducing the number of equation iterations. Specifically, please refer to Figure 2 As shown, it includes the following steps:

[0058] Calculate the velocity of the flow field at each moment through the LSFEM algorithm according to the physical property parameters and the finite element node mesh data; when the iteration residual of the velocity is less than the set value ε 0, import the velocity at this moment into the temperature field calculation.

[0059] Import the velocity at the moment when the iteration residual is less than the set value into the temperature field calculation, and calculate the temperature T at each moment of the temperature field n The calculation is carried out through the UFEM algorithm to obtain the calculated temperature at the moment; when the iteration residual of the temperature is less than the set valueε T At this time, the calculated temperature at this moment is obtained;

[0060] According to the calculated temperature at the said moment, the iterative initial value for the next time step is calculated through the initial solution optimization algorithm, obtaining the initial solution optimization equation. Specifically, the iterative initial value for the next time step is determined through the initial solution optimization algorithm. Otherwise, the physical property parameters of the fluid are updated according to the calculation results, and the iterative calculation at this moment is carried out again. This continues until the set calculation time or the number of calculation time steps is reached.

[0061] The following provides a detailed explanation and description of the calculation of the initial solution optimization algorithm combined with the fluid-thermal coupling finite element equation. Since the oil flow in an oil-immersed power transformer is an incompressible Newtonian fluid, based on the principles of momentum conservation and mass conservation of the fluid and introducing vorticity simultaneously, the control equation for the oil flow is:

[0062] (1)

[0063] In the above formula, U is the velocity vector, m / s; ρ is the fluid density, kg / m 3 ; p is the internal pressure of the fluid, Pa; η is the dynamic viscosity of the fluid, N·s / m 2 ; f is the external force density vector, N / m 3 ; ω is the vorticity, 1 / s.

[0064] Express Equation (1) in a two-dimensional rectangular coordinate system:

[0065] (2)

[0066] In the formula, u is the horizontal velocity, v is the vertical velocity, ω is the vorticity, f x and f y are respectively the horizontal and vertical components of the external force density vector, x and y are the abscissa and ordinate respectively. By using the Backward-Euler method, the time terms of the above equations can be numerically discretized:

[0067] (3)

[0068] In the formula, Δ t is the discrete time step, ([[]] u , v ,p , ω ) n+1 represents n the calculation result at time +1,( u , v , p , ω) n represents n the calculation result at time

[0069] Express it in matrix form as:

[0070] (4)

[0071] In formula (4), g =( u , v , p , ω ) T , matrix operator A 1, A 2, A 0, b is represented as follows:

[0072]

[0073]

[0074] In the formula, u n is u the value at the n th time step, v n is v the value at the n th time step, Δ t is the time step, f x n+1 and f y n+1 are respectively f x and f y the values at the n th +1 time step.

[0075] Discretize formula (4) using the least squares finite element method to obtain the discrete form of the flow field control equation:

[0076] (5)

[0077] In the formula:

[0078]

[0079] For the temperature field, the governing equation is:

[0080] (6)

[0081] In the formula, G is the solution vector matrix; N is the finite element interpolation function; F is the right-hand term; λ is thermal conductivity, W / (m·K); S T Heat generation per unit volume, W / m 3 ; T is temperature, K; is the specific heat capacity at constant pressure, J / (kg·K). It can be seen that when the velocity is 0, the equation represents the heat conduction equation inside the solid; when the velocity is not 0, it is the energy conservation equation of the fluid, so this equation can be used to uniformly represent the temperature field calculation of the solid and fluid.

[0082] The numerical discretization of the streamline upwind finite element method is as follows:

[0083] (7)

[0084] Where:

[0085]

[0086] use θ The discrete method discretizes the time term to obtain:

[0087] (8)

[0088] Pick θ =1 / 2, that is, the Crank-Nicolson discretization format with second-order accuracy, equation (7) can be simplified to:

[0089] (9)

[0090] Where:

[0091]

[0092] By combining equation (5) and equation (9), the transient process of fluid-solid coupled heat transfer of oil-immersed power transformer windings can be calculated. However, for the traditional transient numerical calculation method, if only the converged solution of the previous time step is used as the initial solution of the current time step for calculation, the number of iterations of solving the equation is generally large, which affects the overall solution efficiency. Therefore, the present invention proposes an initial solution optimization method based on Taylor's formula, assuming u 0n+1 is the initial solution at this moment, u n is used to represent the n convergent solution at the t n moment, and Δ n represents the time step at the

[0093] (10)

[0094] wherein, and respectively represent u the first-order derivative and the second-order derivative with respect to time, and they are fitted by the difference method to obtain:

[0095] (11)

[0096] By the above method, the initial solution of each time step of the equation can be made closer to the convergent solution, thereby effectively reducing the number of iterations of the finite element equation and improving the calculation efficiency.

[0097] S2. Solve the optimized equation of the initial solution by the POD-ATS-HTS hybrid variable time step algorithm to obtain the transient temperature rise.

[0098] S2 proposes a hybrid variable time step algorithm based on Proper Orthogonal Decomposition (POD)-Adaptive Time Stepping (ATS)-Heuristic Time Stepping (HTS), and applies it to the finite element calculation equation of the transient temperature rise of the two-dimensional single-segment partitioned winding of an oil-immersed power transformer, so as to achieve the purpose of reducing the matrix order, reducing the condition number of the finite element equation, reducing the number of time steps in transient calculation, and improving the calculation efficiency.

[0099] Specifically, please refer to Figure 3 as shown, solve the optimized equation of the initial solution by the POD-ATS-HTS hybrid variable time step algorithm to obtain the transient temperature rise, including the following steps:

[0100] Calculate for n fixed time steps, and obtain the POD orthogonal basis according to the singular value decomposition, and construct a reduced-order model for improving the condition number;

[0101] According to the reduced-order model, the calculation step size and the calculation result at this moment, judge the future step size by the ATS and HTS algorithms:

[0102] When the calculation result is a failure step, recalculate; otherwise, select the smaller time step value among the results of the ATS and HTS algorithms as the time step calculation result.

[0103] The above-mentioned POD algorithm and hybrid variable time step algorithm are explained and described below.

[0104] For the transient fluid-structure interaction heat transfer calculation based on the hybrid variable time step algorithm, this embodiment proposes an adaptive variable time step method to calculate the local time truncation error by calculating the difference between solutions of different precisions. Assume ψ n is the calculation result at this moment. To determine the maximum time step at the next moment within the allowable calculation precision range, based on the Taylor formula, the estimated value of the calculation result at the next moment is obtained as:

[0105] (12)

[0106] The estimation accuracy can be improved to second-order accuracy:

[0107] (13)

[0108] The difference between the two numerical estimations can be used as the basis for calculating the truncation error of each time step, expressed as:

[0109] (14)

[0110] Traditional adaptive variable time step methods generally use the absolute error as the basis for judging the time step. However, for relatively complex nonlinear problems, the absolute error may not fully reflect the degree of deviation in some cases. Therefore, the present invention adopts an absolute-relative error hybrid criterion as the time step criterion:

[0111] (15)

[0112] Among them, i represents the finite element node label, n +1 represents the n +1th time step, e represents the truncation error, τ A is the set absolute error limit, τ R is the set relative error limit. It can be seen from this calculation formula that when | ψ | is very small, the absolute error dominates, and when | ψ | is very large, the relative error is used as the main judgment basis.

[0113] If the truncation error meets the above conditions, then the value of the next time step can be calculated by the following formula:

[0114] (16)

[0115] If not satisfied, this time step is called a failed time step, and a rollback calculation needs to be performed on this time step. The time step size will be corrected to:

[0116] (17)

[0117] where k represents the number of rollbacks; index represents the node label that satisfies Equation (15). EPS represents the machine zero approximation, aiming to prevent computational divergence caused by an overly large time step size when the truncation error is too small (usually set to 10 -10 -10 -6 ). To avoid large numerical calculation errors caused by excessive changes in the step size between time steps, a step size limit factor r max is introduced, that is r min , (where r max is usually set to 4; r min is usually set to 0.1).

[0118] For strongly nonlinear problems, the adaptive variable time step method based on truncation error may not be able to effectively simulate the nonlinear iterative behavior. Therefore, the present invention proposes to combine the truncation error (ATS) and the convergence criterion (HTS), and adopt an adaptive variable time step strategy that mixes the two. In HTS, the time step size control is achieved by observing the number of iterations required to reach convergence, which is an approximate measure of the nonlinear problem. However, there is no generally applicable method to predict the number of iterations for convergence so far. Therefore, the present invention calculates the number of convergence times for each time step in the temperature rise problem k , and artificially sets its upper and lower limits. k max , k min At the end of each time step, if the number of iterations of this time step is greater than the set upper limit max k , that is:

[0119] (18)

[0120] it means that the selected step size is too large. This time step is called a failed time step and needs to be rolled back and corrected by reducing the time step size by a certain multiple to meet the requirement of the number of iterations, that is:

[0121] (19)

[0122] whereC s The correction factor indicating a step size reduction is an empirical constant less than 1, generally taking a value of 0.8 - 0.9. If the number of iterations in this time step is less than the set lower limit:

[0123] (20)

[0124] It indicates that the selected step size is too small. Then, to improve the calculation efficiency, a certain multiple can be added to this step size to obtain the time step size of the next time step:

[0125] (21)

[0126] Among them, C b The correction factor indicating a step size change is an empirical constant greater than 1, generally taking a value of 4 - 8. If the number of iterations in this time step is within the set limit range, that is:

[0127] (22)

[0128] It indicates that the selected step size for this step is relatively reasonable. To prevent this time step from being fixed at a certain specific value, only a slight change is needed to obtain:

[0129] (23)

[0130] Among them, C m Generally, it takes a value of 1.1 - 1.2. Through the hybrid variable step size method, an appropriate time step size can be selected to reduce the redundant calculation in the transient process. However, in the process of numerical calculation using the finite element method, the condition number of the stiffness matrix is extremely large, and the discrete equation established therefrom is an ill-conditioned system of equations. For ill-conditioned equations, a slight change in the matrix elements will cause a large change in the calculation results. Therefore, it will affect the calculation accuracy of the adaptive variable step size algorithm. The present invention proposes to introduce the method of proper orthogonal decomposition. Based on the singular value decomposition principle, by constructing a reduced-order subspace, the ratio of the largest singular value to the smallest singular value of the finite element stiffness matrix is reduced. On the one hand, the condition number of the finite element stiffness matrix is reduced, and to a certain extent, the ill-conditioned degree of the system is alleviated; on the other hand, the calculation order of the matrix is reduced, further improving the solution efficiency of the finite element equation.

[0131] The following explains and describes the method for improving the condition number based on Proper Orthogonal Decomposition (POD). The POD method can find a set of orthogonal bases through a set of transient system sample data obtained from experiments or numerical calculations, using the least squares method, such that the error between the sample data represented by this set of orthogonal bases and the original data is minimized. At the same time, combined with Galerkin projection, the space where the original system is located is projected onto the subspace composed of the orthogonal bases. By reasonably selecting the number of orthogonal bases, the purpose of reducing the calculation order of the original system and improving the matrix condition number can be achieved.

[0132] According to Equation (9), the solution form of the finite element equation can be simplified as follows:

[0133] (24)

[0134] Among them, K is the stiffness matrix, g is the solution vector, b represents the right-hand side term; assume is the sample data set composed of the calculation results of the first fixed time steps, where n is the number of finite element nodes. Consider finding a set of orthogonal bases and the corresponding coefficient matrix to represent this set of sample data:

[0135] (25)

[0136] At the same time, it is necessary to minimize the error of the sample data represented by this set of orthogonal bases, that is:

[0137] (26)

[0138] Then the relational expression that the above problem needs to satisfy is:

[0139] (27)

[0140] Combined with the relevant derivation of the Lagrange multiplier method

[26] , the above optimization problem can be transformed into the following process of obtaining eigenvectors:

[0141] (28)

[0142] Among them, , , p i is the corresponding matrix GG T eigenvalue λ iThe eigenvector.

[0143] Since G T G is the same as the first s non-zero eigenvalues of GG T Therefore, the eigenvector of the latter can be obtained by calculating the eigenvalues of the former, that is,

[0144] (29)

[0145] The corresponding relationship is:

[0146] (30)

[0147] Combined with the singular value decomposition theory of matrices, it can be seen that is the left singular matrix of G Then, through the singular value decomposition of G the required POD orthogonal basis can be obtained. At the same time, since generally, the first several singular values of the finite element stiffness matrix are much larger than the last few smaller singular values, therefore, the first singular values and the corresponding rows and columns of the singular value matrix can be selected to approximately represent the original matrix.

[0148] According to the basic principle of the proper orthogonal decomposition algorithm, it can be seen that by selecting the first d larger singular value matrices to represent the original matrix, not only the matrix order is reduced, the equation solving efficiency is improved, but also the ratio between the largest eigenvalue and the smallest eigenvalue is reduced, the condition number of the finite element equation is reduced, and the situation of excessive iteration times, too large error or even solution failure that may occur in the numerical solution process is improved.

[0149] In summary, considering the various disadvantages existing in the existing algorithm research, such as: the POD algorithm can only reduce the single-step solution time and cannot reduce the number of transient solution steps, the ATS variable step-size algorithm has poor effects on strong nonlinear problems, and the HTS algorithm is too empirical. One improvement point of the algorithm proposed in this embodiment is to combine the POD-ATS-HTS three algorithms organically, taking advantages of each other's strengths and compensating for each other's weaknesses. By combining the ATS-HTS variable step-size algorithm with the POD reduction algorithm, both the number of transient calculation steps is reduced and the single-step solution efficiency is improved; by combining the HTS algorithm with the ATS algorithm, the adaptability and numerical stability of the traditional variable step-size method to nonlinear problems are improved. In order to improve the ill-conditioned problem caused by the large-scale physical equation system in the calculation process of the oil-immersed power transformer temperature rise, a method of introducing proper orthogonal decomposition is proposed. Based on the singular value decomposition principle, by constructing a reduced-order subspace, the ratio of the maximum and minimum singular values of the finite element stiffness matrix is reduced. On the one hand, the condition number of the finite element stiffness matrix is reduced, and to a certain extent, the ill-conditioned degree of the system is alleviated; on the other hand, the calculation order of the matrix is reduced, and the solution efficiency of the transformer transient temperature rise is further improved. In addition, the hybrid adaptive time-step method in this embodiment predicts and adjusts the time step by controlling the size of the truncation error of each time step, effectively reducing the calculation time and cost, and at the same time solving the problems of excessive result deviation and time redundancy caused by improper step-size setting.

[0150] Embodiment 2

[0151] Embodiment 2 is an illustration of the specific calculation effect of Embodiment 1.

[0152] Based on the above transient fluid-thermal coupling heat transfer calculation method, an initial solution optimization algorithm is introduced, and its solution accuracy and efficiency are discussed. The iterative convergence criterion of the residual is set to 10 -6 , and the relevant data are compared as shown in Table 2.1:

[0153] Table 2.1 Comparison of Initial Solution Optimization Efficiency

[0154]

[0155] It can be seen that the initial solution optimization based on Taylor expansion can effectively reduce the number of iterations of the finite element equation, thereby improving the operation efficiency. The number of iterations of the first-order optimization is reduced by 74 times, and the operation efficiency is increased by about 13.63%. The number of iterations of the second-order optimization is reduced by 111 times, and the operation efficiency is increased by about 21.61%. And because the optimization process only targets the initial solution of the equation, it does not affect the final calculation result of the equation. Therefore, the calculation accuracy of the two is almost exactly the same as that without optimization.

[0156] However, for the transient calculation method with a fixed time step, its calculation efficiency is still limited by the time step setting. Therefore, in order to effectively improve the efficiency of transient calculation and solve the problem of time step setting in the numerical calculation process, the present invention introduces a hybrid time step method based on POD-ATS-HTS.

[0157] To fully illustrate the effectiveness of the proposed hybrid variable time step method in the fluid-thermal coupling calculation, the present invention will separately discuss the effects of the variable time step method in the fluid field and the temperature field.

[0158] First, the hybrid variable time step method based on POD-ATS-HTS is applied to the fluid field, and the relevant parameter settings are as follows: τ A = 0.001, τ R = 0.01, s = 0.8, r max = 4, r min = 0.9, EPS = 10 -8 , C b = 0.8, C m = 4, C s = 1.1. Taking the second oil passage of the model as an example, the simulation time is set to 5 s, and the iterative convergence criterion for the residual is 10 -4 , and after comparing the calculation results of the hybrid variable time step with the calculation results of the fixed time step Δ t = 0.02 s, please refer to Figure 4 As shown, it can be seen that in the hybrid variable time step algorithm, when the oil flow velocity changes violently, to ensure the calculation accuracy, the size of the time step is limited to a smaller interval; while when the oil flow velocity change tends to be gentle, the time step is automatically adjusted to a larger range to improve the overall calculation efficiency.

[0159] Overall, the results of the two are almost the same. When reaching the steady state, the absolute error is only 0.0001 m / s, and the relative error is only 0.46%. At the same time, under the same simulation time of 5 s, the number of time steps of the variable time step is 11 steps, and the number of time steps of the fixed time step is 250 steps. The number of time steps of the variable time step is only 4.4% of that of the fixed time step. From the perspective of calculation time, the calculation time of the fixed time step program is 4874.80 s, and the hybrid variable time step algorithm is 264.23 s. The calculation efficiency of the latter is 18.45 times that of the former. Therefore, when the calculation results are almost the same, the calculation efficiency of the variable time step is much higher than that of the fixed time step.

[0160] To further illustrate the efficiency of the algorithm proposed in the present invention, the total computation time, number of iterations, and equation solving time of the fixed-step algorithm, the fixed-step algorithm with only POD introduced, and the hybrid variable-step algorithm based on POD-ATS-HTS are compared, and the comparison chart of the solving time as shown in Figure 5 is obtained. It can be intuitively seen from the figure that for the hybrid variable-step algorithm based on POD-ATS-HTS, on the one hand, by introducing the POD reduction algorithm, the order of the equation is reduced, the number of iterations of the equation is reduced, and the single-step solving time of the finite element equation is effectively reduced; on the other hand, by combining the ATS-HTS hybrid variable-step algorithm, the total number of time steps for transient calculation is greatly reduced. The combined effect of the two greatly improves the overall solving efficiency of the transient process.

[0161] In the hybrid variable-step algorithm, the relative error limit τ R and the absolute error limit τ A settings are the dominant factors for step size change. Therefore, in order to explore the influence of the hybrid variable-step parameters on the calculation results in the present invention, the numerical solutions with different step sizes under the fixed-step condition and the calculation results of the variable-step algorithm under different τ R and τ A settings are compared, as shown in Table 2.2.

[0162] Table 2.2 Comparison of different parameter settings

[0163]

[0164] It can be seen from Table 2.2 that τ R and τ A have little influence on the calculation accuracy, but have a certain influence on the variable-step effect. This is because during the variable-step process of the algorithm, the step size adjustment is restricted by the truncation error, so that the calculation accuracy can always be guaranteed within the allowable error range. It can be known from Table 2.2 that when τ R = 0.05, τ A = 0.005, the calculation accuracy of the variable step size is already higher than that of the fixed step size Δ t = 0.03 s, and its calculation time is only 5% of the fixed step size. It can be seen that the adaptive step size algorithm of the present invention can effectively reduce the calculation time and number of calculations while ensuring the calculation accuracy.

[0165] Traditional variable step-size methods are based on simple local error estimation formulas, which are easy to calculate and achieve adaptive step-size adjustment, ensuring that the local error at each time step is within the specified accuracy. However, they have low computational efficiency and there are cases where unreasonable single-step size changes lead to non-convergence of the calculation. As shown in Table 2.3, when applying traditional variable step-size methods to large finite element equations, due to the excessive condition number of the finite element stiffness matrix (reaching 10 19 or more in this invention), there may be cases of non-convergence in the calculation when the time step size changes too drastically. It is necessary to limit the step-size change by setting upper and lower limits to improve the numerical stability during the calculation process, which seriously reduces the computational efficiency of the variable step-size algorithm. In this invention, by introducing the POD algorithm, the condition number of the equation is greatly reduced, effectively improving the numerical stability of the equation and enabling it to be applied to large step-size calculations.

[0166] Table 2.3 Comparison of the condition numbers of the equations before and after the introduction of the POD algorithm

[0167]

[0168] At the same time, to illustrate the improvement of the hybrid variable step-size method based on POD-ATS-HTS proposed in this invention compared with traditional variable step-size methods in terms of calculation accuracy, computational efficiency, and variable step-size effect, the two are applied to the model established in this invention, and the results are obtained: In terms of accuracy, compared with the traditional variable step-size method, the results of the hybrid variable step-size method based on POD-ATS-HTS are more fitting with the results of the fixed step-size algorithm. Compared with the calculation results with a fixed step size of Δ t = 0.02s, the maximum relative error of the former is 2.5%, and the maximum relative error of the latter is 0.5%. It can be seen that the hybrid variable step-size algorithm proposed in this invention has a better and more accurate effect in terms of calculation accuracy.

[0169] In terms of efficiency, setting the simulation time to 5s, the number of time steps required by the traditional variable step-size method is 31 steps, while the number of time steps required by the algorithm proposed in this invention is 11 steps, and the latter is only one-third of the former. Therefore, whether in terms of calculation accuracy or computational efficiency, for the transient flow field problem studied in this invention, the hybrid variable step-size algorithm has certain advantages over the traditional variable step-size algorithm.

[0170] Based on the proposed hybrid variable step-size method, when it is applied to the fluid-structure interaction heat transfer equation, since the coupling method used in this invention to calculate the flow field and temperature field is direct coupling, that is, the same equation is used in the solution domain for calculation. Therefore, the time step sizes used in the two fields during the calculation should be the same. Based on this, for the different step sizes obtained by applying the adaptive method to the two fields, the time matching method adopted in this invention is to select the smaller step size as the step size for the next time step calculation of the whole field.

[0171] In summary, the oil-immersed power transformer temperature rise calculation method described in the present invention can reduce the number of iterations for solving equations, improve the calculation efficiency, solve the problems of excessive result deviation and time redundancy caused by improper step size setting, and thus improve the solution efficiency of the transformer transient temperature rise.

[0172] Embodiment III

[0173] Embodiment III discloses a device corresponding to the oil-immersed power transformer temperature rise calculation method corresponding to the above embodiment. For the virtual device structure of the above embodiment, please refer to Figure 6 as shown, including:

[0174] An initial optimization module 310, configured to obtain physical property parameters, finite element node grid data, and boundary conditions. According to the physical property parameters, finite element node grid data, and boundary conditions, based on the least squares-upwind finite element method, through an initial solution optimization algorithm, in combination with the fluid-thermal coupling finite element equation, an initial solution optimization equation is obtained;

[0175] A temperature rise calculation module 320, configured to solve the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise.

[0176] Preferably, obtaining the initial solution optimization equation through an initial solution optimization algorithm in combination with the fluid-thermal coupling finite element equation includes the following steps:

[0177] According to the physical property parameters and the finite element node grid data, calculate the velocity of the flow field at each moment through the LSFEM algorithm;

[0178] Import the velocity at the moment when the iterative residual is less than the set value into the temperature field calculation, and the temperature field calculation is performed through the UFEM algorithm to obtain the calculated temperature at the moment;

[0179] According to the calculated temperature at the moment, calculate the iterative initial value of the next time step through the initial solution optimization algorithm to obtain the initial solution optimization equation.

[0180] Preferably, the calculation of the initial solution optimization algorithm in combination with the fluid-thermal coupling finite element equation includes:

[0181] Introduce the control equation of oil flow, and transform the control equation to a two-dimensional rectangular coordinate system;

[0182] Perform numerical discretization of the time term of the transformed control equation through the Backward-Euler method and convert it into a matrix form;

[0183] Discretize the control equation in matrix form through the least squares finite element method to obtain the discrete form of the flow field control equation;

[0184] Discretize the temperature field control equation by the streamline upwind finite element method;

[0185] By θ The discrete method is used to discretize the time term of the temperature field control equation;

[0186] Combine the discrete form of the flow field control equation with the discretized temperature field control equation to obtain the initial solution optimization equation for transient temperature rise.

[0187] Preferably, solve the initial solution optimization equation by the POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise, including the following steps:

[0188] Calculate the time step size, obtain the POD orthogonal basis according to the singular value decomposition, and construct a reduced-order model;

[0189] According to the reduced-order model, judge the future step size by the ATS and HTS algorithms:

[0190] When the calculation result is a failure step, recalculate; otherwise, select the smaller time step value among the results of the ATS and HTS algorithms as the step size calculation result.

[0191] Embodiment Four

[0192] Figure 7 The structural schematic diagram of an electronic device provided in Embodiment Four of the present invention is shown in Figure 7 As shown, the electronic device includes a processor 410, a memory 420, an input device 430, and an output device 440; the number of processors 410 in the computer device can be one or more, Figure 7 Taking one processor 410 as an example; the processor 410, the memory 420, the input device 430, and the output device 440 in the electronic device can be connected by a bus or other means, Figure 7 Taking the connection by bus as an example.

[0193] The memory 420, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules, such as the program instructions / modules corresponding to the oil-immersed power transformer temperature rise calculation method in the embodiments of the present invention. The processor 410 executes various functional applications and data processing of the electronic device by running the software programs, instructions, and modules stored in the memory 420, that is, realizes the oil-immersed power transformer temperature rise calculation methods in the above Embodiment One to Embodiment Two.

[0194] The memory 420 may mainly include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the terminal, etc. In addition, the memory 420 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some instances, the memory 420 may further include a memory remotely provided with respect to the processor 410, and these remote memories may be connected to the electronic device through a network. Examples of the above-mentioned network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0195] The input device 430 may be used to receive input user identity information, finite element node mesh data, etc. The output device 440 may include a display device such as a display screen.

[0196] Embodiment 5

[0197] Embodiment 5 of the present invention further provides a storage medium containing computer-executable instructions. This storage medium can be used by a computer to execute the oil-immersed power transformer temperature rise calculation method, and this method includes:

[0198] Obtain physical property parameters, finite element node mesh data, and boundary conditions. According to the physical property parameters, finite element node mesh data, and boundary conditions, based on the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtain an initial solution optimization equation;

[0199] Solve the initial solution optimization equation through the POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise.

[0200] Of course, for a storage medium containing computer-executable instructions provided by an embodiment of the present invention, the computer-executable instructions are not limited to the method operations described above, and can also execute related operations in the oil-immersed power transformer temperature rise calculation method provided by any embodiment of the present invention.

[0201] Through the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software and necessary general hardware. Of course, it can also be implemented by hardware, but in many cases the former is a better implementation. Based on this understanding, the technical solution of the present invention, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as a floppy disk, read-only memory (ROM), random access memory (RAM), flash memory (FLASH), hard disk or optical disc of a computer, etc., including several instructions for causing an electronic device (which can be a mobile phone, personal computer, server, or network device, etc.) to execute the methods described in various embodiments of the present invention.

[0202] It should be noted that in the above embodiments of the device for the oil-immersed power transformer temperature rise calculation method, the various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of the functional units are only for the convenience of mutual distinction and do not limit the protection scope of the present invention.

[0203] For those skilled in the art, according to the technical solutions and concepts described above, various corresponding changes and deformations can be made, and all these changes and deformations should fall within the protection scope of the claims of the present invention.

Claims

1. A method for calculating the temperature rise of an oil-immersed power transformer, characterized in that, It includes the following steps: Obtain physical property parameters, finite element node mesh data, and boundary conditions. According to the physical property parameters, finite element node mesh data, and boundary conditions, based on the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtain an initial solution optimization equation; Solve the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise; Among them, solving the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise includes the following steps: Calculate the time step size, and obtain the POD orthogonal basis according to the singular value decomposition, and construct a reduced-order model; According to the reduced-order model, judge the future step size through the ATS and HTS algorithms: When the calculation result is a failure step, recalculate; otherwise, select the smaller time step value among the results of the ATS and HTS algorithms as the step size calculation result; Improve the condition number of the POD orthogonal basis, including: Simplify the initial solution optimization equation to obtain the equation: , where K is the stiffness matrix, g is the solution vector, b represents the right-hand side term; Based on the singular value decomposition, calculate the extracted orthogonal basis; According to the Galerkin projection method, project the space where the original system equation is located onto the subspace composed of the orthogonal basis; Perform transient fluid-structure interaction heat transfer calculation through a POD-ATS-HTS hybrid variable step size algorithm, including: Calculate the estimated value and the second-order accuracy estimated value according to the Taylor formula; Calculate the truncation error according to the difference between the estimated value and the second-order accuracy estimated value; Calculate the time step size according to the truncation error.

2. The oil-immersed power transformer temperature rise calculation method according to claim 1, characterized in that The boundary conditions include the initial oil flow temperature and the initial winding temperature.

3. The oil-immersed power transformer temperature rise calculation method according to claim 1 or 2, characterized in that, According to the physical property parameters, finite element node mesh data, and boundary conditions, based on the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtain an initial solution optimization equation, including the following steps: According to the physical property parameters and the finite element node mesh data, calculate the velocity of the flow field at each moment through the LSFEM algorithm; Import the velocity at the moment when the iterative residual is less than the set value into the temperature field calculation, and the temperature field calculation is performed through the UFEM algorithm to obtain the calculated temperature at the moment; According to the calculated temperature at the moment, calculate the iterative initial value of the next time step through the initial solution optimization algorithm to obtain the initial solution optimization equation.

4. The oil-immersed power transformer temperature rise calculation method according to claim 1, characterized in that The calculation of the initial solution optimization algorithm combined with the fluid-thermal coupling finite element equation includes: Introduce the control equation of the oil flow, and transform the control equation to the two-dimensional rectangular coordinate system; Perform numerical discretization of the time term of the transformed control equation through the Backward-Euler method and convert it into a matrix form; Discretize the control equation in matrix form through the least squares finite element method to obtain the discrete form of the flow field control equation; Discretize the temperature field control equation through the streamline upwind finite element method; By θ using the discrete method to discretize the time term of the temperature field control equation; Merge the discrete form of the flow field control equation and the discretized temperature field control equation to obtain the initial solution optimization equation of the transient temperature rise.

5. An oil-immersed power transformer temperature rise calculation device, characterized in that, It includes: An initial optimization module, configured to obtain physical property parameters, finite element node mesh data, and boundary conditions, and based on the physical property parameters, finite element node mesh data, and boundary conditions, by using the least squares-upwind finite element method, through an initial solution optimization algorithm, and in combination with the fluid-thermal coupling finite element equation, obtain an initial solution optimization equation; A temperature rise calculation module, configured to solve the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain a transient temperature rise; Wherein, solving the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain a transient temperature rise includes the following steps: Calculating a time step size, and obtaining POD orthogonal bases according to singular value decomposition to construct a reduced-order model; Judging the future step size according to the reduced-order model through the ATS and HTS algorithms: When the calculation result is a failure time step, recalculate; otherwise, select the smaller time step value among the results of the ATS and HTS algorithms as the step size calculation result; Improving the condition number of the POD orthogonal bases, including: Simplify the initial solution optimization equation to obtain the equation: , where K is the stiffness matrix, g is the solution vector, b represents the right-hand side term; Calculating the extracted orthogonal bases based on singular value decomposition; Projecting the space where the original system equation is located onto the subspace composed of the orthogonal bases according to the Galerkin projection method; Performing transient fluid-structure interaction heat transfer calculation through a POD-ATS-HTS hybrid variable step size algorithm, including: Calculating an estimated value and a second-order accuracy estimated value according to the Taylor formula; Calculating a truncation error according to the difference between the estimated value and the second-order accuracy estimated value; Calculating the time step size according to the truncation error.

6. An electronic device, comprising a processor, a storage medium, and a computer program stored in the storage medium, characterized in that, When the computer program is executed by a processor, it implements the oil-immersed power transformer temperature rise calculation method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the oil-immersed power transformer temperature rise calculation method according to any one of claims 1 to 4.

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