An oil-immersed transformer winding oil-retaining plate size structure optimization method and system

Abstract

This invention discloses a method and system for optimizing the size and structure of oil baffles in oil-immersed transformer windings, comprising the following steps: constructing an RBF response surface model based on the size and structure parameters of the transformer winding oil baffles; using the whale optimization algorithm to obtain the optimal hyperparameters of the RBF response surface model, and constructing a WOA-RBF response surface model; and optimizing the size and structure of the transformer winding oil baffles based on the WOA-RBF response surface model. This invention uses a WOA-RBF response surface model to optimize the size of transformer winding baffles, which can efficiently and accurately solve the problem of transformer winding baffle structure optimization.

Description

Technical Field

[0001] This invention belongs to the field of oil-immersed transformer winding structure optimization, specifically relating to a method and system for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding. Background Technology

[0002] The temperature of hot spots in transformer windings is one of the key parameters affecting the service life of a transformer. Oil-immersed transformers rely on the flow of transformer oil between the windings for heat dissipation. The distribution of oil channels between the windings affects the heat dissipation capacity of the windings, and the most important factor affecting the distribution of oil channels is the baffle structure between the winding sections. Therefore, optimizing the baffle size, that is, optimizing the size of the oil channels between each section, is of great significance for reducing the temperature rise hot spots of the transformer and improving the operational reliability of the transformer.

[0003] Currently, the main types of transformer baffles are as follows: Figure 1 The two forms shown. Figure 1 Although the baffle structure shown in (a) is simple, its baffle is tightly attached to the winding, blocking all oil flow channels on that side. This significantly worsens heat dissipation on that side of the winding, easily leading to uneven temperature distribution and localized overheating. In contrast, using… Figure 1 The baffle structure shown in (b) retains a certain oil passage gap. While adding the baffle, it does not completely seal the oil passages on both sides of the winding, thus better improving the heat dissipation performance inside the winding.

[0004] for Figure 1 The baffle structure shown in (a) has a fixed size and cannot be optimized because the baffle needs to seal the entire oil passage port; while for Figure 1 (b) shows a baffle structure with a very wide adjustable range of baffle size. Changing the baffle size also means changing the oil passage structure between adjacent sections. Theoretically, this will have a significant impact on the heat dissipation level of the winding. Therefore, for Figure 1 (b) shows a baffle structure. Optimizing the baffle size, given a fixed number of partitions, is of great significance for reducing the temperature rise of the transformer windings.

[0005] Transformer structure optimization is a typical "black box problem." For different structural parameters and optimization indices, it's difficult to accurately express the complex implicit relationships using suitable empirical analytical formulas. Global optimization algorithms and response surface methodology (RSM) are two effective methods for solving such "black box problems." However, global optimization algorithms suffer from low efficiency when dealing with black box optimization problems because they require extensive calls to finite element models to obtain training and optimization samples. In contrast, RSM only needs to compute a certain number of dataset samples to fit a black box problem into a definite expression, and then optimizing that expression significantly improves optimization efficiency.

[0006] In response surface methodology, the radial basis function (RBF) response surface model is widely used due to its advantages in balancing computational accuracy and efficiency. However, traditional RBF response surface models contain some undetermined parameters, which are usually obtained through empirical selection or grid search (GS) optimization. Empirically selected hyperparameter values ​​have low reliability; the GS method is a discrete interpolation optimization, which cannot guarantee global optimization and incurs significant computational costs. Therefore, using traditional RBF response surface models for transformer winding baffle size optimization has certain limitations. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a method and system for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding, using a WOA-RBF response surface model to optimize the size of the transformer winding baffle plate.

[0008] To achieve the above objectives, the present invention provides the following solution:

[0009] A method for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding includes the following steps:

[0010] Based on the size and structural parameters of the transformer winding oil baffle, an RBF response surface model is constructed.

[0011] The optimal hyperparameters of the RBF response surface model are obtained using the whale optimization algorithm, and the WOA-RBF response surface model is constructed.

[0012] Based on the WOA-RBF response surface model, the size and structure of the transformer winding oil baffle were optimized.

[0013] Preferably, methods for constructing RBF response surface models include:

[0014] Based on the size and structural parameters of the transformer winding oil baffle, a Gaussian function is used as the radial basis function.

[0015] An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command.

[0016] Based on the parameter values, the RBF-based response surface model expression is determined.

[0017] Preferably, the expression for the radial basis function is:

[0018]

[0019] in: m is the number of input variables; n is the number of test sets, i.e., the number of hidden layers; j is the j-th output variable; w ijLet be the weights from the i-th hidden layer to the j-th output layer; sti be the value of the t-th input variable in the i-th test set; xt be the t-th input variable; kij be the threshold from the i-th hidden layer to the j-th output layer; b j The intercept of the j-th output.

[0020] Preferably, the method for obtaining the parameter values ​​of the radial basis function using the net. related commands includes:

[0021] In Matlab, the value of `sti` is obtained using `net.LW{1,1}`; the value of `wij` is obtained using `net.LW{2,1}`; the value of `kij` is obtained using `net.b{1,1}`; and the value of `b` is obtained using `net.b{2,1}`. j The value of .

[0022] Preferably, the method for optimizing the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model includes:

[0023] The length of the oil baffle was selected as the optimization variable, and its value range was determined.

[0024] Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets;

[0025] Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench.

[0026] Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set.

[0027] The final WOA-RBF response surface model is generated using the training set and the expanded coefficient values;

[0028] Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

[0029] The present invention also provides a system for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding, comprising: a first construction module, a second construction module, and an optimization module;

[0030] The first construction module is used to construct an RBF response surface model based on the size and structural parameters of the transformer winding oil baffle.

[0031] The second building module is used to obtain the optimal hyperparameters of the RBF response surface model using the whale optimization algorithm, and to construct the WOA-RBF response surface model;

[0032] The optimization module is used to optimize the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model.

[0033] Preferably, the process of constructing an RBF response surface model includes:

[0034] Based on the size and structural parameters of the transformer winding oil baffle, a Gaussian function is used as the radial basis function.

[0035] An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command.

[0036] Based on the parameter values, the RBF-based response surface model expression is determined.

[0037] Preferably, the expression for the radial basis function is:

[0038]

[0039] in: m is the number of input variables; n is the number of test sets, i.e., the number of hidden layers; j is the j-th output variable; w ij The weights from the i-th hidden layer to the j-th output layer; s ti x is the value corresponding to the t-th input variable in the i-th test set; t Let k be the t-th input variable; ij b is the threshold from the i-th hidden layer to the j-th output; j The intercept of the j-th output.

[0040] Preferably, the method for obtaining the parameter values ​​of the radial basis function using the net. related commands includes:

[0041] In Matlab, s can be obtained using net.LW{1,1}. ti The value; obtain w through net.LW{2,1} ij The value of k; obtain k through net.b{1,1}. ij The value of b is obtained through net.b{2,1}. j The value of .

[0042] Preferably, the process of optimizing the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model includes:

[0043] The length of the oil baffle was selected as the optimization variable, and its value range was determined.

[0044] Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets;

[0045] Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench.

[0046] Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set.

[0047] The final WOA-RBF response surface model is generated using the training set and the expanded coefficient values;

[0048] Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] (1) The hyperparameters of the RBF response surface model were optimized using WOA and compared with the grid search optimization method. Under the condition that the overall optimization accuracy was similar, the optimization efficiency of WOA was 3.6 times that of the grid search optimization method, which verified the feasibility of applying WOA to hyperparameter optimization design.

[0051] (2) The WOA-RBF response surface model is proposed to optimize the size of the transformer winding baffle. Compared with the original baffle size, the optimized hot spot temperature is reduced by 3.8K and the maximum temperature rise is reduced by 13.4%. At the same time, it effectively suppresses the phenomenon of large local temperature rise in each zone. The method proposed in this invention can not only reduce the hot spot temperature, but also serve as a measure to improve the global temperature field, and has certain practical application value.

[0052] (3) Compared with the quadratic polynomial (QP) response surface model used in traditional winding structure optimization, the method provided by this invention does not have a significant advantage in fitting ability, but its optimization accuracy is 10.6 times that of the QP response surface model. Moreover, the optimal hot spot value obtained by the RBF response surface model is smaller, which verifies the effectiveness of the RBF response surface model in terms of optimization accuracy and optimization ability.

[0053] (4) To verify the reliability of the optimization results of the WOA-RBF response surface method, it was compared with the optimization results of the genetic algorithm. The relative error of the optimal hot spot value in Celsius was only 0.07%. The baffle combination obtained by the two methods can be regarded as two reliable solutions obtained under the optimal value of the multi-solution problem. The reliability of the method was verified. The optimization result obtained can be regarded as one of the global optimal points. At the same time, the optimization efficiency of the response surface method is 13.5 times that of the genetic algorithm, indicating that the method proposed in this invention can efficiently and accurately solve the optimization problem of transformer winding baffle structure. Attached Figure Description

[0054] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a diagram of the current baffle structure for oil-immersed transformers;

[0056] Figure 2 This is a flowchart illustrating a method for optimizing the size and structure of an oil-immersed transformer winding oil baffle in this embodiment.

[0057] Figure 3 This is a schematic diagram of the eight-section structure of the transformer winding in this embodiment;

[0058] Figure 4 This is a flowchart illustrating the mutual calling process between Matlab and Workbench in this embodiment;

[0059] Figure 5 This is a schematic diagram of the process for establishing the WOA-RBF response surface model in this embodiment;

[0060] Figure 6 This is a schematic diagram of the transformer winding baffle structure optimization process in this embodiment;

[0061] Figure 7 This is a schematic diagram showing the root mean square error values ​​corresponding to the optimal parameters for each group of data classifications in this embodiment.

[0062] Figure 8 This is a schematic diagram of the applicability test of the RBF response surface model in this embodiment, where (a) is a comparison diagram of the predicted values ​​and control values ​​of the test set; and (b) is a diagram of the relative error distribution in Celsius at each point of the test set.

[0063] Figure 9 This is a schematic diagram comparing the flow-heat distribution of the optimized baffle structure and the initial baffle structure in this embodiment. (a) is a comparison diagram of the temperature field results before and after optimization; (b) is a comparison diagram of the velocity field results before and after optimization.

[0064] Figure 10 This is a comparison chart of errors in 20 test set data under different response surface models in this embodiment;

[0065] Figure 11 This is a schematic diagram of the genetic algorithm optimization process in this embodiment. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] like Figure 2 As shown, the present invention provides a method for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding, comprising the following steps:

[0070] Construct an RBF response surface model;

[0071] The optimal hyperparameters of the RBF response surface model are obtained using the whale optimization algorithm, and the WOA-RBF response surface model is constructed.

[0072] Based on the WOA-RBF response surface model, the size and structure of the transformer winding oil baffle were optimized.

[0073] In this embodiment, the method for constructing the RBF response surface model includes:

[0074] Gaussian functions are used as radial basis functions;

[0075] An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command.

[0076] Based on the parameter values, the expression for the RBF-based response surface model is determined.

[0077] In this embodiment, radial basis functions (RBFs) are a class of functions that use the Euclidean distance between unknown points and known data points as independent variables. The model constructed by linearly combining radial basis functions is the radial basis function model. Its basic form is:

[0078]

[0079] in: It is a radial function; r = ||xx i ||2 is the radial distance from the coordinate point to the point; λ i...

[0080] Substituting the Gaussian function, the j-th output can be written as the general formula as follows:

[0081]

[0082] in: m is the number of input variables; n is the number of test sets, i.e., the number of hidden layers; j is the j-th output variable; w ij The weights from the i-th hidden layer to the j-th output layer; s ti x is the value corresponding to the t-th input variable in the i-th test set; t Let k be the t-th input variable; ij b is the threshold from the i-th hidden layer to the j-th output; j The intercept of the j-th output.

[0083] In this embodiment, the `newrb` and `newrbe` functions can be used in Matlab to construct the RBF response surface model. While the `newrb` function can produce a smaller network, it is time-consuming and contains some error. The `newrbe` function, on the other hand, is faster and produces a zero-error model, but its neuron count is related to the size of the training set. If the training set is too large, processing a large amount of data at once will affect its computational performance. Since the training set used in this invention is relatively small, the `newrbe` function, which offers higher model construction efficiency and accuracy, is chosen to construct the RBF response surface model.

[0084] When dealing with this problem in Matlab, the values ​​of each parameter can be obtained using the following function command. Where s ti Obtained via net.LW{1,1}, w ij k is obtained through net.LW{2,1}. ij b is obtained through net.b{1,1}. j The parameters are obtained via net.b{2,1}. Once these parameters are obtained, the response surface model expression based on the radial basis function can be determined, and its optimal solution can be obtained using an intelligent algorithm.

[0085] In this embodiment, the whale optimization algorithm is an algorithm derived from the hunting behavior of humpback whale groups. It iteratively optimizes by imitating three strategies of whales: wandering search, encirclement and contraction, and spiral hunting. The advantages of the algorithm are that it is simple in principle, has strong optimization ability, and requires few parameters to be adjusted. For the hyperparameter optimization problem of the radial basis function response surface model, since there is only one hyperparameter to be optimized, the whale optimization algorithm is very suitable.

[0086] Humpback whales swim in a spiral trajectory around their prey within a gradually shrinking circle. To simulate this behavior, it is assumed that the optimal position of a whale in a certain population is the position of the target prey, and that the probability of choosing either a hunting method that involves searching for an encirclement or a spiral bubble net to update the whale's position during the optimization process is 50% each. That is, there is a random number p between [0,1].

[0087] When p≥0.5, the position update is performed using a spiral bubble net predation method, as shown in equation (3).

[0088] Z(t+1)=L·e bλ cos(2πλ)+Z * (t) (3)

[0089] Z * (t) represents the position of the whale that achieves the global optimal solution within the t-th generation of the population, where L = |Z * (t)-Z(t)| represents the distance between the whale and its prey, b is a constant that controls the shape of the logarithmic spiral, and λ is a random number on [-1,1].

[0090] When p < 0.5, a predation method of searching and surrounding is used for position updates, and the absolute value of the coefficient vector A is used to determine whether it is the prey search phase or the surrounding phase.

[0091] When |A|<1, the prey encirclement phase begins, and the position is updated as shown in equation (4).

[0092]

[0093] Where L' represents the encirclement step size, A and C are coefficient vectors, r is a random number between [0,1], a is the convergence factor, which decreases linearly from 2 to 0 with the increase of the number of iterations, and T max This represents the maximum number of iterations.

[0094] When |A|≥1, the prey search phase begins, and the position is updated as shown in equation (5).

[0095]

[0096] Z rand(t) represents a randomly selected individual position from the current population, and L” represents the search step size. For example... Figure 5 As shown.

[0097] In this embodiment, the method for optimizing the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model includes:

[0098] The length of the oil baffle was selected as the optimization variable, and its value range was determined.

[0099] Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets;

[0100] Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench.

[0101] Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set.

[0102] The final WOA-RBF response surface model is generated using the training set and expanded coefficient values;

[0103] Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

[0104] Specifically, the calculation model of this invention is a 110kV oil-immersed transformer. Considering the axisymmetric structure of its windings, a two-dimensional transformer winding eight-section non-turn model is established, and the length of the baffle in each section is parameterized to facilitate the subsequent acquisition of the output response (i.e., the hot spot temperature under each baffle size) of the training and test sets of the response surface model.

[0105] The test winding was equivalent to an eight-section winding turn-by-turn model, such as Figure 3 As shown in (a), the test winding has eight sections, numbered 1-8 from top to bottom. Sections 1-3 contain 7 coils, and sections 4-8 contain 9 coils, for a total of 66 coils. Each coil consists of 15 turns of wire, and each turn is made of 2 copper wires wound together. Since this invention requires optimization of the winding baffle structure, each update of the baffle size during the acquisition of the training and test sets necessitates re-meshing. To improve the efficiency of modeling and simulation, a non-turn-divided model (such as...) is adopted. Figure 3 (b) The effect of inter-turn insulation is considered by using the equivalent thermal conductivity to reduce the number of mesh divisions and improve computational efficiency. Figure 3(c) The relevant dimensions of a single-turn winding and oil passage within a partition are given, where the baffle thickness is 1.5 mm. The calculated equivalent thermal conductivity is 1.6248 W / (m·K) for axial direction and 0.7813 W / (m·K) for radial direction. The transformer's current-thermal coupling calculation was performed using the finite element software Fluent.

[0106] Since Fluent 18.0 itself does not have the function of modeling and exporting hotspot temperatures, in order to automatically update the baffle size and obtain the hotspot situation under the corresponding size, this invention uses Workbench 18.0 to realize the model building, subdivision, calculation and result export operations. The specific interface is shown in the figure below.

[0107] In the actual calculation process, hotspot temperature response values ​​for the training and test sets are obtained through mutual calls between Matlab and Workbench. The connection between the two is achieved through a GUI command script that records the Workbench operation process. The process of mutual calling to obtain data is described in [link to script]. Figure 4 .

[0108] Specifically, such as Figure 6 As shown, the optimization process for the baffle structure based on the WOA-RBF response surface model is as follows:

[0109] First, we need to determine the optimization variables. According to the calculation model, the winding has been determined to be divided into eight sections, so the number and position of the baffles are fixed. We only need to optimize the baffle size. Since the thickness of each of the seven baffles is much smaller than its length, we select the baffle length as the optimization variable. The number of variables is seven.

[0110] Next, the range of values ​​for the optimization variables needs to be determined. Considering that the function of the baffle is to divide the oil passages, it cannot be too long to completely block a section, nor too short to fail to guide the section. After comprehensive consideration, the range of baffle size variation is selected as the width of the vertical oil passage on the adjacent side plus 138mm (winding width). The lengths of each baffle are named D1, D2, D3, D4, D5, D6, and D7 from top to bottom, as follows: Figure 3 As shown in (b). The lengths of D1, D3, D5, and D7 vary from [10mm to 148mm]; the lengths of D2, D4, and D6 vary from [8mm to 146mm]. Figure 3 (b) The lengths of each baffle structure are [D1,D2,D3,D4,D5,D6,D7] = [148mm,146mm,148mm,146mm,148mm,146mm,148mm].

[0111] Based on the number and range of variables, Latin Hypercube Sampling (LHS) was used for experimental design to obtain the sample distributions of the training and test sets. The response values ​​(hot spot temperatures) of the training and test sets were obtained through mutual calls between Matlab and Workbench. Then, the expansion coefficient values ​​that minimize the root mean square error of the test set were determined using the training and test set data combined with the whale optimization algorithm. The final RBF response surface model was generated using the training set and the optimal expansion coefficient, as shown in Equation (2). This equation was then optimized using an intelligent algorithm to obtain the baffle size parameters that minimize the winding hot spot temperature.

[0112] Example 2

[0113] The present invention also provides a system for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding, comprising: a first construction module, a second construction module, and an optimization module;

[0114] The first building module is used to construct the RBF response surface model;

[0115] The second building module is used to obtain the optimal hyperparameters of the RBF response surface model using the whale optimization algorithm, and to construct the WOA-RBF response surface model.

[0116] The optimization module is used to optimize the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model.

[0117] In this embodiment, the process of constructing the RBF response surface model includes:

[0118] Gaussian functions are used as radial basis functions;

[0119] An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command.

[0120] Based on the parameter values, the expression for the RBF-based response surface model is determined.

[0121] In this embodiment, the expression for the radial basis function is:

[0122]

[0123] in: m is the number of input variables; n is the number of test sets, i.e., the number of hidden layers; j is the j-th output variable; w ij The weights from the i-th hidden layer to the j-th output layer; s ti x is the value corresponding to the t-th input variable in the i-th test set; t Let k be the t-th input variable; ijb is the threshold from the i-th hidden layer to the j-th output; j The intercept of the j-th output.

[0124] In this embodiment, the method for obtaining the parameter values ​​of the radial basis function using the net.related command includes:

[0125] In Matlab, the value of `sti` is obtained using `net.LW{1,1}`; the value of `wij` is obtained using `net.LW{2,1}`; the value of `kij` is obtained using `net.b{1,1}`; and the value of `b` is obtained using `net.b{2,1}`. j The value of .

[0126] In this embodiment, the process of optimizing the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model includes:

[0127] The length of the oil baffle was selected as the optimization variable, and its value range was determined.

[0128] Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets;

[0129] Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench.

[0130] Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set.

[0131] The final WOA-RBF response surface model is generated using the training set and expanded coefficient values;

[0132] Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

[0133] Example 3

[0134] This invention also compares and analyzes WOA with grid search optimization methods from the perspective of hyperparameter optimization. Furthermore, the optimization results are compared with the flow-temperature field distribution under the original baffle size, the optimization results based on the quadratic polynomial response surface model, and the optimization results based on the genetic algorithm to verify the effectiveness of the proposed method.

[0135] In this embodiment, considering the influence of the selection of different training sets and test sets on obtaining the optimal hyperparameters, the present invention performs K-fold cross-validation (K-CV) on this data set. Under different groups of training sets and test sets, the root mean square error is used as the fitness function, and a comparison is made between the Grid Search (GS) optimization method and the WOA hyperparameter optimization method. The initial grouping for cross-validation is 10, the range of variation of the hyperparameter spread is [1, 1800], the step size is 0.8995, and the termination condition for judgment is that the relative error of the optimal value between two adjacent iterations is within 10 -4 or less, and the comparison results are shown in Table 1.

[0136] Where K is the fold in which the test set is located in the 10-fold data. According to Table 1, the root mean square error distribution diagrams are drawn for each group of test sets and data sets when the optimal spread parameter is taken as shown in Figure 7 shown. <0​​​​​​​​​​​​​​​​​​​​​​​It can be seen that the overall fitting effect of the predicted value and the control value tends to be a straight line y=x. The maximum error of the test set data appears in the 7th group, that is, the predicted value data is 360.93K and the control value data is 360.33K. The maximum relative error of Celsius is 0.697%, which meets the error requirement. The established WOA-RBF response surface model meets the applicability test of the model.

[0143] Based on the trained response surface model, the required parameters are obtained using the `net.` command in Matlab, yielding the corresponding radial basis function expression. A genetic algorithm is then used to optimize this expression to obtain the minimum hot spot temperature of the transformer winding and its corresponding baffle size. The initial population size is 40 individuals, with a generation gap of 0.8, a mutation probability of 0.03, a crossover probability of 0.7, and 1000 generations.

[0144] The final solution yielded a minimum hotspot temperature of 359.82 K, corresponding to the dimensions of the seven baffles from top to bottom: D1 = 102.7179 mm, D2 = 111.5001 mm, D3 = 87.6249 mm, D4 = 42.4999 mm, D5 = 115.8886 mm, D6 = 27.8120 mm, and D7 = 113.5001 mm, with a time of 55.16 s.

[0145] Considering the actual manufacturing capabilities of the project, the dimensions were rounded to D1 = 103mm, D2 = 112mm, D3 = 88mm, D4 = 42mm, D5 = 116mm, D6 = 28mm, and D7 = 114mm. Using Fluent, the rounded hotspot value of the baffle was calculated to be 360.05K. This hotspot value was used as a reference value for the optimization results. The lowest hotspot temperature obtained based on the WOA-RBF response surface model differed from the reference value by only 0.23K, with a relative error of 0.265% in Celsius. The optimization results met the accuracy requirements, proving the accuracy of the optimization results based on the WOA-RBF response surface model. The total process time was 390862.16s, approximately 108.57 hours, including 390807s for calculating the hotspot temperature rise of 200 datasets and 55.16s for model training and optimization.

[0146] In this embodiment, a comparison of the results under optimized front and rear baffle dimensions is shown in Table 2.

[0147] Table 2

[0148]

[0149] Table 2 compares the hot spot values ​​before and after baffle size optimization. The optimized winding baffle structure effectively reduced the hot spot value by 3.8K, while the inlet temperature remained at 62.31℃. Under the original structure, the maximum temperature rise was 28.39℃; after optimization, the maximum temperature rise was 25.39℃, a reduction of 13.4%. Detailed comparisons before and after optimization are analyzed based on the flow field and temperature field results for each group, such as... Figure 9 As shown.

[0150] according to Figure 9 (a) It can be observed that before optimization, the highest temperature in each zone occurred on the coil above the baffle of the adjacent zone. The figure marks the coils with large local temperature rises in each zone. Under the optimized baffle size, these areas with large local temperature rises have all improved, especially coils 7, 14, 21, and 30 in the first four zones. Therefore, the optimized baffle structure not only reduces the winding hot spot temperature but also effectively suppresses the excessive local temperature rise in each zone, which is a method for improving the temperature field across the entire winding. This verifies the effectiveness of the optimized baffle size in improving the temperature field distribution of the transformer winding. A comparison of the fluid fields before and after optimization is conducted to analyze the reasons for the above improvements, such as... Figure 9 (b) It can be seen that before optimization, there was almost no oil flow in the oil channel between the baffle between the two sections and the last line cake of the previous section (marked in the figure). However, after optimization, due to the reduction in the size of the baffle, the oil flow can bypass the baffle to a certain extent and contact the adjacent line cake of the previous section. The presence of oil flow will bring better heat dissipation. Therefore, the temperature improvement effect on the last line cake of each section is the most obvious in the temperature field.

[0151] In this embodiment, conventional winding structure optimization typically uses a quadratic polynomial (QP) response surface model, while this invention employs an RBF response surface model. To illustrate the impact of response surface model selection on the optimization results, this invention compares the optimization results with those of traditional QP response surface design optimization to verify the effectiveness of the RBF response surface model of this invention.

[0152] First, K-fold cross-validation is performed on the QP response surface model to obtain the best combination of training and test sets with K=10.

[0153] Table 3

[0154]

[0155] Table 3 shows that the overall mean squared error of the QP response surface model is slightly smaller than that of the RBF response surface model. In the QP response surface model, the minimum mean squared error still occurs in the fourth fold of the test set. The remaining data are used as the training set. Using this data combination, both the RBF and QP response surface models are trained. To better compare the fitting performance of the two response surface models, the errors at each point of the 20 test sets are compared. Figure 10 As shown.

[0156] analyze Figure 10 It can be seen that the maximum relative error in Celsius for both response surface models is 0.697%. Furthermore, the relative errors for other test points show fluctuations between the two models. Considering that the mean square error of the two models is not significantly different when K=4, it is impossible to determine which model is superior in terms of fitting performance. Further optimization of the two models is then performed, and the optimization results are compared, as shown in Table 4.

[0157] Table 4

[0158]

[0159] As shown in Table 4, although the hotspot values ​​calculated by the QP response surface model are smaller, their deviation from the control values ​​is 10.6 times that of the RBF response surface model. Furthermore, the simulated hotspot values ​​corresponding to the QP model's dimensions are also larger than those of the RBF model. This indicates that the RBF model yields a better solution than the QP model. This demonstrates that the optimization accuracy and capability of the QP response surface model are lower than those of the RBF model, validating the effectiveness of using the RBF response surface model in this invention.

[0160] In this embodiment, to verify whether the optimization results obtained by the response surface method have reached the optimal level, the present invention uses a global optimization algorithm—genetic algorithm—for optimization comparison. It should be noted that the construction and optimization of the RBF response surface model under the optimal hyperparameters of the present invention is solved by the genetic algorithm, which is the expression of the radial basis function response surface model. The comparison with the optimization results of the genetic algorithm (GA) is to regard the baffle structure optimization as a "black box problem" and use the genetic algorithm for optimization solution.

[0161] The genetic algorithm parameters are set as follows: population size per generation is 40, generation gap is 0.8, mutation probability is 0.01, and maximum number of iterations is 100. To accelerate computation, this invention uses a distance method to filter individuals in adjacent generations, identifying unmutated individuals to avoid repeated calculations and save computation time. The optimization process of the genetic algorithm results is as follows: Figure 11 As shown.

[0162] Figure 11The variation curves of the hotspot optimal solution of the offspring population after 100 iterations of the genetic algorithm are given. The hotspot optimal solution reaches its minimum value around the 50th generation and stabilizes at a value of 359.99K. The values ​​of the obtained optimization variables are shown in Table 5.

[0163] Table 5

[0164]

[0165] According to Table 5, although the baffle size after optimization by the genetic algorithm is not exactly the same as that of the RBF response surface model, the value trends of each group of variables are consistent. Moreover, the minimum hot spot value after optimization differs by 0.06K, and the relative error in Celsius is only 0.07%, which meets the error requirements. Therefore, it can be found that the baffle structure optimization is a multi-solution problem. Both the RBF response surface model and the GA optimization results can be considered as the global optimal solutions, which verifies the reliability of the RBF response surface model optimization results. Furthermore, the computation time of GA is 13.5 times that of the RBF response surface model, indicating that the RBF response surface model is a method that can balance optimization accuracy and efficiency, and is more suitable for application in engineering practice.

[0166] To address the shortcomings of traditional RBF response surface models, this invention proposes combining intelligent optimization algorithms with RBF response surface models to determine optimal hyperparameters and achieve better model fitting and optimization results. Intelligent optimization algorithms can achieve global optimization through effective design, and for models with explicit expressions, they are extremely efficient. Compared with other optimization algorithms, the Whale Optimization Algorithm (WOA) is not only simple in principle and requires fewer manually adjusted parameters, but also has advantages in computational speed. It is particularly suitable for single-parameter optimization problems such as RBF response surface models. Therefore, this invention considers using a WOA-RBF response surface model to optimize the dimensions of transformer winding baffles.

[0167] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for optimizing the size of an oil retaining plate of an oil immersed transformer winding, characterized in that, Includes the following steps: Based on the size and structural parameters of the transformer winding oil baffle, an RBF response surface model is constructed. The optimal hyperparameters of the RBF response surface model are obtained using the whale optimization algorithm, and the WOA-RBF response surface model is constructed. Based on the WOA-RBF response surface model, the size and structure of the transformer winding oil baffle were optimized. The method for optimizing the size and structure of transformer winding oil baffles based on the WOA-RBF response surface model includes: The length of the oil baffle was selected as the optimization variable, and its value range was determined. Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets; Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench. Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set. The final WOA-RBF response surface model is generated using the training set and the expanded coefficient values; Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

2. The oil-immersed transformer winding oil barrier size structure optimization method according to claim 1, characterized in that, Methods for constructing RBF response surface models include: Based on the size and structural parameters of the transformer winding oil baffle, the Gaussian function is used as the radial basis function; An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command. Based on the parameter values, the RBF-based response surface model expression is determined.

3. The oil-immersed transformer winding oil barrier size structure optimization method according to claim 2, characterized in that, The expression for the radial basis function is: in: , m The number of input variables; n The number of test sets is equivalent to the number of hidden layers; j For the first j One output variable; w ij For the first i The hidden layer to the first j The weights of each output layer; s ti For the first i The first test set t The values ​​corresponding to each input variable; x t For the first t One input variable; k ij For the first i The hidden layer to the first j The threshold for each output; b j For the first j The intercept of each output.

4. The method for optimizing the size and structure of the oil baffle plate of an oil-immersed transformer winding according to claim 3, characterized in that, Methods for obtaining the parameter values ​​of the radial basis function using net-related commands include: In Matlab, you can obtain the value using net.LW{1,1}. The value is obtained through net.LW{2,1}. The value; obtained through net.b{1,1} The value is obtained through net.b{2,1}. The value of .

5. A system for optimizing the size and structure of an oil-immersed transformer winding oil baffle, characterized in that, include: First building module, second building module, and optimization module; The first construction module is used to construct an RBF response surface model based on the size and structural parameters of the transformer winding oil baffle. The second building module is used to obtain the optimal hyperparameter values ​​of the RBF response surface model using the whale optimization algorithm, and to construct the WOA-RBF response surface model; The optimization module is used to optimize the size and structure of the transformer winding oil baffle based on the WOA-RBF response surface model. Based on the WOA-RBF response surface model, the process of optimizing the size and structure of the transformer winding oil baffle includes: The length of the oil baffle was selected as the optimization variable, and its value range was determined. Based on the number of optimization variables and the range of values ​​for each optimization variable, Latin hypercube sampling is used for experimental design to obtain the sample distribution of the training and test sets; Based on the sample distribution of the training and test sets, the response values ​​of the training and test sets are obtained by calling each other between Matlab and Workbench. Using the response values ​​of the training and test sets, and combining them with the whale optimization algorithm, we determine the expansion coefficient value that minimizes the root mean square error of the test set. The final WOA-RBF response surface model is generated using the training set and the expanded coefficient values; Based on the WOA-RBF response surface model, the oil baffle size parameters with the lowest transformer winding hot spot temperature are obtained.

6. The oil-immersed transformer winding oil baffle size and structure optimization system according to claim 5, characterized in that, The process of constructing an RBF response surface model includes: Based on the size and structural parameters of the transformer winding oil baffle, the Gaussian function is used as the radial basis function; An RBF response surface model is constructed based on the newrbe function, and the parameter values ​​of the radial basis function are obtained using the net.related command. Based on the parameter values, the RBF-based response surface model expression is determined.

7. The oil-immersed transformer winding oil baffle size and structure optimization system according to claim 6, characterized in that, The expression for the radial basis function is: in: , m The number of input variables; n The number of test sets is equivalent to the number of hidden layers; j For the first j One output variable; w ij For the first i The hidden layer to the first j The weights of each output layer; s ti For the first i The first test set t The values ​​corresponding to each input variable; x t For the first t One input variable; k ij For the first i The hidden layer to the first j The threshold for each output; b j For the first j The intercept of each output.

8. The oil-immersed transformer winding oil baffle size and structure optimization system according to claim 7, characterized in that, Methods for obtaining the parameter values ​​of the radial basis function using net-related commands include: In Matlab, you can obtain the value using net.LW{1,1}. The value is obtained through net.LW{2,1}. The value; obtained through net.b{1,1} The value is obtained through net.b{2,1}. The value of .

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