Multi-objective optimization method for transformer main insulation-magnetic shield structure considering insulation confidence constraint and multi-physics agent correction

Abstract

The present application relates to a kind of transformer main insulation-magnetic shield structure multi-objective optimization method considering insulation confidence constraint and multi-physical field agent correction, belong to power transformer structure optimization technical field, this method with high-low voltage winding interval main insulation oil gap, iron core and low voltage winding interval oil gap and oil tank magnetic shield patch length-width-thickness as collaborative design variable, establish multi-working condition electric field parameterization finite element model;Kriging target and constraint agent model of output prediction mean and prediction standard deviation are respectively constructed, to construct insulation safety control with insulation safety margin limit value and prediction confidence upper limit;After optimization by constraint domination NSGA-II, based on prediction uncertainty, insulation boundary proximity, Pareto front sparsity and pre-decision priority, candidate solution is selected to carry out finite element review and active point addition correction;Finally, based on insulation safety priority and TOPSIS method, the structure parameters reviewed are output.

Description

Technical Field

[0001] This invention belongs to the field of power transformer structure optimization technology, and relates to a multi-objective optimization method for transformer main insulation-magnetic shielding structure that takes into account insulation confidence constraints and multi-physics proxy correction. Background Technology

[0002] As a core piece of equipment in the power system, the operational reliability, insulation safety, thermal stability, and manufacturing economy of power transformers directly affect grid security and equipment costs. With the development of power systems towards higher voltage, larger capacity, higher load rates, and a higher proportion of renewable energy integration, transformers may experience operating conditions such as load fluctuations, harmonic currents, increased ambient temperature, and decreased cooling capacity. The coupling relationships between internal electromagnetic fields, loss fields, thermal-fluid fields, and insulation electric fields become more complex, making it difficult to meet the requirements of refined design by simply relying on empirical formulas or single-physical field verification.

[0003] The main insulation distance and magnetic shielding structure of a transformer are important structural parameters affecting internal safety margins and manufacturing costs. The distance between the main insulation oil gaps of the high-voltage and low-voltage windings directly affects the maximum electric field strength and insulation margin in the oil, and also changes the leakage flux path and oil channel size between windings; the distance between the core and the low-voltage winding oil gap affects the insulation strength, leakage flux distribution, and oil flow resistance of the inner side of the low-voltage winding; the length, width, and thickness of the magnetic shielding patch in the tank affect the stray losses of the tank wall structural components, the leakage flux density at the winding ends, and the cost of metal materials. These variables do not exist in isolation, but simultaneously affect the electric field, leakage flux, eddy current losses, oil flow resistance, hot spot temperature, and manufacturing costs.

[0004] Existing transformer optimization methods typically use the maximum electric field strength in the oil as the verification index after optimization, or employ a simple penalty function to handle insulation constraints. This approach does not utilize surrogate models to predict uncertainties and cannot conservatively screen candidate solutions near the insulation breakdown boundary, easily leading to situations where the surrogate model predicts feasibility but the finite element method (FEM) verification exceeds limits. For insurmountable hard constraints such as insulation safety, a consistent safety control relationship needs to be established between the allowable electric field strength, safety margin limits, surrogate model prediction confidence upper bounds, and finite element verification results.

[0005] Furthermore, existing surrogate model optimization processes often employ a one-time sample training approach followed by direct optimization. When the initial sample size is limited and the relationship between design variables and multiphysics responses is highly nonlinear, the Kriging model may exhibit significant errors near the Pareto front, insulation constraint boundaries, or in high uncertainty regions, leading to a lack of engineering credibility in the final optimized solution. If active point addition is based solely on prediction errors without simultaneously considering insulation boundaries, Pareto solution sparsity, and engineering decision priorities, finite element verification resources will struggle to concentrate on the candidate solutions with the highest engineering value.

[0006] Therefore, it is necessary to provide a multi-objective optimization method for the main insulation-magnetic shielding structure of transformers, which combines multi-condition multi-physics field finite element response, Kriging prediction mean and prediction standard deviation, insulation confidence constraint, constraint dominance NSGA-II, finite element verification based on multi-factor active point scoring and closed-loop correction, so as to optimize hot spot temperature, leakage flux density and material manufacturing cost while ensuring insulation safety. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide a multi-objective optimization method for transformer main insulation-magnetic shielding structure that takes into account insulation confidence constraints and multi-physics proxy correction.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multi-physics proxy correction includes the following steps: S1: Determine the multi-condition operating set and collaborative design variables of oil-immersed power transformers; S2: Establish a multiphysics parameterized finite element model of the transformer; S3: The initial samples are generated using the Latin hypercube sampling method optimized by the maximum-minimum distance criterion, and the multi-response dataset is obtained using the parameterized finite element model. S4: Establish a Kriging surrogate model of the target response and insulation constraints; S5: Construct an insulation safety control based on the insulation safety margin limit and the upper bound of Kriging prediction confidence, and embed this control as a hard constraint into the constraint-dominated NSGA-II algorithm; S6: Perform multi-objective optimization using the constrained dominance NSGA-II algorithm to obtain the Pareto candidate solution set; S7: Perform finite element verification on the candidate solutions with the highest scores, and add the verified samples to the training sample set to correct the surrogate model; S8: Select the final structural optimization scheme from the qualified Pareto solution set based on insulation safety priority and TOPSIS method.

[0009] Furthermore, in step S1, the multi-condition operating set includes one or more of the following: rated load condition, overload condition, high ambient temperature condition, harmonic current condition, and cooling capacity reduction condition. The collaborative design variables are structural parameters related to main insulation and magnetic shielding, and are expressed as follows:

[0010] In the formula, d1 represents the distance between the main insulating oil gaps of the high-voltage and low-voltage windings. d 2 represents the oil gap distance between the iron core and the low-voltage winding. L s The length of the magnetic shielding patch for the fuel tank. W s The width of the magnetic shielding patch for the fuel tank. T s The thickness of the magnetic shielding patch for the fuel tank.

[0011] Furthermore, in step S2, the oil gap between the high and low voltage windings, the oil gap between the core and the low voltage winding, and the size of the magnetic shielding patch in the oil tank are automatically updated based on the collaborative design variable x. A three-dimensional parametric finite element model is established, and the electromagnetic field, loss field, thermal-fluid field, and insulation electric field are calculated sequentially. The finite element output response vector is:

[0012] In the formula, T hs This refers to the hot spot temperature of the winding. C For material manufacturing costs, B max This refers to the maximum leakage flux density of the winding or the maximum leakage flux density in the critical area. E max The maximum electric field intensity in the main insulating oil gap is used; for the hot spot temperature, leakage flux density, and maximum electric field intensity in the oil, the maximum value among the calculation results for each operating condition is taken as the optimization evaluation response.

[0013] The material manufacturing cost C is calculated based on the volume of insulating oil, the amount of insulating components, and the quality of magnetic shielding patches, as well as their unit material costs, caused by changes in co-design variables.

[0014] Furthermore, in the parameterized finite element model, the electromagnetic field model is used to obtain the winding leakage flux density, winding eddy current loss, and structural component stray loss; the winding eddy current loss and structural component stray loss are mapped to the heat source load input heat-flow field model to obtain the insulating oil velocity distribution, winding hot spot temperature, and top layer oil temperature; the insulating electric field model is used to obtain the maximum electric field intensity in the oil of the main insulating region; under the harmonic current condition, the AC loss corresponding to each frequency component is calculated and superimposed to form the heat source load.

[0015] Furthermore, the insulation safety control in step S5 includes a baseline limit for finite element verification, a safety margin limit for engineering design, and a surrogate model confidence constraint for optimization screening; wherein, the maximum electric field strength in the oil verified by the finite element method does not exceed the allowable electric field strength threshold of the insulating oil, the maximum electric field strength in the oil verified by both the engineering design and the finite element method does not exceed the insulation safety margin limit, and the surrogate model confidence constraint is that the sum of the predicted mean of the maximum electric field strength in the oil and the confidence coefficient times the predicted standard deviation does not exceed the insulation safety margin limit.

[0016] Furthermore, in step S6, the constraint-dominant NSGA-II algorithm prioritizes retaining individuals that satisfy the insulation confidence constraint in the non-dominant sorting; when both individuals satisfy the insulation confidence constraint, they are sorted according to the Pareto dominance relationship and the crowding distance; when neither individual satisfies the insulation confidence constraint, individuals with a smaller degree of insulation constraint violation are prioritized for retention.

[0017] Furthermore, in step S7, the verification samples actively added to the training sample set are determined by active scoring, which is obtained by weighting the normalized Kriging prediction standard deviation, the proximity of the insulation confidence constraint boundary, the Pareto front crowding distance, and the pre-decision TOPSIS priority. A preset number of candidate solutions are selected for finite element verification according to the active scoring from high to low, wherein the candidate solutions with larger Pareto front crowding distances correspond to sparse solution distribution regions.

[0018] Furthermore, the surrogate model error evaluation index includes at least one of RMSE, MAE, coefficient of determination R2, prediction coefficient of determination Q2, leave-one cross-validation error, and insulation constraint boundary sample prediction error; when the surrogate model errors for hot spot temperature, maximum leakage flux density of winding, maximum electric field strength in oil, and material manufacturing cost all meet the preset threshold, and the insulation constraint boundary sample prediction error meets the preset threshold, the optimization step is initiated.

[0019] Furthermore, the TOPSIS method first eliminates candidate solutions that do not meet the insulation confidence constraint and engineering manufacturing constraint before constructing the evaluation matrix; it uses a combination of subjective safety priority weight and objective dispersion weight to determine the weight of each evaluation index, and the weight of the insulation safety margin index and the hot spot temperature index are not less than the weight of the material manufacturing cost index.

[0020] Furthermore, the output includes the final oil gap distance between the main insulation between the high and low voltage windings, the oil gap distance between the core and the low voltage winding, the length of the magnetic shielding patch in the oil tank, the width of the magnetic shielding patch in the oil tank, the thickness of the magnetic shielding patch in the oil tank, as well as the hot spot temperature, material manufacturing cost, maximum leakage flux density of the winding, maximum electric field strength in the oil, insulation safety margin, and finite element verification error corresponding to each operating condition.

[0021] The beneficial effects of this invention are as follows: 1. By limiting the optimization object to the main insulation distance-magnetic shielding structure-oil channel thermal resistance coupling structure, it can reflect the combined effects of five structural variables on electric field, leakage flux, loss, oil flow, hot spot and cost; 2. Insulation safety control is divided into finite element verification benchmark limits, safety margin limits, and surrogate model confidence screening, so that Kriging prediction uncertainty can directly participate in engineering safety judgment; 3. Improve the credibility of the Pareto front in high-risk and high-engineering-value regions by finite element verification and active point addition correction of high uncertainty, near-insulating boundary, sparse region of Pareto front and pre-decision TOPSIS candidate solutions; 4. Use constraint-dominant NSGA-II to reduce the interference of infeasible solutions on the search process; 5. By prioritizing safety, TOPSIS outputs a unique engineering solution, reducing the uncertainty of manual experience-based selection.

[0022] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0023] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating the overall process of the method described in this invention. Figure 2 Schematic diagram of design variables for the main insulation-magnetic shielding structure; Figure 3 A link diagram for multi-condition, multi-physics field finite element simulation; Figure 4 Flowchart for constructing the Kriging proxy model and insulation confidence constraints; Figure 5 NSGA-II optimization flowchart for constraint control; Figure 6 Flowchart for finite element verification and active point addition correction of Pareto candidate solutions; Figure 7 Safety First TOPSIS Engineering Decision Flowchart. Detailed Implementation

[0024] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0025] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0026] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0027] Example 1: Please see Figure 1-Figure 7 This invention provides a multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multi-physics proxy correction, comprising the following steps: S1. Determine multi-condition inputs and structural design variables; In this embodiment, a multi-condition operating set for the target oil-immersed power transformer is established. The multi-condition operating set includes at least one of the following: rated load condition, overload condition, high ambient temperature condition, harmonic current condition, and cooling capacity reduction condition. The main insulation and magnetic shielding related structural parameters are selected as design variables to form a design variable vector:

[0028] In the formula, d 1 represents the distance between the main insulating oil gaps of the high-voltage and low-voltage windings. d 2 represents the oil gap distance between the iron core and the low-voltage winding. L s The length of the magnetic shielding patch for the fuel tank. W s The width of the magnetic shielding patch for the fuel tank. T s The thickness of the magnetic shielding patch for the fuel tank. All design variables satisfy the manufacturing, insulation, and assembly boundary conditions:

[0029] The multi-condition set is represented as:

[0030] S2. Establish a multi-physics parametric finite element model of the transformer; in this embodiment, based on the design variable vector... x The system automatically updates the oil gaps between high- and low-voltage windings, the oil gap between the core and the low-voltage winding, and the dimensions of the magnetic shielding patch in the oil tank. A three-dimensional parametric finite element model is established, and electromagnetic field, loss field, thermal-fluid field, and insulation electric field calculations are performed sequentially. The finite element output response vector is:

[0031] In the formula, T hs This refers to the hot spot temperature of the winding. C For material manufacturing costs, B max This refers to the maximum leakage flux density of the winding or the maximum leakage flux density in the critical area. E max The maximum electric field strength in the main insulating oil gap is taken. For the hot spot temperature, leakage flux density, and maximum electric field strength in the oil, the maximum value among the calculated results for each operating condition is used as the optimized evaluation response.

[0032] The material manufacturing cost C is calculated based on the changes in insulating oil volume, insulating component usage, and magnetic shielding patch mass caused by variations in design variables. Specifically, it includes the cost of insulating oil, insulating materials, magnetic shielding materials, and fixed manufacturing costs that do not change with the design variables. The mass of the magnetic shielding patch is determined by… L s , W s , T s And the density of the magnetic shielding material was determined.

[0033] S3. Generate initial samples and obtain a multi-response dataset; In this embodiment, the Latin hypercube sampling method optimized by the maximum-minimum distance criterion is used to generate initial sample points in the design variable space. For each set of sample points, a parameterized finite element model is called to obtain the corresponding hotspot temperature, manufacturing cost, maximum leakage flux density of the winding, and maximum electric field strength in the oil, forming the initial training dataset.

[0034] S4. Establish Kriging surrogate models for target response and insulation constraints; in this embodiment, Kriging surrogate models are established for hotspot temperature, manufacturing cost, maximum leakage flux density of windings, and maximum electric field strength in oil, respectively. j The Kriging model for each response is represented as:

[0035] in For deterministic regression terms ，Z j (x) With a mean of zero and a variance of s j 2 It is a stochastic process exhibiting spatial correlation. The correlation function can be expressed as:

[0036] The Kriging model outputs the predicted mean and predicted standard deviation:

[0037]

[0038] The surrogate model error is calculated using cross-validation or test set validation. Error metrics include root mean square error, mean absolute error, coefficient of determination, and prediction coefficient of determination.

[0039]

[0040] When both the target response model and the insulation constraint model meet the preset error threshold, and the prediction error of the insulation constraint boundary sample meets the preset threshold, the multi-objective optimization step is entered; when the model error, insulation boundary sample error, or key Pareto candidate solution verification error does not meet the requirements, active point addition update is performed.

[0041] S5. Construct an insulation safety control system based on insulation safety margin limits and Kriging prediction confidence upper bounds, and use this control for optimization screening and finite element verification. In this embodiment, a three-level insulation safety control system of "benchmark limit—safety margin limit—surrogate model confidence screening" is adopted. The first layer is the benchmark limit for finite element verification, used to identify structures that are obviously infeasible.

[0042] The second layer consists of safety margin limits for engineering design and finite element verification:

[0043] The third layer is the surrogate model confidence screening used in the optimization process, constructed based on the Kriging predicted mean and predicted standard deviation:

[0044] In the formula, the first two layers E max ( x The maximum electric field strength in the oil obtained from the finite element method verification is denoted as . m E ( x The value represents the mean value predicted by the surrogate model for the maximum electric field strength in oil. s E ( x ) represents the predicted standard deviation of the maximum electric field strength in oil. k , is the confidence coefficient or For insulation safety margin factor, E lim This refers to the allowable electric field strength threshold for insulating oil determined under corresponding oil type, temperature, water content, field type, and voltage waveform conditions. The insulation constraint violation degree during the optimization phase is defined as:

[0045] only v E ( x Only individuals with )=0 are considered feasible individuals for insulation in the optimization stage; after finite element verification, those that satisfy... E max ( x )≤ theE lim Only those individuals that meet the criteria are considered as ultimately feasible insulators.

[0046] S6. NSGA-II Multi-Objective Optimization Based on Constraint Dominance Rules; In this embodiment, hotspot temperature, manufacturing cost, and maximum leakage flux density of the winding are the objective functions to be minimized, and insulation confidence constraints are used as hard constraints to construct a multi-objective optimization problem:

[0047] In the non-dominated sorting process, if individual a satisfies the insulation confidence constraint while individual b does not, then individual a constrains and dominates individual b; if both individuals a and b satisfy the insulation confidence constraint, then they are sorted according to Pareto dominance and crowding distance; if neither satisfies the insulation confidence constraint, then the one with the lower violation degree takes priority.

[0048] S7. Finite Element Verification and Active Point Addition Correction of Pareto Candidate Solutions: Three types of candidate samples are selected from the Pareto solution set for finite element verification: the first type is candidate solutions with large Kriging prediction standard deviations; the second type is candidate solutions close to the insulation confidence constraint boundary; the third type is candidate solutions ranked high in the pre-decision TOPSIS or in Pareto front areas with large crowding distances and sparse solution distribution. Active point addition scoring can be expressed as:

[0049] In the formula, (x) represents the normalized prediction uncertainty, bE(x) represents the proximity to the insulation boundary, cP(x) represents the normalized Pareto front crowding distance, qT(x) represents the pre-decision TOPSIS priority obtained based on the surrogate model's predicted response, and λ1 to λ4 are non-negative weight coefficients with a sum of 1. A preset number of m candidate solutions are selected from high to low according to Sadd(x) for finite element verification. All verified samples and their finite element responses are added to the training sample set. When the error between the finite element verification result and the surrogate model's prediction result exceeds a preset threshold, or when the verified sample is located near the insulation constraint boundary, the Kriging surrogate model is retrained, and the process returns to step S5 for further optimization.

[0050] The closed-loop stopping condition is that the surrogate model error, the insulation boundary sample error, and the Pareto solution set stability all simultaneously satisfy a threshold:

[0051] S8. Multi-attribute decision-making based on safety priority; a decision matrix is ​​established for the Pareto solution set that has passed finite element verification. First, schemes that do not meet the insulation confidence constraint and engineering manufacturing constraint are eliminated; then, hotspot temperature, manufacturing cost, maximum winding leakage flux density, and insulation safety margin are normalized. For cost-related indicators, the normalization process is as follows:

[0052] The weights of each evaluation index are determined using a combined subjective and objective weighting method. The combined weights are obtained by linearly combining the subjective safety priority weight and the objective dispersion weight, ensuring that the weights of insulation safety margin and hotspot temperature are not less than the weight of material manufacturing cost. The distances between candidate solutions and the positive and negative ideal solutions are calculated.

[0053] The relative proximity is:

[0054] The candidate solution with the highest relative similarity is selected as the final structural optimization solution:

[0055] S9. Output optimized design parameters and technical effects; output the optimal parameter combination of the main insulation oil gap distance between high and low voltage windings, the oil gap distance between the iron core and the low voltage winding, and the length, width and thickness of the magnetic shielding patch in the oil tank, and output the corresponding hot spot temperature, manufacturing cost, maximum leakage flux density of the winding, maximum electric field strength in the oil, insulation safety margin and finite element verification error.

[0056] Example 2: This embodiment takes an oil-immersed power transformer as the implementation object. First, the core size, winding size, main insulation structure, oil channel structure, oil tank structure, magnetic shielding arrangement, cooling method, silicon steel sheet magnetization curve, winding material resistivity, insulating oil thermal properties and insulating oil allowable electric field strength threshold are obtained according to the design drawings, factory test report and material manual.

[0057] This embodiment uses an oil-immersed power transformer with a rated capacity of 50MVA and a rated voltage of 110 / 10.5kV as the target object. Its main structure, insulation constraints, sampling optimization parameters, and comparison results are shown in Tables 1-3. Table 1 shows the target transformer, insulation control, and algorithm parameters; Table 2 shows the range of design variable values, manufacturing and assembly constraints, and final optimal values; and Table 3 shows the finite element verification and surrogate model error comparison of different optimization schemes.

[0058] Table 1

[0059] Table 2

[0060] Table 3

[0061] For the final preferred solution d 1=58mm d 2=28mm L s =2.05m W s =0.44m T s Finite element analysis was performed on a 6mm thick surface. Kriging's predicted hotspot temperature, maximum leakage flux density, and maximum electric field strength in the oil were 91.5℃, 0.060T, and 9.52kV / mm, respectively. The finite element analysis results were 91.8℃, 0.061T, and 9.58kV / mm, respectively. This scheme meets the requirements... m E =9.52kV / mm s E =0.13kV / mm mE + ks E =9.77kV / mm≤10.20kV / mm, and all design variables are within the manufacturing, assembly and minimum oil passage constraints.

[0062] The comparison results show that although the relative costs of the ordinary proxy model optimization and the scheme using only deterministic insulation constraints are 96.9% and 96.4% respectively, which are lower than the 98.2% of the method of this invention, the maximum electric field strength in oil obtained by their finite element verification is 10.68kV / mm and 10.45kV / mm respectively, both of which are higher than the safety margin limit of 10.20kV / mm. This indicates that the low-cost scheme is more likely to get closer to the insulation boundary, and there is a risk of misjudgment by the proxy model or insufficient insulation margin.

[0063] This invention achieves a synergistic trade-off between the main insulation oil gap, the core-to-low-voltage winding oil gap, and the size of the magnetic shielding patch. This reduces the hotspot temperature from the traditionally designed 96.8℃ to 91.8℃, and the maximum leakage flux density from 0.082T to 0.061T, while simultaneously controlling the maximum electric field strength in the oil to 9.58kV / mm. These results demonstrate that while moderately increasing the main insulation distance and magnetic shielding coverage area maintains the relative cost at 98.2%, it yields a more stable insulation safety margin and lower thermal and magnetic risks.

[0064] Regarding the number of finite element method calls, 60 sets of samples were used for initial surrogate model training, 24 sets of samples came from 3 rounds of active point addition, and another 10 sets of Par e The candidate solutions were used for the final finite element verification, totaling 94 times. Compared with directly calling the multiphysics finite element model on each generation and each individual in NSGA-II, this method has a significantly smaller call scale. At the same time, the verification resources are concentrated on candidate solutions with high uncertainty, near-insulating boundaries, and high engineering ranking, thus balancing computational efficiency and the credibility of the final solution.

[0065] In this embodiment, the design variable is selected as the distance between the main insulating oil gaps between the high-voltage and low-voltage windings. d 1. Oil gap distance between the iron core and the low-voltage winding d 2. Length of magnetic shielding patch for fuel tank L s Width of magnetic shielding patch for fuel tank W s And the thickness of the magnetic shielding patch for the fuel tank Ts . d Increasing the value of 1 usually helps to reduce the maximum electric field strength in the oil, but it will increase the distance between windings and material costs, and may change the leakage field path. d Increasing the value of 2 will change the leakage flux and oil flow path inside the low-voltage winding; L s , Ws and T s Increasing the size of the tank wall helps reduce stray losses and local leakage flux density, but it also increases material costs and affects local heat dissipation in the tank.

[0066] The multi-condition set includes the rated load, as well as at least one of the following conditions: 1.1 to 1.3 times short-term overload, high ambient temperature, load current containing specific harmonic components, and reduced cooling capacity. For each set of structural samples, the hot spot temperature, maximum leakage flux density, and maximum electric field strength in the oil are calculated under all selected conditions, and the maximum value of each response is taken as the optimization evaluation response to ensure that the final solution is not only applicable to a single rated condition.

[0067] The parametric finite element model includes an electromagnetic field module, a loss mapping module, a thermo-fluid coupling module, and an insulation electric field module. The electromagnetic field module calculates the leakage flux density near the winding ends and the tank wall, and obtains the winding eddy current loss and the stray loss of the structural components; the thermo-fluid module uses the losses as a volume heat source to calculate the oil flow velocity, the top oil temperature, and the winding hot spot temperature; the insulation electric field module solves for the maximum electric field strength in the oil in the main insulating oil gap region.

[0068] Under harmonic current conditions, the winding AC loss, eddy current loss, and stray loss of structural components are calculated according to the power frequency component and each harmonic frequency component, and the loss of each frequency component is superimposed as the heat source load of the thermal-fluid coupling module. When the operating condition includes harmonic voltage components, the insulation electric field module determines the maximum electric field intensity in the main insulating oil gap according to the quasi-static electric field calculation results of each voltage frequency component.

[0069] Material manufacturing costs are calculated based on the incremental material usage corresponding to each design variable: the oil gap between high and low voltage windings and the oil gap between the core and low voltage windings are used to calculate the volume change of insulating oil and related insulating components; the length, width, and thickness of the magnetic shielding patch are used to calculate the mass change of the magnetic shielding material; the material manufacturing cost is obtained by multiplying each material usage by the corresponding unit material cost and adding it to the fixed manufacturing cost.

[0070] The initial samples are generated using Latin hypercube sampling optimized by the maximum-minimum distance criterion. The number of samples is determined based on the variable dimension, the degree of response nonlinearity, and the cost of finite element computation, preferably no less than ten times the variable dimension. When the insulation boundary is complex or the sample error of the insulation constraint boundary of the surrogate model exceeds a preset threshold, the number of samples is increased by actively adding points. After each set of samples completes multi-condition multi-physics field calculations, a training dataset D0 is formed.

[0071] Kriging surrogate models were trained for hotspot temperature, material manufacturing cost, maximum leakage flux density of windings, and maximum electric field strength in oil, respectively. After training, RMSE, MAE, R², Q², and other indicators were calculated using a test set, K-fold cross-validation, or leave-one-out cross-validation. The electric field strength prediction error for insulation confidence constraint boundary samples was also calculated separately. For safety-related responses such as hotspot temperature and maximum electric field strength in oil, the error threshold should be stricter than that for material manufacturing cost responses; for example, the hotspot temperature prediction error should not exceed the engineering allowable temperature difference, and the electric field strength error for insulation constraint boundary samples should not exceed a preset percentage.

[0072] When constructing insulation safety controls, the first step is to adopt E max ≤ E lim As a benchmark limit for finite element verification; secondly, a safety margin coefficient is introduced. or The limits for engineering design and finite element verification are narrowed down to theE lim Finally, the Kriging prediction standard deviation is introduced to form... m E + ks E ≤ theE lim Optimize the filtering criteria. E lim The determination should be based on the type of insulating oil, moisture content in the oil, temperature, local field type, and insulation design criteria or test data corresponding to the power frequency or harmonic voltage waveform. k The value of is determined based on the engineering safety level; it is increased when a more conservative design is required. k .

[0073] During the NSGA-II optimization process, each individual does not directly call the finite element model. Instead, the Kriging proxy model outputs hotspot temperature, manufacturing cost, maximum winding leakage flux density, and insulation confidence constraint violation degree. Individuals that meet the insulation confidence constraints are given priority in Pareto sorting; individuals that do not meet the insulation confidence constraints are only retained when there is a lack of feasible solutions or the violation degree is small. This mechanism prevents high-risk insulation solutions from entering the final Pareto front.

[0074] After obtaining the initial Pareto solution set, three categories of candidate points were selected for finite element verification. The first category consisted of points with large Kriging prediction standard deviations, used to reduce the uncertainty of the surrogate model; the second category consisted of... μE + ksE near theE limThe first category consists of points used to correct insulation constraint boundaries; the second category consists of points in the TOPSIS ranking of the pre-decision system or in regions with large crowding distances at the Pareto front and sparse solution distribution, used to ensure the accuracy of the surrogate model near the final engineering recommended solution.

[0075] The verification samples and their finite element responses are added to the training set. If the error between the finite element verification results and the Kriging prediction results exceeds a preset threshold, or if the verification samples are located near the insulation constraint boundary, the Kriging model is retrained, and the insulation confidence constraint screening and constraint-dominated NSGA-II optimization are re-executed. This process is repeated until the surrogate model error, insulation boundary error, and Pareto front stability all meet the stopping conditions.

[0076] Before making a TOPSIS decision, schemes that do not meet the insulation confidence constraints, structural assembly constraints, material and process constraints, and minimum oil passage size constraints are eliminated. Then, hotspot temperature, manufacturing cost, maximum winding leakage flux density, and insulation safety margin are normalized. For hotspot temperature, cost, and leakage flux density, lower values ​​are better; for insulation safety margin, higher values ​​are better.

[0077] The weights are determined by combining subjective safety priority weights with objective dispersion weights such as entropy weighting and CRITIC method. To reflect the principle of prioritizing transformer safety, the weights of insulation safety margin and hot spot temperature in the combined weights are not less than the weight of material manufacturing cost. After calculating the distances between each candidate scheme and the positive and negative ideal solutions, the scheme with the greatest relative proximity is selected as the final engineering scheme.

[0078] The final output includes the optimal combination of design variables, hot spot temperatures under various operating conditions, manufacturing cost estimates, maximum leakage flux density of the winding, maximum electric field strength in the oil, insulation safety margin, finite element verification error, and relative closeness. It can also output Pareto front plots, insulation constraint boundary plots, active point-addition convergence curves, and final structural parameter tables for review by engineering designers.

[0079] When using the method of this invention, the finite element method calls are mainly focused on the initial samples and high-value candidate samples selected through active scoring, which avoids directly calling the finite element model for all individuals during the NSGA-II iteration process. The final solution, after finite element verification to meet insulation safety control conditions, outputs a compromise design result between hotspot temperature, material manufacturing cost, and leakage flux density.

[0080] Example 3: An electronic device, comprising a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0081] Example 4: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0082] Example 5: A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0083] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0084] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0085] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0086] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0087] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0088] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0089] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0090] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction, characterized in that: Includes the following steps: S1: Determine the multi-condition operating set and collaborative design variables of oil-immersed power transformers; S2: Establish a multiphysics parameterized finite element model of the transformer; S3: The initial samples are generated using the Latin hypercube sampling method optimized by the maximum-minimum distance criterion, and the multi-response dataset is obtained using the parameterized finite element model. S4: Establish a Kriging surrogate model of the target response and insulation constraints; S5: Construct an insulation safety control based on the insulation safety margin limit and the upper bound of Kriging prediction confidence, and embed this control as a hard constraint into the constraint-dominated NSGA-II algorithm; S6: Perform multi-objective optimization using the constrained dominance NSGA-II algorithm to obtain the Pareto candidate solution set; S7: Perform finite element verification on the candidate solutions with the highest scores, and add the verified samples to the training sample set to correct the surrogate model; S8: Select the final structural optimization scheme from the qualified Pareto solution set based on insulation safety priority and TOPSIS method.

2. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: In step S1, the multi-condition operating set includes one or more of the following: rated load condition, overload condition, high ambient temperature condition, harmonic current condition, and cooling capacity reduction condition. The collaborative design variables are structural parameters related to main insulation and magnetic shielding, and are expressed as follows: In the formula, d 1 represents the distance between the main insulating oil gaps of the high-voltage and low-voltage windings. d 2 represents the oil gap distance between the iron core and the low-voltage winding. L s The length of the magnetic shielding patch for the fuel tank. W s The width of the magnetic shielding patch for the fuel tank. T s The thickness of the magnetic shielding patch for the fuel tank.

3. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: In step S2, the oil gap between the high and low voltage windings, the oil gap between the core and the low voltage winding, and the size of the magnetic shielding patch in the oil tank are automatically updated based on the collaborative design variable x. A three-dimensional parametric finite element model is established, and the electromagnetic field, loss field, thermal-fluid field, and insulation electric field are calculated sequentially. The finite element output response vector is: In the formula, T hs This refers to the hot spot temperature of the winding. C For material manufacturing costs, B max This refers to the maximum leakage flux density of the winding or the maximum leakage flux density in the critical area. E max The maximum electric field intensity in the main insulating oil gap is used; for the hot spot temperature, leakage flux density, and maximum electric field intensity in the oil, the maximum value among the calculation results for each operating condition is taken as the optimization evaluation response. The material manufacturing cost C is calculated based on the volume of insulating oil, the amount of insulating components, and the quality of magnetic shielding patches, as well as their unit material costs, caused by changes in co-design variables.

4. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: In the parametric finite element model, the electromagnetic field model is used to obtain the winding leakage flux density, winding eddy current loss, and structural component stray loss; the winding eddy current loss and structural component stray loss are mapped to the heat source load input heat-flow field model to obtain the insulating oil velocity distribution, winding hot spot temperature, and top layer oil temperature; the insulating electric field model is used to obtain the maximum electric field intensity in the oil in the main insulating region; under harmonic current conditions, the AC loss corresponding to each frequency component is calculated and superimposed to form the heat source load.

5. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: The insulation safety control described in step S5 includes a baseline limit for finite element verification, a safety margin limit for engineering design, and a surrogate model confidence constraint for optimization screening. Specifically, the maximum electric field strength in the oil verified by the finite element method does not exceed the allowable electric field strength threshold for insulating oil; the maximum electric field strength in the oil verified by both engineering design and finite element method does not exceed the insulation safety margin limit; and the surrogate model confidence constraint is that the sum of the predicted mean of the maximum electric field strength in the oil and the confidence coefficient times the predicted standard deviation does not exceed the insulation safety margin limit.

6. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: In step S6, the constraint-dominant NSGA-II algorithm prioritizes retaining individuals that satisfy the insulation confidence constraint during non-dominant sorting; when both individuals satisfy the insulation confidence constraint, they are sorted according to Pareto dominance and crowding distance; when neither individual satisfies the insulation confidence constraint, individuals with lower insulation constraint violation are prioritized.

7. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: In step S7, the verification samples actively added to the training sample set are determined by active scoring. The active scoring is obtained by weighting the normalized Kriging prediction standard deviation, the proximity of the insulation confidence constraint boundary, the Pareto front crowding distance, and the pre-decision TOPSIS priority. A preset number of candidate solutions are selected for finite element verification according to the active scoring from high to low. The candidate solutions with larger Pareto front crowding distances correspond to sparse solution distribution regions.

8. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multi-physics proxy correction as described in claim 1, characterized in that: The surrogate model error evaluation index includes at least one of RMSE, MAE, coefficient of determination R2, prediction coefficient of determination Q2, leave-one cross-validation error, and insulation constraint boundary sample prediction error. When the surrogate model errors for hot spot temperature, maximum leakage flux density of winding, maximum electric field strength in oil, and material manufacturing cost all meet the preset threshold, and the insulation constraint boundary sample prediction error meets the preset threshold, the optimization step is initiated.

9. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: Before constructing the evaluation matrix, the TOPSIS method first eliminates candidate solutions that do not meet the insulation confidence constraints and engineering manufacturing constraints; it uses a combination of subjective safety priority weight and objective dispersion weight to determine the weight of each evaluation index, and the weight of the insulation safety margin index and the hot spot temperature index are not less than the weight of the material manufacturing cost index.

10. The multi-objective optimization method for transformer main insulation-magnetic shielding structure considering insulation confidence constraints and multiphysics proxy correction as described in claim 1, characterized in that: The output includes the final oil gap distance between the main insulation between the high and low voltage windings, the oil gap distance between the core and the low voltage winding, the length of the magnetic shielding patch in the oil tank, the width of the magnetic shielding patch in the oil tank, the thickness of the magnetic shielding patch in the oil tank, as well as the hot spot temperature, material manufacturing cost, maximum leakage flux density of the winding, maximum electric field strength in the oil, insulation safety margin, and finite element verification error for each operating condition.

Images