An Optimization Design Method for High Voltage Stator Superconducting Motor
By combining numerical simulation and analytical methods, and utilizing adversarial neural networks and vector regression, a high-precision optimization design method is constructed, which resolves the contradiction between computational efficiency and accuracy in the design of high-voltage superconducting stator superconducting motors, and achieves rapid and economical optimization design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ELECTRIC POWER RES INST OF STATE GRID ZHEJIANG ELECTRIC POWER COMAPNY
- Filing Date
- 2026-04-02
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies struggle to balance computational efficiency and model accuracy in the optimization design of high-voltage superconducting stator superconducting motors. Analytical methods have limited accuracy, while numerical methods are computationally expensive and time-consuming, making it difficult to support extensive design variable traversal and multi-objective optimization.
By combining numerical simulation and analytical methods, and using adversarial networks and vector regression, a high-precision and low-cost optimization design method is constructed. The agent model is adjusted using adversarial neural networks, and the trust region method and support vector regression are combined to integrate source and target domain datasets to optimize design variables and objectives.
It achieves high-precision and high-efficiency optimized design, solves the problem of non-singular characteristics of superconducting coils, significantly improves calculation speed and resource utilization efficiency, and finds the optimal design scheme.
Smart Images
Figure CN122490881A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of motor optimization, and more specifically, to a method for optimizing the design of a high-voltage stator superconducting motor. Background Technology
[0002] Superconducting motor design optimization methods mainly fall into two categories: analytical methods and numerical methods. However, both have significant limitations in the optimization design of high-voltage superconducting stator superconducting motors. While analytical methods offer fast computation speeds and facilitate the establishment of relationships between optimization variables and objective functions, they are typically based on idealized assumptions and struggle to fully characterize the complex nonlinear and nonsingular characteristics of high-voltage superconducting stator superconducting motors. In particular, they fail to accurately reflect the combined influence of multiple physical field factors, such as the nonsingular resistance characteristics of superconducting coils, high-voltage insulation characteristics, and electromagnetic field coupling, on motor performance, thus limiting model accuracy. In contrast, numerical methods, such as finite element analysis, offer higher accuracy and can more accurately simulate complex electromagnetic behavior. However, due to the involvement of superconducting material properties, high-voltage electric field distribution, and multi-physical field coupling processes in high-voltage superconducting stator superconducting motors, their simulation computational burden is extremely heavy, with long single-solution times, making it difficult to meet the requirements for rapid traversal and flexible adjustment of multiple structural parameters in multi-objective optimization processes. Therefore, both traditional analytical and numerical methods struggle to balance computational efficiency and model accuracy, limiting the effective implementation of multi-objective optimization design for high-voltage superconducting stator superconducting motors.
[0003] One technical solution uses numerical simulation to optimize the magnet parameters in a superconducting motor. Based on this simulation, a comparative analysis of a small number of dimensional parameters is performed. Essentially, this is closer to parameter sensitivity analysis or a limited selection of alternatives than a systematic optimization design addressing complex engineering needs. Furthermore, due to the high computational cost of numerical simulation, this method struggles to support the traversal of a large range of design variables and multi-objective collaborative solutions.
[0004] Based on this, this application aims to provide an optimization design method for high-voltage stator superconducting motors. By combining numerical simulation and analytical methods, and by combining adversarial networks and vector regression methods, it provides a high-precision, high-efficiency, low-cost optimization design method with good generalization ability. It solves the problem that the image method cannot consider the non-singular characteristics of superconducting coils, and at the same time significantly improves the time and computational resources required to complete the calculation using the finite element numerical method. Summary of the Invention
[0005] This invention overcomes the shortcomings of existing analytical and numerical methods, and provides an optimized design method for high-voltage stator superconducting motors. It offers a high-precision, high-efficiency, and low-cost optimization design method with good generalization ability, solves the problem that the image method cannot consider the non-singular characteristics of superconducting coils, and significantly improves the time and computational resources required to complete the calculation using the finite element numerical method.
[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for optimizing the design of a high-voltage stator superconducting motor includes the following steps: S1. Determine several parameters of the high-voltage stator superconducting motor as optimization variables and optimization objectives; S2. Establish a proxy model between the optimization variables and the optimization objective using the mirror method, without considering the non-singular resistance characteristics of the superconducting coil; S3. A numerical model considering the non-singular resistance characteristics of the superconducting coil is established using the finite element method, thereby obtaining the finite element true values of the optimization variables and the corresponding optimization objectives, and constructing the source domain dataset. S4. Based on the agent model and source domain dataset, the agent model is adjusted using the source domain dataset through an adversarial network. S5. Obtain response values within the target domain based on the modified proxy model to construct the target domain dataset; S6. Combine the trust region method with support vector regression, and train the final agent model by fusing the source domain dataset and the target domain dataset. S7. Verify the regression accuracy of the final surrogate model. If it does not meet the requirements, adjust and retrain until the accuracy requirements are met. S8. Based on the optimization algorithm, obtain the optimal optimization variable parameters of the high-voltage stator superconducting motor.
[0007] Preferably, step S4 includes: S41. Establish a generator, which includes the proxy model obtained in step S2 and a correction layer consisting of several fully connected layers. S42. Use the source domain dataset as the standard data; S43. Establish a discriminator composed of convolutional layers, input the generator output or finite element truth value, and output the true / false classification result; S44. Alternately train the discriminator and generator until the output accuracy of the generator meets the preset target requirements.
[0008] As a preferred option, the optimization variables include the inner diameter of the superconducting coil, the number of turns, and the critical current density.
[0009] As a preferred option, the optimization target includes the fundamental frequency amplitude.
[0010] As a preferred option, it also includes setting optimization constraints, such as harmonic order and the amount of superconducting coils used.
[0011] Preferably, the method further includes step S31, constructing a sampler, wherein the sampler optimizes the values of the variables through reinforcement learning methods.
[0012] As a preferred method, the method for ensuring that the accuracy of the surrogate model meets the preset accuracy requirements in step S7 is as follows: by reserving a finite element true value test set, the mean square error or relative error between the predicted value of the surrogate model and the finite element true value is calculated. If the error is lower than the threshold, the requirements are met.
[0013] Preferably, step S6, which combines the trust region method with support vector regression, includes: determining a trust range based on the source domain dataset to generate a trust region, and optimizing the surrogate model in the trust region using a vector regression method to fit the nonlinear mapping relationship between the optimization variables and the optimization objective.
[0014] Preferably, the trust region can be dynamically expanded based on newly added finite element truth data to improve the prediction coverage of the model.
[0015] Preferably, the optimization algorithm is the particle swarm optimization algorithm.
[0016] Compared with the prior art, the beneficial effects of the present invention are: (1) By combining numerical simulation and analytical methods with reinforcement learning methods, high-precision optimization results can be obtained in a short time, solving the problem that the mirror method cannot consider the non-singular characteristics of superconducting coils, and at the same time greatly improving the time and computing resources required to complete the calculation by the finite element numerical method; (2) The final proxy model is obtained by adversarial neural network and vector regression method, which has high precision and reliability; (3) The optimal solution is found efficiently by using particle swarm optimization algorithm, saving computing resources. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the design method of the present invention; Figure 2 This is a schematic diagram of the adversarial network structure of the present invention; Figure 3 This is a schematic diagram illustrating the relationship between optimization variables and optimization objectives obtained through reinforcement learning model training, which is a verification example of the present invention. Figure 4 This is a schematic diagram comparing the rotor position and magnetic field before and after optimization in a verification example of the present invention; Figure 5 This is a schematic diagram comparing the harmonic order and magnetic field before and after optimization in the verification example of this invention; Figure 6 This is a schematic diagram comparing the AC loss before and after optimization at 0.5A / s in the verification example of this invention; Figure 7 This is a schematic diagram comparing the AC loss before and after optimization of the verification example of the present invention at 0.05A / s. Detailed Implementation
[0018] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.
[0019] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0020] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0021] Example: A method for optimizing the design of a high-voltage stator superconducting motor is disclosed. To find the optimal design, common approaches include analytical and numerical solutions to establish the mapping relationship between optimization variables and the objective function. However, both approaches have limitations in the field described in this application. While analytical methods offer fast computation and facilitate the establishment of relationships between optimization variables and the objective function, they are typically based on idealized assumptions and struggle to fully characterize the complex nonlinear and nonsingular characteristics of the high-voltage superconducting stator superconducting motor. In particular, they fail to accurately reflect the combined influence of multiple physical field factors, such as the nonsingular resistance characteristics of the superconducting coils, high-voltage insulation characteristics, and electromagnetic field coupling, on the motor's performance, thus limiting model accuracy. Numerical methods, such as finite element analysis, offer high accuracy and can simulate complex electromagnetic behavior relatively well. However, due to the involvement of superconducting material properties, high-voltage electric field distribution, and multi-physical field coupling processes in the high-voltage superconducting stator superconducting motor, the simulation computation is extremely heavy, with long single-solution times, making it difficult to meet the requirements for rapid traversal and flexible adjustment of multiple structural parameters in multi-objective optimization processes. In short, without considering the non-singular resistance characteristics of the superconducting coil, the analytical solution is fast but has large errors; while considering the non-singular resistance characteristics of the superconducting coil, the numerical solution is accurate but extremely slow. Finding the optimal technical solution using either approach is extremely difficult.
[0022] Therefore, this application aims to combine the advantages of both approaches to provide an optimized design method for high-voltage stator superconducting motors. By combining the advantages of both approaches and with a smaller number of simulation scenarios, the method achieves an accurate mapping between the optimization objective and optimization variables through modifications to the analytical approach, thereby obtaining the optimal design scheme.
[0023] Reference Figure 1 As shown, the specific implementation of this design method is as follows: S1. Determine several parameters of the high-voltage stator superconducting motor as optimization variables and optimization objectives.
[0024] Optimization variables include the inner diameter, number of turns, and critical current density of the superconducting coil. Optimization objectives include the fundamental frequency amplitude. It also includes setting optimization constraints, such as harmonic order and the amount of superconducting coil used. Air gap magnetic flux density is a core indicator of motor energy conversion efficiency and output performance, while amplitude is a key indicator of the air gap magnetic field. The essence of motor optimization is to maximize the effective component of the fundamental frequency and minimize the influence of harmful harmonics. Precisely controlling various fundamental frequency amplitudes (magnetic flux density, current, magnetomotive force, etc.) throughout the design and control process is a key technical path to improve torque density, efficiency, reliability, and reduce vibration and noise.
[0025] S2. Establish a proxy model between the optimization variables and the optimization objective using the mirror method, without considering the non-singular resistance characteristics of the superconducting coil.
[0026] The idea behind the mirror method is as follows: Under the assumptions of ideal ferromagnetic boundaries and ideal superconductivity (no resistance), the magnetization effect of the motor core is equivalently replaced by a mirror coil. This simplifies the magnetic field problem of the superconducting coil to a superposition of magnetic fields in an unbounded space, thereby analytically deriving physical quantities such as air gap magnetic flux density, flux linkage, and fundamental amplitude. Finally, an explicit mathematical relationship is established between optimization variables (structural dimensions, coil parameters) and optimization objectives (fundamental amplitude, torque, etc.). By equivalently eliminating the core boundary, the analytical expression for the air gap magnetic flux density is obtained by integrating using the Biot-Savart law. Fourier decomposition of the magnetic flux density directly yields the analytical formula for the fundamental amplitude, which is the aforementioned surrogate model, referred to as M1.
[0027] This method constructs an analytical solution regarding the relationship between the optimization variables and the optimization objective, and the solution-solving process is highly efficient. However, because it does not consider the non-singular resistance characteristics of the superconducting coil, the model accuracy is limited and cannot accurately reflect the complex nonlinear and non-singular characteristics of the superconducting stator motor. Due to the non-singular resistance characteristics of superconductivity, the superconductor exhibits continuous finite and nonlinear losses, which generate electric fields, losses, and current accumulation phenomena, affecting the final fundamental amplitude. Based on this, we proceed to step S3.
[0028] S3. A numerical model considering the non-singular resistance characteristics of the superconducting coil is established using the finite element method, thereby obtaining the finite element true values of the optimization variables and the corresponding optimization objectives, and constructing the source domain dataset.
[0029] Due to the nonlinear resistance of superconductors, the magnetic field cannot be considered a simple superposition, and the current distribution is no longer uniform, leading to distortion of the air gap magnetic flux density. Expressing this process analytically would be extremely difficult; a better approach is to establish a numerical model considering the non-singular resistance characteristics of the superconducting coil using the finite element method. The finite element method TA is employed for simulation, where A represents the magnetic vector potential, used to describe the magnetic field distribution, and T represents the current vector potential, used to describe the current density, electric field, and resistance loss inside the coil. Through the coupling of these two methods, the entire electromagnetic field can be fully represented. The TA formula is then substituted into the non-singular EJ resistance model. Based on this, the geometry of the motor is modeled, and then solved using finite element discretization, nonlinear equations, and Newton's iteration. The accurate fundamental amplitude is obtained by extracting the air gap magnetic flux density and performing Fourier decomposition. The corresponding numerical solution is obtained by combining several sets of optimization variables. The optimization variables and the true finite element solution constitute the source domain dataset. Compared to the aforementioned surrogate model, this source domain dataset has extremely small errors, but its sample size is small and insufficient to obtain the optimal optimization variables. Subsequent steps are needed to fuse the two datasets to obtain a dataset with smaller errors and a wider range of optimization variables.
[0030] The process also includes step S31, which involves constructing a sampler, wherein the sampler optimizes the values of variables through reinforcement learning.
[0031] To ensure that the combination of selected optimization variables is closer to the optimal solution and that more simulation points fall near the optimal solution, a sampler based on a reinforcement learning scheme is constructed in some embodiments. This sampler uses reinforcement learning methods, through backpropagation, to optimize the values of the optimization variables by taking the true values of the finite element data obtained from the simulation as input. Its specific implementation is common knowledge in the art and is unrelated to the technical solution of this application, and will not be elaborated here.
[0032] S4. Based on the agent model and source domain dataset, the agent model is adjusted using the source domain dataset through an adversarial network.
[0033] Adversarial networks (ANNs) use a source domain dataset as a reference and modify the proxy model to make its output more closely resemble the output of the source domain dataset. Specifically, their implementation involves: Reference Figure 2 As shown, S41, establish a generator, which includes the proxy model obtained in step S2 and a correction layer composed of several fully connected layers; S42. Use the source domain dataset as the standard data; S43. Establish a discriminator composed of convolutional layers, input the generator output or finite element truth value, and output the true / false classification result; S44. Alternately train the discriminator and generator until the output accuracy of the generator meets the preset target requirements.
[0034] The generator in step S41, based on a surrogate model, modifies the output of the surrogate model using a correction layer composed of fully connected layers, making it closer to the output of the source domain dataset. The discriminator in step S43, composed of convolutional layers, receives input from the generator or finite element truth values. Without knowing the source, it determines the truth value of the input: if the input comes from the generator, the output is false; if the input comes from the finite element truth values, the output is true. The discriminator also evaluates the input, connects to the generator, and feeds back the error.
[0035] The alternating training process for the generator and discriminator is as follows: With the generator's parameters locked, the discriminator is trained, and its parameter settings are optimized by feeding back its judgment results and error differences. Then, the generator is trained, and the discriminator's parameters are locked. Its output is input into the discriminator, which compares its output with the error value of standard data and feeds it back to the generator. The optimizer iteratively optimizes the parameters of its fully connected layers. This process iterates until the generator's output accuracy meets the preset performance requirements.
[0036] Adversarial networks consist of a generator and a discriminator. They are trained collaboratively in an adversarial game. The overall process begins with input noise. The generator typically uses fully connected layers or transposed convolutional layers as its core structure. It first receives low-dimensional random latent vectors, maps them to an intermediate feature space through multiple fully connected layers, then progressively upsamples them through multiple transposed convolutional layers. Batch normalization layers stabilize the training, and ReLU activation functions enhance non-linear representation. Finally, a Tanh-activated convolutional layer outputs synthetic samples with the same size as the real data. The discriminator uses a convolutional network structure symmetrical to the generator. Its input is either real samples or pseudo-samples generated by the generator. It downsamples and extracts features through multiple convolutional layers, using LeakyReLU activation functions to alleviate the gradient vanishing problem. Some structures incorporate Dropout layers to prevent overfitting. After global pooling or fully connected layer compression, a single sigmoid output layer provides the probability value that the input data is a real sample. During training, the discriminator alternately labels real samples as 1 and generated samples as 0. Binary classification optimization is performed to minimize the discrimination loss, while the generator aims to deceive the discriminator and maximize the probability that the discriminator will classify the fake sample as real. The two alternately iterate and update the parameters until Nash equilibrium is reached, so that the distribution of generated samples approximates the distribution of real data.
[0037] At this point, the proxy model used by the generator is called M2.
[0038] S5. Obtain response values within the target domain based on the modified surrogate model to construct the target domain dataset. Based on the aforementioned surrogate model M2, combinations of various optimization variables can be inexpensively and quickly input into M2 to obtain the corresponding optimization target values. The target domain dataset is constructed by pairing the optimization variables with the corresponding model output values.
[0039] S6. Combine the trust region method with support vector regression, and train the final proxy model by fusing the source domain dataset and the target domain dataset.
[0040] Step S6, combining the trust region method with support vector regression, includes: determining a trust range based on the source domain dataset to generate a trust region; optimizing the surrogate model within the trust region using vector regression to fit the nonlinear mapping relationship between the optimization variables and the optimization objective. Since M2 is a model obtained using the finite element method and the mirror method, further vector regression is performed on it to find the function graph, ensuring more training points fall around this graph. This allows the model to not only achieve high fitting accuracy for existing data but also exhibit good generalization ability for new parameter combinations. To avoid overfitting, a trust region is introduced. To improve the reliability of the obtained data, predictions are only made within the range of values in the source domain dataset. Based on the optimization variables corresponding to the existing finite element true values, their maximum and minimum values are used as boundaries; predictions are rejected if values exceed these boundaries.
[0041] The trust domain is determined by the maximum and minimum values of the optimization variables in the source domain dataset; predictions are rejected if the values exceed this range. Within the trust domain, the target domain data and source domain data are optimized using vector regression. By assigning appropriate weights to both, a regression image that closely approximates the overall data is fitted, resulting in the final surrogate model M3.
[0042] It is worth noting that the trust region can be extended. By referring to step S3 to obtain a new extended set of finite element truth values for verification, the scope of the trust region can be increased, thereby improving the generalization ability of the surrogate model.
[0043] S7. Verify the regression accuracy of the final surrogate model. If it does not meet the requirements, adjust and retrain until the accuracy requirements are met. The method for ensuring the surrogate model's accuracy meets the preset accuracy requirements in step S7 is as follows: by reserving a finite element true value test set, calculate the mean square error or relative error between the surrogate model's predicted values and the finite element true values. If the error is below a threshold, the requirements are met. In some other embodiments, a new detection set composed of finite element true values for verification can also be obtained by referring to step S3.
[0044] S8. Based on the optimization algorithm, obtain the optimal optimization variable parameters for the high-voltage stator superconducting motor. In some embodiments, the optimization algorithm is a particle swarm optimization algorithm.
[0045] Verification example: We optimized a superconducting motor, such as Figure 3 As shown, based on a reinforcement learning model, the relationship between optimization variables and the optimization objective is trained. This method can learn the correspondence between the optimization objective and the optimization variables, bringing more finite element truth correspondences closer to the optimal optimization variables. Simulations of the obtained optimal solution demonstrate that the proposed model has high prediction accuracy. Figure 4 and Figure 5 After optimization, the air gap magnetic field was compared and found that the air gap harmonics were significantly reduced and the AC loss was greatly reduced.
[0046] For superconducting motors with multiple stacked excitation coils, the performance is significantly improved after the optimization design method described in this application. After optimization, the amount of superconducting material used in the optimized motor is 22.22 km², a reduction of 11%. Notably, the FFT Br first harmonic amplitude remains unchanged, while the maximum magnetic field strength borne by the superconducting coil decreases from 3.78 T to 3.29 T. Simultaneously, through optimization, the maximum jJ / Jc (ratio of current density to critical current density) is reduced from 0.753 to 0.741. (Refer to...) Figure 6 and Figure 7 As shown, at lower current rise rates (0.05 A / s and 0.5 A / s), the optimized transient loss is consistently lower than that before optimization. The parameters before and after optimization are shown in the table below:
[0047] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Other variations and modifications may be made without departing from the technical solutions described in the claims.
Claims
1. An optimized design method for a high-voltage stator superconducting motor, characterized in that, Includes the following steps: S1. Determine several parameters of the high-voltage stator superconducting motor as optimization variables and optimization objectives; S2. Establish a proxy model between the optimization variables and the optimization objective using the mirror method, without considering the non-singular resistance characteristics of the superconducting coil; S3. A numerical model considering the non-singular resistance characteristics of the superconducting coil is established using the finite element method, thereby obtaining the finite element true values of the optimization variables and the corresponding optimization objectives, and constructing the source domain dataset. S4. Based on the agent model and source domain dataset, the agent model is adjusted using the source domain dataset through an adversarial network. S5. Obtain response values within the target domain based on the modified proxy model to construct the target domain dataset; S6. Combine the trust region method with support vector regression, and train the final agent model by fusing the source domain dataset and the target domain dataset. S7. Verify the regression accuracy of the final surrogate model. If it does not meet the requirements, adjust and retrain until the accuracy requirements are met. S8. Based on the optimization algorithm, obtain the optimal optimization variable parameters of the high-voltage stator superconducting motor.
2. The optimized design method for a high-voltage stator superconducting motor according to claim 1, characterized in that, Step S4 includes: S41. Establish a generator, which includes the proxy model obtained in step S2 and a correction layer consisting of several fully connected layers. S42. Use the source domain dataset as the standard data; S43. Establish a discriminator composed of convolutional layers, input the generator output or finite element truth value, and output the true / false classification result; S44. Alternately train the discriminator and generator until the output accuracy of the generator meets the preset target requirements.
3. The optimized design method for a high-voltage stator superconducting motor according to claim 1, characterized in that, The optimization variables include the inner diameter of the superconducting coil, the number of turns, and the critical current density.
4. The optimized design method for a high-voltage stator superconducting motor according to claim 3, characterized in that, The optimization target includes the fundamental frequency amplitude.
5. The optimized design method for a high-voltage stator superconducting motor according to claim 4, characterized in that, It also includes setting optimization constraints, such as harmonic order and the amount of superconducting coils used.
6. The optimized design method for a high-voltage stator superconducting motor according to claim 1, characterized in that, It also includes step S31, constructing a sampler, which optimizes the values of variables through reinforcement learning methods.
7. The optimized design method for a high-voltage stator superconducting motor according to claim 1, characterized in that, Step S6, which combines the trust region method with support vector regression, includes: determining a trust range based on the source domain dataset to generate a trust region; optimizing the surrogate model within the trust region using a vector regression method to fit a nonlinear mapping relationship between the optimization variables and the optimization objective.
8. The optimized design method for a high-voltage stator superconducting motor according to claim 1, characterized in that, The method for ensuring that the accuracy of the surrogate model meets the preset accuracy requirements in step S7 is as follows: by reserving a finite element true value test set, calculate the mean square error or relative error between the predicted value of the surrogate model and the finite element true value. If the error is lower than the threshold, the requirements are met.
9. The optimized design method for a high-voltage stator superconducting motor according to claim 7, characterized in that, The trust region can be dynamically expanded based on newly added finite element truth data to improve the model's prediction coverage.
10. A high-voltage stator superconducting motor optimization design method according to any one of claims 1 to 9, characterized in that, The optimization algorithm is the particle swarm optimization algorithm.