Optimal Design Of Electrical Machines Research Articles

Robust Design Optimization of Electric Machines with Isogeometric Analysis

In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.

Optimal Design of a Surface Permanent Magnet Machine for Electric Power Steering Systems in Electric Vehicle Applications Using a Gaussian Process-Based Approach

The efficient design optimization of electric machines for electric power steering (EPS) applications poses challenges in meeting demanding performance criteria, including high power density, efficiency, and low vibration. Traditional optimization approaches often fail to find a global solution or suffer from excessive computation time. In response to the limitations of traditional approaches, this paper introduces a novel methodology by incorporating a Gaussian process-based adaptive sampling technique into a surrogate-assisted optimization process using a metaheuristic algorithm. Validation on a 72-slot/8-pole interior permanent magnet (IPM) machine demonstrates the superiority of the proposed approach, showcasing improved exploitation–exploration balance, faster convergence, and enhanced repeatability compared to conventional optimization methods. The proposed design process is then applied to two surface PM (SPM) machine configurations with 9-slot/6-pole and 12-slot/10-pole combinations for EPS applications. The results indicate that the 12-slot/10-pole SPM design surpasses the alternative design in torque density, efficiency, cogging torque, torque ripple, and manufacturability.

Multi-Objective Yield Optimization for Electrical Machines Using Gaussian Processes to Learn Faulty Design

This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, a hybrid Gauss-Process regression (GPR) model is employed. In contrast to classic Kriging or Bayesian optimization approaches, we train a GPR surrogate for the performance feature specifications, not for the objective function. A multi-objective optimization problem is formulated, maximizing simultaneously the reliability, i.e., the yield, and further performance objectives, e.g., the costs. A permanent magnet synchronous machine is modeled and simulated in commercial finite element simulation software. Four approaches for solving the multi-objective optimization problem are described and numerically compared, namely: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -constraint scalarization, weighted sum scalarization, a multi-start weighted sum approach and a genetic algorithm. We show that the efficiency gain thanks to our hybrid GPR model enables even computationally heavy multi-objective optimization for real-world applications.

Optimal design of electric machine with efficient handling of constraints and surrogate assistance

An optimal electric machine design task can be posed as a constrained multi-objective optimization problem. While the objectives require time-consuming finite element analysis, constraints, such as geometric constraints, can often be based on mathematical expressions. This article investigates this mixed computationally expensive optimization problem and proposes a computationally efficient optimization method based on evolutionary algorithms. The proposed method always generates feasible solutions by using a generalizable repair operator and also addresses time-consuming objective functions by incorporating surrogate models for their prediction. The article successfully establishes the superiority of the proposed method over a conventional optimization approach. This study demonstrates how a complex engineering design task can be optimized efficiently for multiple objectives and constraints requiring heterogeneous evaluation times. It also shows how optimal solutions can be analysed to select a single preferred solution and harnessed to reveal vital design features common to optimal solutions as design principles.

Systematic Development of a Multi-Objective Design Optimization Process Based on a Surrogate-Assisted Evolutionary Algorithm for Electric Machine Applications

Surrogate model (SM)-based optimization approaches have gained significant attention in recent years due to their ability to find optimal solutions faster than finite element (FE)-based methods. However, there is limited previous literature available on the detailed process of constructing SM-based approaches for multi-parameter, multi-objective design optimization of electric machines. This paper aims to present a systematic design optimization process for an interior permanent magnet synchronous machine (IPMSM), including a thorough examination of the construction of the SM and the adjustment of its parameters, which are crucial for reducing computation time. The performances of SM candidates such as Kriging, artificial neural networks (ANNs), and support vector regression (SVR) are analyzed, and it is found that Kriging exhibits relatively better performance. The hyperparameters of each SM are fine-tuned using Bayesian optimization to avoid manual and empirical tuning. In addition, the convergence criteria for determining the number of FE computations needed to construct an SM are discussed in detail. Finally, the validity of the proposed design process is verified by comparing the Pareto fronts obtained from the SM-based and conventional FE-based methods. The results show that the proposed procedure can significantly reduce the total computation time by approximately 93% without sacrificing accuracy compared to the conventional FE-based method.

Electrical machines surrogate‐based design optimization based on novel waveform targeting strategy with improvement of the computational efficiency

Electrical machine design optimization is an expensive procedure as it contains numerous variables and multiple objectives. Therefore, it might require hundreds of time-consuming finite element analyses (FEA). Surrogate models are one of the superior alternatives that can overcome the computational burden of FEA. However, in optimization problems with sensitive input-output relationships, surrogate models can lack accuracy or suffer from unreasonable initial FE-computational cost. To tackle this problem, this work presents a novel strategy called Waveform-Targeted Surrogate Modeling (WTSM) that improves the computational efficiency of surrogate-based design optimization of electrical machines by modifying the model construction process. In this paper, an Interior Permanent Magnet Machine (IPMSM) is studied to evaluate the proposed strategy's performance compared to the conventional Black Box Modeling (BBM) method. A two-step assessment procedure consisting of multiple scenarios has been developed to analyse the reliability of the WTSM concerning different training-validation datasets. Meanwhile, the Kriging model and Latin-Hypercube-Sampling (LHS) method are employed for surrogate model construction purposes. From the discussion and the results, it can be found that the proposed WTSM strategy can significantly increase the accuracy of the surrogate modelling procedure while the required computational cost can be reduced.

Robust Design Optimization of Electrical Machines and Devices

This article introduces a Special Issue (SI) that contains fourteen chosen articles from robust design optimization of electrical machines and devices [...]

Robust Explorative Particle Swarm Optimization for Optimal Design of EV Traction Motor

This paper proposes a robust optimization algorithm customized for the optimal design of electric machines. The proposed algorithm, termed “robust explorative particle swarm optimization” (RePSO), is a hybrid algorithm that affords high accuracy and a high search speed when determining robust optimal solutions. To ensure the robustness of the determined optimal solution, RePSO employs the rate of change of the cost function. When this rate is high, the cost function appears as a steep curve, indicating low robustness; in contrast, when the rate is low, the cost function takes the form of a gradual curve, indicating high robustness. For verification, the performance of the proposed algorithm was compared with those of the conventional methods of robust particle swarm optimization and explorative particle swarm optimization with a Gaussian basis test function. The target performance of the traction motor for the optimal design was derived using a simulation of vehicle driving performance. Based on the simulation results, the target performance of the traction motor requires a maximum torque and power of 294 Nm and 88 kW, respectively. The base model, an 8-pole 72-slot permanent magnet synchronous machine, was designed considering the target performance. Accordingly, an optimal design was realized using the proposed algorithm. The cost function for this optimal design was selected such that the torque ripple, total harmonic distortion of back-electromotive force, and cogging torque were minimized. Finally, experiments were performed on the manufactured optimal model. The robustness and effectiveness of the proposed algorithm were validated by comparing the analytical and experimental results.

A systematic design optimization approach for interior permanent magnet machines equipped with novel semi-overlapping windings

In this paper, a systematic approach to achieve optimized design of interior permanent magnet machine (IPM) having novel semi-overlapping windings (NSWs) is presented. The optimization parameters have been determined individually by performing sensitivity analyses. Multi-objective global optimization is subsequently performed. Genetic algorithm (GA) approach, which is also known as “random search with learning algorithm” and an effective optimization tool used for design optimization of electric machines, is employed. IPMs equipped with integer-slot distributed winding (ISDW) and NSW are initially designed by using the geometric and operating parameters of Toyota Prius 2010 IPM. Subsequently, a time-stepping 2D finite element analysis (FEA)-based program is employed to perform the optimization and quickly evaluate the optimal solution among the thousands of design candidates thanks to the sensitivity analyses. In order to reveal the effectiveness and rapidity of the multi-objective global optimization, a comprehensive electromagnetic performance comparison between the original (with ISDWs), initial and optimal designs (with NSWs) is presented. Finally, a small IPM prototype globally optimized by using the proposed procedure is manufactured, and the FEA results have been validated by measurements. Our goals in this study is to advance the state of the art in the multi-objective design optimization of NSW IPMs by performing sensitivity analyses to reach the optimal solution quickly and to determine the most sensitive design parameters affecting the key performance characteristics.

Surrogate Vibration Modeling Approach for Design Optimization of Electric Machines

This article presents a surrogate modeling approach to predict the vibrational behavior during electric machine design. The methodology used in identifying and implementing the surrogate model allows a time-efficient integration of the surrogate model in multiphysics geometric optimization of electric machines, especially in scenarios of drop-in replacement. Based on the state-of-the-art review, the use of analytical or numerical techniques alone considering motor frame and support are not adequately accurate, time efficient, and flexible. The proposed method uses the 3-D finite-element (FE) structural simulations for identifying characteristic response profiles in the surrogate model and does not use structural FE simulations in the optimization loop. Experimental tests are performed on a 6/10 switched reluctance machine to validate the 3-D FE model used to identify the surrogate model. The rational fraction polynomial (RFP) method is used to fit the vibration impulse responses for a number of machines geometries defined by three stator dimensions. The impulse response of any geometry can be determined using linear interpolation of the RFP coefficients. Using the radial forces determined from the FE electromagnetic simulation, the deformation is determined using superposition.

Optimal Design of IPMSM for FCEV Using Novel Immune Algorithm Combined with Steepest Descent Method

In this paper, the Novel Immune Algorithm (NIA) is proposed for an optimal design of electrical machines. By coupling the conventional Immune Algorithm and Steepest Descent Method, the NIA can perform fast and exact convergence to both global solutions and local solutions. Specifically, the concept of an antibody radius is newly introduced to improve the ability to navigate full areas effectively and to find new peaks by excluding already searched areas. The validity of the NIA is confirmed by mathematical test functions with complex objective function regions. The NIA is applied to an optimal design of an interior permanent magnet synchronous motor for fuel cell electric vehicles and to derive an optimum design with diminished torque ripple.

Robust Design Optimization of Electrical Machines: Multi-Objective Approach

This article presents a new method for multi-objective robust design optimization of electrical machines and provides a detailed comparison with so far introduced techniques. First, two robust design approaches, worst-case design and design for six-sigma, are compared with the conventional deterministic approach for multi-objective optimization. Through a case study on a permanent magnet motor, it is found that the reliabilities of motors produced based on robust designs are 100% under the investigated constraints, while the reliabilities of deterministic designs can be lower than 30%. A major disadvantage of robust optimization is the huge computation cost, especially for high-dimensional problems. To attempt this problem, a new multi-objective sequential optimization method (MSOM) with an orthogonal design technique and hypervolume indicator (as a measure of convergence) is proposed for both deterministic and robust design optimization of electrical machines. Through another case study, it is found that the new MSOM can improve motor performance and greatly reduce the computational cost. For the robust optimization, the number of required finite element simulations can be reduced by more than 40%, compared with that required by the conventional approach. The proposed method can be applied to many-objective (robust) design optimization of electrical machines.

Robust Design Optimization of Electrical Machines: A Comparative Study and Space Reduction Strategy

This article presents a comparative study on different types of robust design optimization methods for electrical machines. Three robust design approaches, Taguchi parameter design, worst-case design and design for six-sigma, are compared for low-dimensional and high-dimensional design optimization scenarios, respectively. For the high-dimensional scenario, the computational burden is normally massive due to the robustness evaluation of a huge number of design candidates. To attempt this challenge, as the second aim of this paper, a space reduction optimization (SRO) strategy is proposed for these robust design approaches, yielding three new robust optimization methods. To illustrate and compare the performance of different robust design optimization methods, a permanent magnet motor with soft magnetic composite cores is investigated with the consideration of material diversities and manufacturing tolerances. 3-D finite element model and thermal network model are employed in the optimization process and the accuracy of both models has been verified by experimental results. Based on the theoretical analysis and optimization results, a detailed comparison is provided for all investigated and proposed robust design optimization methods in terms of different aspects. It shows that the proposed SRO strategy can greatly improve the design optimization effectiveness and efficiency of those three conventional robust design methods.

Robust Design Optimization of Electrical Machines Considering Hybrid Random and Interval Uncertainties

For robust design optimization (RDO) of electrical machines, cases with random uncertainty and interval uncertainty are generally investigated separately. Accordingly, the performance fluctuation analysis under uncertainty is based on random method and interval method respectively. However, the problem with hybrid uncertainties can also be met yet rarely researched. Under this circumstance, the uncertainty analysis methods for a single type of uncertainty may no longer be applicable, which challenges the robust optimization conduction. For effective RDO of electrical machines with hybrid uncertainties, this article presents a robust optimizer based on evolutionary algorithms and the polynomial chaos Chebyshev interval (PCCI) method. The PCCI method is utilized for effectively modeling the fluctuations caused by the hybrid uncertainty with a small number of samples. As additional enhancements, the filtering strategy for the algorithm with deterministic constraints is proposed to reduce the solutions that require robustness analysis in each iteration and accelerate the optimization further while not affecting the global convergence ability. A design example of a brushless DC motor considering hybrid uncertainties is analyzed and optimized. The results confirm the feasibility of the proposed method.

Optimal design of electrical machines assisted by hybrid surrogate model based algorithm

In this paper, for design of large-scale electromagnetic problems, a novel robust global optimization algorithm based on surrogate models is presented. The proposed algorithm can automatically select a proper meta-model technique among multiple alternatives. In this paper, three representative meta-modeling techniques including ordinary Kriging, universal Kriging, and response surface method with multi-quadratic radial basis functions are applied. In each optimization iteration, the above three models are used for parallel calculation. The proposed hybrid surrogate model optimization algorithm synthesizes advantages of these different meta-models. Without verification of a specific meta-model, a suitable one for the engineering problem to be analyzed is automatically selected. Therefore, the proposed algorithm intends to make a better trade-off between numerical efficiency and searching accuracy for solving engineering problems, which are characterized by stronger non-linearity, higher complexity, non-convex feasible region, and expensive performance analysis.

Multi-Level Modeling Methodology for Optimal Design of Electric Machines Based on Multi-Disciplinary Design Optimization

The transportation sector is undergoing electrification to gain advantages such as lighter weight, improved reliability, and enhanced efficiency. As contributors to the safety of embedded critical functions in electrified systems, better sizing of electric machines in vehicles is required to reduce the cost, volume, and weight. Although the designs of machines are widely investigated, existing studies are mostly complicated and application-specific. To satisfy the multi-level design requirements of power systems, this study aims to develop an efficient modeling method of electric machines with a background of aircraft applications. A variable-speed variable-frequency (VSVF) electrically excited synchronous generator is selected as a case study to illustrate the modular multi-physics modeling process, in which weight and power loss are the major optimization goals. In addition, multi-disciplinary design optimization (MDO) methods are introduced to facilitate the optimal variable selection and simplified model establishment, which can be used for the system-level overall design. Several cases with industrial data are analyzed to demonstrate the effectiveness and superior performance of the modeling method. The results show that the proposed practices provide designers with accurate, fast, and systematic means to develop models for the efficient design of aircraft power systems.

Multifidelity Surrogate Assisted Rapid Design of Transverse-Flux Permanent Magnet Linear Synchronous Motor

Optimal design of electric machines, having complex 3-D magnetic flux path, such as transverse flux or axial flux motors, is computationally demanding owing to the unavailability of a fast 2-D finite-element method (FEM), which leads to the indispensable use of costly 3-D FEM models. With multiobjectives and large design parameter vector, this task is further exacerbated. To accelerate the design procedure, unlike conventional methods, this article proposes the use of two information sources, an expensive but accurate high-fidelity 3-D-FEM model and a fast but inaccurate low-fidelity 2-D-equivalent FEM model to exploit corresponding opposite merits of each and construct a multifidelity surrogate model (response surface) with minimum number of expensive 3-D-FEM simulations. The low-fidelity 2-D model, which intrinsically does not exist for such machines, is generated by ensuring equal magnetic reluctance along main magnetic path despite deformation of model's geometry. The proposed methodology is applied to optimize a novel magnetically levitated transverse flux permanent magnet linear synchronous motor, considering suspension characteristics (lateral and normal stiffnesses) along with thrust as objectives and a seven parameter design vector. Results show significant design time-saving without compromising surrogate accuracy. The optimized design is fabricated and relevant experimental measurements are taken.

Development of Differing Extent Mesh Adaptive Direct Search Applied for Optimal Design of Spoke-Type PMSM

Optimal design of electric machines using finite-element analysis (FEA) necessitates too much computation time to maintain high accuracy. To reduce the computation time and obtain a global optimum in multi-modal problems, this paper presents differing extent mesh adaptive direct search (DEMADS). The proposed algorithm is classified into three groups according to the poll searching frame and mesh size for assigning a global and local searching. In particular, DEMADS shares information among solutions based on a parallel multi-start strategy for earlier stopping by deviation and checking revisits. The effectiveness of DEMADS has been validated and evaluated as the function call number and the convergence number at a global optimum using benchmarking function. Finally, it is applied to an optimization problem that minimize torque ripple of a spoke-type permanent magnet synchronous machine via FEA.

Wind Micro-Turbine Networks for Urban Areas: Optimal Design and Power Scalability of Permanent Magnet Generators

This work is focused on the design optimization of electrical machines that are used in small-scale direct-drive aerogenerators. A ducted wind turbine, equipped with a diffuser, is considered due to its enhanced power capability with respect to bare turbines. An annular type Permanent Magnet brushless generator is integrated in the turbine structure: the stator coils are placed in the internal part of the diffuser, whereas the permanent magnets are on an external ring connected to the turbine blade tips. Moreover, as regards the stator windings, the Printed Circuit Board (PCB) technology is investigated in order to exploit its advantages with respect to conventional wire coils, such as the increased current density capacity, the reduction of costs, and the enhanced precision and repeatability of the PCBs. An original design procedure is presented together with some scalability rules. An automated tool has been developed in order to aid the electrical machine designer in the first design stages: the tool performs multi-objective optimizations (using the Matlab Genetic Algorithm Toolbox), coupled to fast Finite Element analysis (through the open-source software FEMM) for the evaluation of the electromagnetic torque and field distribution. The proposed procedure is applied to the design of an annular PM generator directly coupled to a small-scale turbine for an urban application.

Cuckoo search as a tool for optimal design of PM brushless DC motor

PurposeThe purpose of this paper is to perform an optimal design of a single-phase permanent magnet brushless DC motor (SPBLDCM) by using efficiency of the motor as an objective function. In the design procedure of the motor, a cuckoo search (CS) algorithm is used as an optimization tool.Design/methodology/approachFor the purpose of this research work, a computer program for optimal design of electrical machines based on the CS optimization has been developed. Based on the design characteristics of SPBLDCM, some of the motor parameters are chosen to be constant and others variable. A comparative analysis of the initial motor model and the CS model based on the value of the objective function, as well as the values of the optimization parameters, is performed and presented.FindingsBased on the comparative data analysis of both motor models, it can be concluded that the main objective of the optimization is realized, and it is achieved by an improvement of the efficiency of the motor.Practical implicationsThe optimal design approach of SPBLDCM presented in this research work can be also implemented on other electrical machines and devices using the same or even other objective functions.Originality/valueAn optimization technique using CS as an optimization tool has been developed and applied in the design procedure of SPBLDCM. According to the results, it can be concluded that the CS algorithm is a suitable tool for design optimization of SPBLDCM and electromagnetic devices in general. The quality of the CS model has been proved through the data analysis of the initial and optimized solution. The quality of the CS solution has been also proved by comparative analysis of the two motor models using FEM as a performance analysis tool.