Explore the vast range of titles available.

The bio-inspired algorithms are novel, modern, and efficient tools for the design of electrical machines. However, from the mathematical point of view, these problems belong to the most general branch of non-linear optimization problems, where these tools cannot guarantee that a global minimum is found. The numerical cost and the accuracy of these algorithms depend on the initialization of their internal parameters, which may themselves be the subject of parameter tuning according to the application. In practice, these optimization problems are even more challenging, because engineers are looking for robust designs, which are not sensitive to the tolerances and the manufacturing uncertainties. These criteria further increase these computationally expensive problems due to the additional evaluations of the goal function. The goal of this paper is to give an overview of the widely used optimization techniques in electrical machinery and to summarize the challenges and open problems in the applications of the robust design optimization and the prospects in the case of the newly emerging technologies.

Electrical machines are the hearts of many appliances, industrial equipment and systems. In the context of global sustainability, they must fulfill various requirements, not only physically and technologically but also environmentally. Therefore, their design optimization process becomes more and more complex as more engineering disciplines/domains and constraints are involved, such as electromagnetics, structural mechanics and heat transfer. This paper aims to present a review of the design optimization methods for electrical machines, including design analysis methods and models, optimization models, algorithms and methods/strategies. Several efficient optimization methods/strategies are highlighted with comments, including surrogate-model based and multi-level optimization methods. In addition, two promising and challenging topics in both academic and industrial communities are discussed, and two novel optimization methods are introduced for advanced design optimization of electrical machines. First, a system-level design optimization method is introduced for the development of advanced electric drive systems. Second, a robust design optimization method based on the design for six-sigma technique is introduced for high-quality manufacturing of electrical machines in production. Meanwhile, a proposal is presented for the development of a robust design optimization service based on industrial big data and cloud computing services. Finally, five future directions are proposed, including smart design optimization method for future intelligent design and production of electrical machines.

This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.

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.

Design, tuning and implementation of various control structures, such as one-degree of freedom (DOF) and two-DOF structures of both integer-order and fractional-order proportional integral derivative controller to stabilize the magnetic levitation plant, is proposed in this paper. The two-DOF structure has been formulated by incorporating a separate control loop in the existing one-DOF control structure. The parameters of all the controller structures have been tuned using evolutionary algorithms, namely, particle swarm optimization (PSO), teaching learning-based optimization (TLBO), genetic algorithm (GA) and black widow optimization (BWO). The performance of the algorithms has been compared on the basis of Wilcoxon signed-rank test and Friedman test. The controller structures have also been tested for disturbance rejection, by applying a periodic pulse distribution at the output of the closed loop. It is found that the system achieves iso-damping characteristic, exhibiting flat phase-plot at the vicinity of the gain cross-over frequency. It is also observed that the two-DOF FOPID controller structure exhibits an improvement of 45.02%, 7.6% and 7.81% in peak overshoot (OS), settling time (Ts) and rise time (Tr), respectively, over two-DOF IOPID, in case of GA. In comparison with GA, the improvement of 73.02%, 4.31% and 5.7% is witnessed for OS, Ts and Tr in case of PSO and 20.029%, 11.03% and 10.60% improvement is observed for OS, Ts, Tr in the case of TLBO algorithm. In contrast, the BWO-tuned two-DOF FOPID controller exhibits superior time-domain response as it generates an improvement of nearly 100%, 29.28% and 14.76% for OS, Ts and Tr. The proposed controller achieves superior disturbance rejection ability measured in terms of sensitivity and complementary sensitivity compared to other state-of-art algorithms.

As power network complexity increases, efficient control of frequency deviations and tie-line power fluctuations becomes crucial. Load frequency control (LFC) addresses these issues by managing generation-consumption mismatches. This paper introduces a unique P-P-FOPID cascade controller for LFC, combining a proportional controller with a fractional-order PID. The marine predators algorithm (MPA), known for its benefits like being parameter-less, derivative-free, user-friendly, flexible, and simple, is employed to optimize the controller’s parameters using the integral time absolute error criterion. Tested on three power systems, the proposed controller outperforms single-structure FOPID controller based on MPA and recent approaches in reducing ITAE, settling time, and frequency and tie-line power deviations. In comparative analysis, the proposed MPA-tuned P-P-FOPID controller achieves a 60% and 11% decrease in ITAE compared to the second-best DSA-optimized FOPI-FOPD controller for Systems 1 and 2, respectively, and a 25% decrease compared to the second-best MPA-tuned FOPID controller for System 3. Furthermore, the controller’s robustness against parametric uncertainties is confirmed through variations in fundamental parameters.

In modern electronics, there are many inevitable uncertainties and variations of design parameters that have a profound effect on the performance of a device. These are, among others, induced by manufacturing tolerances, assembling inaccuracies, material diversities, machining errors, etc. This prompts wide interests in enhanced optimization algorithms that take the effect of these uncertainty sources into account and that are able to find robust designs, i.e., designs that are insensitive to the uncertainties early in the design cycle. In this work, a novel machine learning-based optimization framework that accounts for uncertainty of the design parameters is presented. This is achieved by using a modified version of the expected improvement criterion. Moreover, a data-efficient Bayesian Optimization framework is leveraged to limit the number of simulations required to find a robust design solution. Two suitable application examples validate that the robustness is significantly improved compared to standard design methods.

Flux-switching wound field machines (FSWFMs) offer high torque density and independence from rare-earth materials, making them promising candidates for sustainable electric vehicles and industrial applications. However, their adoption is limited by challenges such as high torque ripple, efficiency variations, and sensitivity to manufacturing tolerances. This study presents a Design for Six Sigma (DFSS) optimization framework that integrates sensitivity analysis, response surface modeling (RSM), and multi-objective genetic algorithms to address these challenges. The optimized solution reduces torque ripple by 7.69%, improves torque output, and enhances energy efficiency. By incorporating Six Sigma principles, the framework ensures robust performance under manufacturing variations, bridging the gap between theoretical optimization and practical implementation. This scalable and efficient methodology establishes FSWFMs as viable solutions for industrial applications, revolutionizing electric machine design.

Interior Permanent Magnet Synchronous Motors (IPMSMs) are a leading technology for electric vehicles (EVs) owing to their high efficiency and power density, yet their performance is limited by torque ripple, drive losses, and sensitivity to parameter variations. This paper presents a robust rotor profile optimization (RPO) framework that integrates a modified adaptive particle swarm optimization (MAPSO) algorithm with finite-element analysis to enhance torque production and minimize torque fluctuations. Unlike conventional optimization approaches, the proposed framework incorporates sensitivity and robustness evaluation, ensuring stable performance under input uncertainties. The optimized rotor design achieves an 8.65% increase in average torque (92.45 → 100.45 Nm), a 69.61% reduction in torque ripple (22.17% → 6.74%), and a slight efficiency improvement (97.08% → 97.12%) while maintaining the same 25 kW power rating and 2250 rpm base speed. Additionally, the 6% refers to the overall or representative robustness level, confirming robustness against parameter deviations. These results demonstrate that the proposed optimization method enables reliable rotor geometry refinement within the same motor envelope, leading to higher torque density, reduced pulsations, and improved suitability for high-performance EV traction applications.

The manufacturing tolerance of the permanent magnets (PMs) is inherent in the produce of the machine. These tolerances influence back electromotive force (EMF), which is an important response of the motor. In order to enhance the quality of the product, the authors need to reduce these tolerances, but it is very difficult and involves a number of costs. Therefore, this study presents a robust design of the EMF characteristic analysis considering the manufacturing tolerances of PM in the interior PM synchronous motor (IPMSM). Among the robust optimisation method, Taguchi robust design based on orthogonal array was applied. Finally, the validity of the analysis result is verified by comparing the optimum design model with present design model (mass production model) ones.