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Search Results (195)

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Keywords = permanent-magnet synchronous machine (PMSM)

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14 pages, 8270 KiB  
Article
Design and Analysis of a Highly Reliable Permanent Magnet Synchronous Machine for Flywheel Energy Storage
by Xinjian Jiang, Lei Zhang, Fuwang Li and Zhenghui Zhao
Machines 2024, 12(9), 655; https://doi.org/10.3390/machines12090655 - 19 Sep 2024
Viewed by 319
Abstract
This article aims to propose a highly reliable permanent magnet synchronous machine (PMSM) for flywheel energy-storage systems. Flywheel energy-storage systems are large-capacity energy storage technologies suitable for the short-term storage of electrical energy. PMSMs have been used in the flywheel energy-storage systems due [...] Read more.
This article aims to propose a highly reliable permanent magnet synchronous machine (PMSM) for flywheel energy-storage systems. Flywheel energy-storage systems are large-capacity energy storage technologies suitable for the short-term storage of electrical energy. PMSMs have been used in the flywheel energy-storage systems due to their advantages. One of the key requirements for PMSMs in flywheel energy-storage systems is high reliability. A double redundant winding structure is adopted to ensure fault-tolerant operation of the PMSM. The stator is designed with auxiliary teeth to reduce the short-circuit current. Moreover, the number of slots and poles is determined to ensure the winding factor, heat dissipation, and reduce losses. Moreover, the dual three-phase stator winding structure and auxiliary teeth are adopted on the PMSM to improve reliability. Afterward, the electromagnetic performance is analyzed, and the mechanical stress is investigated to ensure mechanical strength. Finally, a prototype is built and tested to verify the theoretical analysis and performance of the PMSM. Full article
(This article belongs to the Section Electrical Machines and Drives)
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15 pages, 6360 KiB  
Article
Experimental Determination of Influences of Static Eccentricities on the Structural Dynamic Behavior of a Permanent Magnet Synchronous Machine
by Julius Müller, Marius Franck, Kevin Jansen, Gregor Höpfner, Jörg Berroth, Georg Jacobs and Kay Hameyer
Machines 2024, 12(9), 649; https://doi.org/10.3390/machines12090649 - 16 Sep 2024
Viewed by 358
Abstract
In electrified vehicles, the masking noise behavior of internal combustion engines is absent, making the tonal excitation of the electric machine particularly noticeable in vehicle acoustics, which is perceived as disturbing by consumers. Due to manufacturing tolerances, the tonal NVH characteristics of the [...] Read more.
In electrified vehicles, the masking noise behavior of internal combustion engines is absent, making the tonal excitation of the electric machine particularly noticeable in vehicle acoustics, which is perceived as disturbing by consumers. Due to manufacturing tolerances, the tonal NVH characteristics of the electric machine are significantly influenced at wide frequency ranges. This paper presents a systematic exploration of the influence of static eccentricity as one manufacturing tolerance on the NVH behavior of Permanent Magnet Synchronous Machines (PMSMs). The study utilizes a novel test bench setup enabling isolated variations in static eccentricity of up to 0.2 mm in one PMSM. Comparative analysis of acceleration signals reveals significant variations in the dominance of excitation orders with different eccentricity states, impacting critical operating points and dominant frequency rages of the electric machine. Despite experimentation, no linear correlation is observed between increased eccentricity and changes in acceleration behavior. Manufacturing eccentricity and deviations in rotor magnetization are discussed as potential contributors to the observed effects. The findings emphasize static eccentricity as a critical parameter in NVH optimization, particularly in electrified powertrains. However, the results indicate that further investigations are needed to explore the influence of eccentricities and magnetization deviations on NVH behavior comprehensively. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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10 pages, 4839 KiB  
Article
Variable Delayed Time Control for Dual Three-Phase Permanent Magnet Synchronous Motor with Double Central Symmetry Space Vector Pulse Width Modulation
by Tao Tao and Sen Liu
Energies 2024, 17(17), 4347; https://doi.org/10.3390/en17174347 - 30 Aug 2024
Viewed by 379
Abstract
To address the harmonic issues associated with the pulse width modulation (PWM) method, this article introduces variable delayed time (VDT) space vector pulse width modulation (SVPWM) with double central symmetry for dual three-phase permanent magnet synchronous machines (DTP-PMSMs). Firstly, the switching sequence of [...] Read more.
To address the harmonic issues associated with the pulse width modulation (PWM) method, this article introduces variable delayed time (VDT) space vector pulse width modulation (SVPWM) with double central symmetry for dual three-phase permanent magnet synchronous machines (DTP-PMSMs). Firstly, the switching sequence of four traditional vectors undergoes double central symmetry, resulting in the doubling of the frequency of the phase voltage. This alteration eliminates harmonics occurring at odd multiples of carrier frequency. Additionally, the adopting of a single null vector minimizes the additional switching times introduced by the double central symmetry. Subsequently, VDT-SVPWM is employed to further suppress the harmonics at the even multiples of carrier frequency. The implementation of the proposed double central symmetry method involves directly utilizing the calculated duty cycle of the traditional four vectors. Moreover, integrating VDT-SVPWM with the double central symmetry method is straightforward. Simulation and experimental results validate the efficacy of the proposed method in suppressing harmonics and mitigating vibrations in the DTP-PMSM. Full article
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17 pages, 5999 KiB  
Article
Research on Predictive Speed Control Scheme for Surface-Mounted Permanent Magnet Servo Systems
by Zhe Song, Weihong Zhou and Yu Mo
Electronics 2024, 13(17), 3421; https://doi.org/10.3390/electronics13173421 - 28 Aug 2024
Viewed by 492
Abstract
In order to improve the dynamic response and disturbance rejection performance of electric machines, a deadbeat predictive speed control (DPSC) scheme for a permanent magnet synchronous motor (PMSM) is proposed. To begin with, a DPSC controller was proposed with the purpose of achieving [...] Read more.
In order to improve the dynamic response and disturbance rejection performance of electric machines, a deadbeat predictive speed control (DPSC) scheme for a permanent magnet synchronous motor (PMSM) is proposed. To begin with, a DPSC controller was proposed with the purpose of achieving precise control for the next control cycle, and the control parameters were determined based on the optimal parameter design method. For better application, performance comparisons were made with a conventional PI control, and the mismatch effects of inertia and torque were analyzed. In order to improve the disturbance rejection performance of the system, an extended sliding mode observer (ESMO) was constructed to compensate for disturbances. Experimental verification with a conventional PI control indicates that the proposed DPSC control can reduce the speed response time from 0.675 s to 0.650 s. When the electric machine operates stably and is applied to a torque disturbance of 0.4 Nm, the speed fluctuation and settling time can be reduced from 9 rpm and 1.7 s to 6 rpm and 0.5 s, respectively. This proposed method effectively enhances the speed control performance of PMSM and can be applied to high-performance electric machine applications. Full article
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11 pages, 3808 KiB  
Article
Design of Dual Winding Flux Modulation Machine for Performance Improvement in Variable Speed Application
by Min-Gu Lyeo, Kyu-Yun Hwang and Sung-Hyun Lee
Machines 2024, 12(8), 535; https://doi.org/10.3390/machines12080535 - 6 Aug 2024
Viewed by 510
Abstract
In this paper, a Dual Winding Flux Modulation Machine (DWFMM) is proposed for variable speed application. The DWFMM is configured by adding windings to the Single Winding Flux Modulation Machine (SWFMM), consisting of a master winding that drives the motor and a slave [...] Read more.
In this paper, a Dual Winding Flux Modulation Machine (DWFMM) is proposed for variable speed application. The DWFMM is configured by adding windings to the Single Winding Flux Modulation Machine (SWFMM), consisting of a master winding that drives the motor and a slave winding that enables pole changing and performance enhancement. Through pole changing, the DWFMM can operate as two different machines: a Vernier Machine (VM) for varying speeds and torque operations and a Permanent Magnet Synchronous Machine (PMSM). In the VM mode, flux enhancement is applied to improve torque, and in the PMSM mode, Flux Weakening is applied to increase speed. The characteristics of the two different operating modes were analyzed using the Finite Element Method (FEM) to validate the machine’s performance. Finally, the DWFMM and SWFMM were designed and compared as variable speed application machines to confirm their suitability and superiority. Full article
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24 pages, 2447 KiB  
Article
Feasibility Analysis for Active Noise Cancellation Using the Electrical Power Steering Motor
by Dominik Schubert, Simon Hecker, Stefan Sentpali and Martin Buss
Acoustics 2024, 6(3), 730-753; https://doi.org/10.3390/acoustics6030040 - 31 Jul 2024
Viewed by 947
Abstract
This paper describes the use of an electric drive as an acoustic actuator for active noise cancellation (ANC). In the presented application, the idea is to improve the noise, vibration, harshness (NVH) characteristics of passenger cars without using additional active or passive damper [...] Read more.
This paper describes the use of an electric drive as an acoustic actuator for active noise cancellation (ANC). In the presented application, the idea is to improve the noise, vibration, harshness (NVH) characteristics of passenger cars without using additional active or passive damper systems. Many of the already existing electric drives in cars are equipped with the required hardware components to generate noise and vibration, which can be used as compensation signals in an ANC application. To demonstrate the applicability of the idea, the electrical power steering (EPS) motor is stimulated with a control signal, generated by an adaptive feedforward controller, to reduce harmonic disturbances at the driver’s ears. As it turns out, the EPS system generates higher harmonics of the harmonic compensation signal due to nonlinearities in the acoustic transfer path using a harmonic excitation signal. The higher harmonics impair an improvement in the subjective hearing experience, although the airborne noise level of the harmonic disturbance signal can be clearly reduced at the driver’s ears. Therefore, two methods are presented to reduce the amplitude of the higher harmonics. The first method is to limit the filter weights of the algorithm to reduce the amplitude of the harmonic compensation signal. The filter amplitude limitation also leads to a lower amplitude of the higher harmonics, generated by the permanent magnet synchronous machine (PMSM). The second method uses a parallel structure of adaptive filters to actively reduce the amplitude of the higher harmonics. Finally, the effectiveness of the proposed ANC system is demonstrated in two real driving situations, where in one case a synthetic noise/vibration induced by a shaker on the front axle carrier is considered to be the disturbance, and in the other case, the disturbance is a harmonic vibration generated by the combustion engine. In both cases, the subjective hearing experience of the driver could be clearly improved using the EPS motor as ANC actuator. Full article
(This article belongs to the Special Issue Active Control of Sound and Vibration)
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27 pages, 24406 KiB  
Article
Low-Cost Microcontroller-Based System for Condition Monitoring of Permanent-Magnet Synchronous Motor Stator Windings
by Przemyslaw Pietrzak, Marcin Wolkiewicz and Jan Kotarski
Electronics 2024, 13(15), 2975; https://doi.org/10.3390/electronics13152975 - 28 Jul 2024
Viewed by 516
Abstract
Permanent-magnet synchronous motors (PMSMs) have played a key role in recent years in both industrial and commercial applications. Despite their many significant advantages, such as high efficiency, very good dynamics, and high power density, these types of motors are prone to various types [...] Read more.
Permanent-magnet synchronous motors (PMSMs) have played a key role in recent years in both industrial and commercial applications. Despite their many significant advantages, such as high efficiency, very good dynamics, and high power density, these types of motors are prone to various types of faults. This article proposes a low-cost microcontroller-based system for PMSM stator winding condition monitoring and fault diagnosis. It meets the demand created by the use of more and more low-budget solutions in industrial and commercial applications. A printed circuit board (PCB) has been developed to measure PMSM stator phase currents, which are used as diagnostic signals. The key components of this PCB are LEM’s LESR 6-NP current transducers. The acquisition and processing of diagnostic signals using a low-cost embedded system (NUCLEO-H7A3ZI-Q) with an ARM Cortex-M core is described in detail. A machine learning-driven KNN-based fault diagnostic algorithm is implemented to detect and classify incipient PMSM stator winding faults (interturn short-circuits). The effects of the severity of the fault and the motor operating conditions on the symptom extraction process are also investigated. The results of experimental tests conducted on a 2.5 kW PMSM confirmed the effectiveness of the developed system. Full article
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21 pages, 10992 KiB  
Article
Detection of Demagnetization Faults in Electric Motors by Analyzing Inverter Based Current Data Using Machine Learning Techniques
by Daniel Walch, Christoph Blechinger, Martin Schellenberger, Maximilian Hofmann, Bernd Eckardt and Vincent R.H. Lorentz
Machines 2024, 12(7), 468; https://doi.org/10.3390/machines12070468 - 11 Jul 2024
Viewed by 550
Abstract
Demagnetization of the rotor magnets is a significant failure mode that can occur in permanent magnet synchronous machines (PMSMs). Early detection of demagnetization faults can help change system parameters to reduce power output or ensure safety. In this paper, the effects of demagnetization [...] Read more.
Demagnetization of the rotor magnets is a significant failure mode that can occur in permanent magnet synchronous machines (PMSMs). Early detection of demagnetization faults can help change system parameters to reduce power output or ensure safety. In this paper, the effects of demagnetization faults were analyzed both in simulation and experiments using the example of drone motors. An approach was investigated to detect even minor demagnetization faults that does not require any additional sensing effort. Machine learning (ML) techniques are used to analyze the phase current data directly received from the inverter to enable anomaly detection. For this purpose, the phase current is transformed by the Fast Fourier Transform (FFT), the spectral data is then reduced in dimensionality, followed by an anomaly detection algorithm using a one-class support vector machine (OC-SVM). To ensure simplified initialization of the ML model without the need for training sets of damaged drives, only data from magnetically undamaged motors was used to train the models for anomaly detection. Different selections of considered harmonics and different metrics were investigated using the experimental data, achieving a precision of up to 99%, a specificity of up to 98%, and an accuracy of up to 90%. Full article
(This article belongs to the Section Electrical Machines and Drives)
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16 pages, 2152 KiB  
Article
An Improved Near-State Pulse-Width Modulation with Low Switching Loss for a Permanent Magnet Synchronous Machine Drive System
by Pei Qing, Ruoyu Chen and Qiang Gao
Energies 2024, 17(13), 3157; https://doi.org/10.3390/en17133157 - 26 Jun 2024
Viewed by 841
Abstract
Common-mode voltage (CMV) leads to the shaft voltage and shaft current by coupling the capacitor network in the permanent magnet synchronous machine (PMSM), which affects the reliability of the whole motor drive system. Based on the low-CMV modulation strategy for the PMSM drive [...] Read more.
Common-mode voltage (CMV) leads to the shaft voltage and shaft current by coupling the capacitor network in the permanent magnet synchronous machine (PMSM), which affects the reliability of the whole motor drive system. Based on the low-CMV modulation strategy for the PMSM drive system, this paper proposed an improved near-state pulse-width modulation (NSPWM) on switching loss. First, the generation mechanism for the switching signals of NSPWM was analyzed, and it was observed that there exists one phase of switches in an inactive state for every sector. Then, to reduce the switching loss of the NSPWM, this paper proposed an improved NSPWM modulation strategy based on power factor angle to adjust switching action, which ensures the switching tubes that have the biggest conduction current have no switching action. In addition, the switching loss analytic formula of the NSPWM was derived to prove the correctness of the proposed method for optimizing switching loss. Finally, the proposed modulation strategy was carried out in the simulation and experimental platform. Under the premise of good steady and dynamic performance, the results show that the proposed modulation strategy has less switching loss. Full article
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18 pages, 6562 KiB  
Article
Outlier Detection for Permanent Magnet Synchronous Motor (PMSM) Fault Detection and Severity Estimation
by Konstantinos Koutrakos and Epameinondas Mitronikas
Appl. Sci. 2024, 14(10), 4318; https://doi.org/10.3390/app14104318 - 20 May 2024
Viewed by 1531
Abstract
Today, Permanent Magnet Synchronous Motors (PMSMs) are a dominant choice in industry applications. During operation, different possible faults in the system can occur, so early and automated fault detection and severity estimation are required to ensure smooth operation and optimal maintenance planning. In [...] Read more.
Today, Permanent Magnet Synchronous Motors (PMSMs) are a dominant choice in industry applications. During operation, different possible faults in the system can occur, so early and automated fault detection and severity estimation are required to ensure smooth operation and optimal maintenance planning. In this direction, outlier detection methods are employed in this paper. The motor’s current signals are used to extract useful indicators of the fault, along with d-q transform. Statistical indicators in both time and frequency domains are selected to describe fault-related patterns. Based on the extracted features, three outlier detection methods are investigated: the Isolation Forest, the One Class Support Vector Machine, and the Robust Covariance Ellipse. Each method is investigated through different model parameters to evaluate fault detection and severity estimation capabilities. Finally, an ensemble approach is proposed based on decisions and outlier score ensemble. The proposed methodology is verified through different operating conditions in a PMSM test bench. Full article
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27 pages, 5565 KiB  
Article
Influence of High-Frequency Operation on the Efficiency of a PMSM Drive with SiC-MOSFET Inverter
by Paisak Poolphaka, Ehsan Jamshidpour, Thierry Lubin, Lotfi Baghli and Noureddine Takorabet
Energies 2024, 17(10), 2347; https://doi.org/10.3390/en17102347 - 13 May 2024
Viewed by 1326
Abstract
This paper investigates the effects of high-frequency switching and a high fundamental frequency on the parameters and efficiency of a high-speed permanent magnet synchronous machine (PMSM) drive. We discuss the design and modeling of the PMSM, taking into account these high-frequency effects. The [...] Read more.
This paper investigates the effects of high-frequency switching and a high fundamental frequency on the parameters and efficiency of a high-speed permanent magnet synchronous machine (PMSM) drive. We discuss the design and modeling of the PMSM, taking into account these high-frequency effects. The impact of high frequencies is analyzed across three different inverters (IGBT, Fast IGBT, and SiC-MOSFET) and the motor, and we employ theoretical analysis, computer simulations, and experimental tests for validation. Our goal is to enhance our understanding of how these high-frequency factors affect the performance of the motor drive. Full article
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18 pages, 17861 KiB  
Article
Investigation of Torque and Reduction of Torque Ripples through Assisted-Poles in Low-Speed, High-Torque Density Spoke-Type PMSMs
by Sayyed Haleem Shah, Yun-Chong Wang, Dan Shi and Jian-Xin Shen
Machines 2024, 12(5), 327; https://doi.org/10.3390/machines12050327 - 10 May 2024
Viewed by 855
Abstract
In this article, rotor designs utilizing assisted-poles are investigated for a high-torque density spoke-type permanent magnet synchronous machine (PMSM) with fractional slot concentrated winding (FSCW) to explore the rich air-gap magnetic field harmonics and torque generation mechanism. Due to their higher average torque [...] Read more.
In this article, rotor designs utilizing assisted-poles are investigated for a high-torque density spoke-type permanent magnet synchronous machine (PMSM) with fractional slot concentrated winding (FSCW) to explore the rich air-gap magnetic field harmonics and torque generation mechanism. Due to their higher average torque output, spoke-type PMSMs with FSCW are increasingly used in high-torque density applications. However, slot harmonics generate torque ripples that are difficult to eliminate in FSCW spoke-type PMSMs. Removing slot harmonics from the stator or winding results in a large drop in torque since their winding factors are identical to those of the main harmonic. Therefore, rotor designs having assisted-poles (symmetrical and asymmetrical) are investigated in this work to mitigate slot harmonics and minimize torque ripples. Firstly, the air-gap flux density is analyzed for the machines having assisted-poles, and a model of interaction between the stator and rotor-MMF harmonics is created and validated through Finite element analysis (FEA) to analyze the torque production mechanism. In addition, an analytical relationship between the assisted-poles’ dimensions and the generated torque harmonics is proposed. Furthermore, a generalized torque ripple reduction concept for the FSCW spoke-type PMSM having asymmetrically designed assisted-poles is presented. The proposed design and optimization method are validated through analytical calculations and FEA simulations, and a brief comparative analysis is presented for the analyzed machine prototypes. It has been established that the machine designed by applying the proposed asymmetrical assisted-poles can achieve a reduction in torque ripples while also significantly lowering cogging torque in comparison to the conventional spoke-type PMSMs and other spoke-type PMSMs with rotor having symmetrical assisted-poles. Full article
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16 pages, 2445 KiB  
Article
Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features
by Zenon Zwierzewicz, Dariusz Tarnapowicz and Arkadiusz Nerć
Energies 2024, 17(9), 2178; https://doi.org/10.3390/en17092178 - 2 May 2024
Viewed by 672
Abstract
Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors [...] Read more.
Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem. Full article
(This article belongs to the Special Issue Trends and Applications in Permanent Magnet Synchronous Motor)
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22 pages, 7090 KiB  
Article
A Model Predictive Control Scheme with Minimum Common-Mode Voltage for PMSM Drive System Fed by VSI
by Pei Qing, Jialu Xiong and Fengting Ma
Machines 2024, 12(5), 292; https://doi.org/10.3390/machines12050292 - 26 Apr 2024
Cited by 1 | Viewed by 850
Abstract
Common-mode voltage (CMV) brings shaft voltage and shaft current, and corrodes the bearings of the permanent-magnet synchronous machine (PMSM), which affects the reliability of the whole PMSM drive system. Since the CMV applied by the zero voltage vectors (ZVVs) is three times that [...] Read more.
Common-mode voltage (CMV) brings shaft voltage and shaft current, and corrodes the bearings of the permanent-magnet synchronous machine (PMSM), which affects the reliability of the whole PMSM drive system. Since the CMV applied by the zero voltage vectors (ZVVs) is three times that applied by the active voltage vectors (AVVs), a modulation scheme achieving minimum CMV without ZVV is proposed and introduced into the model predictive control structure for the PMSM drive system. Firstly, the whole modulation range is divided into three regions, including the low voltage modulation region (LVMR), high voltage modulation region (HVMR), and over-voltage modulation region (OVMR). Meanwhile, the regional boundary expression is derived. Then, the active zero-state pulse width modulation (AZSPWM) is adopted in LVMR. To improve the steady-state performance, near-state pulse width modulation (NSPWM) without opposite ZVVs is applied to the HVMR. Furthermore, when the reference voltage vector (VV) is located in OVMR, an optimal scheme is proposed to improve the dynamic response. Under the premise of no ZVV existing in the whole modulation region, simulation and experimental results show that the proposed hybrid modulation method can improve the steady-state and dynamic performance of the PMSM drive system. Full article
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18 pages, 1170 KiB  
Article
Robust Design Optimization of Electric Machines with Isogeometric Analysis
by Theodor Komann, Michael Wiesheu, Stefan Ulbrich and Sebastian Schöps
Mathematics 2024, 12(9), 1299; https://doi.org/10.3390/math12091299 - 25 Apr 2024
Viewed by 916
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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