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1.
Heliyon ; 10(17): e36425, 2024 Sep 15.
Artículo en Inglés | MEDLINE | ID: mdl-39281471

RESUMEN

The Gazelle Optimization Algorithm (GOA) is an innovative nature-inspired metaheuristic algorithm, designed to mimic the agile and efficient hunting strategies of gazelles. Despite its promising performance in solving complex optimization problems, there is still a significant scope for enhancing its efficiency and robustness. This paper introduces several novel variants of GOA, integrating adaptive strategy, Levy flight strategy, Roulette wheel selection strategy, and random walk strategy. These enhancements aim to address the limitations of the original GOA and improve its performance in diverse optimization scenarios. The proposed algorithms are rigorously tested on CEC 2014 and CEC 2017 benchmark functions, five engineering problems, and a Total Harmonic Distortion (THD) minimization problem. The results demonstrate the superior performance of the proposed variants compared to the original GOA, providing valuable insights into their applicability and effectiveness.

2.
Semin Hear ; 45(2): 153-171, 2024 May.
Artículo en Inglés | MEDLINE | ID: mdl-38855342

RESUMEN

This chapter will take you through specific patient complaints and the test box measures you can use to address these complaints. These measurements give you data that aid in your decision making about what is wrong, if anything, with the hearing aid and how you might address the problem. Before we discuss specific patient complaints and problems, let us review the American National Standard Institute (ANSI) guidelines for hearing aid testing in a test box.

3.
Sci Rep ; 14(1): 12690, 2024 Jun 03.
Artículo en Inglés | MEDLINE | ID: mdl-38830916

RESUMEN

A random initialization of the search particles is a strong argument in favor of the deployment of nature-inspired metaheuristic algorithms when the knowledge of a good initial guess is lacked. This article analyses the impact of the type of randomization on the working of algorithms and the acquired solutions. In this study, five different types of randomizations are applied to the Accelerated Particle Swarm Optimization (APSO) and Squirrel Search Algorithm (SSA) during the initializations and proceedings of the search particles for selective harmonics elimination (SHE). The types of randomizations include exponential, normal, Rayleigh, uniform, and Weibull characteristics. The statistical analysis shows that the type of randomization does impact the working of optimization algorithms and the fittest value of the objective function.

4.
Sci Rep ; 14(1): 12775, 2024 Jun 04.
Artículo en Inglés | MEDLINE | ID: mdl-38834739

RESUMEN

This paper presents an innovative control scheme designed to significantly enhance the power factor of AC/DC boost rectifiers by integrating an adaptive neuro-fuzzy inference system (ANFIS) with predictive current control. The innovative control strategy addresses key challenges in power quality and energy efficiency, demonstrating exceptional performance under diverse operating conditions. Through rigorous simulation, the proposed system achieves precise input current shaping, resulting in a remarkably low total harmonic distortion (THD) of 3.5%, which is well below the IEEE-519 standard threshold of 5%. Moreover, the power factor reaches an outstanding 0.990, indicating highly efficient energy utilization and near-unity power factor operation. To validate the theoretical findings, a 500 W laboratory prototype was implemented using the dSPACE ds1104 digital controller. Steady-state analysis reveals sinusoidal input currents with minimal THD and a power factor approaching unity, thereby enhancing grid stability and energy efficiency. Transient response tests further demonstrate the system's robustness against load and voltage fluctuations, maintaining output voltage stability within an 18 V overshoot and a 20 V undershoot during load changes, and achieving rapid response times as low as 0.2 s. Comparative evaluations against conventional methods underscore the superiority of the proposed control strategy in terms of both performance and implementation simplicity. By harnessing the strengths of ANFIS-based voltage regulation and predictive current control, this scheme offers a robust solution to power quality issues in AC/DC boost rectifiers, promising substantial energy savings and improved grid stability. The results affirm the potential of the proposed system to set new benchmarks in power factor correction technology.

5.
Sensors (Basel) ; 24(4)2024 Feb 06.
Artículo en Inglés | MEDLINE | ID: mdl-38400214

RESUMEN

Earlier protection methods mainly focused on using communication channels to transmit trip signals between the protective devices (PDs), with no solutions provided in the case of communication failure. Therefore, this paper introduces a dual-layer protection system to ensure secure protection against fault events in the Distribution Systems (DSs), particularly in light of communication failures. The initial layer uses the Total Harmonic Distortion (THD), the estimates of the amplitude voltages, and the zero-sequence grid voltage components, functioning as a fault sensor, to formulate an adaptive algorithm based on a Finite State Machine (FSM) for the detection and isolation of faults within the grid. This layer primarily relies on communication protocols for effective coordination. A Second-Order Generalized Integrator (SOGI) expedites the derivation of the estimated variables, ensuring fast detection with minimal computational overhead. The second layer uses the behavior of the positive- and negative-sequence components of the grid voltages during fault events to locate and isolate these faults. In the event that the first layer exposes a communication failure, the second layer will automatically be activated to ensure secure protection as it operates, using the local information of the Protective devices (PDs), without the need for communication channels to transmit trip signals between the PDs. The proposed protection system has been assessed using simulations with MATLAB/Simulink and providing experimental results considering an IEEE 9-bus standard radial system. The obtained results confirm the capability of the system for identifying and isolating different types of faults, varying conditions, and modifications to the grid configuration. The results show good behavior of the initial THD-based layer, with fast time responses ranging from 6 to 8.5 ms in all the examined scenarios. In contrast, the sequence-based layer exhibits a protection time response of approximately 150 ms, making it a viable backup option in the event of a communication failure.

6.
Sensors (Basel) ; 24(1)2024 Jan 03.
Artículo en Inglés | MEDLINE | ID: mdl-38203149

RESUMEN

The use of advanced modulation and control schemes for power converters, such as a Feedback Quantizer and Predictive Control, is widely studied in the literature. This work focuses on improving the closed-loop modulation scheme called Feedback Quantizer, which is applied to a three-phase voltage source inverter. This scheme has the natural behavior of mitigating harmonics at low frequencies, which are detrimental to electrical equipment such as transformers. This modulation scheme also provides good tracking for the voltage reference at the fundamental frequency. On the other hand, the disadvantage of this scheme is that it has a variable switching frequency, creating a harmonic spectrum in frequency dispersion, and it also needs a small sampling time to obtain good results. The proposed scheme to improve the modulation scheme is based on a Discrete Space Vector with virtual vectors to obtain a better approximation of the optimal vectors for use in the algorithm. The proposal improves the conventional scheme at a high sampling time (200 µs), obtaining a THD less than 2% in the load current, decreases the noise created by the conventional scheme, and provides a fixed switching frequency. Experimental tests demonstrate the correct operation of the proposed scheme.

7.
Sci Prog ; 106(4): 368504231208520, 2023.
Artículo en Inglés | MEDLINE | ID: mdl-37899707

RESUMEN

The grid-connected inverter is the key to ensure stable, reliable, safe, and efficient operation of the power generation system; the quality of the grid-connected output current waveform directly affects the performance of the entire power generation system. To improve the anti-interference performance and reduce the output current harmonic content of the grid-connected inverter, an improved control strategy that combined repetitive control (RC) and auto disturbance rejection control (ADRC) is designed in this paper. Firstly, decoupled the ADRC to realize the individual adaptation between tracking performance parameters and anti-interference performance parameters of the controller, through which the difficulty of adjusting parameters is reduced. Secondly, the control approach is devised by adding RC to ADRC. To demonstrate the effectiveness of the proposed method in this paper, detailed experimental studies are conducted using proportional integral control, traditional ADRC, and the proposed method under normal power grids, weak power grids, and periodic disturbances. And dynamic performance simulation experiment is done to verify the dynamic performance of the self-disturbance rejection controller before and after the addition of RC links. The results indicated the effectiveness and feasibility of the proposed method. Finally, after simulation, the steady state and dynamic performance are conducted on a hardware testing platform. The impacts of the obtained results indicate the effectiveness and feasibility of the control algorithm proposed, the ability to suppress intermediate frequency disturbances is improved, the bandwidth of the auto disturbance rejection controller is expanded, and the harmonic content of the output current is depressed.

8.
Sensors (Basel) ; 23(10)2023 May 18.
Artículo en Inglés | MEDLINE | ID: mdl-37430787

RESUMEN

The integration of Distributed Generators (DGs) into distribution systems (DSs) leads to more reliable and efficient power delivery for customers. However, the possibility of bi-directional power flow creates new technical problems for protection schemes. This poses a threat to conventional strategies because the relay settings have to be adjusted depending on the network topology and operational mode. As a solution, it is important to develop novel fault protection techniques to ensure reliable protection and avoid unnecessary tripping. In this regard, Total Harmonic Distortion (THD) can be used as a key parameter for evaluating the grid's waveform quality during fault events. This paper presents a comparison between two DS protection strategies that employ THD levels, estimated amplitude voltages, and zero-sequence components as instantaneous indicators during the faults that function as a kind of fault sensor to detect, identify, and isolate faults. The first method uses a Multiple Second Order Generalized Integrator (MSOGI) to obtain the estimated variables, whereas the second method uses a single SOGI for the same purpose (SOGI-THD). Both methods rely on communication lines between protective devices (PDs) to facilitate coordinated protection. The effectiveness of these methods is assessed by using simulations in MATLAB/Simulink considering various factors such as different types of faults and DG penetrations, different fault resistances and fault locations in the proposed network. Moreover, the performance of these methods is compared with conventional overcurrent and differential protections. The results show that the SOGI-THD method is highly effective in detecting and isolating faults with a time interval of 6-8.5 ms using only three SOGIs while requiring only 447 processor cycles for execution. In comparison to other protection methods, the SOGI-THD method exhibits a faster response time and a lower computational burden. Furthermore, the SOGI-THD method is robust to harmonic distortion, as it considers pre-existing harmonic content before the fault and avoids interference with the fault detection process.

9.
Sensors (Basel) ; 23(10)2023 May 18.
Artículo en Inglés | MEDLINE | ID: mdl-37430788

RESUMEN

The total harmonic distortion (THD) index and its calculation methods are presented to calibrate the sinusoidal motion of the low-frequency angular acceleration rotary table (LFAART) and make up the incomprehensive evaluation based on the angular acceleration amplitude and frequency error indexes. The THD is calculated from two measurement schemes: a unique scheme combining the optical shaft encoder and the laser triangulation sensor and a regular scheme using the fiber optical gyroscope (FOG). An improved reversing moments recognition method is presented to upgrade the accuracy of solving the angular motion amplitude based on optical shaft encoder output. The field experiment shows that the difference in the THD values achieved using the combining scheme and FOG is within 0.11% when the signal-to-noise ratio of the FOG signal is higher than 7.7 dB, indicating the accuracy of the proposed methods and the feasibility of taking THD as the index.

10.
Sensors (Basel) ; 23(9)2023 Apr 22.
Artículo en Inglés | MEDLINE | ID: mdl-37177409

RESUMEN

Power electronic converters and alternating current motors are the actual driving solution applied to electric vehicles (EVs). Multilevel inverters with high performance are modern and the basis for powering and driving EVs. Fault component detection in multilevel power converters requires the use of a smart sensor-based strategy and an optimal fault analysis and prediction method. An innovative method for the detection and prediction of defects in multilevel inverters for EVs is proposed in this article. This method is based on an algorithm able to determine in a fast and efficient way the faults in a multilevel inverter in different possible topologies. Moreover, the fault detection is achieved not only for a single component, but even for several components, if these faults occur simultaneously. The detection mechanism is based on the analysis of the output current and voltage from the inverter, with the possibility of distinguishing between single and multiple faults of the power electronic components. High-performance simulation programs are used to define and verify the method model. Additionally, with this model, harmonic analysis can be performed to check the correctness of the system's operation, and different fault scenarios can be simulated. Thus, significant results were obtained by simulation on various topologies of multilevel converters. Further, a test bench was developed in order to verify some failure situations on a three-level inverter.

11.
Sensors (Basel) ; 23(2)2023 Jan 14.
Artículo en Inglés | MEDLINE | ID: mdl-36679778

RESUMEN

The rapid growth of the distributed generators (DGs) integration into the distribution systems (DSs) creates new technical issues; conventional relay settings need to be updated depending on the network topology and operational mode as fault protection a major challenge. This emphasizes the need for new fault protection methods to ensure secure protection and prevent undesirable tripping. Total harmonic distortion (THD) is an important indicator for assessing the quality of the grid. Here, a new protection system based on the THD of the grid voltages is proposed to address fault events in the electrical distribution network. The proposed protection system combines the THD with the estimates of the amplitude voltages and the zero-sequence component for defining an algorithm based on a finite state machine (FSM) for the detection, identification, and isolation of faults in the grid. The algorithm employs communication lines between all the protective devices (PDs) of the system to transmit tripping signals, allowing PDs to be coordinated. A second order generalized integrator (SOGI) and multiple SOGI (MSOGI) are used to obtain the THDs, estimated amplitude voltages, and zero-sequence component, which allows for fast detection with a low computational burden. The protection algorithm performance is evaluated through simulations in MATLAB/Simulink and a comparative study is developed between the proposed protection method and a differential relay (DR) protection system. The proposed method shows its capability to detect and isolate faults during different fault types with different fault resistances in different locations in the proposed network. In all the tested scenarios, the detection time of the faults has been between 7-10 ms. Moreover, this method gave the best solution as it has a higher accuracy and faster response than the conventional DR protection system.


Asunto(s)
Algoritmos , Comunicación , Fenómenos Físicos , Sistemas de Computación , Electricidad
12.
Artículo en Inglés | MEDLINE | ID: mdl-38545927

RESUMEN

A boost Power Factor Correction (PFC) circuit is connected between the AC grid and converters to meet Electromagnetic Interference (EMI) and Total Harmonic Distortion (THD) standards. An EMI filter should be utilized at the input of the PFC to attenuate high-frequency noise injected into the grid. This article discusses the low-conducted EM emission boost PFC with Sliding Frequency Modulation (SFM) proposed by Power Integrations. The proposed boost PFC is compared with a conventional boost PFC operated using Constant Frequency Modulation (CFM) at 120 kHz. Both PFCs are rated for the same nominal power (i.e., 300 W) and output voltage (i.e., 383 V). An analytical loss model is also developed to compare the performance of the SFM and CFM PFCs. The analytical findings are verified by means of simulations and experiments.

13.
Heliyon ; 8(12): e11733, 2022 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-36478823

RESUMEN

Optimization of supply current total harmonic distortion (THD) of multi-pulse AC-DC power converter fed induction motor drive (IMD) is always a challenging issue. Higher amount of supply current THD degrades the input power quality of IMD. The supply current THD should be controlled in such a way so that it adheres the power quality standard of IEEE-519. With the increase of the pulse number of multi-pulse AC-DC converter, supply current THD increases. In this work, an investigation has been carried out on 6-pulse, 12-pulse, 18-pulse, and 24-pulse AC-DC power converters based IMD. A thorough analysis of input current profile, THD, dynamic responses including stator current, speed, torque profile of the induction motor are highlighted in this work with the various load perturbation conditions. This work will provide a message to the industrial community about the proper selection of AC-DC power converter for IMD application considering power quality and circuit configuration issues. All the investigating works are conducted in MATLAB/Simulink platform.

14.
Sensors (Basel) ; 22(20)2022 Oct 13.
Artículo en Inglés | MEDLINE | ID: mdl-36298118

RESUMEN

Different methods for galvanically isolated monitoring of the mains voltage waveform were evaluated. The aim was to determine the level of distortion of the output signal relative to the input signal and the suitability of each method for calculating active power values. Six fixtures were tested: two voltage transformers, an electronic circuit with a current transformer, a standalone current transformer, a simple circuit with optocouplers, and a circuit with an A/D-D/A converter with capacitive coupling. The input and output waveforms were mathematically analyzed by three methods: (1) calculating the spectral components of waveforms and the relative changes in their THD (total harmonic distortion) values, (2) determining the similarity of waveforms according to the size of the area bounded by the input and output waveform curves, and (3) determining the accuracy of the active power calculation based on the output waveform. The time difference in the zero crossing of the input and output signals was measured, and further calculations for the second and third method were performed on the zero-crossing time shift-corrected waveforms. Other aspects of selecting the appropriate type of monitoring element, such as power consumption or overall circuit complexity, were also evaluated.


Asunto(s)
Suministros de Energía Eléctrica , Electrónica
15.
Sensors (Basel) ; 22(20)2022 Oct 19.
Artículo en Inglés | MEDLINE | ID: mdl-36298336

RESUMEN

The field of advanced digital signal processing methods is one of the fastest developing scientific and technical disciplines, and is important in the field of Shunt Active Power Filter control methods. Shunt active power filters are highly desirable to minimize losses due to the increase in the number of nonlinear loads (deformed power). Currently, there is rapid development in new adaptive, non-adaptive, and especially hybrid methods of digital signal processing. Nowadays, modern methods of digital signal processing maintain a key role in research and industrial applications. Many of the best practices that have been used to control shunt active power in industrial practice for decades are now being surpassed in favor of new progressive approaches. This systematic research review classifies the importance of using advanced signal processing methods in the field of shunt active power filter control methods and summarizes the extant harmonic extraction methods, from the conventional approach to new progressive methods using genetic algorithms, artificial intelligence, and machine learning. Synchronization techniques are described and compared as well.


Asunto(s)
Algoritmos , Inteligencia Artificial , Procesamiento de Señales Asistido por Computador , Aprendizaje Automático
16.
Sensors (Basel) ; 22(11)2022 May 28.
Artículo en Inglés | MEDLINE | ID: mdl-35684722

RESUMEN

The use of controlled power converters has been extended for high power applications, stacking off-the-shelve semiconductors, and allowing the implementation of, among others, AC drives for medium voltages of 2.3 kV to 13.8 kV. For AC drives based on power cells assembled with three-phase diode rectifiers and cascaded H-bridge inverters, a sophisticated input multipulse transformer is required to reduce the grid voltage, provide isolation among the power cells, and compensate for low-frequency current harmonics generated by the diode-based rectifiers. However, this input multipulse transformer is bulky, heavy, and expensive and must be designed according to the number of power cells, not allowing total modularity of the AC drives based on cascade H-bridges. This study proposes and evaluates a control strategy based on a finite control set-model predictive control that emulates the harmonic cancellation performed by an input multipulse transformer in a cascade H-bridge topology. Hence, the proposed method requires conventional input transformers and replaces the three-phase diode rectifiers. As a result, greater modularity than the conventional multicell converter and improved AC overall input current with a THD as low as 2% with a unitary displacement power factor are achieved. In this case, each power cell manages its own DC voltage using a nonlinear control strategy, ensuring stable system operation for passive and regenerative loads. The experimental tests demonstrated the correct performance of the proposed scheme.

17.
ISA Trans ; 131: 377-396, 2022 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-35643879

RESUMEN

To well manage the quality of the injected electrical power into the grid from a variable speed wind turbine (VSWT), direct power control (DPC) scheme using second order sliding mode control (SOSMC) based on super-twisting algorithm (STA) approach is proposed. Meanwhile, for reaching the adequate gains of STA, an appropriate optimizer should be implemented. Therefore, shuffled complex evolution (SCE) algorithm-based parameter identification is suggested. To verify the effectiveness of the proposed SCE based controller, several well-known algorithms have been tested under various operating conditions namely: particle swarm optimizer (PSO), artificial bee colony optimizer (ABCO), ant colony optimization (ACO), rooted tree optimizer (RTO) and gray wolf optimizer (GWO). The results confirm the superiority of the proposed SCE algorithm among the competing algorithms and classic SMC regarding the active power steady-state error (0.7233%), undershoot percentage (0.1333%), settling time (0.6810 × 10-3 s), rise time (1.7515 × 10-4 s), peak value (7.0521 × 103 W), overall efficiency (99.2800%), and total harmonic distortion (0.7900%). The proposed SCE based controller allows getting important performances under various operating condition of wind speed and load variations with interesting electrical network stability.


Asunto(s)
Algoritmos , Modelos Teóricos , Electricidad , Sistemas de Computación
18.
Micromachines (Basel) ; 13(2)2022 Jan 25.
Artículo en Inglés | MEDLINE | ID: mdl-35208304

RESUMEN

Multilevel inverters are a type of power electronic circuit that converts direct current (DC) to alternating current (AC) for use in high-voltage and high-power applications. Many recent studies on multilevel inverters have used field-programmable gate arrays (FPGAs) as a switching controller device to overcome the limitations of microcontrollers or DSPs, such as limited sampling rate, low execution speed, and a limited number of IO pins. However, the design techniques of most existing FPGA-based switching controllers require large amounts of memory (RAM) for storage of sampled data points as well as complex controller architectures to generate the output gating pulses. Therefore, in this paper, we propose two types of FPGA-based digital switching controllers, namely selective harmonic elimination (SHE) and sinusoidal pulse width modulation (SPWM), for a 21-level multilevel inverter. Both switching controllers were designed with minimal hardware complexity and logic utilisation. The designed SHE switching controller mainly consists of a four-bit finite state machine (FSM) and a 13-bit counter, while the SPWM switching controller employs a simple iterative CORDIC algorithm with a small amount of data storage requirement, a six-bit up-down counter, and a few adders. Initially, both digital switching controllers (SHE and SPWM) were designed using the hardware description language (HDL) in Verilog codes and functionally verified using the developed testbenches. The designed digital switching controllers were then synthesised and downloaded to the Intel FPGA (DE2-115) board for real-time verification purposes. For system-level verification, both switching controllers were tested on five cascaded H-Bridge circuits for a 21-level multilevel inverter model using the HDL co-simulation method in MATLAB Simulink. From the synthesised logic gates, it was found that the designed SHE and SPWM switching controllers require only 186 and 369 logic elements (LEs), respectively, which is less than 1% of the total LEs in an FPGA (Cyclone IV E) chip. The execution speed of the SHE switching controller implemented in the FPGA (Cyclone IV E) chip was found to be a maximum of 99.97% faster when compared with the microcontroller (PIC16F877A). The THD percentage of the 21-level SHE digital switching controller (3.91%) was found to be 37% less than that of the SPWM digital switching controller (6.17%). In conclusion, the proposed simplified design architectures of SHE and SPWM digital switching controllers have been proven to not only require minimal logic resources, achieve high processing speeds, and function correctly when tested on a real-time FPGA board, but also generate the desired 21-level stepped sine-wave output voltage (±360 VPP) at a frequency of 50 Hz with low THD percentages when tested on a 21-level cascaded H-Bridge multilevel inverter model.

19.
Sensors (Basel) ; 22(3)2022 Jan 28.
Artículo en Inglés | MEDLINE | ID: mdl-35161771

RESUMEN

An on-line multi-frequency electrical resistance tomography (mfERT) device with a melt-resistive sensor and noise reduction hardware has been proposed for crystalline phase imaging in high-temperature molten oxide. The melt-resistive sensor consists of eight electrodes made of platinum-rhodium (Pt-20mass%Rh) alloy covered by non-conductive aluminum oxide (Al2O3) to prevent an electrical short. The noise reduction hardware has been designed by two approaches: (1) total harmonic distortion (THD) for the robust multiplexer, and (2) a current injection frequency pair: low fL and high fH, for thermal noise compensation. THD is determined by a percentage evaluation of k-th harmonic distortions of ZnO at f=0.1~10,000 Hz. The fL and fH are determined by the thermal noise behavior estimation at different temperatures. At  f <100 Hz, the THD percentage is relatively high and fluctuates; otherwise, THD dramatically declines, nearly reaching zero. At the determined fL≥ 10,000 Hz and fH≈ 1,000,000 Hz, thermal noise is significantly compensated. The on-line mfERT was tested in the experiments of a non-conductive Al2O3 rod dipped into conductive molten zinc-borate (60ZnO-40B2O3) at 1000~1200 °C. As a result, the on-line mfERT is able to reconstruct the Al2O3 rod inclusion images in the high-temperature fields with low error, ςfL, T = 5.99%, at 1000 °C, and an average error ⟨ςfL⟩ = 9.2%.

20.
Sensors (Basel) ; 22(1)2022 Jan 04.
Artículo en Inglés | MEDLINE | ID: mdl-35009894

RESUMEN

For the optimization of three-phase hybrid stepper motors with complex electromagnetic structures, an optimization method is presented in this paper. The method is a combination of 3D-FEM and the Taguchi optimization method intended to reduce the dependence on FEM results during the optimization calculation. In this paper, the optimization method is used in the optimization of the tooth shape of the three-phase hybrid stepper motor, and the objective is to reduce the noise caused by harmonics in the "torque-angle characteristic" of the motor. It is clear that traditional optimization methods make it very difficult to carry out such an optimization calculation as a large number of finite element calculations have to be used in the optimization process, and the required computation time is extremely long. Using the optimization method presented in the paper, the optimization becomes feasible because the number of finite element calculations is greatly reduced and the computation time is thus greatly reduced. In order to check the effectiveness of the optimization, the waterfall diagram for noise analysis and its application to check torque ripple are also presented in the paper. Both simulation and test results show that the optimized structure can significantly reduce the motor noise caused by torque ripple. Therefore, the optimization method proposed in this paper can be an effective tool for the optimal design of high-performance motors, including stepper motors.

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