• Korean Journal of Mathematics
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• v.29 no.2
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• pp.253-266
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• 2021

This work is devoted to the study of a q-harmonic analysis related to the q-analog of the Bessel-Wright integral transform [6]. We establish some important properties of this transform and we focalise our attention in studying the associated transmutation operator.

• Journal of Power Electronics
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• v.8 no.1
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• pp.91-100
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• 2008

The d-q harmonic detecting algorithms are dominant methods to generate current references for active power filters (APF). They are often implemented in the synchronous frame and time domain. This paper researches the frequency characteristics of d-q synchronous transformations, which are closely related to the analysis and design issues of control system. Intuitively, the synchronous transformation is explained with amplitude modulation (AM) in this paper. Then, the synchronous filter is proven to be a time-invariant and linear system, and its transfer function matrix is derived in the stationary frames. These frequency-domain models imply that the synchronous transformation has an equivalent effect of frequency transformation. It is because of this feature, the d-q method achieves band-pass characteristics with the low pass filters in the synchronous frame at run time. To simplify these analytical models, an instantaneous positive-negative sequence frame is proposed as expansion of traditional symmetrical components theory. Furthermore, the synchronous filter is compared with the traditional bind-pass filters based on these frequency-domain analytical models. The d-q harmonic detection methods are also improved to eliminate the inherent coupling effect of synchronous transformation. Typical examples are given to verify previous analysis and comparison. Simulation and experimental results are also provided for verification.

• Journal of Power Electronics
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• v.11 no.6
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• pp.922-930
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• 2011

In this paper, two radial basis function neural networks (RBFNNs) are used to dynamically identify harmonics content in converter waveforms based on the p-q (real power-imaginary power) theory. The converter waveforms are analyzed and the types of harmonic content are identified over a wide operating range. Constant power and sinusoidal current compensation strategies are investigated in this paper. The RBFNN filtering training algorithm is based on a systematic and computationally efficient training method called the hybrid learning method. In this new methodology, the RBFNN is combined with the p-q theory to extract the harmonics content in converter waveforms. The small size and the robustness of the resulting network models reflect the effectiveness of the algorithm. The analysis is verified using MATLAB simulations.

• Journal of Power Electronics
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• v.11 no.4
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• pp.401-407
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• 2011

In order to enhance torque density of five-phase permanent magnetic synchronous motor with third harmonic injection for electric vehicles (EVs) applications, optimum seeking method for injection ratio of third harmonic was proposed adopting theoretical derivation and finite element analysis method, under the constraint of same amplitude for current and air-gap flux. By five-dimension space vector decomposition, the mathematic model in two orthogonal space plane, $d_1-q_1$ and $d_3-q_3$, was deduced. And the corresponding dual-plane vector control method was accomplished to independently control fundamental and third harmonic currents in each vector plane. A five-phase PMSM prototype with quasi-trapezoidal flux pattern and its fivephase voltage source inverter were designed. Also, the dual-plane vector control was digitized in a single XC3S1200E FPGA. Simulation and experimental results prove that using the proposed optimum seeking method, the torque density of five-phase PMSM is enhanced by 20%, without any increase of power converter capacity, machine size and iron core saturation.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.789-817
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• 2004

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called "delta-point" technique.

• Journal of Power Electronics
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• v.11 no.6
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• pp.914-921
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• 2011

Commencing with incandescent light bulbs, every load today creates harmonics. Unfortunately, these loads vary with respect to their amount of harmonic content and their response to problems caused by harmonics. The prevalent difficulties with harmonics are voltage and current waveform distortions. In addition, Electronic equipment like computers, battery chargers, electronic ballasts, variable frequency drives, and switching mode power supplies generate perilous amounts of harmonics. Issues related to harmonics are of a greater concern to engineers and building designers because they do more than just distort voltage waveforms, they can overheat the building wiring, cause nuisance tripping, overheat transformer units, and cause random end-user equipment failures. Thus power quality is becoming more and more serious with each passing day. As a result, active power filters (APFs) have gained a lot of attention due to their excellent harmonic compensation. However, the performance of the active filters seems to have contradictions with different control techniques. The main objective of this paper is to analyze shunt active filters with fuzzy and pi controllers. To carry out this analysis, active and reactive current methods ($i_d-i_q$) are considered. Extensive simulations were carried out. The simulations were performed under balance, unbalanced and non sinusoidal conditions. The results validate the dynamic behavior of fuzzy logic controllers over PI controllers.

• Journal of the Korean Institute of Telematics and Electronics
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• v.6 no.4
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• pp.1-7
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• 1969

A Series Inverter circuit is analyzed and Fourier analysis is applied to its output waveform. It is proved that under the optimum condition the Output is nearly sinusoidal wave which contains only odd harmonic Components and the relative amplitude of the hramonic components are expressed with very simple formula which contain only "Q" of the circuit as a parameter.parameter.

• Journal of Power Electronics
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• v.16 no.3
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• pp.1163-1175
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• 2016

In recent years, microgrids have been the focus of considerable attention in distributed energy distribution. Microgrids contain a large number of power electronic devices that can potentially cause negative impedance instability. Harmonic impedance is an important tool to analyze stability and power quality of microgrids. Harmonic impedance can also be used in harmonic source localization. Precise measurement of microgrid impedance and analysis of system stability with impedances are essential to increase stability. In this study, we introduce a new square wave current injection method for impedance measurement and stability analysis. First, three stability criteria based on impedance parameters are presented. Then, we present a new impedance measurement method for microgrids based on square wave current injection. By injecting an unbalanced line-to-line current between two lines of the AC system, the method determines all impedance information in the traditional synchronous reference frame d-q model. Finally, the microgrid impedances of each part and the overall microgrid are calculated to verify the measurement results. In the experiments, a simulation model of a three-phase AC microgrid is developed using PSCAD, and the AC system harmonic impedance measuring device is developed.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.985-986
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• 2011

This paper deals with d-q axis equivalent circuit analysis of IPMSM(Interior Permanent Magnet Synchronous Motors) considering voltage harmonics. In the field weakening region, as the current vector angle increased, back-emf contains large harmonics, therefore, significant underestimation of voltage or overestimation of speed can be occurred from the conventional d-q axis equivalent circuit analysis. In order to consider the effects of voltage harmonics, a harmonic coefficient is introduced and verified by experiments.