• Kyungpook Mathematical Journal
• /
• v.61 no.1
• /
• pp.169-179
• /
• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.819-835
• /
• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.62 no.5
• /
• pp.604-611
• /
• 2013

This paper presents an second harmonic elimination method based on the impedance variation scheme. Through the power quality analysis from the nonlinear loads connected on the power system, the second harmonic problems have been analyzed with a case study analysis and the experiments. In the paper, the second Harmonic generation was simulated with a single phase SCR rectifier and the analytical model is proposed for the second harmonic generation. A novel impedance variation scheme is proposed and analyzed to eliminate the second harmonic. The experiment has been performed on the 60(MVA) industry manufacturing plant. The experimental result demonstrates the proposed impedance variation scheme successfully operate on the 60(MVA) industry manufacturing plant.

• Proceedings of the KIEE Conference
• /
• 2005.07a
• /
• pp.205-207
• /
• 2005

In this paper, the Point of Common Coupling (PCC) is selected to analyze harmonic characteristic of distribution system by IEC 61000 - 3 - 6 in Electromagnetic Compatibility(EMC). Harmonic voltage and current were measured at the PCC of real distribution system. Harmonic distribution, nonlinear load component and Total Harmonic Distortion(THD) were verified by measurement. The effective and accurate modelling of real distribution system were proved through a analysis of harmonic impedance, voltage and current in steady-state. Harmonic transfer characteristic in distribution system were summarized and investigated through a analysis of harmonic voltage and harmonic current in harmonic current source.

• Journal of Magnetics
• /
• v.1 no.2
• /
• pp.90-93
• /
• 1996

For the design of high efficiency electric machines, analysis of higher harmonic frequency components of the magnetic induction is necessary. We have measured ac magnetic properties of non-oriented silicon steel under harmonic frequencies ranging from $3^rd$ (180 Hz) to $9^th$(540 Hz) and harmonic amplitude components from 10% to 50% of the total amplitude ($B_max$=1.5T). From the experiment, it is found that, if the magnetic induction waveform has above $9^th$ harmonic frequency components of the magnetic induction, the core losses only depended on the harmonic amplitude component, but if harmonic frequency becomes lower than 9th harmonic frequency, the core losses depend on the phase angle and the harmonic amplitude, and phase angle should be considered in the design of electric machine.

• Journal of international Conference on Electrical Machines and Systems
• /
• v.2 no.3
• /
• pp.254-259
• /
• 2013

We examined the generation of harmonic voltage by a synchronous machine adding d-axis and q-axis harmonic field windings in order to reduce the harmonics in a power line. We derived the expressions of the armature voltage in the case of supplying the currents with the frequency nf to the d-axis and q-axis harmonic field windings. We constructed the synchronous machine adding the harmonic windings. In this paper, the expressions and the experimental results on the generation of harmonic voltages by the synchronous machine are presented.

• Journal of international Conference on Electrical Machines and Systems
• /
• v.3 no.2
• /
• pp.132-138
• /
• 2014

We investigated the harmonic voltages generated by a synchronous machine adding d-axis and q-axis harmonic field windings to reduce the harmonics in a power line. First, electronic circuits such as a frequency multiplier, band-pass filter, and phase shifter were newly designed and made to carry out the experiment. Next, an experimental circuit, for which an AC voltage of frequency 6f synchronized to the power line voltage of frequency f could be obtained, was constructed to examine the generation of harmonic voltage in more detail. Finally, an experiment involving the generation of harmonic voltage was performed using an experimental synchronous generator with harmonic windings in the d-axis and q-axis. In this paper, the power spectrum and the waveforms of the harmonic voltages in the armature winding are presented. Moreover, the values calculated from theoretical expressions of harmonic voltages in armature winding are compared with the values obtained by the experiment.

• Journal of Power Electronics
• /
• v.10 no.2
• /
• pp.138-145
• /
• 2010

This paper presents a single phase multilevel inverter for using as a voltage harmonic source. First, a single phase multilevel inverter system is presented and the structural parts of the inverter are described. In order to obtain multilevel output voltage waveforms, a switching strategy based on calculating switching angles is explained and an improved formula for determining switching angles is given. Simulation and experimental results of multilevel voltage waveforms are given for 15, 31 and 127 levels. The proposed topology does not only produce output voltages with low THD values. It also produces the required harmonic components on the output voltage. For this purpose, equations for switching angles are constituted and the switching functions are obtained. These angles control the output voltage as well as provide the required specific harmonics. The proposed inverter structure is simulated for various functions with the required harmonic components. The THD values of the output voltage waves are calculated. The simulated functions are also realized by the proposed inverter structure. By using a harmonic analyzer, the harmonic spectrums, which belong to the output voltage forms, are found and the THD values are measured. Simulation and experimental results are given for the specific functions. The proposed topology produces perfectly suitable results for obtaining the specific harmonic components. Therefore, it is possible to use the structure as a voltage harmonic source in various applications.

• Proceedings of the KIPE Conference
• /
• 2018.11a
• /
• pp.95-97
• /
• 2018

The power quality of Single Phase Grid-Connected Inverters (GCIs) has received much attention with the increasing number of Distributed Generation (DG) systems. However, the performance of single phase GCIs get degraded due to several factors such as the grid voltage harmonics, the dead time effect, and the turn ON/OFF of the switches, which causes the harmonics at the output of GCIs. Therefore, it is not easy to satisfy the harmonic standards such as IEEE 519 and P1547 without the help of harmonic compensator. To meet the harmonic standards a certain kind of harmonic controller needs to be added to the current control loop to effectively mitigate the low order harmonics. In this paper, the harmonic compensation is performed using a novel robust harmonic compensation method based on Digital Lock-in Amplifier (DLA). In the proposed technique, DLAs are used to extract the amplitude and phase information of the harmonics from the output current and compensate it by using a simple PI controller in the feedforward manner. In order to show the superior performance of the proposed harmonic compensation technique, it is compared with those of conventional harmonic compensation methods in terms of the effectiveness of harmonic elimination, complexity, and implementation. The validity of the proposed harmonic compensation techniques for the single phase GCIs is verified through the experimental results with a 5kW single phase GCI. Index Terms -Single Phase Grid Connected Inverter (SPGCI), Harmonic Compensation Method, Total Harmonic Distortion (THD) and Harmonic Standard.

• Korean Journal of Mathematics
• /
• v.11 no.1
• /
• pp.31-34
• /
• 2003

In this paper, we introduce the notion of F-harmonic maps and we study the stability of F-harmonic map.