• Honam Mathematical Journal
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• v.40 no.1
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• pp.199-210
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• 2018

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

• The Transactions of the Korean Institute of Power Electronics
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• v.27 no.2
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• pp.126-133
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• 2022

This study proposes a suppression of zero sequence current (ZSC), which is caused by zero sequence voltage (ZSV) for a dual two-level inverter with single DC bus. Large output voltages enable the dual inverter with single DC bus to improve a system efficiency compared with single inverter. However, the structure of dual inverter with single DC bus inevitably generates ZSC, which reduces the system efficiency and causes a current ripple. ZSV is also produced by dead time, and its magnitude is determined by the DC bus and current direction. This study presents a novel space vector modulation method that allows the instantaneous suppression of ZSC. Based on a condition where a switching period is twice a sampling (control) period, the proposed control method is implemented by injecting the offset voltage at the primary inverter. This offset voltage is injected in half of the switching period to suppress the ZSC. Simulation and experiments are used to compare the proposed and conventional methods to determine the ZSC suppression performance.

• Journal of Power Electronics
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• v.15 no.1
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• pp.268-277
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• 2015

In this paper, a dual-converter three-phase pulse width modulation (PWM) rectifier based on unbalanced one-cycle control (OCC) strategy is proposed. The proposed rectifier is used to eliminate the second harmonic waves of DC voltage and distortion of line currents under unbalanced input grid voltage conditions. The dual-converter PWM rectifier employs two converters, which are called positive-sequence converter and negative-sequence converter. The unbalanced OCC system compensates feedback currents of positive-sequence converter via grid negative-sequence voltages, as well as compensates feedback currents of negative-sequence converter via grid positive-sequence voltages. The AC currents of positive- and negative-sequence converter are controlled to be symmetrical. Thus, the workload of every switching device of converter is balanced. Only one conventional PI controller is adopted to achieve invariant power control. Then, the parameter tuning is simplified, and the extraction for positive- and negative-sequence currents is not needed anymore. The effectiveness and the viability of the control strategy are demonstrated through detailed experimental verification.

• Journal of Power Electronics
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• v.17 no.1
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• pp.67-75
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• 2017

Due to the excessive zero-sequence voltage in dual three-level inverter fed open-end winding induction motor systems, zero-sequence circumfluence which is harmful to switching devices and insulation is then formed when operating in a single DC voltage source supplying mode. Traditionally, it is the mean value instead of instantaneous value of the zero-sequence voltage that is eliminated, through adjusting the durations of the operating vectors. A new strategy is proposed for zero-sequence voltage elimination, which utilizes unified voltage modulation and a decoupled SVPWM strategy to achieve two same-sized equivalent vectors for an angle of $120^{\circ}$, generated by two inverters independently. Both simulation and experimental results have verified its efficiency in the instantaneous value elimination of zero-sequence voltage.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.341-348
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• 1998

In this paper, we show that Schlumprecht space is reflexive and the Dual of Schlumprecht space has the Banach-Saks property and study behavior of block basic sequence in Schlumprecht space.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.401-418
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• 2005

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.39-47
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• 2009

Pan, Shen and Woo [8] introduced the concept of the G-sequence of a map. We introduce the G'-sequence of a map, which is a dual concept of the G-sequence of a map. We obtain some sufficient conditions for the all sets in the G'-sequence of a map are groups, and for the exact G'-sequence of a map.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.255-258
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• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.55 no.1
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• pp.54-60
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• 2006

A power limiting algorithm is proposed for stable operation of grid-connected inverter in case of grid voltage unbalance considering the operation limit of inverter. During the voltage unbalance the control performance of Inverter. is degraded and the output power contains 120Hz ripple due to the negative sequence of voltage. In this paper, conventional dual sequence current controller is implemented to solve these problems using separated control of positive and negative sequence. Especially the maximum power limit which guarantees the maximum rated current of the inverter is automatically calculated as the instant grid voltage changes. As soon as the voltage recovers the proposed algorithm can return to the normal power control mode accomplishing low voltage ride through. Proposed algorithm is verifed using PSCAD/EMTDC simulations and tested experimentally at 4.4kW wind turbine simulator set-up.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.851-853
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• 2005

It is well known that the general term of a sequence can be represented by a linear combination of binomial coefficients. In this paper we give a simple proof for this fact.