• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.11
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• pp.1560-1565
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• 2013

This paper proposes the control method for compensating for unbalanced grid current and reducing a total harmonic distortion (THD) of the grid current at the three-phase grid-connected inverter systems under unbalancd and distorted grid voltage conditions. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for a minimum point of THD. Both the gain and angle of a compensation voltage at the minimum point of THD of the grid current are derived. The negative-sequence components in the three-phase unbalanced grid voltage are cancelled in order to achieve the balanced grid current. The simulation and experimental results show the validity of the proposed control methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.91-100
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• 2018

In this paper, we propose a new method for template matching, patch ratio, to inpaint unknown pixels. Before this paper, many inpainting methods used sum of squared differences(SSD) or sum of absolute differences(SAD) to calculate distance between patches and it was very useful for closest patches for the template that we want to fill in. However, those methods don't consider about geometric similarity and that causes unnatural inpainting results for human visuality. Patch ratio can cover the geometric problem and moreover computational cost is less than using SSD or SAD. It is guaranteed about finding the most similar patches by Cauchy-Schwarz inequality. For ignoring unnecessary process, we compare only selected candidates by priority calculations. Exeperimental results show that the proposed algorithm is more efficent than Criminisi's one.

• Journal of Power Electronics
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• v.13 no.4
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• pp.712-718
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• 2013

This paper proposes a control method for reducing the total harmonic distortion (THD) of the grid current of three-phase grid-connected inverter systems when the grid voltage is distorted. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for the minimum point of the THD. Both the gain and angle of the compensation voltage at the minimum point of the THD of the grid current are derived with the variation of cut-off frequencies of the hardware LPF. Simulation and experimental results show the validity of the proposed control methods.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.931-942
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• 2020

For a polynomial $P(z)={\sum_{{\nu}=0}^{n}}\;a_{\nu}z^{\nu}$ of degree n having all its zeros in |z| ≤ k, k ≥ 1, it was shown by Rather and Dar [13] that ${\max_{{\mid}z{\mid}=1}}{\mid}P^{\prime}(z){\mid}{\geq}{\frac{1}{1+k^n}}\(n+{\frac{k^n{\mid}a_n{\mid}-{\mid}a_0{\mid}}{k^n{\mid}a_n{\mid}+{\mid}a_0{\mid}}}\){\max_{{\mid}z{\mid}=1}}{\mid}P(z){\mid}$. In this paper, we shall obtain some sharp estimates, which not only refine the above inequality but also generalize some well known Turán-type inequalities.