• Journal of Electrical Engineering and Technology
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• v.10 no.3
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• pp.865-876
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• 2015

Voltage stability is one of the most critical security issues which has not yet been well resolved to date. In this paper, an analytical method called PQ plane analysis with consideration of the reactive power capability of wind turbine generator and the wake effect of wind farm is proposed for voltage stability study. Two voltage stability indices based on the proposed PQ plane analysis method incorporating the uncertainties of load-increasing direction and wind generation are designed and implemented. Cases studies are conducted to investigate the impacts of wind power incorporation with different control modes. Simulation results demonstrate that the constant voltage control based on reactive power capability significantly enhances voltage stability in comparison of the conventional constant power factor control. Some meaningful conclusions are obtained.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.507-514
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• 2023

Suppose that a line passing through a given point P intersects a given circle 𝓒 at Q and R in the Euclidean plane. It is well known that |PQ||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

• The Korean Journal of Physiology
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• v.18 no.1
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• pp.51-65
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• 1984

In an effort to elucidate the effect of physical training on the electrocardiographic amplitudes, QRS vector, axis and QRS vector amplitude, electrocardiograms were recorded before and 1, 5 and 10 minutes after 3 minute rebounder exercise in 23 healthy male students aged between 18 and 21 years in two groups of athletes and non-athletes. ECG amplitudes were measured from lead I, $V_1$ and $V_5$ and axis and amplitudes of QRS vectors were measured from lead I and III in frontal plane, from lead $V_2$ and lead $V_6$ in horizontal plane. The results obtained are summarized as follows. ECG amplitudes: The R wave amplitude was $23.38{\pm}1.14\;mm$ in athletes which was higher than $17.91{\pm}2.00\;mm$ in non-athletes. After exercise, the difference in two groups remained significant throughout the recovery period. The S wave amplitude was increased significantly, and the T wave amplitude was decreased in both groups after exercise. The P wave amplitude was increased in both groups after exercise, and it was lower in athletes than in non-athletes. The PQ segment amplitude was zero in athletes but negative in non-athletes than in the resting state. The J point amplitude was positive in resting state and was negative after exercise in both groups. J+0.08 sec point amplitude was also lowered after exercise, and it was higher in athletes than in non-athletes. Therefore the whole ST segment was proved to be decreased after exercise. The summated amplitude of R in $V_5$ plus S in $V_1$ was $38.74{\pm}2.71\;mm$ in athletes which was higher than $32.82{\pm}2.90\;mm$ in non-athletes. After exercise, it was also significantly higher in athletes than in non-athletes. Axis of QRS vector: In frontal plane, axis of QRS vector was $62.7{\pm}7.36^{\circ}$ in athletes, it showed no significant difference between the two groups. In horizontal plane, axis of QRS vector was $-23.5{\pm}7.2^{\circ}$ in athletes which was significantly higher than $-38.8{\pm}8.2^{\circ}$ in non-athletes. After exercise, it was significantly higher than the resting state in both groups. Amplitude of QRS vector : In frontal plane, amplitude of QRS vector was $13.86{\pm}1.44\;mm$ in athletes which was significantly higher than $9.62{\pm}0.97\;mm$ in non-athletes. After exercise, it was also significantly higher in athletes than in non-athletes. In horizontal plane, amplitude of QRS vector was $19.82{\pm}2.10\;mm$ in athletes which was significantly higher than $16.90{\pm}1.39\;mm$ in non-athletes. After exercise, it was also significantly higher in athletes than in non-athletes. From the above, these results indicate that R wave amplitude in athletes was significantly higher than in non-athletes before and after exercise, and that the summated amplitude of R in $V_5$ plus S in $V_1$ in athletes was also $38.74{\pm}2.71\;mm$ suggesting a left ventricular hypertrophy We should note that the PQ segment and ST segment amplitude were higher in athletes than in non-athletes, and they were decreased with exercise in both groups. In particular, the fact that amplitudes of QRS vector in frontal plane or in horizontal plane were significantly greater in athletes than in non-athletes may be an index in evaluating athletes.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.