• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.515-528
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• 2023

In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.299-304
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• 2008

Catenary and Pantograph are a power supply devices for electric trains and shall be steadily contacted. Rail catenary must be installed precisely and managed for stable train operations. But external factors such as weathers, nature, etc., or aging affect catenary geometry. Changed catenary height causes high voltage spark or instant electric disconnection. Big spark and disconnection damage pantograph shoe and catenary coating and might interrupt rail operations. To prevent a big scale spark or electric disconnection catenary maintenance shall be required with catenary geometry measurement systems. In this paper, we describe the development of catenary height and stagger measurement system. The catenary height and stagger measurement system uses Acuity company's AR4000 Range Finder for distance measurement and AccuRange Line Scanner for degree measurement. This system reports suspicious overhead line sections with excessive height and stagger variance.

• Proceedings of the KSR Conference
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• 1999.11a
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• pp.550-557
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• 1999

Results of the dynamic simulation on KTX catenary and catenary-pantograph interface are presented. Simulation programs based on finite element and finite difference models of the catenary are developed, while the pantograph is modeled as a linear 3-degree-of-freedom system. The catenary motion dynamics are primarily determined by the transmission and reflection of the propagating disturbance wave at the hanger and span boundaries. On the other hand, the catenary-pantograph contact characteristics are primarily influenced by the movement of the pantograph across the hanger and span boundaries, the amount of damping present in the contact wire, and the resonant frequencies of the pantograph.

• Proceedings of the KSR Conference
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• 1999.05a
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• pp.176-184
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• 1999

Dynamic characteristics of pantograph-catenary system that supplies electrical power to high-speed trains are investigated. A simple catenary is composed of the contact and messenger wires connected by hamgers possessing bi-directional stiffness properties. The influences of parameters that determine the contact properties of pantograph-catenary system are investigated through numerical simulations. For the catenary, a finite difference model composed of 10 spans is constructed. The contact and messenger wires are modeled as strings with respective tension and damping ratio values. The pantograph is modeled as a linear 3-degree-of-freedom system. It is found that the tension, number of hangers and damping ratios as well as the speed of the train significantly influence the contact forces and contact separation rate

• Journal of Electrical Engineering and Technology
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• v.10 no.3
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• pp.1370-1376
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• 2015

Generally, an autotransformer(AT) feeding system consists of double tracks, up and down, with the trolley wire and feeder wire of the up and down tracks connected in the sectioning post(SP). Consequently, load current or fault current flows on two tracks based on catenary impedance characteristics, making it difficult to estimate catenary impedance accurately. This paper presents a technique for the estimation of catenary impedance using boosting current compensation based on the current division characteristics of an AT feeding system to improve the operation performance of impedance relay. To verify the technique, we model an AT feeding system through a power analysis program (PSCAD/EMTDC) and simulate various operation and fault conditions. Through the simulation, we confirmed that the proposed technique has estimated catenary impedance with a similar degree of accuracy to the actual catenary impedance

• Ocean Systems Engineering
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• v.10 no.1
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Journal of the Korean Society for Railway
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• v.11 no.6
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• pp.569-574
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• 2008

Catenary and Pantograph are used to transmit electrical energy to electric railways. Catenary (Overhead Contact Lines) should be installed precisely and managed for stable train operations. But external factors such as weather, temperature, etc., or aging affect catenary geometry. Changed catenary stagger and height cause high voltage spark or instant electric contact loss. Big spark derived from contact loss can damage the pantograph carbon strip and overhead contact lines that might interrupt the train operations. Therefore, to prevent a big scale spark or electric contact loss, catenary maintenance are required catenary geometry measurement systems with catenary maintenance capability. In this paper, we describe the development of catenary height and stagger measurement system. The catenary height and stagger measurement system uses Acuity company's AR4000 Laser Range Finder for distance measurement and AccuRange Line Scanner for degree measurement. This system detects suspicious overhead line sections with excessive stagger and height stagger variance.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2007.11a
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• pp.502-502
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• 2007

A catenary system should be designed to have an uniform elasticity over a span in order to maintain the lowest possible loss of contact between a pantograph and a contact wire. A elasticity uniformity of a catenary can be regarded as a important design factor used for predicting the current collection performance for a catenary. There are a couple of formulas to calculate the degree of elasticity uniformity of a catenary according to the literature survey. The effectiveness of these formulas is reviewed by performing catenary elasticity and loss of contact analysis for various different configurations of catenary systems using a beam element based FEM program. The results reveals that these formulas are not suitable to predict the current collection performance for a catenary. Therefore, a new formula based on the standard deviation of the elasticity over a span is proposed in this study. The analysis results show that the new formula for an elasticity uniformity of a catenary is very effective in predicting the current collection performance for a catenary.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.9
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• pp.147-152
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• 2015

Almost all existing inspection methods for catenary system have relied on dedicated track inspection cars. Two factors make it necessary to modify the conventional method: First, the climate has become increasingly similar to that of a subtropical area. In addition, high speed trains have been developed that can run as fast as 450Km/h. This paper presents a visual catenary inspection system structure that incorporates roadbed information for high-speed running environments. Conventional catenary inspection systems determined the degree of wearing only for the trolley wire. The facility inspection system presented in this paper on the other hand utilizes visual and sound data of inspection targets and adjusts inspection frequency and sensitivity depending on the geographic data.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.1020-1026
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• 2011

In this paper, we propose a method that measures the height and stagger of an catenary using the laser profile images. One line laser and area scanner CCD cameras are used. To quickly and accurately extract, from a photographed image, the area of the overhead line on which the line laser is shone, we consider the established fact that the catenary is the lowest among the electric wires. Here we are solving the the distance to the catenary if we know the distance the camera is from the ground and the angle of the catenary in the field of view. The angle will be related to the number of pixels in the image. This pixels per degree is a constant for the camera. Also, because of the different pixel resolution of the camera according to the overhead line position, we compensate the measurement result through camera calibration.