• Title, Summary, Keyword: Catenary equation

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Current Collection of Catenary System with Time-Varying Stiffness (시변강성 가선계의 집전성능)

  • 최연선
    • Journal of the Korean Society for Railway
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    • v.3 no.3
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    • pp.131-138
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    • 2000
  • The design of current collection system of high speed train requires the fundamental understandings for the dynamic characteristics of catenary system and pantograph. The stiffness of catenary system of high speed train has the varying characteristics for the change of contact point with pantograph, since the supporting pole and hanger make the different boundary conditions for the up-down stiffness of a trolley wire. The variation of stiffness results in Mathiue equation, which characterizes the stability of the system. However, the two-term variation of the stiffness due to span length and hanger distance cannot be solved analytically. In this paper, the stiffness variations are calculated and the physical reasoning of linear model and one term Mathieu equation are reviewed. And the numerical analysis for the two-term variation of the stiffness is done for the several design parameters of pantograph.

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A Study on Real Time Catenary Impedance Estimation Technique using the Synchronized Measuring Data between Substation and Train (변전소와 차량간의 동기화를 통한 실시간 전차선로 임피던스 예측 기법 연구)

  • Jung, Hosung
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.10
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    • pp.1458-1464
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    • 2013
  • This paper proposed a new real time catenary impedance estimation technique using synchronized power data from the measured data of operating vehicle and substation for catenary protective relay and fault locator setting. This paper presented estimation equation of catenary impedance using synchronized power data between substation and vehicle of AT feeding system for the performance verification of the proposed technique. Also AC feeding system is modeled through power analysis program and performance was verified through simulation according to various load changes. We verified that average 2.38%(distance equivalent 23.8 m) error appeared between the proposed estimation equation of catenary impedance and power analysis program simulation output in no connection double track system between up track and down track. Furthermore, We confirmed that estimation error is bigger depending on the increasing the distance from substation and vehicle impedance using only using vehicle current when calculating vehicle impedance in connection double track system between up track and down track. But, We confirmed that the proposed technique estimated accurately catenary impedance regardless of vehicle impedance and distance from substation.

Utilizing Technology in Measurement System for Catenary Current: - Focusing on Testing Results for Kyoungbu High-speed Line in Korea - (조가선 전류 검측 시스템의 활용기술 연구 - 고속선 경부2단계 시험결과를 중심으로 -)

  • Park, Young;Jung, Hosung;Lee, Kiwon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.10
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    • pp.1465-1469
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    • 2013
  • The resent developed high speed train called HEMU-430X (Highspeed Electric Multiple Unit - 430km/h eXperiment) recorded a 421.4 km/h in Kyoungbu high speed line in Korea. A verity of measurement systems are used to check the performance between pantograph and catenary system. An innovative measurement system is adopted to check the current of catenary wire in the track side during HEMU-430X test running. This paper presents the measurement results of catenary current in kyoungbu high-speed line and describe its utilizing technology in the experimental results of catenary current. In order to analyze field testing results, the current ratio between contact and catenary current have been analyzed by means of Carson-Pollaczek equation. And the current wave forms between catenary and contact wire are presented based on the simulation results.

Analysis for Catenary Voltage of The ATs-Fed AC Electric Railroad System (단권변압기 교류전기철도 급전시스템의 전차선 전압해석)

  • 정현수;이승혁;김진오
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.52 no.9
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    • pp.493-499
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    • 2003
  • This paper presents exact Autotransformers(ATs)-fed AC electric Railroad system modeling using constant current mode for locomotives. An AC electric railroad system is rapidly changing single-phase load, and at a feeding substation, 3-phase electric power is transferred to paired directional single-phase electric power. As the train moves along a section of line between two adjacent ATs. The proposed AC electric railroad system modeling method considers the line self-impedances and mutual-impedances. The constant current mode model objectives are to calculate the catenary and rail voltages with the loop equation. When there are more than one train in the AC electric railroad system, the principle of superposition applies and the only difference between the system analyses for one train. Filially, this paper shows the general equation of an AC electric railroad system, and that equation has no relation with trains number, trains position, and feeding distance.

Development of quasi-static analysis program for catenary mooring system using OpenFOAM (OpenFOAM을 이용한 catenary 계류시스템의 준정적 해석 프로그램 개발)

  • Choi, Jun Hyeok;Lee, Seung Jae
    • Journal of Ocean Engineering and Technology
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    • v.31 no.4
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    • pp.274-280
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    • 2017
  • Generally, global performance analysis in offshore platforms is performed using potential-based numerical tools, which neglect hydrodynamic viscous effects. In comparison with the potential theory, computational fluid dynamics (CFD) methods can take into account the viscous effects by solving the Navier-Stokes equation using the finite-volume method. The open-source field operation and manipulation (OpenFOAM) C++ libraries are employed for a finite volume method (FVM) numerical analysis. In this study, in order to apply CFD to the global performance analysis of a hull-mooring coupled system, we developed a numerical wave basin to analyze the global performance problem of a floating body with a catenary mooring system under regular wave conditions. The mooring system was modeled using a catenary equation and solved in a quasi-static condition, which excluded the dynamics of the mooring lines such as the inertia and drag effects. To demonstrate the capability of the numerical basin, the global performance of a barge with four mooring lines was simulated under regular wave conditions. The simulation results were compared to the analysis results from a commercial mooring analysis program, Orcaflex. The comparison included the motion of the barge, catenary shape, and tension in the mooring lines. The study found good agreement between the results from the developed CFD-based numerical calculation and commercial software.

A study on the non-linear analysis of the elastic catenary cable considering kinetic damping (동적감쇠를 고려한 탄성 현수선 케이블의 비선형 해석에 관한 연구)

  • 한상을;정명채;이진섭
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.331-338
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    • 2000
  • In this paper, a non-linear finite element formulation for the spatial cable-net structures is simulated and using this formulation, the characteristics of structural behaviors for the elastic catenary cable are examined In the simulating procedure for the elastic catenary cable, nodal forces and tangential stiffness matrices are derived using catenary parameters of the exact solutions by a governing differential equation of catenary cable, cable self-weights and unstressed cable length. Dynamic Relaxation Method that considers kinetic damping is used for the structure analysis and Newton Raphson Method is used to verify the accuracy of solutions. In the analysis of two dimensional cable, the results obtain from the elastic catenary elements are shown more accurate than does of truss elements and in the case of spatial cable-net structures, Dynamic Relaxation Method is more stable to be converged than Newton Raphson Method.

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A Study on Calculation of Permissible Current Capacity on Catenary System (시간 변수를 고려한 전차선로 허용전류 계산 기법 연구)

  • Kim, Joo-Rak;Kwon, Sam-Young;Lee, Ki-Won;Chang, Sang-Hoon
    • Proceedings of the KIEE Conference
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    • pp.401-403
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    • 2001
  • This paper presents an advanced calculation method of permissible current capacity on catenary system. If the permissible current calculation method used in electric power system is applied to electric railroad system, it is troublesome. Because electric load in catenary system varies periodically according to time. Therefore, this study proposes permissible current calculation method through heat equation according to time variation.

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Time-varying Stiffness of Catenary System and its Effect on Current Collection by Pantograph (가선계의 강성변화와 판토그래프의 집전성능)

  • 최연선
    • Proceedings of the KSR Conference
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    • pp.598-605
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    • 2000
  • The design of a current collection system of high speed train requires the fundamental understandings fer the dynamic characteristics of a catenary system and pantograph. The stiffness of the catenary system of high speed train has the varying characteristics for the change of the contact point with a pantograph, since the supporting pole and hanger make the different boundary conditions for the updown stiffness of a trolley wire. The variation of stiffness results in Mathiue equation, which characterizes the stability of the system. However, the two terms variation of the stiffness due to span length and hanger distance cannot be solved analytically. In this paper, the stiffness variations are calculated, and the physical reasoning of linear model and one term Mathieu equation are reviewed. And the numerical analysis for the two term variation of the stiffness is done for the several design parameters of the pantograph.

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Dynamic Analysis of a Pantograph-Catenary System for High-Speed Train(II. Analysis of the Integrated Current Collection System) (고속전철 집전시스템의 동역학 해석에 관한 연구(II. 집전시스템 통합 해석))

  • Seo Jong-Hwi;Mok Jin-Yong;Jung Il-Ho;Park Tae-Won;Kim Young-Guk;Kim Seok-Won
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.1
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    • pp.160-166
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    • 2005
  • In this paper, the combined system equation of motion, which can analyze the dynamic interaction between pantograph and catenary system, is derived by adopting absolute nodal coordinates and rigid body coordinates. The analysis results are compared with real experiment data from test running of Korean high-speed train (HSR 350x). In addition, a computation method for the dynamic stress of contact wire is presented using the derived system equation of motion. This method might be good example and significant in that the structural and multibody dynamics model can be unified into one numerical system.

Free vibration analysis of large sag catenary with application to catenary jumper

  • Klaycham, Karun;Nguantud, Panisara;Athisakul, Chainarong;Chucheepsakul, Somchai
    • 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.