Stochastic modelling and stabilization of galloping transmission lines |
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| Affiliation: | 1. Institute for Computational Science, University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzerland;2. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA;3. Department of Astronomy, Cornell University, Ithaca, NY 14853, USA;4. Southwest Research Institute, San Antonio, TX 78238, USA;5. DLR Berlin, Institut für Planetenforschung, Rutherfordstr. 2, 12489 Berlin, Germany;6. University of Michigan, Climate and Space Sciences and Engineering, Ann Arbor, MI 48109, USA;7. Universite Cote d Azur, OCA, Lagrange CNRS, 06304 Nice, France;8. Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA;9. Department of Astronomy, University of California, Berkeley, CA 94720, USA;10. SRON Netherlands Institute for Space Research, Sorbonnelaan 2, NL-358 CA Utrecht, The Netherlands;11. Leiden Observatory, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands;12. Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA;2. Orthopaedic Surgery, University of Michigan Medical School, Ann Arbor, Michigan;3. Department of Epidemiology, School of Public Health, University of Michigan, Ann Arbor, Michigan;4. National Fibromyalgia Association, Newport Beach, California;5. Community Health Focus Inc., Ann Arbor, Michigan;1. College of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, China;2. Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | Galloping of overhead transmission line causes low frequency high amplitude oscillations resulting in line outages due to flashover between the phases, or between the phases and the ground wire. It is known that galloping is the result of aerodynamic instability of the iced conductors. In the commonly used approach to the analysis of galloping, the aerodynamic effects are represented by a deterministic coefficient in the system model. However, because of randomness of the wind velocity and direction, and of the shape of ice accumulation on the conductor surface, the aerodynamic forces could be better represented by a random process. In this paper, a stochastic model has been presented for modelling the galloping transmission lines considering the randomness of aerodynamic forces. Stochastic calculus has been used to obtain sufficient conditions for stability and instability. It has been shown that exponential stabilization of the conductor oscillations could be obtained by applying a suitable amount of mechanical damping to the conductor. The value of critical damping for the fastest decay of oscillations has also been obtained.The stability criterion given in this paper is based on rigorous analysis of the stochastic model. This gives a conservative estimate of the damping constant which can be relied upon under the worst possible disturbances. |
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