Dynamic analysis and monitoring of power transmission cables using fibre optic sensors
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- Institutt for elkraftteknikk 
Aeolian vibration is a well known phenomen that can occur on overhead power lines in light to moderate steady winds. The amplitude of these vibrations is usually less than the conductor diameter, while the frequency, governed by the wind speed and conductor diameter, is in the range of a few Hertz to 50-100 Hz. Even though the amplitude of the vibrations is small, they can be harmful to the operation of an overhead line by causing fatigue damage on the conductor and on secondary equipment. Ultimately, the accumulated fatigue damage can lead to total mechanical failure of the overhead line, resulting in power outage and need for repair or reconstruction of the line. On overhead spans that are susceptible to excessive aeolian vibrations, dampers are usually installed in order to reduce the vibration amplitudes to harmless levels. However, there is still a need for measuring the occurring aeolian vibrations for assessing the fatigue damage being experienced by the conductor, and estimating a safe operating life time for the conductor and span. Different methods for measuring vibrations on overhead spans have been developed and used. The present work considers the use of vibrations sensors based on fibre Bragg gratings inscribed in the core of an optical fibre. The use of fibre optical sensors on overhead lines is advantageous due to the immunity of the sensors to electromagnetic fields. The installation and continuous operation over several months of fibre Bragg grating sensors on two spans in the transmission grid in Norway have been demonstrated. The first installation was on a short span operating at 300 kV. The second installation was on a span with a length of 3000 meters crossing a fjord. On this span, operating at a voltage of 420 kV, some of the sensors were installed at mid-span 1200 meters from the nearest tower. On both spans the installed sensor systems were able to detect and measure vibrations. The fibre Bragg grating sensors measure mechanical strain in a comparatively small area, and can not measure vibration amplitude directly. To determine the vibration amplitude an analytical model linking the local (strain) behaviour with global (displacement) behaviour of a line span has been developed. The dynamic strains in a vibrating conductor is shown to consists of two components; bending strain and membrane strain. The frequency of the membrane strain is twice that of the bending strains (which is equal to the vibration frequency). By using filters with appropriate frequency response it is thus possible to distinguish between the bending and membrane strains. The analytical model for the strains in a vibrating conductor has been verified in wellcontrolled laboratory measurements on a short test span, and proved reasonably correct for small vibration amplitudes. For larger vibration amplitudes greater deviations were observed between predicted and measured strains, probably due to the effect of slippage between different strands and layers of the conductor. However, by basing the assessment on the membrane strain in the conductor good prediction of vibrations levels could still be obtained. This is due to the special properties of the membrane strain. The membrane strain is directly related to the vibration amplitude and wavelength, and it is essentially equal at all positions along a span section. With basis in strain measurements a reliable estimate of the vibration amplitude can be obtained from the membrane strain magnitude, regardless of sensor location relative to nodes and anti-nodes and where on the circumference of the conductor the sensors are mounted. A model of an overhead span was also made in an available finite element program. This model was compared with dynamic experiments on an overhead span. The model was able to reproduce the observed global behaviour of an overhead span. More realistic spans with dampers and aircraft warning spheres installed require more sophisticated models or a larger number of sensors to give out reliable vibration level assessments.