Modelling of Subspan Oscillations of Bundled Conductors

Subspan oscillations are a well-known phenomenon in high voltage and ultra high voltage overhead transmission lines (HV and UHV OHTL). It occurs on conductor bundles and it is due to the effect of the wake produced by the windward conductor on the leeward one. For this reason, the phenomenon is also classified as wake induced oscillations: this phenomenon is a flutter type instability due to the coupling of vertical and horizontal modes in a frequency range between 0.5 and 2 Hz. It may lead to conductor failure in the spacer clamp (see Fig. 1) or suspension clamps or to spacer damper articulation failure. Recently, problems associated with this phenomenon have become more recurrent, attracting the attention of transmission line operators, hence WG B2.46 decided to evaluate the developments in this field In the past, several simulation models have been developed. In these models, the motion of the leeward cylinder is studied along two orthogonal directions, the windward cylinder being still. Then, the linearized quasi-steady theory (in the following QST) is employed and the drag and lift coefficients on the leeward cylinder are deduced from static measurements in wind tunnel, as a function of the relative position of the leeward cylinder with respect to the windward one (Fig. 2). Such models are linear and clearly simplify the structural behaviour of the bundle subconductors, taking it back to a two degrees of freedom system in which the leeward conductor is the only one moving. Nowadays, the finite element model (in the following FEM) analysis allows for the reproduction of the bundle dynamics and for the application of the aerodynamic forces to each subconductor using the QST with a nonlinear approach. However, FEM analyses in the time domain are not always a practical tool for subspan oscillation simulation also because of the computation time required to obtain results. All the models developed up to now are based on the QST: according to this, the field of forces in the wake of the windward conductors is accounted for using static aerodynamic coefficients measured in the wind tunnel and the effect of relative motion between subconductors corresponds to a relative velocity with respect to the approaching flow. Another important issue faced in the work is the Reynolds number (Re) effect on the phenomenon. In fact, for stranded conductors, i.e. rough cylinders, with the typical values of conductor diameter and wind speed involved by subspan oscillations, Re may be close to the critical zone: hence the Re number could significantly affect the phenomenon, due to the non-negligible variations of the drag coefficient with Re itself. The study presents several approaches to the evaluation of the subspan phenomenon, ranging from approaches based on the EBP to approaches relying on FEM modelling. In the work, a benchmark within the different type of models available for subspan oscillation studies is carried out comparing numerical results with measurements on the IREQ Varennes test line equipped with a quad bundle of ACSR Bersimis conductors and spacer dampers. The obtained results allow to state that: • the QST seems able to well reproduce the aerodynamic forces produced during subspan oscillations; • the Reynolds number affects in a large amount the energy introduced by the wind; • the numerical model based on EBP approach and on sophisticated wind tunnel tests to identify the aerodynamic parameters seems to be a useful tool for analysing the subspan oscillations phenomenon. This document is highlighting what can be expected from numerical models regarding conductor vibrations. • assessment of the aeolian vibration condition of particular lines, with conductors whose mechanical properties are poorly defined, or with special terrain conditions, may require field measurements; • analytical methods based on the EBP and shaker-based technology can provide a useful tool to design damping systems for the protection of single conductors against aeolian vibrations; • future research work is needed to improve the EBP technology, which generally produces a safe design of the damping system, in order to provide reliable results on long spans. This document is reporting on the state of the art regarding aeolian vibrations and subspan oscillations modelling. Of course, this field of expertise is not static and research, numerical as well as experimental, is still going on in order to improve our knowledge of the phenomenon and translate it into improved numerical models.