Transmission Line Conductor Galloping Analysis using FEM

To find a mathematical standard of the galloping mechanism, and it is required to compare the existing mathematical standards on the conductor galloping. In this paper, using the Hamilton principle the continuum cable standard for transmission lines was proposed. Discrete standards of one degree of freedom, two degree of freedom, and three degree of freedom were obtained from the Garlekin function. And the standards were compared with different influence factors by analyzing the galloping vertical amplitude. The influence factors were wind velocity, flow density, damping ratio, span length, and initial tension. The three-degree of freedom design standard is more accurate than the other two standards for galloping characteristics calculation. The variation of the galloping amplitude relative to the influence factors was also obtained using finite element method (FEM). This analysis isvery useful for galloping analysis and anti-galloping design. Keyword: Finite Element Method(FEM) Galloping Transmission Line Conductor Torsional Design Nonlinear INTRODUCTION Conductor galloping is that the high-amplitude, low-frequency oscillation of overhead power lines owing to wind. Galloping can cause various kinds of structural and electrical losses for overhead transmission lines[1]. This conductor motion is of large amplitude (approximately>10 m) and low frequency (approximately 0. 1-3 Hz) [2]. The movement of the wires mostly occurs in the vertical plane, although rotational and horizontal movements are also possible [3]. Therefore, it has become a problem for transmission technology and require large attention in the globalContinuum cable standard for transmission lines using the Hamilton principle. In this paper, to find an effective mathematical design standard for the galloping mechanism in transmission cable is proposed. This study gives the comparison between existing design standard and continuum cable standard for transmission lines. Garlekin methodis used forthree different discrete design standards of one degree of freedom, two degree of freedoms, and three degree of freedoms are from the continuum standards was obtained. On comparing galloping vertical amplitude with different influence factors analyzed inthestandards. Various factor important for anti-galloping design of transmission line, synthesis of galloping amplitude with respect to influence factors is obtained. These factor are cable span length,, wind velocity, and flow density etc. Figure 1: Design Standard of the transmission line: (a) cable standard and (b) infinitesimal element Conductor galloping presents a magnificent motion volatility mechanism in the consistent flow over a noncircular crosssection caused by ice on the conductor. It is non-irrelevant to find an effective mathematical standard to understand the galloping mechanism. The galloping design standard have been studied. International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 10 (2016) pp 6972-6982 © Research India Publications. http://www.ripublication.com 6977 The quasi-steady hypothesis (QHS) was used to explain the nonlinear mechanics power, wherever when Nigol and Buchan [6]. It was established that torsional oscillation typically plays a crucial role to excite the galloping process, particularly for the conductors. After that, Yu et al. designed a three-degree of freedoms oscillator design standard [8, 9], having flat, and torsional oscillations. It was found that horizontal oscillation has a crucial influence on the galloping major conditions and galloping characteristics. Some important factors, such as span length, startup tension, and sag, cannot be considered in these standards. Tangent to the cable is violated [15], So a coherent cablebeam standard has become a material goods of great interest, which can be able to take into consideration of all the factors [16] & [17]. Then, Luongo et al. [18] & [19] have given compatible linear and nonlinear standards of cable-beam accounting for both compress and bending. In behest to use within the actual conditions easily, [20] & [21] simply constructed one-degree of freedom, two-degree of freedom, and three-degree of freedom standards from the continuum standards of transmission lines by using Hamilton concept. However the analysis of the one, two and three degree freedom design standard was not studied, which is extremely vital within the application of those standard. In this paper, transmission line continuum cable standard is proposed using the Hamilton concept, where the non-linearity and initial displacement, caused by thedeformation, and the nonlinearity caused by force were analyzed. And discrete standards of one degree of freedom with vertical movement, two degree of freedoms withvertical and torsional coupling movement, and three degree of freedoms with horizontalvertical and torsional movement were derived from thecontinuum standard by using the Galerkin method. In order to compare the three design standards of the galloping amplitude was observed by the other factors including wind velocity, flow density and span length. The difference in the three standard was proposed by comparing the vertical amplitude because of the conductor galloping. And the alteration of the galloping amplitude relative to the influence factors was also introduced, which is much important to the anti-galloping design applied in the actual engineering Figure 2: Standard of the transmission line: (a) cable standard and (b) infinitesimal element. DESIGN OF THE CABLE MODEL Cable Design Standard Schematic diagram of the transmission line given is shown in Figure 1(a) in which the initial tension is represented by T0. lis denoting the span length, and v, u and w are the displacements of an arbitrary pointAin the longitudinal, perpendicular, and horizontal direction respectively. It is assumed that initial state of transmission cable is static balance state. A small displacement dx in the line is described schematically in Figure 1(b). ABis the initial position with the static arc length ds0and A”B” is the position of the movement with the changed arc lengthds taken from the line at time Δt. Suppose that the displacements of the beginning and the end in longitudinal (x), horizontal(z), and perpendicular(y) directions are u(x, t), w(x, t) and v(x, t) and u + uxdx, w + wxdx and v + vxdx respectively, where the subscript x represents derivative with respect to x coordinate. The initial arc length vector of the line infinitesimal element can be described as ds0 ⃑⃑ ⃑ = dxi + dyj + dzk⃑ (1) wherei⃗, j⃗ and k⃑⃗ are the unit vectors of x, y and z directions. Then, arc length vector after movement can be derived as ds = ds0 ⃑⃑ ⃑ + BB′ ⃑⃑ ⃑⃑ ⃑⃑ − AA ′ ⃑⃑ ⃑⃑ ⃑⃑ + B′B′′ ⃑⃑ ⃑⃑ ⃑⃑ ⃑⃑ − A′A′′ ⃑⃑ ⃑⃑ ⃑⃑ ⃑⃑ = (dx + uxdx)i + (dy + vxdx)j + wxdxk⃑ (2) The length of arc can be given at the start and end in the movement can be described as