Finite element modeling of transmission line under downburst wind loading
Introduction
The interruption of electrical service due to failure of transmission line structures can have devastating economical and social consequences. In September 1996, Manitoba Hydro Company, Canada, reported wind damage of about ten million US dollars due to the failure of 19 transmission towers [1]. Investigation of transmission line failures in the Americas, Australia, South Africa, and many other utility organizations has reported that more than 80% of the majority of all weather related line failures were the results of high intensity winds (HIW), ranging from fully mature tornadoes to various forms of downbursts and microbursts that are associated with the occurrence of thunderstorms [2]. Downbursts can be defined as an intensive downdraft air that induces very strong wind in all directions when striking the ground. Microbursts are smaller and more concentrated downbursts, the physical size of which is up to 4 km [3].
The design of transmission line structures is consistently governed by wind loading. The wind loads used in most codes of practice, standards, and design recommendations for transmission line design [4], [5], [6] are based almost entirely on large-scale wind storms, which may include severe tropical storms such as hurricanes and typhoons. In spite of the fact that the majority of transmission line failures have been due to severe local wind storms, such as downbursts, very limited guidance is provided in the design codes of practice to cover this type of loading. In addition, the conventional boundary layer vertical profile, of increasing wind velocity with height, is no longer valid for downbursts where a region of maximum wind velocity exists close to the ground with a decrease in velocity with height. Therefore, normal design methods of transmission line structures evidently are not adequate because of the off-design conditions arising from the loading associated with HIW.
A downburst event is very localized, such that its structure, scale, and intensity cannot readily be measured in the field by conventional recording stations. This is quite different from the large-scale wind, whereby a whole reference area of the transmission line is subjected to similar wind conditions. Two basic models have been developed for the wind field accompanying a downburst event, namely the ring vortex model [7], [8], [9], [10] and the impinging jet model [10], [11]. The ring vortex model simulates a descending air column that forms a vortex ring prior to reaching the ground surface. The impinging jet model was found to provide a better representation of the fully-developed downburst as it simulates the radial flow that dominates the wind field after the downburst touches the ground. Simulations of scaled microburst event in a laboratory using a large impinging jet have shown good agreement with full-scale data [12], [13].
Computational fluid dynamic model (CFD) for downbursts have been developed by Wood et al. [14] and the results were used to provide an equation describing the variation of the mean radial velocity as a function of elevation relative to the ground. A detailed CFD model was then developed and experimentally validated by Hangan et al. [15]. It led to the development of a series of time history data for both the radial and vertical components of the velocity profile. This downburst wind field data are used in the current study. Details of the CFD model employed by Hangan et al. [15] will be discussed in the next section.
In the current study, the downburst wind velocity data from the model CFD are converted to loads acting on a full-scale transmission tower using appropriate scaling factors. These factors scale the initial vertical velocity in the downburst, obtained from the model, to the full-scale value selected by the user for a real event and also scale the initial downburst diameter from the model to the full-scale value, again selected by the user. These two scalings produce the full-scale wind velocity distribution as a function of space and time. The resulting loadings on the transmission tower and line components, at any time step during the event, are determined using loading coefficients that are presently taken from design codes of practice. The loads obtained are then incorporated into a finite element program that takes into account the non-linear large deformation behaviour of the conductors and the ground wires. These loads depend on the characteristics of the downburst event including its diameter and velocity as well as its location relative to the tower. Finally, a case study is conducted using specific downburst parameters and different angles relative to the transmission tower. Results of this case study are used to compare the responses of the transmission tower under both downburst wind loads and those due to conventional atmospheric boundary layer winds.
Section snippets
Downburst computational fluid dynamic (CFD) model
The downburst wind field utilized in this paper is based on a CFD simulation conducted by Hangan et al. [15]. The CFD simulation was carried out using the commercial software Fluent 6.0. In the same study, Hangan et al. [15] reported the results of an experimental program carried out in an impinging jet facility where pressure and hot-wire velocity measurements were used to validate the assumptions employed in the CFD simulation. A schematic diagram of the computational domain used in the CFD
Conversion of downburst wind data
For each velocity component, the following scaling equations are used to obtain the velocity profile acting on a full-scale structure:where and are the radial and vertical coordinates of the point of interest of the full-scale structure, respectively, and is the time increment to be used in the full-scale analysis. The full-scale downburst is defined by its jet diameter and its jet velocity .
The following steps are
Description of the transmission line system
In the current study, a Manitoba Hydro transmission tower (Tangent Suspension Tower Type (A)) is chosen as a generic lattice tower to illustrate the application of downburst wind loading on transmission line/tower. This tower is one of the structures that failed during the downburst wind storm that occurred in Manitoba, Canada, in 1996 [1].
A photo of the transmission line system considered is provided in Fig. 7. The system includes a large number of towers that are supported using four guys
Finite element modelling of transmission line/tower
Modeling of various components of the transmission line, including the tower members, the guys, the conductors and the ground wires, and the insulator strings, is discussed below.
Evaluation of forces on the transmission tower and cables
A free vibration analysis of the tower-cables system (taking into account the effect of the pre-tension load applied to the conductors) is conducted and the obtained results reveal the following:
- (1)
The fundamental period of the tower vibration is 0.58 s.
- (2)
The fundamental period of the conductors is 8.25 s.
Determination of the number of transmission line spans to be considered in the analysis
The purpose of this section is to determine the minimum number of conductors and ground wires spans to be considered in order to accurately predict the behaviour of a tower. A large number of analyses were conducted by modelling two, four, six and eight cable spans, respectively. These models are denoted as 2-B, 4-B, 6-B and 8-B for the two, four, six and eight cable spans, respectively. The tower of interest is located at the central location between those cable spans. At the location of the
Steps of analysis
The following steps are conducted to evaluate the response of a transmission tower to downburst loads:
- 1.
Read raw downburst wind data resulting from the CFD analysis.
- 2.
Assume certain values for the downburst parameters , , and .
- 3.
Read the nodal coordinates for tower, guys, conductors and ground wires.
- 4.
Based on the scaling approach and the force calculation procedure described above, the nodal forces are evaluated.
- 5.
Non-linear analyses are
Case study
As an illustration, the results of the analysis of three different downburst configurations are presented in this paper. For all cases the downburst is assumed to have a diameter , a jet velocity and radial distance relative to the tower . The difference from one case to another is in the angle that is taken as , and , respectively. The angle indicates that the centres of the downburst and the tower are located in a vertical plane perpendicular
Conclusions
This paper describes in detail the procedure to model and predict the behaviour of a transmission line structure subjected to downburst wind loads. The wind load data are based on previously developed CFD model. Procedures to scale up the wind data generated by the CFD model as well as to evaluate the associated forces acting on the transmission line are presented. The modelling procedure for the tower, the guys, the conductors, the ground wires, and the connections that takes into account the
Acknowledgements
The authors are indebted to the Natural Sciences and Engineering Research Council of Canada (NSERC) and Manitoba Hydro Company, Canada, for the financial and in-kind support provided to this research work. Also, the authors deeply appreciate the SHARCNET facility and staff at the University of Western Ontario, Canada. Finally, the authors acknowledge Prof. H. Hangan and Dr. J-D. Kim at the Boundary Layer Wind Tunnel Laboratory, the University of Western Ontario, Canada, for their effort in
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