Electricity is a vital component of our contemporary way of living. The reliability of such a crucial element to socio-economical growth is heavily dependent on the sustainability and resiliency of transmission line system components facing various weather-related loading conditions. Aside from the conventional loading attributed to synoptic wind, loading cases associated with thunderstorms (i.e., tornadoes and downbursts), have recently been acknowledged for their devastating impact on transmission line systems. Fujita (1985a) first defined downbursts as “a strong downdraft that induces an outburst of damaging wind near the ground” are believed to be the major cause of transmission line failures (Miguel et al., 2018). Kanak et al. (2007) reported the failure of 19 towers in Slovakia due to a downburst event. Another event that occurred in Manitoba, Canada, has been reported by McCarthy and Melsness (1996) and resulted in the failure of 19 transmission towers. Similarly, Hydro One Ontario Company (Ontario, Canada) revealed that the failures of their two towers near Waubaushene were due to a downburst event (Hydro One Failure Report, 2006). These incidents, as well as those that occurred in Australia as reported by Li (2000), and in China as reported by Zhang (2006), have directed researchers to study the effect of downburst loading on transmission line systems.

Researchers studying the effect of downbursts on transmission line systems have followed different paths in choosing the wind field used to examine the behavior of different transmission line components corresponding to downburst loading cases. Despite the availability of different numerical approaches to generate thunderstorm outflows (Ponte and Riera, 2007; Solari et al., 2017), many researchers used wind fields developed using computational fluid dynamics (CFD). Shehata et al. (2005) scaled up the wind field resulting from the CFD simulation conducted by Kim and Hangan (2007) to study the behavior of both the conductors and the supporting towers due to the applied downburst wind field. Finite element analysis showed that downburst loading might yield higher peak values of internal forces than that resulting from straight line winds. The study also concluded that the consideration of six spans should suffice when studying a localized downburst event. Building on that study, another investigation was conducted by Shehata and El Damatty (2007) to study the spatial configuration of a downburst that would lead to the highest forces in the members of a guyed tower. The results of that study emphasize the importance of considering the spatial locality of the event, which proved to be essential when studying transmission line structures extending for great horizontal distances. To generate the wind field, the same procedures were adopted by Darwish and El Damatty (2011) and Mara and Hong (2013) who also concluded that downburst loading can lead to more severe loading conditions compared to normal wind loading cases depending on the jet velocity considered.

It is worth mentioning that all the aforementioned studies could only use the quasi-static analysis approach, given only time-varying mean velocity fields were available from the URANS simulations of Kim and Hangan (2007). This was generally justified by the fact that the studied structural components, whether the conductors or the tower structures, have distinctive natural periods, which are relatively distant from that of the loading phenomenon. Yet, further studies have considered the dynamic effect associated with downburst loading to investigate its impact on the structural elements. To do so, researchers had to produce the fluctuating component using different techniques, and then super-impose it on the mean component. In the case of Darwish et al. (2010), researchers extracted the turbulent component from field measurements that were reported by Holmes et al. (2008), and then added it to the time histories of the moving mean component produced by RANS CFD simulations. The study concluded that inclusion of the turbulent component into the dynamic analysis showed minor differences compared to the quasi-static analysis, which was attributed to the high aerodynamic damping exhibited by the conductors, attenuating the dynamic response. Another approach was used by Wang et al. (2009) who studied the dynamic response of tall transmission towers, where the turbulent component was synthetically produced using harmony superposition method combined with Fast Fourier Transform (FFT) algorithm, and the same conclusion was reached, that the dynamic effect could be neglected due to the difference in frequencies between the tower and the studied event.

Savory et al. (2001) utilized the empirical model developed by Holmes and Oliver (2000) to produce downburst wind field, and evaluate the loading on lattice towers by performing dynamic analysis on the tower structures. The analysis concluded that the tower structures were found to be safe, suggesting failure occurrence is dependent on the inclusion of conductor loading in the analysis. Dynamic performance was also evaluated by Lin et al. (2012), who used the slot jet model discussed by Lin and Savory (2006) to test an aero-elastic model of a transmission line system in a boundary layer wind tunnel, simulating downburst wind field. Results from the downburst wind field test cases were compared to those of the synoptic wind, and results showed less significance of dynamic effect, and a generally quasi-static behavior.

Furthermore, researchers studying downbursts on transmission line systems can also be categorized based on the components examined in their studies. While Aboshosha et al. (2016), Lin et al. (2012), Shehata et al. (2005), Shehata and El Damatty (2007), Darwish and El Damatty (2011), and Elawady et al. (2017) considered the combined tower-line system, Mara et al. (2010), Mara and Hong (2013), and Savory et al. (2001) have considered the effect of downburst loading on the supporting tower structures alone with no regard for the conductors. On the other hand, Aboshosha and El Damatty (2014a,b); Aboshosha and El Damatty (2015b), Darwish et al. (2010), and Elawady and El Damatty (2016) have focused on the conductors, studying their impact either on the loading process, or their aerodynamic damping. The current study is an extension of the work performed by Elawady and El Damatty (2016). It examines the limitations associated with the analysis of Elawady and El Damatty (2016), the validity of their assumptions, and finally the applicability of the wind field used.

Elawady and El Damatty (2016), complimented a series of previous studies that investigated the effect of downburst loading on transmission line systems. The studies performed by Darwish and El Damatty (2011) and Shehata and El Damatty (2007) looked into the effect of the localized nature of downburst loading on transmission line systems. This special feature of downburst loading, where the loading is not constant across spans, results in different structural behavior than that resulting from straight line winds. One of their cases, which they termed oblique load case, has the downburst positioned such that the angle theta “θ” between a line perpendicular to the tower and a line joining the downburst center with the tower is >0, as shown in Figure 1.

Such cases result in differential loading on the consecutive conductor spans attached to the tower of interest. Figure 1 illustrates that through areas A1 and A2. Area A1 represents the total force acting on the conductors to the right of the tower of interest (closer to the downburst center), and area A2 represents the total force on the conductors to the left of the tower of interest (away from the downburst center). The loading exhibited due to this case is similar in configuration to that of the broken wire loading case considered by ASCE-74 (2010). This case is of particular importance to components like the cross-arms that can experience large moments due to the longitudinal forces. Aboshosha and El Damatty (2013) showed that these longitudinal forces can exceed the associated transverse forces by up to 60%. Yet, varying downburst parameters like the radial distance R, obliquity angle θ and jet diameter D_j, can lead to loading cases that are more severe than that of the broken wire.

As such, Elawady and El Damatty (2016) conducted an elaborate parametric study to find the configuration resulting in the highest longitudinal loading. To do so, the authors utilized the technique described by Aboshosha and El Damatty (2015b) to compute the reactions on a six-span conductor system. The loads applied to the system were those corresponding to the downburst wind field generated by Kim and Hangan (2007). However, the wind field used only contains the moving mean component of the flow and did not contain the fluctuating component. As such, the dynamic effect of the wind loading is excluded. In addition, extruding a three dimensional wind field from two dimensional CFD analysis results in the assumption of full correlation. This can result in computing values of longitudinal reactions that are not conservatives.

This study aims to quantify the influence of these limitations and judge the applicability of quasi-static analysis compared to dynamic analysis. To do so, the current study will conduct the following steps:

Develop a numerical structural analysis model for calculating the response of a multi-spanned conductor system to downburst wind loading.

Accordingly, the following sections outline the current study. The second section (section Model-Scale Analysis) describes the analysis performed at model-scale. The full-scale analysis is presented in the third section (section Full-Scale Analysis). The technique used in generating the turbulent component is described, and the analysis results are demonstrated. Section Analysis of Result's Sensitivity to Wind Field Parameters examines the sensitivity of the computed results to the wind field characteristics used in the full-scale analysis, and compares it to the characteristics of wind fields reported by previous literature. Finally, the last section (section Conclusions) lists the conclusions drawn from the conducted work.

Dynamic analysis of conductor systems under downburst loading is a complicated task due to the geometric nonlinearity of the conductors. In addition, the time varying properties of the wind field require properties such as the aerodynamic damping to be modified throughout time. Previous studies that conducted dynamic analyses on transmission line systems due to synoptic wind such as Dua et al. (2015), Keyhan et al. (2013), and McClure and Lapointe (2003) considered an equivalent viscous damping to account for the aerodynamic damping. The values used by Dua et al. (2015) and Keyhan et al. (2013) were those resulting from the fluid structure interaction model computed by the latter study. These values were then implemented through different commercial software packages to enable 3D finite element analysis. It can be argued that the constant damping values used are in line with the expression proposed by Davenport (1962) and shown in equation (1). The aerodynamic damping value per mode i is shown to depend on the air density ρ, the drag coefficient C_D, the conductor diameter D, the wind velocity V, conductor mass m, and finally the frequency of the ith mode f_i. Thus, for studies such as these that considered synoptic wind, a constant damping value is considered reasonable, as synoptic wind can be reasonably approximated as a stationary random process with a constant statistical mean.

In contrast, researchers like Darwish et al. (2010) and Aboshosha and El Damatty (2015b) used a modified version of the aerodynamic damping expression to account for the temporal variation of wind speed and resultant aerodynamic damping. The time dependent damping is a special feature that complicates the analysis and requires special numerical tools. To overcome this, it is proposed that a single value of aerodynamic damping, representative of the entire event, be implemented. An experiment that was part of the research program presented by Elawady et al. (2017) will be used to verify the numerical model. The next sub-section (Model Scale Results and Verification) will elaborate on the experimental setup and verification of the numerical model.

A SAP2000 model was developed to simulate a single span of cable elements with a span of 2.5 m and a sag of 0.0975 m as shown in Figure 2. The boundary conditions were set as hinged on both ends, and the simulated 2-noded cable element had the properties reported by Elawady et al. (2017). Modal analysis was first conducted to determine the natural frequencies for different modes of the system, and damping values were computed per mode using equation (1). The most challenging aspect of the procedure was the choice of a single value of velocity that could represent the whole time history in calculating a fixed aerodynamic damping value.

The mean wind field used in this analysis was that resulting from the CFD analysis simulating the WindEEE dome downburst as reported by Ibrahim et al. (2017). As for the turbulent component used, the wind field reported by Elawady et al. (2017) was superimposed on the mean component. This was done using an approach similar to that used by Darwish et al. (2010). Examining the resulting velocity time history shown in Figure 3, it appears that the early part of the time history, where the ramping occurs, is completely governed by the mean part of the flow. This can be concluded since the amplitudes of the higher frequencies related to the turbulent component are small during this period. Yet, the part that follows the ramping appears to have a rather constant mean, with fluctuating velocity fluctuating around that fixed value. Hence, it is suggested that the constant value of damping is to be calculated using the constant value following the ramping, which will be annotated V_pr in the sections that follow.

With the velocity value known, damping values were computed, and proportional damping coefficients were calculated based on the frequencies provided by the modal analysis. Loads were implemented as time histories of transverse forces acting as point loads on cable nodes. The analysis was then conducted as a transient non-linear direct integration case, considering the p-delta effect with large displacements. To test the sensitivity of the computed response to the chosen constant damping computed based on V_pr, the analysis was repeated two more times; using half the initial damping, and a quarter of it. The results presented in Figure 4, which shows the time history of the computed longitudinal reaction R_X, suggest that the assumption of concentrating on the post ramping region for evaluating the aerodynamic damping values is in fact a valid assumption. This is due to the agreement between the three plots for the ramping zone, despite the significantly varying damping values, and the differences being limited to the post ramping part of the time history. Elaborating more on that, it appears that the zone right after the ramping, denoted as Zone 1, is also insensitive to the change of damping values. Meanwhile, the time history beyond that zone, denoted as Zone 2, is the part affected by the change in damping values, implying the importance of considering damping for this zone.

As mentioned in section Numerical Model, the experiment conducted was part of the research program presented by Elawady et al. (2017) to test aeroelastic models of transmission line systems under the action of downbursts simulated at the Wind Engineering, Energy and Environment (WindEEE) Research Institute. To simulate downbursts, an upper chamber that has six fans is pressurized until a steady pressure is reached. The flow is then released from the upper chamber through a 3.2 m opening (jet diameter) toward the hexagonal testing chamber (25 m edge-to-edge with height of 3.8 m). The flow impinges the ground, creating a downburst that radiates in every direction until it exits through the opening on the peripheral walls. Further details regarding the facility can be found in the work presented by Jubayer et al. (2016). It is worth noting that although the facility is capable of producing horizontal background flow, this study only considered the basic impinging jet model. This decision was based on the study conducted by Darwish et al. (2010) who found the basic impinging jet model with no background flow to cause the most critical loading condition on the cross-arms by producing the highest longitudinal reactions.

As for the tested structure, a single cable span, similar to the schematic shown in Figure 2 with dimensions similar to the numerical model in the previous section, was hung between two rigid frames using leaf springs to measure the resulting straining actions as presented in Figure 5.

Results from the numerical simulation were compared to the experimental data to verify the numerical model, as well as the validity of considering a constant damping value. As shown in Figure 6, the time history of the longitudinal reaction seems to be comparable. Yet, there seems to be discrepancy in the zone preceding time step number 600. This discrepancy is believed to have no effect on judging the sensitivity to dynamics due to two reasons; first, the time zone at which it happens is not expected to experience dynamic amplification as it is in the immediate vicinity of the ramping zone. This means it is in Zone 1 in Figure 4, which was found to be insensitive to change the damping values. Second, close examination of the response at that zone show clearly that the abrupt increase in the response value is a mean governed behavior due to the relatively low frequency at which the increase happens. This sudden increase is believed to be related to the vertical component of the wind speed, which is ignored in the current wind field due to its secondary effect compared to the radial component (Elawady and El Damatty, 2016). It appears that the leading vortex would cause such effect due to the downward directed vertical component of the flow at the trailing edge of the vortex. Nevertheless, considering the zone beyond time step number 600, which is where the dynamic action is expected to develop, the difference in peak dynamic amplification was found to be < 5%, which was assumed an acceptable level of agreement between the experimental and the numerical results. Hence, building on the agreement found, the current numerical model with the assumptions elaborated will be used for the full-scale analyses discussed in the following sections.

The next step was to convert the velocity time history of each point into a force time history using equation (3), where the force F_(t) depends on the air density ρ, the drag coefficient C_D, and finally the velocity V_(t). The force time histories are then applied as point loads at the corresponding nodes, similar to the model-scale numerical model verified experimentally in section Model-Scale Analysis. A schematic of the modeled structure is shown in Figure 8.

The current model is that proposed by Shehata et al. (2005), who showed that modeling three spans at both sides from the considered tower should suffice to model the effect of consecutive spans on the computed reactions. As illustrated by the schematic, the connection between the cable spans and the towers, modeled as hinged boundary conditions due to their relative stiffness, is also complimented by insulators at the intermediate connections, which are modeled as frame elements. Finally, the conductor spans are modeled as 2-noded cable elements that are divided into 90 segments per span to enable load application. Dimensions and properties of the considered conductor system and downburst data are shown in Table 1.

As applied in the model-scale analysis, a damping value that is independent of time will be used for the full-scale analysis. The velocity used to compute damping is the V_pr of the node corresponding to the tower of interest. Damping coefficients were then computed, and implemented into the SAP2000 model as discussed in section Model-Scale Analysis.

The resulting time history of the longitudinal reaction from the dynamic analysis is shown in Figure 9. It is obvious that the peak response is entirely governed by the ramping part, which is less sensitive to the dynamic effect as proven in section Model-Scale Analysis. For the sake of comparison, and similar to the approach Elawady and El Damatty (2016) used in their analysis, the current analysis was done quasi-statically using the technique developed by Aboshosha and El Damatty (2015a). The analysis only used the mean component of the flow which was scaled up to reach the peak value of the ramping zone. This is based on the hypothesis that the ramping zone does not experience any dynamic amplification, and thus the background value can be considered as the peak value with no reduction. The resulting time history from the quasi-static analysis is also plotted in Figure 9.

To quantify the effect of the correlation between spatially separated points on the computed reactions, analysis was conducted using a fully correlated wind field. To achieve full correlation a single turbulent time history was scaled at each point based on its peak mean velocity. The resulting time history is plotted against that resulting from the turbulent (uncorrelated) wind field in Figure 10. As shown in the magnified portion of the plot, the increase in the computed reaction due to considering full correlation of turbulence is in the order of 0.5%. This was expected due to the fact that the generated turbulence had significant correlation in the circumferential direction (i.e., C in the R.θ direction = 0.05).

Accordingly, judging based on the resulting time histories plotted in Figures 9, 10, the following conclusions can be drawn:

The peak value of the reaction is governed by the mean component, as no amplification was found within the ramping zone for Figure 9, at which the peak reaction occurs. This clearly means that the dynamic effect on the computed reactions is negligible.

Another factor that might be of significance is that the ratio between V_pr, the post ramping velocity, and V_p, the peak velocity, where the ratio considered in the current analysis was about 0.65. This ratio is squared when considering forces, and thus would have considerable effects on the computed results within the post ramping section. Therefore, it is essential to know where this ratio stands compared to full-scale measurements in the literature, to determine whether this analysis is on the conservative side of computing the longitudinal reaction due to downburst loading or not. Another factor that can be of importance when calculating the longitudinal reaction due to downburst loading is the ramping period T_R shown in Figure 11. This is the period enclosed by the ramping zone between the value of V_pr before and after the ramping. The fact that the differential loading is the main cause of the longitudinal reaction gives a high significance to the period T_R, since the phenomenon is localized and heavily time dependent. The next section of this study will examine the effect of the ratio between V_pr and V_p, as well as the value of T_R, on the computed longitudinal reaction values for different values of jet speed.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.