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Nonlinear seismic behaviors of different boundary conditions of transmission line system under earthquake loading are investigated in this paper. The transmission lines are modeled by cable element accounting for the nonlinearity of the cable. For the suspension type, three towers and two span lines with spring model (Model 1) and three towers and...
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In this paper the hybridisation of the 2D time-domain boundary element method (BEM) with the unstructured transmission line method (UTLM) will be introduced, which enables accurate modeling of radiating boundary conditions and plane wave excitations of uniform and non-uniform targets modelled by geometrically accurate unstructured meshes. The metho...
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... To improve the seismic performance of transmission lines and mitigate the earthquake disasters, many efforts have been made by researchers to investigate the seismic behaviors of transmission lines. Under earthquakes, there is a significant dynamic coupling effect [5] between transmission conductors and towers, which is revealed from a mechanistic perspective by analyzing the seismic responses [6,7], dynamic characteristics [8,9], and failure modes [10,11] of tower-line systems using theoretical, numerical, and experimental methods. Moreover, the elastic-plastic dynamic problems of tower-line systems are paid much attention to by some scholars to ensure the functionality of power system under an earthquake with intensity greater than the design intensity. ...
To improve the seismic design of long-span truss structures (LSTSs, supporting-equipment structures) in ultra-high voltage substations and evaluate their seismic risk, the responses, collapse performances, and fragilities of LSTS considering peak ground acceleration (PGA) and duration as variables are examined in this study. The nonlinear finite element model of LSTS-tower-line system is established by considering the tower-line dynamic interaction, and it is excited by 17 far-field ground motions having varying durations (i.e., significant durations, DS90). Seismic responses of LSTS increase linearly with increasing DS90 , and more significantly under earthquakes with a higher intensity. The duration effect on LSTS responses consists of excitation-amplifying and damage-cumulating effects, which leads to that the increasing D S90 accelerates the development of plasticity in LSTS subjected to major earthquakes, and thus reduces its collapse load in a nonlinear manner. The displacement-based and IM-based joint probabilistic seismic fragility methods are proposed by regarding the record-to-record, structure-to-structure, and duration-to-duration uncertainties. The fragility curves with DS90 as a variable and fragility planes with PGA and DS90 as variables are generated to provide an important reference for LSTS seismic risk assessment.
... When studying the dynamic coupling effect of tower-line systems subjected to seismic loads, transmission conductors are generally simulated using chain [7], cable [34], and spring [35] models. The chain model is derived based on the elastic seismic force theory and is primarily applied in a linear elastic analysis. ...
The transmission line is a vulnerable lifeline system when subjected to extreme loads, such as earthquakes and heavy ice loads. This study numerically investigates the structural performance of ultrahigh voltage long-span truss structures (LSTSs) under the multi-hazard action of earthquake and icing to mitigate disaster losses. A typical LSTS-3-tower-3-line system was selected as an analytical model. Its finite element model was established using a simplified spring model to simulate an ice-covered transmission conductor; it was excited by seven multi-component far-field ground motions. The natural vibration characteristics, structural responses, earthquake failure modes, and bearing capacities of LSTS affected by icing were comprehensively analyzed. The results showed that the seismic response of LSTS decreased, and its total response (induced by the tension of the conductor, ice load, and earthquake) increased with an increase in ice thickness. In addition, icing severely reduced the bearing capacity of LSTS with average reductions of 11.7% and 39.1% when the ice thicknesses were 15 and 50 mm, respectively. Moreover, the influence mechanism of icing on LSTS seismic responses and the failure mechanism of LSTS under the multi-hazard action of earthquake and icing were revealed. Specifically, the failure modes of LSTS, namely flexural (mode 1), mixed (mode 2), and shear failures (mode 3), were determined by the ice condition. Finally, prediction models for the structural responses and bearing capacity of LSTS were developed to facilitate the design of electrical equipment and LSTS and improve design efficiency.
... Also, these forces depend upon the horizontal and vertical components of the seismic acceleration. In the case when only horizontal seismic forces are considered (11) Similarly, when only vertical seismic forces are acting ) (12) In fact, the horizontal and the vertical components of the seismic forces act simultaneously. In this paper, it is assumed that the vertical component of the ground acceleration is two-third of the horizontal component of the ground acceleration with same frequency content. ...
Weightless sagging elasto-flexible cables lack unique natural state. However, heavy cables are assumed their natural state under their self-weight for predicting their static and dynamic response. In most of the existing literatures the nodal coordinates or placements are generally defined in reference to the chosen Cartesian coordinate system for the discrete formulation called here Placement Model. In this paper, Placement Model is applied to predict the seismic response of weightless sagging cables. The cable is fixed at their both the ends and two masses are attached in its intermediate points leading to a 2-node 4-DOF system. The dynamic response of the cable node is investigated by applying two different seismic excitations in three different conditions as only horizontal excitation, only vertical excitation and both horizontal and vertical excitation act simultaneously. El-Centro and Loma Preta Seismic excitation is applied to predict the seismic response of the cables.
... In the numerical simulation of transmission lines, cable [42], chain [ 43], and spring [44,45] models are widely used. Gong et al. [45] proposed a spring model (SM) based on the horizontal dynamic stiffness (HDS) (SM-HDS) that significantly improved the computational efficiency while ensuring an accurate analysis by implementing shaking table test and numerical methods. ...
1000 kV outgoing line frame (OLF1000), which is an important and long-span supporting frame in ultrahigh-voltage substations (UHVSs), is prone to damage or collapse under strong earthquakes, resulting in serious power system outage. This study numerically investigates the seismic fragility of OLF1000, which has complex and multiple interactions with transmission towers and lines, subjected to earthquakes with multiple angles of seismic incidence (multi-ASI). A new multi-ASI seismic fragility analysis method (N-MASI-SFAM) considering the orientation layout of the structure and strike of the fault zone is proposed; it fully reflects record-to-record, structure-to-structure, and direction-to-direction uncertainties. The samples of structure-record-ASI pairs and structure-record pairs are generated using Latin hypercube sampling to develop probabilistic seismic capacity models and probabilistic seismic demand models for OLF1000. In addition, fragility planes of OLF1000 for different limit states are generated by performing the N-MASI-SFAM, which provide suggestions for the orientation layout of OLF1000-tower-line coupling system outside the UHVSs. Further, the results obtained by N-MASI-SFAM and seismic fragility analysis method based on the traditional excitation method (TEM-SFAM) are compared, and they demonstrate that the TEM-SFAM cannot identify the maximum seismic risk of the OLF1000; the guarantee rates of TEM-SFAM are 51% and 45% under far-field and near-fault pulse-like earthquakes, respectively, indicating that its reliability in the seismic fragility analysis of OLF1000 is very low. Finally, a seismic risk assessment method based on the epicenter position is proposed, and the seismic risk of built engineering structures is quantitatively evaluated.
... Cable [31], chain [32], and spring [33,34] models are widely used in the dynamic analysis of transmission lines. According to Gong and Zhi's research [33], the spring model based on the horizontal dynamic stiffness, validated by shaking table test and numerical methods under different ground motions, could significantly improve the calculation efficiency while ensuring an accurate analysis. ...
As a typical and important supporting structure in ultra-high voltage substations, the 1000 kV outgoing line frame (OLF1000) bears the role of supporting electrical equipment and long-span transmission lines. The interaction between transmission towers, lines and OLF1000 makes it exhibit asymmetric stress and deformation states in normal use. For this kind of irregular coupling system (i.e., OLF1000-tower-line coupling system), the seismic incident directionality effect (SIDE) with high uncertainty may be a disadvantage. To investigate the effect of incident directionality on the seismic responses and ultimate bearing capacity of the OLF1000, and provide a reference for its seismic design, this study numerically evaluated the seismic responses of the OLF1000 by considering the dynamic coupling effect between a tower-line system and OLF1000 (DCE-TLS-OLF1000) under 40 multi-direction ground motions. According to our results, the seismic incident directionality significantly affects seismic responses, participation of vibration modes, plastic development law, failure modes, and ultimate bearing capacity of the OLF1000. In contrast, traditional approaches (i.e., 0° directional excitations) cannot ensure the seismic safety of the OLF1000 in arbitrary incident direction as the guarantee rate is less than 50%. Furthermore, the direction-to-direction (DTD) and record-to-record (RTR) uncertainties were theoretically derived; moreover, 95% guarantee models based on the two uncertainties and prediction models by considering the DCE-TLS-OLF1000 and SIDE were proposed to ensure the seismic safety of the OLF1000 under excitations exhibiting arbitrary incident direction and provide a helpful seismic design method for designers.
... The ITLS has been considered in many studies on the seismic responses of transmission towers [9][10][11][12][13][14], with the analytical models for transmission lines including spring [15,16], chain [17], and cable [18] models. Li et al. performed a shaking table test on a simplified model of a transmission line system (TLS), and suggested that the ITLS has an evident influence on the seismic responses of transmission towers [17]. ...
This study investigated the seismic responses, earthquake failure modes, and collapse fragility of a 1000 kV outgoing line frame (OLF1000, a supporting-equipment structure used in substations), by considering the interactions in the tower line system (ITLS). First, three analytical models of the OLF1000 were established, in which transmission lines were represented as massless springs based on their dynamic stiffness, and the lattice transmission tower was simplified to an elastic beam tower. Additionally, 40 real seismic records with similar spectral characteristics were used to analyze the seismic responses of the OLF1000 by considering the ITLS under minor, moderate, major and extremely major earthquakes. Moreover, a time history analysis was carried out to investigate the failure modes, and the collapse risk of the OLF1000 was considered from a probabilistic perspective. According to our results, the OLF1000 remains mostly elastic under minor and moderate earthquakes, as the energy consumption and elastic constraints of the transmission lines reduce the seismic response of the OLF1000. However, amplification of excitations by the transmission tower increases the previously reduced responses. Additionally, in the case of major and extremely major earthquakes, when considered in isolation, the OLF1000 remains intact or is only slightly damaged, but it becomes seriously damaged and can even collapse when the ITLS is considered. Furthermore, the failure mode of the OLF1000 is that of an in-plane global collapse, whereas the inclusion of the ITLS in the model suggests that an out-of-plane continuous collapse will be caused by a local failure. The ITLS significantly reduces the collapse load of the OLF1000. Finally, the ITLS substantially increases the probability of collapse of the OLF1000 under strong earthquakes.
... In the research on power systems, three types of transmission-line dynamic models are considered: The suspended cable model was used by Tian and Gai [4], who studied the nonlinear seismic responses of a transmission-line system under various boundary conditions by simulating the transmission lines as cable elements and pursuing an explicit analysis to perform the calculations. This modeling method can provide more accurate results than the chain model, although its calculation is very inefficient. ...
... The three analysis models commonly used to study tower-line systems are the suspended cable model [4], chain model [5], and spring model [7]. Their computational efficiency and precision will be compared in this section. ...
Inclined suspended cables (ISCs) have several applications in the transmission lines of power network systems. This study attempts to simplify the modeling of ISCs by addressing their static and dynamic stiffness. The dynamic problem of a uniform damping ISC under a harmonic excitation is studied under the assumptions that the suspended cable is deflected in a parabolic profile during static equilibrium and all the displacements in the dynamic in-plane motion are small. A closed expression for the frequency response function (FRF) is derived, based on which the static stiffness of the ISC is established; this aids in modifying the Ernst's formula. Furthermore, the cable dynamic coefficient is defined by considering the participation factors and the minimum number of vibration modes. The dynamic stiffness of the ISC is established by combining the static stiffness and cable dynamic coefficient. In addition, a shaking table test of a reduced-scale tower-line system model is performed to verify the correctness of the finite element model of the suspended cable. The results of the static and dynamic analyses indicate that the spring model based on the dynamic stiffness, showing a good precision, has a higher computational efficiency compared with the suspended cable model. Finally, the spring model, which is applied to the tower-line system by choosing different seismic excitations, inclinations, sag-to-span ratios, and spans of ISCs, is valid for an arbitrary angle of inclination ranging between 0° and 50°. Moreover, its results are in very good agreement with those of the suspended cable model.
... Extensive research on transmission line DCEs has been conducted for transmission tower-line systems. For example, suspended cable [7], chain [8], and spring [9][10][11] models have been adopted in DCE research. Li and Shi et al. [12] carried out shaking table tests on transmission line and support tower coupled systems to verify rationality of proposed approaches [8] and concluded that transmission line DCE significantly influenced the seismic responses in support towers, which could not be neglected in seismic design. ...
To figure out the influence mechanism of the dynamic coupling effect of transmission lines on seismic responses of the 1000 kV outgoing line frame under longitudinal excitations and discuss the influence of sag-span ratios of transmission lines， shaking table tests were performed on a single-span 1000 kV outgoing line frame by considering the dynamic coupling effect of transmission lines with a scale factor of 1 ∶ 15. Moreover， transmission lines were simulated by the massless springs with equivalent dynamic stiffness. Test results indicate that the seismic responses of 1000 kV frame
are reduced by the strong dynamic coupling effect of transmission lines; with the decrease in sag-span ratio， the energy dissipated by the suspended system increases and the elastic constraints of transmission lines on the frame enhance， resulting in further reducing the seismic responses of 1000 kV frame. Furthermore， the results of numerical reconstruction analysis of the experiments indicate that the finite element analysis can simulate the dynamic coupling effect between transmission lines and 1000 kV frame very well.
... Extensive research on transmission line DCEs has been conducted for transmission tower-line systems. For example, suspended cable [7], chain [8], and spring [9][10][11] models have been adopted in DCE research. Li and Shi et al. [12] carried out shaking table tests on transmission line and support tower coupled systems to verify rationality of proposed approaches [8] and concluded that transmission line DCE significantly influenced the seismic responses in support towers, which could not be neglected in seismic design. ...
Earthquake damage data show that substation long-span frames (LSFs) have remained intact under many strong earthquakes, even when electric power facilities and transmission towers had sustained serious damage. Therefore, the influence of the suspended system (SS) dynamic coupling effect (DCE) on LSF seismic responses is a matter of great concern. For that reason, this study focused on seismic responses of a 1000-kV outgoing line frame called OLF1000, which is a type of LSF, as it is subjected to the SS DCE. A scaled-down experimental model of a single-span OLF1000 was tested using a shaking table. An SS showing different sag–span ratios was applied to OLF1000 to determine how DCE influenced OLF1000 seismic responses. DCE was numerically simulated and analyzed according to different site classifications and ground motion intensities. Results showed that the DCE between the SS and OLF1000 was significant. In addition, the DCE reduced OLF1000 seismic responses owing to energy consumption and elastic constraints. Moreover, the DCE was found to be an SS structural attribute and was therefore unaffected by external loads. The DCE more significantly affected the single-span OLF1000 than the three-span OLF1000.
Past major earthquakes have witnessed extensive pile-supported transmission tower-line systems (PSTLs) failing, which highlights the great susceptibility of PSTLs to damage from earthquakes. However, a comprehensive literature review in seismic analysis of PSTLs reveals that two critical aspects, i.e. soil-structure interaction (SSI) and depth-varying spatial ground motions (DVSGMs), have been completely overlooked in numerous previous studies. To be specific, pile-supported transmission towers are generally assumed to be fixed to the ground surface and are excited using uniform ground motion inputs. Such analytical schemes may result in severe misestimates of seismic response predictions of PSTLs. Within this context, the main objective of the present study is to accurately assess the seismic performance of PSTLs by considering SSI and using DVSGMs as inputs. For this purpose, an existing prototype PSTL is firstly selected and the corresponding three-dimensional finite element model is created in ABAQUS software, in which SSI is simulated by the Beam on Nonlinear Winkler Foundation (BNWF) model. Then, the three-dimensional DVSGMs are stochastically synthesized based on the computed ground motion transfer functions (GMTFs) of local sites. Next, seismic performance of the PSTL with SSI, including dynamic responses, ultimate bearing capacity and failure mechanism, is assessed using the generated DVSGMs as seismic inputs. Finally, a parametric study is conducted to comprehensively examine and discuss the influences of SSI, seismic excitation types, coherence loss and local site conditions on seismic performance of the PSTL. Numerical results show that seismic performance of PSTLs can be affected significantly by the above mentioned influencing factors. This research is expected to offer a meaningful reference to seismic performance assessments of PSTLs.
