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Masterarbeit, 2015
58 Seiten, Note: Merit
LIST OF FIGURES
LIST OF TABLES
ABSTRACT
ACKNOWLEDGEMENT
DEDICATION
1. INTRODUCTION
1.1 SCOPE OF PROJECT
1.2 AIMS AND OBJECTIVES
2. LITRATURE REVIEW
2.1 OVERVIEW OF CONDUCTOR WIND-INDUCED VIBRATIONS
2.2 ENERGY BALANCE PRINCIPAL RELATIONSHIP TO AEOLIAN VIBRATIONS ...
2.2.1 WIND POWER INPUT
2.2.2 SELF-DAMPING PROPERTY OF CONDUCTORS
2.2.3 POWER DISSIPATED BY VIBRATION DAMPERS
2.3 AEOLIAN VIBRATIONS PHENOMENON
2.3.1 AEOLIAN VIBRATIONS FREQUENCY
2.3.2 METRICS QUANTITIFYING AEOLIAN VIBRATIONS PERFORMANCE
2.4 VIBRATION DAMPERS
3. METHODOLOGY
3.1 METHOD BASED ON SAFE DESIGN TENSION
3.1.1 SAFE DESIGN TENSION METHOD EVALUATION PARAMETERS
3.1.2 RELATIONSHIP OF DESIGN TENSION AND SPAN LENGTH
3.2 METHOD BASED ON ENERGY BALANCE PRINCIPAL
3.2.1 WIND POWER INPUT AND SELF-DAMPING PROPERTY
3.2.2 POWER DISSIPATED BY VIBRATION DAMPERS
3.2.3 EXPERIMENTAL SETUP TO FIND MAXIMUM BENDING AMPLITUDE
3.2.4 CALCULATION METHODS OF BENDING STRAIN AND STRESS
3.2.5 SUMMARY OF CALCULATION METHODS
3.3 DEVELOPMENT OF EXCEL BASED ASSESSMENT TOOL
4. RESULTS AND DISCUSSIONS
4.1 FINDINGS OF SAFE DESIGN TENSION METHOD
4.1.1 SAFE DESIGN TENSION FOR ACSR CONDUCTORS
4.1.2 COMPARISON BETWEEN ACSR AND AAAC CONDUCTORS
4.2 EFFECT OF CONDUCTOR TYPE ON SYSTEM SPAN LENGTH
4.2.1 ACSR CONDUCTORS AT DIFFERENT TERRAINS
4.3 AEOLIAN VIBRATIONS PERFORMANCE USING MAXIMUM BENDING
AMPLITUDE
4.3.1 BENDING STRAIN AND STRESS
4.4 AEOLIAN VIBRATIONS PERFORMANCE USING MAXIMUM ANTINODE
AMPLITUDE
4.4.1 CASE STUDIES EVALAUTED USING THE ASSESSMENT TOOL
5. CONCLUSION
6. REFRENCES
APPENDIX
Fig. 1: Resultant curves of reduced power function obtained by different researchers[13].
Fig. 2: The relationship between Strouhal number and Reynolds number[5]
Fig. 3: Parameters influencing amplitude of Aeolian vibrations. Conductor fixed on the left
Fig. 4: Vibration dampers including a) Elgra, b) torsional, c) Spiral dampers[9]
Fig. 5: Original design of the Stockbridge damper using concrete blocks (on left) and modern design of stock bridge dampers (on right)[10]
Fig. 6: Recommended criteria for safe design tension with and without dampers
Fig. 7: ACSR-Hawk recommended safe design tension at span length of 350 m
Fig. 8: Plot of ACSR-Drake conductor using the catenary and span parameters
Fig. 9: Plot of ACSR-Drake showing the effect of changing span length at each RTS
Fig. 10: Plot of RTS in % versus span length for ACSR-Drake. The maximum span length found considering terrain D.
Fig. 11: Principal of conductor fatigue test setup based on IEEE Std. 1386-2006
Fig. 12: Fatigue test bench adopted from 3M
Fig. 13: Representation of maximum bending amplitude and maximum antinode vibration amplitude on span[16]
Fig. 14: Procedure of applying proposed fatigue endurance limit method
Fig. 15: Interface of the designed assessment tool
Fig. 16: The assessment tool calculations based on maximum antinode amplitude
Fig. 17: ACSR-Drake conductor safe tension at span of 150m, 250, 350m, and 450m
Fig. 18: ACSR (Penguin) and AAAC (Alliance) safe tension assessment at 350 m span length
Fig. 19: Finding maximum span length at various tension levels for ACSR-Drake
Fig. 20: ACSR- Drake tensile strength as a function of maximum span length
Fig. 21: ACSR- Drake and Hawk span length at various tensile strength at terrain C and D.
Fig. 22: ACSR- Drake and Penguin span length at various tensile strength at terrain C and D
Fig. 23: Comparison between ACSR- Drake and AAAC- Greeley span length at different RTS
Fig. 24: Comparison between ACSR-Hawk and AAAC-Darien span length at different RTS
Fig. 25: Comparison between ACSR- Penguin and AAAC-Alliance span length at different RTS
Fig. 26: Characteristic curve of Stockbridge damper adopted from international standards of IEC 6189
Fig. 27: Comparison of maximum vibration amplitude with and without vibration dampers at different wind speeds
Fig. 28: Maximum bending strain with and without vibration dampers
Fig. 29: Maximum antinode amplitude for ACSR (Cardinal), ACSR (Drake), AAAC (Greely), and ACCR (477 kcmil) at different wind speeds
Fig. 30: for ACSR (Cardinal), ACSR (Drake), AAAC (Greely), and ACCR (477 kcmil) at different wind speeds
Table 1: Summary of Wind-induced vibrations characteristics [1, 2, 7]
Table 2: Experimental measurements of regression coefficients a,b, and c.[13]
Table 3: Recommended safe design tension for ACSR and AAAC conductors. The tension is expressed as percentage of rated tensile strength (RTS)[12]14
Table 4: Catenary Parameter limits for protection from vibration damages[12]
Table 5: Properties of ACSR- HAWK including rated tensile strength, diameter, and mass per unit length
Table 6: ACSR- Drake properties and vibrations performance parameters at various RTS.
Table 7: ACSR-Drake properties, catenary and span parameters at various RTS levels. ...
Table 8: Properties of ACSR conductors selected to investigate the safe design tension method
Table 9: Mechanical properties of ACSR (Penguin) and AAAC (Alliance)
Table 10: Properties of ACSR and AAAC conductors used to obtain tensile strength as a function of span length
Table 11: ACSR-Drake properties, catenary parameter, span parameter, and span length at corresponding RTS. Results shown are for terrain D.
Table 12: Span length for ACSR Hawk and Penguin at corresponding tensile strength
Table 13: Reduction in span length when using AAAC instead of an equivalent ACSR.
Table 14: Technical specifications of selected ACSR conductors
Table 15: Equivalent bending strain and bending stress at 5%, 10%, 15% and 20% RTS for single aluminium layer and multi-aluminium layer ACSR conductors
Table 16: Properties of ACSR- Cardinal Conductor
Table 17: Effect of dampers on maximum antinode amplitude, bending strain, and stress. Results shown for ACSR (Cardinal) at 30% RTS
Table 18: Properties of ACSR (Cardinal), ACSR (Drake), AAAC (Greely), ACCR (477 kcmil)
This dissertation introduces wind-induced vibrations that influence the performance of overhead line structures. The main focus in this study is on Aeolian vibrations and the quantities related to the calculations of its performance such safe design tension and fatigue limits. However, there are three main methods that are proposed to evaluate conductors with respect to vibrations which are Safe Design Tension Method, Fatigue Endurance Limits Method, and Energy Balance Method. The safe design tension method is applied on Aluminium Composite Steel Reinforced (ACSR) and All Aluminium Alloy Composite (AAAC). Eventually, a relationship is established between tension of conductor and span length. The fatigue endurance limits method uses bending strain and stress to evaluate the fatigue level on the conductor. The effect of vibration dampers to overcome vibration problems on overhead line conductors is also considered. Moreover, an assessment tool based on Microsoft EXCEL is developed which allows the evaluation of overhead line system conductors based on environmental conditions, mechanical properties, and system specifications. The assessment tool evaluates the overhead line system with respect to bending amplitude or alternatively using the antinode amplitude. The analysis of finding the antinode amplitude is performed using trial and error method by solving the energy balance principal. There are a number of case studies which are analysed using the proposed assessment tool to validate the results and establish a comparison between different types of conductors including 3M Aluminium Conductor Composite Reinforced (ACCR). The comparison includes the role of dampers on mitigating vibration issues using the IEC 6189 Stockbridge damper as a reference in the evaluation process.
In the name of Allah, the Most Gracious and the Most Merciful
All praises to Allah for the strengths and His blessings in completing this dissertation. Special appreciation goes to my supervisor, Dr. Konstantinos Kopsidas, for his supervision and great support. His precious help of constructive comments and suggestions throughout the analysis and progress of this study which contributed to the success of this research.
Sincere thanks to all my friends especially Gonzalo, Andy, AJ, Asem and others for their kindness and moral support during my study. Thanks for the friendship and memories. Last but not least, my deepest gratitude and appreciations goes to my beloved parents; Dr. Abdulaziz Al-Aqil and Mrs. Shaikhah Al-Mubarak and also to my brothers and sisters for their endless love, prayers and encouragement. Also not forgetting my wife, Amirah for her love and care and my sons, Abdulaziz and Abdullah. To those who indirectly contributed in this research, your kindness means a lot to me. Thank you very much.
This work is dedicated to my wife, Amirah A. Al-Aqil, to my sons Abdulaziz and Abdullah without whose caring support it would not have been possible, and to my parents, Dr. Abdulaziz Al-Aqil and Mrs. Shaikhah Al-Mubarak, who passed on a love of reading and respect for education, to my brothers Engineer Ahmed, Zeyad, Omar, Nowaf, and Fahad and to my beloved sisters Accountant Weam, and Meral.
Nowadays electricity is becoming one of the necessities in people’s lives. Electrical power systems are constructed to connect consumers to the network. Conventionally, electrical power systems consist of three main stages which are generation, transmission, and distribution. In transmission and distribution stages, electrical power is usually transmitted by conductors that are placed either underground or on overhead line structures. Since this study intends to investigate conductor vibrations, it is obvious that overhead line structures are considered. Nevertheless, vast majority of overhead line structures are located in wide open areas that have various natural topographies. Natural climate conditions play a crucial role in identifying overhead line structure design specifications especially in the planning stage. In fact, wind as a natural element has a significant impact on conductors installed on overhead line structures. This impact is a result of wind streams flowing across tensioned conductors and inducing a series of aerodynamic forces which, in overhead line structures, initiate conductor vibrations. These vibrations affect the lifetime of the conductor and the reliability of the overhead line system. For this reason, a lot of effort is made to reduce such weaknesses in overhead lines related studies.
Initially, wind-induced vibrations must be studied in order to understand their mechanisms and characteristics. However, wind streams flowing through conductors induce vibrations in different forms including; Aeolian vibrations, sub-span oscillations, and galloping. Though, the main focus in this study is Aeolian vibrations. It is also important to protect overhead lines from these vibrations to avoid damage exerted on conductors such as fatigue problems.
Electricity demand is increasing worldwide and the need of additional planning is required. In addition to that, electrification of energy sources is becoming commonly applied. One of the solutions to overcome these issues is either to build supplementary lines or to upgrade existing overhead line structures. Basically, wind-induced vibrations have an impact on overhead line conductors as it might damage conductors affecting their rating and lifetime. Consequently, damaged conductors may lead to tripping of lines or at worst cutting the service until maintenance is scheduled causing a significant effect on the operation of the entire network. In this study, an assessment tool is developed and presented to evaluate conductor vibrations and methods of reducing effect of vibrations are introduced.
The aim of this study is to define vibration problems that could harm overhead line structures. These problems are encountered by identifying relevant mathematical models and calculation methods which are developed in a user-friendly assessment tool based on Microsoft EXCEL. The tool enables users to adjust input parameters such as environmental conditions, conductor properties and overhead line system specifications. In effect, the parameters are processed and the feedback of the tool is provided through tables and plots with reference to pre-defined evaluation criteria such as fatigue endurance limits and maximum vibration amplitude. Actually, the tool is created using Microsoft EXCEL for the purpose of simplicity, powerful capabilities, and efficient productivity that EXCEL provides. These advantages permit an effective two way communication between designers and the tool and, essentially, the tool can be managed easily unlike other sophisticated programs.
This study intends to investigate and identify the following objectives:
- To identify and develop the methods used in assessing damage caused by wind induced vibrations on overhead lines.
- To build a methodology to calculate metrics of wind-induced vibrations on conductor overhead line structures.
- To develop a Microsoft EXCEL based assessment tool with an adjustable input parameters to provide output results based on fatigue endurance limits evaluation criteria to assess overhead line structures.
- To evaluate and compare the effect of wind induced vibrations on different conductor types and suggest mitigation methods to reduce vibrations based on case studies.
Overhead line structures are placed at various types of topologies which make them susceptible to different natural climate conditions. Conductors used on these structures are exposed to the flow of wind streams through tensioned conductors generating vibrations. Aerodynamic forces that cause vibrations may damage the conductors causing the so-called fatigue. In fact, conductor vibrations have to be studied in the planning stage of the design process to minimize the fatigue damage[1]. To prevent damage of conductors, an assessment of conductor resistance to wind-induced vibrations on the overhead line structure must be carried out. In some cases protection devices might be required to reduce the damage of vibrations.
Vibrations are induced on overhead line conductors in different forms. These include Aeolian vibrations, sub-span oscillations, and galloping. Each type of vibrations has its own mechanism and characteristics as described below.
Aeolian Vibrations
Aeolian vibrations can be defined as wind-induced vibrations that occur when a light wind streams flow across cylindrical shaped objects, which are in this case conductors, creating vortex on the surface of the conductor. The vortices are created on the leeward (back side) of the conductor forming forces that alternate from top to bottom of the conductor’s surface[1]. Due to this fact, Aeolian vibrations are described as vertical shaped vibrations with amplitudes reaching conductor diameter[2]. Additionally, Aeolian vibrations are classified as high frequency vibrations with frequencies ranging from 3 to 100 Hz according to[1]. Even so, studies performed by[7]showed that Aeolian vibrations frequencies may reach up to 150 Hz.
Sub-Span Oscillations
Sub-span oscillations is a phenomenon that occurs at overhead line bundled conductors, precisely, with sub-conductors placed on the direction of wind beside each other. Sub-span oscillations can be defined as wind-induced vibrations that arises when wind streams flow across the first conductor of the bundle fronting the direction of wind (windward) creating a non-uniform aerodynamic forces on the back of its surface which excites the conductor next to it (leeward). In fact, frequencies of such oscillations range from 1 to 5 Hz which are equivalent to wind velocities ranging from 4 to 18 m/s according to[1]. Amplitudes of subspan oscillations may reach up to half of the spacing between the sub-conductors initiating conductors clashing.
Galloping
Galloping is a type of wind-induced vibrations that takes place on single and bundled conductor overhead line systems. Practically, bundled overhead line systems are prone to galloping more often than single conductor structures[1]. Furthermore, galloping may cause clash between bundled conductors or, in fact, flashovers in some cases with amplitudes reaching the conductor sag. Besides, galloping occurs at frequencies that are less than 1 Hz which describes the purpose of it being classified as low frequency oscillations. According to[2], galloping is excited at wind velocities ranging from 6 to 25 m/s.
A summary of the characteristics of Aeolian vibrations, sub-span oscillations, and galloping is presented in Table 1 including type, cause, and mechanism of each vibration form. The direction denotes the physical direction of vibrations whereas frequency and wind velocity indicate vibrations excitation frequencies and wind velocities at which they occur.
Table 1: Summary of Wind-induced vibrations characteristics [1,2, 7],
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One of the main principals when considering Aeolian vibrations is the Energy Balance Principal (EBP). As wind induces energy (Pw) on a vibrating conductor, it increases the vibration amplitude. The induced wind energy is balanced by the dissipated energy of the conductor (Pc) combined with the damping power (PD) of external damping devices installed in the system. Each portion of these powers is described individually in more details in sections 2.2.1, 2.2.2, and 2.2.3. The Energy Balance equation is shown in Equation (1)[1].
Pw = Pd + Pc (1)
In principle, wind power input into a conductor is related to conductor properties and the environment at which the overhead line system is installed. In other words, wind power input depends on conductor size, vibration frequency, and vibration amplitude[3]. According to[4], wind power input can be expressed by Equation (2) which was developed in 1930 after conducting experiments on different sizes of conductors.
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P^{w}: Wind power input (W/m).
f : Wind excitation frequency (Hz).
d : Conductor diameter (mm).
a : Span length of overhead line system (m).
g(y^{max} /d) : Reduced power function which is a function of vibration amplitude and conductor diameter.
The term g(y^{max} /d) is known as the reduced power function which is a function of vibration amplitude and diameter of conductor. It is obtained from experimental data that were conducted by many researchers[13]as shown in Fig. 1.
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Fig. 1: Resultant curves of reduced power function obtained by different researchers[13].
There is a substantial difference in the results obtained in Fig. 1 above. This is due to the difficulties of the experiment setup to obtain the wind power input. However, the most recent curve is the one that falls in the middle between Carroll (1936) and Diana & Falco (1971)[3]. Researchers have developed a polynomial for their corresponding curves to provide an analytical method of calculating the reduced power[8]. The most recent curve is represented by the polynomial shown in Equation (3)[13].
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Self-damping is a property of many types of conductors used in overhead line systems. It is described by the fact that energy induced by wind onto a conductor is dissipated through the friction between the conductor strands and the property of metallic damping[3]. There are many factors that affect conductor self-damping property of conductors such as tension, operating temperature, and conductor age. In spite of that, self-damping property depends extremely on the level of conductor tension.
The dissipated energy of a conductor can be measured experimentally or alternatively using Equation (4) [1, 14].
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P^{c}: Power dissipated by conductor per unit length (W/m).
a: Span length (m).
d : Conductor diameter (mm).
f : Wind excitation frequency (Hz).
y^{max}: Vibration amplitude limited conductor diameter.
T : Tensile strength of conductor (N).
a, b, c: Regression coefficients obtained by laboratory tests.
K: Proportionality factor ranges between 1.5 and 2.
Damping constant exponents a, b, and c were obtained experimentally by many researchers. Typical values of damping constants were obtained experimentally by number of researchers and their values are presented in Table 2 accordingly.
Table 2: Experimental measurements of dampiing coefficients a, b, and c.[13].
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In some cases, it is true fact that wind power input is greater than dissipated power of a conductor. As a result, installation of vibration dampers is the traditional solution to overcome such situations[1]. They are common due to their capability to reduce the effect of Aeolian vibrations on overhead line conductors. Generally, the dissipated damping power is determined experimentally. Though, Equation (5) can be used to calculate the damping power[1].
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Where, P^{D}: Power dissipated by installed dampers in W.
V^{e}: Damper clamp Velocity.
R[z] : Real component of frequency dependent damper impedance.
An appropriate selection of PD must be achieved in order to overcome vibration problems. The frequency dependent term R[z] defines PD that is determined by experiments in test laboratories. According to[6], laboratory experiments were established to calculate PD that is shown in Equation (5). The frequency dependent quantity of R[z] consists of the value of phase angle between the amount of force induced and the damper clamp velocity. Vibration dampers are elaborated in more details in section 2.4.
Audible noises emerging from telephone wires due to wind have been observed since the 19th century. Since that time, it have been the backbone of the discovery of the so-called Aeolian vibrations[3]. Essentially, Aeolian vibrations are formed once smooth wind streams flow through a conductor forming vortices on its back side. The performance of Aeolian vibrations can be described by different metrics such as vibration frequency, bending strain, and vibration amplitude [1, 12, 13].
It is well known that Aeolian vibrations are generated at low wind velocities and vibrate in the vertical direction. However, Aeolian vibrations occur at frequencies that are defined by the so-called Strouhal relationship[1]. This relationship is a dimensionless quantity that was introduced by Cenek Vincent Strouhal in 1878 based on frequency f (Hz) measurements of audible noises emerging from wires and rods with diameter d (mm) at wind velocities V (m/s). The Strouhal relationship is expressed by Equation (6) as suggested in the study of Henri Bénard in 1926[5].
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According to[5], in 1985 the Strouhal number was related to Reynolds number by Zdravkovich. In fact, Reynolds number is expressed by Equation (7) which is a function of wind velocity V (m/s), diameter d of conductor (mm), and kinematic viscosity of the fluid v (m[2]/s).
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Furthermore,[5]produced a graph as illustrated in Fig. 2 showing Strouhal number as a function of Reynolds number. In Fig. 2, it is apparent that a Strouhal number of 0.185 is an acceptable quantity for most overhead line conductors as suggested by[7]. Actually, the corresponding Reynolds numbers of most common conductors used in overhead lines are within the range of 500 to 20,000 meaning that 0.185 is reasonable value[5].
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Fig. 2: The relationship between Strouhal number and Reynolds number[5].
In the context of Aeolian vibrations, vibration amplitudes caused by wind flowing across overhead line conductors are expressed in two forms which are maximum bending amplitude and maximum antinode vibration amplitude. The difference between these two amplitudes is the position of measurement as seen in Fig. 3. Moreover, vibration amplitude is an important quantity that must be obtained in order to evaluate if a design is safe. The maximum antinode Vibration amplitude is obtained by solving the Energy Balance equation whereas the maximum bending amplitude is obtained experimentally[1].
An alternative way to measure vibration amplitude is the free span angle (^). It defines the intensity of vibration through the wavelength, excitation frequency, and tensile strength of conductor. The free span angle is expressed by Equation (8).
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In Equation (8), ψ is the vibration angle defining the displacement of conductor, f is the vibration frequency in Hz, A is the amplitude of vibrations in mm, λ wavelength of vibration frequency, T conductor horizontal tensile force. In some literature the amplitude of vibrations is denoted as YB instead of A.
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Fig. 3: Parameters influencing amplitude of Aeolian vibrations. Conductorfixed on the left[1].
Vibration dampers are installed to minimize the effect of Aeolian vibrations which may in turn damage the conductor. The level of vibration protection required depends on many factors such as conductor tension, conductor type, wind velocity, and terrain. It is essential to consider these factors when evaluating the requirements of vibration dampers. Aeolian vibrations affect overhead line conductors through a relationship defined by Strouhal (f = 0.185 X V/d)[1]. Nevertheless, there are many commercial vibration dampers that can be used to damp vibrations. However, each type has its own drawbacks. In Fig. 4, Elgra dampers, torsional dampers, and spiral dampers are shown.
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Fig. 4: Vibration dampers including a) Elgra, b) torsional, c) Spiral dampers[9].
The dampers shown in Fig. 4 have many drawbacks compared to the most common Stockbridge damper. Practically, Elgra dampers have two weights that move up and down to damp vibrations. Unfortunately, they produce very loud noises and can damage the conductor strands on the point of contact. On the other hand, torsional dampers are capable of damping vibrations perfectly except that they are restricted to a narrow range of frequencies[9]. Additionally, they are likely to freeze in cold weather conditions. Furthermore, spiral dampers have the ability to damp vibrations effectively but for frequencies ranging from 100 Hz to 300 Hz which means that they are suitable for conductors of small diameters. Studies showed that spiral dampers are suitable for conductors with diameters of about 18 mm and less [1, 9].
During the 1920s, Stockbridge dampers were invented by George H. Stockbridge which were made of concrete blocks placed in a symmetrical manner on the messenger cable as shown in Fig. 5[10].
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Fig. 5: Original design of the Stockbridge damper using concrete blocks (on left) and modern design of stock bridge dampers (on right)[10].
Since the invention of Stockbridge dampers, they have been the most common damping devices used to reduce vibrations in overhead lines since they are tuneable dampers. This is due to the fact that Stockbridge dampers dissipate vibrations when their natural frequency matches with the excitation frequency of the vibrating conductor. The way that these dampers work is that vibrations passes across the clamp of the damper finding their way to the metal weights. After that, the metal weights causes the messenger cable to bend leading to interfriction of strands dissipating the vibration energy [9, 11].
This chapter consists of three main parts that are employed to investigate the damage caused by Aeolian vibrations on overhead lines which forms the methodology of this study. In the first part, a method is proposed to determine overhead line system safe design tension under different terrains. The basic input parameters of this method are conductor properties and overhead line system specifications such as span length. In the second part, Energy Balance Principal is used to develop an assessment of Aeolian vibrations severity based on quantities related to fatigue endurance limits such as bending amplitude, bending strain, and stress. In addition, the effect of vibration dampers on overhead lines to mitigate vibration problems is also considered. In the third part, the interface of the Microsoft EXCEL based assessment tool is illustrated together with available input parameters and expected output results. Moreover, case studies will be applied on different conductors to illustrate the capabilities of the assessment tool and to compare the performance of each conductor type.
The first method, Safe Design Tension, is derived from studying different conductors and finding fatigue test results. After that, recommended safe design tension values are established and used in vibration studies. More details about this method is found in section 3.1. The second method, Energy Balance Principal, is the most common practical method to assess damages caused by stresses on overhead line conductors through the Energy Balance Principal and the so-called Poffenberger and Swart formula which has been developed for round wire conductors. This method is extensively recommended by the Institute of Electrical and Electronic Engineers (IEEE)[8]and implemented by the International Council (CIGRE) on large electric applications and networks. In fact, the Electrical Power Research Institute (EPRI) adopted this approach in overhead lines vibration studies[1]. This method is described in more details in section 3.2 below.
For many years, studies have been carried out to investigate fatigue damages caused by Aeolian vibrations on overhead lines. Essentially, everyday tension (EDT) must be selected optimally to reduce the damage caused by Aeolian vibrations. In fact, recommended EDT values were proposed by[12]as shown in Table 3. Due to the lack of data for AAAC, there is no defined maximum safe design tension with dampers.
Table 3: Recommended safe design tension forACSR and AAAC conductors. The tension is expressed
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Aeolian vibrations are affected by the amount of wind power induced within the conductor. Additionally, wind power is influenced by the turbulence in the wind which in turn affects Aeolian vibrations severity[1]. The turbulence is a result of interaction of mean wind with ground depending on the ground's nature and surrounding environment. In effect, obstructions such as buildings, trees, and bushes shed the vortices leading to a high level of turbulence. Despite the fact that large obstructions cause high turbulence, mountains and hills do not cause turbulence as they shape the flow of wind instead[12]. In fact, roughness of ground can also affect the turbulence of the wind such as desert areas.
A safe design tension is aimed at which fatigue endurance limits are not exceeded. The endurance limits can be used to select a safe design tension besides evaluation of vibrations severity. Basically, there are two parameters used to evaluate the effect of tension on conductor self-damping and span length which are as follows [1, 12]:
Catenary Parameter, T/w (m)
Span Parameter, a x d/m (m[3]/kg)
Where T is tension of conductor in N, w is weight of conductor per unit length in N/m, a is span length in m, d is conductor diameter in mm, and m is conductor mass per unit length in kg/m.
These two parameters are applied to evaluate if the selected conductor needs external dampers for the sake of safe design. However, for a safe design without dampers the catenary parameter is only used to assess overhead lines design which has pre-established limits. These limits were introduced by[12]using the energy balance principal and practical experience taking into account the effect of terrain. Limits of catenary parameter (T/w) are illustrated in Table 4[12].
Table 4: Catenary Parameter limits for protection from vibration damages [12].
The assessment of a particular design is categorized into three regions as shown in Fig. 6. These regions are safe design region without damping, safe design region with damping, and non-safe design region which requires special studies to establish a safe design [12]. Nevertheless, the design is assessed by the catenary parameter only if a safe design is targeted without damping. Conversely, both parameters must be used to assess the design when damping is required. In addition, the non-safe region encounters for designs that require special vibration studies and damping installations such as towers with aeroplane radar systems [9].
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Fig. 6: Recommended entena for safe design tension with and without dampers.
The safe design tension method illustrated in Fig. 6 can be applied to any type of conductors. It correlates tensile strength of the conductor with span length of the design.
An illustration of this method is shown in Fig. 7 using ACSR- Hawk conductor with properties shown in Table 5.
Table 5: Properties of ACSR- HAWK including rated tensile strength, diameter, and mass per unit
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Plotting the conductor on the recommended safe design tension diagram provides an assessment of the conductor selected at a particular Rated Tensile Strength (RTS) and span length. The assessment in Fig. 7 is made at a span length of 350 m. For instance, at 30% RTS the design using Hawk conductor falls within the non-safe design region whereas at other lower RTS levels it is considered safe regardless of the terrain type.
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Fig. 7: ACSR-Hawk recommended safe design tension at span length of 350 m.
In the previous section, conductors are evaluated for maximum safe design tension at a particular span length. However, it is more convenient to find a relationship between design tensions and span length. Such relationship can be achieved by following the proposed steps shown below to plot the tension of a conductor as a function of span length. The steps are accompanied with an example for illustration purposes.
Step 1: Select a conductor and specify the span length.
Select a conductor and a span length to find the catenary parameter (T/w) and span parameter (a X d/m). For example, selecting ACSR- Drake results in the findings shown in Table 6.
Table 6: ACSR- Drake properties and vibrations performance parameters at various RTS.
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Step 2: Plot vibrations performance parameters on the recommended safe design tension diagram.
Plot the conductor vibration performance parameters calculated in the previous step. The abscissa is span parameter whereas the ordinate is the catenary parameter. The obtained result should be similar to the one shown in Fig. 8.
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Fig. 8: Plot of ACSR-Drake conductor using the catenary and span parameters.
Step 3: Evaluating design tension by changing the span length.
Vary the span length at each RTS level until the points denoted on the graph as 5% -32% fall on the desired terrain curve. For example, considering terrain D, span length field in Table 7 is altered until the corresponding point falls at the desired terrain curve as illustrated in Fig. 9.
Table 7: ACSR-Drake properties,catenary and span parameters at various RTS levels.
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Fig. 9: Plot of ACSR-Drake showing the effect of changing span length at each RTS.
Step 4: Produce a plot of tensile strength as a function of span length.
In this step, the corresponding span length for each RTS level is plotted. The data are attained from Table 7 above. Therefore, the plot obtained is similar to the one shown in Fig. 10 below. It shows the span length that is required at the corresponding tension.
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Fig. 10: Plot of RTS in % versus span length for ACSR-Drake. The maximum span length found considering terrain D.
In practice, engineers in industry are concerned to know if a particular conductor requires external damping besides its self-damping capability. The main aim is finding wind power input into the conductor and the power dissipated by conductor to specify the amount of damping required if needed. The Energy Balance Principal is implemented to calculate the wind power input into overhead line conductors and conductors self-damping capabilities to withstand vibrations.
Wind induces energy on a conductor at a frequency that is defined by Strouhal relationship described by Equation (6) previously. Wind power input is calculated analytically using Equation (2). In this study the polynomial that will be used to calculate g(y^{max} /d) is the one shown in Equation (3) previously and recalled below. It is the most recent and falls in the middle between Carroll (1936) and Diana & Falco (1971) as shown in Fig. 1 above.
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The power dissipated by an overhead line conductor can be calculated using Equation (4) mentioned previously and recalled below.
The power dissipated by a vibration damper can be expressed by Equation (9) shown below[14].
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Where, c^{w}: Wave velocity (m/s).
k_{w} : Wave number (rad/s).
h,g: Damping constants.
The wave velocity, wave number, and damping constants can be calculated from Equation (10), Equation (11), Equation (12), Equation (13), and Equation (14).
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Where, l_{1}: Distance from suspension clamp to damper position (m).
α: Angle between force and velocity at damper test (rad).
Z: Damper impedance obtained from damper specifications.
γ: Damping constant.
In some cases, if a damper is placed at a node on the vibrating conductor, the term (h[2]+ g[2]) in Equation (9) results in an amount equals to one which means that PD is zero indicating that external damping is not needed.
Bending amplitude is measured using different types of conductors at laboratories equipped with test benches for vibration studies. Such testing experiments show the relationship between bending amplitude and conductor bending strain. In fact, measurements of bending amplitude are performed on typical experimental fatigue test spans constructed in laboratories that comply with international standards such as IEEE Std. 1386-2006[17]. The principal of fatigue testing is shown below followed by a real commercial test benches.
Typical Standard Aeolian Vibrations Fatigue Test
A typical conductor fatigue test is shown in Fig. 11 below. The conductor is clamped at midspan point at the suspension clamp while adjusting the height of the clamp to maintain the sag of the conductor at different tensions[11]. In addition, gauges (resistance foil strain gauges) are applied on selected strands of the outermost layer of conductor located on the clamp. Test conductor is vibrated by a vibration generator over a series of frequencies and amplitudes.
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Fig. 11: Principal of conductor fatigue test setup based on IEEE Std. 1386-2006.
Conductor wires must be tight during the experiment under real field conditions in order to form severe vibration conditions. The experiment illustrated in Fig. 11 allows performing the following three vibration tests:
- Vibration bending amplitude (Yb ) relationship to bending strain.
- Measurement of bending amplitude at a distance of 89 mm from last point of contact with suspension clamp.
- Measurement of antinode amplitude (ymax) at various frequencies.
Fatigue Test Bench Adopted from 3M Test Procedure
A Vibration fatigue test setup is adopted from 3M for composite conductors as shown in Fig. 12. Vibration bending amplitude is varied at a range from 0.7 to 1.4 mm which is measured at a distance of 89 mm from the last point of contact with the clamp. The vibration test span length is 7 m long equipped with cap-groove suspension clamp[15]. This type of clamps provides a convenient way to study the effect of severe Aeolian vibrations conditions since it is rigid and has sharp edges surrounding the conductor.
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Fig. 12: Fatigue test bench adopted from 3M.
Vibration Generator and Accelerometer
The vibrations generator is positioned at 1.2 m away from the terminal clamp. In addition, the terminal clamps are tightened at torque of 52 Nm to rigidly fix the conductor on the base of the clamp. The bending amplitude is measured at a distance of 89 mm from the mouth of the suspension clamp as shown in Fig. 11. An accelerometer is used to record the amplitudes as recommended by IEEE standards.
Tensioning of Conductor and Vibration Frequencies
The conductor is tensioned at various RTS while the natural frequency is determined at tension by applying suitable frequencies that are close to the resonance frequencies (7-25 Hz) where Aeolian vibrations oscillate at frequencies between 5 and 150 Hz. Frequencies below 3 Hz are not used to avoid any interference with the vibrations generator own resonance which may lead to excessive heating and eventually damage of vibration generator.
Strain Gauges
The strain gauges are glued on 1.5 mm from the mouth clamp forming four vertical and two horizontal axes[10]. Two of the vertical strain gauges are placed on top (traction side when the conductor bends downward) and the other two are placed on bottom of the conductor (compression side). The strains picked on strands through the gauges are expressed in terms of bending stress of the outermost layer. For aluminium alloy wires bending stress is given by the product of measured strain (ε) and young modulus (Eai).
The evaluation of bending stress is important to determine if the conductor chosen for a specific design does not experience fatigue problems. Noramlly, fatigue is assessed using either the maximum bending amplitude (Yb) or the maximum antinode amplitude (ymax). In this section, equations to find bending strain and stress are shown.
Conductor Bending Strain Using Maximum Bending Amplitude
The relationship introduced by Poffenberger and Swart allows the calculation of bending strain (ε) by utilization of bending amplitude. The Poffenberger-Swart relationship is expressed by Equation (15), Equation (16), and Equation (17)[10].
In fact, bending amplitude is obtained from experimental testing of conductors described in section 3.2.3. In addition, a list of Yb values at rated tensions of 15%, 25%, and 35% RTS for ACSR conductors can be found in[5]. For other tension values, bending amplitude can be obtained by interpolation of existing bending amplitude data as the assessment tool designed here provides such interpolation as will be described in section 3.3.
Where, ε: Maximum dynamic bending strain of conductor µm/m).
d: Diammeter of outermost conductor strand (mm).
p: Bending stiffness of conductor (m^{-1} ).
x: Distance between conductor and last point of contact with clamp
(89mm).
Y_{b} : Maximum bending amplitude measured at distance x from the clamp
position (mm).
T : The conductor tension (N).
El^{min}: Sum of rigidities of condcutor individual strands (N'mm[2]).
The parameter E7^{min} is used assuming the strands of the conductor are acting seperately and individually. In other words, it represents the total bending strength of individual strands of a conductor acting seperately. As a result, Equation (17) shows the way that £7min can be obtained[1].
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Where, N^{al}: Number of aluminium strands.
N^{st}: Number of steel strands.
E^{al}: Young modulus of Aluminium strands (MPa).
E^{st}: Young modulus of steel strands (MPa).
d^{al}: Diammeter of one Aluminium strand (mm).
d^{st}: Diammeter of one Steel strand (mm).
Bending Strain Using Maximum Antinode Vibrations Amplitude
An alternative way of finding the bending strain is by utilizing the maximum antinode vibration amplitude instead of the maximum bending amplitude. Equation (18) shows the relationship between maximum antinode vibration amplitude and bending strain.
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Fig. 13: Representation of maximum bending amplitude and maximum antinode vibration amplitude on span[16].
Conductor Bending Stress
The maximum safe vibration amplitudes are usually expressed in terms of bending stress or bending amplitude. In fact, a large number of conductors were analyzed based on Poffenberger-Swart relatioship formula in terms of bending stress[10]. Consequently, the bending stress (σ in MPa) can be calculated once the bending strain is known by the expression shown in Equation (19)[5].
σ = Ε^{al} Χ ε (19)
The bending strain is expressed as bending stress of the outermost layer. In other words, bending stress of aluminium alloy wires is given by the product of measured strain (ε) by young modulus of aluminium (Eai ).
A summary of the calculation sequence that is followed in this study is shown in Fig. 14. The calculations can flow in two different directions depending on the amplitude used. The calculations of bending amplitude are based on experimental data whereas antinode amplitude is based on the energy balance principal. There are two paths that can be followed to calculate bending strain and enventually stress. If bending amplitude is used, the arrows indicated with Yb must be followed. Either amplitudes will lead to the fatigue quantities; bending strain and stress.
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Fig. 14: Procedure of applying proposed fatigue endurance limit method.
In this section, a detailed description is provided of the designed assessment tool showing the interface, input and output parameters. The interface of the assessment tool is presented and calculations integrated in the tool programming are also shown.
One of the main principals used in the assessment tool is the Energy Balance Principal which comprise wind power input, power dissipated by the conductor, and the additional power of vibration dampers. The main input parameters of the tool are extracted from the Energy
Balance Principal. These input parameters include environmental conditions, conductor properties, and the characteristics of the vibration dampers selected. The vibrations amplitude is found by solving the energy balance equation Pw = PD + Pc which is extended as in Equation (20).
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It is noticed that the variables in Equation (20) are provided in the tool as inputs. However, the maximum vibration amplitude (ymax) is the only variable that needs to be calculated. Although there are other numerical methods to solve Equation (20), trial and error computation method is used here. This is an estimation method which may acquire a computational error of ±0.001 mm.
Nevertheless, after finding the maximum antinode amplitude, the bending strain and stress can be calculated using Poffenberger and Swart formula which was described in section 3.2.4. Eventually, tables and plots can be found to establish relationships between maximum vibration amplitude and other quantities related to Aeolian vibrations such as bending stress and tensile strength of conductor. The interface of the assessment tool is shown in Fig. 15.
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Fig. 15: Interface of the designed assessment tool.
The assessment tool consists of two main spreadsheets namely, bending amplitude based tool and antinode amplitude based tool. However, input parameters are found in the first spreadsheet and contains three main sections which are list of conductors, system specifications, and conductor technical specifications as in Fig. 15. If the user select one conductor from the dropdown list, the technical specifications of the conductor will be modified simultaneously based on the pre-defined values in the database of the tool. In fact, if for any other reason the user wishes to change the input data that can be simply done by entering the values desired manually. It must be noted that maximum bending amplitude is calculated automatically whenever a conductor is selected. Actually, the calculation of bending amplitude is done by interpolation of data provided from experiments because they are provided for a certain range of tensions. Therefore, the tool provides calculation of bending amplitude at any tensile strength that the user select. It must be mentioned that computation of bending strain and stress is performed instantly with respect to maximum bending amplitude. In other words, the bending strain and bending stress are computed at the instant that the input parameters are modified.
In Fig. 16, the second spreadsheet is shown which provides the calculation of fatigue endurance limits quantities by utilization of maximum antinode vibration amplitude. Unlike maximum bending amplitude, there are no experimental data available for the maximum antinode vibrations amplitude which means that it must be computed analytically. The method that is used in the tool is based on trial and error. This means that maximum antinode vibration amplitude value is altered until an equilibrium (Pw = Pc) is reached indicating the maximum vibration amplitude. Additionally, the bending strain and stress are computed when maximum antinode vibration amplitude value is achieved.
Furthermore, calculations of damping power is integrated in the tool by knowing the characteristics of the damper that the user wishes to use as well as the position of the damper from the suspension clamp. There are a list of damper already built in in the assessment tool database, however, the user can input the data of damper characteristics manually. Although the assessment tool provides a computation of the damping power, it requires a trial and error method to establish an equilibrium state in the energy balance principal. This means that maximum antinode vibrations amplitude is altered until P_{W} - P_{D} + P_{C}.
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Fig. 16: The assessment tool calculation based on maximum antinode amplitude
In this chapter, the results of applying safe design tension and Energy Balance Principal methods are presented and discussed accordingly. In particular, results and discussions of safe design tension method and Energy Balance Principal can be found in sections 4.1 and 4.2 respectively. In addition, sections 4.3 and 4.4 provide a discussion about the designed EXCEL assessment tool.
The safe design tension method has been applied on different types of conductors such as Aluminium Composite Steel Reinforced (ACSR) and All Aluminium Alloy Composite (AAAC). The reason of that is to investigate the effect of conductor type on achieving a safe design. The analysis has been discussed below in three different scenarios. In the first scenario, maximum safe design tension is determined for ACSR conductors by evaluating them at different tensile strength and various span lengths. In the second scenario, AAAC conductors are selected and evaluated at different tensile strengths while varying the span length. In the third scenario, a comparison between ACSR and AAAC conductors is obtained. Eventually, the tensile strength is plotted as a function of span length.
In this case, the variation of tensile strength of ACSR conductors at different span lengths are investigated. The analysis were conducted on ACSR conductors shown in Table 8 which, in fact, differ in their mechanical properties.
Table 8: Properties of ACSR conductors selected to investigate the safe design tension method.
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The span parameter depends on span length of design and properties of conductor. However, variation of span length leads to change of conductor safe design tension condition. For example, Fig. 17 below shows the resultant condition of Drake conductor at different span lengths as horizontal lines. Each line indicates a different span length at tensile strengths that ranges between 5%-30% RTS. It has been observed that the horizontal line shifts upwards or downwards depending on the span length of the system. As the span length is increased from 150 m to 450 m, the design condition is shifted from safe region to the non-safe region at the same tensile strength of that particular conductor.
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Fig. 17: ACSR-Drake conductor safe tension at span of 150m, 250,350m, and 450m.
Furthermore, it is considered as safe design if the conductor is tensioned at 30% RTS with a span length of 150 m whereas at a span of 450 m it is non-safe. Seeing the type of terrain, the intersection points (1, 2, 3, 4) of the horizontal lines in Fig. 17 indicate the maximum safe tension of the conductor, without dampers, for the corresponding terrain type (A, B, C, D). In addition, intersection points (5, 6, 7, 8) indicate the maximum safe tension of the conductor, with damping, for the same terrain.
The safe design tension method that was applied to ACSR conductors has been applied on other conventional conductors used in overhead line systems with aluminium or aluminium alloys such as All Aluminium Alloy Conductors (AAAC)[9]. It is important to analyse the effect of conductor properties on safe design tension and span length of a design by comparing an ACSR conductor with an equivalent AAAC conductor to observe such effect. Table 9 shows the properties of ACSR (Penguin) compared to AAAC (Alliance) which have similar mechanical properties.
Table 9: Mechanical properties of ACSR (Penguin) and AAAC (Alliance).
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Both conductors are evaluated at RTS of 5% - 25% for a span length of 350 m as shown in Fig. 18. It can be seen that without dampers Penguin has a maximum safe design tension of 16.5% RTS, at terrain D, whereas Alliance maximum safe design is 12.7% RTS. Additionally, with dampers, Penguin and Alliance have maximum safe tension of 25.9% RTS and 19.25% RTS respectively. In general, AAAC conductors can be tensioned less than ACSR conductors under similar circumstances.
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Fig. 18: ACSR (Penguin) and AAAC (Alliance) safe tension assessment at 350 m span length.
The method to plot tension of conductor as a function of span length has been applied by following the proposed steps described in section 3.1.2 previously. It is performed in this analysis on ACSR and AAAC conductors that have the properties shown in Table 10. The selected conductors are different in type but have similar mechanical properties.
Table 10: Properties of ACSR and AAAC conductors used to obtain tensile strength as a function of span length.
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The maximum span length is determined for ACSR conductors at different tensile strengths. Drake was used which has the properties shown in Table 10. After choosing the conductor, the catenary parameter, and span parameter were calculated and results are as shown in Table 11 and Fig. 19. The span length is varied at every RTS value until the tension falls within the safe design region. In this case, the procedure is executed for terrain D and similar analysis was done for the other terrains.
Table 11: ACSR-Drake properties, catenary parameter, span parameter, and span length at corresponding RTS. Results shown are for terrain D.
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Fig. 19: Finding maximum span length at various tension levels for ACSR-Drake.
The points shown in Fig.19 define the maximum safe design tension. They are used to plot the safe tensile strength of the conductor as a function of span length. As a result, Fig. 20 shows the resultant curves for safe design tension in terms of span length for terrains A, B, C, and D.
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Fig. 20: ACSR- Drake tensile strength as a function of maximum span length.
In a similar way, the results for different types of conductors can be achieved through the same proposed procedure as was done for Drake above. In Table 12, resulting span length for ACSR Hawk and Penguin at various terrain types are illustrated. It can be observed that the mechanical properties have a significant impact on the maximum span length. Eventually, a plot of tensile strength as a function of span length was established for each conductor as shown in Fig. 21 and Fig. 22 below.
Table 12: Span length for ACSR Hawk and Penguin at corresponding tensile strength.
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It is observed in Fig. 21, and Fig. 22 that span length depends on conductor properties. It is clear that the rated tensile strength and mass per unit length of the conductor are proportional to the span length. In effect, Drake which has a rated tensile strength of 139.7 kN and mass per unit length of 1.627 kg/m requires longer span length compared with Hawk and Penguin which has lower rated tensile strength and mass per unit length. Besides, the relationship between span length and tensile strength of one conductor is inversely proportional. For instance, Hawk conductor requires a span length of 550 m at 25% RTS and 280 m at 27% RTS. Although the tensile strength is nearly the same, the span length changes significantly. It is essential to mention that this discussion is valid neglecting the effect of wind turbulence.
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Fig. 21: ACSR- Drake and Hawk span length at various tensile strength at terrain C and D.
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Fig. 22: ACSR- Drake and Penguin span length at various tensile strength at terrain C and D.
Considering the effect of terrain, it is clear that span length changes under different environmental surroundings. Therefore, the presence of obstacles entails a longer span length as in terrain D when compared to other terrains. This is due to the effect of air turbulence level in the surrounding of the overhead line structures.
Comparing an ACSR conductor with an AAAC conductor of similar mechanical properties is an effective way to analyse the effect on span length required. Such comparison was done between ACSR- Drake and ACCC- Greely. The results of the comparison is shown in Fig. 23, Fig. 24 and Fig. 25 followed by the discussion.
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Fig. 23: Comparison between ACSR- Drake and AAAC- Greeley span length at different RTS.
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Fig. 24: Comparison between ACSR- Hawk and AAAC- Greeley span length at different RTS.
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Fig. 24: Comparison between ACSR- Penguin and AAAC- Alliance span length at different RTS.
It is observed that there is a significant reduction in the required span length when using AAAC conductor instead of an ACSR of similar properties. In fact, AAAC requires a lower span length when both conductors have same RTS level. Fig. 23, Fig. 24, and Fig. 25 show the comparison results between both types of conductors. It has been noticed that there is a reduction in span length of 20.81% when using AAAC (Greely) instead of ACSR (Drake) at 5%-20% RTS. In a similar manner, replacing ACSR (Hawk) with AAAC (Darien) results in 11.20% reduction in span length at 5%-19% RTS. A summary of span length reduction is illustrated in Table 13.
Table 13: Reduction in span length when using AAAC instead of an equivalent ACSR.
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The reason of reduction in span lengths for AAAC conductors is because ACSR conductors combine the advantage of light weight and good conductivity with high tensile strength and ruggedness of steel as well. In fact, ACSR conductors provide higher tension and longer span lengths than AAAC overhead line conductors. In contrast, AAAC consists of high-strength aluminium alloy and is commonly used for overhead line installations adjacent to ocean coastlines where there can be a problem of corrosion in the steel of an ACSR construction[1].
The type of conductor is important when assessing the severity level of Aeolian vibration on overhead lines. In this section, the discussion is based on the endurance limits for single conductor overhead line structures. The analysis has been performed on single layer ACSR conductors, multi-layer ACSR conductors, and AAAC as discussed below. The calculations are obtained using the assessment tool that was designed on EXCEL as described previously in section 3.3.
The conductors selected to illustrate the vibration fatigue caused by Aeolian vibrations on overhead line conductors are listed in Table 14. The bending strain for each conductor can be calculated using Equation (15) shown previously and knowing the measured value of bending amplitude (Yb) at the corresponding tensile strength. Originally, Yb is obtained using an experiment setup in laboratories. Ultimately, there are two types of ACSR conductors in terms of layering; single-layer ACSR and Multi-layer ACSR.
Table 14: Technical specifications of selected ACSR conductors.
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The bending stress is found for each conductor using the relationship between strain and stress which was introduced in Poffenberger and Swart formula. In fact, the stresses obtained are evaluated based on the recommended permissible bending stress values. The bending stress values are evaluated with reference to stress endurance limits which are 22.5 MPa for single layer ACSR conductors and 8.5 MPa for multi-layer conductors. The stresses for each type of conductors shown on Table 14 are obtained and compared with maximum endurance values. The corresponding bending stresses at tensile strength of 5%, 10%, 15% and 20% RTS are shown in Table 15.
Table 15: Equivalent bending strain and bending stress at 5%, 10%, 15% and 20% RTS for single aluminium layer and multi-aluminium layer ACSR conductors.
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The bending stress data obtained for single layer and multi-layer ACSR conductors shows different stress values when calculated using bending amplitude. However, it seems that there is no significant effect of stranding on bending stress. For instance, Drake, Owl, Falcon, and Bunting have close results at RTS ranging from 5% to 20% as multi-layer ACSR conductors. In other words, the equation used to calculate bending stress using the bending amplitude takes into account the effect of changing installation tension. In addition, most of the trials that have been performed to calculate the bending stress for single layer ACSR conductors resulted in stress values between 19 MPa and 25 MPa for RTS ranging from 5% to 40%.
In practice, experiments showed that single layer ACSR conductors at stress of 25 MPa had a failure in the first strand. For this reason it is recommended to use 22.5 MPa as a reference standard limit for single layer ACSR conductor[5].
In Table 15, calculated values of multi-layer ACSR conductors indicated that the higher the diameter of the conductor, the lower the allowed tensile strength. Referring to Table 15 above, it can be noticed that Falcon exceeds the standard bending stress endurance limit (8.5 MPa) at 15% RTS onwards. This means that it can be tensioned at RTS level less than 15%. In comparison, Drake and Owl can be tensioned at higher RTS values as their stress values do not exceed 8.5 MPa at 15%. In spite of that, Drake does not exceed 8.5 MPa at 20% RTS whereas ACSR- Owl does exceed the limit. Technically, there exists some multi-layer ACSR conductors that does not comply with the stress endurance limits where research is still undertaken to study such situations[5].
In this section, calculation results are discussed which are attained using the assessment tool that was presented earlier in section 3.3. A number of case studies have been evaluated using the assessment tool with and without vibration dampers to observe the effect of Aeolian vibration dampers on each case.
There are a number of case studies that have been evaluated using the designed assessment tool shown above. Precisely, there are two case studies illustrating different situations. The first case study evaluates the maximum vibration amplitude of conductor before and after installation of vibration dampers to observe the influence of that on maximum antinode vibration amplitude. In fact, dampers are installed with a spacing of 1.5 m from the clamp position. The second case study examines the maximum antinode vibration amplitude and fatigue severity for different types of conductors.
The vibration damper used in these case studies is Stockbridge vibration damper. The characteristic curve of the Stockbridge damper used here is shown in Fig. 26 which is adopted from the international standard of IEC 6189.
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Fig. 26: Characteristic curve of Stockbridge damper adopted from international standards of IEC 6189.
Case 1: Assessment of Overhead Line Conductors with and without Vibration Dampers Installed.
The conductor used in this case is ACSR (Cardinal) with properties shown in Table 16.
Table 16: Properties of ACSR- Cardinal Conductor.
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The results of solving the Energy Balance Principal by trial and error to find the maximum vibration amplitude are illustrated in Fig. 27. Cardinal was evaluated at three different RTS levels which are 22%, 26%, and 30%. Results showed that without dampers maximum vibration amplitudes are higher at low wind speeds as shown in Fig. 27. It is evident that the self-damping capability of the conductor reduces as the conductor is tensioned at higher levels. The reason of that is because strands of the outermost layer of the conductor become tighter as the conductor is tensioned reducing the free movement between wire strands and eventually reducing power dissipated by the conductor. On the other hand, installation of vibration dampers reduces the maximum vibration amplitudes significantly. The results are shown in Table 17 below.
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Fig. 27: Comparison of maximum vibration amplitude with and without vibration dampers at different wind speeds.
Table 17: Effect of dampers on maximum antinode amplitude, bending strain, and stress. Results shown for ACSR (Cardinal) at 30% RTS.
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In Fig. 27, it was observed that there is an increase in vibration amplitudes at wind speeds ranging from 30 to 35 m/s which corresponds to frequencies of 20 to 23 Hz. This behaviour is due to the fact that vibration damper used have a higher power dissipation at 20-23 Hz as shown in Fig. 26 of damper characteristic curve. It was found that there is a reduction of 68% in vibration amplitude at frequencies in the least damped region at 30 Hz. The impedance of the damper at 30 Hz is higher than other values, as in Fig. 26, which explains the reason of the trough shown.
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Fig. 28: Maximum bending strain with and without vibration dampers.
In Fig. 28, the maximum bending strain calculated is plotted as a function of frequency. It is found that introducing vibration dampers reduces the bending strain significantly. In other words, the risk of fatigue damage on conductors is reduced on conductors even though there is an increase in bending strain at 20 Hz but it is considered trivial compared to the curve without damping.
Case 2: Vibration Amplitudes and Fatigue Level for Different Types of Overhead Line Conductors
In this case study, the maximum antinode vibration amplitude and fatigue level are determined for different types of conductors. It must be mentioned that the examined conductors are equivalent to each other except their material construction and formations. In other words, composite conductors are compared to all aluminium by considering ACSR, AAAC, and ACCR. Table 18 shows mechanical properties of the selected conductors.
Table 18: Properties of ACSR (Cardinal), ACSR (Drake), AAAC (Greely), ACCR (477 kcmil).
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The results showed that ACCR conductors have better fatigue resistance than an equivalent AAAC and ACSR conductors. It is evident from Fig. 29 below that AAAC conductor is prone to higher levels of vibration amplitudes which means that fatigue damage is more severe. In other words, AAAC conductors are more likely to be exposed to fatigue failures compared to composite conductors. The reason of this is due to the fact that ACCR conductors are more resistance to fatigue compared to AAAC. It is observed that the fatigue level on AAAC is similar to ACSR conductors as seen in Fig. 29 and Fig. 30. As a result, it can be treated as ACSR conductors when evaluating their fatigue damage.
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Fig. 29: Maximum antinode amplitude for ACSR(Cardinal), ACSR (Drake), AAAC (Greely), and ACCR (477 kcmil) at different wind speeds.
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Fig. 30: for ACSR (Cardinal), ACSR (Drake), AAAC (Greely), and ACCR (477 kcmil) at different wind speeds.
This study aims to investigate and evaluate the effect of wind-induced vibrations on overhead line structures. The analyses have been based on Safe Design Tension, Fatigue Endurance Limits and Energy Balance Principal. Eventually, a user-friendly Microsoft EXCEL assessment tool have been designed and used to obtain the results.
The Safe Design Tension method has been applied on ACSR conductors and their equivalent of AAAC conductors for comparison purposes. Conductors were evaluated by the parameters (T/w) and (a x d/m) which lead to plotting the tension of conductor as a function of span length. The results have shown that ACSR conductors require longer span lengths when compared to AAAC conductors. This is due to the fact that ACSR conductors combine the advantages of light weight, good conductivity through aluminium strands, and strength and ruggedness of steel in its construction. In addition, ACSR conductors provide a much better tension to weight ratio which makes it suitable for long spans designs. On the other hand, an equivalent AAAC conductors require less span length, however, they still have high tension to weight ratio. The reduction in span can reach up to 70% at 25% RTS.
Furthermore, the assessment tool developed has a user friendly interface designed using EXCEL. The interface of the tool provides a computation of fatigue level using the built in database or by entering data manually. There are two main methods of calculations which are using bending amplitude or alternatively antinode maximum amplitude. The results have shown that the bending amplitude decreases as the conductor is tensioned more which indeed increases the fatigue level. In fact, single layer ACSR conductors resulted in bending stress in the range of 19-25 MPa whereas multi-layer ACSR conductors had a range of 7-9.5 MPa which comply with the standard fatigue endurance limits which are 22.5 MPa and 8.5 MPa respectively.
With respect to antinode amplitude, the maximum antinode amplitude has been determined by solving the Energy Balance equation. The results have shown that the highest vibration amplitudes are observed at low wind excitation frequencies where the role of vibration dampers is more effective than the self-damping of the conductor. This is not valid for high excitation frequencies where vibration amplitudes are much lower compared to those at low frequency. In fact, the results have also shown that bending strain is highest at low frequencies and vice versa. Additionally, it has been observed that vibration dampers have a significant impact on reduction of vibration amplitudes. However, the characteristics of the installed vibration dampers have a great influence on dissipating the power of vibrations. If the damper is not selected carefully it might have a negative effect on the system.
Case studies have shown that there is a reduction of about 68% in vibration amplitudes when the vibration dampers were installed at distance of 1.5 m. Despite that, in some cases there have been an increase in the vibration amplitude due to improper location of vibration damper. This was investigated in the assessment tool by altering the position of the damper by increasing the distance from the clamp. Besides, ACCR conductors have shown a better performance in resisting fatigue compared to equivalent AAAC and ACSR conductors. In fact, AAAC conductors have similar performance as ACSR conductors which lead to concluding that AAAC conductors can be evaluated the same way as ACSR conductors when fatigue issues are considered. The results has shown that AAAC and ACSR conductors are more susceptible to fatigue damage during their operational time than an equivalent ACCR.
In future, this work can be extended to include the effect of bundled configuration on damping of wind induced vibrations which can be a massive add up to the assessment tool. Additionally, the vibration problems of galloping can also be studied and related to the current work. Moreover, the assessment tool can be upgraded to a more advanced interface by integrating the current EXCEL spreadsheets with Microsoft Visual Basic design packages.
[1]Kiessling F, Nefzger P, Nolasco JF. Overhead Power Lines: Planning, Design, Construction. Germany: Springer-Verlag Berlin and Heidelberg GmbH & Co. K; 2003.
[2]Wareing B. Woodpole Overhead Lines. United Kingdom: Institution of Engineering and Technology; 2009.
[3]Roughan JC. Estimation of conductor vibration amplitudes caused by aeolian vibration. Journal of Wind Engineering and Industrial Aerodynamics. 1983;14(1- 3):279-88.
[4]Meynen S., Verma H., Hagedorn P., Schäfer M. On the numerical simulation of vortex-induced vibrations of oscillating conductors. Journal of Fluids and Structures. 2005;21(1):41-8.
[5]EPRI, “Updating the EPRI Transmission Line Reference Book: Wind-Induced Conductor Motion (The Orange Book)”, 2005 Progress Report, 1010223, CA, (2005).
[6]Schmidt JT, Biedenbach G., Krispin HJ. Laboratory measurement of the power dissipation characteristics of aeolian vibration dampers. IEEE Transactions on Power Delivery. 1997;12(4):1614-21.
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Diplomarbeit, 109 Seiten
Diplomarbeit, 109 Seiten
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