Tutorials

Tutorials

Dynamic Analysis of Lightly Iced Conductor Galloping in Two Degrees of Freedom

A.S. Richardson, Jr., B.Sc., M.Sc., Sen. Mem. I.E.E.E.

This particular paper was selected for the first Tutorial is because it illustrates the "Root Locus Method," as it is applied to the control of Galloping Conductors. This method has been applied in automatic control theory and in the field of Aeroelasticty for well over thirty years. It is a powerful tool to use in explaining the variation of system parameters, such as wind speed, on the dynamic response of the system. Here, the system is assumed to behave linearly; i.e., a particular input parameter, when varied, produces a proportional response in the variables of the system. Usually, the theory is limited to "small changes of the variables about some initial condition". If the root locus identifies certain ranges of the parameters that become unstable, then that regime of amplitude build-up must be treated by other methods to be introduced in subsequent Tutorials. Such responses are termed "non-linear."

Link to text entitled: Dynamic Analysis of Lightly Iced Conductor Galloping in Two Degrees of Freedom

Predicting Galloping Amplitudes

by A. S. Richardson, Jr., P.E.

These companion papers are based on the Describing Function Method used by control system designers to predict behavior of dynamic systems. The method is based on the assumption that the system is lightly damped and when it vibrates it takes on the response of one mode at a time, which simplifies the analysis. In the case of galloping conductor motion the assumption may be applied to the first mode or second mode. In part I of the paper the analysis assumes zero mechanical damping. The predicted amplitude of gallop is a limit reached by energy balance between wind input and aerodynamic drag. The amplitude of gallop in this case is found from the dynamic angle of attack, which in this case is constant, and depends upon the ice shape. The gallop amplitude increases with wind speed and is inversely proportional to the gallop natural frequency. In part II of the paper the role of mechanical damping is introduced. The dynamic angle of attack is found to build up from zero to the same angle of attack found in Part I for the given ice shape. Again, the gallop amplitude may be calculated as in Part I along this build-up curve. The mechanical damping is what establishes a “critical wind speed” at which galloping is initiated. Above the critical wind speed the dynamic angle of attack increases rapidly, reaching more than 60% of its final value at two times the critical wind speed.

Link to text entitled: Predicting Galloping Amplitudes by A. S. Richardson, Jr., P.E.

Link to text entitled: Predicting Galloping Amplitudes II by A. S. Richardson, Jr., P.E.

Predicting Galloping Fatigue Cycles in Quad Bundles

by Richardson, Lilien & Dubois

The first part of this paper discusses test data obtained in Japan on a quad bundled transmission line during galloping episodes. The measurement of galloping was by recording the dynamic tensions experienced at dead-end structure supports, where time recordings and frequency spectra were obtained. The second part of the paper discusses calculations of dynamic galloping composed of up and down motion of the conductor span and the bundle rotation of the span. Various conditions of structural damping were included in the this study. Observations were made of large up and down motion accompanied by large rotation. The existence of a critical wind speed and a build-up of gallop amplitude is found to agree with earlier work on non-linear build-up of gallop according to wind speed.

Link to text entitled: Predicting Galloping Fatigue Cycles in Quad Bundles

Vibration of Bundled and Single Conductors: A Comparative Case Study

by A. S. Richardson, Jr., P.E.

A series of field tests were undertaken during December 1985 in Littleton, New Hampshire for the New England Power Company to measure the Aeolian vibration of a new triple bundle DC transmission line. The objective was to evaluate the performance of the damping devices installed on the Phase I transmission line. These measurements utilized an accelerometer and an FFT Analyzer, both commercially available devices. These tests provided design data for specifying vibration control devices for the Phase II line. The conclusions reached were: (1) vibration of a single conductor is 4-5 times less than the vibration of the triple bundle having five spacer-dampers of a particular type, and (2) the level of vibration of the bundle having only one spacer-damper at mid-span and one end-point damper per sub-conductor is the same as a single conductor.

Link to text entitled: Vibration of Bundled and Single Conductors: A Comparative Case Study

Vibration Damping Required for Overhead Lines

by A. S. Richardson, Jr., P.E.

This paper describes a method for calculating energy input from the wind by an empirical formula. This results in a curve plotted vs. wind speed for a specific conductor diameter and span length when the conductor vibrates in sine waves at 200mm per second transverse velocity. The methods used to illustrate energy loss in a vibrating conductor were: (A) data obtained from laboratory tests, and (B) calculations based on the hysteretic damping constant for the conductor. These methods include conductor creep as well. At each conductor tension there is only one wind speed at which the two energies balance. If the energy loss in the vibrating conductor exceeds the wind energy over the entire wind speed range, no external dampers are required. If the wind energy input exceeds the energy loss of the conductor over the entire wind speed range then dampers will be required. The process of making this selection was illustrated by studying two conductors, 795 ACSR Drake and 954 ACSR Cardinal.

Link to text entitled: Vibration Damping Required for Overhead Lines

Performance Requirements for Vibration Dampers

by A. S. Richardson, Jr., P.E.

The quantitative prediction of damper requirements in terms of energy or power dissipation was studied as a function of either frequency or wind speed. The two are interchangeable through the Stouhal relation, which also considers the diameter of the conductor. The former companion paper developed the methodology including the wind energy input and the conductor energy loss by internal friction. The loop amplitude is considered to be moving at a maximum transverse velocity of 200mm/sec., where vibration damper requirements are developed for this IEEE limit velocity. The calculation method is introduced by way of four specific examples to illustrate a range of conductor diameters and span lengths. In the case of a single conductor the effect of changing tension on vibration damper requirements is illustrated. Two different types of dampers, a Stockbridge damper and an Impact damper are compared in terms of power loss vs. wind speed. For the triple bundled conductor the wind power input of a 250ft. sub-span is compared to the power loss of the spacer damper over a wind speed range of zero to 16 mph. Field test data on the four conductors were used to validate these calculations. By comparing power required of dampers vs. wind speed (or frequency) for two different conductor diameters and span lengths, it was verified that larger diameters and longer span lengths increased the power required levels and also increased the frequency band-width requirements of the damper.

Link to text entitled: Performance Requirements for Vibration Dampers

A Study of Galloping Conductors on a 230 kV Transmission Line

by A. S. Richardson, Jr., P.E.

This study was motivated by galloping of 20 miles of transmission line running south of Kokomo, Indiana. The actual galloping occurred on February 14, 1990, where field observations confirmed a solid hard glaze surface had formed on the windward side of the conductor. The thickness was estimated at 1/8in. to 1/4in., where temperature was just below freezing, and wind gusts had increased to 18-27mph (8-12 m/s).

The scope of this study includes the theoretical basis for galloping caused by light ice. Each span length was examined to determine the likelihood of galloping, and anti-galloping devices were studied with field observations of two different types of devices made in the U.S and Canada. A ranking of the various remedies was provided according to installed cost, performance, including other factors.

A performance index was identified which compares the anti-galloping concepts based on field observations for each device. This index is a ratio of PASS/FAIL of the device to the PASS/FAIL of the placebo/no device, where the placebo index is simply the number of untreated spans that do not gallop divided by the number of spans that do gallop. In the case of the two devices studied, the actual field data shows a performance index equal to 109 for the first device and a performance index of 1.18 for the second device, indicating the first device is 92 times more effective than the second device in terms of actual field observations. This means the first device is 109 times more effective than its untreated span reference, where as the second device is only 18% more effective than its untreated span reference.

Subsequent to this study, the 230kV transmission line was treated with AR WINDAMPER® anti-galloping devices on one phase, with AR TWISTER™ anti-galloping devices on a second phase, while the remaining phase was left untreated. In an ice storm that occurred the following year, the treated spans were observed to have galloping amplitudes of only 2-3ft. while the untreated span were observed to gallop 10-12ft. (Video of field observations available upon request).

Link to text entitled: A Study of Galloping Conductors on a 230 kV Transmission Line

Guideline for Vibration Control of Tower Guy Cables

by A. S. Richardson, Jr., P.E.

Link to text entitled: Guideline for Vibration Control of Tower Guy Cables, presented by A. S. Richardson, Jr., P.E.

Limiting the Dynamic Loads on Tall Towers

by A. S. Richardson, Jr., P.E.

Link to text entitled: Limiting the Dynamic Loads on Tall Towers, presented by A. S. Richardson, Jr., P.E.

Limits of Vibration Damper Performance

by A. S. Richardson, Jr., P.E.

Link to text entitled: Limits of Vibration Damper Performance, presented by A. S. Richardson, Jr., P.E.

How to Improve Transmission Capacity by AR Devices

by A. S. Richardson, Jr., P.E.