Shaft Oscillations Research Articles

Variable-Speed Wind Turbines with Doubly-Fed Induction Generators Part IV: Uninterrupted Operation Features at Grid Faults with Converter Control Coordination

A model of variable-speed wind turbines equipped with doubly-fed induction generators (DFIG) and controlled by partial-load frequency converters described in [1,2] is applied in power stability investigations. A technical feature of uninterrupted operation at grid disturbances of large wind farms with such variable-speed wind turbines is suggested and discussed. This technical feature is based on fast re-start of the rotor converter, which blocks at grid faults. The main reactive power control is organised by the rotor converter [3]. The new part is that reactive power is controlled by the grid-side converter when the rotor converter blocks. Possible discrepancies between the results reached with the detailed representation of the frequency converter and the representation where only the rotor converter is regarded are notified and explained. The converter representation details influence on the machine current transients modelled at grid disturbances and also on damping characteristics of torsional shaft oscillations.

Excitation of torsional oscillations in generator shaft lines by plasma feedback control

The ASDEX Upgrade (AUG) tokamak requires an electrical power up to a few hundred MVA for a time period of 10–20 s. The power and energy is provided by three separate networks based on flywheel generators. In 1999, during a routine check performed on generator EZ3, it was discovered that coupling bolts of the flywheel generator shaft were deformed. Given that the active load of the generator (∼100 MW) in service is well below the design value of the shaft (∼800 MW), the damages may only be explained by a torsional resonance of the shaft line, itself excited by active power transients from the converter loads. A value of 23.6 Hz was calculated for the first eigen-frequency of the shaft line. Frequencies between 10 and 30 Hz have been identified in the spectrum of the load curves. Since torsional shaft oscillations are characterised by very low damping, torsional resonance can become dangerous even for over-dimensioned generator shafts. Therefore, a novel ‘torque’ measurement system was installed. The paper presents results from calculations and measurements showing that devices capable to measure the stress in the shaft line are essential for generator protection in feedback controlled fusion experiments.

Blind sensing

Describes a precise and accurate noncontact measuring device based on eddy currents. It is based on the principle that when an oscillator induces an eddy current in an electrically conductive target, the circuit loses energy. It works at high speeds, is nonoptical and is impervious to variations in temperature and other ambient conditions (oil, dirt, water, electromagnetic fields etc.). Electrical runout (inhomogeneity) disturbs the propagation of the eddy currents and affects the transducer output, which in turn results in noise and degraded resolution, but this effect can be reduced by an appropriate design. The sensors are used for various measurements, including distance, thickness, deflection, position, eccentricity, shaft run-out, imbalance, lubrication gap, vibration, deformation, valve stroke, compression gap, wear, shaft oscillation, shaft elongation and centring. The sensor has frequency output distance measurement; thickness measurement; deflection measurement; position measurement; eccentricity measurement; shaft run-out measurement; imbalance measurement; lubrication gap measurement; vibration measurement; deformation measurement; valve stroke measurement; compression gap measurement; wear measurement; shaft oscillation measurement; shaft elongation measurement; centring measurement;.

The damping effect of the flywheel dampers installed at different shaft couplings on torsional oscillations

This paper eamines the damping effect of flywheel dampers installed at different shaft couplings on torsional oscillations on the 951 MW turbine-generator shafts due to network faults. A studied system is described and torsional fatigue on the turbine shafts following various electrical system disturbances is analyzed and evaluated. Moreover, the influence of the safety factor selected and set at the design stage to the shaft life expenditure due to fatigue damage is also presented. Useful additional insight into their modes of operation is obtained from the fast Fourier transform of the transient response results. All computer simulations thus show that the proposed dampers are effective in suppressing the torsional oscillations on the shafts. In this paper, time-domain torque evaluation is also combined with the fast Fourier transform method to derive a selection procedure for obtaining suitable flywheel dampers to depress the amplitude of these critical shaft oscillations to acceptable levels.

Effect of non-linearities in elastomeric material dampers on torsional vibration control

The effect of non-linearities in clastomeric-material dampers used to quiet torsional oscillations of internal-combustion engines shafts is investigated. The method of multiple scales is used to solve the equations for the case of primary resonance. Steady-state solutions are obtained and their stability examined. A relationship that relates the elastomer properdes (for stable solutions) and other system parameters is found. The steady-state response shows a softening behavior of the system although the actual material non-linearity is of the hardening type.

A large-scale mechanical filter—the application of turbogenerator flywheel coupling

The paper suggests the use of a detailed equivalent mechanical lumped system model to simulate the perturbation of shaft oscillations and blade vibrations. The relationship between the vibration frequencies and amplitudes can be expressed with more accuracy by the derived equivalent electrical circuits. The major parameters for a mechanical model of flywheel coupling are inertia and the stiffness coefficient. These parameters are equivalent to inductance and capacitance in electrical circuits. If a suitably designed flywheel coupling is produced and the parameters are chosen carefully it may be possible to reduce the major torsional torques caused by power system disturbances. Well-designed flywheel coupling can also depress the vibration amplitudes significantly. A realistic example simulating the transient behavior of an actual operating generation unit is presented to support the validity of the method.

On the vibration spectrum of high‐speed spur gear boxes

An analytical model is presented to simulate the effect of tooth backlash and ball‐bearing radial clearance on the vibration spectrum of high‐speed spur gear boxes. Included in this model are elasticity in bending and torsion of the shafts, friction between meshing teeth, interaction between gear box casing and internals, and time‐varying tooth backlash, mesh stiffness (stiffness is calculated based on the strain energies of the tooth, which is treated as a cantilever beam of involute shape), and Hertzian mesh damping. The bearing loads are calculated with consideration of shaft oscillations and speed, bearing radial clearance, ball centrifugal force, and bearing outer ring oscillations. To demonstrate the model, a single stage gear box is analyzed, and equations of motion are numerically integrated to obtain system response in the time domain. This response is transformed into the frequency domain using a fast Fourier transform (FFT) algorithm and samples of the results are shown for different values of backlash and bearing clearance.

Turbine-generator shaft oscillation monitoring with PCs

The use of a PC-based system to record the speed of the shaft on five of Utah Power & Light's largest steam turbine-generator units is described. This quantity will be fed to special protective relays. The relays are designed to detect mechanical resonance with natural frequencies below 60 Hz, called subsynchronous resonance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stabilizing SSR oscillations with a shunt reactor controller for uncertain levels of series compensation

The authors demonstrate how frequency-domain techniques based on I. Horowitz et al.'s (1986) quantitative feedback theory can be applied to the design of fixed-parameter controllers in power systems where the plant parameters have large uncertainties. They present the design of a controller for a shunt reactor to eliminate torsional shaft oscillations in a turbogenerator susceptible to subsynchronous resonance (SSR). The considered parameter uncertainty is the series capacitor compensation level, which has been assumed to vary between 12% and 76%. Simulated transients results of the uncontrolled/controlled system are depicted.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Damping of Torsional Shaft Oscillations in Two Interacting Neighbouring Turbogenerators

This paper investigates the damping of torsional oscillations in a power station with two identical 1072 MVA generating units connected to an infinite bus through a series capacitor compensated transmission line. It considers a single common controlled shunt reactor to damp torsional oscillations of both turbogenerator shafts. To overcome the mathematical difficulties arising from having to use a high order model of the power system, together with powerful techniques for controller design, the order of the system model is firstly reduced by considering an 'equivalent' single generator and then applying a known model reduction method to this 'equivalent' generator's model. The transient response of the complete unreduced system is then evaluated when the two generator units are equipped with this single common controlled shunt reactor (1SR) and compared against the case when each generator unit has its own separate controlled shunt reactor (2SR). The results show that torsional oscillations in the turbogenerator shafts of such a multimachine system can be damped by the action of a single common controlled shunt reactor; nevertheless, a system where each turbogenerator is equipped with its own individual shunt reactor shows better overall system behavior.

Damping of Torsional Shaft Oscillations in Two Interacting Neighboring Turbogenerators

Damping of Torsional Shaft Oscillations in Two Interacting Neighboring Turbogenerators

How HVDC schemes can excite torsional oscillations in turbo-alternator shafts

Recent experience has shown that a variable-frequency drive of modest size produced torsional oscillations in a turbo-alternator shaft which were of such a level as to put the shaft at risk. The paper therefore describes a method by which such subsynchronous frequencies can be identified and calculated. The method used considers the convertor as a type of modulator capable of producing sideband frequencies, some of which are at subsynchronous frequencies. The simple mathematical model developed is used to show that HVDC schemes are also capable of exciting steady-state subsynchronous oscillations in turbo-alternator shafts which are electrically close to the convertor station. Different types of scheme are examined, and it is shown that asynchronous links of both the frequency changer and system interconnector type are potential sources of steady-state shaft oscillations.

Laser Tools for Diesel Engine Diagnosis

Two portable laser instruments are described which allow the engineer to simply ‘stand and point’ laser beams at a target surface in order to obtain a measurement of time-resolved vibration velocity. The first supplements the accelerometer and measures normal surface velocity but offers the advantage of non-contact measurement. Its use is demonstrated in detecting reduced nozzle pressures in fuel injectors. The second instrument is a laser torsional vibrometer which measures torsional oscillations of rotating machinery parts and in particular crankshaft oscillation. Comparisons are made with the more standard technique which utilizes a slotted disc. The new instrument provides advantages of non-contact measurement, insensitivity to shaft radial motion and the ability to measure oscillations of shafts of arbitrary cross-section.

A New Real-Time Simulator for Power System Studies

A new real-time simulator for power system studies is presented, including static VAR compensators, machines, HVDC stations, filters, lines, torsional shaft oscillation model. It is suitable for the study of the dynamic behaviour of complex systems and investigation of control problems also with real control apparatus. Mathematical models, the simulation principle, the hardware realization and experience with the simulator are described.

A New Real Time Simulatro for Power System Studies

A new real-time simulator for power system studies is presented, including static VAR compensators, machines, HVDC stations, filters, lines, torsional shaft oscillation model. It is suitable for the study of the dynamic behaviour of complex systems and investigation of control problems also with real control apparatus. Mathematical models, the simulation principle, the hardware realization and experience with the simulator are described.

Dynamic Stabilizer On-Line Experience

A brief description is presented of the Westinghouse Torsional Dynamic Stabilizer, which was developed primarily as a countermeasure to "torsional interaction" subsynchronous resonance. Two such systems were installed and commissioned at the San Juan Generating Station, Waterflow, New Mexico in July, 1980. This paper describes the maintenance procedures and operating experience to date of these two units. The only known instance of operation at the high level bias point of the Stabilizer appears to indicate that the unit helped to dampen a turbine-generator shaft oscillation transient.

Damping of subsynchronous resonance in series-compensated systems by excitation control

Fast-response excitation systems are capable of influencing turbogenerator performance at subsynchronous resonance frequencies, and this paper shows how suitable excitation control can improve the damping of generator subsynchronous shaft oscillations. A multivariate frequency response method is used to investigate control capabilities and to identify the most beneficial control signals and stabilization requirements. An excitation control scheme is designed, employing a differential shaft speed signal, which stabilizes an initially unstable resonance condition and provides rapid damping of subsynchronous shaft oscillations.

On the Subharmonic Oscillations of Unsymmetrical Shafts

When a rotating shaft is supported by single-row deep groove ball bearings, the restoring force of the shaft has nonlinear spring characteristics. In the case of an unsymmetrical shaft, the subharmonic oscillation of order 1/2 of the forward precession shows unique features owing to the influence of some of the nonlinear components which have no effects on such an oscillation of a symmetrical shaft. By changing the assembly of the experimental apparatus and the degree of unbalance, we could obtain three kinds of resonance curves concerning this subharmonic oscillation. They are the following: a stable resonance curve of the hard spring type, an unstable region where unstable vibration with frequency 1/2·ω(ω: angular velocity of the shaft) appears, and the case where no subharmonic oscillation appears. In the analysis of such an unsymmetrical shaft system with nonlinear characteristics, the method utilizing normal coordinates cannot be used. We can explain such phenomena theoretically by the method proposed in this paper.

On the Subharmonic Oscillations of Unsymmetrical Shafts

On the Subharmonic Oscillations of Unsymmetrical Shafts

Paper 11: Anti-Vibration Journal Bearings

An experimental rig has been constructed to establish the vibration characteristics of plain, dammed groove, and tilting pad bearings having a variety of clearances. The rig is perhaps unusual in not being a small piece of laboratory equipment, but consisting of a naval anti-submarine frigate turbo rotor (15 000 rev/min) running in two journal bearings each supported by an isotropic cantilever system of variable stiffness. Two pairs of induction probes mounted close to the test bearing monitored the shaft movement and provided an oscilloscope display of the movement of the bearing centre. Detailed information about the shaft oscillations was obtained from a wave analyser and vibration meter. The static rig natural frequencies with various bearing housing support stiffnesses were primarily determined. From preliminary running tests a fairly stiff bearing housing support, which gave a strong vibration of approxi-mately half rotational speed, was chosen for all subsequent work. With the rotor wheel balanced the tilting pad bearing tested was found to be free from serious vibration. The dammed groove type of bearing tested was also stable at low speeds but was not capable of stable operation at 15 000 rev/min and above. The plain bearing tested produced serious vibration above 9000 rev/min. The frequencies and amplitudes of vibration which occurred in different bearings with a deliberate rotor unbalance were also measured. Increase of the clearance lowered the onset speed of serious vibration. The locus of the mean position of the journal centre of the tilting pad bearing was almost a vertical straight line whereas all the other bearings showed the usual approximate semi-circle. Instantaneous oil film pressures up to 900 lb/in2 were measured using a pressure transducer in the bearing. As the design particulars of the bearings tested differed somewhat the results were not strictly comparable but nevertheless an approximate design rule has been suggested. Practical data provided about the vibration behaviour of the different journal bearing designs can be used by the many theoretical investigators in this field. This is important in view of the lack of practical attested results to substantiate or otherwise the many theories advanced.