Subsynchronous resonance (SSR) is one of the major obstacles for the wide spread of high degrees (60% and higher) of series capacitor compensation. Recently, a new obstacle, namely Subsynchronous Interaction (SSI) has been added to the list after the Zorillo Gulf wind farm incident in Texas in October 2009. SSI is due to the interaction between large Doubly Fed Induction Generator (DFIG)-based wind farms and series capacitor compensated transmission systems. In integrated power systems incorporating series capacitor compensated transmission lines and high penetration of wind energy conversion systems, especially DFIG-based wind farms, SSR and SSI could occur concurrently as a result of some system contingences. Therefore, mitigating SSR and SSI is an important area of research and development targeting at developing practical and effective countermeasures. This thesis reports the results of digital time-domain simulation studies that are carried out to investigate the potential use of offshore and DFIG-based wind farms for simultaneous mitigation of SSR and SSI. This is achieved through introducing supplemental control signals in the reactive power control loops of the grid side converters of the DFIG wind turbines or the HVDC onshore Modular Multilevel Converter (MMC) connecting the offshore wind farm to the grid. In this context, two supplemental controls designated as Supplemental Controls I and II are examined. Supplemental Control I introduces a signal in the HVDC onshore converter to damp both SSR and SSI oscillations. On the other hand, Supplemental Control II introduces a signal in the HVDC onshore converter for damping SSR oscillations and another signal in the grid side converters of the DFIG wind turbines for damping SSI oscillations. Time-domain simulations are conducted on a benchmark model using the ElectroMagnetic Transients program (EMTP-RV). The results of the investigations have demonstrated that the presented two supplemental controls are very effective in mitigating the SSR and SSI phenomena at different system contingencies and operating conditions.

Subsynchronous Resonance (SSR) phenomena in a thermal-electric power system with series-capacitor-compensated transmission lines may cause damaging torsional oscillations in the shaft of the turbine-generator. This thesis deals with a wide-range multi-mode stabilization of single-machine and multi-machine SSR systems using output feedback excitation control. Chapter 1 summarizes the SSR countermeasures to date. Chapter 2 presents a unified electro-mechanical model for SSR studies, illustrates the torsional interaction between the electrical and mechanical systems, and demonstrates that multi-mass representation of the turbine-generator must be used for SSR studies. For the control design, a reduced order model is desirable. For the model reduction, modal analysis is applied to identify the excitable torsional modes, and a mass-spring equivalencing technique to retain only the unstable modes is developed in Chapter 3. Using the reduced order one: machine models, linear optimal excitation controls are designed in Chapter 4. The controls are further simplified by examining the eigenvalue sensitivity, and the results are tested on the linear and nonlinear full models. In Chapter 5, the stabilization technique is further extended and applied to a two-machine system and a three-4nachine system. The stabilizers still can be designed one machine at a time using a one-machine equivalent for each machine by retaining only the path with the strongest interacting current and the critical electrical resonance frequency as seen by the machine. To coordinate all controllers for the entire system, an iterative process is developed. The controllers thus designed are tested on linear and nonlinear full models. From both eigenvalue analysis and nonlinear dynamic performance tests of the one-machine, two-machine, and three-machine systems, a conclusion is drawn in Chapter 6 that the excitation controls thus designed by the methods developed in this thesis can effectively stabilize single-machine and multi-machine SSR, systems over a wide range of capacitor compensation. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Rotordynamic instability is present in most or all automotive turbochargers. High subsynchronous amplitudes can cause a variety of problems in areas such as mechanical failures, emissions regulations and rotor design. Self-excited vibrations from sources of damping can lock in at lateral natural frequencies causing dangerously high vibration levels. The resulting high-amplitude conical and bending modes can be reduced in order to achieve a more robust system. This research focuses on the relationship between synchronous and subsynchronous amplitude levels. It is theorized that an increase in unbalance could cause a reduction in subsynchronous vibration amplitudes. Through the use of a custom turbocharger, a series of unbalances were applied to both the turbine and compressor wheels and the resulting amplitudes were recorded off a modified compressor nut. The resulting data were reduced and are presented at the end of this paper. / Master of Science

Various computer programs are currently used by electric utilities to determine if potential subsynchronous resonance problems exist which can impact turbine-generators. One of the most popular of these is the frequency scanning program. The representative transmission system input data for these programs are generally based on constant temperature and frequency. However, as conductor temperatures and applied frequencies fluctuate, the resistances also change. This thesis investigates the effects that resistance variations, due to temperature and frequency, have on frequency scanning results. The maximum resistance change (increased and decreased) from the standard value is determined and applied to the transmission lines in four study system cases. The frequency scan output for the modified cases is used to determine if torsional interaction has become more severe. It is found that, under extreme conditions, the net system damping can decrease by over one hundred percent.

Three aspects of Subsynchronous Resonance (SSR) related problems in power systems are addressed in this dissertation which aims at contributing to a better understanding of these problems. Subsynchronous Resonance (SSR) problems in series compensated steam-turbine power systems co-exist with the beneficial effects provided by the series capacitors. Since the early 1930s, numerous researchers have addressed issues relating to these problems. The development of a generalized frequency scan method for analyzing SSR in a Single-Machine Infinite-Bus (SMIB) power system equipped with fixed series capacitor compensation is presented. This method overcomes shortcomings present in the traditional frequency scan technique which is widely used in power system analysis. It has been noticed that there are nonlinear dynamic phenomena in power systems which can not be explained by linear system theory. This includes limited oscillations in a power system when it experiences SSR at a frequency close to one of the system modes. The phenomenon can be explained by Hopf bifurcations. This dissertation presents an analysis for a high dimensional model of a SMIB power system equipped with fixed series capacitor compensation. The results obtained can lead to a more precise understanding of this phenomenon than those available to date which use perturbation methods and highly simplified second-order power system models. Compared with fixed series capacitor compensation in power systems, the newly developed Thyristor Controlled Series Compensation (TCSC) scheme has some well known advantages with regard to flexible power system control. It has been noted that vernier mode TCSC operation can provide for SSR mitigation. In this thesis, such beneficial effect is demonstrated and analyzed for a simplified North-Western American Power System (NWAPS) model, based on EMTP simulations. Issues relating to modelling and simulation of power system and TCSC are addressed. / Graduation date: 1995

Gas foil bearings (GFB) appear to satisfy most requirements for oil-free turbomachinery, i.e. relatively simple in construction, ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal amounts of damping. A test rig for the rotordynamic evaluation of gas foil bearings was constructed. A DC router motor, 25 krpm max speed, drives a 1.02 kg hollow rotor supported on two bump-type foil gas bearings (L = D = 38.10 mm). Measurements of the test rotor dynamic response were conducted for increasing mass imbalance conditions. Typical waterfalls of rotor coast down response from 25 krpm to rest evidence the onset and disappearance of severe subsynchronous motions with whirl frequencies at ~ 50% of rotor speed, roughly coinciding with the (rigid mode) natural frequencies of the rotor-bearing system. The amplitudes of motion, synchronous and subsynchronous, increase (non) linearly with respect to the imbalance displacements. The rotor motions are rather large; yet, the foil bearings, by virtue of their inherent flexibility, prevented the catastrophic failure of the test rotor. Tests at the top shaft speed, 25 krpm, did not excite subsynchronous motions. In the experiments, the subsynchronous motion speed range is well confined to shaft speeds ranging from 22 krpm to 12 krpm. The experimental results show the severity of subsynchronous motions is related to the amount of imbalance in the rotor. Surprisingly enough, external air pressurization on one side of the foil bearings acted to reduce the amplitudes of motion while the rotor crossed its critical speeds. An air-film hovering effect may have enhanced the sliding of the bumps thus increasing the bearings’ damping action. The tests also demonstrate that increasing the gas feed pressure ameliorates the amplitudes of subsynchronous motions due to the axial flow retarding the circumferential flow velocity development. A finite element rotordynamic analysis models the test rotor and uses predicted bearing force coefficients from the static equilibrium GFB load analysis. The rotordynamic analysis predicts critical speeds at ~8 krpm and ~9 krpm, which correlate well with test critical speeds. Predictions of rotordynamic stability are calculated for the test speed range (0 to 25 krpm), showing unstable operation for the rotor/bearing system starting at 12 krpm and higher. Predictions and experimental results show good agreement in terms of critical speed correlation, and moderate displacement amplitude discrepancies for some imbalance conditions. Post-test inspection of the rotor evidenced sustained wear at the locations in contact with the bearings' axial edges. However, the foil bearings are almost in pristine condition; except for top foil coating wear at the bearing edges and along the direction of applied static load.

A new closed-loop frequency-domain model is developed to incorporate the water hammer effect with pump rotordynamics, in order to investigate the sub-synchronous instability problem observed in a field pump. Seal flow-rate perturbations due to eccentricity are calculated from Soulas and San Andres's seal code. A complete transfer function matrix between rotor motion and reaction force due to pressure perturbation is developed in detail. Stability analysis with transfer-function'add-in' modules is conducted in XLTRC2. Seal clearances and the reaction force angle are found to be important in shifting natural frequencies and damping. The sub-synchronous instability observed in field is duplicated successfully with double-clearance seals.

A problem of interest in the power industry is the mitigation of severe torsional oscillations induced in turbine-generator shaft systems due to Subsynchronous Resonance (SSR). SSR occurs when a natural frequency of a series compensated transmission system coincides with the complement of one of the torsional modes of the turbine-generator shaft system. Under such circumstances, the turbine-generator shaft system oscillates at a frequency corresponding to the torsional mode frequency and unless corrective action is taken, the torsional oscillations can grow and may result in shaft damage in a few seconds. <p> This thesis reports the use of a supplementary controller along with the Voltage Source Converter (VSC) HVDC back-to-back active power controller to damp all SSR torsional oscillations. In this context, investigations are conducted on a typical HVAC/DC system incorporating a large turbine-generator and a VSC HVDC back-to-back system. The generator speed deviation is used as the stabilizing signal for the supplementary controller. <p>The results of the investigations conducted in this thesis show that the achieved control design is effective in damping all the shaft torsional torques over a wide range of compensation levels. The results and discussion presented in this thesis should provide valuable information to electric power utilities engaged in planning and operating series capacitor compensated transmission lines and VSC HVDC back-to-back systems.

A problem of interest in the power industry is the mitigation of severe torsional oscillations induced in turbine-generator shaft systems due to Subsynchronous Resonance (SSR). SSR occurs when a natural frequency of a series compensated transmission system coincides with the complement of one of the torsional modes of the turbine-generator shaft system. Under such circumstances, the turbine-generator shaft system oscillates at a frequency corresponding to the torsional mode frequency and unless corrective action is taken, the torsional oscillations can grow and may result in shaft damage in a few seconds. <p> This thesis reports the use of a supplementary controller along with the Voltage Source Converter (VSC) HVDC back-to-back active power controller to damp all SSR torsional oscillations. In this context, investigations are conducted on a typical HVAC/DC system incorporating a large turbine-generator and a VSC HVDC back-to-back system. The generator speed deviation is used as the stabilizing signal for the supplementary controller. <p>The results of the investigations conducted in this thesis show that the achieved control design is effective in damping all the shaft torsional torques over a wide range of compensation levels. The results and discussion presented in this thesis should provide valuable information to electric power utilities engaged in planning and operating series capacitor compensated transmission lines and VSC HVDC back-to-back systems.

A new closed-loop frequency-domain model is developed to incorporate the water hammer effect with pump rotordynamics, in order to investigate the sub-synchronous instability problem observed in a field pump. Seal flow-rate perturbations due to eccentricity are calculated from Soulas and San Andres's seal code. A complete transfer function matrix between rotor motion and reaction force due to pressure perturbation is developed in detail. Stability analysis with transfer-function'add-in' modules is conducted in XLTRC2. Seal clearances and the reaction force angle are found to be important in shifting natural frequencies and damping. The sub-synchronous instability observed in field is duplicated successfully with double-clearance seals.