Electric power utilities are faced with the challenge of meeting increasing demand for electric power whilst many factors prevent traditional remedies such as the expansion of transmission networks and the construction of new generating facilities. Due to issues of environment, health and rights-of-way, the construction of new generating plants and transmission lines were either excessively delayed or prevented in many parts of the world in past years. An alternative resides in loading the existing transmission network beyond its present operating region but below its thermal limit, which would ensure no degradation of the system. This alternative approach has been possible with the emergence of Flexible AC Transmission Systems (FACTS) technology. The FACTS concept involves the incorporation of power-electronic controlled devices into AC power transmission systems in order to safely extend the power-transfer capability closer of these systems to their stability limits. One member of the family of FACTS series compensators is the Static Synchronous Series Compensator (SSSC), and this thesis considers the use of the SSSC to carry out closed-loop control of AC power flow in a transmission system. Although the SSSC has the potential to enhance the operation of power systems, the introduction of such a device can cause adverse interactions with other power system equipment or existing network resonances. This thesis examines the interaction between high-level power flow controllers implemented around the SSSC and a particular form of system resonance, namely subsynchronous resonance (SSR) between a generator turbine shaft and the electrical transmission network. The thesis initially presents a review of the background theory on SSR and then presents a review of the theory and operation of two categories of SSSC, namely the reactance-controlled SSSC and the quadrature voltage-controlled SSSC. The two categories of SSSC are known to have different SSR characteristics, and hence this thesis considers the impact on the damping of subsynchronous torsional modes of additional controllers introduced around both categories of SSSC to implement AC power flow control. The thesis presents the development of the mathematical models of a representative study system, which is an adaptation of the IEEE First Benchmark system for the study of SSR to allow it to be used to analyse the effect of closed-loop power flow control on SSR stability. The mathematical models of the study system are benchmarked against proven and accepted dynamic models of the study system. The investigations begin by examining the effect of a reactance-controlled SSSC-based power flow controller on the damping of torsional modes with an initial approach to the design of the control gains of the power flow controller which had been proposed by others. The results show how the nature and extent of the effects on the damping of the electromechanical modes depend on both the mode in which the power flow controller is operated and its controller response times, even for the relatively-slow responding controllers that are obtained using the initial controller design approach. The thesis then examines the impact of a reactance-controlled SSSC-based power flow controller on the damping of torsional modes when an improved approach is used to design the gains of the power flow controller, an approach which allows much faster controller bandwidths to be realised (comparable to those considered by others). The results demonstrate that for both of the modes in which the power flow controller can be operated, there is a change in the nature and extent of the power flow controller’s impact on the damping of some the torsional modes when very fast controller response times are used. Finally, the thesis investigates the impact of a quadrature voltage-controlled SSSC-based power flow controller on the damping of torsional modes in order to compare the influence of the design of both Vsssc-controlled and Xsssc-controlled SSSC-based power flow controllers on torsional mode damping for different power flow controller response times. The results obtained indicate that a Vsssc-controlled SSSC-based power flow controller allows a larger range of SSR stable operating points as compared to a Xsssc-controlled SSSC-based power flow controller. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

Κύριος στόχος της εργασίας αυτής είναι η κατανόηση της διαδικασίας της μοντελοποίησης Συστήματος Ηλεκτρικής Ενέργειας, και πως η διαδικασία αυτή βοηθά στην αντιμετώπιση του φαινομένου της υποσύγχρονης αντίδρασης. Το φαινόμενο αυτό εμφανίζεται όταν ΣΗΕ στο οποίο ενυπάρχει αντιστάθμιση σε σειρά συνδέεται με ατμοστρόβιλο. Αντικείμενο μελέτης της εργασίας αυτής είναι με ποιο τρόπο η εν σειρά αντιστάθμιση συντελεί στην εμφάνιση του φαινομένου. Μελετώνται αναλυτικές υπολογιστικές μέθοδοι διάγνωσης του, και τέλος προτείνονται τρόποι αντιμετώπισης. / The main target of this project is the understanding of modeling an electrical system, and how can this help in the specific case of sub synchronous resonance studies. This phenomenon occurs when a series compensated electrical system is connected with a steam turbine, sometimes resulting in torsional stress. In addition, computational methods for the study of the phenomenon are presented. Last, but not least, countermeasures are suggested.

This thesis investigates the phenomenon of subsynchronous resonance (SSR) in meshed series compensated AC/DC systems in the presence of operational uncertainties. The main contribution of this research is the novel application of risk assessment methods to SSR studies. In terms of network topology, future electric power transmission networks alongside the current power networks are expected to be meshed, and consequently, exposed to relative low risk of subsynchronous resonance. However, power systems are increasingly operated closer to stability limits in order to enhance efficiency and economics of their use. These stressed operating conditions may contribute to the deterioration in the system reliability. Uncertainty associated with the loads will also further diversify in the future due to new type of devices connected to the network whilst the integration of stochastic renewable generation sources will add another layer of uncertainty to system operation. There is a growing necessity to explore the challenges created by the increased uncertainty in generation and loads, and quantify risk to keep a balance between avoiding potentially catastrophic systems failures and mitigating for extremely rare event. This research work introduces risk assessment in subsynchronous resonance studies. Two indices are developed to quantify the severity of dynamic instability and transient torque amplification. Using these indices generators in the network can be ranked based on potential exposure to SSR. Following the development of indices, a methodology is proposed to evaluate the risk of SSR. The developed methodology takes into account the severity of SSR problem and probabilities of different contingencies and different operating conditions of a turbine generator. A robust investigation, into the effect of uncertainties on both aspects of SSR with symmetrical and asymmetrical compensation schemes, is also performed. The results of the analysis reveal that a critically compensated system in normal meshed network configuration may become dynamically unstable with as low as ±5% uncertainty in mechanical parameters. The critical compensation level with asymmetrical compensation in normal network configuration and each contingency becomes higher. It is also shown that the risk level assessed with the developed methodology does not change under the influence of ±5% uncertainties in the mechanical parameters. After establishing, that risk, based approach provides a better picture of all credible scenarios and risk of SSR in compensated power network, a methodology based on risk evaluation of SSR for selecting an optimal combination of TCSCs and fixed series capacitors for compensation of transmission lines is presented. This proposed methodology maximizes the use of fixed capacitors whilst maintaining the risk of SSR within an acceptable level in all credible contingencies and operating conditions.

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Electricity systems are very complex systems and are composed of numerous transmission lines, generators and loads. The generating stations are generally far away from load centres and that may cause transmission line congestion and overloading. Series capacitive compensation is the most economical way to increase transmission capacity and improve transient stability of transmission grids. However, one of the impeding factors for the widespread use of series capacitive compensation is the potential risk of Subsynchronous Resonance (SSR). Subsynchronous Resonance is a phenomenon in which electrical power is exchanged with the generator shaft system in an increasing manner which may result in damage to the turbine generator shaft system. Therefore, mitigating SSR continues to be a subject of research and development aiming at developing effective SSR countermeasures.<p>This research work presents new methods of alleviating the SSR problem using a Static Synchronous Series Compensator (SSSC) and a Static Synchronous Compensator (STATCOM). These methods are based on using the SSSC and STATCOM to inject unbalanced series quadrature voltages and unbalanced shunt reactive currents in transmission line just after clearing faults. When the subsynchronous oscillations drive unsymmetrical phase currents, the developed electromagnetic torque will be lower than the condition when the three-phase currents are symmetrical. The unsymmetrical currents result in a lower coupling strength between the mechanical and the electrical system at asynchronous oscillations. Therefore, the energy exchange between the electrical and the mechanical systems at subsynchronous oscillations will be suppressed, thus, avoiding the build-up of torsional stresses on the generator shaft systems under subsynchronous resonance condition. The validity of proposed methods are demonstrated by time simulation results using the electromagnetic transient program EMTP-RV.

Electricity systems are very complex systems and are composed of numerous transmission lines, generators and loads. The generating stations are generally far away from load centres and that may cause transmission line congestion and overloading. Series capacitive compensation is the most economical way to increase transmission capacity and improve transient stability of transmission grids. However, one of the impeding factors for the widespread use of series capacitive compensation is the potential risk of Subsynchronous Resonance (SSR). Subsynchronous Resonance is a phenomenon in which electrical power is exchanged with the generator shaft system in an increasing manner which may result in damage to the turbine generator shaft system. Therefore, mitigating SSR continues to be a subject of research and development aiming at developing effective SSR countermeasures.<p>This research work presents new methods of alleviating the SSR problem using a Static Synchronous Series Compensator (SSSC) and a Static Synchronous Compensator (STATCOM). These methods are based on using the SSSC and STATCOM to inject unbalanced series quadrature voltages and unbalanced shunt reactive currents in transmission line just after clearing faults. When the subsynchronous oscillations drive unsymmetrical phase currents, the developed electromagnetic torque will be lower than the condition when the three-phase currents are symmetrical. The unsymmetrical currents result in a lower coupling strength between the mechanical and the electrical system at asynchronous oscillations. Therefore, the energy exchange between the electrical and the mechanical systems at subsynchronous oscillations will be suppressed, thus, avoiding the build-up of torsional stresses on the generator shaft systems under subsynchronous resonance condition. The validity of proposed methods are demonstrated by time simulation results using the electromagnetic transient program EMTP-RV.

Subsynchronous Resonance (SSR) is a condition which occurs when turbogenerators are connected to series capacitively compensated transmission systems and it can cause large scale damage to the turbogenerators. The accuracy of predictions of this phenomenon are limited by the accuracy of the mathematical models used for the various system elements. The modal method of modelling a turbogenerator shaft, in which parameters are associated with each natural torsional mode of the shaft, is investigated in detail and the sensitivity of SSR predictions (both small signal and transient) to uncertainties in the mode parameters is evaluated. The modal model is then used to obtain reduced order shaft models and the accuracy of these reduced order modal models in SSR predictions is ascertained. The determination of mode parameters from generator transient response waveforms is investigated. A continuing problem in this field is the separation of damping values obtained from measurements on a synchronized generator, into their mechanical and electrical components. A method is proposed in this thesis which uses eigenvalue scanning techniques together with FFT analysis to achieve this separation. The SSR stability of, and the torsional interaction between two adjacent generators at a power station is studied. The analysis covers identical generators, nominally identical generators with small differences between their mode parameters and different generators with a coincident torsional mode. In addition, the torsional interaction between generators at different power stations which are remote from each other is investigated. This entire analysis is greatly assisted by modelling the turbogenerator shafts in modal form. Finally the damping of SSR oscillations in two non-identical adjacent turbogenerators with a single controlled shunt reactor, which uses the sum of the generator speed signals as an input to the controller, is investigated. / Thesis (Ph.D.)-University of Natal, Durban, 1987.

A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical compensation values, while in the CHOLLA#4 system, we show that there is only one Hopf bifurcation. The results show that as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability via a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. When a damper winding is placed either along the q-axis, or d-axis, or both axes of the BOARDMAN system and the machine saturation is considered in the CHOLLA#4 system, the study shows that, there is only one Hopf bifurcation and it occurs at a much lower level of compensation, indicating that the damper windings and the machine saturation destabilize the system by inducing subsynchronous resonance. Finally, we investigate the effect of linear and nonlinear controllers on mitigating subsynchronous resonance in the CHOLLA#4 system . The study shows that the linear controller increases the compensation level at which subsynchronous resonance occurs and the nonlinear controller does not affect the location and type of the Hopf bifurcation, but it reduces the amplitude of the limit cycle born as a result of the Hopf bifurcation. / Ph. D.

Subsynchronous oscillations (SSO) were an issue that occurred in the past with conventional generators and were studied extensively throughout the years. However, with the rise of inverter-based resources, a new form of SSO emerged under the name subsynchronous control interaction (SSCI). More specifically, a resonance case occurs between Type-3 wind turbines and series compensation that can damage equipment within the wind farm and disrupt power generation. This work explores the types of SSCI and the various analysis methods as well as mitigation of SSCI. The work expands on the concept of frequency scan to be able to use it in an on-line setting with its output data used to mitigate SSCI through the modification of wind turbine parameters. Multiple frequency scans are conducted using PSCAD/EMTDC software to build a lookup table and harmonic injection is used in a parallel configuration to obtain the impedance of the system. Once the impedance of the system is obtained then the value of the parameters is adjusted using the look-up table. Harmonic injection is optimized through phase shifts to ensure minimal disruption of the steady-state operating point and is conducted using Python programming language with PSCAD Automation Library. Simulation results demonstrate the effectiveness of this approach by ensuring oscillations do not grow exponentially in comparison to the regular operation of the wind farm. / Master of Science / Due to climate change concern and the depletion of fossil fuel resources, electrical power generation is shifting towards renewables such as solar and wind energy. Wind energy can be obtained using wind turbines that transform wind energy into electrical energy, these wind turbines come in four different types. Type-3 wind turbines are the most commonly used in the industry which use a special configuration of the classical induction generator. These wind turbines are typically installed in a distant location which makes it more difficult to transfer energy from its location to populated areas, hence, series capacitors can be used to increase the amount of transferred energy. However, these series capacitors can create a phenomenon called subsynchronous control interaction (SSCI) with Type-3 wind turbines. In this phenomenon, energy is exchanged back and forth between the series capacitors and the wind turbines causing the current to grow exponentially which leads to interruptions in service and damage to major equipments within the wind turbine. This work explores SSCI, the tools to study it, and the currently available mitigation methods. It also presents a method to identify the cases where SSCI can happen and mitigates it using adjustable parameters.

Subsynchronous vibrations such as those caused by rotor instability represent one of the most harrowing scenarios of rotor vibration. They are related to a great diversity of destabilizing forces and some of them are not well understood yet. Therefore, special attention must be paid to this type of vibration. Active Magnetic Bearings (AMBs) monitor the position of the shaft and change the dynamics of the system accordingly to keep the rotor in a desired position, offering the possibility of being used as dampers for vibration control. In the present work, a single-disk and a three-disk rotor were built to evaluate the effectiveness of an Active Magnetic Damper (AMD) in damping subsynchronous vibrations. An AMD was used to inject a signal simulating a subsynchronous vibration in the rotor, as another AMD was used to perform active control. Two locations of the AMD were considered for each rotor. For the single-disk rotor, experimental data was taken with the AMD located at three-quarters of the rotor-span and with the AMD located at midspan. For the three-disk rotor, experimental data was taken with the AMD located at a quarter-span and with the AMD at two-thirds of the rotor span. An undamped critical speed and a forced response analysis were performed on the rotors in order to predict the dynamic characteristics of the rotors with and without the AMD. It was demonstrated that an AMD is effective in damping subsynchronous vibrations. The addition of an AMD introduces damping and stiffness to the rotor-bearing system resulting in a change in the synchronous response and a consequent increase of the amplitude of vibrations at synchronous frequencies. This effect must be carefully considered when designing a system with an AMD. / Master of Science