In a large and dense power network, the transmission lines, the generators and the loads are considered to be continuous functions of space. The continuum technique provides a macro-scale analytical tool to gain an insight into the mechanisms by which the disturbances initiated by faults and other random events propagate in the continuum. This dissertation presents one-dimensional and two-dimensional discrete models to illustrate the propagation of electromechanical waves in a continuum system. The more realistic simulations of the non-uniform distribution of generators and boundary conditions are also studied. Numerical simulations, based on the swing equation, demonstrate electromechanical wave propagation with some interesting properties. The coefficients of reflection, reflection-free termination, and velocity of propagation are investigated from the numerical results. Discussions related to the effects of electromechanical wave propagation on protection systems are given. In addition, the simulation results are compared with field data collected by phasor measurement units, and show that the continuum technique provides a valuable tool in reproducing electromechanical transients on modern power systems. Discussions of new protection and control functions are included. A clear understanding of these and related phenomena will lead to innovative and effective countermeasures against unwanted trips by the protection systems, which can lead to system blackouts. / Ph. D.

The behavior of large and tightly interconnected power systems resembles, in certain circumstances, the behavior of a continuously distributed system. This resemblance motivated the derivation of continuum models, which were used to explain and predict disturbance propagation, un-damped power oscillations, and the stability of power systems. In this dissertation, we propose a one-dimensional continuum representation suitable for meshed power systems. Previous continuous representations of meshed power systems used two-dimensional spatial domains. Thus our approach has the potential to provide better resolution for comparable computational burden. It is important to note that, the computational burden required to obtain solutions for PDEs involved in the continuum representation varies notably with the solver implementation. The contributions of this dissertation are: a) Reviewing a previous continuum model and providing a detailed derivation for the one-dimensional version of it. b) Providing and describing in detail a parameter distribution technique adequate for the continuum approach. c) Identifying and documenting limitations on the continuum model voltage calculation. e) Providing a procedure to simulate the behavior of meshed power systems using the one dimensional continuum model. And f) Identifying and applying a numerical PDE solver for the continuum approach. / Ph. D.

When a power system is subjected to a disturbance, the power flow changes, leading to deviations in the synchronous generator rotor angles. The rotor angle deviations propagate as electromechanical waves (EMWs) throughout the power system. These waves became observable since the development of synchrophasor measurement instruments. The speed of EMW propagation is hundreds of miles per second, much less than the electromagnetic wave propagation speed, which is the speed of light. Recently, with the development of renewable energy resources and a growth in using HVDC and FACTS devices, these waves are propagating slower, and their impacts are more considerable and complicated. The protection system needs a control system that can take suitable action based on local measurements to overcome the results of power system faults. Therefore, the dynamic behavior of power systems should be properly observed. The EMW propagation in the literature was studied using assumptions such as constant voltage throughout the entire power system and zero resistances and equal series reactances for the transmission lines. Although these assumptions help simplify the power system study model, the model cannot capture the entire power system's dynamic behaviors, since these assumptions are unrealistic. This research will develop an accurate model for EMW propagation when the system is facing a disturbance using a continuum model. The model includes a novel inertia distribution. It also investigates the impacts of voltage changes in the power system on EMW behaviors and when these impacts are negligible. Furthermore, the impacts of the internal reactances of synchronous generators and the resistances of transmission lines on EMW propagation are explored. / Doctor of Philosophy / Power systems, essential for electricity supply, undergo disturbances causing changes in power flow and synchronous generator behavior. These disturbances create electromechanical waves (EMWs) that influence system dynamics. Recent advancements, including renewable energy integration and new technologies, alter EMW behavior, posing challenges for control and protection systems. Existing studies simplify models, limiting their accuracy. This research aims to develop a realistic EMW propagation model considering factors like novel inertia distribution, voltage changes, and internal generator properties. This work addresses the evolving power landscape, enhancing our understanding of power system dynamics for improved control and reliability.

A global view of power system's frequency opens up a new window to the "world" of large system's dynamics. With the aid of global positioning system (GPS), measurements from different locations can be time-synchronized; therefore, a system-wide observation and analysis would be possible. As part of the U.S. nation-wide power frequency monitoring network project (FNET), the first part of the study focuses on utilizing system simulation as a tool to assess the frequency measurement accuracy needed to observe frequency oscillations from events such as remote generation drops in three U.S. power systems. Electromechanical wave propagation phenomena during system disturbances, such as generation trip, load rejection and line opening, have been observed and discussed. Further uniform system models are developed to investigate the detailed behaviors of wave propagation. Visualization tool is developed to help to view frequency behavior simulations. Frequency replay from simulation data provides some insights of how these frequency electromechanical waves propagate when major events occur. The speeds of electromechanical wave propagation in different areas of the U.S. systems, as well as the uniform models were estimated and their characteristics were discussed. Theoretical derivation between the generator's mechanical powers and bus frequencies is provided and the delayed frequency response is illustrated. Field-measured frequency data from FNET are also examined. Outlier removal and wavelet-based denoising signal processing techniques are applied to filter out spikes and noises from measured frequency data. System's frequency statistics of three major U.S. power grids are investigated. Comparison between the data from phasor measurement unit (PMU) at a high voltage substation and from FNET taken from 110 V outlets at distribution level illustrates the close tracking between the two. Several generator trip events in the Eastern Interconnection System and the Western Electricity Coordinating Council system are recorded and the frequency patterns are analyzed. Our trigger program can detect noticeable frequency drop or rise and sample results are shown in a 13 month period. In addition to transient states' observation, the quasi-steady-state, such as oscillations, can also be observed by FNET. Several potential applications of FNET in the areas of monitoring & analysis, system control, model validation, and others are discussed. Some applications of FNET are still beyond our imagination. / Ph. D.

Changes in power system operating conditions cause dynamic changes in angle and frequency. These disturbances propagate throughout the system area with finite speed. This propagation takes the form of a traveling wave whose arrival time at a particular point in the system can be observed using a wide-area measurement system (WAMS). Observations of these waves both through simulation and measurement data have demonstrated several factors that influence the speed at which a disturbance propagates through a system. Results of this testing are presented which demonstrate dependence on generator inertia, damping and line impedance. Considering a power system as an area with and uneven distribution of these parameters it is observed that a disturbance will propagate throughout a system at different rates in differing directions. This knowledge has applications in locating the originating point of a system disturbance, understanding the overall dynamic response of a power system, and determining the dependencies between various parts of that system. A simplified power system simulator is developed using the swing equation and system power flow equations. This simplified modeling technique captures the phenomenon of traveling electromechanical waves and demonstrates the same dependencies as data derived from measurements and commercial power system simulation packages. The ultimate goal of this research is develop a methodology to approximate a real system with this simplified wave propagation model. In this architecture each measurement point would represent a pseudo-bus in the model. This procedure effectively lumps areas of the system into one equivalent bus with appropriately sized generators and loads. With the architecture of this reduced network determined its parameters maybe estimated so as to provide a best fit to the measurement data. Doing this effectively derives a data-driven equivalent system model. With an appropriate equivalent model for a given system determined, incoming measurement data can be processed in real time to provide an indication of the system operating point. Additionally as the system state is read in through measurement data future measurements values along the same trajectory can be estimated. These estimates of future system values can provide information for advanced control and protection schemes. Finally a procedure for the identification and extraction of inter-area oscillations is developed. The dominant oscillatory frequency is identified from an event region then fit across the surrounding dataset. For each segment of this data set values of amplitude, phase and damping are derived for each measurement vector. Doing this builds up a picture of how the oscillation evolves over time and responds to system conditions. These results are presented in a graphical format as a movie tracking the modal phasors over time. Examples derived from real world measurement data are presented. / Ph. D.