Techniques for determining hidden properties of large-scale power systems

The contributions in this dissertation are towards augmenting and enhancing the knowledge in power system equivalent modeling, and dynamic mode estimation. Work related to these respective topics is presented herein in two parts -- (i) Network Based Methods, and (ii) Measurement Based Methods. The first part focuses on the problem of creating limit preserving equivalents (LPEs). There is a push to develop LPEs for power system interconnections to be used in markets and reliability studies. The equivalents that exist for these interconnections do not capture thermal limits of equivalent lines, which results in their transmission limits being significantly different from the original interconnection limits. Assigning non-infinite and non-zero limits to equivalent lines is the niche of this work. This is done by considering an unloaded network, which is operating point independent. A solution method is developed and discussed, which is capable of assigning lower, best and upper estimates for equivalent line limits, and is proposed for use towards developing LPEs. In the second part, a relatively new method for simultaneous modal analysis of multiple time-series signals is presented. Here, Dynamic Mode Decomposition (DMD) is successfully applied towards transmission-level power system measurements in an implementation that is able to run in real-time. Since power systems are considered as non-linear and time-varying, on-line modal identification is capable of monitoring the evolution of large-scale power system dynamics by providing a breakdown of the constituent oscillation frequencies and damping ratios, and their respective amplitudes. The outputs provided by DMD can enable on-line spatio-temporal analyses, improve situational awareness, and could even contribute towards control strategies. This work presents the theory of DMD, followed by results and visualization. It shows that using frequency and voltage data together helps with precision, while maintaining fast calculation speeds. The key advantage of this implementation is its relatively fast computation; for example, it is able to process each time-window, consisting of 3392 signals with 211 time points, in 0.185 s. Modal content alarm processing, and efficient wide-area modal visualization are two proposed on-line applications. The desire to reduce model-dependency has driven measurement-based modal identification methods, as an alternative to analyzing linearized system models. Using this relatively fast DMD algorithm, this work also presents an interactive modal-identification tool for spatio-temporal analysis of measurement data. The tool can automatically scan through measurements, and display the values of oscillation frequency and damping ratio, as well as reconstruct signals. The use of this tool, its options, and visualization capabilities are illustrated using simulated measurements from an interconnected power grid. DMD being a data-driven modeling technique is able to handle large data sets and has shown fast computation times. The by-products of DMD provide an understanding of the wide-area spatio-temporal structures in power systems. Studies based on a large-scale model of an interconnected power grid are presented, along with visualizations that elucidate the spatial structure of wide-area dynamics, and their dependency on operating points