Date of Award

December 2013

Degree Type


Degree Name

Master of Science



First Advisor

David C. Yu

Committee Members

Adel Naseri, Hossein Hosseini


Jacobian Matrix, Modal Analysis, Voltage Stability


The central focus of this thesis is on long-term static voltage stability analysis of large power transmission grid. This thesis work is a product of an attempt to comprehend the numerous researches that has been done over the years on voltage security assessment. Voltage stability is one of the essential components influencing the reliability of a power network. There are several Transmission planning and operation compliance standards pertaining to voltage criterion from NERC and Independent System Operators (ISO) directed toward the utilities to operate their grid within tight voltage limits. This requires the utility to perform comprehensive planning studies of the power system frequently for different load profiles like summer and winter - peak load and light load conditions taking into account several contingency scenarios. The humongous number of nodes and branches in a typical preset-day power network has increased the complexity of conventional voltage stability analysis methods like PV / QV curves.

Initially, this study discusses various linear algebraic techniques used in steady-state power system analysis and presents the results on the simulations of IEEE test systems - 14 bus, 30 bus and 118 bus system. Later, it introduces an idea of performing a spectral (Symmetric Eigenvalue) analysis of the power system Jacobian and a rigorous testing of the same IEEE bus test systems was performed. Finally, it concludes by presenting a comparative result against other eigenvalue-based methods. The entire analysis has been performed by a combination of custom-written MATLAB programs, Python scripts and Siemens PTI PSS/E software for its one-line diagram capabilities.