Statistical Analysis of High Sample Rate Time-series Data for Power System Stability Assessment

The motivation for this research is to leverage the increasing deployment of the phasor measurement unit (PMU) technology by electric utilities in order to improve situational awareness in power systems. PMUs provide unprecedentedly fast and synchronized voltage and current measurements across the system. Analyzing the big data provided by PMUs may prove helpful in reducing the risk of blackouts, such as the Northeast blackout in August 2003, which have resulted in huge costs in past decades. In order to provide deeper insight into early warning signs (EWS) of catastrophic events in power systems, this dissertation studies changes in statistical properties of high-resolution measurements as a power system approaches a critical transition. The EWS under study are increases in variance and autocorrelation of state variables, which are generic signs of a phenomenon known as critical slowing down (CSD). Critical slowing down is the result of slower recovery of a dynamical system from perturbations when the system approaches a critical transition. CSD has been observed in many stochastic nonlinear dynamical systems such as ecosystem, human body and power system. Although CSD signs can be useful as indicators of proximity to critical transitions, their characteristics vary for different systems and different variables within a system. The dissertation provides evidence for the occurrence of CSD in power systems using a comprehensive analytical and numerical study of this phenomenon in several power system test cases. Together, the results show that it is possible extract information regarding not only the proximity of a power system to critical transitions but also the location of the stress in the system from autocorrelation and variance of measurements. Also, a semi-analytical method for fast computation of expected variance and autocorrelation of state variables in large power systems is presented, which allows one to quickly identify locations and variables that are reliable indicators of proximity to instability