Outlier Identification in Spatio-Temporal Processes

This dissertation answers some of the statistical challenges arising in spatio-temporal data from Internet traffic, electricity grids and climate models. It begins with methodological contributions to the problem of anomaly detection in communication networks. Using electricity consumption patterns for University of Michigan campus, the well known spatial prediction method kriging has been adapted for identification of false data injections into the system. Events like Distributed Denial of Service (DDoS), Botnet/Malware attacks, Port Scanning etc. call for methods which can identify unusual activity in Internet traffic patterns. Storing information on the entire network though feasible cannot be done at the time scale at which data arrives. In this work, hashing techniques which can produce summary statistics for the network have been used. The hashed data so obtained indeed preserves the heavy tailed nature of traffic payloads, thereby providing a platform for the application of extreme value theory (EVT) to identify heavy hitters in volumetric attacks. These methods based on EVT require the estimation of the tail index of a heavy tailed distribution. The traditional estimators (Hill et al. (1975)) for the tail index tend to be biased in the presence of outliers. To circumvent this issue, a trimmed version of the classic Hill estimator has been proposed and studied from a theoretical perspective. For the Pareto domain of attraction, the optimality and asymptotic normality of the estimator has been established. Additionally, a data driven strategy to detect the number of extreme outliers in heavy tailed data has also been presented. The dissertation concludes with the statistical formulation of m-year return levels of extreme climatic events (heat/cold waves). The Generalized Pareto distribution (GPD) serves as good fit for modeling peaks over threshold of a distribution. Allowing the parameters of the GPD to vary as a function of covariates such as time of the year, El-Nino and location in the US, extremes of the areal impact of heat waves have been well modeled and inferred.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145789/1/shrijita_1.pd

Reliability in a smart power system with cyber-physical interactive operation of photovoltaic systems and heat pumps

The connectivity of the power grid is increasing with the internet of things, and low carbon technologies being deployed to help enhance smart grid performance and reliability. Meanwhile, they also increase the digital complexity and dependency of cyber assets, which might be vulnerable to cyber-physical threats, and hence may impact the reliability of power systems. Due to cyber-threats’ unpredictable nature, the interactive operation of low carbon technologies with cyber-physical systems is becoming a challenging task for smart grids. This thesis proposes novel mathematical frameworks to estimate the availability of photovoltaics and heat pumps with cyber-physical components. These frameworks are developed to quantify the level of risk posed by cyber-threats to the interactive operation of photovoltaics and heat pumps, using Markov-Chains. The availability framework considers the severity of random cyber-attacks on photovoltaics and the probability of cyber-threats with mean time to detection-time on heat pump operation. Sensitivities of the repair times of cyber-physical component for photovoltaics and sensitivities of cyber-attack-detection time for heat pumps are also evaluated. The impact of cyber threats on the interactive operation of photovoltaics and heat pumps are considerable and inconsistent, however the propagation of cyber-threats can be restricted by appropriate means of photovoltaics. For heat pumps, operational reliability substantially decreases due to the unavailability of their control panel. Contributions of this thesis include an availability model for photovoltaic configurations, an innovative approach to assess the reliability of a photovoltaic integrated power system with cyber-physical interactions, the availability estimation of heat pump with variable detection time, and an enhanced cyber-intrusion process model for reliability analysis of heat pumps. The findings offer insight into the impact of cyber-physical system availability and its importance on power system reliability