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Browsing by Author "Kokoszka, Piotr, advisor"

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    Application of statistical and deep learning methods to power grids
    (Colorado State University. Libraries, 2023) Rimkus, Mantautas, author; Kokoszka, Piotr, advisor; Wang, Haonan, advisor; Nielsen, Aaron, committee member; Cooley, Dan, committee member; Chen, Haonan, committee member
    The structure of power flows in transmission grids is evolving and is likely to change significantly in the coming years due to the rapid growth of renewable energy generation that introduces randomness and bidirectional power flows. Another transformative aspect is the increasing penetration of various smart-meter technologies. Inexpensive measurement devices can be placed at practically any component of the grid. As a result, traditional fault detection methods may no longer be sufficient. Consequently, there is a growing interest in developing new methods to detect power grid faults. Using model data, we first propose a two-stage procedure for detecting a fault in a regional power grid. In the first stage, a fault is detected in real time. In the second stage, the faulted line is identified with a negligible delay. The approach uses only the voltage modulus measured at buses (nodes of the grid) as the input. Our method does not require prior knowledge of the fault type. We further explore fault detection based on high-frequency data streams that are becoming available in modern power grids. Our approach can be treated as an online (sequential) change point monitoring methodology. However, due to the mostly unexplored and very nonstandard structure of high-frequency power grid streaming data, substantial new statistical development is required to make this methodology practically applicable. The work includes development of scalar detectors based on multichannel data streams, determination of data-driven alarm thresholds and investigation of the performance and robustness of the new tools. Due to a reasonably large database of faults, we can calculate frequencies of false and correct fault signals, and recommend implementations that optimize these empirical success rates. Next, we extend our proposed method for fault localization in a regional grid for scenarios where partial observability limits the available data. While classification methods have been proposed for fault localization, their effectiveness depends on the availability of labeled data, which is often impractical in real-life situations. Our approach bridges the gap between partial and full observability of the power grid. We develop efficient fault localization methods that can operate effectively even when only a subset of power grid bus data is available. This work contributes to the research area of fault diagnosis in scenarios where the number of available phasor measurement unit devices is smaller than the number of buses in the grid. We propose using Graph Neural Networks in combination with statistical fault localization methods to localize faults in a regional power grid with minimal available data. Our contribution to the field of fault localization aims to enable the adoption of effective fault localization methods for future power grids.
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    ItemOpen Access
    Heavy tail analysis for functional and internet anomaly data
    (Colorado State University. Libraries, 2021) Kim, Mihyun, author; Kokoszka, Piotr, advisor; Cooley, Daniel, committee member; Meyer, Mary, committee member; Pinaud, Olivier, committee member
    This dissertation is concerned with the asymptotic theory of statistical tools used in extreme value analysis of functional data and internet anomaly data. More specifically, we study four problems associated with analyzing the tail behavior of functional principal component scores in functional data and interarrival times of internet traffic anomalies, which are available only with a round-off error. The first problem we consider is the estimation of the tail index of scores in functional data. We employ the Hill estimator for the tail index estimation and derive conditions under which the Hill estimator computed from the sample scores is consistent for the tail index of the unobservable population scores. The second problem studies the dependence between extremal values of functional scores using the extremal dependence measure (EDM). After extending the EDM defined for positive bivariate observations to multivariate observations, we study conditions guaranteeing that a suitable estimator of the EDM based on these scores converges to the population EDM and is asymptotically normal. The third and last problems investigate the asymptotic and finite sample behavior of the Hill estimator applied to heavy-tailed data contaminated by errors. For the third one, we show that for time series models often used in practice, whose non–contaminated marginal distributions are regularly varying, the Hill estimator is consistent. For the last one, we formulate conditions on the errors under which the Hill and Harmonic Moment estimators applied to i.i.d. data continue to be asymptotically normal. The results of large and finite sample investigations are applied to internet anomaly data.