Title: Computational and Analytical Tools for Resilient and Secure Power Grids
Description: Enhancing power grids' performance and resilience has been one of the greatest challenges in engineering and science over the past decade. A recent report by the National Academies of Sciences, Engineering, and Medicine along with other studies emphasizes the necessity of deploying new ideas and mathematical tools to address the challenges facing the power grids now and in the future. To full this necessity, numerous grid modernization programs have been initiated in recent years. This thesis focuses on one of the most critical challenges facing power grids which is their vulnerability against failures and attacks. Our approach bridges concepts in power engineering and computer science to improve power grids resilience and security. We analyze the vulnerability of power grids to cyber and physical attacks and failures, design efficient monitoring schemes for robust state estimation, develop algorithms to control the grid under tension, and introduce methods to generate realistic power grid test cases.

Our contributions can be divided into four major parts: Power Grid State Prediction: Large scale power outages in Australia (2016), Ukraine (2015), Turkey (2015), India (2013), and the U.S. (2011, 2003) have demonstrated the vulnerability of power grids to cyber and physical attacks and failures. Power grid outages have devastating effects on almost every aspect of modern life as well as on interdependent systems. Despite their inevitability, the effects of failures on power grids' performance can be limited if the system operator can predict and understand the consequences of an initial failure and can immediately detect the problematic failures. To enable these capabilities, we study failures in power grids using computational and analytical tools based on the DC power flow model. We introduce new metrics to efficiently evaluate the severity of an initial failure and develop efficient algorithms to predict its consequences. We further identify power grids' vulnerabilities using these metrics and algorithms.

Power Grid State Estimation: In order to obtain an accurate prediction of the subsequent effects of an initial failure on the performance of the grid, the system operator needs to exactly know when and where the initial failure has happened. However, due to lack of enough measurement devices or a cyber attack on the grid, such information may not be available directly to the grid operator via measurements. To address this problem, we develop efficient methods to estimate the state of the grid and detect failures (if any) from partial available information. Power Grid Control: Once an initial failure is detected, prediction methods can be used to predict the subsequent effects of that failure. If the initial failure is causing a cascade of failures in the grid, a control mechanism needs to be applied in order to mitigate its further effects. Power Grid Islanding is an effective method to mitigate cascading failures. The challenge is to partition the network into smaller connected components, called islands, so that each island can operate independently for a short period of time.

This is to prevent the system to be separated into unbalanced parts due to cascading failures. To address this problem, we introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem and provide an efficient algorithm to partition the power grid into two operating islands. Power Grid Test Cases for Evaluation: In order to evaluate algorithms that are developed for enhancing power grids resilience, one needs to study their performance on the real grid data. However, due to security reasons, such data sets are not publicly available and are very hard to obtain. Therefore, we study the structural properties of the U.S. Western Interconnection grid (WI), and based on the results we present the Network Imitating Method Based on LEarning (NIMBLE) for generating synthetic spatially embedded networks with similar properties to a given grid. We apply NIMBLE to the WI and show that the generated network has similar structural and spatial properties as well as the same level of robustness to cascading failures.

Overall, the results provided in this thesis advance power grids' resilience and security by providing a better understanding of the system and by developing efficient algorithms to protect it at the time of failure.