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Title: Sample-Based Conservative Linear Power Flow Approximations: Computational Methods and Applications
Committee:
Dr. Molzahn, Advisor
Dr. Meliopoulos, Chair
Dr. Romberg
Abstract: The objective of the proposed research is to address challenges of the nonlinear power flow equations in power system optimization problems by using conservative linear approximations of the power flow equations. These linear approximations, unlike other existing power flow linearizations, intend to overestimate or underestimate a quantity of interest in order to enable tractable algorithms that avoid constraint violations. By using a sample-based approach, conservative linear approximations are also tailored to a specific system and operating range, thereby increasing accuracy. To prove the effectiveness of conservative linear approximations, we examine their applications, with a particular focus on an optimal sensor placement problem that we formulate as a bilevel problem. We replace the nonlinear power flow equations with conservative linear approximations to make the bilevel problem tractable. With conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. We demonstrate the effectiveness of our proposed method for several test cases.
