Improving Power System Approximations Through Machine Learning-Inspired Optimization Methods
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Taheri, Babak
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Abstract
This dissertation aims to improve electric power system optimization algorithms using optimization and techniques inspired by machine learning. Power system optimization problems are inherently nonlinear and involve large-scale computations, making them challenging for real-time applications and for scenarios requiring complex models, such as bilevel formulations, mixed-integer nonlinear programs, and stochastic programs. To address these challenges, researchers and practitioners frequently simplify these problems using methods like relaxations, approximations, machine learning models, and reduced networks. However, such simplifications often introduce approximation errors, potentially leading to suboptimal or infeasible operational decisions. Drawing inspiration from computational methods used in machine learning, this dissertation develops algorithms to optimize parameter selection in power flow approximations, construct reduced network models, and restore feasibility in alternating current (AC) power flow solutions derived from simplified models. First, an improved version of the direct current (DC) power flow model is proposed. This model adaptively selects coefficients and bias parameters through machine learning-inspired techniques. The result is a significant improvement in the accuracy of the DC power flow approximation while preserving the model's simple structure, enabling seamless integration into existing computational workflows. Next, the dissertation introduces a novel algorithm for network reduction. This method optimizes the process of creating reduced network models, ensuring that the DC power flow solutions for the reduced networks align closely with the AC power flow results of the original, larger networks across a variety of operational scenarios. This advancement enhances the accuracy of inter-zonal flow predictions, providing a more dependable tool for power system analysis. The dissertation also tackles challenges associated with the nonlinearities of the DistFlow model, commonly used for distribution systems. A parameter optimization algorithm is developed to enhance the accuracy of the linearized DistFlow approximation for both single-phase equivalent and three-phase distribution network models. By optimizing the coefficients and bias parameters in the linearized model using sensitivity information, the algorithm reduces errors in voltage magnitude predictions compared to the nonlinear DistFlow model. Furthermore, this work proposes an algorithm to improve the accuracy of DC optimal power flow (DC-OPF) solutions relative to nonlinear AC optimal power flow (AC-OPF) solutions under various operating conditions. Using machine learning-inspired methods, this algorithm adjusts coefficients and bias parameters in the DC-OPF model, yielding more accurate generator set points and better alignment with the AC-OPF results. Additionally, the dissertation enhances the DC optimal transmission switching (DC-OTS) model. Traditional DC-OTS formulations, which simplify the AC optimal transmission switching (AC-OTS) problem into a mixed-integer linear program, often result in suboptimal or infeasible outcomes due to errors in the DC power flow approximation. The proposed DC-OTS algorithm addresses this issue by optimizing the parameters in the DC-OPF model to better represent AC-OPF results. Specifically, it captures both real and reactive power flows, improving congestion modeling and enhancing the accuracy of transmission switching decisions. This improvement reduces approximation errors, ultimately enhancing system reliability and operational efficiency. Finally, the dissertation introduces an AC power flow feasibility restoration algorithm. This algorithm employs a state estimation-based post-processing approach to adjust solutions from simplified optimization problems, ensuring they satisfy the AC power flow equations. By leveraging techniques inspired by machine learning, the algorithm learns the reliability of outputs from simplified optimization models, optimizing weight and bias parameters to improve the accuracy of these adjustments.
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2024-12-07
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Dissertation