TITLE: Load Flow and Optimal Power Flow in Power Distribution Systems - Application of Riemannian Optimization and Holomorphic Embedding Techniques
ABSTRACT:Distribution networks are undergoing unprecedented challenges guided by the desire for highly efficient, reliable, and environmentally friendly grids, characterized by high penetration of intermittent renewable energy sources, storage devices, flexible loads, and electric transportation. Fast and reliable Load Flow (LF) and Optimal Power Flow (OPF) solution methods facilitate the transition to an increasingly active, distributed and dynamic power system. This research work presents tractable LF and OPF solution methods for radial distribution networks.
We thoroughly review and evaluate the performance of existing LF solution methods on several IEEE standard test systems. While the backward-forward sweep method is generally the most efficient algorithm, it does not guarantee to find the solution if it exists. The Holomorphic Embedding Load flow Method (HELM), on the other hand, promises convergence to the correct solution and signals non-existence, but is computationally expensive. We propose modifications that improve the computational efficiency of HELM while maintaining its convergence properties.
Most of the research work is focused on presenting novel LF and OPF solution methodologies using Riemannian Optimization (RO) techniques. We employ the well-known branch flow model, which has recently been included into an OPF setting, resulting in a non-convex optimization problem, due to a quadratic equality constraint, which when relaxed to an inequality yields a convex Second Order Cone Programming (SOCP) problem. However, this relaxation is exact only when certain conditions are satisfied, and may occasionally provide solutions that do not satisfy the LF equations, hence physically meaningless.
Unlike the approach taken in SOCP relaxation, we guarantee satisfaction of the non-convex constraint by defining it as a Riemannian manifold. We formulate LF as an unconstrained Riemannian optimization problem and present the application of Riemannian Gradient Descent and Riemannian Newton’s methods. We define alternative retraction methods to approximate the geodesics. Our main contribution is the introduction of a novel RO approach to the LF problem that is shown to fall into the category of approximate Newton methods with guaranteed descent at each iteration and superlinear convergence rate. Extensive numerical comparisons on several test networks illustrate that the proposed method outperforms other Riemannian optimization methods, and achieves comparable performance with the traditional Newton-Raphson method. Lastly, we consider an approximate LF solution obtained by employing only the first step of the proposed method, and we show that it significantly outperforms other approximants in the LF literature.
In order to tackle the inexactness of OPF in radial distribution systems, we define the concept of a power flow manifold as the set of points that satisfy power flow constraints. We formulate OPF as an instance of RO with additional inequality constraints. We employ Riemannian Augmented Lagrangian Method (RALM) in which the sub-problems are Riemannian optimization problems over the power flow manifold. We present a powerful solution method and compare the performance of the proposed OPF methodology with that of BARON, a global optimization solver for non-convex problems using branch-and-bound algorithm.
COMMITTEE: Advisor/Chair
Michael Caramanis, SE/ME; Yannis Paschalidis, SE/ECE/BME; Pablo Ruiz, ME;
Na Li, Harvard University; Marija Ilic, MIT |