Related papers: Spectral solution of load flow equations
We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power…
Optimal Power Flow (OPF) is an important tool used to coordinate assets in electric power systems to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of…
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
Graph Neural Networks (GNNs) are the subject of intense focus by the machine learning community for problems involving relational reasoning. GNNs can be broadly divided into spatial and spectral approaches. Spatial approaches use a form of…
Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example,…
The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…
Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a…
The large penetration of distributed generations impacts both the secondary low-voltage (LV) and the primary medium-voltage (MV) segments of the distribution network. Optimizing power flow calculations for the integrated MV/LV networks is…
Power flow calculation in EMS is required to accommodate a large and complex power system. To achieve a faster than real-time calculation, a graph based power flow calculation is proposed in this paper. Graph database and graph computing…
This paper investigates the uncertain power flow analysis in distribution networks within the context of renewable power resources integration such as wind and solar power. The analysis aims to bound the worst-case voltage magnitude in any…
This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric…
Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the…
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find the "high-voltage" solution to the power flow equations,…
The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such…
We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1-Laplacian ?$\Delta_1$. The eigenvalue problem is to solve a nonlinear system involving a set valued function. In the study, we investigate the…