Related papers: Spectral solution of load flow equations
Power flow analysis plays a crucial role in examining the electricity flow within a power system network. By performing power flow calculations, the system's steady-state variables, including voltage magnitude, phase angle at each bus,…
Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this…
A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the form $$(pu')'+qu=u\sum_{k=1}^{N}\lambda^{k}r_{k}$$ is obtained. It allows one to write a general solution of the equation as a power…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is…
The pathway is a biological term that refers to a series of interactions between molecules in a cell that causes a certain product or a change in the cell. Pathway analysis is a powerful method for gene expression analysis. Through pathway…
In this contribution we analyze the exponential stability of power networks modeled with the Telegrapher's equations as a system of balance laws on the edges. We show the equivalence of periodic solutions of these Telegrapher's equations…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to biological and biomedical problems. The graph matching…
This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent…
The paper proposes a solution an actual scientific problem related to load balancing and efficient utilization of resources of the distributed system. The proposed method is based on calculation of load CPU, memory, and bandwidth by flows…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
Using networks as a means of computing can reduce the communication flow or the total number of bits transmitted over the networks. In this paper, we propose to distribute the computation load in stationary networks, and formulate a…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand…
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections…
We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in…