Related papers: Superposition theorem for flexible grids
The capacitance between two adjacent nodes on an infinite square grid of identical capacitors can easily be found by superposition, and the solution is found by explotting the symmetry of the grid. The mathematical problem presented in this…
The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
The increasing penetration of renewable energy sources introduces significant variability and uncertainty in modern power systems, making accurate state prediction critical for reliable grid operation. Conventional forecasting methods often…
Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derived a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
To perform any meaningful optimization task, distribution grid operators need to know the topology of their grids. Although power grid topology identification and verification has been recently studied, discovering instantaneous interplay…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The large-scale integration of renewable generation directly affects the reliability of power grids. We investigate the problem of power balancing in a general renewable-integrated power grid with storage and flexible loads. We consider a…
This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…
The growing prevalence of extreme weather events driven by climate change poses significant challenges to power system resilience. Infrastructure damage and prolonged power outages highlight the urgent need for effective grid-hardening…
We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…
We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…