Geometric Design and Stability of Power Networks
arXiv:1011.2924
Abstract
From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of the imaginary power flow. The Gaussian fluctuations about the equilibrium basis accomplish a well-defined, non-degenerate, curved regular intrinsic Riemannian surfaces for the purely real and the purely imaginary power flows and their linear combinations. An explicit computation demonstrates that the underlying real and imaginary power correlations involve ordinary summations of the power factors, with and without their joint effects. Novel aspect of the intrinsic geometry constitutes a stable design for the power systems.
arXiv comment23 pages, 11 figures, Keywords: Correlation; Geometry; Power Flow; Network; Stability
References in corpus (24)
- N=2 Extremal Black Holes
- All supersymmetric solutions of minimal supergravity in five dimensions
- Supersymmetry and Attractors
- Macroscopic Entropy of Extremal Black Holes
- General supersymmetric AdS5 black holes
- Exact Counting of Black Hole Microstates
- General Concentric Black Rings
- Precision Counting of Small Black Holes
- Thermodynamic curvature and phase transitions in Kerr-Newman black holes
- Geometry of Higher-Dimensional Black Hole Thermodynamics
- Microscopic Entropy of N=2 Extremal Black Holes
- On the Thermodynamic Geometry of BTZ Black Holes
- On some properties of the Attractor Equations
- d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms
- Extremal Black Hole and Flux Vacua Attractors
- Attractors with Vanishing Central Charge
- Attractors in Black
- On the Microscopic Perspective of Black Branes Thermodynamic Geometry
- Attractor Horizon Geometries of Extremal Black Holes
- State-space Correlations and Stabilities
- Sur les corrections de la géométrie thermodynamique des trous noirs
- State-space Manifold and Rotating Black Holes
- Thermodynamic Geometric Stability of Quarkonia states
- A geometric approach to correlations and quark number susceptibilities