Intrinsic geometric analysis of the network reliability and voltage stability

Abstract

a b s t r a c tThis paper presents the intrinsic geometric model for the solution of power system planning and its operation. This problem is large-scale and nonlinear, in general. Thus, we have developed the intrinsic geometric model for the network reliability and voltage stability, and examined it for the two and three parameter systems. The robustness of the proposed model is illustrated by introducing variations of the network parameters. Exact analytical results show the accuracy as well as the efficiency of the proposed solution technique.

A Fluctuation Theory of Topological Susceptibility

“…In this section, we provide a brief review of the lattice QCD models as proposed by Aoki, Cossu, Fukaya, Hashimoto, and Kaneko [7] and its relation to the fluctuation theory [21,22,26,[45][46][47][48][49][50][51][52][53][54][62][63][64][65][66][67][68]. First of all, in order to invoke the setup of the lattice gauge theory, one considers a domain wall based fermionic action for gauge ensemble generations [70][71][72] in the Symanzik gauge.…”

“…, x n ). Hereby, the Ruppeiner's proposition [21,22,26,[45][46][47][48][49][50][51][52][53][54][62][63][64][65][66][67][68] results in to the following statistical versus intrinsic geometric equivalence…”

“…In the case of two variables (x 1 , x 2 ), that is, for the embedding function φ : M 2 → R, it follows [21,22,26,[45][46][47][48][49][50][51][52][53][54][62][63][64][65][66][67][68] that the corresponding correlation area varies as the curvature R(x 1 , x 2 ) (see the below Eqn. ( 19)), whose discontinuities give the nature of underlying phase transitions on the fluctuation surface M 2 of the system with a pair of parameters {x 1 , x 2 }.…”

“…Fluctuation theory [21,22,26, offers various notions to understand statistical and quantum properties of an ensemble of observations and instrumental technology towards a high precision measurement. À priori, we have investigated the above perspectives in the light of configurations emerging from condensed matter systems, e.g., [22,45,64], electrical engineering [50,51], computer science and engineering [52], and various high energy configurations such as the flat information geometries [48,53] and counting entropy [54] that it arises as a fluctuation theory of counting systems whose degeneracy is described as a selection problem. Hereby, we have examined statistical correlations and instabilities undermining the combinatorics of selecting n boxes out m = N 2 boxes, where n ≤ m. Further, we have extended studies of fluctuations for the configurations whose embedding function are defined by the Shannon entropy, Rènyi entropy, Tsallis entropy [46,47] and other higher order corrected entropies in the large charge limit of observations [48,49].…”

An Introduction to Dynamic Optical Optimization

“…In this setup, we analyze stability properties of the image thus formed via lenses and mirrors by invoking the notion of stability analysis [10] and associated critical points and concerning scaling hypothesis [11]. Interesting fluctuation theory applications include notions of thermodynamic Ruppeiner geometry [12,13], black branes thermodynamic geometry [14], power networks [15], network reliability and voltage stability [16] and equilibrium thermodynamic configurations and chemical equilibria [17,18].…”