Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1909.08800

A Novel Fully Informed Water Cycle Algorithm for Solving Optimal Power Flow Problems in Electric Grids

Alireza Barzegar·Ali Sadollah·Rong Su
View original source ↗Read source document ↗Export metadata ↓

Abstract

Optimal power flow (OPF) is a key tool for planning and operations in energy grids. The line-flow constraints, generator loading effect, piece-wise cost functions, emission, and voltage quality cost make the optimization model non-convex and computationally cumbersome to solve. Metaheuristic techniques for solving the problem have emerged as a promising solution to solve the complex OPF problem. Recently, the water cycle algorithm (WCA), a method inspired by the observation of the water cycle process and the surface run-off model was proposed for solving optimization problems. This paper proposes an improved version of WCA that uses the concept of sharing global and local information among individuals to improve the exploitation ability compared with the standard WCA. The so called fully informed WCA (FIWCA) is tested against standard WCA and other metaheuristic techniques studied in the literature on IEEE 30 and 57 bus systems for various scenarios. Comparison and discussion regarding the performance and reliability of the metaheuristics approaches studied in literature are discussed. The obtained optimization results show that the better performance of proposed FIWCA comparing with the WCA and other algorithms especially in term of stability performance over replications. Consequently, it emerges as a tool for solving OPF in a reliable and efficient manner.

Explore related subjects

math.OCcs.SYeess.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alireza Barzegar, Ali Sadollah, Rong Su. 2019-09-19. A Novel Fully Informed Water Cycle Algorithm for Solving Optimal Power Flow Problems in Electric Grids. https://arxiv.org/abs/1909.08800

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

We address the behavior of idealized deep residual neural networks (ResNets), modeled via an optimal control problem set over continuity (or adjoint transport) equations. The continuity equations describe the statistical evolution of the features in the asymptotic regime where the layers of the network form a continuum. The velocity field is expressed through the network activation function, which is itself viewed as a function of the statistical distribution of the network parameters (weights and biases). From a mathematical standpoint, the control is interpreted in a relaxed sense, taking values in the space of probability measures over the set of parameters. We investigate the optimal behavior of the network when the cost functional arises from a regression problem and includes an additional entropic regularization term on the distribution of the parameters. In this framework, we focus in particular on the existence of stable optimizers --that is, optimizers at which the Hessian of the cost is non-degenerate. We show that, for an open and dense set of initial data, understood here as probability distributions over features and associated labels, there exists a unique stable global minimizer of the control problem. Moreover, we show that such minimizers satisfy a local Polyak--Lojasiewicz inequality, which can lead to exponential convergence of the corresponding gradient descent when the initialization lies sufficiently close to the optimal parameters. This result thus demonstrates the genericity (with respect to the distribution of features and labels) of the Polyak--Lojasiewicz condition in ResNets with a continuum of layers and under entropic penalization.

math.OC↗
arXiv2026

A regret minimization approach to fixed-point iterations

We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical Krasnoselskii--Mann iterations, as the latter are recovered by converting the Online Gradient Descent algorithm. This approach yields new simple iterations for finding fixed points of non-self operators. We also focus on converting algorithms from the AdaGrad family of regret minimizers, and thus obtain fixed point iterations with adaptive guarantees of a new kind. Numerical experiments on various problems demonstrate faster convergence of AdaGrad-based fixed point iterations over Krasnoselskii--Mann iterations.

math.OC↗
arXiv2026

Variational Analysis in Spectral Decomposition Systems

This work is concerned with the variational analysis of functions defined on Euclidean spaces whose values depend solely on certain invariants (``spectrum'') of their arguments, a class we term ``spectral functions.'' Building on our previous work \cite{PartI} on the convex analysis of such functions, we work in the abstract framework of spectral decomposition systems, which covers a wide range of previously studied settings, including eigenvalue decomposition of Hermitian matrices and singular value decomposition of rectangular matrices, and allows the derivation of new results in more general settings such as normal decomposition systems. The main results of this work provide constructive formulae for computing the regular, limiting, and Clarke subdifferentials of a spectral function in terms of the corresponding objects of the associated invariant function. Finally, we obtain a generalization of Lidski\uı's theorem on the spectrum of additive perturbations of Hermitian matrices to arbitrary spectral decomposition systems.

math.OC↗