arXiv subjects

Calvin Alvares

Publications and source records attributed to Calvin Alvares.

3 recordsLinked to original sources

arXiv2025

How Network Topology Affects the Strength of Dangerous Power Grid Perturbations

Reasonably large perturbations may push a power grid from its stable synchronous state into an undesirable state. Identifying vulnerabilities in power grids by studying power grid stability against such perturbations can aid in preventing future blackouts. Probabilistic stability quantifiers such as basin stability, which measures the asymptotic stability of a system, and survivability, which measures the transient stability of a system, have been commonly used to quantify the stability of nodes in a power grid. However, these quantifiers do not provide information about the strength of perturbations that destabilize the system. To measure the strength of perturbations beyond which the stability of the system gets compromised, we employ two probabilistic distance-based stability measures -- basin stability bound, which deals with a system's asymptotic behaviour, and survivability bound, a newly defined stability measure that deals with a system's transient behaviour. Using these stability quantifiers, we conduct a detailed study on the impact of network topology on the strength of dangerous power grid perturbations. In this, we uncover a new class of highly vulnerable nodes that were previously unknown. Additionally, we establish connections with tree-like network structures and node connectivity to lowly stable nodes.

nlin.AO↗

arXiv2024

A Probabilistic Distance-Based Stability Quantifier for Complex Dynamical Systems

An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important to quantify the stability of such systems against reasonably large perturbations. In this paper, we introduce a distance-based measure of stability, called 'basin stability bound', to characterise the stability of dynamical systems against finite perturbations. This stability measure depends on both the size and the shape of the basin of attraction of the desirable attractor. A probabilistic sampling-based approach is used to estimate basin stability bound and quantify the associated estimation error. This approach allows for the easy estimation of basin stability bound regardless of the structure of the basin of attraction and is readily applicable to high-dimensional systems. We demonstrate the merit of the proposed stability measure using an ecological model of the Amazon rainforest, a ship capsize model, and a power grid model.

nlin.CD↗

arXiv2024

Discovering governing equation in structural dynamics from acceleration-only measurements

Over the past few years, equation discovery has gained popularity in different fields of science and engineering. However, existing equation discovery algorithms rely on the availability of noisy measurements of the state variables (i.e., displacement {and velocity}). This is a major bottleneck in structural dynamics, where we often only have access to acceleration measurements. To that end, this paper introduces a novel equation discovery algorithm for discovering governing equations of dynamical systems from acceleration-only measurements. The proposed algorithm employs a library-based approach for equation discovery. To enable equation discovery from acceleration-only measurements, we propose a novel Approximate Bayesian Computation (ABC) model that prioritizes parsimonious models. The efficacy of the proposed algorithm is illustrated using {four} structural dynamics examples that include both linear and nonlinear dynamical systems. The case studies presented illustrate the possible application of the proposed approach for equation discovery of dynamical systems from acceleration-only measurements.

stat.ML↗