## Research Output

Now showing 1 - 10 of 21
• Publication
Primal and Dual Generalized Eigenvalue Problems for Power Systems Small-Signal Stability Analysis
(Institute of Electrical and Electronics Engineers (IEEE), 2017-03-07)
The paper presents a comprehensive study of small-signal stability analysis of power systems based on matrix pencils and the generalized eigenvalue problem. Both primal and dual formulations of the generalized eigenvalue problem are considered and solved through a variety of state-of-the-art solvers. The paper also discusses the impact on the performance of the solvers of two formulations of the equations modelling the power systems, namely, the explicit and semi-implicit form of differential-algebraic equations. The case study illustrates the theoretical aspects and numerical features of these formulations and solvers through two real-world systems, namely, a 1,479-bus model of the all-island Irish system, and a 21,177-bus model of the ENTSO-E network.
• Publication
Analytic loss minimization: Theoretical framework of a second order optimization method
(MDPI, 2019-01-26)
In power engineering, the Y bus is a symmetric N × N square matrix describing a power system network with N buses. By partitioning, manipulating and using its symmetry properties, it is possible to derive the K GL and Y GGM matrices, which are useful to define a loss minimisation dispatch for generators. This article focuses on the case of constant-current loads and studies the theoretical framework of a second order optimization method for analytic loss minimization by taking into account the symmetry properties of Y bus . We define an appropriate matrix functional of several variables with complex elements and aim to obtain the minimum values of generator voltages.
• Publication
Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network
(MDPI, 2019-01-20)
Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis.
• Publication
A mathematical model for plasticity and damage: A discrete calculus formulation
(Elsevier BV, 2017-03-01)
In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of plastic deformations and damage, i.e. stiffness degradation. By using discrete calculus and introducing non-local potential for plasticity, a force-based approach, we provide a matrix formulation necessary for software implementation. The output is a non-linear system with allowance for elasticity, plasticity and damage in lattices. This is the key tool for explicit analysis of micro-crack generation and population growth in plastically deforming metals, leading to macroscopic degradation of their mechanical properties and fitness for service. An illustrative example, analysing a local region of a node, is given to demonstrate the system performance.
• Publication
Spreading of memes on multiplex networks
(IOP Publishing, 2019-02-28)
A model for the spreading of online information or 'memes' on multiplex networks is introduced and analyzed using branching-process methods. The model generalizes that of (Gleeson et al 2016 Phys. Rev. X) in two ways. First, even for a monoplex (single-layer) network, the model is defined for any specific network defined by its adjacency matrix, instead of being restricted to an ensemble of random networks. Second, a multiplex version of the model is introduced to capture the behavior of users who post information from one social media platform to another. In both cases the branching process analysis demonstrates that the dynamical system is, in the limit of low innovation, poised near a critical point, which is known to lead to heavy-tailed distributions of meme popularity similar to those observed in empirical data.
• Publication
A stability result for a network of two triple junctions on the plane
(Wiley, 2017-11-30)
In this article, we study the problem of a bounded network of two triple junctions in a planar domain with fixed angle conditions at the junctions and at the points at which the curves intersect with the boundary. We introduce the evolution problem of this type of networks, identify the steady states, and study their stability in terms of the geometry of the boundary.
• Publication
A mathematical model for elasticity using calculus on discrete manifolds
(Wiley Online Library, 2018-04-27)
We propose a mathematical model to represent solid materials with discrete lattices and to analyse their behaviour by calculus on discrete manifolds. Focus is given on the mathematical derivation of the lattice elements by taking into account the stored energy associated with them. We provide a matrix formulation of the nonlinear system describing elasticity with exact kinematics, known as finite strain elasticity in continuum mechanics. This formulation is ready for software implementation and may also be used in atomic scale models as an alternative to existing empirical approach with pair and cohesive potentials. An illustrative example, analysing a local region of a node, is given to demonstrate the model performance.
• Publication
Small-signal stability analysis of neutral delay differential equations
(IEEE, 2017-11-01)
This paper focuses on the small-signal stability analysis of systems modeled as Neutral Delay Differential Equations (NDDEs). These systems include delays in both the state variables and their first time derivatives. The proposed approach consists in descriptor model transformation that constructs an equivalent set of Delay Differential Algebraic Equations (DDAEs) of the original NDDE. The resulting DDAE is a non-index-1 Hessenberg form, whose characteristic equation consists of a series of infinite terms corresponding to infinitely many delays. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on a variety of physical systems, including a population-growth model, a partial element equivalent circuit and a neutral delayed neural network.