Now showing 1 - 10 of 21
  • Publication
    On the Stability Analysis of Systems of Neutral Delay Differential Equations
    This paper focuses on the stability analysis of systems modeled as neutral delay differential equations (NDDEs). These systems include delays in both the state variables and their time derivatives. The proposed approach consists of a descriptor model transformation that constructs an equivalent set of delay differential algebraic equations (DDAEs) of the original NDDEs. We first rigorously prove the equivalency between the original set of NDDEs and the transformed set of DDAEs. Then, the effect on stability analysis is evaluated numerically through a delay-independent stability criterion and the Chebyshev discretization of the characteristic equations.
    Scopus© Citations 46  602
  • Publication
    Small-Signal Stability Analysis for Non-Index 1 Hessenberg Form Systems of Delay Differential-Algebraic Equations
    (Institute of Electrical and Electronics Engineers (IEEE), 2016-07-11) ;
    This paper focuses on the small-signal stability analysis of systems modelled as differential-algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic-differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines.
      340Scopus© Citations 48
  • Publication
    Small-signal stability analysis of neutral delay differential equations
    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.
    Scopus© Citations 6  406
  • Publication
    Geometric relation between two different types of initial conditions of singular systems of fractional nabla difference equations
    (Wiley Online Library, 2017-11-30)
    In this article, we study the geometric relation between two different types of initial conditions (IC) of a class of singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. For these kinds of systems, we analyze how inconsistent and consistent IC are related to the column vector space of the finite and the infinite eigenvalues of the pencil of the system and analyze the geometric connection between these two different types of IC. Numerical examples are given to justify the results.
    Scopus© Citations 18  320
  • 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.
      371Scopus© Citations 21
  • Publication
    Visualizing voltage relationships using the unity row summation and real valued properties of the FLG matrix
    By manipulating the bus admittance matrix of a power system, a useful submatrix, FLG, can be derived. This matrix identifies, for every load bus, the set of generators that establish its no-load voltage, and the varying degree of their influence. The first contribution of the present work is to rigorously prove two observed properties of the FLG matrix; that it is substantially real-valued, and that its rows sum close to one. Six test systems are used in this work to validate these properties. With this proof in hand, this work also introduces a new conception of voltage profile monitoring in power systems, by explicitly mapping the relationships between load and generator voltages. This new visualization makes it easier to identify how influential each generator is in establishing the network's voltage profile. Poorly supported load buses, which may be vulnerable to voltage deviations, are clearly identified. This new visualization framework is suitable for pedagogy, research, and control room applications.
    Scopus© Citations 18  469
  • Publication
    Spreading of memes on multiplex networks
    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.
    Scopus© Citations 15  220
  • Publication
    Stability Analysis of Power Systems with Inclusion of Realistic-Modeling of WAMS Delays
    The paper studies the impact of realistic WideArea Measurement System (WAMS) time-varying delays on the dynamic behaviour of power systems. A detailed model of WAMS delays including pseudo-periodic, stochastic and constant components is presented. Then, the paper discusses numerical methods to evaluate the small-signal stability as well as the timedomain simulation of power systems with inclusion of such delays. The small-signal stability analysis is shown to be able to capture the dominant modes through the combination of a characteristic matrix approximation and a Newton correction technique. A case study based on the IEEE 14-bus system compares the accuracy of the small-signal stability analysis with Monte-Carlo time-domain simulations. Finally, the numerical efficiency of the proposed technique is tested through a real-world dynamic model of the all-island Irish system.
    Scopus© Citations 77  666
  • Publication
    Caputo and related fractional derivatives in singular systems
    (Elsevier, 2018-11-15) ;
    By using the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo–Fabrizio (CF) and the Atangana–Baleanu (AB) fractional derivative, firstly we focus on singular linear systems of fractional differential equations with constant coefficients that can be non-square matrices, or square & singular. We study existence of solutions and provide formulas for the case that there do exist solutions. Then, we study the existence of unique solution for given initial conditions. Several numerical examples are given to justify our theory.
      347Scopus© Citations 47
  • Publication
    Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network
    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.
      348Scopus© Citations 10