Now showing 1 - 10 of 20
  • 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
    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 and Robustness of Singular Systems of Fractional Nabla Difference Equations
    (Springer Nature, 2017-01)
    In this article, we study the stability and robustness of a class of singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. Firstly, by assuming that the singular fractional system has a unique solution for given initial conditions, we study the asymptotic stability of the equilibria of the homogeneous system. We also prove conditions on the input vector under which the solution of the non-homogeneous system converges. Next, since it is known that existence and uniqueness of solutions depend on the invariants of the pencil of the system, by taking into consideration the fact that small perturbations can change the invariants, we perturb the singular fractional system and obtain bounds on the perturbation effect of the invariants of the pencil. In addition, by using this result, we study the robustness of solutions of the system. Finally, we give numerical examples based on a real singular fractional nabla dynamical system to illustrate our theory.
    Scopus© Citations 33  463
  • 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.
      430Scopus© Citations 25
  • 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
    Analytic Loss Minimization: A Proof
    Loss minimizing generator dispatch profiles for power systems are usually derived using optimization techniques. However, some authors have noted that a system’s KGL matrix can be used to analytically determine a loss minimizing dispatch. This letter draws on recent research on the characterization of transmission system losses to demonstrate how the KGL matrix achieves this. A new proof of the observed zero row summation property of the YGGM matrix is provided to this end.
    Scopus© Citations 11  592
  • Publication
    A stability result for a network of two triple junctions on the plane
    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.
    Scopus© Citations 13  305
  • 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
    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
    A macroeconomic mathematical model for the national income of a union of countries with interaction and trade
    (Springer Nature, 2016-06-08) ;
    In this article, we assume a union of countries where each national economy interacts with the others. We propose a new model where (a) delayed variables are incorporated into the system of equations and (b) the interaction element is restricted into the annual governmental expenditure that is determined according to the experience of the total system and the trade relations of these countries (exports–imports). In addition, we consider the equilibrium(s) of the model (a discrete-time system) and study properties for stability, the appropriate control actions as well as the total system design in order to obtain a stable situation. Finally, a practical application is also investigated that provides further insight and better understanding as regards the system design and produced business cycles.
      369Scopus© Citations 11