Now showing 1 - 10 of 39
  • Publication
    Stability Criterion of a Class of Non-causal Systems of Differential Equations
    In this paper, we focus on a class of non-causal systems of differential equations, namely systems the variables of which can depend not only from the current or past time, but also from future time. For this type of systems, we study their solutions and present new and easily testable conditions under which any state of the system is stable. The stability analysis of a future-state-dependent set of differential equations has its relevance also in practical applications. Numerical examples, as well as an application in electric power engineering, are provided to justify our theory.
    Scopus© Citations 2  7
  • Publication
    Small-signal stability analysis of implicit integration methods for power systems with delays
    The paper focuses on the accuracy and stability of implicit numerical methods when utilized for the Time Domain Integration (TDI) of power systems with inclusion of time delays. In particular, a small-disturbance analysis technique is proposed to evaluate the numerical distortion that TDI methods induce to the dynamic modes of power systems modeled as Delay Differential Algebraic Equations (DDAEs). The case study illustrates the features of the proposed technique through simulations conducted using the IEEE 14-bus test system, and considering three examples of implicit integration methods, namely Backward Euler Method (BEM), Implicit Trapezoidal Method (ITM), and 2-stage Radau IIA.
    Scopus© Citations 5  7
  • 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.
      331Scopus© Citations 18
  • 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.
      376Scopus© Citations 11
  • 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.
      599Scopus© Citations 11
  • Publication
    Model-Independent Derivative Control Delay Compensation Methods for Power Systems
    The paper examines the effectiveness of utilizing the derivatives of time delayed, wide-area signals in mitigating their destabilizing impact on power system dynamic response. In particular, the paper discusses two derivative control-based delay compensation methods, namely proportional-derivative (PD) and predictor-based delay compensation. The two methods are compared in terms of their open-loop signal fidelity and their impact on the closed-loop system stability. The paper also provides a technique to carry out small-signal stability analysis with inclusion of derivative control based compensation, which leads to a Neutral Time-Delay System (NTDS). In addition, we provide a new theorem on the stability of the NTDS. Finally, nonlinear time domain simulations and eigenvalue analysis based on the IEEE 14-bus and New England 39-bus systems were carried out for the sake of comparison of the two delay compensation methods.
    Scopus© Citations 13  6
  • Publication
    A practical formula of solutions for a family of linear non-autonomous fractional nabla difference equations
    (Elsevier, 2018-09)
    In this article, we focus on a generalized problem of linear non-autonomous fractional nabla difference equations. Firstly, we define the equations and describe how this family of problems covers other linear fractional difference equations that appear in the literature. Then, by using matrix theory we provide a new practical formula of solutions for these type of equations. Finally, numerical examples are given to justify our theory.
      391Scopus© Citations 27
  • 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.
      484Scopus© Citations 33
  • 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.
      357Scopus© Citations 48
  • Publication
    Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
    (Institute of Electrical and Electronics Engineers, 2022-06-28) ; ; ; ;
    This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system.
    Scopus© Citations 2  8