Now showing 1 - 10 of 28
  • Publication
    Modal Participation Factors of Algebraic Variables
    (Institute of Electrical and Electronics Engineers, 2020-01) ; ;
    This paper proposes an approach to determine the participation of algebraic variables in power system modes. The approach is based on a new interpretation of the classical participation factors, as well as on the definition of adequate output variables of the system's state-space representation. The paper considers both the linear and generalized eigenvalue problems for the calculation of the participation factors and presents a theorem to cope with eigenvalue multiplicities. An illustrative example on the two-area system, as well as a study on a 1479-bus dynamic model of the all-Irish transmission system are carried out to support the theory and illustrate the features of the proposed approach.
    Scopus© Citations 30  9
  • Publication
    Participation Factors for Singular Systems of Differential Equations
    In this article, we provide a method to measure the participation of system eigenvalues in system states, and vice versa, for a class of singular linear systems of differential equations. This method deals with eigenvalue multiplicities and covers all cases by taking into account both the algebraic and geometric multiplicity of the eigenvalues of the system matrix pencil. A Möbius transform is applied to determine the relative contributions associated with the infinite eigenvalue that appears because of the singularity of the system. The paper is a generalization of the conventional participation analysis, which provides a measure for the coupling between the states and the eigenvalues of systems of ordinary differential equations with distinct eigenvalues. Numerical examples are given including a classical DC circuit and a 2-bus power system dynamic model.
    Scopus© Citations 23  5
  • Publication
    Unified Numerical Stability and Accuracy Analysis of the Partitioned-Solution Approach
    (Institute of Electrical and Electronics Engineers (IEEE), 2024-03) ;
    This paper focuses on the Partitioned-Solution Approach (PSA) employed for the Time-Domain Simulation (TDS) of dynamic power system models. In PSA, differential equations are solved at each step of the TDS for state variables, whereas algebraic equations are solved separately. The goal of this paper is to propose a novel, matrix-pencil based technique to study numerical stability and accuracy of PSA in a unified way. The proposed technique quantifies the numerical deformation that PSA-based methods introduce to the dynamics of the power system model, and allows estimating useful upper time step bounds that achieve prescribed simulation accuracy criteria. The family of Predictor-Corrector (PC) methods, which is commonly applied in practical implementations of PSA, is utilized to illustrate the proposed technique. Simulations are carried out on the IEEE 39-bus system, as well as on a 1479-bus model of the All-Island Irish Transmission System (AIITS).
  • Publication
    Small-Signal Stability Analysis of Numerical Integration Methods
    (Institute of Electrical and Electronics Engineers, 2022-11) ; ;
    The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1,479-bus dynamic model of the All-Island Irish Transmission System.
    Scopus© Citations 9  6
  • Publication
    Theory and Implementation of Fractional Order Controllers for Power System Applications
    (Institute of Electrical and Electronics Engineers, 2020-11) ; ; ;
    The paper presents the theoretical foundation and practical implementation aspects of Fractional Order Controllers (FOCs) for power system applications. With this aim, the paper provides a comprehensive mathematical background on the stability analysis of dynamic systems with inclusion of fractional order derivatives and discusses their software implementation based on the Oustaloup's Recursive Approximation (ORA) method. Then the paper illustrates a variety of examples of ORA-based FOCs, namely, automatic generation control of synchronous machines; frequency control of a converter-interfaced energy storage system; and voltage control through a static synchronous compensator. The WSCC 9-bus test system and a realistic 1,479-bus model of the Irish transmission system are employed to test and compare the examined FOCs with their integer-order versions.
    Scopus© Citations 41  12
  • Publication
    Stability Analysis of Wide Area Damping Controllers with Multiple Time Delays
    The paper discusses the impact of multiple time delays on the stability of centralized wide area damping controllers (WADCs). These controllers are utilized in electric power systems to damp the interarea oscillations. With this aim, an ideal WADC is first designed based on the well-known H∞ control scheme. Then delays are included for all remote signals of the WADC and different delay models, namely, constant, stochastic and periodic delays with dropout, are considered and compared. Both nonlinear time domain simulations and closed-loop eigenvalue analysis based on the 2-area test system are carried out. Finally, a probabilistic method to evaluate the impact of stochastic communication delays on small-signal stability is discussed.
    Scopus© Citations 4  7
  • Publication
    Robust stability criterion for perturbed singular systems of linearized differential equations
    In this article, we consider a class of singular linear systems of differential equations whose coefficients are constant matrices, and study the response of its stability after a perturbation is applied into the system. We use a linear fractional transformation and through its properties we provide a practical test for robust stability. This test requires only the knowledge of the invariants of the initial system. This means it can be used without resorting to any further processes of computations to obtain invariants of any other perturbed system. Finally, numerical examples are given to support and discuss practical applications of the proposed theory.
    Scopus© Citations 10  6
  • Publication
    A bounded dynamical network of curves and the stability of its steady states
    In this article, we study the dynamic behavior of a network that consists of curves that are in motion and bounded. We first focus on the construction of the model which is a system of nonlinear partial differential equations (PDEs). This system is subject to four conditions: angle and intersection conditions between the curves at the point that they meet and angle and intersection conditions between the curves and the boundary from which the network is bounded. Then, we define a linear operator and study the stability of the steady states of the corresponding boundary value problem (BVP).
    Scopus© Citations 1  7
  • Publication
    Damping Power System Electromechanical Oscillations Using Time Delays
    (Institute of Electrical and Electronics Engineers (IEEE), 2021-06) ; ;
    This paper proposes to utilize intentional time delays as part of controllers to improve the damping of electromechanical oscillations of power systems. Through stability theory, the control parameter settings for which these delays in Power System Stabilizers (PSSs) improve the small signal stability of a power system are systematically identified, including the key parameter settings for which stability regions in the parameter plane remain connected for effective operation. The paper shows that PSSs with two control channels can be effectively designed to achieve best damping characteristics for a wide range of delays. Analytical results are presented on the One-Machine Infinite-Bus (OMIB) electromechanical power system model. To demonstrate the opportunities in more realistic dynamic models, our results are then implemented via numerical analysis on the IEEE standard 14-bus system.
    Scopus© Citations 13
  • Publication
    Applications of the Frenet Frame to Electric Circuits
    (Institute of Electrical and Electronics Engineers, 2022-04) ; ; ;
    The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of 'torsional frequency.' Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper.
    Scopus© Citations 14  9