- Tzounas, Georgios

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# Tzounas, Georgios

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Tzounas, Georgios

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- PublicationA discrete model for force-based elasticity and plasticityThe article presents a mathematical model that simulates the elastic and plastic behaviour of discrete systems representing isotropic materials. The systems consist of one lattice of nodes connected by edges and a second lattice with nodes placed at the centres of the existing edges. The derivation is based on the assumption that the kinematics of the second lattice is induced by the kinematics of the first, and uses stored energies in edges of both lattices to derive a edge forces in the first lattice. This leads to a non-linear system of algebraic equations describing elasticity and plasticity in lattices. A numerical solution to the non-linear system is proposed by providing a matrix formulation necessary for software implementation. An illustrative example is given to justify the formulation and demonstrate the system behaviour.
ScopusÂ© Citations 1 20 - PublicationComparison of Numerical Methods and Open-Source Libraries for Eigenvalue Analysis of Large-Scale Power SystemsThis paper discusses the numerical solution of the generalized non-Hermitian eigenvalue problem. It provides a comprehensive comparison of existing algorithms, as well as of available free and open-source software tools, which are suitable for the solution of the eigenvalue problems that arise in the stability analysis of electric power systems. The paper focuses, in particular, on methods and software libraries that are able to handle the large-scale, non-symmetric matrices that arise in power system eigenvalue problems. These kinds of eigenvalue problems are particularly difficult for most numerical methods to handle. Thus, a review and fair comparison of existing algorithms and software tools is a valuable contribution for researchers and practitioners that are interested in power system dynamic analysis. The scalability and performance of the algorithms and libraries are duly discussed through case studies based on real-world electrical power networks. These are a model of the All-Island Irish Transmission System with 8640 variables; and, a model of the European Network of Transmission System Operators for Electricity, with 146,164 variables.
ScopusÂ© Citations 7 39 - PublicationEnhancing Frequency Control Through Rate of Change of Voltage Feedback(Institute of Electrical and Electronics Engineers (IEEE), 2024-01)
; ; This letter proposes a simple and inexpensive technique to improve the frequency control of distributed energy resources. The proposed control consists in modifying the conventional estimated bus frequency signal with an additional feedback signal that utilizes the rate of change of the voltage magnitude measured at the same bus. The case study showcases the benefits of the proposed control and compares its performance with standard frequency control schemes through time-domain simulations.ScopusÂ© Citations 1 27 - PublicationA Formula of Solutions for Non-Autonomous Linear Difference Equations With a Fractional Forward Operator(American Society of Mechanical Engineers, 2023-07)
; ; In this article, we define a fractional forward discrete operator. Then, for a family of linear nonautonomous fractional difference equations constructed by using this fractional discrete operator, we provide a practical formula of solutions. This family of problems covers several linear fractional difference equations that appear in the literature. Numerical examples are given to justify our theory.41ScopusÂ© Citations 3 - PublicationSmall-signal stability analysis of implicit integration methods for power systems with delaysThe 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.
ScopusÂ© Citations 6 28 - PublicationTheory 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.ScopusÂ© Citations 47 44 - PublicationA dynamic behavioral model of the long-term development of solar photovoltaic generation driven by feed-in tariffsThis work aims to assess the impact of renewable energy incentives, particularly that of the feed-in tariff (FiT), on the long-term development of solar photovoltaics (PVs). With this aim, the paper introduces a dynamic model based on nonlinear delay differential algebraic equations to simulate the evolution of the PV capacity and its commitment in the power grid. The model assumes the FiT budget, the PV cost and willingness of the public to install PVs as the main drivers for solar PV installations. In particular, the learning-by-doing concept to model the PV cost and consequently the PV deployment is proposed for the first time in this paper. The accuracy of the model is validated against historical data of two of the biggest PV markets in the world driven by FiT, namely, Italy during 2008â€“2014, and Germany during 2000â€“2014. A sensitivity analysis based on the Italian PV market is carried out to identify the impact of the parameters of the proposed model. Results indicate that the proposed model is a valuable tool that can help policymakers in the decision-making process, such as the definition of the FiT price and the duration of the incentives.
30ScopusÂ© Citations 7 - PublicationA bounded dynamical network of curves and the stability of its steady statesIn 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).
ScopusÂ© Citations 2 36 - PublicationParticipation Factors for Singular Systems of Differential EquationsIn 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 MÃ¶bius 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.
ScopusÂ© Citations 23 27 - PublicationApplications 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.ScopusÂ© Citations 14 25