Now showing 1 - 10 of 28
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Generalized fractional controller for singular systems of differential equations

2020-11, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

In this article we consider a class of singular linear systems of first order, and introduce a generalized fractional order feedback controller of Caputo type. The closed loop system in question is a singular system of differential equations having both first, and fractional order derivatives. We provide a comprehensive theory for the existence and uniqueness of solutions, as well as for the stability of the system with inclusion of the fractional order controller. An example of a singular system with a fractional order proportional integral controller, as well as an example on a 3-bus power system with inclusion of a fractional order damping controller, is given to illustrate our theory.

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On-line inertia estimation of Virtual Power Plants

2022-11, Zhong, Weilin, Tzounas, Georgios, Liu, Muyang, Milano, Federico

This paper presents an on-line estimation method to track the equivalent, time-varying inertia provided by Virtual Power Plants (VPPs). The proposed method relies on the estimation of the rate of change of the active and reactive power at the point of connection of the VPP with the rest of the grid and provides, as a byproduct, an estimation of the VPP's internal equivalent reactance. The accuracy of the proposed method is first validated by estimating the rotational inertia of Synchronous Machines (SMs), and then tested for a VPP, based on a comprehensive case study carried out based on the WSCC 9-bus test system.

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Model-Independent Derivative Control Delay Compensation Methods for Power Systems

2020-01-10, Liu, Muyang, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

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.

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Theory and Implementation of Fractional Order Controllers for Power System Applications

2020-11, Tzounas, Georgios, Dassios, Ioannis K., Murad, Mohammed Ahsan Adib, Milano, Federico

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.

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Modal Participation Factors of Algebraic Variables

2020-01, Tzounas, Georgios, Dassios, Ioannis K., Milano, Federico

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.

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Power system modelling as stochastic functional hybrid differential-algebraic equations

2022-10, Milano, Federico, Liu, Muyang, Murad, Mohammed Ahsan Adib, Jónsdóttir, Guðrún M., Tzounas, Georgios, Adeen, Muhammad, Ortega, Alvaro, Dassios, Ioannis K.

This paper presents the software tools developed for the research project Advanced Modelling for Power System Analysis and Simulation (AMPSAS) funded by Science Foundation Ireland from 2016 to 2021. The main objective of AMPSAS was the development of novel analytical and computational tools to understand, efficiently design, and optimise ever-changing modern power systems and smart grids, through model-based approaches. In particular, the paper discusses (i) stochastic differential equations for modelling power systems, which are subject to large stochastic perturbations (e.g. wind and solar generation); (ii) the effect of controller and modelling imperfections, for example, delays, discontinuities, and digital signals, on both local and area-wide regulators in power systems; and (iii) the stability analysis and dynamic performance of power systems modelled through stochastic, delay and hybrid implicit differential-algebraic equations. The software tool developed during the execution of AMPSAS integrates areas of applied mathematics, automatic control, and computer science. Several implementation features and open challenges of this software tool are also discussed in the paper. A variety of examples that illustrates the features of this software tool are based on a dynamic model of the all-island Irish transmission system.

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A bounded dynamical network of curves and the stability of its steady states

2023-05-20, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

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).

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Delay-Based Decoupling of Power System Models for Transient Stability Analysis

2021-01, Tzounas, Georgios, Milano, Federico

This paper proposes a delay-based method to reduce the coupling of the equations of power system models for transient stability analysis. The method consists in identifying the variables that, when subjected to a delay equal to the time step of the numerical integration (one-step delay), leave practically unchanged the system trajectories. Automatic selection of the variables based on a geometric controllability/observability approach and estimation of the maximum admissible delay are duly discussed. Such a one-step-delay approximation increases the sparsity of the system Jacobian matrices and can be used in conjunction with state-of-the-art techniques for the integration of differential-algebraic equations. The proposed approach is evaluated in terms of accuracy, convergence and computational burden, by means of the New England 39-bus system; a 21,177-bus model of the ENTSO-E transmission system.

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Applications of the Frenet Frame to Electric Circuits

2022-04, Milano, Federico, Tzounas, Georgios, Dassios, Ioannis K., Kërçi, Taulant

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.

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The Möbius transform effect in singular systems of differential equations

2019-11-15, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of differential equations and the solutions of its proper M-systems, i.e., systems that appear after applying the generalized Möbius transform to the pencil of the original singular system (prime system). Firstly, we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of its proper M-systems. Moreover these solutions can be explicitly represented without resorting to any further processes of computations. Finally, numerical examples are given to illustrate our theory.