Now showing 1 - 10 of 28
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Small-Signal Stability Techniques for Power System Modal Analysis, Control, and Numerical Integration

2021, Tzounas, Georgios, 0000-0002-1464-3600

This thesis proposes novel Small-Signal Stability Analysis (SSSA)-based techniques that contribute to electric power system modal analysis, automatic control, and numerical integration. Modal analysis is a fundamental tool for power system stability analysis and control. The thesis proposes a SSSA approach to determine the Participation Factors (PFs) of algebraic variables in power system dynamic modes. The approach is based on a new interpretation of the classical modal PFs as eigen-sensitivities, as well as on the definition of adequate inputs and outputs of the system's state-space representation. Both linear and generalized eigenvalue problems are considered for the calculation of PFs and a theorem to cope with eigenvalue multiplicities is presented. SSSA is also ubiquitous in the synthesis of controllers for power systems. The thesis explores SSSA techniques for the design of power system controllers. The contributions on this topic are twofold, as follows: (i) Investigate a promising control approach, that is to synthesize automatic regulators for power systems based on the theory of fractional calculus. In particular, using eigenvalue analysis, a comprehensive theory on the stability of power systems with inclusion of Fractional Order Controllers (FOCs) is provided. Moreover, the software implementation of FOCs based on Oustaloup's Recursive Approximation (ORA) method is discussed. A variety of FOC applications are illustrated, namely, automatic generation control of synchronous machines; frequency control of a converter-interfaced energy storage system; and voltage control through a static synchronous compensator. (ii) Propose a novel perspective on the potential impact of time delays on power system stability. In general, measurement and communication of control signals in electric energy networks introduces significant time delays that are known to be a threat for the dynamic performance of power systems. However, research in control theory has shown that, by nature, delays are neutral and, if properly introduced, can also stabilize a dynamical system. Through SSSA, the thesis systematically identifies the control parameter settings for which delays in Power System Stabilizers (PSSs) improve the damping of a power system. Both analytical and simulation-based results are presented. Finally, SSSA is utilized in the thesis to systematically propose 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, leave practically unchanged the system trajectories. Automatic selection of the variables and estimation of the maximum admissible delay are carried out by SSSA-based techniques. Such an 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 (DAEs). The proposed approach is evaluated in terms of accuracy, convergence and computational burden. Throughout the thesis, the proposed techniques are duly validated through numerical tests based on real-world network models.

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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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Stability Criterion of a Class of Non-causal Systems of Differential Equations

2023-04, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

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.

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Participation Factors for Singular Systems of Differential Equations

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

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.

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Improving the Power System Dynamic Response Through a Combined Voltage-Frequency Control of Distributed Energy Resources

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

The paper proposes a control scheme to improve the dynamic response of power systems through the automatic regulators of converter-based Distributed Energy Resources (DERs). In this scheme, both active and reactive power control of DERs are varied to regulate both frequency and voltage, as opposed to current practice where frequency and voltage controllers are decoupled. To assess the proposed control against the current state-of-art, the paper also defines a metric that captures the combined effect of frequency/voltage response at any given bus of the network. Results indicate that the proposed control strategy leads to a significant improvement in the stability and performance of the overall power system. These results are based on a comprehensive case study carried out by employing a modified version of the IEEE 39-bus benchmark system, where a portion of the synchronous machines is substituted by converter-interfaced DERs. The impact on the proposed control of load models, the R/X ratio of network lines, as well as the level of DER penetration to the grid, are properly evaluated and conclusions are duly drawn.

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Damping Power System Electromechanical Oscillations Using Time Delays

2021-06, Tzounas, Georgios, Sipahi, Rifat, Milano, Federico

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.

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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.

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Stability Analysis of Power Systems with Inclusion of Realistic-Modeling of WAMS Delays

2019-01, Liu, Muyang, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

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.

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Comparison of Numerical Methods and Open-Source Libraries for Eigenvalue Analysis of Large-Scale Power Systems

2020-10-28, Tzounas, Georgios, Dassios, Ioannis K., Liu, Muyang, Milano, Federico

This 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.

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A Formula of Solutions for Non-Autonomous Linear Difference Equations With a Fractional Forward Operator

2023-07, Dassios, Ioannis K., Tzounas, Georgios, Milano, Federico

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.