Research Output
1 - 10 of 30
Publication
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.
Publication
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.
Publication
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.
Publication
A dynamic behavioral model of the long-term development of solar photovoltaic generation driven by feed-in tariffs
2022-10-01, Kërçi, Taulant, Tzounas, Georgios, Milano, Federico
This 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 2008–2014, and Germany during 2000–2014. 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.
Publication
Small-Signal Stability Analysis of Numerical Integration Methods
2022-11, Tzounas, Georgios, Dassios, Ioannis K., Milano, Federico
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.
Publication
Singular over-determined systems of linear differential equations
2022-07, Dassios, Ioannis K., Tzounas, Georgios, Liu, Muyang, Milano, Federico
We study a class of singular over-determined systems of differential equations and firstly prove that there exist solutions under certain conditions. For the case of existence we provide closed formulas of solutions and based on the spectrum of the pencil of the system we study uniqueness of solutions. Then, we extend these results to higher order singular overdetermined systems. Finally, we use this type of systems to model electrical power systems and provide numerical examples.
Publication
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.
Publication
Curvature-Based Control for Low-Inertia Systems
2022-09, Sanniti, Francesco, Tzounas, Georgios, Benato, Roberto, Milano, Federico
This letter proposes a simple and inexpensive control of distributed energy resources aimed at improving the power system dynamic performance. The rationale behind the proposed control relies on a recent interpretation of the frequency in the differential geometry framework. A comparison with well-established controls in terms of eigensensitivity and time-domain performance is carried out to show the effectiveness of the proposed control.
Publication
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.
Publication
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.