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Mathematical Modelling, Control, and Stability Studies of Electrical Power Systems

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Energy Science and Technology".

Deadline for manuscript submissions: closed (10 August 2021) | Viewed by 9247

Special Issue Editors


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Guest Editor
School of Electrical and Electronic Engineering, University College Dublin, D04 V1W8 Dublin, Ireland
Interests: differential/difference equations; dynamical systems; modeling and stability analysis of electric power systems; mathematics of networks; fractional calculus; mathematical modeling (power systems, materials science, energy, macroeconomics, social media, etc.); optimization for the analysis of large-scale data sets; fluid mechanics; discrete calculus; Bayes control; e-learning
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
School of Electrical & Electronic Engineering, University College Dublin, Belfield, Dublin 4, Ireland
Interests: power system modelling; control and stability analysis; stochastic and functional differential algebraic equations; software architecture and parallel computing for power system analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims at collecting the latest results related to applications of Differential Equations, Systems Theory, Linear Algebra, Mathematics of Networks, Optimization, etc in the mathematical modelling of Electrical Power Systems and in studying Power System Control and Stability.  

This Special Issue will accept high-quality papers having original research results, and its purpose is to bring together Mathematicians with Electrical Engineers, as well as other scientists. 

Topics to be covered included but are not limited to: 

  • Differential Equations;
  • Partial Differential Equations;
  • Dynamical systems;
  • Mathematics of networks;
  • Optimization;
  • Fractional calculus;
  • Electrical Power Systems;
  • Mathematical Modelling;
  • Stability;
  • Control.

Prof. Dr. Ioannis Dassios
Prof. Dr. Federico Milano
Guest Editors

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Published Papers (3 papers)

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Research

31 pages, 4257 KiB  
Article
Analysis of Synchronous Generators’ Local Mode Eigenvalues in Modern Power Systems
by Jožef Ritonja and Boštjan Polajžer
Appl. Sci. 2022, 12(1), 195; https://doi.org/10.3390/app12010195 - 25 Dec 2021
Cited by 3 | Viewed by 2977
Abstract
New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to [...] Read more.
New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to analyze local oscillations and the causes that affect them in order to reduce their negative impact. There are no recognized analyses of the oscillations of modern operating synchronous generators exposed to new conditions in power systems. The basic idea is to perform a numerical analysis of local oscillations of a large number of synchronous generators in the power system. The paper represents the local mode data obtained from a systematic analysis of synchronous generators in the Slovenian power system. Analyzed were 74 synchronous generators of the Slovenian power system, plus many additional synchronous generators for which data were accessible in references. The mathematical models convenient for the study of local oscillations are described first in the paper. Next, the influences of transmission lines, size of the synchronous generators, operating conditions, and control systems were investigated. The paper’s merit is the applicable rules that have been defined to help power plant operators avoid stability-problematic situations. Consequently, boundaries were estimated of the eigenvalues of local modes. Finally, experiments were performed with a laboratory-size synchronous generator to assess the regularity of the numerically obtained conclusions. The obtained results enable the prediction of local oscillations’ frequencies and dampings and will be useful in PSS planning. Full article
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13 pages, 1099 KiB  
Article
Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative
by Nehad Ali Shah, Abdul Rauf, Dumitru Vieru, Kanokwan Sitthithakerngkiet and Poom Kumam
Appl. Sci. 2021, 11(9), 4142; https://doi.org/10.3390/app11094142 - 30 Apr 2021
Cited by 3 | Viewed by 2332
Abstract
A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New [...] Read more.
A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad. Full article
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25 pages, 10205 KiB  
Article
Modeling of Voltage Fluctuations Generated by Arc Furnaces
by Zbigniew Olczykowski
Appl. Sci. 2021, 11(7), 3056; https://doi.org/10.3390/app11073056 - 29 Mar 2021
Cited by 8 | Viewed by 2716
Abstract
Arc furnaces can be classified as electricity receivers, which largely affect the quality of electricity in the power system. Voltage fluctuations are the main disturbance generated by arc furnaces. The effects of voltage fluctuations include the phenomenon of flickering light. Apart from voltage [...] Read more.
Arc furnaces can be classified as electricity receivers, which largely affect the quality of electricity in the power system. Voltage fluctuations are the main disturbance generated by arc furnaces. The effects of voltage fluctuations include the phenomenon of flickering light. Apart from voltage fluctuations, arc devices, to a lesser extent, are the source of current and voltage asymmetry, voltage curve distortion, and voltage dips. The main purpose of theoretical considerations is to assess the voltage fluctuations generated by arc furnaces. The article presents a model of an arc device in which the arc has been replaced by a voltage whose value depends on the arc length. It presents also the results of the analysis of measurements of the parameters characterizing voltage fluctuations and flicker indicators. Full article
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