Abstract
The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid’s bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.
Zusammenfassung
Die Energiewende bringt viele neue Herausforderungen mit sich, insbesondere die Sicherstellung der Netzstabilität im Energieversorgungsnetz. Die transiente Stabilität bezeichnet dabei die Fähigkeit der in einem Energieversorgungssystem angeschlossenen rotierenden Erzeugern und Verbrauchern nach schwerwiegenden Störungen den Synchronismus zu wahren. In diesem Artikel präsentieren wir einen mengenbasierten Ansatz zur Bewertung der transienten Stabilität von Energieversorgungssystemen. Diese Methode basiert auf der Barrierentheorie, um eine exakte Beschreibung der Grenzen von zulässigen Mengen und maximal robusten invarianten Mengen zu erhalten. Wir gliedern das betrachtete Energieversorgungsnetz in Generator- und Verbraucherkomponenten auf und ersetzen die Kopplung der Komponenten mit beschränkten Störtermen. Anschließend berechnen wir die Mengen für jede Einzelkomponente und schließen daraus auf die transiente Stabilität des Gesamtsystems. Die Ergebnisse dieser Methode werden anhand eines Systems mit einem Generator und einem dazu verbundenen Verbraucher sowie eines Systems mit einer Vielzahl von verbundenen Generatoren beziehungsweise Verbrauchern gezeigt.
Funding source: European Social Fund
Award Identifier / Grant number: 100327773
Funding source: Bundesministerium für Bildung und Forschung
Award Identifier / Grant number: 05M18OCA
Funding statement: This project has received funding from the European Social Fund (ESF) Grant Number: 100327773. This work was partially funded by BMBF-Projekt 05M18OCA: “Verbundprojekt 05M2018 – KONSENS: Konsistente Optimierung und Stabilisierung elektrischer Netzwerksysteme”.
About the authors
Tim Aschenbruck received his B. Eng. degree from the Magdeburg-Stendal University of Applied Science (Germany) in 2015 and his M. Sc. degree from the Chemnitz University of Technology (Germany) in 2018. He is currently pursuing his Ph. D. degree in the Automatic Control and System Dynamics Laboratory of the Chemnitz University of Technology (Germany). His research interests include set-theoretic methods for nonlinear systems, networked systems, optimal and robust control as well as solving problems in the application areas of agriculture, epidemiology and energy systems.
Willem Esterhuizen grew up in Johannesburg and received his B. Sc. in mechatronics from the University of Cape Town, his M. Sc. in electrical engineering from Boston University, and his Ph. D. in mathematics and control from the Centre Automatique et Systèmes, MINES-ParisTech in 2015. Between 2016 and 2018 he was a postdoc at the Institute for Intelligent Systems at the University of Johannesburg, and worked as a data scientist at Praelexis, Stellenbosch. Since 2018 he has been a post-doc with the Automatic Control and System Dynamics Laboratory at the Chemnitz University of Technology (Germany). His research interests are in set-theoretic methods, optimal control, robust control, and model-predictive control, and in solving problems appearing in epidemiology, power systems, robotics and aero-space.
Stefan Streif received his doctoral degree from the University of Magdeburg and the Max Planck Institute of Dynamics of Complex Technical Systems (Germany) in 2011. He also was a postdoctoral researcher at the Massachusetts Institute of Technology (USA), at the Norwegian University of Science and Technology in Trondheim (Norway), and at the Laboratory for Analysis and Architecture of Systems in Toulouse (France). In 2014, he became an Assistant Professor at the Ilmenau University of Technology, and in 2015 a full Professor at the Chemnitz University of Technology (Germany). His research interests include optimal, adaptive and robust control, estimation of uncertain and nonlinear systems as well as set-based methods for uncertain nonlinear systems. These methods are applied in various application areas including agriculture, automation engineering, biotechnology, and energy systems. He serves as an Associate editor within the IEEE CSS and was actively involved in organization of several international conferences.
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