Yves Narcisse Nguegan Tchokonte Real‐time identification and monitoring of the voltage stability margin in electric power transmission systems using synchronized phasor measurements kassel university press This work has been accepted by the faculty of Electrical Engineering and Computer Science of the University of Kassel as a thesis for acquiring the academic degree of Doktor der Ingenieurwissenschaften (Dr. –Ing.). Supervisor: Prof. Dr. Albert Claudi Co‐Supervisor: Prof. Dr. Bernd Weidemann Defence Day 29. Juni 2009 Bibliographic information published by Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.d‐nb.de. Zugl.: Kassel, Univ., Diss. 2009 ISBN print: 978‐3‐89958‐756‐2 ISBN online: 978‐3‐89958‐757‐9 URN: urn:nbn:de:0002‐7573 © 2008, kassel university press GmbH, Kassel www.upress.uni‐kassel.de Printed in Germany Acknowledgements This work has been carried out during my employment as a research assistant at the chair for Power Systems and High Voltage Engineering of the University of Kassel in Germany. At this point I would like to express my sincere gratitude to a number of people for the support and the assistance during the realization of this thesis. Firstly thanks to the almighty and merciful God for the blessings that have been extend to me all my life and during the time at the University of Kassel. I would like to express my deep thanks and profound regard to the head of the chair: Prof. Dr. Albert Claudi who hired me, became my supervisor and thus gave me the possibility to write this thesis. Thank him I had the opportunity to get better acquainted to the academic world. He majorly contributed to this thesis by giving me the possibility of sole responsible research, by providing me excellent working conditions, and by his priceless advices and encouraging discussions. I am very thankful to my co‐supervisor Prof. Dr. Bernd Weidemann for his constructive comments during the very few discussions we had. I acknowledge Mr. Holger Kühn from E.ON Netz in Germany, as it was through discussion with him that the main idea of this dissertation was born. Also thank you for the constructive discussions and ideas. I would like to thank my colleagues at the University of Kassel: Günther Köhler, Dr. Gernot Finis, Mrs. Ursula Henrich, Oliver Schröder, and Oliver Belz for being there when I needed them, for the very good teamwork and for contributing to a pleasant work atmosphere. Special thanks to Oliver Belz, who occupied the neighbour office. He has been listening to all my complaints and thoughts on the matters of this thesis, and has contributed in the span of his possibility with constructive comments although being busy with his own thesis. He has also been my main partner for discussions beyond the scope of the thesis. I would also like to thank particularly all the students who have worked with me during my time at the University of Kassel. Their ideas have inspired me and their preliminary works were an important condition to complete this work. I would like to name at this point: Christoph Reinbold, Sven Behnke, Timm Eberwein, Aboubakar Ismaila, Thorsten Reimann, Jian Jun Wang, Mohammad Dawood, Andrea Schmitt, Mathias Eisenberg, and Franck Martin. The thesis would have not been possible to realize in this form without the support of the Danish TSO Energinet DK. For the generously share of data, thoughts and ideas as well as field experience at our meetings I would like to thank: Dr. Per Lund, Carsten Strunge, Dr. Torsten Lund, Hans Abildgaard and particularly Samuel Thomasson. They all pointed out the study direction and I am very thankful to all of them. At some occasions I had the luck to experience very inspiring discussions with Prof. Dr. Thierry Van Cutsem (University of Liège, Belgium), Prof. Dr. Michael Fette (University of applied sciences, Bielefeld, Germany), Dr. Walter Sattinger (SwissGrid, TSO Switzerland) and with Prof. Dr. István Erlich (University of Duisburg, Germany). I would like to thank them for their patience and for finding time for meetings. I would like to express my deepest appreciation to my parents, brothers and sisters and to Patrick Pouedogo for their love, support and encouragement throughout all these years. And definitely I must thank above all my wife Natalia and my both children Eva and Olga for their support, their limitless love and to have arranged themselves so well at home during the time dad was physically seldom present and spiritually often absent. Kassel, 09.04.2009 Yves Nguegan Abstract The changes which appeared during the last decades in the electricity markets led to an increased utilization and a higher loading of the electric transmission grids worldwide. The power transmission systems are nowadays operated on the brink of their technical limits and thus became more vulnerable to instabilities and cascading failures than before. The increase number of yearly power systems outages worldwide shows that the need of better monitoring concepts and tools fitted to the actual and future situation of power systems became urgent. Such systems will support the transmission system operators by the online assessment of the system state and permit the transition from a reacting system operation to a foresighted system operation. In this context, the use of synchronized phasor measurements is becoming an important tendency for the surveillance of the power systems. They are provided by phasors measurements units (PMUs) considered to be one of the most important measuring devices in the future of power systems. Defining the appropriate PMU system application is a utility problem that still must be studied and optimised. To make sense of the PMUs data, the system operators need tools that will help them infer the meaning of the data and to discern their interrelationships. In this thesis, the PMUs are turned to useful sources of real‐time data. They provided the required information needed by the grid operator on the actual system state and are combined with relevant data of the given system with the aim to early detect impending voltage instability. Furthermore the data are used to define the minimal voltage stability margin i.e. how far a given system operating state is from a state where voltage instability will occur. Thereby, a statement on the actual system operating state is made on the base of the actual active load transfer on each individual transmission line of the grid section considered. 5 The illustration of the power transfer situation on the lines is made on the base of a new developed mathematical function, in an active power‐voltage plane using the so‐called PU‐characteristics. A progressive calculation of the transfer function during the system operation leads to PU‐curves for each new operating point. The assessment of the voltage stability state is carried out by the coeval consideration of predefined criteria, from an optimized stability index determined, for the power transfer stability, and for the stability of the voltage profile at the line receiving end. The method developed in this work can be used for the monitoring of individual power lines of the power system as well as for the monitoring of transmission zones retaining several transmission lines, whereby it uses the advantage of the synchronization of the measurements from a minimal number of PMUs. The principles of the method build the foundations of the development of a tool for the analysis and the visualization on the voltage stability situation in power transmission systems using simulated or field PMU data sets. The exactness, the robustness and the applicability of the method is verified on a two‐bus test‐system as well as on the western Danish power system, wherefore a digital model was provided by the Danish transmission system operator Energinet DK. The optimal positioning of a minimal number of PMUs for the monitoring of the determined transmission zones within the section of the western Danish transmission grid considered, according to the principles of the developed method, is realized by means of an elaborated strategy for PMUs placement. The monitoring method proposed in this thesis described an innovative and efficient alternative for the online surveillance of the voltage stability in power transmission systems using PMUs data. The work realized shows on the example of an existing power system structure how measurements from distributed PMUs can be combined with relevant transmission lines parameters, and be handled to detect forthcoming voltage stability problems in power systems at early stage. 6 Kurzfassung Titel der Arbeit: „Online Identifikation und Überwachung der Spannungsstabilitätsreserve in elektrischen Übertragungsnetzen unter Verwendung zeitsynchronisierter Zeigermessungen“ Die aktuellen Veränderungen im Bereich der Elektrizitätswirtschaft führen weltweit zu einer erhöhten Ausnutzung sowie zu einer stärkeren Auslastung der Übertragungsnetze. Durch einen Betrieb dieser Netze nahe an ihren technischen Grenzen steigt damit die Wahrscheinlichkeit des Auftretens von Stabilitätsproblemen. Die weltweit zunehmende Anzahl an Netzausfällen zeigt, dass der Betrieb elektrischer Übertragungssysteme am Rand ihrer technischen Grenzen immer schwieriger zu realisieren ist. Daher nimmt die Notwendigkeit moderner Überwachungskonzepte, methoden sowie‐tools, angepasst bzw. anpassbar an die derzeitigen und zukünftigen Betriebsbedingungen, immer weiter