Imperial College London > Talks@ee.imperial > Control and Power Seminars > Complex Frequency: A Geometric Approach to Unravel the Link between Power and Frequency in AC Power Systems

Complex Frequency: A Geometric Approach to Unravel the Link between Power and Frequency in AC Power Systems

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The conventional power system model for transient stability analysis is based on the assumption of quasi-steady-state phasors for voltages and currents. The crucial hypothesis on which such a model is defined is that the frequency required to define all phasors and system parameters is constant and equal to its nominal value. This model is appropriate as long as only synchronous machines regulate the system frequency through standard primary and secondary frequency regulators. In recent years, however, an increasing number of devices other than synchronous machines are expected to provide frequency regulation. These include, among others, distributed energy resources such as wind and solar. There is thus, from a modeling point of view, the need to define with accuracy the local frequency at every bus of the network.

The lecture consists of two parts. The first part presents a novel definition of “geometric frequency” based on the interpretation of the voltage as the “velocity” of a trajectory in a multidimensional space. The second part particularizes the geometric frequency for the electromechanical model of AC power systems for transient angle and voltage stability analysis. This special case leads to the definition of a “complex frequency” and a set of equations that link this new quantity with the active and reactive power injections at network buses. These relationships allow defining how device models and their controllers impact the frequency at their point of connection. This is particularly relevant in the context of low-inertia systems where the frequency support has to be provided by power electronic converters and devices other than conventional synchronous power plants. All concepts are illustrated through examples based on IEEE benchmark systems.

Bio of the Speaker: Federico Milano received from the Univ. of Genoa, Italy, the ME and Ph.D. in Electrical Eng. in 1999 and 2003, respectively. From 2001 to 2002 he was with the University of Waterloo, Canada, as a Visiting Scholar. From 2003 to 2013, he was with the University of Castilla-La Mancha, Spain. In 2013, he joined the University College Dublin, Ireland, where he is currently a Professor of Power Systems Control and Protection. He has authored 8 books and about 250 papers. He was elevated to IEEE Fellow in 2016 for his contributions to power system modeling and simulation, IET Fellow in 2017, and IEEE PES Distinguished Lecturer in 2020. He has been an editor of several international journals published by IEEE , IET, Elsevier, and Springer, including the IEEE Transactions of Power Systems and the IET Generation, Transmission & Distribution.

This talk is part of the Control and Power Seminars series.

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