Elsevier

Automatica

Volume 133, November 2021, 109861
Automatica

Brief paper
Frequency-driven market mechanisms for optimal dispatch in power networks

https://doi.org/10.1016/j.automatica.2021.109861Get rights and content
Under a Creative Commons license
open access

Abstract

This paper studies real-time bidding mechanisms for economic dispatch and frequency regulation in electrical power networks described by topologies with edge-disjoint cycles. We consider a market administered by an independent system operator (ISO) where a group of strategic generators participate in a Bertrand game of competition. Generators bid prices at which they are willing to produce electricity. Each generator aims to maximize their profit, while the ISO seeks to minimize the total generation cost while respecting line flow limits and regulate the frequency of the system. We consider a continuous-time bidding process coupled with the swing dynamics of the network through the use of frequency as a feedback signal for the negotiation process. We analyze the stability of the resulting interconnected system, establishing frequency regulation and the convergence to a Nash equilibrium and optimal generation levels. Simulations illustrate our theoretical findings.

Cited by (0)

Ashish Cherukuri is an Assistant Professor in Engineering and Technology Institute Groningen, University of Groningen, Netherlands. Previously, he was a Postdoctoral Researcher at the Automatic Control Laboratory, ETH Zürich, Switzerland. He received the B.Tech degree in Mechanical Engineering from the Indian Institute of Technology, Delhi, India, in 2008, the M.Sc degree in Mechanical Engineering from ETH, Zürich, Switzerland, in 2010, and the Ph.D. degree in Mechanical and Aerospace Engineering at the University of California, San Diego, CA, USA, in 2017. His research interests include distributed optimization, game theory, optimization under uncertainty with applications in power and transportation networks.

Tjerk Stegink received his Ph.D. degree (2018, cum laude) in Modeling and Nonlinear Distributed Control of Power Systems at the Engineering and Technology Institute, Faculty of Mathematics and Natural Sciences, University of Groningen, the Netherlands. He received his B.Sc. (2012) in Applied Mathematics and M.Sc. (2014, cum laude) in Systems, Control and Optimization from the same university. Since 2018 he works as an OR Engineer at ORTEC — Optimize Your World.

Claudio De Persis is a Professor with the Engineering and Technology Institute, University of Groningen, The Netherlands. He received the Laurea and Ph.D. degree in Engineering in 1996 and 2000 both from the University of Rome ”La Sapienza,” Italy. His main research interest is in automatic control and its applications.

Arjan van der Schaft received the (under)graduate and Ph.D. degrees in Mathematics from the University of Groningen, the Netherlands, and joined the University of Twente, where he was appointed as full professor in Mathematical Systems and Control Theory in 2000. In 2005 he returned to his Alma Mater as professor in Mathematics.

Books authored by him include Variational and Hamiltonian Control Systems (1987, with P.E. Crouch), Nonlinear Dynamical Control Systems (1990, 2016, with H. Nijmeijer), L2-Gain and Passivity Techniques in Nonlinear Control (1996, 2000, 2017), An Introduction to Hybrid Dynamical Systems (2000, with J.M. Schumacher), and Port-Hamiltonian Systems: An Introductory Overview (2014, with D. Jeltsema).

Arjan van der Schaft is Fellow of the Institute of Electrical and Electronics Engineers (IEEE), Fellow of the International Federation of Automatic Control (IFAC), and was the 2013 recipient of the 3-yearly awarded Certificate of Excellent Achievements of the IFAC Technical Committee on Nonlinear Systems. He was Invited Speaker at the International Congress of Mathematicians, Madrid, 2006.

Jorge Cortés received the Licenciatura degree in mathematics from Universidad de Zaragoza, Zaragoza, Spain, in 1997, and the Ph.D. degree in Engineering Mathematics from Universidad Carlos III de Madrid, Madrid, Spain, in 2001. He held postdoctoral positions with the University of Twente, Twente, The Netherlands, and the University of Illinois at Urbana-Champaign, Urbana, IL, USA. He was an Assistant Professor with the Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, USA, from 2004 to 2007. He is currently a Professor in the Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA. He is the author of Geometric, Control and Numerical Aspects of Nonholonomic Systems (Springer-Verlag, 2002) and co-author (together with F. Bullo and S. Martínez) of Distributed Control of Robotic Networks (Princeton University Press, 2009). He is a Fellow of IEEE and SIAM. His research interests include distributed control and optimization, network science, nonsmooth analysis, reasoning and decision making under uncertainty, network neuroscience, and multi-agent coordination in robotic, power, and transportation networks.

This work is supported by the NWO (Netherlands Organisation for Scientific Research) Uncertainty Reduction in Smart Energy Systems (URSES) programme and the ARPA-e, United States of America Network Optimized Distributed Energy Systems (NODES) program. The material in this paper was partially presented as Stegink et al. (2018) at the 2018 Power Systems Computation Conference, June 11–15, 2018, Dublin, Ireland. This paper was recommended for publication in revised form by Associate Editor Gurdal Arslan under the direction of Editor Ian R. Petersen.