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Graph Laplacian Spectrum and Primary Frequency Regulation

Guo, Linqi and Zhao, Changhong and Low, Steven H. (2018) Graph Laplacian Spectrum and Primary Frequency Regulation. In: 2018 IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 158-165. ISBN 978-1-5386-1395-5.

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We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that the impact of network topology on a power system can be quantified through the network Laplacian eigenvalues, and such eigenvalues determine the grid robustness against low frequency disturbances. Moreover, we can explicitly decompose the frequency signal along scaled Laplacian eigenvectors when damping-inertia ratios are uniform across buses. The insight revealed by this framework partially explains why load-side participation in frequency regulation not only makes the system respond faster, but also helps lower the system nadir after a disturbance. Finally, by presenting a new controller specifically tailored to suppress high frequency disturbances, we demonstrate that our results can provide useful guidelines in the controller design for load-side primary frequency regulation. This improved controller is simulated on the IEEE 39-bus New England interconnection system to illustrate its robustness against high frequency oscillations compared to both the conventional droop control and a recent controller design.

Item Type:Book Section
Related URLs:
URLURL TypeDescription Paper
Zhao, Changhong0000-0003-0539-8591
Low, Steven H.0000-0001-6476-3048
Additional Information:© 2018 IEEE. The authors thank Janusz Bialek and Oleg Khamisov from Skoltech for helpful discussions. This work has been supported by Resnick Research Fellowship, Linde Institute Research Award, DOE through the ENERGISE program (Award #DE-EE-0007998), NSF grants through CCF 1637598, ECCS 1619352, CNS 1545096, ARPA-E grant through award DE-AR0000699 (NODES) and GRID DATA, DTRA through grant HDTRA 1-15-1-0003 and Skoltech through collaboration agreement 1075-MRA.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Resnick Sustainability InstituteUNSPECIFIED
Linde Institute of Economic and Management ScienceUNSPECIFIED
Department of Energy (DOE)DE-EE-0007998
Advanced Research Projects Agency-Energy (ARPA-E)DE-AR0000699
Defense Threat Reduction Agency (DTRA)HDTRA 1-15-1-0003
Record Number:CaltechAUTHORS:20190204-110323666
Persistent URL:
Official Citation:L. Guo, C. Zhao and S. H. Low, "Graph Laplacian Spectrum and Primary Frequency Regulation," 2018 IEEE Conference on Decision and Control (CDC), FL, USA, 2018, pp. 158-165. doi: 10.1109/CDC.2018.8619252
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92626
Deposited By: Tony Diaz
Deposited On:04 Feb 2019 20:50
Last Modified:16 Nov 2021 03:52

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