Modeling and control of wave propagation in a ring with applications to power grids

Lea Sirota*, Anuradha M. Annaswamy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper concerns the treatment of swing dynamics in a power grid using a continuous approach. Rather than addressing the problem as oscillations in a discrete system, we model the swing dynamics as a propagating electro-mechanical wave using a partial differential equation. A ring geometry with a one-dimensional wave equation is used to analyze the underlying dynamics. A control method is proposed to damp the system dynamics using the concept of Interior Wave Suppression. Unlikedomains withboundaries such as strings, any concentrated input to the ring generates waves in two directions, thereby preventing total absorption. Using a judicious combination of concentrated control inputs, it is shown that a near unidirectional wave can be generated, with minimal backwaves. The resulting closed-loop system is proved to be stable. The overall modeling and control methods are shown to be implementable in a power grid using phasor measurement units as sensors and flexible ac transmission system devices, such as thyristor controlled series compensator, as actuators. How, the proposed methods of modeling and control can be applied to a network of rings is briefly discussed. Numerical simulations are carried out to validate the theoretical derivations.

Original languageEnglish
Article number8585095
Pages (from-to)3676-3689
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - Sep 2019
Externally publishedYes


FundersFunder number
Air-Force Research Laboratory
Ford-MIT Alliance
National Science Foundation1745547, EFRI-1441301, ECCS-1135815
U.S. Department of Energy


    • Swing oscillation damping
    • Unidirectional wave generation
    • Wave equation on a ring
    • Wave suppression


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