IJPAM: Volume 47, No. 2 (2008)

NONLINEAR CONTROLLABILITY OF SINGULARLY
PERTURBED MODELS OF POWER FLOW NETWORKS

Steven Ball$^1$, Ernest Barany$^2$, Steve Schaffer$^3$, Kevin Wedeward$^{4}$
$^1$Science Applications International Corporation
Columbia, MD, USA
email: steven.c.ball@saic.com
$^2$Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM, USA
email: ebarany@nmsu.edu
$^3$Department of Mathematics
New Mexico Institute of Mining and Technology
Socorro, NM, USA
email: schaffer@nmt.edu
$^4$Department of Electrical Engineering
New Mexico Institute of Mining and Technology
801 Leroy Place, Socorro, NM 87801, USA
email: wedeward@nmt.edu


Abstract.A method based on differential geometric control theory is presented to provide insight into how nodes (busses) of a power network affect each other. The network model considered is derived from a singular perturbation of the standard power flow equations. Accessibility properties of the model are investigated, and it is shown that a network with chain topology is feedback linearizable. This result is illustrated through computer simulation and control of an example network. The findings are extended to input-output linearization of large power networks where full feedback linearization is not feasible. Simulation results are shown for control across an IEEE test system with 118 busses.

Received: June 11, 2008

AMS Subject Classification: 93B05, 93B52, 58E25

Key Words and Phrases: power networks, accessibility, feedback linearization, control

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 2