Premium
On the determination of the solutions and maximum admissible power of the load flow equation via LMIS
Author(s) -
Chesi G.,
Hung Y. S.
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.414
Subject(s) - mathematics , eigenvalues and eigenvectors , subspace topology , computation , upper and lower bounds , power (physics) , flow (mathematics) , convex optimization , regular polygon , mathematical optimization , mathematical analysis , algorithm , geometry , physics , quantum mechanics
It is well‐known that the load flow equation plays a key role in power systems. This paper investigates the load flow equation addressing two fundamental problems, namely the determination of the solutions of this equation in a given region of interest, and the computation of the maximum admissible power for which this equation has a solution in such a region. For the first problem, it is shown that the sought solutions can be computed by solving an eigenvalue problem (EVP), i.e. a convex optimization problem with linear matrix inequality (LMI) constraints, and by looking for vectors with special structure into a linear subspace. For the second problem, it is shown that an upper bound of the sought maximum admissible power can be found by solving another EVP, moreover a sufficient and necessary condition for establishing the tightness of the found upper bound is provided. The proposed methodology is illustrated by some numerical examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society