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Two algorithms for obtaining sparse loop matrices

This paper deals with the problem of obtaining a linearly independent set of loop matrix equations, whose nonzero pattern is as sparse as possible. Unlike existing procedures, based on trees and associated fundamental loops, the two algorithms proposed in this paper attempt to find as short as possible loops by means of systematic breadth-first searches. Linear independence of the resulting loops is assured by forcing each loop to contain a characteristic branch that cannot belong to future or past loops, respectively. Such a branch plays the role of links in fundamental loops, providing more flexibility in the way loops are closed. Experimental results on benchmark systems show that the proposed methods yield loop matrices that are much sparser than those provided by existing methods.