Several approaches have been proposed in the literature to analyze system v
oltage collapse, based on indices that can efficiently evaluate the load ma
rgin for which the system remains stable. All this discussion, including po
ssible methods of solution, is being carried out under deterministic assump
tions; load, generation and transmission are defined for each operating con
dition. The basic idea is to obtain the maximum amount of load the system c
an support, and what distance it is from this condition. In this work, the
voltage collapse problem is reviewed, considering the stochastic nature of
the load. A probabilistic methodology is developed to provide risk indices
of voltage collapse, based on a combination of the tangent vector and Monte
Carlo simulation methods. It is also shown how a probabilistic load flow a
nalysis can be adapted to evaluate the proposed risk indices. In order to i
llustrate the proposed approach, a modification of the IEEE reliability tes
t system is used and the applicability of the results to operation and expa
nsion planning is discussed. (C) 2000 Elsevier Science S.A. All rights rese
rved.