Enhanced Power System Security Assessment Through Intelligent Decision Trees - Complex System Modelling and Control Through Intelligent Soft Computations - page 340

speci c distribution of loading conditions in the hyperspace was not shown, and

doubts were also cast over its applicability to a large power system with dimension
of the hyperspace in 100 s, as will be dealt in the case study of this chapter.
This chapter proposes a sampling space characterization method that uses Latin
hypercube sampling (LHS) of homothetic stress directions and linear sensitivities,
which promises to reduce the computational requirements. Using this approach the
multivariate load state space for a given historical distribution is quickly charac-
terized, under various combinations of Static Var Compensator (SVC) and gener-
ator unavailability states. The boundary identi

cation method is described in
Sect. 4.1.1 , while the stress direction sampling approach (central piece of the
proposed state space characterization method) is described in Sect. 4.1.2 .

4.1.1 Fast Boundary Region Identi cation in Multivariate Space

For voltage stability related problems, voltage stability margin (VSM) can be used
as the performance measure and hence voltage stability margin sensitivities (Greene
et al. 1997 ; Long and Ajjarapu, 1999 ; Krishnan et al. 2009 ) with respect to oper-
ational parameters such as individual loads, generator availability, etc. can be used
to identify the boundary. VSM is de

ned as the amount of additional load in a
specific pattern of load increase (also termed as stress direction) that would cause
voltage instability. It is computed using the continuation power

ow (CPF) method.
The assumption of a stress direction is important to perform CPF for identifying
the voltage collapse point in that direction. Figure 4 depicts existence of several
homothetic stress directions for load increase in the two dimensional space de

fl

ned

by loads A and B. The line Load A + Load B = C de nes various basecases with

different inter-node repartitions among loads A and B for the same system load C.
These basecases de ne various homothetic stress directions in the state space, as

shown by the various lines from the origin.
The same concept of multiple stress directions is shown in a 3-D load space in
the left-hand side of Fig. 5 . CPF is performed on these basecases along their

Fig. 4 Multiple homothetic
stress directions