Enhanced Power System Security Assessment Through Intelligent Decision Trees - Complex System Modelling and Control Through Intelligent Soft Computations - page 339

4.1 Stage I Boundary Region Identi cation

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This section develops a LHS method that uses linear sensitivity information to trace
the boundary region in a computationally effective manner.
The sampling procedure is computationally very burdensome for a very large
dimensional sampling space, especially if the individual load s mutual correlation

information is taken into account. So, in order to provide a more reasonable sampling
space which would reduce the computation, typically a very strong assumption is
made that all loads vary in proportion to the total (also known as homothetic load
distribution), so that the load at any bus i maintains a constant percentage of the total
load, i.e., PT0 Li ¼ P Li0 = P T ð Þ P T , where P Li0 and P T0 are the bus i load and total load in
the reference or base case; and PT Li and P T are for any new loading scenario. In the
language of voltage stability analysis, these assumptions amount to de

'

ning a par-
ticular stress direction through the space of possible load increases. Therefore, when
a single stress direction is assumed, the uncertainty in load can be simply expressed in
terms of the total system load (PT). T ). So in this case, the sampling is performed only in
the univariate space of total system load (PT) T ) to identify the boundary region.
Generally, this assumption of individual loads having a homothetic distribution
along the most probable stress direction is typically done in studies to reduce the
computational burden. However, in reality the individual loads may vary along
multiple stress directions each having substantial likelihood, and therefore con ning

to a single stress direction may result in incomplete characterization of the entire load
state space. So it is important to consider the multivariate distribution of loads to
capture the boundary region effectively. Otherwise, single stress direction assump-
tion will identify only some portion of boundary, and consequently the rules derived
from such a database may face challenges when applied to realistic operating con-
ditions. Through the strati ed sam-

pling), we would want to obtain the boundary region in the multi-dimensional load
sampling state space, and then apply the importance sampling to bias the sampling
towards this boundary region, which would capture maximum information content
including the relative likelihood of sampled operating conditions.
In order to accomplish this, it is necessary to capture inter-load correlations from
historical information while sampling from multivariate load distribution to create
the training database, where such

ed sampling stage (LHS is one kind of strati

finer details will have crucial impact in a decision

tree find rules suitable for realistic scenarios. While we can be assured of

more information content from this approach, it is likely to increase computing
requirements; especially for boundary region identi

' s ability to

ed sam-
pling. Singh and Mitra ( 1997 ) proposed a state space pruning method to identify the
important region in a discrete parameter space composed of generation levels and
transmission line capacities under a single load level for system adequacy assess-
ment. Yu and Singh ( 2004 ) proposed self-organized mapping together with MCS to
characterize the transmission line space. Dobson and Lu ( 2002 ) proposed a direct
and iterative method to

cation using strati

find the closest voltage collapse point with reduced com-
putation in the hyperspace de ned by loads. But the method ' s applicability to a