Enhanced Power System Security Assessment Through Intelligent Decision Trees - Complex System Modelling and Control Through Intelligent Soft Computations - page 341

Fig. 5 Multiple homothetic stress directions in 3-D and boundary identi cation

intrinsic load increase directions, and the maximum loadability along each stress
direction is computed. From these the boundary limits, {P Lmin ,P Lmax }, in the total
system load space is found, as shown in the right-hand side of Fig. 5 . This limit in
the hyperspace is subject to variation due to the in

uence of discrete variables such
as SVC and generator unavailability states. The effect of these two variables is
estimated using VSM sensitivities with respect to real and reactive power injections
along every stress direction, and is given by the Eq. ( 2 ). Usage of such linear
sensitivities signi

fl

cantly reduces the computational burden in characterizing a
multi-dimensional operational parameter state space.

P sv L ¼ Q svc

dVSMdQ svc ð 2 Þ

D

P svc
L

where D is the change in boundary limit in a particular stress direction due to

uence of SVC unavailability, Q svc is the amount of unavailable SVC reactive
power at the collapse point, and dVSMdQ svc is the linear sensitivity of voltage
stability margin with respect to reactive power injection at the SVC node, which is
computed as a by-product of CPF study in that particular stress direction.
Finally, the boundary limits in the total system load space is identi

the in fl

ed, subject to

these discrete variable in fl uences. The key in realizing the computational bene tin

boundary region identi cation lies in the manner in which the multiple homothetic

stress directions are sampled from the historical data.

4.1.2 Sampling Homothetic Stress Directions Using Latin Hypercube
Method

Latin Hypercube Sampling (LHS) is very prevalently used in Monte Carlo based
reliability studies in many

fields. LHS of multivariate distribution is performed by