Enhanced Power System Security Assessment Through Intelligent Decision Trees - Complex System Modelling and Control Through Intelligent Soft Computations - page 333

Optimal power flow: Initial states for every case is obtained using OPF

￿

Contingency assessment: Using steady-state or time-domain tools contingency
events are simulated, and post-contingency performance measures are obtained.

￿

The machine learning methods (Wehenkel 1998 ; Witten and Frank 2000 ) are
used to extract a high level information, or knowledge from a huge database
containing post-contingency responses obtained from the database generation
step. These machine learning or data mining techniques are broadly classi

ed as:

Unsupervised learning: Those methods which do not have a class or target
attribute. For example, association rule mining can be used to

￿

nd the corre-
lation between various attributes. Clustering methods such as k-means, EM etc.
are generally used to discover classes.

Supervised learning: Those methods that have a class or target attribute, such as
classi

￿

cation, numerical prediction etc., and use the other attributes (other
observable variables) to classify or predict class values of scenarios. For
example, na ve bayes, decision trees, instance based learning, neural network,

support vector machine, regression etc.

ï

Among these, decision tree based inductive learning method serves as an
attractive option for preventive-control approach in power system security assess-
ment (Zhou et al. 1994 ; Wehenkel 1997 ; Zhou and McCalley 1999 ; Niimura et al.
2004 ; Wehenkel et al. 2006 ). It identifies key pre-contingency attributes that

in uence the post-contingency stability phenomena and provides the corresponding

acceptable scenario thresholds. Based on it, security rule or guidelines are devel-
oped, which can be deductively applied to ascertain any new pre-contingency
scenario

fl

s post-contingency performance. Information required for building deci-
sion tree are:

'

A training set, containing several pre-contingency attributes with known class
values

￿

The classi cation variable (i.e., class attribute with class values such as “ secure ”

￿

or “ insecure ” ), which could be based on post-contingency performance indices

An optimal branching rule, i.e., a rule to find critical attribute

￿

A stopping rule, such as maximum tree length or minimum instances

￿

es new
instances well and produces simple to interpret rules. Ideally we would like to get
the best model that has no diversity (impurity), i.e., all instances within every
branch of the tree belong to the same class. But due to many other uncertainties or
interactions that have not been accounted for in the model, there would be some
impurity (i.e., non-homogeneous branch) at most of the levels. So the goal is to
select attributes at every level of branching such that impurity is reduced. There are
many measures of impurity, which are generally used as optimal branching criteria
to select the best attribute for splitting. Some of those are entropy, information gain,
Gini index, gain ratio etc.

The aim of inducing a decision tree is to obtain a model that classi