Page 23 - Decision Making Applications in Modern Power Systems

4 Decision Making Applications in Modern Power Systems

weighted sum method (WSM);
weighted product method (WPM);
AHP;
TOPSIS;
ELECTRE; and
preference ranking organization method for enrichment evaluation
(PROMETHE).
The hybrid methods are based on fuzzy, and two types of hybrid methods
are discussed in the chapter: fuzzy with AHP and fuzzy with TOPSIS. Each
method is described with detailed description of steps and a flowchart to
briefly describe the process to the readers. Each method and its utilization in
energy planning are cited from the literature.

1.2.1 Weighted sum method
This method is most commonly used for single-dimension problem. This
method is widely used in the structural optimization and energy planning.
The ease in the computation to select alternatives brings in the significance
of this method for utilization. The selection of alternatives is made by using
the following mathematical equation:
m
X
W s 5 v nm w m ð1:1Þ
n
where W s is the value of weighted sum, n is the number of alternative, and m
is the number of criteria. v nm is the function of the formulated vector and cal-
culated as the normalized value for nth alternative and mth criteria. w m is
the weight of mth criteria. W s is the score calculated for each alternative.
The best alternative is determined as max(W s ). This value of W s can also
be used for ranking the alternatives based on the scores. This method pro-
vides a basic estimate of the function and fails to integrate multiple prefer-
ences [24].

1.2.2 Weighted product method

Alike WSM, this method performs multiplication. The comparison of each
alternative is done by multiplying the ratios based on the number of criteria.
While multiplying, the ratio is raised to the power of a value equivalent to
the relative weight of the corresponding criteria. The comparison of the two
alternatives can be defined by the following mathematical expression:
m w i

P k p K i
W 5 L ð1:2Þ
P L p L i
i51