Page 31 - Decision Making Applications in Modern Power Systems

10 Decision Making Applications in Modern Power Systems

Step 4. Determine the geometrical separation measures for alternatives
Compute the geometrical separation measures of the alternatives using
1 2
the PIA and NIA solutions obtained from Step 3.
The geometrical separation measure (S 1 ) based on the PIA 1 of each
hðPIAÞ
alternative is given by the following equation:
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c
u X

S 1 5 u v gh 2v g 2 ð1:9Þ
t
hðPIAÞ
g51
Similarly, from the negative ideal, the separation measure (S 2 )is
hðNIA 2 Þ
given as
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u c
2 u X 2
S 2 5 t v gh 2v g 2 ð1:10Þ
hðNIA Þ
g51
Step 5. Find out the relative closeness to the ideal solution for
alternatives

The relative closeness (Cl ) of the alternative from the ideal solution can
h
be calculated using the following equation:
S 2
2
hðNIA Þ
h
Cl 5 ð1:11Þ
S 1 1 1 S 2
hðPIA Þ hðNIA 2 Þ

The numeric value of Cl lies between 0 and 1, where 0 signifies the
h
worst and 1, the best possible solution.
Step 6. Determine the ranking of alternatives based on preference
order

Once the value of Cl for each alternative has been determined, arrange
h
them in the descending order and rank the alternatives. The alternative

attaining the highest values of Cl should be ranked first and proposed as the
h
best possible solution. Table 1.2 illustrates a few studies based on TOPSIS
with its applicability to design and evaluation of energy system.
1.2.5 Elimination and choice translating reality
ELECTRE also called elimination and choice translating reality was pro-
posed by Benayoun et al. in 1966 [52]. The method finds its application in
energy, financial and business management, information technology and
communication, logistics and transportation engineering. This is an outrank-
ing method as it develops a binary association between alternatives w.r.t. to
all criteria [53]. The literature gives several forms of ELECTRE. A brief
description of this method is given in the following subsections [54].