Page 30 - Decision Making Applications in Modern Power Systems

Multicriteria decision-making methodologies Chapter | 1 9

Calculate normalized values from the initial decision matrix to get nor-
malized matrix. The normalized value (acv gh ) is given by

f gh
ð1:4Þ
acv gh 5 s ffiffiffiffiffiffiffiffiffiffiffiffi
a
P 2
f
gh
h51
where f gh is the value of the gth criterion function for the alternative Ah
(h 5 1,..., a and g 5 1,..., c).
Step 2. Obtain the weighted normalized decision matrix
Calculate the weighted normalized value v gh as
v gh 5 w c g acv gh ð1:5Þ
where the weight of the criterion/performance indicator g is such that
c
X
5 5 1 ð1:6Þ
w c g w c g
g51
The weight of the criteria/performance indicators can be determined by
using AHP method as described in the previous subsection or using special-
ized software packages such as Triptych or Expert Choice as given in [8].
Step 3. Obtain the possible solutions as positive ideal and negative ideal
First, the classification of the selected essential performance indicators
(EPIs)/criteria into two groups has to be done, which is as follows:
Maximum value/benefit criterion: The EPI whose maximum value is
sought among the alternatives is termed benefit criterion. The criteria, such
as renewable fraction, total electrical energy production, storage autonomy,
and grid sells whose maximum values are advantageous for the microgrid
alternatives, fall under this category.
Minimum value/performance/economic criterion: Minimum value crite-
rion is that whose low value is better for the microgrid alternatives. These
consist of economic indicators such as capital cost, net present cost, and
cost of electricity as well as performance criteria such as storage power
losses, excess electricity, and grid energy purchase whose minimal values
are sought.
1 2
After the classification of the EPIs/criteria, the PIA and NIA can be
obtained as
1 1 1
0
PIA 5 v ; ...; v 5 max h v gh =gAG ; min h v gh =gAGv ð1:7Þ
1 n
2
2

0
NIA 5 v ; .. .; v 2 5 min h v gh =gAG ; max h v gh =gAGv ð1:8Þ
1 n
where G is the EPIs/criteria representing the benefit criterion whose maxi-
0
mum values are pursued. Gv is the EPIs associated with the performance/
minimum value criterion.