Transmission Expansion Planning in Deregulated Power ... - tuprints

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Transmission Expansion Planning in Deregulated Power ... - tuprints

7 Stakeholders’ Desires 96

[ ( X ⊗Y

) ⊕ ( X ⊗Y

) ⊕...

⊕ ( X Y ) ]

1

= 1 i1

2 i2

Nst

i N for i=1,…, Nsd (7.3)

st

N

U i


st

with:

U i importance degree of desire i from the viewpoint of transmission planners

Nst

number of stakeholder groups

Fuzzy arithmetic operations are defined using α-cuts of fuzzy intervals [74]-[75]. If Xj and Yij

are substituted by triangular fuzzy numbers i.e. Xj=(aj, bj, cj) and Yij=( oij, pij, qij), U i is

approximated by (li, mi, ni) [27].

where:

1

Nst

li = ∑ N st j=

1

1

o

Nst

mi = ∑ N st j=

1

1

Nst

ni = ∑ N st j=

1

ij

q

p

ij

a

ij

c

j

b

j

, i=1,…, Nsd (7.4)

j

, i=1,…, Nsd (7.5)

, i=1,…, Nsd (7.6)

Appropriateness degree of plan k versus combination of all decision criteria is equal to

weighted mean of

k

N i , i.e.:

k

k

k

[ ( U ⊗ N ) ⊕ ( U ⊗ N ) ⊕...

⊕ ( U N ) ]

1

= 1 1 2 2

Nd

N for k=1, …, Np (7.7)

N

k Fap ⊗

sd

sd

with:

k F ap fuzzy appropriateness index of plan k versus combination of all decision criteria

Np

with considering importance degree of stakeholders in decision making

number of expansion plans

7.4.2 Selecting the Final Plan

The expansion plan which has the greatest fuzzy appropriateness index is the optimal plan. As

chapter 6, convex combination of left and right integral value [27], [75]-[76], centroid indices

[77], and extended centroid index [77] are used for ranking fuzzy numbers.

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