Transmission Expansion Planning in Deregulated Power ... - tuprints

6 Fuzzy Risk Assessment 86
order 5 (i=7) of plan k. Smaller maximum regret and smaller average regret indicate better
situation. Therefore, inverse of these criteria are used to measure the appropriateness degrees
of expansion plans versus maximum and average regret. Greater degree of robustness of order
m for m=1, …, 5 indicate better situation. Therefore, these criteria are used to measure the
appropriateness degrees of expansion plans versus degree of robustness of order m. Suppose
k
A i is the appropriateness degree of plan k versus decision criterion i, then:
A = 1/
C
for i=1, 2 (6.1)
k
i
k
i
k
i
k
i
C A = for i=3, …, 7 (6.2)
For aggregating the appropriateness degrees of expansion plans versus different decision
criteria, the appropriateness degrees must be comparable versus different decision criteria.
Therefore,
k
A i is normalized on its maximum value over different expansion plans:
k k
k
N = A / max(
A )
(6.3)
i
with:
i
k
i
k
N i normalized appropriateness degree of plan k versus decision criterion i
6.4.1.3 Fuzzy Appropriateness Index
Let Wi∈W be the importance weight of decision criterion i. Appropriateness degree of plan k
versus combination of all decision criteria is equal to weighted mean of
k
k
k
[ ( ) ( ) ... ( ) ] N W
N W N W ⊗ ⊕ ⊗ ⊕ ⊕
k 1
F 1 1 2 2
N ⊗
c
N
with:
ap Ndc
dc
k
N i , i.e.:
= (6.4)
k
F ap fuzzy appropriateness index of plan k versus combination of all decision criteria
N dc number of decision criteria
⊕ fuzzy addition operator
⊗ fuzzy multiplication operators
Fuzzy arithmetic operations are defined using α-cuts of fuzzy intervals [74]-[75].
6.4.1.4 Selecting the Final Plan
The expansion plan that has the greatest fuzzy appropriateness index is selected as the final
plan. To find the plan which has maximum fuzzy appropriateness index, fuzzy