Transmission Expansion Planning in Deregulated Power ... - tuprints

6 Fuzzy Risk Assessment 85
6.4.1 Fuzzy Risk Assessment
Consider a network and assume we want to design a transmission expansion plan for a
specified planning horizon. Suppose steps 1-3 have been done and we are in the step 4 of
transmission expansion planning. In step 3, a market based criterion, say weighted standard
deviation of mean of LMP, has been computed for measuring the goodness of each expansion
plan in each scenario. Regrets are computed considering the occurrence degrees of future
scenarios. Now there is a table of regrets and the desire is to select the final plan. In this
section fuzzy multi criteria decision making is used for selecting the final plan [27]. In this
method a fuzzy appropriateness index is defined for selecting the final plan. The fuzzy
appropriateness index is computed by aggregation of importance degrees of decision criteria
and appropriateness degrees of expansion plans versus decision criteria.
6.4.1.1 Importance Weights of Decision Criteria
The presented decision criteria for risk assessment do not have the same degree of
importance. To represent the importance weights of decision criteria, the following linguistic
variables are used:
W = {VL, L, M, H, VH}
where VL, L, M, H, and VH are abbreviations of very low, low, medium, high, and very high
respectively. Degree of robustness of order 1 is very important in decision making. Maximum
and average of regret are also important. Degree of robustness of order 5 has the lowest
importance in decision making. Table 6.5 shows the selected importance weights for the
decision criteria. A triangular fuzzy number is assigned to each linguistic variable. Table 6.6
shows the triangular fuzzy numbers.
6.4.1.2 Appropriateness Degrees of Expansion Plans Versus Decision Criteria
Suppose
k
C i for i=1, …7 is the criterion which is used for measuring maximum regret (i=1),
average regret (i=2), degree of robustness of order 1 (i=3), …, and degree of robustness of
Table 6.5- Importance degrees of decision criteria
Criterion MR AR R1 R2 R3 R4 R5
Importance Weight H H VH H M L VL
Table 6.6- Triangular fuzzy numbers corresponding to linguistic variables
Linguistic Variable VL L M VH H
Fuzzy Number (0, 0, 1/4) (0, 1/4, 2/4) (1/4, 2/4, 3/4) (2/4, 3/4, 1) (3/4, 1, 1)