Transmission Expansion Planning in Deregulated Power ... - tuprints

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Transmission Expansion Planning in Deregulated Power ... - tuprints

8 Transmission Expansion Planning Under Uncertainty and Vagueness 105

$8/MWhr a new transmission line is suggested as expansion candidate, 12 candidates will

result. The set of transmission candidates is as bellow:

{do nothing, line 1-3, line 1-4, line 1-7, line 1-8, line 5-3, line 5-4, line 5-7, line 5-8,

line 6-3, line 6-4, line 6-7, line 6-8 }

3) Computing fuzzy appropriateness index

Importance degrees of stakeholders’ desires from the viewpoint of transmission planners (Ui)

were computed by aggregating importance degrees of stakeholders in decision making (tables

7.2) and importance degrees of stakeholders’ desires from viewpoint of different stakeholders

(table 7.3) using equation (7.3). Importance degrees of stakeholders’ desires from the

viewpoint of transmission planners are given in table 7.4. Appropriateness degrees of

expansion plans versus stakeholders’ desire are computed for each scenario using the criteria

presented in section 7.2 and equations (7.1)-(7.2). Table 8.2 shows the appropriateness

degrees of expansion plans versus stakeholders’ desires in different scenarios. Network

charge and environmental impacts of expansion plans are the same in scenarios 1 to 4. Fuzzy

k

appropriateness index ( F ap ) for measuring the goodness of expansion plans versus

combination of all decision criteria is computed for each plan in each scenario by aggregating

importance degrees of stakeholders’ desires (tables 7.4) and appropriateness degrees of

expansion plans (table 8.2) using equation (7.7). Table 8.3 shows the fuzzy appropriateness

index of expansion plans in different scenarios. In this table the optimal plan of each scenario

was marked. All the ranking methods select the same optimal plan.

4) Computing the fuzzy regret and selecting the final plan using fuzzy risk assessment

Fuzzy regret of each plan in each scenario is computed by considering occurrence degrees of

future scenarios using equation (8.1). Table 8.4 shows the fuzzy regret of expansion plans in

different scenarios. Fuzzy risk assessment is applied to table 8.4 for selecting the final plan.

Maximum regret, average regret, and degree of robustness of order one to five are computed

for each plan. Maximum regret, average regret, and degree of robustness of order one to five

will be as columns 2-8 of table 8.5, if convex combination of right and left integral values

with α=0.5 is used for assigning a crisp value to fuzzy regrets. Fuzzy appropriateness index

( F ) is computed for selecting the final plan by aggregating importance degrees of decision

k

ap

criteria (table 6.5) and appropriateness degrees of expansion plans versus decision criteria

(columns 2-8 of table 8.5). Column 9 of table 8.5 shows the appropriateness indices. Convex

combination of right and left integral values of fuzzy appropriateness indices with α=0.5 are

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