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 102

8.2 Model in detail

Steps 1 and 2 are the same as chapters 5 and 6. In step 3 the fuzzy appropriateness index,

which is defined in chapter 7 for measuring the goodness of expansion plans, is computed for

each plan in each scenario. The fuzzy appropriateness index is computed by aggregating

importance weights of stakeholders in decision making, importance degrees of stakeholders’

desires from the viewpoint of different stakeholders, and appropriateness degrees of

expansion plans versus stakeholders’ desires using equations (7.1)-(7.7). Step 4 is described in

detail in the following subsections. Step 5 is the same as chapters 5 and 6.

8.2.1 Fuzzy Regret and Risk Assessment

k,

l

Suppose F is the fuzzy appropriateness index of plan k in scenario l which was computed

ap

in step 3. After computing the fuzzy appropriateness index for each plan in each scenario, we

k , l

have a table of fuzzy appropriateness indices, i.e. F for k = 1,…, Np, and l = 1,…, Ns. The

final plan must be selected by taking into account the occurrence degrees of future scenarios.

Due to vagueness in occurrence degrees of future scenarios, the following linguistic variables

are used to represent the occurrence degrees of scenarios:

ap

Z = {VL, L, M, H, VH}

where VL, L, M, H, and VH are abbreviations of very low, low, medium, high, and very high

respectively. A triangular fuzzy number is assigned to each linguistic variable according to

table 6.6.

Definition:

Weighted fuzzy regret of plan k in scenario l is equal to difference between the fuzzy

appropriateness index of plan k in scenario l and fuzzy appropriateness index of optimal

plan of scenario l multiplied by the occurrence degree of scenario l:

with:

k , l l R Z ⊗

k,l

= (F F )

(8.1)

op,

l

ap

ap

k , l R fuzzy regret of plan k in scenario l

Z l ∈Z occurrence degree of scenario l

F fuzzy appropriateness index of plan k in scenario l

k , l

ap

F fuzzy appropriateness index of the optimal plan of scenario l

op,

l

ap

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