Transmission Expansion Planning in Deregulated Power ... - tuprints

8 **Transmission** **Expansion** **Plann ing** Under Uncerta

8.2 Model **in** detail

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

which is def**in**ed **in** chapter 7 for measur**in**g the goodness of expansion plans, is computed for

each plan **in** each scenario. The fuzzy appropriateness **in**dex is computed by aggregat**in**g

importance weights of stakeholders **in** decision mak**in**g, importance degrees of stakeholders’

desires from the viewpo**in**t of different stakeholders, and appropriateness degrees of

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

detail **in** the follow**in**g 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 **in**dex of plan k **in** scenario l which was computed

ap

**in** step 3. After comput**in**g the fuzzy appropriateness **in**dex for each plan **in** each scenario, we

k , l

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

f**in**al plan must be selected by tak**in**g **in**to account the occurrence degrees of future scenarios.

Due to vagueness **in** occurrence degrees of future scenarios, the follow**in**g l**in**guistic 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 l**in**guistic variable accord**in**g to

table 6.6.

Def**in**ition:

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

appropriateness **in**dex of plan k **in** scenario l and fuzzy appropriateness **in**dex 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 **in**dex of plan k **in** scenario l

k , l

ap

F fuzzy appropriateness **in**dex of the optimal plan of scenario l

op,

l

ap