Transmission Expansion Planning in Deregulated Power ... - tuprints

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Transmission Expansion Planning in Deregulated Power ... - tuprints

2 Transmission Expansion Planning Approaches 7

Min E

k

with:

k


= l

l k , l

υ f

(2.1)

k

E expected cost of plan k

l

υ occurrence degree of scenario l

f

k l

, cost of plan k in scenario l

2. Minimax regret criterion (risk analysis): in risk analysis the best solution is

determined by minimizing the regret [14]-[22]. Regret is a measure of risk.

Regret of plan k in scenario l is defined as difference between the cost of plan k in

scenario l and cost of the optimal plan of scenario l, i.e.:

r

k,

l k , l op,

l

= f − f

(2.2)

with:

k l

r , regret of plan k in scenario l

f

op l

, cost of the optimal plan of scenario l

In risk analysis the plan that minimizes the maximum weighted regret over all

future scenarios is selected as the final plan, i.e.:

Min

k

l k , l { Max(

r ) }

l

υ (2.3)

3. Laplace criterion: according to this criterion the plan that minimizes the sum of

costs over all scenarios is selected as the final plan [14].

4. Von Neumann-Morgenstern criterion: this criterion is extremely pessimist and

believes that the most unfavorable scenario is bound to occur [14]. According to

this criterion the plan that minimizes the maximum cost over all scenarios is

selected as the final plan, i.e.:

Min

k

k , l { Max(

f ) }

l

(2.4)

Alternatively, an extremely optimist criterion can be also used for selecting the

final plan, i.e.:

Min

k

k , l { Min(

f ) }

l

(2.5)

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