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50 Decision Making Applications in Modern Power Systems
each scenario, hourly random load demand is generated according to the
assigned PDF.
2.3.2.2 Scenario reduction
Initially, a large number of scenarios are generated by MCS. To simplify the
computation requirements the generated scenarios should be reduced. Some
of the different scenario reduction techniques are presented in Refs. [19,39].
In this chapter the fast forward selection algorithm is used. The base of this
method is to calculate the distance between the scenarios; therefore the most
possible scenarios with more probability are selected. The fast forward selec-
tion algorithm works as per the following steps [19]:
Step 1: Consider Ω as the initial set of the scenarios:
Ω 5 1; ...ω 1 ; ω 2 ; ...ω ; ...N Ω g. Compute the cost function υðω; ω Þ for
0
0
f
each pair of scenarios ω and ω in Ω. For example, two simulated wind
0
speeds corresponding to ω and ω 0th scenarios are 15 and 10 m/s, respec-
th
υ
tively; therefore the cost function ðÞ for these two scenarios is
υðω; ω Þ 5 15 2 10 5 5:
0
Step 2: Compute the distance between each pair of the scenarios as
follows:
N Ω
X
d ω 5 π ω υðω; ω Þ; ’ωAΩ ð2:21Þ
0
0
0
ω 51
ω 6¼ ω
0
where π ω 0 is the probability of ω 0th scenario. The scenario with minimum
d ω is selected (e.g., ω 1 ) and Ω 5 fω 1 g: Ω ½1 demonstrates the new set of
½1
s
s
the most probable scenarios in the first iteration. When ω 1 is selected, Ω ½1
j
is defined. Ω ½1 is equal to the initial set of the scenarios ΩðÞ except ω 1 ;
j
½1
therefore Ω 5 1; 2; ...; N ω g=ω 1 :
f
j
0
Step 3: Compute υðω; ω Þ for the new set of scenarios as
υ ðω; ω Þ 5 min υ ½i21 ðω; ω Þ; υ ½i21 ðω; ω i21 Þ ; ’ω; ω AΩ ½1
0
0
0
½2
j ð2:22Þ
½2
According to υ , the distance between each pair of scenarios is com-
puted as (2.21). Like Step 2, the scenario with minimum d ω is selected
(e.g., ω 2 ); therefore Ω s and Ω j are updated as
½2
Ω 5 fω 1 ; ω 2 g
s
f1; 2; .. .; N ω g
Ω 5 ð2:23Þ
½2
s
ω 1 ; ω 2
(the number of scenarios in Ω th
s
Step 4: Repeat Steps 2 and 3 until N Ω s
set) is equal to the desired number of scenarios.
