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mode and the start-up cost for such units is small. Hence, the start-up cost STi i can
be modeled by the following function system:
OFF
i
HSC i si MDTi i s
MDT i þ
SC i
ST i ¼
ð
3
Þ
OFF
i
CSC i si
s
MDT i þ
SC i
with:
a i , b i and c i Coef
cients of the production cost,
P ih
Active power generated by the ith unit hth hour, i =1,2,3,
, N g
and h =1,2,3,
., H
U ih
On/off status of the ith production unit at the hth hour, U ih = 0 for the
Off status of one generating unit and U ih = 1 for the operating status
of one generating unit,
HSC i
Hot start-up cost of the ith unit,
CSC i
Cold start-up cost of the ith unit,
MDT i
Minimum down-time of the unit i,
τ i OFF
Continuously off-time of unit i,
SC i
Cold start time of unit i,
N g
Number of generating units,
H
Time horizon for UC (h).
Unit Commitment is a highly constrained optimization problem. Different power
systems have a different set of imposed constraints. The most common can be
divided into two categories. The
first, called unit constraints, represents the con-
straints that are applied to the single units; the second type, system constraints,
contain those that are applied to the whole power system.
System Constraints
￿
Power balance constraints:
At any time over the planning horizon the total real power generation of the
system must be equal to the total demand.
-
N g
X
P ih U ih
P dh
P Lh ¼
0
ð
4
Þ
i¼1
Spinning reserve constraints
-
X
N g
U i P i
P dh þ
P rh þ
P Lh
ð
5
Þ
i¼1
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