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Ta b l e 1 . Constraints of the 10-unit system for daily scheduling
Units Constraints
1
u t 1 = 1 r t = 1to24 (must-run)
initial status T 2 = 1 (already online for an hour)
2
MU T 2 = 8
initial status T 3 = 2 (already offline for 2 hours)
3
MDT 3 = 6
u t 4 = 1 r t = 6to20 (must-run)
4
u t 6 = 0 r t = 1to7 (must-off)
6
u t 10 = 0 r t = 1to24 (must-off)
10
process and the THMCA process to ensure that the positions of all companies are fea-
sible and near-optimal solutions for the UC problem.
4.1
Pre-scheduling Using Expert Rules(ER) to Generate Initial Competition
Companies
Pre-scheduling Using to Determine the Initial Status of Units. In this paper, pre-
scheduling expert rules are developed to guarantee not only that it can satisfy some
constraints in advance, but also that it can reduce the problem dimensions.
ER1: For a must-run unit, assign online status “1” between t =[ t run
i , begin , t run
i , end ].
ER2: For a must-off unit, assign offline status “0” between t =[ t of f
i , begin , t of f
i , end ].
ER3: Examine if the initial status T i satisfies the minimum up/down time constraints
(12) and (13). If not, continue the initial status u i until it does.
To demonstrate the pre-scheduling using expert rules, consider a popular test system
with 10 units over a 24 hour scheduling horizon. The constraints of the units are given
in Table 1.
Competition Company Position Definition. The position of a competition company
in integer-coded THMCA for a UC problem is composed of a sequence of online
or offline cycle durations of the units during the scheduling horizon. A positive in-
teger in the Company i vector represents duration of continuous online status of that
unit, while a negative one represents duration of continuous offline status. Accord-
ing to a general daily load profile with two peaks, the maximum number of online
or offline cycles for peak load to be units is 5. Therefore, the number of schedul-
ing cycles is set 5 and a competition company in THMCA implementation for daily
scheduling is a vector with 5
×
N unit elements. The remaining blanks represented by
”inthe Company vector are filled with randomly generated integer numbers ac-
cording to (5).The encoding of a company comprising online or offline cycle dura-
tion of units and the unit commitment schedule is Company =[24,0,0,0,0,7,
,
,
,
,-
4,
,
,
,
,
,15,
,
,
,
,
,
,
,
,-7,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,-24,0,0,0,0].
4.2
Constraints Handling Using Expert System
System Constraints. Combining the system power balance equality (10) and spinning
reserve requirement inequality (11) with the generation limits inequality (5) enables the
coupling constraints to be integrated and modified as shown in (23) and (24):
 
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