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strategy with fast computing speed. But a large storage capacity is required to com-
plete the computation. Shuffled frog leaping algorithm (SFLA) combines the benefits
of both the genetic-based memetic algorithm and the social behavior-based PSO al-
gorithm. However, most of these methods suffer from the curse of dimension when
applied to a modern large-scale power system with heavy constraints. Moreover, these
methods commonly get stuck at a local optimum rather than reaching the global opti-
mum. Even small percentage reduction in fuel costs typically leads to considerable sav-
ings for electric utilities. In this paper, a new fast approach called two-layer hierarchical
market competition algorithm (THMCA) combined with expert system is proposed to
efficiently solve the constrained UC problem.
2
Formulation of the Unit Commitment (UC) Problem
The UC problem is to determine the start-up and shut-down schedules and outputs of
generation units to meet the dynamic demand load during the scheduling horizon at a
minimal total cost. In general, the fuel cost(
FC
)ofthe
i
th generator is described as:
FC
i
(
P
i
)=
a
i
+
b
i
P
i
+
c
i
(
P
i
)
2
,
i
= 1
,
2
,
···
,
N
unit
(1)
where
a
i
,
b
i
,and
c
i
are fuel cost coefficients of the
i
th unit,
N
unit
represents the number
of units,
t
is the index for time intervals,
P
i
is the power output of the
i
th unit.
The total operating cost is expressed as the sum of fuel costs, start-up costs, and
shutdown costs of the generating units:
T
t
=1
N
unit
i
=1
FC
i
(
P
i
)
u
i
+
SUC
i
(1
−
u
t
−
1
)
u
i
+
SDC
i
u
t
−
1
u
i
)
TFC
=
(1
−
(2)
i
i
SUC
i
=
SUC
ihot
if T
i
∈
[
MDT
i
,
MDT
i
+
T
icold
]
(3)
T
i
≥
SUC
icold
if
−
MDT
i
+
T
icold
where
SUC
i
and
SDC
i
are start up and shut down costs respectively.
u
i
is the status of
the
i
th unit at time
t
.
SUC
ihot
is the hot start-up cost,
SUC
icold
is the cold start-up cost
and
T
icold
is the cold start time.
u
i
= 1
or u
i
= 0
i f
online
if
of fline
(4)
The units and system constraints of UC problem, which must be satisfied during the UC
scheduling period, are as follows:
The
i
th online unit generation limits:
P
i
min
≤
P
i
≤
P
i
max
(5)
where
P
i
min
and
P
i
max
are minimum and maximum output power of
i
th online unit.
For security requirements and economic reasons, some units are assigned with the
must-run status:
u
i
= 1
t
=[
t
run
i
,
begin
,
t
run
for
i
,
end
]
(6)
where
t
run
i
,
begin
and
t
run
i
,
end
are beginning and ending time of
i
th online must-run unit.
For maintenance requirements, some units are assigned with the must-off status:
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