Information Technology Reference
In-Depth Information
The optimization problem can be stated as
minimize
f
CHP
(3)
subject to operational constraints
1. electrical balance:
P
e
(
i
)+
P
p
(
i
)
−
P
s
(
i
)=
U
e
(
i
);
D
t
(
i
)+
S
t
(
i
−
1)
−
S
t
(
i
)
2. thermal balance:
P
t
(
i
)+
B
t
(
i
)
−
=
U
t
(
i
);
Δt
3. dissipation of thermal power produced by CHP:
D
t
(
i
)
−
P
t
(
i
)
≤
0;
4. thermal and electrical CHP characteristic (1):
k
t
P
e
(
i
)
−
P
t
(
i
)=0;
5. MOT, MST and ramp limit satisfaction.
Variables are bounded by their upper and lower bounds
P
min
e
P
max
e
≤
P
e
(
i
)
≤
B
max
t
0
≤
B
t
(
i
)
≤
0
≤
P
s
(
i
)
(4)
0
≤
P
p
(
i
)
0
≤
D
t
(
i
)
S
max
t
0
≤
S
t
(
i
)
≤
The first bounds do not hold during the starting-up and shutting-down phases.
3
Mixed Integer Scheduling Approach
The scheduling problem can be directly formulated as a MILP [1,3]. This means
that the problem is still linear, but it has both continuous and integer vari-
ables. This class of problems can be solved by exact methods like Branch and
Bound technique [4]. The MILP approach requires to define the on/off status of
the CHP as a logical variable
δ
(
i
) defined for all
i
-th time interval. Moreover,
two additional sets of logical variables must be considered to take into account
MOT/MST constraints and up/down ramps [5] (see Fig. 2)
y
(
i
)=
1ifCHPturnsonat
i
−
th time interval
(5)
0otherwise
z
(
i
)=
1ifCHPturnsoffat
i
−
th time interval
(6)
0otherwise
The complexity of the problem hardly depends on time discretization, because
the finer the discretization the higher the number of integer variables. Besides,
the model of ramp limits, MOT and MST limits introduce several additional
constraints which must be explicitly added to the model. In [5] it is shown that
it is possible to model start-up and shut-down power trajectories with eleven
