Civil Engineering Reference
In-Depth Information
Lagrangian dual approach. Although the Lagrangian approach could handle inequal-
ity constraints directly, the proposed strategy gives a satisfactory solution while being
simpler and effective as will be demonstrated with simulation results presented in
the following sub-section. For more information about this optimisation strategy, the
interested reader is referred to Álvarez et al. (
2013
).
5.6.3 Illustrative Results
For the sake of understanding, the total number of rooms in the building has been
fixed to 3, that is
M
=
3. For these three rooms, the total water flow has been set to:
M
1
˙
q
w
i
≤
60 1
/
min
,
i
=
which determines the inequality constraint.
Notice that the total water flow constraint (common resource) is actually a
sequence of inequalities over the predicted horizon. At this time, it is important
to make a remark regarding the actual application of the optimisation algorithm.
Initially, the whole set of sub-problems is solved without these coupling constraints
over the prediction horizon. Then, the given rates are implemented if the water flows
are below the limits. On the other hand, if the water flow limit (
q
w
>
˙
/
min) is
violated, for one or more periods of the horizon, the ones that have been violated are
fixed as equalities and only then the Lagrangian dual procedure is applied.
Furthermore, for each room
i
, the following settings have been considered taking
into account the layout of the building and the physical features of the absorption
machine and the fancoil systems:
60 1
•
The prediction horizon,
N
, and the control horizon,
N
u
, have been set to 10 and
4, respectively. That is:
N
i
=
10
N
u
i
=
4
•
The water flow restrictions have been set to:
21
/
min
≤˙
q
w
i
≤
25 1
/
min
•
The minimum and maximum variations of the water flow have been set to:
−
11
/
min
≤
˙
q
w
i
≤
11
/
min
•
The air velocity restrictions have been set to:
0
.
2m
/
s
≤
V
Fan
i
≤
1
.
5m
/
s
