Page 308 - Distributed model predictive control for plant-wide systems

282 Distributed Model Predictive Control for Plant-Wide Systems

We use the regression analysis to get a function with input as cooling water temperature, power
consumption, and the cooling power so that we can get a binary quadric function with input
as cooling water temperature and cooling power:
P = g(P , T) (13.3)
in out
Then we can get the cost of cooling as
C = Y × g(P , T)× p × t (13.4)
out
where p is the electricity price of cooling and t is the time length for cooling.

13.3.1.2 Cooling Power of Ice Storage Tank and its Economic Model

The dual mode electric refrigerator can make ice in the ice storage tank while the machine is
under the cooling state. Part of energy is stored in the ice storage tank, so it is not reasonable
to put the cost of making ice consumption into the total consumption. We define an average
s
price p of the ice storage tank to describe the cost per cooling energy, which is related with
cooling energy, the power price, and ice-making condition of dual mode electric refrigerator:
in
p init W init + pT P − p init out s s
T
P Y
s
p = (13.5)
in
P Y
W init + T P − T out s s
where p init is the initial value of average price, W init is the initial value of energy reserves in ice
in
storage tank, T is time of making ice, T out is soaking time, P is total power of the dual mode
s
s
electric refrigerator, P is the cooling power for the ice storage, and Y is the start or stop sign
of ice storage. From the definition of average price of ice in the ice storage tank, we can see
that the average price has nothing to do with the ice storage tank soaking, without considering
the decreasing ice product with the time consumption. It is only related to the ice storage tank
while making ice.
13.3.1.3 Objective Function
The objective function is to minimize the electricity power from the sum of power cost of
supplying cold in the air mode and ice storage tank, shown as follows:
∑ s s s
min J = pt Y g (P out,i , T )+ p tP Y (13.6)
i
i i
Y i ,Y s ,P out,i ,P s
where P is the supplying cold power of the ith electric refrigerator. The cost of dual mode
out,i
electric refrigerator in the ice mode is not included in the objective function in the current
optimization period, so the ice mode of the dual mode electric refrigerator does not impact
the optimal value of the optimization problem. In the application, we can use the starting and
stopping sign solved by the optimization problem to start or stop the ice-making for the dual
mode electric refrigerator, which means any two dual mode electric refrigerators cannot have
a state such that one is ice mode and the other is air mode to make sure that the working state
of the electric refrigerators has the same mode.