Page 312 - Distributed model predictive control for plant-wide systems

286 Distributed Model Predictive Control for Plant-Wide Systems

Step 3. Subsystem optimization. Each subsystem solves the optimal Problem 13.1, and then
gets the solution U l+1 .
s
Step 4. Check and update. Check all the subsystems’ conditions of convergence, which is for
the given

∈ ℝ(s = 1, 2, … , N, )
s
l
‖U l+1 − U ‖ < (s = 1, 2, … , N)
s
s
s
If all the subsystems can satisfy the conditions of convergence, then let the optimal
l
∗
variable of each subsystem be U = U (l∗) ,gotoStep5;otherwise,let U l+1 = U +
s
s
s
s
l
(1 − )U (s = 1, 2, … , N), is the constant between 0 and 1, which is decided by the
s
need of subsystems, l = l + 1. Go to Step 2.
[ ] ∗
∗
Step 5. Control variables decision. At the time k, apply u = 10 ··· 0 U (s = 1, 2, … , N)
s
s
to the subsystem.
Step 6. Receding optimization. Move to the next sampling time, k + 1 → k, return Step 1,
repeat.
By the distributed predictive control algorithm, the optimal problem for the globally supply-
ing cold dynamic system can be divided into each subsystem made by electric refrigerator and
corresponding MPC, which can reduce the complexity and calculation of the control problem
and improve the response speed. To testify the effectiveness of the two-level control strategy,
this chapter applies the method to a cooling system of a super-high building.
13.4 Results and Analysis of Simulation
To validate the scheduling algorithm, this chapter applies the above method to the low-district
cooling system of a super-high building in Shanghai, China. The main cold sources of the
system are three conventional centrifugal refrigerators, three dual operating mode centrifugal
refrigerators, an ice storage tank, a ground-source heat pump, and lithium-bromide absorp-
tion refrigerators. To simplify the system, considering high-efficiency and low-output power
of ground-source heat pump and lithium-bromide absorption refrigerators, we preferentially
let them loaded fully and jointly dispatch conventional electric refrigerators and ice storage
system to satisfy the rest load.
There are three conventional electric refrigerators. For two of them, the cooling power is
3900 kW, while for the third one the cooling power is 2150 kW. There are three dual operating
mode electric cooling refrigerators. The rated cooling power of dual operating mode centrifu-
gal refrigerators in the air mode is 6392 kW and in the ice-making mode is 3868 kW. We use
the regression analysis to get a function with input as cooling water temperature, power con-
sumption, and the cooling power so that we can get a binary quadric function with input as
cooling water temperature and cooling power. Power unit is kilowatt and temperature unit is
degree centigrade, as shown in Table 13.1.
For the ice mode of electric refrigerator, to make ice as quickly as possible, refrigerators
work under the condition of rated power in the ice mode. Then, the cooling power cold and