Page 309 - Distributed model predictive control for plant-wide systems

Operation Optimization of Multitype Cooling Source System Based on DMPC 283

13.3.1.4 Constraint Conditions
The main constraints include the output power of refrigerators and the power balance between
refrigerator and predictive load:
{
s s
Y P + P Y = P p
i out,i
(13.7)
P ≤ P out,i ≤ P i,rated
i i,rated
p
where, P is predictive load, ∈ (0, 1) is the minimum power ratio of the ith electric refriger-
i
ator, and P i,rated is the rated output power of the ith electric refrigerator.
According to the objective function and constraint conditions form, we can see that the
economic optimization problem is made up of continuous variables and integer variables. It
is a mixed programming problem, which can be solved by the branch and bound tool in the
s s
MATLAB. The solution is Y , Y , P , P .
i out,i
13.3.2 Design of Distributed Model Predictive Control in Multitype Cold
Source System

Bottom control system can be divided into N subsystems according to the number of air-mode
electric refrigerators, which is made up with a MPC and the plant electric refrigerator. Dif-
ferent MPCs from subsystems can share the data from the communicators to track the total
expected power.

13.3.2.1 Model of Subsystems
Browne and Bansal [143] introduce the dynamic process of the starting state of the electric
refrigerator. From the curves of the starting process of an electric refrigerator, we can see that
the real-time output power can be seen as a step response of a first-order system, for which the
response time is four times of the time constant in the first-order system. Then, we can estimate
the time constant from the starting time of the electric refrigerator. Considering the delay in the
real control system, the process transfer function of tracking the electric refrigerator cooling
power reference is
1 − d s
H(s)= e (13.8)
1 + s
where is time constant of the first-order inertial element and is the delay time. Then, the
d
discrete space state for the sth subsystem is
{
x (k + 1) = A x (k)+ B u (k)
s s
s s
s
(13.9)
p (k)= C x (k)
s s s
s = 1, 2, … , N
where u(k) is the output power reference of electric refrigerator at time k, which is the opti-
mal variable in the following optimal problem, p (k) is the real output power of the electric
s
refrigerator at the time k +1, n is the times between the delay time of electric refrigerator and
d