Centralized and Decentralized Optimal Control of Variable Speed Heat Pumps

Round 1

Reviewer 1 Report

No specific comment!The paper is very well organized and developed. Authors are properly addressing the research question with an innovative method which is backed up with a case study. The manuscript is written in plain English and does not need that much language editing.

Author Response

We thank the reviewer for the comments.

Reviewer 2 Report

This paper develop  a  decentralized  control framework to optimally schedule the control actions of a population of VSHPs. 

The results show through minimal  network  communication that decentralized  control  framework  performs  on  par  with  a  similarly  structured  centralized  controller  with omniscient knowledge of the state and control actions of its population. 

The topic looks intesting.

1. Reasons of failing to converge under some simulated conditions for the  RLS  algorithm  should be given and analized more.  

2. All algorithms are performed in a simulated environment and experimental validation is recommended.

 

Author Response

Please see the attached PDF document.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper describes results of a decentralized optimal control framework for a variable speed heat pumps system. Presented problem is very interesting and ha a big scientific potential. The introduction of this work is good enough and analyses are provided in an appropriate way. After reading this paper I have some questions and concerns:
-    How the PI controller presented in equation (8) was tuned?
-    What is the reason for using the differential part in PID controller?
-    The meaning of the caption of figure 4 is incomprehensible
-    Why are the PID controller gains negative ?
-    The description of the state observer is poorly understood by me.

In conclusion, the article is interesting and worthy of publication in a journal, but the main caveat is the lack of experimental studies to confirm the issue presented. Similar predictive systems work in many applications and I see no reason to present the results of just a simulation.

Author Response

REVIEWER #3
The paper describes results of a decentralized optimal control framework for a variable speed heat pumps system. Presented problem is very interesting and ha a big scientific potential. The introduction of this work is good enough and analyses are provided in an appropriate way. After reading this paper I have some questions and concerns:

We thank the reviewer for the accurate comments, which we address in the sequel.
Q. 3.1 — How the PI controller presented in equation (8) was tuned?
A. 3.1 — The gains of the PID controller were judicially tuned to balance
the temperature and power curves in Figure 4. This means that, we performed
an empirical optimization of the PID gains such that the temperature and power
response of the system is the best that we could achieve.The gains of the PID controller in Equation (8) are judicially selected in order tobalance the indoor temperature and the aggregate power of the population. This means that, we performed an empirical optimization of the PID gains such that the temperature and power response of the system is the best that we could achieve.

Q.3.2 — What is the reason for using the differential part in PID controller?
A. 3.2 — We have experimented with having KD zero or nonzero. It turns
out that setting KD = 0 does not change the output by a considerable amount,
most probably because the system already has more than enough inherent damping.Hence, the effect of this term on the system may be considered minimal.

Q. 3.3 — The meaning of the caption of figure 4 is incomprehensible
A. 3.3 — Figure 4 depicts the response of the population under the action of
a baseline PID controller without any communication between homes (see the block diagram in Figure 3). In this baseline simulation, N = 1000 homes are simulated and the PID gains are selected to be (KP = ..0:4, KI = ..0:001, KD = ..0:01). Figure 4: PID controller (N = 1000, KP = ..0:4, KI = ..0:001, and KD = ..0:01). Figure 4: The response of the population under the action of a baseline PID controller without any communication between homes (see the block diagram in Figure 3). In this baseline simulation, N = 1000 homes are simulated and the PID gains
are selected to be (KP = ..0:4, KI = ..0:001, KD = ..0:01).

Q. 3.4 — Why are the PID controller gains negative?
A. 3.4 — The term  in the system dynamics given by equation (3) is a
negative number. We have missed explicitly stating this fact and we are grateful for the reviewer catching this oversight.The negative constant term,  < 0, represents the heat removal capacity of the homes HVAC system and m, a controllable parameter, scales  according to the governing control algorithm.

Q. 3.5 — The description of the state observer is poorly understood by me.
A. 3.5 — Even though we have used the term “observer” in Section 2 of
the manuscript, we have not strictly used any state observers in our simulation
experiments as the term is typically used in the controls community. This term
was selected because it was the choice in the reference we provided for the recursive least squares algorithm. However, since this has the potential to lead to confusion we have changed the term observer to control input since the known vector that the recursive least squares algorithm operates upon consists of the total control input.
When it is desired to implement our control algorithm on a real world scenario,
the rate of change of the indoor temperature, _TA will have to be estimated (or
observed in the real sense of the word). This estimation may be performed with
a state estimator, or using a model-free derivative estimator (such as a forward
Euler-scheme).

In conclusion, the article is interesting and worthy of publication in a journal, but the main caveat is the lack of experimental studies to confirm the issue presented. Similar predictive systems work in many applications and I see no reason to present the results of just a simulation.

We thank the reviewer for the kind comments about the submission being worthy of publication. Our future work will concentrate on obtaining experimental results,analyze and report the real world performance of our controller.

Further experimental validation is needed to show the efficacy of our simulation.
Such experiments will be the focus of future research. Due to the approvals needed by local utilities, regulators, and participants alike, significant planning is required to perform the necessary experiments. This research serves as an important precursor to future experimental studies.

Round 2

Reviewer 3 Report

Thank you for answering my questions and clarifying the doubts I had after reading the first version of the article. Taking into account the responses received and the changes made, I recommend the paper for publication.