Abstract

Variable refrigerant flow (VRF) system has been an appealing solution of air conditioning for residential and commercial buildings, due to its flexibility and cost effectiveness, while lack of ventilation capability is a major drawback. Incorporation of dedicated outdoor air system (DOAS) is a typical practice. However, good coordination between DOAS and VRF is critical for achieving desired thermal comfort is challenging due to the possible complexity of mixed sensible and latent heat exchanges. In this paper, to handle the nonlinear dynamic characteristics of VRF-DOAS system, we propose an offset-free Koopman model predictive control (MPC) strategy for thermal comfort regulation, in which the MPC design is computationally more efficient due to the convex problem formulation and the use of reduced-order Koopman models, and the offset-free MPC structure enhances the robustness to model uncertainties and unmeasured disturbances. A control-oriented model is obtained by hybridizing the first-principle and data-driven modeling approach. The proposed controls strategy is evaluated with a Modelica simulation model of a VRF-DOAS system. A Dymola-Python cosimulation platform is developed via the functional mockup interface (FMI), for which the MPC algorithms are implemented in Python. Simulation results show significantly better performance of the offset-free Koopman MPC in thermal comfort regulation.

References

1.
Wan
,
H.
,
Cao
,
T.
,
Hwang
,
Y.
, and
Oh
,
S.
,
2020
, “
A Review of Recent Advancements of Variable Refrigerant Flow Air-Conditioning Systems
,”
App. Therm. Eng.
,
169
, p.
114893
.10.1016/j.applthermaleng.2019.114893
2.
Lin
,
J. L.
, and
Yeh
,
T. J.
,
2009
, “
Control of Multi-Evaporator Air-Conditioning Systems for Flow Distribution
,”
Energy Convers. Manage.
,
50
(
6
), pp.
1529
1541
.10.1016/j.enconman.2009.02.018
3.
Jain
,
N.
,
Koeln
,
J. P.
,
Sundaram
,
S.
, and
Alleyne
,
A. G.
,
2014
, “
Partially Decentralized Control of Large-Scale Variable-Refrigerant-Flow Systems in Buildings
,”
J. Process Control
,
24
(
6
), pp.
798
819
.10.1016/j.jprocont.2014.02.001
4.
Dong
,
L.
,
Li
,
Y.
,
House
,
J. M.
, and
Salsbury
,
T. I.
,
2020
, “
Model-Free Control and Staging for Real-Time Energy Efficient Operation of a Variable Refrigerant Flow System With Multiple Outdoor Units
,”
App. Therm. Eng.
,
180
, p.
115787
.10.1016/j.applthermaleng.2020.115787
5.
Elliott
,
M. S.
, and
Rasmussen
,
B. P.
,
2013
, “
Decentralized Model Predictive Control of a Multi-Evaporator Air Conditioning System
,”
Control Eng. Pract.
,
21
(
12
), pp.
1665
1677
.10.1016/j.conengprac.2013.08.010
6.
Park
,
B. R.
,
Choi
,
E. J.
,
Hong
,
J.
,
Lee
,
J. H.
, and
Moon
,
J. W.
,
2018
, “
Development of an Energy Cost Prediction Model for a VRF Heating System
,”
Appl. Therm. Eng.
,
140
, pp.
476
486
.10.1016/j.applthermaleng.2018.05.068
7.
Moon
,
J. W.
,
Yang
,
Y. K.
,
Choi
,
E. J.
,
Choi
,
Y. J.
,
Lee
,
K. H.
,
Kim
,
Y. S.
, and
Park
,
B. R.
,
2019
, “
Development of a Control Algorithm Aiming at Cost-Effective Operation of a VRF Heating System
,”
App. Therm. Eng.
,
149
, pp.
1522
1531
.10.1016/j.applthermaleng.2018.12.044
8.
Drgoňa
,
J.
,
Arroyo
,
J.
,
Cupeiro Figueroa
,
I.
,
Blum
,
D.
,
Arendt
,
K.
,
Kim
,
D.
,
Ollé
,
E. P.
, et al.,
2020
, “
All You Need to Know About Model Predictive Control for Buildings
,”
Ann. Rev. Control
,
50
, pp.
190
232
.10.1016/j.arcontrol.2020.09.001
9.
Zhang
,
G.
,
Xiao
,
H.
,
Zhang
,
P.
,
Wang
,
B.
,
Li
,
X.
,
Shi
,
W.
, and
Cao
,
Y.
,
2019
, “
Review on Recent Developments of Variable Refrigerant Flow Systems Since 2015
,”
Energy Build.
,
198
, pp.
444
466
.10.1016/j.enbuild.2019.06.032
10.
Fan
,
H.
,
Shao
,
S.
, and
Tian
,
C.
,
2014
, “
Performance Investigation on a Multi-Unit Heat Pump for Simultaneous Temperature and Humidity Control
,”
Appl. Energy
,
113
, pp.
883
890
.10.1016/j.apenergy.2013.08.043
11.
Zhao
,
L.
,
Jianbo
,
C.
,
Haizhao
,
Y.
, and
Lingchuang
,
C.
,
2017
, “
The Development and Experimental Performance Evaluation on a Novel Household Variable Refrigerant Flow Based Temperature Humidity Independently Controlled Radiant Air Conditioning System
,”
Appl. Therm. Eng.
,
122
, pp.
245
252
.10.1016/j.applthermaleng.2017.04.056
12.
Mumma
,
S. A.
,
2001
, “
Overview of Integrating Dedicated Outdoor Air Systems With Parallel Terminal Systems/Discussion
,”
ASHRAE Trans.
,
107
, pp.
545
552
.http://doas-radiant.psu.edu/7-1.pdf
13.
Zakula
,
T.
,
Armstrong
,
P. R.
, and
Norford
,
L.
,
2015
, “
Advanced Cooling Technology With Thermally Activated Building Surfaces and Model Predictive Control
,”
Energy Build.
,
86
, pp.
640
650
.10.1016/j.enbuild.2014.10.054
14.
Li
,
H.
,
Lee
,
W. L.
, and
Jia
,
J.
,
2016
, “
Applying a Novel Extra-Low Temperature Dedicated Outdoor Air System in Office Buildings for Energy Efficiency and Thermal Comfort
,”
Energy Converse. Manage.
,
121
, pp.
162
173
.10.1016/j.enconman.2016.05.036
15.
Kim
,
W.
,
Jeon
,
S. W.
, and
Kim
,
Y.
,
2016
, “
Model-Based Multi-Objective Optimal Control of a VRF (Variable Refrigerant Flow) Combined System With DOAS (Dedicated Outdoor Air System) Using Genetic Algorithm Under Heating Conditions
,”
Energy
,
107
, pp.
196
204
.10.1016/j.energy.2016.03.139
16.
Wang
,
S.
, and
Jin
,
X.
,
2000
, “
Model-Based Optimal Control of VAV Air-Conditioning System Using Genetic Algorithm
,”
Build. Environ.
,
35
(
6
), pp.
471
487
.10.1016/S0360-1323(99)00032-3
17.
Sun
,
Z.
,
Wang
,
S.
, and
Zhu
,
N.
,
2011
, “
Model-Based Optimal Control of Outdoor Air Flow Rate of an Air-Conditioning System With Primary Air-Handling Unit
,”
Indoor Built Environ.
,
20
(
6
), pp.
626
637
.10.1177/1420326X11411511
18.
Lee
,
J. M.
,
Hong
,
S. H.
,
Seo
,
B. M.
, and
Lee
,
K. H.
,
2019
, “
Application of Artificial Neural Networks for Optimized AHU Discharge Air Temperature Set-Point and Minimized Cooling Energy in VAV System
,”
Appl. Therm. Eng.
,
153
, pp.
726
738
.10.1016/j.applthermaleng.2019.03.061
19.
Serale
,
G.
,
Fiorentini
,
M.
,
Capozzoli
,
A.
,
Bernardini
,
D.
, and
Bemporad
,
A.
,
2018
, “
Model Predictive Control (MPC) for Enhancing Building and HVAC System Energy Efficiency: Problem Formulation, Applications and Opportunities
,”
Energies
,
11
(
3
), p.
631
.10.3390/en11030631
20.
Goyal
,
S.
, and
Barooah
,
P.
,
2012
, “
A Method for Model-Reduction of Non-Linear Thermal Dynamics of Multi-Zone Buildings
,”
Energy Build.
,
47
, pp.
332
340
.10.1016/j.enbuild.2011.12.005
21.
Laughman
,
C. R.
,
Qiao
,
H.
,
Bortoff
,
S. A.
, and
Burns
,
D. J.
,
2017
, “
Simulation and Optimization of Integrated Air-Conditioning and Ventilation Systems
,”
Proceedings of 15th International Building Performance Simulation Association Conference
, San Francisco, CA, Aug. 7–9, pp.
1824
1833
.10.26868/25222708.2017.491
22.
Qiao
,
H.
,
Laughman
,
C. R.
,
Burns
,
D. J.
, and
Bortoff
,
S. A.
,
2017
, “
Dynamic Characteristics of an R-410A Multi-Split Variable Refrigerant Flow Air-Conditioning System
,”
12th IEA Heat Pump Conference
,
Rotterdam, The Netherlands
, May 15–18, pp.
1
11
.https://www.merl.com/publications/docs/TR2017-055.pdf
23.
Yang
,
S.
,
Wan
,
M. P.
,
Ng
,
B. F.
,
Dubey
,
S.
,
Henze
,
G. P.
,
Chen
,
W.
, and
Baskaran
,
K.
,
2020
, “
Experimental Study of Model Predictive Control for an Air-Conditioning System With Dedicated Outdoor Air System
,”
Appl. Energy
,
257
, p.
113920
.10.1016/j.apenergy.2019.113920
24.
Korda
,
M.
, and
Mezić
,
I.
,
2018
, “
Linear Predictors for Nonlinear Dynamical Systems: Koopman Operator Meets Model Predictive Control
,”
Automatica
,
93
, pp.
149
160
.10.1016/j.automatica.2018.03.046
25.
Kaiser
,
E.
,
Kutz
,
J. N.
, and
Brunton
,
S. L.
,
2018
, “
Sparse Identification of Nonlinear Dynamics for Model Predictive Control in the Low-Data Limit
,”
Proc. R. Soc. A
,
474
(
2219
), p.
20180335
.10.1098/rspa.2018.0335
26.
Brunton
,
S. L.
,
Proctor
,
J. L
, and
Kutz
,
J. N.
,
2016
, “
Discovering Governing Equations From Data by Sparse Identification of Nonlinear Dynamical Systems
,”
PNAS
,
113
(
15
), pp.
3932
3937
.10.1073/pnas.1517384113
27.
Pan
,
C.
, and
Li
,
Y.
,
2023
, “
Koopman Model Predictive Control of an Integrated Thermal Management System for Electric Vehicles
,”
ASME J. Dyn. Sys. Meas. Contr.
,
145
(
5
), p.
051005
.10.1115/1.4062160
28.
Maeder
,
U.
,
Borrelli
,
F
, and
Morari
,
M.
,
2009
, “
Linear Offset-Free Model Predictive Control
,”
Automatica
,
45
(
10
), pp.
2214
2222
.10.1016/j.automatica.2009.06.005
29.
Morari
,
M
&amp., and
Maeder
,
U.
,
2012
, “
Nonlinear Offset-Free Model Predictive Control
,”
Automatica
,
48
(
9
), pp.
2059
2067
.10.1016/j.automatica.2012.06.038
30.
Pannocchia
,
G.
, and
Rawlings
,
J. B.
,
2003
, “
Disturbance Models for Offset-Free Model-Predictive Control
,”
AIChE J.
,
49
(
2
), pp.
426
437
.10.1002/aic.690490213
31.
Wallace
,
M.
,
Mhaskar
,
P.
,
House
,
J. M.
, and
Salsbury
,
T. I.
,
2015
, “
Offset-Free Model Predictive Control of a Heat Pump
,”
Ind. Eng. Chem. Res.
,
54
(
3
), pp.
994
1005
.10.1021/ie5017915
32.
Vega Lara
,
B. G.
,
Castellanos Molina
,
L. M.
,
Monteagudo Yanes
,
J. P.
, and
Rodríguez Borroto
,
M. A.
,
2016
, “
Offset-Free Model Predictive Control for an Energy Efficient Tropical Island Hotel
,”
Energy Build.
,
119
, pp.
283
292
.10.1016/j.enbuild.2016.03.040
33.
Chen
,
J.
,
Dang
,
Y.
, and
Han
,
J.
,
2022
, “
Offset-Free Model Predictive Control of a Soft Manipulator Using the Koopman Operator
,”
Mechatronics
,
86
, p.
102871
.10.1016/j.mechatronics.2022.102871
34.
Son
,
S. H.
,
Choi
,
H.
, and
Kwon
,
J. S.
,
2021
, “
Application of Offset‐Free Koopman‐Based Model Predictive Control to a Batch Pulp Digester
,”
AIChE J.
,
67
(
9
), p.
e17301
.10.1002/aic.17301
35.
Dassault Systèmes
,
2020
, “
FMpy
,” accessed Jan. 20, 2024, https://fmpy.readthedocs.io/en/latest/
36.
TLK-Thermo GmbH
,
2019
, “
TIL Suite
,” accessed Jan. 20, 2024. https://www.tlk-thermo.com/index.php/en/ software-products/overview/38-til-suite
37.
Wetter
,
M.
,
2020
, “
Modelica Buildings Library
,” accessed Jan. 20, 2024, https://simulationresearch.lbl.gov/modelica
38.
Rasmussen
,
B. P.
, and
Alleyne
,
A. G.
,
2004
, “
Control-Oriented Modeling of Transcritical Vapor Compression Systems
,”
ASME J. Dyn. Sys. Meas. Contr.
,
126
(
1
), pp.
54
64
.10.1115/1.1648312
39.
Seem
,
J. E.
, and
House
,
J. M.
,
2010
, “
Development and Evaluation of Optimization-Based Air Economizer Strategies
,”
Appl. Energy
,
87
(
3
), pp.
910
924
.10.1016/j.apenergy.2009.08.044
40.
Benner
,
P.
,
2006
, “
A MATLAB Repository for Model Reduction Based on Spectral Projection
,”
IEEE Conference on Computer-Aided Control System Design
, Munich, Germany, Oct. 4–6, pp.
19
24
.10.1109/CACSD-CCA-ISIC.2006.4776618
41.
FMpy
,
2020
, “
Dassault Systèmes
,” accessed Jan. 20, 2024, https://fmpy.readthedocs.io/en/latest/
42.
Diamond
,
S.
, and
Boyd
,
S.
,
2016
, “
CVXPY: A Python-Embedded Modeling Language for Convex Optimization
,”
J. Mach. Learn. Res.
,
17
(
83
), pp.
1
5
.
43.
Gurobi Optimization, LLC
,
2023
, “
Gurobi Optimizer Reference Manual
,” accessed Jan. 20, 2024, https://www.gurobi.com
44.
Crawley
,
D. B.
,
Lawrie
,
L. K.
,
Winkelmann
,
F. C.
,
Buhl
,
W. F.
,
Huang
,
Y. J.
,
Pedersen
,
C. O.
,
Strand
,
R. K.
, et al.,
2001
, “
EnergyPlus: Creating a New-Generation Building Energy Simulation Program
,”
Energy Build.
,
33
(
4
), pp.
319
331
.10.1016/S0378-7788(00)00114-6
You do not currently have access to this content.