This paper presents a new lumped-parameter model for describing the dynamics of vapor compression cycles. In particular, the dynamics associated with the two heat exchangers, i.e., the evaporator and the condenser, are modeled based on a moving-interface approach by which the position of the two-phase/single-phase interface inside the one-dimensional heat exchanger can be properly predicted. This interface information has never been included in previous lumped-parameter models developed for control design purpose, although it is essential in predicting the refrigerant superheat or subcool value. This model relates critical performance outputs, such as evaporating pressure, condensing pressure, and the refrigerant superheat, to actuating inputs including compressor speed, fan speed, and expansion valve opening. The dominating dynamic characteristics of the cycle around an operating point is studied based on the linearized model. From the resultant transfer function matrix, an interaction measure based on the Relative Gain Array reveals strong cross-couplings between various input-output pairs, and therefore indicates the inadequacy of independent SISO control techniques. In view of regulating multiple performance outputs in modern heat pumps and air-conditioning systems, this model is highly useful for design of multivariable feedback control.

Issue Section:
Technical Papers
Topics:
Compression, Cycles, Feedback, HVAC equipment, Modeling, Vapors, Design, Dynamics (Mechanics), Heat exchangers, Pressure, Refrigerants, Air conditioning, Compressors, Condensers (steam plant), Couplings, Evaporation, Heat pumps, Subcooling, Transfer functions, Valves
1.
Anonymous, “Innovative air conditioning and refrigeration research: meeting global opportunities,” The Air Conditioning and Refrigeration Institute Report, Dec. 1993.
2.
Bristol
E. H.
, “
On a new measure of interaction for multivariable process control
,”
IEEE Trans. Automatic Control
,
AC-11
, pp.
133
–
134
,
1966
.
3.
Broersen
P.
, and
van der Jagt
M.
, “
Hunting of evaporators controlled by a thermostatic expansion valve
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
102
, pp.
130
–
135
, June
1980
.
4.
Chi
J.
, and
Didion
D.
, “
A simulation of the transient performance of a heat pump
,”
Int. J. Refrigeration
, Vol.
5
, No.
3
, pp.
176
–
184
,
1982
.
5.
Den Braven
K.
,
Herold
K.
,
Mei
V.
,
O’Neal
D.
, and
Penoncello
S.
, “
Improving heat pumps and air conditioning
,”
ASME Mechanical Engineering
, Vol.
115
, Sept
1993
, pp.
98
–
102
.
6.
Dhar, M., and Soedel, W., “Transient analysis of a vapor compression refrigeration system,” Proc. 25th Int. Cong, of Refrigeration, Venice, Italy, 1979.
7.
Domanski, P., and Didion, D., “Computer modeling of the vapor compression cycle with constant flow area expansion device,” National Bureau of Standard, PB83–226639, 1983.
8.
Edgar
T. F.
, “
Least squares model reduction using step response
,”
Int. J. Control
, Vol.
22
, No.
2
, pp.
261
–
270
,
1975
.
9.
Grald
E. W.
, and
MacArthur
J. W.
, “
A moving-boundary formulation for modeling time-dependent two-phase flows
,”
Int. J. Heat and Fluid Flow
, Vol.
13
, No.
3
, pp.
266
–
272
,
1992
.
10.
Gruhle
W.-D.
, and
Isermann
R.
, “
Modeling and control of a refrigerant evaporator
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
107
, pp.
235
–
239
, December,
1985
.
11.
He, X., Liu, S., and Asada, H., “A moving-interface model of two-phase flow heat exchanger dynamics for control of vapor compression cycle,” Heat Pump and Refrigeration System Design, Analysis, and Application, K. R. Den Braven and V. Mei, eds., ASME AES-Vol. 32, pp. 69–75, 1994.
12.
Hiller, C. C., and Glicksman, L. R., “Improving heat pump performance via compressor capacity control—analysis and test,” MIT Heat Transfer Laboratory, Report No. 24525–96, 1976.
13.
Kapa, M., and Wolgemuth, C. H., “A dynamic model of a condenser in a closed Rankine cycle power plant,” Proc. 1984 American Control Conf., pp. 79–84.
14.
Koudo, I., Miyake, I., and Suda, H., “Two-variable control of refrigeration cycle using electronic expansion valves and inverters,” 1986 Japaness Refrigeration Conf., pp. 77–80, 1986.
15.
MacArthur
J. W.
, “
Transient heat pump behavior: a theoretical investigation
,”
InT. J. Refrigeration
, Vol.
7
, No., pp.
123
–
132
,
1984
.
16.
MacArthur
J. W.
, and
Grald
E. W.
, “
Unsteady compressible two-phase flow model for predicting cyclic heat pump performance and a comparison with experimental data
,”
Int. J. Refrigeration
, Vol.
12
, pp.
29
–
41
,
1989
.
17.
McQuiston, F., and Parker, J., Heating, Ventilating, and Air Conditioning, Design and Analysis, 4th edition, Wiley, 1994.
18.
Moore
B. C.
, “
Principle component analysis in linear systems: controllability, observability, and model reduction
,”
IEEE Trans. Automatic Control
,
AC–26
, pp.
17
–
31
,
1981
.
19.
Sami
S. M.
 et al., “
Prediction of the transient response of heat pumps
,”
ASHRAE Trans.
, Vol.
93
, Part 2, pp.
471
–
489
,
1987
.
20.
Shoureishi, R., and McLaughlin, K., “Modeling and dynamics of two-phase flow heat exchangers using temperature-entropy bond graphs,” Proc. 1984 American Control Conf., pp. 93–98, 1984.
21.
Safonov, M. G., and Chiang, R. Y., “Model Reduction for Robust Control: A Schur Relative-Error Method,” Proc. 1988 American Control Conf., pp. 1685–1690.
22.
Wedekind
G. L.
,
Bhatt
B. L.
, and
Beck
B. T.
, “
A system mean void fraction model for predicting various transient phenomena associated with two-phase evaporating and condensing flows
,”
Int. J. Multiphase Flow
, Vol.
4
, pp.
97
–
114
,
1978
.
23.
Yasuda, H., and Ishibane, H., “Analysis of evaporator superheat control using electronic expansion valves,” Proc. 1986 Japaness Refrigeration Conf.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.