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A study on the operational stability of a refrigeration systemhaving a variable speed compressor

Yiming Chen, Shiming Deng*, Xiangguo Xu, Mingyin Chan

Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China

a r t i c l e i n f o

Article history:

Received 7 January 2008

Received in revised form

14 April 2008

Accepted 21 April 2008

Published online 10 May 2008

Keywords:

Refrigeration system

Compression system

Compressor

Variable speed

Experiment

Superheating

* Corresponding author. Tel.: þ852 2766 5859E-mail address: besmd@polyu.edu.hk (S.

0140-7007/$ – see front matter ª 2008 Elsevidoi:10.1016/j.ijrefrig.2008.04.012

a b s t r a c t

The increased use of variable speed compressors (VSC) in refrigeration systems can poten-

tially lead to the unstable operation when compressor speed is varied from time to time for

capacity control. The causes of unstable operation may be classified into two groups, one

relating to control algorithms and the other to the inherent characteristics of systems. This

paper reports on a study on the operational stability of a VSC refrigeration system due to its

inherent characteristics. Based on experimental results, a new modified minimal stable su-

perheat (MSS) line having a maximum MSS value and a minimal MSS value has been pro-

posed. Using the modified MSS line, and supported by a series of purposely designed

experiments, a detailed analysis on the operational stability of a VSC refrigeration system

due to its inherent characteristics when its compressor speed is changed for capacity con-

trol has been carried out and presented.

ª 2008 Elsevier Ltd and IIR. All rights reserved.

Etude sur la stabilite lors du fonctionnement d’un systemedote d’un compresseur a vitesse variable

Mots cles : Systeme frigorifique ; Systeme a compression ; Compresseur ; Vitesse variable ; Experimentation ; Surchauffe

1. Introduction

In vapour compression refrigeration systems, there exists an

expansion valve – evaporator control loop which regulates

the refrigerant flow into the evaporator. The instability of

such a control loop and the fluctuations of certain other oper-

ational parameters such as the degree of refrigerant superheat

(DS), normally known as hunting, have been noted in several

previous studies for thermostatic expansion valve (TEV)

; fax: þ852 2765 7198.Deng).er Ltd and IIR. All rights

controlled evaporator refrigeration systems (Wedekind, 1971;

Wedekind and Stoecker, 1966; Wedekind and Stoecker, 1968;

Ibrahim, 2001; Mithraratne and Wijeysundera, 2002; Mithrar-

atne et al., 2000).

Two groups of possible causes have been suggested in

explaining the cause of hunting. The first concentrated on

the influence of the control characteristics of an expansion

valve on system stability (Dhar and Soedel, 1979; Brobesen,

1982; Higuchi and Hayano, 1982). Another, however, tried to

reserved.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 4 1369

explain the cause of hunting based on the inherent cha-

racteristics of an evaporator. Random fluctuations in the re-

frigerant mixture–vapour transition point due to the nature

of two-phase evaporating flow were described (Wedekind,

1971; Wedekind and Stoecker, 1966; Wedekind and Stoecker,

1968). The concept of minimal stable superheat (MSS), which

was defined as a critical minimal DS at which a refrigeration

system could exhibit unstable operation, was first proposed

by Huelle (1967). Huelle observed that hunting often occurred

when a low DS was set in a refrigeration system even when its

TEV was replaced by a manually operated expansion valve.

Huelle (1972) later introduced conceptually a so-called mini-

mal stable superheat signal line as shown in Fig. 1. The MSS

signal line suggested by Huelle was a monotone conic curve

starting from the original point. In addition, Huelle considered

that the MSS in a refrigeration system was influenced by the

inherent characteristics of its evaporator itself. Chen et al.

(2002) experimentally confirmed the existence of such a MSS

line, without further verifying whether the MSS line was actu-

ally a monotone conic curve as suggested by Huelle (1972).

When the concept of MSS line was introduced by Huelle

(1972) based on his experiments, variable speed compressors

had not been used. Hence, his MSS line was proposed based

on a single speed compressor working with a narrow capacity

modulating range. However, variable speed compressors are

increasingly used nowadays because of their higher operating

efficiency and wider capacity modulating ranges. Electronic

expansion valves (EEV), on the other hand, have found more

and more applications in refrigeration systems due to their

quick response and the increased use of variable speed com-

pressor (Lars, 1999). There have also been a number of

reported studies on the hunting observed in EEV-controlled

refrigeration systems (Outtagarts et al., 1997; Li et al., 2004;

Aprea and Mastrubllo, 2002; Chen, 2005). Therefore, it became

necessary to revisit the MSS line concept in the context of vari-

able speed compressor refrigeration systems which have

larger capacity modulating ranges.

This paper reports on a study on the operational stability

for a VSC refrigeration system due to its inherent characteris-

tics. Firstly, an experimental direct expansion (DX) air condi-

tioning (A/C) plant, where all related experimental work was

carried out, is briefly described. Secondly, the experimental

work on qualitatively determining the relationship between

MSS and the load imposed on a refrigeration system is

QM

Q

M

MSS line

Unstable region

Stable region

θθM

Degree of superheat (°C)

Ref

rige

rati

on lo

ad (

kW)

Fig. 1 – The MSS line as proposed by Huelle (1972).

presented, and a modified MSS line proposed. This is followed

by reporting a detailed analysis on the operational stability of

a VSC–EEV DX A/C system due to changes in compressor

speed, using the modified MSS line and supported by a series

of purposely designed experiments.

2. Description of the experimentalDX A/C plant

All the experimental work involved was carried out in the

experimental DX A/C plant whose schematic diagram is shown

in Fig. 2. The major components in the plant included a variable

speed rotor compressor, a high-efficiency tube-louver-finned

DX evaporator and an air-cooled tube-plate-finned condenser.

The nominal output cooling capacity from the DX air condi-

tioning plant was 9.9 kW (w2.8 RT), but its actual output cool-

ing capacity can, however, be modulated from 15% to 110% of

the nominal capacity through varying compressor speed.

The plant included a simulated air conditioned space,

where load generating units (LGUs), having an adjustable

heating capacity of up to 33.6 kW, were placed for simulating

space cooling load.

The experimental DX A/C plant has been fully instru-

mented. All measurements were computerized, so that all

the measured data can be recorded for subsequent analysis.

3. Experimentation on qualitativelydetermining the MSS line

3.1. Experimental conditions

Using the experimental DX A/C plant, a series of steady-state

experiments were carried out to measure the MSS at different

cooling loads, or equivalently the output cooling capacity of

the DX A/C plant. Since the TEV and the EEV were installed

in parallel, experiments were carried out in either a TEV- or

an EEV-controlled DX A/C system.

Considering the inherent operational characteristics of

a refrigeration system, at steady-state operation, a prescribed

range of fluctuation of �0.5 �C in DS was set. This range was

used to assess whether hunting of DS occurred.

The procedures ofexperimentation were as follows. For both

the TEV- and EEV-controlled systems, a fixed compressor speed

corresponding to a fixed cooling load and a relatively high value

of DS were firstly set. After the system reached a steady-state

operation, the setting of DS was gradually lowered with an in-

terval of w0.1 �C, with the actually operating DS being moni-

tored. When the actually operating DS could no longer be

controlled within the �0.5 �C of its setting, i.e., the prescribed

fluctuation range, the last DS setting was then taken as the min-

imal stable superheat under that fixed system cooling load.

The corresponding load imposed on the experimental DX

A/C system, at which the MSS was determined, was evaluated

by

Q ¼ maðhai � haoÞ (1)

where ma was the mass flow rate of air passing through the DX

evaporator, at w0.513 kg/s; hai the enthalpy of air at the

Variable-speed compressor

Refrigerant side

Air side

LGUs

Air-conditioned space

Variable-speed supply fan

EEV

(7.8m×3.4m×2.9m)

DX evaporator cooling coil

Air-cooled condenser

Variable-speed condenser fan

Stop valve

TEV

Stop valve

Fig. 2 – The schematic diagram of the experimental DX A/C plant.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 41370

evaporator inlet, kJ/kg; hao the enthalpy of air at the evapora-

tor outlet, kJ/kg. With the measured air dry bulb and wet bulb

temperature at the evaporator outlet, and known air temper-

atures at the inlet, i.e., 25.0 �C dry bulb and 19.5 �C wet bulb

(indoor air temperature settings), both hai and hao can be

determined.

The same were repeated at other experimental compressor

speeds or cooling loads. For the EEV-controlled system, the

cooling load covered a range between 5.3 and 9.9 kW. For the

TEV-controlled system, the cooling load was between 5.3

and 9.7 kW.

Since the objective of the study was to investigate the

cause of the unstable operation of a VSC refrigeration system

due to its inherent characteristics, the simplest control algo-

rithm necessary for enabling system’s operation was adopted,

as using more advanced control algorithms such as multi-

input–multi-output (MIMO) may well complicate the cause

of unstable operation. Therefore, in order to eliminate the

possible impact of different control algorithms or parameter

settings on operational stability, during all experiments,

expansion valves were P- (for TEV) or PID (for EEV) feedback

controlled, and compressor speed was manually altered.

Furthermore, for the EEV used, a set of constant P-I-D values,

520, 186 and 11, respectively, was adopted. This set of P-I-D

parameters was proved to have caused stable operation of

the experimental refrigeration system under a wide range of

cooling loads when the degree of refrigerant superheat was

set at 6 �C. On the other hand, while it was understood that

the experimental results reported in this paper were obtained

under this setting, and the numerical values obtained under

other P-I-D settings may be different, the general principle

and its related analysis shall remain valid.

3.2. Results and discussions

Fig. 3 shows the measured relationship between MSS and

cooling load in the TEV-controlled system. As seen, the mea-

sured MSS increased generally with the increase of cooling

load. However, when the cooling load was lower than

w5.8 kW, the MSS remained steady at w3.2 �C. When the cool-

ing load increased to greater than w8.4 kW, the MSS did not

further increase, but stayed at w6.5 �C. Similar phenomena

were also observed in the EEV-controlled system, as shown

in Fig. 4.When the cooling load was lower than w6.8 kW, the

MSS stayed steady at w4.2 �C, and when the cooling load

was higher than w9.2 kW, the MSS stayed steady at w6.1 �C.

An examination of both Fig. 3 and Fig. 4 suggested that for

the two different systems, the shapes of curve representing

the relationship between MSS and cooling load looked similar.

Both were a piecewise function rather than a monotone func-

tion as suggested by Huelle. Hence, the shape of a modified

MSS line has been suggested as a piecewise curve shown in

Fig. 5, having a minimum MSS value, qmin and a maximum

MSS value, qmax. Between qmin and qmax, the curve is of conical

shape.

The existence of both qmin and qmax in a refrigeration sys-

tem is significant with respect to both its operational stability

and energy efficiency. The existence of qmin requires that the

DS should not be set at below qmin even when the system is

operated with a very small load, or unstable operation may

occur. On the other hand, the existence of qmax implies that

there is no need to have a large DS setting when the system

is operated with a larger load, resulting in a poor operational

efficiency. Ideally, DS should be set along a MSS line, for

both operational stability and efficiency.

QM

Q

M

MSS line

θ

Unstable region

Stable region

θMSS θmax.θmin.

Degree of superheat (°C)

Coo

ling

load

/Out

put

cool

ing

capa

city

(kW

)

Fig. 5 – A modified MSS line for a refrigeration system.

Coo

ling

load

/Out

put

cool

ing

capa

city

(kW

)

Minimal stable superheat (°C)

4

5

6

7

8

9

10

3 3.5 4 4.5 5 5.5 6 6.5 7

Fig. 3 – Minimal stable superheat at different cooling loads

(TEV-controlled system).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 4 1371

4. Analysis on the operational stability ofa VSC–EEV DX A/C system due to thechanges in compressor speed

Varying compressor speed has been widely recognized as the

most energy efficient way for capacity control in a refrigera-

tion system. Various control strategies (Chen, 2005; Li and

Deng, 2007a,b) have been developed for capacity control

through varying compressor speed. In response to system

load changes, compressor speed may be continuously altered

from time to time to adjust output cooling capacity to match

the changes in cooling load. As observed previously (Chen,

2005), changing compressor speed can well lead to the unsta-

ble operation of a VSC–EEV DX A/C system. It is also noted that

in practical operation, while compressor speed may be either

increased or reduced, the setting of DS of the system would

normally remain unaltered.

This section presents a detailed analysis on the operational

stability of a VSC–EEV DX A/C system due to the changes in

compressor speed for capacity control, using the modified

MSS line and supported by a series of purposely designed

experiments carried out in the experimental VSC–EEV DX A/

C plant. These experiments were designed with reference to

MSS experimental results shown in Fig. 4, having a qmax of

w6.1 �C and a qmin of w4.2 �C, respectively.

As mentioned earlier, compressor speed may be either

increased or reduced. Because there existed fundamental dif-

ferences with regard to the operational stability for the two

4

5

6

7

8

9

10

11

3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Minimal stable superheat (°C)

Coo

ling

load

/Out

put

cool

ing

capa

city

(kW

)

Fig. 4 – Minimal stable superheat at different cooling loads/

output cooling capacities (EEV-controlled system).

speed changing modes, i.e., an increasing mode and a decreas-

ing mode, the analysis was also separated into two parts,

corresponding to the two speed changing modes.

4.1. Operational stability analysisat speed increasing mode

Using the modified MSS line shown in Fig. 5, the operational

stability analysis for the experimental VSC–EEV DX A/C

system at speed increasing mode is illustrated in Fig. 6.

Depending on the value of DS setting, a steady-state operating

point of the experimental system may be on the either side of

qmax, such as points m and n in Fig. 6.

In Fig. 6 n represents that the VSC–EEV DX A/C system

operates steadily at a cooling load Qn, with its DS setting, qn,

greater than qmax. If compressor speed is increased, the oper-

ating point will move from n to n0, which represents that the

system operates at a larger cooling load of Qn0 but with the

same DS setting, qn. As seen from Fig. 6, both n and n0 are sit-

uated in the stable region. Hence the increase in compressor

speed for capacity control (from Qn to Qn0) would not lead to

the hunting of DS when the system finally operates steadily

at point n0. However, immediately after the increase of com-

pressor speed, more refrigerant is sucked into compressor

from the evaporator while the EEV would need time to

respond allowing more refrigerant flowing into the

Q

m

MSS line

θ

Unstable region

θm

Degree of superheat (°C)

Coo

ling

load

/Out

put

cool

ing

capa

city

(kW

)

m

Stable region

n

θn

nQm´

(Qn´)

Qm

(Qn)

θmin. θmax

Expected locusof DS change

Fig. 6 – Analysis of the operational stability of a VSC–EEV

DX A/C system at speed increasing mode.

20304050607080

02468

101214

0 300 600 900 1200 1500 1800 2100

Time (s)

of

max

.co

mpr

esso

r sp

eed

Deg

ree

ofsu

perh

eat

(°C

)

DS setting = 8.0°C

Fig. 7 – The measured DS at speed increasing mode (DS

setting [ 8.0 8C).

30

40

50

60

70

80

00 600 9001 200 1500 1800 2100

Time (s)

of

max

.co

mpr

esso

r sp

eed

Deg

ree

ofsu

perh

eat

(°C

)

02468

101214

0 300 600 900 1200 1500 1800 2100

Time (s)

DS setting = 4.8°C

DS setting = 7.0°C

Fig. 9 – The measured DS at speed increasing mode (with

varied DS setting from 4.8 to 7.0 8C).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 41372

evaporator. Therefore, these exists a short period when there

is less than required refrigerant in the DX evaporator, causing

a sudden increase in DS. Then the operating DS will gradually

return to its setting. The expected locus of DS should not be

simply a straight line connecting the two points, but like those

shown in Fig. 6. The expected locus of DS change will not cross

the MSS line; hence no hunting of DS is expected.

Fig. 7 shows the results of a related experiment to support

the above analysis. The DS setting was 8.0 �C, which was

greater than the reference qmax of w6.1 �C. At about t¼ 300 s

when the compressor speed was step increased from 40% to

70% of its maximum speed, the measured DS also significantly

increased to 14 �C, within a very short period, and then grad-

ually reduced to restore its setting. No fluctuation of the mea-

sured DS may be observed.

On the other hand, in Fig. 6, m represents that the DX A/C

system operates steadily with its DS setting, qm, lower than

qmax. If the compressor speed is increased, the operating point

will move from m to m0. Unlike the n–n0 point case, while point

m is situated in the stable region, point m0 is in the unstable

region. Hence, when the system is eventually operated at

point m0, fluctuation of DS cannot be avoided. In fact, fluctua-

tion of DS may occur as soon as the expected locus of DS

change crosses the MSS line. Fig. 8 shows the results of

a related experiment to support the above analysis. The DS

20304050607080

00 6009 00 1200 1500 1800

Time(s)

% o

f m

ax.

com

pres

sor

spee

dD

egre

e of

supe

rhea

t (°

C)

0

2

4

6

8

10

0 300 600 900 1200 1500 1800 2100

Time (s)

DS setting = 4.8°C

Fig. 8 – The measured DS at speed increasing mode (DS

setting [ 4.8 8C).

setting was 4.8 �C, which was between the reference qmax of

w6.1 �C and the reference qmin of w4.2 �C. From Fig. 8, it can

be seen that the measured DS firstly increased to over 10 �C

following a step increase in compressor speed from 40% to

70% of its maximum speed. After the EEV allowed more refrig-

erant flow, the measured DS then gradually reduced to

approach to its setting, with, however, noticeable fluctuation

of DS occurring from approximately t¼ 1100 s onwards, to

the end of experiment.

For a VSC–EEV refrigeration system having a DS setting

smaller than qmax, in order to avoid the possible fluctuations

of DS due to speed increase, it is possible to simultaneously

increase its DS setting to greater than qmax. Fig. 9 shows the

results of a specially designed experiment to verify this infer-

ence. The original DS setting was 4.8 �C. At t¼ 300 s, when the

compressor speed was step increased from 40% to 70% of its

maximum speed, the DS setting was also increased to 7.0 �C

(>qmax of w6.1 �C). Therefore, the fluctuations of DS in Fig. 8

can no longer be observed in Fig. 9, in the late part of the

experimental period.

4.2. Operational stability at speed decreasing mode

Also using the MSS line shown in Fig. 5, the analysis of opera-

tional stability for the experimental VSC–EEV DX A/C system

Qp

´Qo

Q

o

MSS line

θ

Unstable region

θo

Degree of superheat (°C)

Coo

ling

load

/Out

put

cool

ing

capa

city

(kW

)

o´

Stable region

p

θp

p´

Qp

Qo

θmin. θmax.

Expected locusof DS change

Fig. 10 – Analysis of the operational stability of a VSC–EEV

DX A/C system at speed decreasing mode.

of m

ax.

com

pres

sor

spee

d D

egre

e of

supe

rhea

t (°

C)

40

50

60

70

80

90

300 600 9001 200 1500 18002 100

Time (s)

0

2

4

6

8

0 300 600 900 1200 1500 1800 2100 2400

Time (s)

DS setting = 7.0°C

Fig. 11 – The measured DS at speed decreasing mode

(DS setting [ 7.0 8C).

40

50

60

70

80

00 600 900 1200 1500 18002 100

Time (s)

0

2

4

6

8

10

0 300 600 900 1200 1500 1800 2100

Time (s)

of

max

.co

mpr

esso

r sp

eed

Deg

ree

ofsu

perh

eat

(°C

)

DS setting = 7.0°C

Fig. 13 – The measured DS at speed decreasing mode with

a small magnitude of speed change.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 4 1373

at speed decreasing mode is shown in Fig. 10. Similarly DS set-

ting may be on either side of qmax, as represented by point o

and p. For both cases, unlike speed increasing mode, both

starting points and ending points are situated in the stable

region. Hence, no fluctuation of DS would be expected when

the system is eventually operated steadily at either point o0

and p0. Nevertheless, it is possible that during the transit

from o to o0 or from p to p0, fluctuations of the measured DS

can actually occur as the expected locus of DS change may

well cross the MSS line, depending on the magnitude of the

step decrease in compressor speed.

Figs. 11 and 12 show the results of two related supporting

experiments, where the settings of DS were 7.0 �C (>the refer-

ence qmax of w6.1 �C) and 5.5 �C (<the reference qmax of

w6.1 �C), respectively. The compressor speed reductions

were from 80% to 50% and from 60% to 40% of its maximum

speed, respectively. In Fig. 11, it can be seen that immediately

after the speed decrease at t¼ 300 s, there was a significant

drop in DS to below 2.0 �C. This was because there was more

refrigerant than needed inside the evaporator and it took

time for the EEV to reduce refrigerant flow. This means that

the expected locus of DS change could well cross the MSS

line during transit, so that the measured DS fluctuated. At

about t¼ 620 s, fluctuations of the measured DS could no lon-

ger be observed, suggesting that the operating point returned

3040506070

300 600 900 1200 1500 1800 2100

Time (s)

0123456

0 300 600 900 1200 1500 1800 2100

Time (s)

of

max

.co

mpr

esso

r sp

eed

Deg

ree

ofsu

perh

eat

(°C

)

DS setting = 5.5°C

Fig. 12 – The measured DS at speed decreasing mode

(DS setting [ 5.5 8C).

to the stable region. Afterwards, the measured DS gradually

returned to its setting at 7.0 �C. Similar observations may

also be obtained from Fig. 12.

For these two experiments, as the magnitudes of speed

decrease are relatively significant, it is then possible for the

actual operating point to cross the MSS line and move into

the unstable region during transit. Therefore, it intuitively fol-

lows that limiting the magnitude of each step decrease in

compressor speed may help avoid the possible occurrence of

DS fluctuation. However, although this may help achieve a bet-

ter operational stability, the sensitivity of capacity control

may be lowered when a compressor speed decrease of a larger

magnitude is called for.

Fig. 13 shows the results of a follow-up experiment, from

that shown in Fig. 11. The operational conditions including

the DS for both experiments were the same, except the magni-

tude of speed reduction, i.e., 10% (60–50%), compared to 30%

(80–50%). It can be seen from Fig. 13 that when the step change

in compressor speed took place at t¼ 300 s, the measured DS

also dropped, but afterwards gradually increased to approach

to its setting. During the transit, no oscillations of measured

DS may be observed. This implied that the actual operating

point did not cross the MSS line and stayed in the stable region.

5. Conclusions

This paper reports on a study on the operational stability due

to systems’ inherent characteristics in a VSC refrigeration

system. The following conclusions may be drawn:

� The so-called minimal stable superheat (MSS), as proposed

by Huelle (1972), does exist in both a TEV- and an EEV-

controlled refrigeration system.

� A modified MSS line would possess a piecewise function

shape instead of a monotone function shape, having a min-

imum MSS value and a maximum MSS value, as shown in

Fig. 5.

� The modified MSS line can be used to analyze and explain

the operational stability of a VSC–EEV DX A/C system due

to the changes in compressor speed for capacity control.

In a VSC–EEV DX A/C system, if its DS setting is lower

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 1 ( 2 0 0 8 ) 1 3 6 8 – 1 3 7 41374

than qmax, increasing compressor speed may lead to the

hunting of DS if the final operating point is in the unstable

region. On the contrary, if the DS setting is already greater

than qmax, no hunting of DS would occur.

� Also in a VSC–EEV DX A/C system, decreasing compressor

speed may cause hunting of the operating DS during transit,

but no hunting of DS is expected after the system reaches

a steady-state operation under the new compressor speed.

� It is beneficial to operational stability to have speed reduc-

tions of smaller varying magnitudes, although this may

reduce the sensitivity of a capacity controller.

The modified MSS line and its related analysis as well as

the related experimental results reported provide detailed

insights to the operational stability of a VSC refrigeration sys-

tem due to its inherent characteristics. The other group of the

cause of unstable operation, which is related to control algo-

rithms or setting adopted by various controllers installed in

the system, was not addressed in the current study. Further-

more, it is noted that the current trend in developing

advanced control strategies for EEV–VSC systems is increas-

ingly based on MIMO (He et al., 1998; Skogestad and

Postletheaite, 1996; Qi and Deng, 2008). Nevertheless, the

results reported in this paper are as a matter of fact part of sys-

tem’s inherent characteristics and can therefore be used in

assisting the further design of controllers, such as those

MIMO based, for a VSC refrigeration system.

Acknowledgements

The authors thank The Hong Kong Polytechnic University for fi-

nancially supporting the work reported (Project No.: A – PG 40).

r e f e r e n c e s

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