Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 16
62
~
1
672
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.1
022
2
1
662
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Applicat
ion of
a Cont
roll
ed Outsi
d
e Cold Airfl
o
w by a PID
Cont
roll
er to Im
prove th
e
Performance of a Household
Refrigerator
Emna Aridhi
1
, Me
hdi
Abbe
s
2
, Abdelk
ade
r
Mami
1
1
Unive
r
sité
de
Tunis El Ma
na
r
,
Ecole Nation
a
le d
'
Ingénieurs d
e
Tu
nis,
LR11
ES20
Laboratoire d’A
n
aly
s
e, de Conception
et d
e
Commande des S
y
s
t
èmes (L
ACS), Faculté d
e
s Scien
ces d
e
Tunis, 1002, Tun
i
s, Tunisie
2
Unive
r
sité
de
Tunis El Ma
na
r
,
Ecole Nation
a
le d
'
Ingénieurs d
e
Tu
nis,
LR11
ES20 Laboratoire
d’A
n
aly
s
e, de Conception
et d
e
Commande des S
y
s
t
èmes (LACS), 1002,
Tu
nis, Tun
i
sie
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 12, 2016
Rev
i
sed
Mar
14
, 20
16
Accepted
Mar 25, 2016
The pr
esent pap
e
r aims to prove the effi
ci
enc
y
o
f
using th
e co
ld
to im
prov
e
the performance of a household refrigera
tor. I
t
is produced naturally
in
countries that ar
e character
i
zed b
y
a se
vere wintr
y
climate. The cold airflo
w
is spread out inside a cav
it
y
cov
e
ring the side wall of the appl
ia
nce, which is
connected to the inlet and outlet ducts.
For that purpose, a Simulink model is
proposed to mod
e
l this installatio
n
. The
internal
air temperatur
e is computed
accord
ing to the
evaporator t
e
m
p
eratur
e and the
outs
i
de cold air
f
low that is
als
o
com
puted a
ccording
to the
outs
i
de tem
p
er
at
ure and con
t
roll
ed b
y
a P
I
D
controll
er.
The s
i
m
u
lation res
u
l
t
s
s
how that when the intern
al a
i
r t
e
m
p
eratur
e
is higher than the desired one an
d the
outside temperature is low enough, the
controlled co
ld
airflow used as
a s
econd coo
lin
g source allowed to speed-up
the
cooling
insid
e
th
e ref
r
iger
ator
co
mpartment of
about 36.21%
and to r
each
an energ
y
sav
i
n
g
of about 36.2
3
% compared with the
classical
thermostatic
control.
Keyword:
Co
ld
airflow
Energy e
fficie
n
cy
PI
D Con
t
ro
ller
Refrige
rato
r
R
e
newa
bl
e e
n
e
r
gy
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Em
na Ari
d
hi
,
Depa
rt
m
e
nt
of
Phy
s
i
c
s,
Uni
v
ersi
t
é
de Tu
ni
s
El
M
a
na
r,
F
acul
t
é
des Sci
e
nces de
T
u
ni
s,
10
0
2
, Tu
ni
s, T
uni
si
e.
Em
a
il: e
m
n
a
.arid
h
i
@fst.rnu
.tn
1.
INTRODUCTION
Nowad
a
ys, th
e u
s
e
of electricity in
air-cond
itio
n
i
ng
a
n
d re
frigeration
syste
m
s greatly increases see
n
that the com
f
ort dem
a
nd wa
s accentuate
d
a
nd m
a
ny products (food, c
h
e
m
ical,
etc.) ha
ve to
be
kept c
h
illed.
In
dee
d
, t
h
ey
ar
e est
i
m
a
t
e
d t
o
be res
p
o
n
si
bl
e
fo
r 1
5
% o
f
t
h
e
gl
obal
el
ect
ri
ci
t
y
consum
pt
i
on [1]
.
F
u
rt
her
m
ore,
th
e co
nv
en
tion
a
l refrig
eratio
n
cycles d
r
i
v
en
g
e
n
e
rally b
y
th
e trad
ition
a
l v
a
por com
p
ressio
n
contrib
u
t
ed
si
gni
fi
ca
nt
l
y
i
n
a
n
o
p
p
o
s
i
t
e
way
t
o
t
h
e s
u
s
t
ai
nabl
e de
vel
opm
ent
co
nce
p
t
,
due t
o
t
w
o
m
a
jor p
r
obl
e
m
s:
t
h
e
gl
o
b
al
i
n
creasi
ng c
ons
um
pt
i
on of l
i
m
i
t
e
d pri
m
ary
energy
re
sou
r
ces an
d t
h
e refri
gera
nt
s u
s
ed are ha
rm
ful
and
cause se
ri
o
u
s e
nvi
ro
nm
ent
a
l
pro
b
l
e
m
s
.
Recently, an increasing intere
st was conc
ent
r
ated on
the te
chnological de
velopm
ent, and the ha
rne
s
s
of t
h
e
rene
wa
bl
e ene
r
gy
res
o
u
r
ces l
i
k
e
t
h
e sol
a
r
,
geot
h
e
rm
al
, wi
nd,
et
c. They
a
r
e
pr
o
duce
d
by
nat
u
ral
resources, whi
c
h are free and inexha
us
tib
l
e
. Th
ese so
lu
tio
n
s
can
offer
a redu
ctio
n
o
f
th
e co
nsu
m
p
tio
n, th
e
dem
a
nd and the cost of electrical ener
g
y
with
ou
t lo
wering
th
e d
e
sired
com
f
o
r
t lev
e
l. Fo
r in
stan
ce, the so
lar
energy is extensively use
d
in cla
ssical refrig
eration
in
st
allatio
n
s
d
r
i
v
e
n
by the va
por com
p
ression cycle
(VC
C
)
. A
n
en
ergy
savi
ng
of
abo
u
t
50%
w
a
s obt
ai
ne
d [
2
]
.
C
o
m
b
i
n
ed a
b
so
r
p
t
i
o
n
-
c
o
m
p
ressi
o
n
sy
st
em
s ar
e
also assisted
by the re
newa
ble ener
gy res
o
urces
. Indeed, a cool cham
be
r with
a sol
a
r-
dri
v
en
a
b
s
o
rptio
n
ref
r
i
g
erat
or
wa
s desi
g
n
e
d
i
n
[
3
]
.
It
di
d
n
o
t
cons
um
e an
y electrical energy. The
sola
r
ene
r
gy
i
s
st
r
o
ngl
y
usef
u
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
App
lica
tio
n o
f
a
C
o
n
t
ro
ller Ou
tsid
e C
o
ld
Airflo
w b
y
a
PID
Co
n
t
ro
ller to
Imp
r
o
v
e th
e
.... (Emna
Aridh
i
)
1
663
in the
desert z
one
s whe
r
e the
electricity is not easily av
ai
l
a
bl
e. M
o
re
ove
r,
ge
ot
herm
al
energy
resource is als
o
in
v
e
sted
in
refrig
eration
in
m
a
n
y
co
un
tries. Fo
r in
stan
ce, i
n
Tu
ni
si
a, t
h
e va
po
r ge
ner
a
t
i
on
was m
a
de wi
t
h
i
n
a
cool
i
n
g sy
st
em
wi
t
h
va
p
o
r a
b
sor
p
t
i
o
n, casca
ded
by
a VC
C
.
The i
n
st
al
l
a
t
i
on al
l
o
we
d
pr
od
uci
n
g ap
p
r
o
x
i
m
at
ely
90
t
o
ns of
i
ce per h
o
u
r
i
n
or
d
e
r
t
o
p
r
eser
ve agri
c
u
l
t
u
ral
a
n
d
fi
s
h
i
n
g pr
o
d
u
c
t
s
[4]
.
Li
ke
wi
se,
i
n
Icel
an
d,
70
%
o
f
th
e fact
o
r
ies
u
s
e th
e
g
e
o
t
h
e
rm
al en
erg
y
for ind
u
s
t
r
ial
activ
ities su
ch
as refri
g
e
ration
and
heatin
g
[5
],[6
].
Th
e op
timizati
o
n
o
f
th
e
refrig
eratio
n cycles also has a tre
m
endous ef
fec
t
on the ene
r
gy use. It aim
s
to
g
e
t rid
d
e
finitiv
ely so
m
e
refrig
e
ran
t
s in
futu
re m
a
g
n
e
tic
o
r
th
erm
o
-acou
s
tics refri
g
e
rato
rs,
w
h
ich
u
s
e so
und
wave
s t
o
pum
p t
h
e heat
[7]
.
Al
t
e
rnat
i
v
el
y
,
i
t
i
s
carri
ed out
usi
ng a
d
v
a
nced
ref
r
i
g
er
at
i
on t
echni
q
u
e
s. Fo
r
instance, t
h
e hybrid
refrige
r
a
tion cycle allowed a
n
e
n
e
r
g
y
s
a
v
i
ng
o
f
ab
ou
t 52
.7
%
co
mp
a
r
ed
w
ith
th
e V
C
C
[8]
.
F
u
rt
he
rm
ore, t
h
e n
ovel
h
ous
eh
ol
d re
fri
g
e
rat
o
r
s
w
ith shape-sta
b
ilized PCM (Phase C
h
ange Material) heat
sto
r
ag
e con
d
e
nsers also
con
c
ed
e an
en
erg
y
sav
i
ng
o
f
abou
t 12
%
[9
],[1
0
]
.
Th
e
v
e
n
tilatio
n
o
f
th
e co
m
p
ressor
sur
r
o
u
ndi
n
g
s a
l
l
o
wed
dec
r
eas
i
ng i
t
s
t
e
m
p
erat
ure a
nd t
h
en
,
red
u
ci
n
g
t
h
e e
n
er
gy
co
ns
um
pt
i
on
o
f
ab
o
u
t
9.
17
%
[1
1]
. O
n
t
h
e
ot
he
r ha
nd
, s
e
veral
co
nt
r
o
l
al
gori
t
h
m
s
were
devel
o
p
e
d t
o
o
p
t
i
m
i
z
e t
h
e cool
i
n
g
i
n
t
h
e
ref
r
i
g
erat
i
on s
y
st
em
s
l
i
k
e ho
use
hol
d ref
r
i
g
erat
or
s an
d
to minimize the
electrical
energy
use. Am
on
g t
h
em
,
m
a
ny
researc
h
ers ha
ve ca
rri
e
d
o
u
t
ada
p
t
i
v
e
[1
2]
,[
13]
,
fu
z
z
y
l
ogi
c [
14]
,
[
15]
,
ne
ural
net
w
o
r
k
s
[
14]
, a
n
d PI
D
[1
6]
,[
1
7
]
t
e
m
p
erat
ure c
o
nt
rol
.
Ot
he
r st
u
d
i
e
s were f
o
c
u
sed
on M
odel
-
base
d Pre
d
i
c
t
i
v
e C
ont
rol
(M
PC
) of t
h
e
te
m
p
eratu
r
e insid
e
th
e refri
gerato
r co
m
p
artmen
t in
o
r
d
e
r
to re
duce the e
n
ergy
use
u
p
t
o
30
% [1
8]
an
d 36
%
[1
9]
.
Beyo
nd
th
at, th
e v
e
ry co
ld
cl
i
m
ate
in
h
i
g
h
altitu
d
e
reg
i
ons p
e
rsists ov
er lo
ng
er
p
e
ri
o
d
s
o
f
th
e year.
Howev
e
r, th
e
co
o
ling
systems lik
e refrig
erato
r
s an
d
co
ld
s
t
ora
g
e are
plac
ed in lo
c
a
tions
whe
r
e the am
bient
t
e
m
p
erat
ure i
s
aro
u
nd
2
5
°C
.
C
onse
q
uent
l
y
,
an ene
r
gy
was
t
i
ng i
s
cause
d.
Hence
,
em
erges t
h
e i
d
ea
of
usi
n
g
th
e free an
d
ab
und
an
t co
ld airflow to coo
l
th
e refri
g
e
rator co
m
p
artm
en
t
th
ro
ugh
d
u
c
ts, wh
ich
conn
ect th
e
ap
p
lian
c
e to the co
ld ou
tsid
e
su
rroun
d
i
ng
s.
In
th
e
p
r
esen
t
p
a
p
e
r, th
e
ou
tsid
e co
ld
airflow is u
s
e
d
as a
second c
ooli
n
g source.
It circulates in an
in
let d
u
c
t connected
to
a cav
i
t
y co
v
e
ri
n
g
th
e sid
e
wall o
f
t
h
e refrig
e
rator
ch
am
b
e
r th
ro
ug
h
an
in
let op
en
ing
.
At th
e ex
it, it is also
conn
ected
to
an
ou
tlet d
u
c
t th
rou
g
h
an
o
p
e
n
i
ng
.
Th
e
ou
tsid
e airflow is co
n
t
ro
lled
u
s
i
n
g
a
PID co
n
t
ro
ller
in
o
r
d
e
r to
co
ntro
l th
e te
m
p
eratu
r
e in
sid
e
the ch
am
b
e
r. Thu
s
, it allo
ws im
p
r
o
v
i
ng
th
e co
o
l
i
ng
process
and als
o
reducing t
h
e
ener
gy
c
ons
um
pt
i
o
n
.
The
pa
per i
s
o
r
ga
ni
zed
as
fol
l
ows:
Sect
i
o
n
2
descri
bes t
h
e
i
n
st
al
l
a
t
i
on t
o
m
odel
.
Sect
i
o
n
3
prese
n
t
s
t
h
e pl
a
n
t
s
use
d
i
n
t
h
e m
odel
and
w
h
i
c
h
are
det
e
rm
i
n
ed by
l
i
n
eari
zat
i
o
n
of
t
h
e
pse
u
do
bo
n
d
gra
p
h m
odel
o
f
the sam
e
installation. Secti
on
4 is
devote
d to illustra
ting t
h
e
control m
e
thod
using
the Si
m
u
link e
nvi
ronm
ent.
In
sect
i
o
n
5
,
t
h
e si
m
u
l
a
ti
on
re
sul
t
s
are
p
r
ese
n
t
.
Sect
i
o
n
6
gi
ves t
h
e c
oncl
u
s
i
on.
2.
MO
DEL DE
S
CRI
PTIO
N
In
t
h
e
p
r
esen
t
p
a
p
e
r, a con
t
ro
lled
co
ld
ou
tsid
e airf
low is spread ou
t at
th
e sid
e
wall
lev
e
l of th
e
ap
p
lian
c
e. Th
is wall is co
v
e
red
with
a cav
ity in
wh
ich
fl
ows th
e co
ld
air. Th
is cav
ity is also
con
n
ected
to
in
let
and
out
l
e
t
d
u
c
t
s
t
h
ro
ug
h t
w
o
ope
ni
n
g
s
,
see Fi
gure
1. It
i
s
rect
ang
u
l
a
r
,
of si
z
e
0.8
1
4
×0
.4
7
7
×0
.1m
(hei
ght
×l
en
gt
h
×
wi
dt
h
)
, a
n
d
m
a
de of
pl
ast
i
c
. The i
n
l
e
t
d
u
c
t
i
s
a py
ram
i
d-s
h
a
p
ed
am
ong
w
h
i
c
h t
h
e
wi
dt
h
o
f
t
h
e bi
g a
nd t
h
e sm
al
l base i
s
equal
t
o
0
.
2
and
0.
1m
, resp
ect
i
v
el
y
.
Ho
w
e
ver
,
t
h
e o
u
t
l
e
t
duct
i
s
rect
ang
u
l
a
r
.
B
o
t
h
d
u
ct
s are
3-m
e
t
e
rs l
e
ngt
h a
n
d
al
so
m
a
de o
f
pl
ast
i
c
. Fu
rt
herm
ore,
t
h
e
t
h
i
c
kne
ss
of
w
a
l
l
s
i
s
3m
m
.
NO
MEN
C
LA
TURE
C
p
ṁ
P
T
V
Vol
Specific
heat c
a
pacity of air a
t
0°C
Mass flow
Press
u
re
Tem
p
erature
Spee
d
Vol
u
m
e
(J.
k
g
-1
.K
-1
)
(k
g.s
-1
)
(ba
r
)
o
r
(Pa)
(°C)
o
r
(K
) (m
.
s
-1
)
(m
3
)
Ab
brevi
at
i
o
ns
com
p
evap
in
it
out
VCC
Com
p
ressor
Ev
ap
or
ator
in
itial
o
u
t
si
d
e
/ ou
tlet
Vapor Co
m
p
ressio
n
Cycle
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
62
–
1
672
1
664
Fig
u
re
1
.
Ou
tsid
e co
ld
ai
rfl
o
w
d
i
ffusion
at the sid
e
wall level o
f
th
e
refrigerato
r
co
m
p
art
m
en
t
M
o
re
ove
r, w
e
sup
p
o
se t
h
at
t
h
e col
d
ai
rfl
o
w
st
em
m
i
ng fr
o
m
t
h
e out
si
de sur
r
o
u
ndi
ng
s i
s
pus
he
d by
a
sm
a
ll fan
an
d
in
th
e sim
u
lat
i
o
n
,
we ad
m
i
t
two
ou
tsid
e
airfl
ow te
m
p
erature values: -20°C and
18°C. The
first
o
n
e
correspon
ds to
t
h
e
win
t
ry
cli
m
ate in
h
i
g
h
altitu
d
e
co
un
tries lik
e in
Canad
a
.
3.
PLANTS
The i
n
st
al
l
a
t
i
on de
pi
ct
ed i
n
Fi
gu
re 1 wa
s m
odel
e
d usi
n
g
t
h
e bo
nd
gra
p
h ap
pr
oac
h
. It
i
s
sket
ched i
n
Fi
gu
re 2.
Fi
gu
re
2.
Pse
u
do
b
o
n
d
g
r
a
p
h
m
odel
of t
h
er
m
a
l
t
r
ansfer
s
between
t
h
e
refrig
e
ration
cav
ity an
d th
e
ou
tsid
e co
ld
airflo
w
The
‘R
ef
ri
gera
t
i
on ca
vi
t
y
’ bl
ock
i
s
t
h
e
pse
u
d
o
b
o
n
d
gra
p
h m
odel
o
f
t
h
erm
a
l
t
r
ansfers
by
nat
u
ral
co
nv
ection
i
n
sid
e
th
e coo
ling
co
m
p
art
m
ent [20].
It com
putes
the i
n
ternal
air tem
p
erature acc
ordi
ng to the
te
m
p
erature at
the eva
p
orator wall level
T_evap
unde
r the
influe
nce
of t
h
e am
bient te
m
p
erature
T_am
b
i
en
t
.
The ‘Outside c
o
ld air
flow’
bloc
k c
o
m
putes the outside fl
ow accord
i
ng t
o
the outside tem
p
erature
T_ou
t
and
t
h
e m
a
ss fl
ow
.
The
‘
I
nl
et
du
ct
’, t
h
e
‘
O
ut
l
e
t
d
u
ct
’ a
n
d t
h
e
‘C
avi
t
y
co
veri
ng
t
h
e
si
de
wa
l
l
’
bl
oc
ks m
o
d
e
l
t
h
e
th
erm
a
l
tran
sfers in
sid
e
th
e
in
let d
u
c
t, th
e o
u
tlet d
u
c
t
and
th
e cav
ity co
v
e
ring
th
e sid
e
wall, resp
ectiv
ely,
unde
r the
infl
uence
of the am
bient tem
p
erature
T_
am
b
i
en
t
an
d
th
e ou
tsid
e
te
m
p
erature
T_
ou
t
.
To c
o
nt
r
o
l
t
h
e
t
e
m
p
erat
ure
i
n
si
de t
h
e
c
ool
i
n
g c
o
m
p
artm
ent
,
t
h
e
p
s
eu
d
o
bo
nd
gra
p
h
m
ode
l
sh
oul
d
be
lin
earized
aroun
d th
e
o
p
e
ratin
g po
in
t
(T
0
= 25
.1
°C),
fo
r an
am
b
i
en
t te
mp
er
at
ure
val
u
e
eq
ual
t
o
25
°C
. Th
e
l
i
n
eari
zat
i
on
gi
ves t
w
o co
nt
i
n
uo
us t
r
a
n
sfe
r
f
unct
i
o
ns:
H
2
c
a
lculates the internal air te
m
p
erature acc
ordi
ng t
o
the tem
p
erature at the e
v
aporator wall leve
l, and
H
3
calculates it according to the c
o
ntrolled
outside col
d
airflo
w
.
54
3
2
2
65
43
2
()
1
.
00
4
0
.00
5067
0
.
08
148
0.030
08
0.0010
3
()
(
)
11
.57
18.68
6.991
0.2
808
0.001
311
I
n
te
r
nal
evap
Tp
pp
p
p
p
Hp
T
p
pp
pp
p
p
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
App
lica
tio
n o
f
a
C
o
n
t
ro
ller Ou
tsid
e C
o
ld
Airflo
w b
y
a
PID
Co
n
t
ro
ller to
Imp
r
o
v
e th
e
.... (Emna
Aridh
i
)
1
665
62
6
3
65
43
2
()
3.8
4
.10
2
.727
.10
()
_
(
)
11
.57
18.
68
6.
991
0.
2808
0.001
311
I
n
te
r
nal
Tp
pp
Hp
Fl
ow
out
p
p
p
p
p
p
p
(2)
Th
e system
ran
k
is th
e
n
u
m
ber of C elem
en
ts o
f
t
h
e
p
s
eudo
b
ond
grap
h
m
o
d
e
l in
in
tegral cau
sality
(he
r
e
6). Furt
herm
ore, t
h
e t
e
m
p
erature at
the eva
p
orat
or wall level
T
ev
ap
was c
o
m
put
ed acc
or
di
n
g
t
o
t
h
e
com
p
ressor speed
V
comp
u
s
ing
th
e fo
llowing
con
tin
uou
s tran
sfer fu
n
c
tion H
1
t
h
at
was obt
ai
ned
by
t
h
e Sy
st
em
Ide
n
t
i
f
i
cat
i
o
n
To
ol
b
o
x
.
It
i
s
wo
rt
h
n
o
t
i
n
g t
h
at
t
h
e
be
havi
or
o
f
t
h
i
s
t
e
m
p
erat
ure
acc
or
di
ng
t
o
t
h
e c
o
m
p
ress
o
r
sp
eed
is sim
ila
r to th
at
o
f
a fi
rst-ord
e
r system.
6
1
()
6.5
58.10
()
(
)
0.0001509
eva
p
co
m
p
Tp
Hp
Vp
p
(
3
)
4.
TEMPER
A
T
URE
CO
NT
R
O
L IN
SIDE
THE REF
R
IG
ERATO
R
CO
MP
ART
MEN
T
In th
is section
,
a PID con
t
ro
l
l
er is
u
s
ed to
co
n
t
ro
l t
h
e
ou
tsid
e co
ld
ai
rfl
o
w
in ord
e
r t
o
con
t
ro
l th
e
te
m
p
erature
inside the
cabi
n
e
t
.
4.
1.
Co
nve
n
ti
onal
On/
O
f
f
c
o
n
t
ro
l
In t
h
e m
o
st cooling system
s,
the co
m
p
ress
or is dri
v
en by a
classical
th
ermo
static con
t
ro
l. Acco
rd
i
ng
to
th
e th
erm
o
stat p
o
w
er ad
just
m
e
n
t
, th
e in
tern
al air tem
p
eratu
r
e v
a
ries
in
an
i
n
terv
al
[T
mi
n
, T
ma
x
].
W
h
en
it
exceeds
T
max
, t
h
e co
m
p
ressor
switch
e
s
on
.
It
sto
p
s
if t
h
e in
tern
al tem
p
eratu
r
e b
e
co
m
e
s lo
wer th
an
T
min
.
4.
2.
P
I
D
co
nt
ro
lle
r
Th
e co
n
t
ro
l loo
p
of th
e
o
u
t
sid
e
co
ld
airfl
ow and
thu
s
o
f
th
e in
tern
al te
m
p
eratu
r
e is illu
strated
i
n
Fi
gu
re 3.
Fi
gu
re
3.
PI
D
cont
rol
l
e
r
base
d cl
o
s
ed
-l
o
o
p
t
e
m
p
erat
ur
e c
o
nt
r
o
l
i
n
si
de
t
h
e
cabi
n
et
The ‘C
om
pres
sor
f
unct
i
o
ni
n
g
’
bl
ock i
s
use
d
t
o
speci
fy
t
h
e
val
u
e
of t
h
e co
m
p
ressor s
p
ee
d ‘
V
comp
’ (0
or 5
0
H
z) acc
o
r
di
ng t
o
t
h
e v
a
ri
at
i
on
of the
internal air tem
p
erature
T
Internal
. Th
e co
n
t
ro
lled
ou
tsid
e airflow
‘
Fl
ow
_o
ut
’ sp
read
ou
t at th
e wall lev
e
l o
f
t
h
e refrigerator
co
m
p
artm
ent is com
puted in
(4), acc
ording
to the
m
a
ss flow
ṁ
t
h
at
i
s
al
so c
o
m
put
ed acc
o
r
di
ng
t
o
t
h
e
co
nt
r
o
l
si
gnal
usi
n
g
(
5
).
_.
.
_
p
F
l
o
w
o
ut
m
C
T
out
(4
)
with
Cp
is the
specific
heat c
a
paci
t
y
of
ai
r a
t
0°C
,
T_
ou
t
is
th
e ou
tsid
e temp
erat
u
r
e and
ṁ
is calcu
lated
i
n
(5).
_
.(
)
.
s
co
nt
r
o
l
s
i
g
n
a
l
ms
i
g
n
P
P
R
(5)
Here
,
R
s
is the
hydraulic re
sistance,
which
c
h
aracterizes
the
press
u
re drop
a
n
d
∆
P
is the pressure di
ffe
rence in
th
e in
let an
d ou
tlet d
u
c
ts. The PID equ
a
tio
n is written
in
(6).
()
1
1
i
PI
D
p
d
K
N
Cp
K
K
p
N
p
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
62
–
1
672
1
666
whe
r
e, K
p
=435
00
, K
i
=1
8.25
, an
d K
d
=
4
.
5
6
.
They
we
re
det
e
rm
i
n
ed usi
n
g
t
h
e Zi
egl
e
r
-
N
i
c
hol
s m
e
t
hod
of t
h
e
cri
t
i
cal
poi
nt
[
21]
.
The
pa
ram
e
t
e
r N
i
s
eq
ual
t
o
1
0
0
.
4.
3.
Simulink m
o
d
e
l
In
th
is section
,
a Si
m
u
lin
k
mo
d
e
l of th
e in
tern
al air
t
e
m
p
er
at
ure co
nt
r
o
l
i
s
pro
p
o
se
d. It
i
s
depi
ct
ed i
n
Fi
gu
re 4.
Fi
gu
re
4.
Si
m
u
l
i
nk m
odel
of t
h
e t
e
m
p
erat
ure
co
nt
r
o
l
i
n
si
d
e
t
h
e re
fri
gerat
o
r
com
p
art
m
ent
Th
e co
n
t
ro
lled co
ld
airflow is co
m
p
u
t
ed
usin
g
th
e
‘Flow_co
m
p
u
tin
g’ Matlab
fun
c
tion
.
As fo
r t
h
e
internal air tem
p
erature, it
is calculated
according to the controlled outsi
de airflow
Flo
w
_ou
t
and t
h
e
te
m
p
erature at
the evaporator wall level
Tevap
u
s
ing
th
e t
h
eorem
o
f
superpo
s
itio
n. The Si
m
u
lin
k
m
o
d
e
l of
the re
fri
geratio
n ca
vity
‘Refri
geratio
n
_
cavit
y
_
A
N
D
_
fl
ow
_
cavity
’ is de
pic
t
ed in
Fig
u
re
5
.
Fi
gu
re
5.
Si
m
u
l
i
nk m
odel
of t
h
e
ref
r
i
g
erat
i
o
n ca
vi
t
y
The tem
p
erature at the
ev
ap
orato
r
wall
lev
e
l
Tevap
de
pe
n
d
s o
n
t
h
e swi
t
c
hi
n
g
cy
cl
es. Indee
d
, i
n
t
h
e
m
odel, the stop and t
h
e swi
t
ching
on
of t
h
e com
p
ress
or
cor
r
es
po
n
d
t
o
0 a
nd
5
0
Hz
, res
p
ect
i
v
el
y
.
Thi
s
beha
vi
o
r
depe
nds
o
n
t
h
e i
n
t
e
rnal
ai
r t
e
m
p
erat
ure
val
u
e
and i
s
m
odel
e
d by
t
h
e
‘o
utp
u
t_c
o
m
p
’
signal. Th
e
Matlab
fun
c
tion
‘C
o
n
t
ro
l_switch
’
is add
e
d
to
th
e m
o
d
e
l i
n
ord
e
r to
sp
ecify in
wh
ich
case th
e co
m
p
ressor
swi
t
c
hes
on a
n
d st
o
p
s.
It
al
so
i
ndi
cat
es w
h
e
n
t
h
e c
ont
rol
l
e
d
ou
tsid
e co
ld
airflow is u
s
ed to
coo
l
th
e side wall
of t
h
e ca
bi
net
.
In
fact
, se
ve
ra
l
scenari
o
s ca
n
occ
u
r acc
or
di
ng t
o
t
h
e
val
u
e of t
h
e
out
si
d
e
t
e
m
p
erat
ure
T_
out
,
the internal te
m
p
erature
T
Inter
nal
, and the
de
sired tem
p
erature
T
Desired
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
I
S
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8-8
7
0
8
App
lica
tio
n o
f
a
C
o
n
t
ro
ller Ou
tsid
e C
o
ld
Airflo
w b
y
a
PID
Co
n
t
ro
ller to
Imp
r
o
v
e th
e
.... (Emna
Aridh
i
)
1
667
If
T
Internal
< or
=
T
Desired
, t
h
e com
p
resso
r i
s
st
op
pe
d an
d t
h
e
out
si
de ai
rfl
ow
i
s
not
ap
pl
i
e
d
t
o
t
h
e si
de wal
l
o
f
t
h
e app
liance. Ho
wev
e
r,
th
is con
t
ro
lled secon
d
coo
ling
so
urce is u
s
ed
to
m
a
in
tain
th
e in
tern
al air
te
m
p
erature
ne
ar the
desi
red one.
If
T
Internal
>
T
D
e
sired
and
T
_
out
<
T
Desired
, t
h
e
com
p
ress
or
s
w
i
t
c
hes
o
n
a
n
d t
h
e
out
si
de
ai
r i
s
used
f
o
r
t
h
e
co
o
ling
.
In
t
h
is case, it allowed
to
sp
eed-up
t
h
e co
o
lin
g
com
p
ared with the classi
cal therm
o
static control
.
Hence
,
t
h
e
du
r
a
t
i
on
of
t
h
e c
o
m
p
ressor
f
unct
i
oni
n
g
i
s
re
du
c
e
d. C
o
nseq
ue
n
t
l
y
, t
h
e el
ect
ri
cal
ener
gy
wo
ul
d
be sa
ve
d.
If
T
Internal
>
T
D
e
sired
and
T_
ou
t
>
T
Desired
, th
e
o
u
t
si
d
e
airfl
o
w
will n
o
t
b
e
ab
le an
ym
o
r
e to
co
o
l
t
h
e sid
e
wall
of
t
h
e
fri
dge
, e
s
peci
al
l
y
, w
h
e
n
T
_
out
ex
ceeds 15
°C.
The control signal
‘si
g
nal
_pi
d
’
is assig
n
e
d
to th
e
‘out
put
_v
a
l
ve’
sig
n
a
l, which
allo
ws co
m
p
u
ting
th
e
out
si
de c
o
l
d
ai
rfl
o
w
.
5.
RESULTS
A
N
D
DI
SC
US
S
I
ON
During
th
e simu
latio
n
,
Th
e i
n
itial v
a
lu
e
T
Init
of t
h
e internal
air te
m
p
erature
is chose
n
acc
ordi
ng t
o
the
following case
s
. T
h
e desire
d
te
m
p
erature is
equal t
o
6°C.
Whe
n
t
h
e internal tem
p
erature reac
hes this
value
,
the com
p
ress
or switches
off, a
n
d whe
n
it
is e
x
ceede
d
, the
c
o
m
p
ressor s
w
itches
on.
5.
1.
Case
o
f
T
Internal
>T
Desired
and T
_
out
=
-2
0°
C
In t
h
is case, the appliance
is tu
rn
ed
on
. Th
erefo
r
e,
T
Init
is
ch
osen
equ
a
l to
2
5
.1°C. Th
e si
m
u
latio
n
was
per
f
o
r
m
e
d du
ri
n
g
4h
o
u
rs
(1
4
4
0
0
s
)
. T
h
e
sim
u
l
a
t
i
on res
u
l
t
s
of t
h
e Si
m
u
l
i
nk m
odel
s
h
ow t
h
at
t
h
e i
n
t
e
rnal
air te
m
p
erature reache
d
the
desire
d one a
f
ter about
2h a
nd
13m
i
n (approxim
a
tely 8
0
00s
)
, for whi
c
h the
co
m
p
ressor is
tu
rn
ing
on
(the ‘ou
t
pu
t_co
m
p
’
sign
al is assig
n
e
d
to 50Hz), an
d th
e con
t
ro
lled
o
u
t
side co
ld
airflow is app
lied
to th
e
sid
e
wall of th
e applian
ce.
T
h
e int
e
rnal air tem
p
erature
be
ha
vi
o
r
an
d t
h
e
com
p
r
e
ssor
fun
c
tion
i
ng
are bo
th
illu
strated
in Figure
6
an
d Figure
7
,
resp
ectiv
ely.
Fi
gu
re
6.
Im
pact
of
t
h
e c
o
nt
r
o
l
l
e
d o
u
t
s
i
d
e c
o
l
d
airflow
on the internal air te
m
p
erature
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
62
–
1
672
1
668
Fi
gu
re
7.
Im
pact
of
t
h
e c
o
nt
r
o
l
l
e
d o
u
t
s
i
d
e c
o
l
d
ai
r
f
l
o
w
on
t
h
e com
p
ress
or
f
unct
i
o
ni
n
g
As s
h
own in Figure 7, the int
e
rnal air tem
p
erat
ure
dec
r
ease
d
t
o
0.
46
°C
d
u
r
i
n
g ap
pr
o
x
i
m
at
el
y
3
m
i
n
.
At th
e sam
e
ti
me, th
e co
m
p
resso
r was
swit
ch
ed
off, wh
ich
allowed
an
en
erg
y
sav
i
ng
of abou
t 1
.
25
%. After
that, the internal air te
m
p
erature
was
in
creased
to
6
°
C,
due to
th
e action
o
f
t
h
e PID co
ntro
ller. Th
e cu
rv
es
o
f
th
e ou
tsid
e airflo
w and
th
e
‘Ou
t
pu
t_v
a
lv
e’ sig
n
a
l are en
larged
and
p
l
o
tted
in
Fig
u
re 8. It is n
o
t
ed
th
at th
e co
ld
airflow value was
sta
b
ilized at
about -7.5kJ
.s
-1
.
Fi
gu
re
8.
The
pr
ofi
l
e
of
t
h
e c
ont
rol
l
e
d
o
u
t
s
i
d
e c
o
l
d
ai
rfl
ow
an
d t
h
e
co
nt
r
o
l
si
gnal
‘O
ut
p
u
t
_val
v
e
’
In t
h
e
no
rm
al
ope
rat
i
n
g co
nd
i
t
i
ons wi
t
h
out
t
h
e su
pp
ort
of
t
h
e out
si
de col
d
ai
rfl
o
w
, t
h
e i
n
t
e
rnal
ai
r
te
m
p
eratu
r
e tak
e
s ab
ou
t
3
h
an
d 29
m
i
n
to
reach
th
e d
e
si
red te
m
p
eratu
r
e [20
]
.
Wh
ile in
t
h
e p
r
esen
t case,
it o
n
l
y
t
a
kes 2
h
an
d 1
3
m
i
n, for
whi
c
h t
h
e rat
e
o
f
t
h
e com
p
resso
r f
unct
i
o
ni
n
g
i
s
a
b
o
u
t
6
3
.
7
7%.
There
f
ore, t
h
e out
si
de
airflow allowe
d accelerating
the cooli
ng
of about 36.21%
during 3h a
nd
29m
in. Thus,
an ene
r
gy savi
ng
of
abo
u
t
36
.2
3%
i
s
achi
e
ve
d,
fo
r w
h
i
c
h
,
t
h
e c
o
m
p
ressor i
s
s
w
i
t
c
hed
of
f d
u
ri
ng
1
h
a
nd
1
6
m
i
n. It
i
s
i
m
port
a
nt
t
o
not
e t
h
at
t
h
e r
e
fri
ge
rat
i
o
n sy
st
em
i
s
not
di
st
ur
bed
.
It
m
e
an
s th
at th
e co
ld
ou
tsid
e air te
m
p
erature,
and the
am
bi
ent
one ar
e const
a
nt
du
ri
ng t
h
e si
m
u
l
a
t
i
on
. He
nce,
the
com
p
ressor
re
m
a
ins at rest after the achie
v
e
m
e
nt
of the desi
red te
m
p
erature.
The com
p
aris
on re
sults of
the internal air te
m
p
erat
ure
beha
vi
o
r
, i
n
n
o
rm
al
ope
rat
i
n
g c
o
n
d
i
t
i
ons a
n
d
wi
t
h
t
h
e
prese
n
ce
o
f
t
h
e
col
d
out
si
de ai
r
f
l
o
w, a
r
e
sho
w
n i
n
Fi
gu
r
e
9.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
App
lica
tio
n o
f
a
C
o
n
t
ro
ller Ou
tsid
e C
o
ld
Airflo
w b
y
a
PID
Co
n
t
ro
ller to
Imp
r
o
v
e th
e
.... (Emna
Aridh
i
)
1
669
Fi
gu
re
9.
I
n
t
e
r
n
al
ai
r t
e
m
p
era
t
ure
be
havi
or
wi
t
h
a
n
d
wi
t
h
o
u
t
t
h
e
su
p
p
o
r
t
of
t
h
e c
o
nt
rol
l
e
d
out
si
de c
o
l
d
ai
rfl
o
w
5.
2.
Case
o
f
T
Internal
> T
Desired
and T_ou
t =
18°
C
In
t
h
is case, the in
itial te
m
p
eratu
r
e
T
Init
is ch
o
s
en
equ
a
l to 15
°C
(Th
e
app
lian
ce is
op
eratin
g
)
.
Here,
t
h
e out
si
de co
l
d
ai
rfl
o
w
wa
s not
us
ed f
o
r
a
sm
uch as t
h
e out
si
de t
e
m
p
erat
ure i
s
hi
g
h
er t
h
a
n
1
5
°C
. The
si
m
u
latio
n
duratio
n
is
4h
ours (1
440
0
s
), and
th
e resu
lts
o
b
t
ain
e
d
i
n
d
i
cate th
at th
e in
tern
al
air tem
p
eratu
r
e to
ok
about one hour and
37m
in to r
each the desire
d one, see Fi
gure 10. In th
is c
a
se, there is not an im
provement in
the cooling e
ffi
ciency or a
re
duc
t
i
o
n
o
f
t
h
e e
n
er
gy
c
ons
um
pt
i
on.
Figure 10. Inte
rnal
air
tem
p
erat
u
r
e
p
r
ofile wh
en th
e con
t
ro
lled
ou
tsid
e co
l
d
airflow
was
n
o
t
u
s
ed
Mo
reov
er, Fi
gu
re 11
illu
strat
e
s th
e co
m
p
resso
r
fu
nctio
n
i
n
g
.
Fig
u
re
11
. Th
e co
m
p
resso
r
operatio
n wh
en
t
h
e co
n
t
ro
lled ou
tsid
e co
ld airflo
w
was
no
t
u
s
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
62
–
1
672
1
670
5.
3.
Case
o
f
T
Internal
< or
= T
Desired
In
th
is case, the in
itial
te
m
p
e
r
atu
r
e
T
init
i
s
chos
en e
qual
t
o
5°C
(l
o
w
er t
h
an
T
Desired
). C
o
nse
que
nt
l
y
,
t
h
e t
w
o c
o
ol
i
n
g so
u
r
ces (t
he
com
p
resso
r a
nd t
h
e co
nt
r
o
l
l
ed
ou
tsid
e cold
airflow) are in
activ
e. Th
us, th
e
refrigerat
or does not c
o
nsum
e ene
r
gy.
N
oneth
eless, it is i
m
p
o
r
tan
t
to clarify th
at i
n
t
h
e Sim
u
lin
k
m
o
d
e
l, t
h
is
situ
atio
n
m
a
k
e
s th
e i
n
ternal air tem
p
eratu
r
e
eq
u
a
l t
o
t
h
e in
i
tial te
m
p
eratu
r
e
T
init
. T
h
i
s
be
havi
or
r
u
n
s
c
o
nt
rary
to what is
ha
ppeni
n
g in the
real cas
e.
Indee
d
, t
h
e i
n
ternal
air tem
p
eratur
e
is inc
r
easing s
een t
h
at the
cooling
sources
are
both inactive.
To
re
m
e
d
y
th
is, a co
n
tinuo
us tran
sfer
fu
n
c
tion
H
4
was use
d
a
n
d defi
ned
i
n
(7
).
4
2.77
4
()
2
.
771
Hp
p
(
7
)
It m
o
d
e
ls th
e i
n
tern
al air temp
er
at
u
r
e profile wh
en th
e com
p
resso
r is not runn
ing
an
d i
s
d
e
term
in
ed
b
y
th
e Syste
m
Id
en
tificatio
n
Too
l
bo
x. In
fact, it calcu
lates
th
e in
tern
al air te
m
p
eratu
r
e
T
I
n
ternal
accordi
n
g to the
te
m
p
erature at
the eva
p
orat
or wall level
T
evap
. The c
h
a
n
ges m
a
de t
o
t
h
e Si
m
u
l
i
nk
m
odel
of t
h
e
cool
i
n
g
com
p
artm
ent (Figure
5) are
d
e
pi
ct
ed i
n
Fi
gu
re
12
.
Fig
u
re
12
. C
o
m
p
le
te Si
m
u
lin
k
m
o
d
e
l of t
h
e
co
o
ling
co
m
p
artm
en
t
In
t
h
e
Si
m
u
l
i
nk m
odel
,
t
h
e
M
a
t
l
a
b f
unct
i
o
ns
‘S
wi
t
c
h_
Te
vap
’
a
n
d
‘S
wi
t
c
h_
Ti
nt
’
ha
ve
been
a
dde
d i
n
o
r
d
e
r to
test the v
a
lu
e of th
e te
m
p
erat
u
r
e at th
e ev
aporato
r
wall lev
e
l as
follo
ws: if t
h
is tem
p
eratu
r
e is eq
u
a
l
t
o
zero, the tra
n
s
f
er function
H
4
is u
s
ed
to
co
mp
u
t
e t
h
e tem
p
eratu
r
e in
th
e refrig
e
rator.
Otherwise, it is com
p
u
t
ed
usi
n
g t
h
e t
r
a
n
sfer
f
unct
i
o
ns
H
2
and H
3,
see Figu
re 5. The resu
lts ach
iev
e
d fo
r an hou
r are illu
st
rated
in
F
i
g
u
r
e
13
.
Figure 13. Inte
rnal
air
tem
p
erature profile
wh
en it is lower
th
an
t
h
e
d
e
sired
tem
p
eratu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
App
lica
tio
n o
f
a
C
o
n
t
ro
ller Ou
tsid
e C
o
ld
Airflo
w b
y
a
PID
Co
n
t
ro
ller to
Imp
r
o
v
e th
e
.... (Emna
Aridh
i
)
1
671
Fro
m
th
e
resu
l
t
s ob
tain
ed, it i
s
no
ted th
at t
h
e in
tern
al air te
m
p
eratu
r
e reach
e
d th
e d
e
sired
o
n
e
(6
°C
)
after approxim
a
tely 2
m
in.
When it exceed
e
d
6°C, the c
o
mpress
or was switched
on to de
crease it. In this case,
th
e con
t
ro
lled
o
u
t
si
d
e
co
l
d
ai
rflow
will b
e
u
s
ed
on
ly
if its te
m
p
eratu
r
e
is lo
wer th
an
1
5
°C.
Ind
e
ed
,
th
ese
si
m
u
latio
n
resu
lts are ach
ieved
fo
r an
ou
tsi
d
e tem
p
eratu
r
e
T_
out
e
qual
t
o
-2
0°C
.
He
nce,
du
ri
n
g
t
h
e
rest
of t
h
e
si
m
u
latio
n
p
e
ri
o
d
, th
e in
tern
al air te
m
p
eratu
r
e was stab
ilized
at 6
°
C,
wh
i
c
h
allo
ws th
e
switch
i
ng
off
o
f
th
e
com
p
resso
r.
6.
CO
NCL
USI
O
N
Th
e cu
rren
t
wo
rk
inv
e
stig
ates th
e
im
pact of an
outsi
de col
d
airflo
w o
n
t
h
e co
ol
i
ng
p
r
oc
ess an
d t
h
e
effi
ci
ency
o
f
a ho
use
hol
d r
e
fri
ge
rat
o
r. It
can be c
onsi
d
ered as a si
g
n
i
fi
cant
pr
om
i
s
ing s
o
l
u
t
i
o
n f
o
r t
h
e
envi
ronm
ental and ene
r
gy–related issu
e
s
, e
s
pecially in hi
gh altitude
c
ountries where
the
clim
ate condit
i
ons
are
very
fa
vo
r
a
bl
e t
o
p
r
od
uc
e t
h
e c
o
ld freely. Th
e sim
u
la
tio
n
resu
lts of
th
e Sim
u
lin
k
m
o
d
e
l sh
ow t
h
at when
the internal air te
m
p
erature i
s
high
er t
h
an t
h
e de
sired
one
and t
h
e outsi
d
e tem
p
erature
is enough l
o
w, the
co
n
t
ro
lled ou
tsid
e co
l
d
airflow allows to
im
p
r
ov
e th
e app
lian
ce p
e
rform
a
n
ce
o
f
abo
u
t
36
%.
In
add
ition
,
t
h
e
effect of th
e
ou
tsid
e co
ld
airflow b
e
g
i
n
s
t
o
b
e
le
ss sign
ifican
t as th
e ou
tsid
e tem
p
erature
becom
e
s high.
More
ove
r, the
internal ai
r temperat
ure
be
ha
vior
wa
s als
o
m
odelled whe
n
t
h
e
fridge is
turned off.
ACKNOWLE
DGE
M
ENTS
Th
e au
tho
r
s
wish
t
o
th
an
k th
e Laborato
r
y tea
m
o
f
Energy Pe
rform
a
nce of Refrigerators in t
h
e
Technical Center of Mec
h
anic
al and
El
ectrical Industries in Tu
ni
s f
o
r
hi
s
hel
p
t
o
car
ry
o
u
t
t
h
e e
xpe
ri
m
e
nt
o
n
th
e refri
g
e
rat
o
r witho
u
t
an
y seco
nd
coo
lin
g so
urce.
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