TELKOM
NIKA
, Vol. 11, No. 9, September 20
13, pp.
5378
~53
8
3
ISSN: 2302-4
046
5378
Re
cei
v
ed Ma
rch 2
2
, 2013;
Re
vised June
13, 2013; Accepte
d
Ju
ne
24, 2013
Analysis on Issues of Variable Flow Water System
Jinming Yang
T
a
iyua
n Univ
er
sit
y
of T
e
chnol
og
y, T
a
i
y
ua
n 0
300
24, Sha
n
x
i,
Chin
a
e-mail: 2
376
03
686
@qq.com
A
b
st
r
a
ct
Varia
b
le fl
ow
w
a
ter system
has p
l
ay
ed a
n
importa
nt rol
e
in the
fiel
d of
ener
gy sav
i
ng
w
i
th the
Electron
ic
Vari
abl
e
F
r
eque
nc
y
Drive
(VF
D
) w
i
dely
use
d
i
n
practica
l pr
oj
ec
ts. How
to co
ntrol th
e fre
q
u
e
n
c
y
converter to w
o
rk pro
perly
is
an ess
enti
a
l
issue w
h
ic
h w
e
must first emp
hatic
ally s
o
l
v
e. T
he contr
o
l
techno
lo
gy of frequ
ency c
onv
erter is cl
osely
relate
d to
char
acteristics of pumps.
Base
d o
n
the
mat
h
mati
ca
l
a mod
e
l of
pu
mps w
i
th
or w
i
thout inv
e
rters, the articl
e dis
c
usses so
me i
ssues i
n
det
ail,
such as
invert
er
s
config
uratio
n, flow
rate regul
ation a
nd ov
erlo
ad. T
hese ar
e key issues of c
ontrol tech
no
lo
gy of variab
le fl
ow
water system
. For those
m
u
ltiple-
p
um
p water system
s,
the engineers m
a
y
select
sync
h
r
onous frequency
convers
i
on co
ntrol techn
o
lo
g
y
or Add-Sub
pu
mps co
ntrol
techn
o
l
ogy
to
ach
i
eve
th
e
max
i
mu
m
en
er
gy-
savin
g
be
nefits
.
Ke
y
w
ords
:
v
a
riabl
e fl
ow
, mathe
m
atic
al
mode
l
of p
u
mp,
pu
mp
overl
o
a
d
, w
a
ter p
u
m
p
inv
e
rter, co
ntro
l
techno
lo
gy
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In re
cent yea
r
s, the h
eating
and ai
r
con
d
i
t
i
oning water system beg
a
n
usi
ng
va
ria
b
le
flow
techn
o
logy.
Circul
ation
pu
mp moto
rs a
r
e drive
n
by i
n
verters to
red
u
ce
en
ergy consumption, and
the advantag
es that the variable flo
w
technolo
g
y bring
s
is obvio
us [
3
-5].
Nume
ro
us st
udie
s
con
d
u
c
ted by many rese
arche
r
s have identified signifi
cant
energy
saving
s
pote
n
tial by regul
ating flo
w
rates to
me
et
pro
c
e
s
s de
m
and
s. But, chara
c
te
risti
c
s of
pump
s
with Variabl
e
F
r
e
quen
cy Drive
tech
nolo
g
y are quite different
f
r
om
t
hose
of pum
ps
without inve
rt
ers,
and
pu
mps i
n
pa
rall
el of mu
ltipe
-
pump
s
syste
m
wo
uld m
a
ke thi
s
situat
ion
more compl
e
x. In other
way t
here are
still many issues worth di
scussi
ng, for example, how
to
config
ure
inv
e
rters fo
r
wat
e
r
pump
s
,
ho
w to
chan
ge
system
flow
corre
c
tly, an
d ho
w to avo
i
d
pump
s
overl
o
ad? Thi
s
arti
cle will add
re
ss these issue
s
ba
sed o
n
the pump mo
de
ls [10].
2. Mathmatical Model of Pump
2.1. Model of Pump
w
i
thout Inv
e
rter
The ba
sic
pa
ramete
rs
of water p
u
mp i
n
clu
de the p
u
mp flow an
d pump he
a
d
. Unde
r
norm
a
l
con
d
i
t
ions
we
can
use th
e p
u
m
p
cha
r
a
c
teristics
cu
rve t
o
exp
r
e
s
s th
e mo
del
of
water
pump. The
Figure 1 sket
che
s
the rela
tionshi
p between pum
p he
ad with pum
p
flow, the sin
g
le
pump characteristics curv
e is illu
strate
d with curve
1 and the cu
rve 2 illustrat
e
s two pa
rall
el
pumps characteri
stics curv
e in
Figure 1.
The curve 3 i
n
Figure1
illustrates the
pi
pe system hea
d
curv
e.
The wate
r pu
mp union o
p
e
rating p
o
int is point A un
der de
sig
ned
operatin
g co
ndition,
and
ope
ratin
g
poi
nt of th
e
sin
g
le
pum
p
is p
o
int
C,
Fi
gure
1
bel
ow sketche
s
th
e
s
e
rel
a
tionshi
ps.
Whe
n
the t
w
o pum
ps
all p
u
t in op
eratio
n, the total flo
w
is
0
2
Q
(
0
Q
is
rate
d flow
of sin
g
l
e
pum
p)
and flow
rate
provide
d
by each pum
p is
0
Q
. We ca
n al
so use formul
a to expre
s
s
mathemati
c
al
model of wat
e
r pum
p:
2
Q
C
Q
B
A
H
(1)
2
n
n
Q
C
n
Q
B
A
H
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis o
n
Issue
s
of Vari
able Flo
w
Wa
ter System
(Ji
n
m
i
ng Yang)
5379
In formula (1
) and (2) ab
ove, variable
is single p
u
m
p head, va
riable is the
parallel
pump
s
h
ead,
is flow rate
of wate
r
syst
em, and
vari
able i
s
th
e n
u
mbe
r
of
parallel pu
mp
s,
and
are con
s
tant coeffici
ents [1
].
Figure 1. Model of Pump without Invert
er
Figure 2. Model of Pump with Inverter
2.2. Model of Pump
w
i
th I
n
v
e
rter
In orde
r to re
alize the va
ri
able flow te
chnol
o
g
y, the water
pump
motors are a
c
tuated
by
the inverters.
For this rea
s
on the mathe
m
atical
mod
e
l
of the pump with new fea
t
ures
woul
d be
more compli
cated.
Similar to the
Figu
re 1, th
e
singl
e p
u
mp
ch
ar
a
c
teri
sti
c
s curve i
s
ill
ustrate
d
with
curve
1
and the
curv
e 2 illu
strate
s two p
a
rall
el
pump
s
cha
r
a
c
teri
stics
curv
e in Fig
u
re 2,
and th
e pum
ps
operate un
de
r the po
we
r freque
ncy. According to
th
e pump l
a
w
of hydrauli
c
similarity, we
can
get the different pump
ch
ara
c
teri
stics
curve
s
u
nde
r different fre
quen
cy, and
the formula
(3)
below illustrates the pum
p law of hydraul
i
c similarity.
2
/
1
2
1
2
1
2
1
2
1
H
H
Q
Q
n
n
f
f
(3)
The math
em
atical formul
a of wate
r p
u
mp wi
th i
n
verters i
s
still
equatio
n (1
), but the
con
s
tant coe
fficients
A
,
B
and
C
is not the origin
al value
.
Furthermore, there is
a
simil
a
r
equatio
n wit
h
different coefficient
s correspon
ding
to the pump run
n
ing
at any operating
freque
ncy.
In Figure 2, curve 4 ca
n b
e
derived b
a
s
ed o
n
cu
rve
1 and the cu
rve 5 can b
e
derived
based on
curve 2. The curve 4 illust
rates si
ngl
e
pump characteristics curv
e, the curve
5
illustrates parallel pump
characte
ri
stics curve, whi
c
h operatin
g frequencies are all 25Hz.
3. Anal
y
s
is o
f
Pump Ov
er
load
3.1. Pipe Sy
s
t
em He
ad Cu
r
v
e
Pump ove
r
lo
ad is a
com
m
on fault, which
co
uld b
e
ca
used
by many rea
s
o
n
s. Th
e
unre
a
sona
ble
de
sign
and
unre
a
sona
ble
ope
ration
re
gulation
is th
e main
cau
s
e. Prior to th
e
further stu
d
y of the i
s
sue
,
we le
arn a
bout the
pip
e
sy
stem ch
ara
c
teri
stics. Usually
we
u
s
e
formula (4) b
e
low illu
strate
s pipe
system
model [1]:
2
Q
S
P
(4)
In formula (4),
P
is hea
d
loss of pi
p
e
line
system,
S
is the
pip
e
line resi
sta
n
ce
numbe
rs, variable
Q
is flow rate of pipel
ine syste
m
. We kno
w
tha
t
variable
S
is a con
s
tant
whe
n
the pipe network stru
cture do
es not c
han
ge. The gra
phical rep
r
e
s
entation of the
cha
r
a
c
teri
stics is sho
w
n wi
th curve 3 in
Figure 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 9, September 201
3: 537
8 – 5383
5380
3.2. Analy
s
is
of Pump Ov
erload
As mentione
d above, one
of the main cause
that cau
s
e pum
p overload is un
rea
s
on
able
operation re
gulation, the
heati
ng or air conditio
n
ing wate
r system ad
o
p
t variable flow
techn
o
logy. T
he flow rate
need
s to
be
regul
ated
by cha
ngin
g
nu
mbers of
ope
rating
pump
s
or
pump ope
rati
ng
fre
que
ncy
whe
n
the b
u
ilding heatin
g
or co
oling
load cha
nge
s,
espe
cially
f
o
r
those multipl
e
-pu
m
p
s
syst
em.
Take
s th
e Fi
gure
2
above
as ou
r di
scu
ssi
on
obje
c
ts, the rate
d flo
w
of
wate
r
system i
s
0
2
Q
under de
sig
ned ope
ratin
g
conditio
n
when two pa
ral
l
el pump
s
are
all put in operation. The
union
ope
rati
ng p
o
int of two pa
rallel
pu
mps i
s
poi
nt A
and sin
g
le operating poi
nt
of
ea
ch
pu
mp
is p
o
int
C, ob
viously e
a
ch
pump
ru
ns n
o
rmally
with i
t
s rated flo
w
0
Q
. The
point B
is
ope
ratin
g
point of singl
e pump when
only one pu
mp is put in
o
peratio
n. The
Figure 2
sho
w
s that the water
pump a
c
tual
flow is
mu
ch
gre
a
ter tha
n
its rate
d flo
w
, pum
p ha
d
been
overlo
aded. T
he p
u
mp
head
exceed
s the
pip
e
line
syste
m
re
sistance
when
system flo
w
re
duces,
and
this i
s
th
e
ba
sic
rea
s
on that causes p
u
mp
overloa
d
[2, 7].
4. Contr
o
l Technolog
y
of
Variable Flow
Wa
ter s
y
stem
4.1. In
v
e
rter Con
f
igura
t
ion
For si
ngle p
u
m
p system th
e config
uratio
n of in
verter i
s
sim
p
le, one
inverter d
r
ives only
one pu
mp mo
tor. But for multiple pump
system h
o
w
t
o
config
ure th
e inverters?
Whi
c
h meth
o
d
is
corre
c
t choi
ce, one inve
rter d
r
ives
one
pump m
o
to
r
or on
e inve
rter d
r
ives
more pump
moto
rs?
The co
rrect
method is th
at one invert
er drive
s
one
pump motor, so the num
ber of pump
s
is
equal to
the n
u
mbe
r
of inve
rters. The
Fig
u
re
3 bel
ow
shows thi
s
p
r
in
ciple. In Fi
gu
re 3
curve
1, 2
,
and 3 i
s
sin
g
le pum
p ch
ara
c
teri
stics
curve
at
different freque
ncy. The
r
e a
r
e three diffe
rent
situation
s
fo
r water
pum
ps operating at
different
freq
uen
cy in p
a
ra
llel. The
cu
rve 4 i
s
the
uni
on
operating cha
r
acte
ri
stics curve of two p
u
mps
whi
c
h
operates at t
he sam
e
freq
uen
cy, and this is
an
id
eal co
m
p
lete
p
a
rall
el mode. No
w we de
cre
a
se freque
ncy
of one pump
to lowe
r
frequ
en
cy
whi
c
h
corre
s
pond
s to
curve 2. The un
ion op
erat
in
g
cha
r
a
c
teri
sti
cs
cu
rve of two p
u
mp
s which
operates at
different freq
uen
cy c
han
g
e
s to
curve
5, and
thi
s
i
s
a
p
a
rtial
p
a
rallel
mo
de.
If
contin
ue de
crease frequ
en
cy to freque
n
c
y the val
ue whi
c
h corre
s
pond
s to cu
rv
e 3, we can see
the two pump
s
coul
d not operatin
g in pa
rallel, t
he pu
mp operating
in lower freq
uen
cy would
not
work effe
ctively. So it may
be unrea
son
a
b
le
that one i
n
verter d
r
ives more pum
ps
motors.
4.2. Sy
nchronization F
r
e
quency
Conv
ersion Technolog
y
No
w we
can
assume th
at the flow rate o
f
the system requireme
nt is chan
ged to
50% o
f
the rated flo
w
, how
can
we a
c
hieve t
h
is go
al
? Th
e easi
e
st me
thod is to use the synchronou
s
freque
ncy
co
nversi
on te
ch
nology, that all pump
s
ru
nning at the
same f
r
equ
e
n
cy. As sho
w
n in
Figure 2, th
e ope
ration
freque
ncy of
all pump
s
i
s
re
du
ced to
25
H
z
and pa
rallel pum
ps
cha
r
a
c
teri
stics chan
ges f
r
om cu
rv
e 2 t
o
cu
rve 5, at
the sam
e
ti
me the unio
n
o
peratin
g poi
nt of
the pa
rallel
p
u
mps chan
ge
s from
poi
nt A to point
B.
All the pum
p
s
in
parallel b
y
simultan
eo
usly
cha
ngin
g
the operation fre
quen
cy, just like on
e pump
[8].
4.3. Anti-ov
e
rload Techn
o
log
y
Synchrono
us inverter con
v
erter is a g
ood te
chnol
o
g
y to meet the nee
ds of
the wate
r
system with variable
flow;
it
also ca
n effect
ively avoid the
wate
r pump
and i
n
verter
overl
oad.
This te
chni
qu
e is suita
b
le f
o
r the water
system with th
e small n
u
mb
er of pump
s
.
Ho
wever,
wh
e
n
the wate
r sy
stem with l
a
rge num
be
r o
f
pumps
nee
ds
smalle
r fl
ow, Add
-
Sub
pump
s
cont
rol
techn
o
logy i
s
a b
e
tter
choi
ce. T
hen it
is a vi
abl
e te
chnolo
g
y to
chang
e the
nu
mber of runni
ng
pump
s
, but this ap
proa
ch
applied i
nap
prop
riately would lea
d
to water
pump
s
and inverte
r
s
overloa
d
. Ho
w ca
n we avo
i
d this? Let u
s
take Fi
gure 4 as an exam
ple to analyze.
No
w we
can
assume th
at the flow rate o
f
the system requireme
nt is chan
ged to
50% o
f
the rated flo
w
, how
can
we a
c
hieve t
h
is go
al
? Th
e easi
e
st me
thod is to use the synchronou
s
freque
ncy
co
nversi
on te
ch
nology, that all pump
s
ru
nning at the
same f
r
equ
e
n
cy. As sho
w
n in
Figure 2, th
e ope
ration
freque
ncy of
all pump
s
i
s
re
du
ced to
25
H
z
and pa
rallel pum
ps
cha
r
a
c
teri
stics chan
ges f
r
om cu
rv
e 2 t
o
cu
rve 5, at
the sam
e
ti
me the unio
n
o
peratin
g poi
nt of
the pa
rallel
p
u
mps chan
ge
s from
poi
nt A to point
B.
All the pum
p
s
in
parallel b
y
simultan
eo
usly
cha
ngin
g
the operation fre
quen
cy, just like on
e pump
[6].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis o
n
Issue
s
of Vari
able Flo
w
Wa
ter System
(Ji
n
m
i
ng Yang)
5381
Figure 3. Inverter Configu
r
a
t
ion
Figure 4. Pump Overlo
ad
Analysis
In Figure 4, the sin
g
le pu
mp cha
r
a
c
terist
ics cu
rve is illustrated
with cu
rve 1 and th
e
pump
ru
nnin
g
at the
po
wer frequ
en
cy. T
he
curve
2
ill
ustrate
s
two
parall
e
l p
u
mp
s
cha
r
a
c
teri
st
ics
curve
and
all
the two p
a
rall
el pump
s
run
n
ing at the
po
wer freq
uen
cy also. Th
e curve 3 ill
ustra
t
es
the pip
e
syst
em h
ead
curv
e. We
still a
s
sume
that
th
e
flow
rate
of t
he
wate
r
syst
em requi
rem
e
n
t
is ch
ang
ed to
50% of the rated flow. First of a
ll, what
would
happ
e
n
whe
n
only
one pu
mp is
put
into ope
ratio
n? A pump
operating p
o
int is point B
and the water pum
p a
c
tual flow i
s
m
u
ch
greate
r
tha
n
its rated flo
w
, the pump
and inve
rt
er
overloa
d
o
r
even sto
p
worki
ng. We can
cha
nge
sin
g
l
e
pum
p cha
r
acteri
stics
cu
rve from
cu
rv
e 1 to
cu
rve
4 by chan
gin
g
the o
perating
freque
ncy, a
nd then pum
p operating p
o
int chan
ge
s
from point B to point D.
The pump a
c
tual
flow rate is jus
t
equal to
its
rated flow, wh
ich
can
be cl
ea
rly se
en from
Figu
re 4.
No
w th
e
remai
n
ing
qu
estion i
s
h
o
w
to solve the freq
uen
cy
value corre
s
po
nd
s to th
e cu
rve 4. T
h
e
followin
g
example illust
rat
e
s the calcula
t
ion method [1].
Table
1 bel
o
w
sho
w
s the
pump
param
eters, th
e left data i
s
pe
rcent of rate
d f
l
ow
(%)
and the rig
h
t data is pum
p head (
KPa
).
Table 1. Perf
orma
nce Parameters of Pump
List
Percent of rat
ed f
l
ow
(
%
)
Pump head(KP
a)
1 0
380
2 70
350
3 100
330
4 120
310
Pump p
e
rfo
r
mance
can
b
e
expresse
d
with
the
form
ula (1)
abov
e, all the
co
efficient
C
B
A
,
,
can be calcul
ated by curve
fitting of the
dat
a in the table. The cal
c
ulated re
sult i
s
380
A
2619
.
-0
B
and
-0.00238
C
. Then the com
p
lete
formula to ex
pre
ss the p
u
m
p cha
r
a
c
teristics
list as bel
ow:
2
0.00238
-
0.2619
-
380
Q
Q
H
(5)
For t
h
is
w
a
t
e
r
sy
st
em,
wh
en
sy
st
em
f
l
o
w
i
s
rat
e
d
f
l
o
w
t
h
e
pi
pelin
e sy
st
em
re
si
st
an
ce i
s
330Kpa, so pi
pe syste
m
he
ad ch
ara
c
te
ri
stics list as fo
rmula (6) b
e
l
o
w.
2
2
2
2
0.00825
200
330
Q
Q
Q
S
P
(6)
In fact formul
a (5) i
s
the e
x
pressio
n
of t
he cu
rve 1 a
nd formul
a (6
) is the expre
ssi
on of
the cu
rve 3.
Point D is int
e
rsectio
n
poi
nt of cu
rve
1 and
curve
3. We
can g
e
t the value of p
o
int D
by solving formula (5
) and
formula (6).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 9, September 201
3: 537
8 – 5383
5382
2
2
0.00825
0.00238
-
0.2619
-
380
Q
Q
Q
(7)
The an
swer i
s
177.15
B
Q
.
Variabl
e
1
f
is operating fre
quen
cy corre
s
po
nd
s to th
e cu
rve 1
a
nd Vari
able
4
f
is
operating fre
quen
cy co
rre
spo
n
d
s
to the curve 4.
So according t
o
the pump law of hydra
u
lic
s
i
milarity, we c
an get:
D
B
Q
Q
f
f
4
1
(8)
100
15
.
177
50
4
f
(9)
By solving th
e Equatio
n (9), we
can
g
e
t
2
.
28
4
f
. We
ca
n
dra
w
the
con
c
lu
sion
that
whe
n
the pu
mp ope
rate
s at 28.2
H
z
, th
e pump flo
w
had re
ache
d its rated fl
ow. If pump
operating fre
quen
cy exce
eds thi
s
valu
e, it is
boun
d to cau
s
e the wate
r pu
mp and inve
rter
overloa
d
.
4.4. Variable Flo
w
Con
t
rol
l
er
Author
devel
oped
an i
n
tell
igent
controll
er b
a
sed on singl
e
bo
ard comp
uter
a
s
sho
w
n
in
Figure 5
bel
ow,
whi
c
h a
dopts varia
b
l
e
flow te
ch
n
o
logy.
The
controlle
r m
a
i
n
in
clude
s
CPU
module,
real
-time clo
ck, a
nalog
-t
o-digital co
nverte
r (ADC), digi
ta
l-to-a
nalo
g
converte
r (DA
C
),
digital-in
put
module
with optical isolati
on, digital-o
u
tput
with opti
c
al isol
ation,
and RS23
2
&
RS485
com
m
unication m
odule. Th
e controlle
r com
p
letes d
a
ta a
c
qui
sition th
rough the di
gi
tal-
input and a
n
a
l
og-in
put ch
a
nnel
s and
ca
rries
on the a
nalysi
s
to the data, then control the p
u
m
ps
and frequ
en
cy converte
rs to
wo
rk
corre
c
tly thro
ugh th
e digit
a
l-outp
u
t an
d an
alog
-out
put
cha
nnel
s [5].
Figure 5. Con
t
roller for Va
ri
able Flo
w
Te
chn
o
logy
The de
dicate
d control alg
o
rithm
s
and
control
strategi
es for va
riabl
e flow water
system
s
are
develop
e
d
for the
con
t
roller. T
he
control
algo
rithms
i
n
cl
ude norm
a
l
PID control algo
rithm
and fuzzy control alg
o
rit
h
m for differ
ent cont
r
o
l purp
o
se. Pra
c
tice ha
s pr
oved that fuzzy
algorith
m
is
more
rea
s
o
n
able than th
e PID algo
rithm for mo
st
variable flo
w
control. T
he
dedi
cated co
ntrol strate
gi
es
i
n
cl
ude synchrono
us
frequ
en
cy co
nversi
on te
chnolo
g
y, Add
-
Sub
pump
s
co
ntro
l technol
ogy and anti-overl
oad technol
o
g
y. Many pro
j
ects h
a
ve achieved obvio
us
eco
nomi
c
re
sults at minim
u
m co
sts [3].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis o
n
Issue
s
of Vari
able Flo
w
Wa
ter System
(Ji
n
m
i
ng Yang)
5383
5. Conclusio
n
Pumps are t
he most
com
m
on engineering facilit
ies
in the fiel
d of
building, but
we still
need to fig
u
re out ho
w to
make
them
work corre
c
tl
y. Most imp
o
rta
n
tly, inverters have come i
n
to
wide u
s
e no
wad
a
ys with t
he develop
m
ent of variabl
e flow tech
no
logy. Combin
ed appli
c
atio
n of
inverters an
d
water pu
mp
s brin
gs u
s
not
only goo
d energy-sav
ing benefit
s but some n
e
w
probl
em
s, su
ch a
s
invert
ers
config
ura
t
ion
and ove
r
load et
c. This pa
per h
a
s presented
a
theoreti
c
al st
udy to solve the pro
b
lem
s
.
To unde
rsta
n
d
the cha
r
a
c
teristi
cs of the
pump,
establ
ishme
n
t of mathematical model of
water pum
p i
s
the
premi
s
e. Form
ula
(1) and fo
rmul
a (2) illustrat
e
the
pump performance and
they are
ba
si
c e
quatio
ns for
pump
with
out invert
s.
We
ca
n d
e
riv
e
mathe
m
atical mod
e
l of
water
pump with inv
e
rter by comb
ining the ba
si
c form
ul
a wit
h
the pump la
w of hydrauli
c
similarity.
For those m
u
ltiple-pump
system
s, it is cl
ear that th
e numbe
r of
inverters sh
ould be
equal to the
numbe
r of pu
mps. Thi
s
is
determi
ned
b
y
the charact
e
risti
cs
of pu
mps in p
a
rall
el.
Synchrono
us frequ
en
cy
conversion te
chnolo
g
y may be a
good
choi
ce fo
r
water
system
with
smalle
r num
b
e
r of pump
s
.
The pa
per
al
so di
scu
sse
d
the issue
s
rel
a
ted
to overl
o
ad. From th
e
discu
ssi
on, o
ne ma
y
con
c
lu
de that
the most im
portant rea
s
o
n
wh
i
c
h cau
s
es ove
r
load i
s
pum
p hea
d
exceed
s th
e
pipeline
syste
m
requi
reme
nt. For those
multiple-
pum
p system
s, this pro
b
lem o
c
curs often wh
en
only a fra
c
tio
n
of pump
s
are p
u
t into operation.
Freque
ncy con
v
ersio
n
techn
o
logy is a va
lid
method of ov
ercomin
g
overloa
d
. Meth
od of cal
c
ul
a
t
ing ope
ratin
g
frequ
en
cy is mo
re comp
lex
and th
e a
r
ticl
e illu
strate
s
calcul
ation m
e
thod
with
a
n
example. T
h
i
s
m
e
thod
ne
eds not
only
the
mathemati
c
al
formula
s
but also a
c
tual p
e
rform
a
n
c
e p
a
ram
e
ters of pump.
For proj
ect
s
appli
c
ation, a
suitable controlle
r i
s
n
e
ce
ssary. T
h
e controll
er
with the
dedi
cated control alg
o
rit
h
ms an
d co
n
t
rol strate
gie
s
for variable
flow tech
nolo
g
y can solve
all
those i
s
sue
s
discu
s
sed ab
ove.
Referen
ces
[1]
Z
hang
Li
n,
Xu
Hui, Yu
Yo
ngh
ai. F
i
tting M
e
th
od for P
u
mp
C
haracter
i
stic C
u
rve B
a
sed
on
Optimal kn
ot
s
Spli
ne Ap
pro
x
i
m
ation.
Jour
na
l of Hydroe
lectr
i
c Engi
neer
in
g
. 2008; 2
7
(2): 1
41-1
44.
[2]
Korvin
g H, Ot
tenhoff EC.
A
nal
ysis
of th
e
Ca
us
es
of P
u
mp F
a
ilur
e
a
nd
Differenc
es
of F
a
i
l
ure
Char
acteristics
.
W
a
ter Science and T
e
ch
no
l
ogy
. 200
8; 57(
8): 1271-
12
76.
[3]
Jinmin
g Ya
ng,
Yi Li
n.
Co
ntrol Al
gorith
m
s
and
Contr
o
l St
rategi
es for V
a
ria
b
le Pr
i
m
ar
y F
l
ow
Chil
led
Water Systems.
Proceed
in
g
s
of the 2
0
1
2
Internatio
na
l
C
onfer
ence
on
Comp
uter Ap
plicati
on
an
d
S
y
stem Mo
del
i
ng. Shen
ya
n
g
. 201
2; 634-
637.
[4]
Jinmin
g
Ya
ng.
F
u
zz
y
C
ontro
l for Vari
abl
e
Cool
in
g W
a
ter
F
l
ow
System
. Procee
din
g
s
of the 20
1
2
Internatio
na
l C
onfere
n
ce o
n
Build
in
g Materia
l
s and Structura
l
Engi
neer
in
g. W
uhan. 20
12;
105-
108.
[5]
Jinmin
g Yan
g
, Yi Lin.
Devel
o
p
m
e
n
t of Dedicate
d Contro
ller for HVAC.
Proceed
ings
of the 20
1
2
Internatio
na
l C
onfere
n
ce F
r
o
n
tiers of A
d
va
nced M
a
teri
als
and
Eng
i
n
eer
ing T
e
chn
o
lo
g
y
.
Xi
amen
.
201
2; 147
2-14
79.
[6]
Jinming
Yang.
Variabl
e F
l
o
w
T
e
chniqu
e for Heati
ng C
i
r
c
ulati
ng Pu
mp
. Proceedi
ngs
of the 201
0
Internatio
na
l C
onfere
n
ce o
n
Comp
uter Appl
icatio
n an
d S
y
s
t
em Model
ing.
T
a
iyua
n. 201
0; 1307-
13
10.
[7]
Yang
Jun
hu,
Guo Bi
n, W
a
ng Y
ue, Z
h
a
n
g
Yu
nz
ho
u. R
e
lati
onsh
i
p
of
Performanc
es
an
d D
e
sig
n
Parameters for
Non-ov
erl
oad
Centrifu
gal P
u
mps.
T
r
ansacti
ons of the C
h
i
nese S
o
ciety o
f
Agricultur
a
l
Machi
nery
. 20
12; 43(1
1
): 119
-122.
[8]
Edson, Ro
bert
o
Alves, Vian
a, Augusto Ne
lson
Carv
al
ho.
Optimization
of Parall
el Var
i
abl
e-sp
ee
d-
drive
n
Centrifu
gal Pum
p
s Operatio
n.
Energy
Efficiency
. 200
8; 1(3): 167-1
7
3
.
[9]
Burt Charl
e
s
M, Piao Xia
n
s
hu, Gaud
i F
r
anklin, Bu
sc
h B
r
y
a
n, T
aufik N N. Electric Motor Efficienc
y
und
er Vari
abl
e
F
r
eque
ncies
a
nd L
oads.
Jo
ur
nal of Irrig
a
tio
n
and Dr
ain
a
g
e
Engi
neer
in
g
. 2
008; 1
34(2):
129-
136.
[10]
Miller A
Keith,
Bode
Joh
n
R
,
Sachs R
ober
t, Jensen K
i
rt.
Innovativ
e D
e
vices T
hat E
n
abl
e Vari
ab
l
e
F
l
ow
Systems
for En
ergy
S
a
vin
g
s
. Proc
ee
din
g
s of
Intern
ation
a
l M
e
ch
a
n
ical
En
gi
neer
i
ng
Con
g
ress
and E
x
p
o
siti
on
. Denver. 201
1
;
453-46
0.
Evaluation Warning : The document was created with Spire.PDF for Python.