TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3799 ~ 38
0
4
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5113
3799
Re
cei
v
ed
No
vem
ber 1
1
, 2013; Re
vi
sed
De
cem
ber 2
9
,
2013; Accep
t
ed Jan
uary 1
1
, 2014
Resear
ch on Power Load Modeling Based on
Improved
Perturbed Method
Shi Guoping*
1,2
, Liang Jun
1
, Liu Xiang
s
heng
3
1
School of Elec
trical Eng
i
ne
eri
ng, S
han
do
ng
Univers
i
t
y
, Ji
na
n, 2500
61, Ch
i
n
a
2
School of inf
o
rmation a
nd e
l
e
c
trical en
gin
eer
ing,
Sha
n
d
ong
Jianz
hu Un
iver
sit
y
, Jina
n, 25
0
101, Ch
in
a
3
Qingda
o po
w
e
r suppl
y com
p
a
n
y
, Qin
gda
o, 2
660
02, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: shigu
opi
ng
@
s
djzu.e
du.cn
A
b
st
r
a
ct
T
h
is pa
per i
n
troduc
es a c
onv
entio
nal sy
nthe
sis pow
er
l
oad
mo
de
l
cons
id
er
ing distrib
u
tio
n
netw
o
rk
in PSASP, throug
h an
aly
z
i
n
g the mod
e
l structure an
d
ac
hievi
ng
proces
s, proposes
a pow
er loa
d
mo
d
e
l
para
m
eter id
e
n
tificatio
n
met
hod
base
d
o
n
improv
e
d
p
e
r
t
urbed
metho
d
.
T
he pap
er
gives
para
m
eters
ide
n
tificatio
n
method
of compl
e
te synthes
is l
oad
mo
de
l, incl
udi
ng re
active
pow
er co
mp
en
sator para
m
ete
r
s.
T
he p
a
ra
met
e
rs id
entificati
o
n
meth
od
co
mb
i
nes
para
m
et
er
id
entificati
o
n
p
r
ocess w
i
th s
e
nsitivity
ana
ly
z
i
ng
process t
ogeth
e
r, not o
n
ly c
a
n g
e
t mod
e
l
pa
rameters b
u
t a
l
so can
o
b
tain
the se
nsitiv
ity o
f
all
para
m
eter
s,
w
h
ich sav
e
s c
o
mputi
n
g
time
and
re
duces
th
e a
m
ou
nt of
c
a
lcul
atio
n, the
final
si
mu
latio
n
resu
lts pr
ove t
h
e
meth
od is effec
t
ive and fe
asib
l
e
.
Ke
y
w
ords
:
po
w
e
r system, pe
rturbed
meth
od
, load
mod
e
li
ng
, par
a
m
eter se
nsitivity, synthe
s
is loa
d
mode
l
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
At the p
r
e
s
e
n
t time, digit
a
l si
mulation
ha
s
been
t
he m
a
jor me
ans in
po
we
r syste
m
planni
ng, de
signing, di
spat
chin
g and
an
alyzing [1
-2]. The math
e
m
atical m
ode
l of each ci
rcuit
comp
one
nt is the basi
s
of
digital simul
a
tion expe
rim
ent in po
wer
system [3]. T
he accu
ra
cy
of
load mod
e
l will dire
ctly affect the si
mulation re
sult of entire system a
nd
the final stra
tegic
deci
s
io
n [4-5]
.
This paper uses the conv
entional
synt
hes
i
s
l
oad m
odel i
n
PSASP [6], analysis the
model struct
ure and its achiev
em
ent process in PSASP, proposes
a parameter identificati
o
n
method ba
se
d on improve
d
pertu
rbed
method, t
he method com
b
ine
s
param
eters id
entification
pro
c
e
s
s with
paramete
r
s sen
s
itivity analyzin
g
p
r
o
c
e
ss, and re
duce
mo
re computation
a
n
d
comp
uting time, the simul
a
tion re
sult
s
proved its vali
dity and feasi
b
ility.
2. Rese
arch
Metho
d
2.1. Complete Sy
nthesis Load Model
The
stru
ctu
r
e
of the
synth
e
si
s lo
ad
mo
del di
re
ctly consi
deri
ng
di
stributio
n net
work
is
sho
w
n a
s
Fig
u
re 1 [5], the
model in
clud
es the e
qual
static loa
d
, the equal
elect
r
ic moto
r loa
d
,
the
equal dist
ribution network circuit
a
n
d
com
pen
sa
t
o
r of re
active
powe
r
, there
is a virtual b
u
s
betwe
en b
u
s
bar
and
power loa
d
, an
d i
t
is the e
qui
valent impe
da
nce
of the di
stribution n
e
twork
betwe
en virtu
a
l bus
L
U
and a
c
tual bus
S
U
[10].
Extended ZIP model ca
n b
e
denote
d
as:
2
00
0
2
00
0
(/
)
(
/
)
(/
)
(
/
)
ss
Z
I
P
s
sZ
I
P
PP
P
U
U
P
U
U
P
QQ
Q
U
U
Q
U
U
Q
(
1
)
W
h
er
e
s
P
,
s
Q
,
0
s
P
,
0
s
Q
indicate a
c
tive po
we
r,
rea
c
tive po
we
r,
the initial
ste
ady-stat
e
values of the
active power and re
active
powe
r
,
Z
P
,
I
P
,
P
P
indicate a
c
tive powe
r
ch
aract
e
risti
c
s
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046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3799 – 38
04
3800
para
m
eters,
Z
Q
,
I
Q
,
P
Q
indicate
rea
c
tive powe
r
characteristics p
a
rameters, an
d satisfy
1
ZI
P
PP
P
,
1
ZI
P
QQ
Q
,
U
and
0
U
are bu
s voltage and
bus voltag
e initial steady-state value.
Figure 1. The
Synthesis Lo
ad Model Structure
Di
re
ctly Consi
deri
n
g
Distrib
u
tion
Network
Dynami
c
pa
rt
of the synth
e
si
s loa
d
mo
del
us
es
th
re
e
-
or
de
r
indu
c
t
io
n
e
l
ec
tr
ic
mo
tor
model, the st
ate equatio
n and outp
u
t eq
uation of whi
c
h sho
w
a
s
bel
ow [7]:
'
0
'
0
2
1
()
(
)
1
()
(
)
1
()
)
d
dq
r
q
q
qd
r
d
r
dd
q
q
L
r
r
dE
EX
X
I
E
dt
T
dE
EX
X
I
E
dt
T
d
E
IE
I
T
A
B
C
dt
H
(
(
2
)
22
22
1
()
(
)
1
()
(
)
ds
d
d
q
q
s
qs
q
q
d
d
s
IR
U
E
X
U
E
RX
IR
U
E
X
U
E
RX
(
3
)
The Equatio
n
(2) a
nd (3)
are the
state
equat
ion
an
d output eq
u
a
tion of the indu
ction
motor’
s three
-
order ele
c
tro
m
ech
ani
cal transi
ent mod
e
l
[8].
U
is the
system i
nput,
d
I
and
q
I
are the
syste
m
output,
is the system
operating fre
quen
cy.
s
R
and
s
X
are the eq
u
i
valent
resi
ste
r
a
nd l
eakage
impe
dan
ce
of
the stator
win
d
in
g,
r
R
an
d
r
X
are
the eq
uivalen
t
re
sist
e
r
and lea
k
a
ge i
m
peda
nce of the rotor
wind
ing,
m
X
is the m
u
tual indu
cta
n
ce im
peda
n
c
e bet
wee
n
rotor
windi
ng
and stato
r
winding, an
d satisfy
m
s
X
X
X
,
'
0
()
/
rm
r
TX
X
R
,
)
/(
'
r
m
r
m
s
X
X
X
X
X
X
.
r
is the
spe
e
d
of rotation,
'
0
T
is the o
pen
–
c
ircuit tra
n
si
e
n
t time co
nst
ant of the st
a
t
or,
H
is
inertia
co
nst
ant of ind
u
ction motor,
)
(
2
C
B
A
T
T
r
r
L
m
is the
me
chani
cal to
rqu
e
of the
indu
ction mot
o
r,
q
q
d
d
I
E
I
E
T
'
'
e
＝
is the electrom
agn
etic torque,
L
T
is th
e load co
efficient.
A
,
B
and
C
are the mechani
cal torq
ue coefficient of
the inducti
on motor, a
nd filled with
1
AB
C
.
pm
K
is denoted a
s
the rate of the equivalen
t
electric mot
o
r over the total powe
r
lo
ad,
whic
h is
defined as
following:
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Powe
r Loa
d Modelin
g Based on
Im
proved Perturbed
Method (Shi
Guopi
ng)
3801
'
00
/
pm
KP
P
(
4
)
In Equation (4),
0
P
is the init
ial active po
wer
of the lo
ad test no
de,
'
0
P
is the the initial
active po
wer
of the equival
ent electri
c
m
o
tor.
lf
M
is the rated i
n
itial load rat
e
coeffici
ent, whi
c
h is d
e
fin
ed as b
e
lo
w:
'
00
lf
M
BB
PU
M
SU
(5)
In Equation
(5),
M
B
S
and
B
U
are t
he rated
ca
p
a
city an
d rate
d voltage
of t
he e
quivalen
t
elec
tric
motor,
0
U
is the initial voltage of the load testing
node.
Acco
rdi
ng to
the structu
r
e of the com
p
lete
synthe
sis load mo
de
l, the reactive power
comp
en
satio
n
capa
citor conne
cts to th
e virtual
bu
s
L
U
dire
ctly, so t
he voltag
e of
the
cap
a
cito
r
is
L
U
, by definition,
2
CC
C
QI
X
, where
L
C
C
U
I
X
, arriv
i
n
g
at
2
L
C
C
U
Q
X
, fo
llowing it,
2
2
L
C
Q
C
f
U
(
6
)
2.2. The Parameter
s
of S
y
nthesis
Load Model Nee
d
to be Inde
ntified
There are 15
para
m
eters n
eed to b
e
ide
n
tified in synt
hesi
s
lo
ad m
odel [8-9], including
8
electri
c
moto
r param
eters:
R
s
, X
s
, X
m
, R
r
, X
r
, H
，，
AB
，
4 static mo
del paramete
r
s: P
Z
, P
I
, Q
Z
, Q
I
and othe
r pa
rameters:
K
pm
, M
lf
and
X
c
.
This
pap
er i
d
entifies th
e m
odel p
a
ramet
e
rs
by the
m
e
thod
of Parti
c
le
swarm al
gorithm
[10-11], it is
d
i
fficult and in
accurate to id
entify
model
para
m
eters
o
ne by on
e, so
this pa
pe
r o
n
ly
identifies the
pa
ramete
rs
with hi
gh
se
n
s
itivity ac
cording to
sen
s
i
t
ivity analyzin
g results
set
by
improve
d
pert
u
rbe
d
metho
d
.
2.3. Sensitiv
it
y
Analy
s
is
Bas
e
d on Improv
ed Perturbation M
e
thod
Given pe
rturbed p
r
obl
em
s belo
ng to
a cla
ss
of fixed probl
ems in
clu
d
in
g small
para
m
eters, just like differential equ
atio
n:
,,
0
,0
Lu
x
Bu
, where
01
(7)
If the sol
u
tio
n
of Eq
uatio
n (8
)
ca
n b
e
de
scribe
d b
y
a po
we
r
serie
s
of
:
,
ux
～
0
1
n
n
n
ux
u
x
x
, and is unif
o
rmly valid i
n
Ω
dom
ain,
then the Eq
uation (7) i
s
a
can
oni
cal pe
rturbed P
r
oble
m
in
Ω
doma
i
n, otherwise is a si
ngula
r
probl
em, sin
g
u
lar p
e
rtu
r
be
d
method u
s
e
s
in solving the
pertu
rbe
d
pro
b
lems
whe
n
the ca
noni
cal
pertu
rbe
d
me
thod fails [11]
.
In sh
ort, pe
rt
urbe
d m
e
tho
d
mea
n
s adj
u
s
t the val
ue o
f
one
parame
t
er fixing the
others by
certai
n step l
ength in its value ra
nge, a
nd anal
y
s
is th
e respon
se v
a
riation of the
model.
This
pap
er
uses
s a
n
imp
r
o
v
ed pe
rturb
e
d
metho
d
in
p
a
ram
e
ter i
d
e
n
tification, na
mely, fix
one p
a
ramet
e
r
with the ty
pical val
ue, a
nd ide
n
tify
other
paramete
r
s, if the
curv
e fitting re
sul
t
s
are p
e
rfe
c
t, the pa
ramete
r is co
nsi
dere
d
rathe
r
low in sensitivity, other
wise, the pa
ramete
r is
con
s
id
ere
d
rather hig
h
in
sen
s
itivity a
nd nee
d
to be identified. The metho
d
can a
nalysi
s
the
sen
s
itivity of the model p
a
rameters an
d ident
ify the paramete
r
’s val
ue at the sam
e
time.
The identifica
t
ion pro
c
e
ss
based on imp
r
oved pe
rturb
ed method i
s
as follo
ws:
Step 1: Set p
o
we
r n
e
two
r
k fault, obtain
meas
ured
active and
rea
c
tive power
re
spo
n
se
unde
r differe
nt fault.
Step 2: Fix one p
a
ra
met
e
r
with the t
y
pical valu
e, identify other pa
ram
e
ters of the
compl
e
te syn
t
hesi
s
load m
odel u
s
ing Pa
rticle
swa
r
m
algorith
m
, if the identifyi
ng
erro
r is little, the
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TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3799 – 38
04
3802
para
m
eter
se
nsitivity is rather lo
w, the value of pa
ra
meter can b
e
ty
pical, then turn to step
3
,
in
contrast, the
para
m
eter n
e
eds to be id
e
n
tified ane
w, repe
at step 2.
Step 3: Choo
se an
other p
a
ram
e
ter with
typical
value, identify the rest paramete
r
s, if the
identificatio
n results a
r
e p
e
rfect, the pa
ramete
r sen
s
i
t
ivity
is rathe
r
low, the valu
e of para
m
et
er
can b
e
typical
,
then turn to st
ep 4, othe
rwise rep
eat step 3.
Step 4: O
n
t
he a
nalo
g
y
of this, the
sensit
ivity of
all the
mode
l pa
ramete
rs ca
n b
e
obtaine
d o
n
e
by on
e, the
paramete
r
s
with lo
w
se
n
s
itivity
can u
s
e
typi
cal provided by
EPRI
dire
ctly, other param
eters with hi
gh
sen
s
itivity need to be identifie
d.
3. Results a
nd Analy
s
is
To take the
EPRI-36
nodal sy
stem as an illu
stration in the Power System
A
nalysi
s
Package (PS
ASP), EPRI-36 nodal
sy
stem is show
n in
Figure
2. The transi
ent data of t
h
e
compl
e
te synthesi
s
load
m
odel
can be gotten by
PSASP, the dataset of
each nodal point
can
be
see
n
as field
measured dat
a from po
wer
fault wave re
corde
r
s.
The typical p
a
ram
e
ters value of the com
p
lete
synthe
si
s load mo
del
is sh
own in Table 1
Figure 2. EPRI-36
Nod
a
l Point System
Table 1. The
Typical Para
meters Value
of the Electric Motor Provided by EPRI
R
s
X
s
X
m
R
r
X
r
H A
B
C
EPRI 0
0.120
3.5
0
.020
0.12
2
0.85
0
0
.15
3.1. Fix One Parameter, Identify
other
Parameter
s
Fix param
ete
r
X
m
and set
X
m
=3.5, the curve fitting
comp
arin
g the re
spo
n
se
of load
model with m
easure
d
re
sp
onse is sho
w
n in Figure 3.
It can be de
ri
ved from Fig
u
re 3 that the
param
eter
X
m
take typical
value, the simulation
result is still very well, t
herefore, the se
nsitivity of
X
m
is rathe
r
low
and ne
ed not
to be identified.
The se
nsitivity of
X
m
is high enou
gh an
d
need
s to be determi
ned o
n
the cont
rary
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Powe
r Loa
d Modelin
g Based on
Im
proved Perturbed
Method (Shi
Guopi
ng)
3803
Figure 3. The
Curve Fitting
of Model Re
spo
n
se
Com
parin
g with M
easure
d
Re
spon
se (fix
X
m
)
3.2. Fix another Parame
ter, Identif
y
t
h
e Res
t
of
th
e Parameter
s
Paramete
r X
m
and X
s
ta
ke typical va
lue, namely
X
m
=3.5 and
X
s
=
0
.18, identify the
others,
the si
mulation re
su
lt
comp
ari
ng model re
sp
o
n
se
with m
e
a
s
ured
respon
se is displayed
in
Figure 4.
Figure 4. The
Curve Fitting
of Model Re
spo
n
se
Com
parin
g with M
easure
d
Re
spon
se (fix
X
m
and
X
s
)
It is
clea
r fro
m
Figu
re
4 t
hat when
X
s
take
s typical
value recom
m
ende
d by
EPRI, the
curve fitting i
s
very bad, the model
re
spon
se is
n
o
t in confo
r
mity with the me
asu
r
ed
re
spo
n
se
throug
hout th
e pe
riod,
so
the
sen
s
itivity of
X
s
is
high,
can
not ta
ke
typical val
ue
a
nd n
eed
s to
b
e
determi
ned rene
w.
3.3. Determine the Sensitivit
y
of
All
Model Parameters One
b
y
One
Acco
rdi
ng to
the ab
ove-m
entione
d met
hod
s,
the
sen
s
itivity of all model
param
eters ca
n
be g
o
tten. Th
e final
co
ncl
u
sion
is that th
e sen
s
itivity of
X
s
,
R
r
,
K
pm
, M
lf
,
P
V
,
Q
V
is high eno
ugh
to
need to be id
entified and the sen
s
itivit
y
of the others i
s
very low to take typical va
lue provide
d
by
EPRI.
3.3. The Verification o
f
Improv
ed Per
t
ur
ba
tion Me
thod Sensi
t
iv
it
y
Analy
z
in
g Method
Take th
e BUS20 load u
n
d
e
r fault 1 for
an exampl
e, the identification
re
sult is
shown in
Table 2. The
curve fitting of model re
spo
n
se
only identifying 6 para
m
eters compa
r
ing wit
h
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3799 – 38
04
3804
measured re
spo
n
se is
sh
own i
n
Figu
re 5. Accord
in
g to the re
sul
t
s, the sim
p
lified ide
n
tificat
i
on
strategy n
o
t only red
u
ce
s comp
utation
,
but al
so g
e
t better cu
rve fitting of
model respo
n
se
comp
ari
ng
wi
th mea
s
ured
re
spo
n
se, which
will o
n
ly identify 6 p
a
ram
e
ters, th
e identificatio
n
result is not
worse com
parin
g with i
dentifyi
ng all param
eters, even better, and prove
s
the
identificatio
n strategy’
s
validity.
Figure 5.
The
Curve Fitting
of Model Re
spo
n
se Com
parin
g with M
easure
d
Re
spon
se (o
nly 6
para
m
eters)
Table 2. The
Paramete
rs Identificatio
n Re
sult
of BUS20 unde
r Fa
ult 1 Only with Determinin
g 6
Parameters
X
s
R
r
K
p
m
F1B20
0.1993
0.0188
0.6139
M
lf
P
v
Q
v
Error
J
0.5120
0.6273
0.2476
0.0034
4. Conclusio
n
This p
ape
r p
r
opo
se
s a
pa
ramete
r ide
n
tification meth
od ba
sed
on
improved
pe
rturb
e
d
method, the
method
com
b
ine
s
pa
ram
e
ters ide
n
ti
fication p
r
o
c
ess with
pa
ra
meters sen
s
i
t
ivity
analyzi
ng p
r
o
c
e
s
s togethe
r, and
red
u
ce
more
co
m
put
ation an
d
co
mputing time,
the si
mulatio
n
results p
r
ove
d
its validity and feasi
b
ility.
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