Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 3,
Jun
e
201
6, pp. 554 ~ 56
5
DOI: 10.115
9
1
/ijeecs.v2.i3.pp55
4-5
6
5
554
Re
cei
v
ed Ma
rch 3, 2
016;
Re
vised
Ma
y 10, 2016; Accepted Ma
y 24
, 2016
Design of Robust UPFC Based Damping Controller
Using Biogeography Based Optimization
SA Al-Ma
w
s
a
w
i
*
1
, A Haid
er
2
, SA Al-Qallaf
3
Dep
a
rtment of Electrical
and
Electron
ics En
gin
eeri
ng, Co
ll
ege of En
gin
e
e
r
ing, Un
iversit
y
of Bahrain
Univers
i
t
y
of POB 32038, Sak
heer, Bahr
ai
n
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: aalmoss
a
w
i
@
uo
b.edu.
bh
1
, aakab
har@
u
o
b
.edu.b
h
2
,
saa1
98
5@h
o
tmail.com
3
A
b
st
r
a
ct
In
this paper a new
optimiz
ation algorithm
, the biogeography based opt
imiz
ation (BBO) is
employed
to design a robust pow
er oscillation damping
(P
OD) controller using unified pow
er flow
controller
(UPFC). The controller
that is
used to damp
low
frequency
oscillation
is designed
over a
w
i
de range
of
operating
points using tw
o different
objective functions. T
he obtained
c
ontrollers are then verified through
time-domain simulation over
different
loading conditi
ons
w
i
th different system uncertainties
introduced.
Ke
y
w
ords
:
P
o
w
e
r system
oscill
atio
n, unif
i
ed p
o
w
e
r flo
w
controller, Biog
eogr
ap
hy b
a
sed o
p
ti
mi
z
a
t
i
on,
mu
ltip
oint opti
m
i
z
at
io
n
Copy
right
©
2016 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
In
the past
few decades the
power system
s
have witnessed a
tremendous increase in
size due to the rapid and
continuous demand for pow
er. This
gave rise to the interconnection
of
power
networks, thus increas
ing the
systems complexity. This is
due to the limited and
restricted resources
and the
stri
ct environmental
constraints.
The interconnection
of remote
power networks usually
introduce low frequency
o
scillations in the
range of 0.1~3.0Hz
[1].
These oscillations can
deteriorate the
system per
formance if
they are
not
sufficiently
damped as
they grow in magnitude, and finally lead to loss of synchronism [1, 2].
This
problem lead to
use of power
syst
em stabilizers (PSS),
are used to provide
damping for generator oscillations. The PSS
is a
supplementary controller in the
excitation
systems.
The PSS provides satisfactory oper
ation under unusual or abnormal conditions which
maybe encountered some times
[1]
. While PSS are effective in damping power oscillations, they
suffer
a drawback of
being responsible of
causi
ng significant variations
in voltage profile and
they may even result in a leading power fact
or operation under sever disturbance conditions
[3]
.
On the other hand, FACTS controllers hav
e come up as another solution for this
problem.
The flexiable AC transmission systems
(FACTS) controllers were intended to solve
various power
system steady
st
ate control
problems such
as
voltage regulation,
power flow
control, and transfer capability enhancement. The
damping of the power system oscillations
were
introduced in FACTS as
a supplementary c
ontrol function
[4]. Due to these capabilities,
FACTS c
ontrollers
’ ins
t
allation provides
a better s
o
lution over PSS.
Wang
[5], has investigated the capabilities
of Static Var Compensator (SVC),
Controllable Series Compensator (CSC), and P
hase Shifters (PS) to damp power system
oscillations
in an SMIB system. In [3], a c
oordinated control of PSS and SVC was introduced.
Several references in literatures have invest
igated the capability of the Thyristor
Controlled
Series
Capacitor (TCSC) to damp the power
system oscillations through different approaches.
In [6], a Genetic Algorithm (GA) based power
system stabilizer using TCSC was designed.
STATCOM
capability to damp power system o
scillations
was superior to that of SVC
[4]. In [7], a singular value decomposition (SVD)
was introduced to investigate the controllability
of poorly damped electromechanical modes via STATCOM input channels.
Being the most
versatile FACTS
controller,
UPFC had
become an
interesting field
of
research
for damping power system oscillations
. In
[8], a UPFC based stabilizer was developed
to
mitigate torsional
oscillations using shunt
c
onverter phase angle
as a control
signal. Abido et
al [9], has introduced a particle swarm based stabiliz
er using UPFC in which he has investigated
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 554
– 565
555
the controllability of the
UPFC different input
channel to damp power
system oscillations. It
was
observed that the shunt
converter phase angle
provides
better controllability for
damping
electromechanical
oscillations compared to t
he other input channels. In [2], a coordinated
control design for UPFC and PSS based on particle swarm was developed.
In
this paper, biogeography
based optimization
(BBO)
algorithm is used
to find the
optimal parameters for
the UPFC
based damping cont
roller.
In order
to find the
optimal set
of
parameters to
ensure the
system
robustness, the BBO
searches for
optimal sets
of a time
based
objective function over a wide range
of oper
ating conditions. This time based objective
function eliminates the need to linearize the sy
stem for finding the system eigenvalues.
The
time-based objective function
for robust
tuning
is compared
to the
eigenvalue-based objective
function for robust tuning of the controller.
2. Sy
stem Modeling
2.1. Po
w
e
r S
y
stem and Unified Po
w
e
r
Flo
w
Contro
ller Model
Figure 1, shows
a single machine
infinite
bus (SMIB)
system with double
transmission
line circuits
equipped with
a UPFC.
The UPFC
consists
of two
three phase
GTO based voltage
source converters (VSC) connected back to
back through a common DC link capacitor. The
shunt converter or the excitation
converter
is coupled to
the system through an
excitation
transformer
(ET). The
series converter or
t
he boosting
converter is coupled
to the system
through a boosting transformer (BT).
Figure 1. SMIB powe
r
syst
em equip
ped
with UPF
C
By applying
Park's tran
sf
ormatio
n
a
n
d
by n
egle
c
tin
g
the
re
si
sta
n
ce
s
and
tra
n
sie
n
ts
of
the excitation
and boo
sting
transfo
rme
r
s the UPFC ca
n be model
ed
as
[5, 8, 9]
:
0
0
2
cos
sin
(1)
0
0
2
cos
sin
(2)
3
4
|
cos
sin
|
3
4
|
cos
sin
|
(3)
Whe
r
e;
v
Et
: Excitation transf
o
rme
r
voltage
i
E
: Exc
i
tation
c
u
rrent
v
Bt
: Boosting
transfo
rme
r
voltage
i
B
: Boosting current
C
dc
:
DC link
cap
a
cit
a
nc
e
v
dc
: DC link v
o
ltage
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IJEECS
ISSN:
2502-4
752
De
sign of Ro
bust UPF
C
B
a
se
d Dam
p
in
g Controlle
r Usi
ng Bioge
o
g
rap
h
y …
(S
A Al-Maw
sa
w
i
)
556
The
UPF
C
h
a
s fo
ur control inp
u
t si
gn
als
wh
ere
m
E
and
δ
E
are
t
he ex
citation
bran
ch
amplitude
an
d pha
se
angl
es
re
spe
c
tivel
y
, and
m
B
and
δ
B
a
r
e the
b
oostin
g
b
r
an
ch amplitu
de a
nd
pha
se an
gle resp
ectively.
The nonlinear model of the generator shown in Figure 1 is given as:
1
(4)
1
1
(5)
′
1
′
′
′
(6)
1
(7)
Where;
,
′
′
,
,
,
,
and
From the above equations, the network
currents can be rewritten as:
1
2
sin
cos
(8)
1
2
cos
sin
(9)
′
2
sin
cos
2
sin
(10
)
2
cos
sin
2
cos
(11
)
′
2
sin
cos
2
sin
(12
)
2
cos
sin
2
cos
(13
)
where
x
E
and
x
B
represents the leakage
reactances
of ET
and BT respectively,
while
x
BB
,
x
d1
-
x
d7
, and
x
q1
-x
q7
are given in
[10]
.
2.2. Sy
stem
Linearized M
odel
In order to assess the stability of the sy
stem, and to construct an objective function
based on
the system
eigenvalues, a
linearized model
of
the
system is
to be
determined. For
this
purpose,
the system
has to be
linearized around di
fferent
operating points. The
linear model is
given by:
(14
)
where
x
is the state vector and
u
is the input vector :
∆
∆
∆
′
∆
∆
(15
)
∆
∆
∆
∆
(16
)
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 554
– 565
557
where
A
and
B
are:
0
00
0
0
′
0
′
1
′
′
0
1
0
0
(17
)
00
0
0
′
′
′
′
(18
)
Whe
r
e;
K
1
-K
9
, K
pu
,K
qu
,
and
K
cu
are the lineari
z
ation
co
nstant
s.
2.3. UPFC-Based Damping Con
t
rolle
r
The structure of the damping controller is shown in
Figure
2
. It
consists of
a washout
circuit which
is provided
to eliminate
the steady state
bias from the output of the damping controller.
Figure 2. UPFC Based Da
mping Contro
ller
A
common practice
for the design
of the dynam
ic
compensator is
the use of
a two stage
lead-lag
stage compensator. The two stage cont
roller
is also widely used for FACTS based
damping controllers. On the
other hand, PID cont
rollers,
as dynamic compensator in
power
system stabilizers,
have also
been implemented
in damping
system oscillations.
In [11],
a
PID
controller design based on particle swarm optim
ization for a multimachine system was
implemented. In this paper the two stage lead-lag
compensator is used. The transfer function
of
the two stages controller is given by:
1
1
1
1
(19
)
The control signal
u
of the UPFC can be
any
of the input signals
m
E
,
δ
E
,
m
B
, or
δ
B
.
Based on
[2, 9,
10]
, a singular
variable decomposition was app
lied to measure the controllability
of
the electromechanical (EM)
mode,
and it was
found that
δ
E
had the best
controllability
measurement
compared to the other UPFC
contro
l signals. Thus it is
logical to consider
δ
E
as
the control signal when designing a damping controller.
u
u
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IJEECS
ISSN:
2502-4
752
De
sign of Ro
bust UPF
C
B
a
se
d Dam
p
in
g Controlle
r Usi
ng Bioge
o
g
rap
h
y …
(S
A Al-Maw
sa
w
i
)
558
2.4. Objectiv
e Functio
n
In order to find the
optimal set of param
eters of
the damping controller using BBO,
an
objective function
needs to
be optimized.
Seve
ral time
domain based
performance indices have
been proposed
in literatures,
such as
integral of
time
multiplied by
the absolute
value of error
(ITAE) criterion. In other performance i
ndices such as eigenvalue based functions, the
parameters
are tuned in
stabilizing power syst
ems. This
section presents two objective
functions that are used to des
ign a robust damping controller.
2.4.1. Eigen
v
alue Bas
e
d
Objectiv
e Function
In this approach, the damping coefficients
of the eigenvalues are to be
maximized.
Then the damping coefficient
ζ
i
of the
i-th
eigenvalue is defined through the following equation:
(20
)
Where
α
i
and
β
i
are the real
and imaginary parts
of t
he dominant
eigenvalue respectively. A
well
damped power
system is
said to
have a
dam
ping for
all eigenvalues
greater than
5%
[
Error!
Reference
source not found.
]
. Thus,
the objective
of the optimization
problem is
to achieve
a
damping for all eigenvalues greater than 5%
over the range of the operating points.
Let
Ξ
p
be a vector of the damping factors of all eigenv
alues of the p-th operating point in the set,
where p=1,2,..,n for n operating points. Then
the objective function to be maximized is:
max
(21
)
Where;
Ξ
2.4.2. Time Based Obje
cti
v
e
Function
For
a robust tuning using
the ITAE criterion,
the objective
function for set of operating
points is designed as:
|
∆
|
(22
)
In both cases, the eigenvalue based objective
function is to be maximized, while the
time based objective
function is
to be
minimized.
The objective
functions are
subject to
the
following constraints:
(23
)
In both cases
only a DC
voltage regulator is
incorporated in the
system in order
to
stabilize the DC link
voltage. The parameters
for the DC regulator
are obtained beforehand
and
kept constant during t
he optimization process.
3. Biogeogr
a
p
h
y
Based O
p
timization
Biogeography-Based Optimization (BBO), introduced
by Simon [
Error! Reference
source
not found.
] is a population based stochastic based ev
olutionary algorithm. Based on
island
biogeography theory, biogeography is the nature
wa
y to achieve optimal condition of
life
through the distribution of species
among islands
. This can
be translated to a
mathematical
optimization
problem, in
which a number
of c
andidate
solutions referred to
as population and
each solution from the population
is termed as i
ndividual. An
individual that performs well on
the
objective function is analogous to an island that
attr
acts different spices and it is said to
have
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752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 554
– 565
559
high
suitability index (HSI), and the individuals t
hat perform poor on the objective function are
analogous to low HSI islands where it
attracts lower number of species.
The mathematical model of biogeography descr
ibes the immigration and emigration of
species from an
island. Islands with
high HS
I have
high emigration rates
and low
immigration
rates, due to the
high population of species
in t
hat island. Low
HSI islands have low
emigration
rates
and high immigration rates and
that is due
to the large
space and low species in these
islands.
The factors that
characterize the HSI
of
an island are
called suitability index variables
(SIV),
and it includes
vegetativ
e diversity, rain
fall, topographic diversity,
land area and
temperature.
If an optimization
problem was
to be
solv
ed using
BBO, the
independent variables
of
the problem are analogues to the SIV of an island,
and the solutions for that proposed
individual
is the
HSI of
such an
island. As
in biogeogr
aphy theory
that high
HSI islands
having lower
immigration rate thus
it will
be more relu
ctant
to change
than the low
HSI islands
having
immigration rates. Therefore, a good
indi
vidual will have low
tendency to change than
poor
individuals. On the other
hand, the high
HS
I islands have high
emigration rate and
hence
tendency
to share its
features with the low
HSI
islands having low
emigration rates. Thus, the
good
individuals will share its features
with the poor
individuals. The
addition of new features to
poor individuals may raise the quality of those individuals.
MacArthur and Wilson [14], has illustrated
the model of species abundance on a single
island as shown in
Figure 3. Immigration
rate
λ
and
emigration rate
µ
are functions of
the
number of species in the island.
Figure 3. Specie
s migratio
n model of an
is
land, ba
se
d on [MacA
r
thur an
d Wil
s
o
n
, 1967 [
Error
!
Reference s
o
urce not found.
]]
In BBO each individual
is represented by
an identical species count
curve with
E=
I
for
simplicity, as illustrated in Figure
4. The mi
gration model shown
below is called a
linear
migration model where
λ
and
µ
are both linear functions of the cost.
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IJEECS
ISSN:
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752
De
sign of Ro
bust UPF
C
B
a
se
d Dam
p
in
g Controlle
r Usi
ng Bioge
o
g
rap
h
y …
(S
A Al-Maw
sa
w
i
)
560
Figure 4. BBO individual
speci
e
s
cou
n
t curve
with E=I
BBO has two
major o
perations:
3.1. BBO Mi
gration
Con
s
id
er the
followin
g
con
s
train
ed opti
m
ization p
r
o
b
l
em:
min
∈
(24
)
whe
r
e
,
,⋯
,
x
would be an individual
which is analogous to an
island, and
x
1
,
x
2
,…,
x
n
would be
analogous
to SIV of an island.
Hence when a migrat
ion occurs the
SIV's of an island will either
immigrate
to the individual or the
will emigrate
from the individual.
In BBO a use of migration
rates of
each individual
to probabilistically
s
hare
information between
individuals. There are
different ways to
implement migration in
BBO,
but in
this study the
original BBO developed
in
[
Error! Reference
source not
found.
] will
be used which
is referred to
as partial immigration
based.
Suppose
that there are a population of size
N
and
that
x
k
is the
k-t
h
individual in the
population where
∈
1,
,
and the size
of the
optimization problem is
n.
x
k
(s)
is
the
s-t
h
independent variable
in the
individual, where
∈
1
,
. Based
on the
cost function
evaluation
the immigration
probability
λ
k
, is
given for
the
k-t
h
individual
and for
all of
its solution features
∈
1,
, so
in each
generation there
would be
a probability
of
λ
k
that this
individual will be
replaced.
Once a solution
feature is selected
to be
replaced, then selection
of the
emigrating
solution feature is done based on the emig
rating probability of that individual {
µ
i
}.
3.2. BBO Mu
tation
In
BBO there are two
main operators, i.e, migration
and mutation. Simon
[
Error!
Reference source not
found.
]
, has referred to mutation of SIV to be analogous to the introduction
of
an excursion to
a habitat that will
drive it
away
from its equilibrium point
and that can happen
randomly. An
example is
the arrival
of large
piec
e of
flotsam to
the island.
Mutation rates
are
determined through the species count probabilities using equation (25).
µ
µ
,
0
µ
µ
,1
1
µ
,
(25
)
From
Figure 4,
it can
be seen
that for lo
w
species count
and high
species count both
have relatively low probabilities.
While for medi
um
species count they
have high probabilities
for
change as they are near the equilibrium point.
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IJEECS
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2, No. 3, Jun
e
2016 : 554
– 565
561
The mutation rates can be found as:
1
(26
)
Where;
m
i
: the
i-th
individual mutation rate
m
ma
x
:
the maximum mutation rate
P
i
:
i-th
individual species count probability
P
ma
x
:
Maximum species count probability from all individuals
4. Simulation Resul
t
s
In this paper, the robust
UPFC based dampi
ng controllers are
tuned using BBO at
30
different
loading conditions. The resulting controlle
rs are tested for 4 different loading conditions
with different parameters uncertainti
es that are presented in Table 1:
Table 1. System ope
rating
points a
nd its unce
r
taintie
s
Loading Conditio
n
P
e
Q
e
S
y
stem Paramet
e
r uncertaint
y
Light Loading
0.30
0.015
30% increase in line reactance
x
t1
Nominal Loading
1.0
0.015
No param
eter un
certaint
y
Heav
y
Loa
ding
1.1
0.4
25% increase in
machine inertia
M
Leading po
w
e
r fa
ctor
0.7
-0.03
30% increase in f
i
eld time constan
t
T'
d0
By applying BBO for the two objective
functi
ons mentioned above, and
by initializing
the
BBO
for 100 generations, 100 individuals and for
a maximum mutation rate of 0.005, the
following results are obtained as
shown in the Figure 5
and Figure 6. The figures
below
demonstrate the convergence curv
e of the objective
functions. For Figure 5, as it
was
mentioned
earlier, the
objective is to
maximize
the
damping ratio of
the
system
where it reached
(
ζ
i
=0.2496). As for the time based controller the obj
ective was to minimize the absolute time
error.
It can be seen from the Figure 6, that the
cost function has reached
a value of 0.1247, i.e.
∑
0
.
1247
.
Figure 5. Con
v
ergen
ce
cha
r
acte
ri
stic curve
for a robu
st eigenvalue
UPFC b
a
sed
dampin
g
controlle
r usi
ng BBO
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IJEECS
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De
sign of Ro
bust UPF
C
B
a
se
d Dam
p
in
g Controlle
r Usi
ng Bioge
o
g
rap
h
y …
(S
A Al-Maw
sa
w
i
)
562
Figure 6. Con
v
ergen
ce
cha
r
acte
ri
stic curve
for a robu
st time-value UPFC b
a
sed
dampin
g
controlle
r usi
ng BBO
The obtain
ed
para
m
eters o
f
the lead lag cont
rolle
r for the two obj
ecti
ve function
s are
sho
w
n in
Table
2
.
Table 2. Opti
mal paramete
r
setting of th
e dampi
n
g
co
ntrolle
r for the two obje
c
tive function
s
Time-value base
d
objective functi
on
Eigenvalue based obj
ective function
K
p
-94.8712
-95.7387
T
1
0.0143
0.0759
T
2
0.3284
0.7685
T
3
0.7778
1.4892
T
4
0.7126
0.5692
In order to analyze and
compare the perform
ance of
the system
using the
resulting
controllers, simulations
were carried
out for
10% step
change in
the mechanical
power input
P
m
at
the four
different cases illustrated
in Table
1.
Table 3,
shows the sy
stem
eigenvalues for the
two optimization approaches compared with the
uncontrolled case. It can be shown that the
system is stabilized for all the test cases.
Table 3. System eigenval
u
e
s for
controll
ed and u
n
con
t
rolled cases
Light
Nominal
Heav
y
Leading
p.f
No
Control
-15
-5.4
0.2±j3.3
-0.4995
-15.7
-4.8
0.6±j3.7
-1.3
-15.6
-5.1
0.5± j3.6
-0.8
-16.8
0.4 ± j3.5
-3.0
-1.4
Eigen-value
Based
Control
-14.9
-6.2±j6.8
-1.4±j3.9
-6.1±j0.1
-1.1
-0.02
-0.2
-15.7
-6.6±j8.0
-1.4±j4.2
-5.4±j0.5
-1.1
-0.02
-0.2
-15.4
-6.9±j7.8
-1.3±j4.0
-5.3±j0.4
-1.1
-0.02
-0.2
-16.8
-6.9±j
7.5
-1.4±j
4.3
-4.5±j
0.6
-1.1
-0.02
-0.2
Time- value
Based Control
-15.2
-14.8
-1.9±j6.6
-5.7
-2.0±j4.0
-1.4
-0.02
-0.2
-15.8
-14.6
-1.8±j7.0
-5.2
-2.2±j4.2
-1.4
-0.02
-0.2
-15.6
-14.0
-2.4±j6.5
-5.3
-1.9±j4.4
-1.4
-0.02
-0.2
-16.8
-14.4
-1.8±j6.6
-3.9
-2.4±j4.3
-1.4
-0.02
-0.2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 554
– 565
563
4.1. Light Lo
ading Con
d
ition
Figure
7, shows
the system response
for
10%
step change in
mechanical input power
under light loading
conditions for
the two
designed damping
controllers from
the two
approaches. It can
be seen
that the
proposed ti
me-value based
tuned controller
has greater
overshoot compared
with the
eigenvalue based
tuned
controller which
exhibits more damped
response.
Moreover, the settling time
and the peak
time are
almost identical for both resulting
controllers.
Figure 7: Dynamic
re
spo
n
s
e to a 10% increa
se
in m
e
ch
ani
cal inp
u
t powe
r
for li
ght loadin
g
con
d
ition: soli
d line eigenv
alue ba
se
d controlle
r, da
shed line time
value ba
sed
controlle
r
4.2. Nominal Loading Co
ndition
The dynamic response of a nominal
loaded generator for a 10% step change in
P
m
is
illustrated in Figure 8. Similar to light loaded ca
se the time-value based controller has an
inferior
response compared to the eigenvalue based contro
ller in terms of the overshoot and damping.
Figure 8. Dyn
a
mic respon
se to a 10% incre
a
se in me
cha
n
ical input
powe
r
for no
minal loadi
ng
con
d
ition: soli
d line eigenv
alue ba
se
d controlle
r, da
shed line time
value ba
sed
controlle
r
Evaluation Warning : The document was created with Spire.PDF for Python.