Energy Conversion and Management 51 (2010) 2299–2306
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Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
Tuning of damping controller for UPFC using quantum particle swarm optimizer
H. Shayeghi a,*, H.A. Shayanfar b, S. Jalilzadeh c, A. Safari c
a
Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil, Iran
Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran
c
Technical Engineering Department, Zanjan University, Zanjan, Iran
b
a r t i c l e
i n f o
Article history:
Received 23 December 2008
Received in revised form 8 August 2009
Accepted 25 April 2010
Keywords:
UPFC
Quantum particle swarm optimization
Damping controller
Low frequency oscillations
Power system dynamics
a b s t r a c t
On the basis of the linearized Phillips–Herffron model of a single machine power system, we design optimally the unified power flow controller (UPFC) based damping controller in order to enhance power system low frequency oscillations. The problem of robustly UPFC based damping controller is formulated as
an optimization problem according to the time domain-based objective function which is solved using
quantum-behaved particle swarm optimization (QPSO) technique that has fewer parameters and stronger search capability than the particle swarm optimization (PSO), as well as is easy to implement. To
ensure the robustness of the proposed damping controller, the design process takes into account a wide
range of operating conditions and system configurations. The effectiveness of the proposed controller is
demonstrated through non-linear time-domain simulation and some performance indices studies under
various disturbance conditions of over a wide range of loading conditions. The results analysis reveals
that the designed QPSO based UPFC controller has an excellent capability in damping power system
low frequency oscillations in comparison with the designed classical PSO (CPSO) based UPFC controller
and enhance greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions show that the dE based damping controller is superior to the mB
based damping controller.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
As power demand grows rapidly and expansion in transmission
and generation is restricted with the limited availability of resources and the strict environmental constraints, power systems
are today much more loaded than before. This causes the power
systems to be operated near their stability limits. In addition, interconnection between remotely located power systems gives rise to
low frequency oscillations in the range of 0.2–3.0 Hz. If not well
damped, these oscillations may keep growing in magnitude until
loss of synchronism results [1,2]. In order to damp these power
system oscillations and increase system oscillations stability, the
installation of power system stabilizer is both economical and
effective. PSSs have been used for many years to add damping to
electromechanical oscillations. However, PSSs suffer a drawback
of being liable to cause great variations in the voltage profile and
they may even result in leading power factor operation and losing
system stability under severe disturbances, especially those threephase faults which may occur at the generator terminals [3].
* Corresponding author. Address: Technical Engineering Department, University
of Mohaghegh Ardabili, Daneshgah Street, P.O. Box: 179, Ardabil, Iran. Tel.: +98 451
5517374; fax: +98 451 5512904.
E-mail address: hshayeghi@gmail.com (H. Shayeghi).
0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.enconman.2010.04.002
In recent years, the fast progress in the field of power electronics had opened new opportunities for the application of the FACTS
devices as one of the most effective ways to improve power system
operation controllability and power transfer limits [1–4]. Through
the modulation of bus voltage, phase shift between buses, and
transmission line reactance, FACTS devices can cause a substantial
increase in power transfer limits during steady-state. Because of
the extremely fast control action associated with FACTS device
operations, they have been very promising candidates for utilization in power system damping enhancement. It has been observed
that utilizing a feedback supplementary control, in addition to the
FACTS device primary control, can considerably improve system
damping and can also improve system voltage profile, which is
advantageous over PSSs.
The unified power flow controller is regarded as one of the most
versatile devices in the FACTS device family [5,6] which has the
ability to control of the power flow in the transmission line, improve the transient stability, mitigate system oscillation and provide voltage support. It performs this through the control of the
in-phase voltage, quadrate voltage and shunts compensation due
to its mains control strategy [1,4]. The application of the UPFC to
the modern power system can therefore lead to the more flexible,
secure and economic operation [7]. When the UPFC is applied to
the interconnected power systems, it can also provide significant
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
Nomenclature
BT
D
DC
E0q
Efd
ET
FACTS
FD
GA
GTO
ITAE
K
KA
M
mE
mB
OS
Pe
PI
Pm
PSO
PSS
QPSO
boosting transformer
machine damping coefficient
direct current
internal voltage behind transient reactance
equivalent excitation voltage
excitation transformer
flexible alternating current transmission systems
figure of demerit
genetic algorithm
gate turn off thyristor
integral of the time multiplied absolute value of the
error
proportional gain of the controller
regulator gain
machine inertia coefficient
excitation amplitude modulation ration
boosting amplitude modulation ration
overshoot of speed deviation
electrical output power
proportional integral
mechanical input power
particle swarm optimization
power system stabilizer
quantum-behaved particle swarm optimization
damping effect on tie line power oscillation through its supplementary control.
An industrial process, such as a power system, contains different
kinds of uncertainties due to continuous load changes or parameters drift due to power systems highly non-linear and stochastic
operating nature. Consequently, a fixed parameter controller based
on the classical control theory is not certainly suitable for the UPFC
damping control design. Thus, it is required that a flexible controller
be developed. Several trials have been reported in the literature to
dynamic models of UPFC in order to design suitable controllers for
power flow, voltage and damping controls [8]. Dash et al. [9], Vilathgamuwa et al. [7] and Pal [10] suggested neural networks based
method and robust control methodologies, respectively to cope
with system uncertainties to enhance the system damping performance using the UPFC. However, the parameters adjustments of
these controllers need some trial and error. Also, although using
the robust control methods, the uncertainties are directly introduced to the synthesis, but due to the large model order of power
systems the order resulting controller will be very large in general,
which is not feasible because of the computational economical difficulties in implementing. Also, Kazemi and Vakili Sohrforouzani
[11], Dash et al. [12] and Limyingcharone et al. [13] used fuzzy logic
based damping control strategy for TCSC, UPFC and SVC in a multimachine power system. The damping control strategy employs
non-optimal fuzzy logic controllers that is why the system’s response settling time is unbearable. Moreover, the initial parameters
adjustment of this type of controller needs some trial and error.
Khon and Lo [14] used a fuzzy damping controller designed by micro genetic algorithm for TCSC and UPFC to improve powers system
low frequency oscillations. The proposed method may have not enough robustness due to its simplicity against the different kinds of
uncertainties and disturbances. Mok et al. [15] applied a GA based
PI type fuzzy controller for UPFC to enhance power system damping. Although, the fuzzy PI controller is simpler and more applicable
to remove the steady-state error, it is known to give poor performance in the system transient response.
Recently, the PSO technique is used for optimal tuning of UPFC
based damping controller [1]. PSO is a novel population based
SMIB
SVC
T1
T2
T3
T4
TA
TCSC
T 0do
Te
Ts
Tw
UPFC
US
V
vref
VSC
x
d
dB
dE
DPe
DVdc
single machine infinite bus
static var compensator
lead time constant of controller
lag time constant of controller
lead time constant of controller
lag time constant of controller
regulator time constant
thyristor controlled series compensator
time constant of excitation circuit
electric torque
settling time of speed deviation
washout time constant
unified power flow controller
undershoot of speed deviation
terminal voltage
reference voltage
voltage source converter
rotor speed
rotor angle
boosting phase angle
excitation phase angle
electrical power deviation
DC voltage deviation
metaheuristic, which utilize the swarm intelligence generated by
the cooperation and competition between the particle in a swarm
and has emerged as a useful tool for engineering optimization [16].
Unlike the other heuristic techniques, it has a flexible and well-balanced mechanism to enhance the global and local exploration abilities. Also, it suffices to specify the objective function and to place
finite bounds on the optimized parameters. However, the main disadvantage is that the PSO algorithm is not guaranteed to be global
convergent. In order to overcome this drawback and improve optimization synthesis, in this paper, a quantum-behaved PSO technique is proposed for optimal tuning of UPFC based damping
controller for enhancing of power systems low frequency oscillations damping. QPSO algorithm is depicted only with the position
vector without velocity vector, which is a simpler algorithm and
the results show that QPSO performs better than standard PSO
and is a promising algorithm due to its global convergence guaranteed characteristic [17].
In this study, the problem of robust UPFC based damping
controller design is formulated as an optimization problem. The
controller is automatically tuned with optimization a time
domain-based objective function by QPSO such that the relative
stability is guaranteed and the time-domain specifications concurrently secured. The effectiveness of the proposed controller is demonstrated through non-linear time simulation studies and some
performance indices to damp low frequency oscillations under different operating conditions. Results evaluation show that the QPSO
based tuned damping controller achieves good robust performance
for a wide range of operating conditions and is superior to the designed controller using CPSO technique.
2. PSO and QPSO
2.1. Particle swarm optimization
Particle swarm optimization algorithm, which is tailored for
optimizing difficult numerical functions and based on metaphor
of human social interaction, is capable of mimicking the ability
of human societies to process knowledge [18]. It has roots in two
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
main component methodologies: artificial life (such as bird flocking, fish schooling and swarming); and evolutionary computation.
As it is reported in [19–21], this optimization technique can be
used to solve many of the same kinds of problems as GA, and does
not suffer from some of GAs difficulties. It has also been found to be
robust in solving problem featuring non-linearity, non-differentiability and high-dimensionality.
PSO starts with a population of random solutions ‘‘particles” in
a D-dimension space. The ith particle is represented by Xi = (xi1,
xi2,. . ., xid). Each particle keeps track of its coordinates in hyperspace, which are associated with the fittest solution it has achieved
so far. The value of the fitness for particle i (pbest) is also stored as
Pi = (pi1, pi2, . . ., pid). The global version of the PSO keeps track of the
overall best value (gbest), and its location, obtained thus far by any
particle in the population. PSO consists of, at each step, changing
the velocity of each particle toward its pbest and gbest according
to Eq. (1). The velocity of particle i is represented as Vi = (vi1, vi2,
. . ., vid). Acceleration is weighted by a random term, with separate
random numbers being generated for acceleration toward pbest
and gbest. The position of the ith particle is then updated according
to Eq. (2) [1,18].
v id ðt þ 1Þ ¼ w v id ðtÞ þ c1 r1 ðPid xid ðtÞÞ þ c2 r2 ðPgd xid ðtÞÞ
xid ðt þ 1Þ ¼ xid ðtÞ þ cv id ðt þ 1Þ
ð1Þ
ð2Þ
where Pid and Pgd are pbest and gbest. Several modifications have
been proposed in the literature to improve the PSO algorithm speed
and convergence toward the global minimum. One modification is
to introduce a local-oriented paradigm (lbest) with different neighborhoods. It is concluded that gbest version performs best in terms
of median number of iterations to converge. However, pbest version
with neighborhoods of two is most resistant to local minima. PSO
algorithm is further improved via using a time decreasing inertia
weight, which leads to a reduction in the number of iterations [22].
2.2. Quantum-behaved particle swarm optimization
The main disadvantage is that the PSO algorithm is not guaranteed to be global convergent. In classical PSO technique, a particle
is depicted by its position vector xi and velocity vector vi, which
determine the trajectory of the particle. The dynamic behavior of
the particle is widely divergent form that of that the particle in
the CPSO systems in that the exact values of xi and vi cannot be
determined simultaneously. In quantum world, the term trajectory
is meaningless, because xi and vi of a particle cannot be determined
simultaneously according to uncertainty principle. Therefore, if
individual particles in a PSO system have quantum behavior, the
PSO algorithm is bound to work in a different fashion [17]. In the
quantum model of a PSO called here QPSO, the state of a particle
is depicted by wave function W(x, t) instead of position and velocity. Employing the Monte Carlo method, the particles move according to the following iterative equation:
xi ðt þ 1Þ ¼ p þ b jMbesti xi ðtÞj lnð1=uÞ if k 6 0:5
xi ðt þ 1Þ ¼ p b jMbesti xi ðtÞj lnð1=uÞ if k > 0:5
show that the QPSO described by the following procedure has better performance than the PSO [17].
Where Mbest called mean best position is defined as the mean
of the pbest positions of all particles. i.e.:
Mbest ¼
N
1 X
p ðtÞ
N d¼1 id
ð4Þ
Trajectory analyses in [24] demonstrated the fact that convergence of the PSO algorithm may be achieved if each particle converges to its local attractor, p defined at the coordinates:
p ¼ ðc1 pid þ c2 Pgd Þ=ðc1 þ c2 Þ
ð5Þ
The procedure for implementing the QPSO is given by the following steps:
Step 1. Initialization of swarm positions: Initialize a population
(array) of particles with random positions in the n-dimensional
problem space using a uniform probability distribution
function.
Step 2. Evaluation of particle’s fitness: Evaluate the fitness value
of each particle.
Step 3. Comparison to pbest (personal best): Compare each particle’s fitness with the particle’s pbest. If the current value is
better than pbest, then set the pbest value equal to the current
value and the pbest location equal to the current location in ndimensional space.
Step 4. Comparison to gbest (global best): Compare the fitness
with the population’s overall previous best. If the current value
is better than gbest, then reset gbest to the current particle’s
array index and value.
Step 5. Updating of global point: Calculate the Mbest using Eq.
(4).
Step 6. Updating of particles’ position: Change the position of
the particles according to Eq. (3), where c1 and c2 are two random numbers generated using a uniform probability distribution in the range [0, 1].
Step 7. Repeating the evolutionary cycle: Loop to step 2 until a
stop criterion is met, usually a sufficiently good fitness or a
maximum number of iterations (generations).
3. Description of case study system
Fig. 1 shows a SMIB power system equipped with a UPFC. The
synchronous generator is delivering power to the infinite bus
through a double circuit transmission line and a UPFC. The UPFC
consists of an excitation transformer, a boosting transformer, two
three-phase GTO based voltage source converters, and a DC link
capacitors. The four input control signals to the UPFC are mE, mB,
dE, and dB, where mE is the excitation amplitude modulation ratio,
mB is the boosting amplitude modulation ratio, dE is the excitation
phase angle and dB is the boosting phase angle [1,8].
ð3Þ
where u and k are values generated according to a uniform probability distribution in range [1], the parameter b is called contraction–expansion coefficient, which can be tuned to control the
convergence speed of the particle. In the QPSO, the parameter b
must be set as b < 1.782 to guarantee convergence of the particle
[23]. Thus, the Eq. (3) is the fundamental iterative equation of the
particle’s position for the QPSO. Moreover, unlike the PSO, the QPSO
needs no velocity vectors for particles at all, and also has fewer
parameters to control (only one parameter b except population size
and maximum iteration number), making it easier to implement.
The experiment results on some well-known benchmark functions
Vt
Tr. Line
VEt
iB
XB
iE
VSC-E
VSC-B
XE
Vdc
mE dE
mB dB
Fig. 1. SMIB power system equipped with UPFC.
Vb
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
3.1. Power system non-linear model with UPFC
The dynamic model of the UPFC is required in order to study the
effect of the UPFC for enhancing the small signal stability of the
power system. The system data is given in the Appendix. By applying Park’s transformation and neglecting the resistance and transients of the ET and BT transformers, the UPFC can be modeled
as [4,25]:
v Etd
v Etq
¼
0
xE
xE
0
v Btd 0
¼
v Btq
xB
xB
0
3mE
½ cos dE
4C dc
v_ dc ¼
iEd
iBd
cos dE v dc
2
mE sin dE v dc
2
þ
iEq
"m
"m
iBq
cos dB v dc
2
mB sin dB v dc
2
þ
sin dE E
iEd
B
iEq
þ
#
ð6Þ
#
ð7Þ
3mB
½ cos dB
4C dc
xBB 0 mE sin dE v dc xBd
xdE
mB sin dB v dc
v
cos
d
þ
E
þ
b
xd P q
2xd P
xd P
2
mE cos dE v dc xBq
xqE
mB cos dB v dc
P v b sin d þ
iEq ¼
2xq P
xq
2
xE 0 mE sin dE v dc xdE
xdt
mB sin dB v dc
P v b cos d þ
iBd ¼ P Eq þ
P
xd
2xd
xd
2
mE cos dE v dc xqE
xqt
mB cos dB v dc
þ P v b sin d þ
iBq ¼ 2xq P
xq
2
iEd ¼
sin dB iBd
ð8Þ
iBq
where vEt, iE, vBt, and iB are the excitation voltage, excitation current,
boosting voltage, and boosting current, respectively; Cdc and vdc are
the DC link capacitance and voltage. The non-linear model of the
SMIB system as shown in Fig. 1 is described by [1,25]:
ð16Þ
ð17Þ
ð18Þ
ð19Þ
Where
xL xq P ¼ ðxq þ xT þ xE Þ xB þ
þ xE ðxq þ xT Þ
2
xL
xBq ¼ xq þ xT þ xB þ
2
xL xqt ¼ xq þ xT þ xE ; xqE ¼ xq þ xT ; xd P ¼ ðx0d þ xT þ xE Þ xB þ
2
þ xE ðx0d þ xT Þ
xL
xBd ¼ x0d þ xT þ xB þ ; xBd ¼ x0d þ xT þ xE ; xdE ¼ x0d þ xT ;
2
xL
xBB ¼ xB þ
2
xE, xB, xd, x0d and xq are the ET, BT reactance’s, d-axis reactance, d-axis
transient reactance, and q-axis reactance, respectively.
3.2. Power system linearized model
d_ ¼ x0 ðx 1Þ
x_ ¼ ðP m Pe DDxÞ=M
ð9Þ
ð10Þ
E_ 0q ¼ ðEq þ
E_ fd ¼ ðEfd þ K a ðV ref V t ÞÞ=T a
ð11Þ
Efd Þ=T 0do
ð12Þ
where
Dd_ ¼ x0 Dx
_ ¼ ðDPe DDxÞ=M
Dx
DE_ 0 ¼ ðDEq þ DEfd Þ=T 0
ð22Þ
DE_ fd ¼ ðK A ðDv ref Dv Þ DEfd Þ=T A
Dv_ dc ¼ K 7 Dd þ K 8 DE0q K 9 Dv dc þ K ce DmE þ K cde DdE
¼ X q Itq ; V tq ¼ E0q X 0d Itd ; Itd ¼ Itld þ IEd þ IBd ; Itq ¼ Itlq þ IEq þ IBq
ð23Þ
ð24Þ
From Fig. 2 we can have:
þ K cb DmB þ K cdb DdB
DPe ¼ K 1 Dd þ K 2 DE0q þ K pd Dv dc þ K pe DmE þ K pde DdE
ð25Þ
ð13Þ
þ K pb DmB þ K pdb DdB
DE0q ¼ K 4 Dd þ K 3 DE0q þ K qd Dv dc þ K qe DmE þ K qde DdE
ð14Þ
ð26Þ
þ K qb DmB þ K qdb DdB
DV t ¼ K 5 Dd þ K 6 DE0q þ K v d Dv dc þ K v e DmE þ K v de DdE
ð15Þ
ð27Þ
where it and vb, are the armature current and infinite bus voltage,
respectively. From the above equations, we can obtain:
ð20Þ
ð21Þ
do
q
Pe ¼ V td Itd þ V tq Itq ; Eq ¼ E0qe þ ðX d X 0d ÞItd ; V t ¼ V td þ jV tq ; V td
v t ¼ jxtE ðiB þ iE Þ þ v Et
v Et ¼ v Bt þ jxBViB þ v b
v td þ jv tq ¼ xq ðiEq þ iBq Þ þ jðE0q x0d ðiEd þ iBd ÞÞ
¼ jxtE ðiEd þ iBd þ jðiEq þ iBq ÞÞ þ v Etd þ jv Etq
A linear dynamic model is obtained by linearizing the non-linear model round an operating condition. The linearized model of
power system as shown in Fig. 1 is given as follows:
þ K v b DmB þ K v db DdB
K1, K2, . . ., K9, Kpu, Kqu and Kvu are linearization constants. The statespace model of power system is given by:
x_ ¼ Ax þ Bu
ð28Þ
where the state vector x, control vector u, A and B are:
ΔP
+ + ΔP + m
1
−e
MS +D
+ +
K pu
K1
0
x ¼ ½ Dd Dx DEq
w0
S
2
K2
K pd
K5
K4
K6
ΔEq/
K qu
K8
U
K cu
+ +
+
−
−
1
K3 + STdo/
1
S +K9
+
−
K qd
ka
1+ST a
− ΔVref
+
− −
−
K vu
K vd
ΔVdc
K7
Fig. 2. Modified Herffron–Phillips transfer function model.
DEfd
Dv dc ;
0
0
6 K1
6
M
6
6 K
A ¼ 6 T 04
do
6
6 KA K5
4 T
w0
0
0
KM2
0
0
TK03
1
T 0do
0
K TA KA 6
T1A
K7
2
0
6 K pe
6
M
6
6 K0qe
B¼6
T do
6
6 K A K vc
4 TA
0
K8
0
A
K ce
do
0
K pde
M
K
Tqde
0
do
0
K
Mpb
K
T 0qb
do
K ATKAv de
K ATKAv b
K cde
K cb
u ¼ ½ DmE
3
0
7
7
7
7
7;
7
KA Kvd 7
T 5
K
Mpd
K
T 0qd
do
A
K 9
3
0
K pdb 7
M 7
7
K
7
Tqdb
0
7
do
7
K A K v db 7
TA 5
K cdb
Dd E
DmB
DdB T
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
U ref
KS
1 + STS
Δω
??
STW
K
1 + STW
⎛ 1 + ST1
⎜⎜
⎝ 1 + ST2
⎞⎛ 1 + ST3
⎟⎟⎜⎜
⎠⎝ 1 + ST4
U
⎞
⎟⎟
⎠
Table 1
The optimal parameter settings of the proposed controllers.
Controller
parameters
QPSO based
dE controller
PSO based dE
controller
QPSO based
mB controller
PSO based
mB controller
K
T1
T2
T3
T4
97.75
0.7111
0.6206
0.5776
0.6412
74.35
0.0665
0.0177
0.2565
0.1908
96.70
0.0105
0.1112
0.4667
0.1230
89.12
0.3227
0.1408
0.9457
0.5011
Fig. 3. UPFC with lead–lag controller.
The block diagram of the linearized dynamic model of the SMIB
power system with UPFC is shown in Fig. 2.
3.3. UPFC based damping controller
the objective function as given in Eq. (30), which considers a multiple of operating conditions. The operating conditions are considered as:
Base case: P = 0.80 pu, Q = 0.114 pu and XL = 0.3 pu. (Nominal
loading.)
Case 1: P = 0.2 pu, Q = 0.01 and XL = 0.3 pu. (Light loading.)
Case 2: P = 1.20 pu, Q = 0.4 and XL = 0.3 pu. (Heavy loading.)
Case 3: The 30% increase of line reactance XL at nominal loading
condition.
Case 4: The 30% increase of line reactance XL at heavy loading
condition.
The damping controller is designed to produce an electrical torque in-phase with the speed deviation according to phase compensation method. The four control parameters of the UPFC (mB, mE, dB
and dE) can be modulated in order to produce the damping torque.
In this paper, dE and mB are modulated in order to damping controller design. The speed deviation Dx is considered as the input to the
damping controller. The structure of UPFC based damping controller is shown in Fig. 3. This controller may be considered as a lead–
lag compensator [1]. However, an electrical torque in-phase with
the speed deviation is to be produced in order to improve damping
of the system oscillations. It comprises gain block, signal-washout
block and lead–lag compensator. The parameters of the damping
controller are obtained using QPSO algorithm.
In this work, in order to acquire better performance, number of
particle, particle size, number of iteration and b is chosen as 30, 5,
50 and 1.5, respectively. It should be noted that QPSO algorithm is
run several times and then optimal set of UPFC controller parameters is selected. The final values of the optimized parameters with
objective function, J, are given in Table 1.
3.4. UPFC controller design using QPSO
4. Non-linear time-domain simulation
To acquire an optimal combination, this paper employs QPSO
[17] to improve optimization synthesis and find the global optimum value of fitness function. For our optimization problem, an
integral of time multiplied absolute value of the error is taken as
the objective function. The objective function is defined as follows
[22]:
To assess the effectiveness and robustness of the proposed controllers, simulation studies are carried out for various fault disturbances and fault clearing sequences for two scenarios.
J¼
Np Z
X
i¼1
tsim
tjDxi jdt
ð29Þ
0
In the above equations, tsim is the time range of simulation and
Np is the total number of operating points for which the optimization is carried out. For objective function calculation, the time-domain simulation of the power system model is carried out for the
simulation period. It is aimed to minimize this objective function
in order to improve the system response in terms of the settling
time and overshoots. The design problem can be formulated as
the following constrained optimization problem, where the constraints are the controller parameters bounds [1,25]:
Minimize J
Subject to :
T min
2
T max
2
T2 T min
3
T min
4
T 3 T max
3
In this scenario, the performance of the proposed controller under transient conditions is verified by applying a 6-cycle threephase fault at t = 1 s, at the middle of the one transmission line.
The fault is cleared by permanent tripping of the faulted line. The
performance of the controllers when the quantum-behaved particle swarm optimization is used in the design is compared to that
of the controllers designed using the classical particle swarm optimization. The speed deviation of generator at nominal, light and
heavy loading conditions due to designed controller based on the
dE and mB are shown in Figs. 4 and 5. It can be seen that the QPSO
based UPFC controller achieves good robust performance, provides
superior damping in comparison with the CPSO based UPFC controller and enhance greatly the dynamic stability of power system.
4.2. Scenario 2
K min K K max
T min
T 1 T max
1
1
4.1. Scenario 1
ð30Þ
T 4 T max
4
Typical ranges of the optimized parameters are [0.01–100] for K
and [0.01–1] for T1, T2, T3 and T4. The proposed approach employs
QPSO algorithm to solve this optimization problem and search for
an optimal or near optimal set of controller parameters. The optimization of UPFC controller parameters is carried out by evaluating
In this scenario, another severe disturbance is considered for
different loading conditions; that is, a 6-cycle, three-phase fault
is applied at the same above mentioned location in scenario 1.
The fault is cleared without line tripping and the original system
is restored upon the clearance of the fault. The system response
to this disturbance is shown in Figs. 6 and 7. It can be seen that
the proposed QPSO based optimized UPFC controller has good performance in damping low frequency oscillations and stabilizes the
system quickly.
From the above conducted tests, it can be concluded that the dE
based controller is superior to the mB based controller.
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
-3
x 10
-3
0
x 10
3
Speed deviation
Speed deviation
2.5
Speed deviation
x 10
3
-3
0
0
-1
(a)
0
2.5
5
-0.5
(b)
0
Time (sec)
2.5
-1
5
0
(c)
Time (sec)
2.5
5
Time (sec)
Fig. 4. Dynamic responses for Dx in scenario 1 at (a) nominal (b) light (c) heavy loading conditions; solid (QPSO based dE controller) and dashed (PSO based dE controller).
-3
x 10
-3
0
0
-2
(a)
0
2.5
5
-2
x 10
5
Speed deviation
Speed deviation
5
-3
Speed deviation
x 10
5
0
(b)
0
Time (sec)
2.5
5
-2
(c)
0
Time (sec)
2.5
5
Time (sec)
Fig. 5. Dynamic responses for Dx in scenario 1 at (a) nominal (b) light (c) heavy loading conditions; solid (QPSO based mB controller) and dashed (PSO based mB controller).
-3
2.5
x 10
-3
Speed deviation
Speed deviation
x 10
Speed deviation
3
0
x 10
3
-3
0
0
-1 0
(a)
2.5
5
-0.5
(b)
0
Time (sec)
2.5
5
-2
(c)
0
Time (sec)
2.5
5
Time (sec)
Fig. 6. Dynamic responses for Dx in scenario 2 at (a) nominal (b) light (c) heavy loading conditions; solid (QPSO based dE controller) and dashed (PSO based dE controller).
x 10
-3
4
x 10
-3
4
0
-1
(a)
2.5
Time (sec)
5
-3
0
0
0
x 10
Speed deviation
Speed deviation
Speed deviation
4
-1
0
(b)
2.5
Time (sec)
5
-1
0
(c)
2.5
5
Time (sec)
Fig. 7. Dynamic responses for Dx in scenario 2 at (a) nominal (b) light (c) heavy loading conditions; solid (QPSO based mB controller) and dashed (PSO based mB controller).
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H. Shayeghi et al. / Energy Conversion and Management 51 (2010) 2299–2306
Table 2
Values of performance index ITAE.
Fault case
Type of algorithm
Scenario 1
CPSO
QPSO
CPSO
QPSO
Scenario 2
Base case
Case 1
Case 2
Case 3
Case 4
dE
mB
dE
mB
dE
mB
dE
mB
dE
mB
1.2711
1.1769
1.3422
1.2225
1.542
1.4376
1.3656
1.2446
1.0913
1.0605
1.2007
1.1645
1.3187
1.2671
1.2602
1.2028
1.172
1.0691
1.2229
1.081
1.4607
1.3507
1.2421
1.1151
1.0718
1.0446
1.0542
0.9875
1.8583
1.8582
1.3293
1.2222
1.0194
0.9889
0.9675
0.8868
1.876
1.8696
1.282
1.1657
Table 3
Values of performance index FD.
Fault case
Type of algorithm
Scenario 1
CPSO
QPSO
CPSO
QPSO
Scenario 2
Base case
Case 1
ITAE ¼ 100
Case 3
Case 4
mB
dE
mB
dE
mB
dE
mB
dE
mB
24.87
15.62
27.60
17.12
29.26
29.08
22.78
15.51
16.87
7.21
13.49
7.659
32.12
31.51
21.84
15.16
25.88
16.07
28.78
24.22
29.74
30.56
23.17
16.48
22.75
16.38
22.84
14.82
55.22
43.46
26.24
26.11
25.05
17.05
24.88
15.88
58.82
46.11
27.92
27.72
To demonstrate performance robustness of the proposed method, two performance indices: the ITAE and FD based on the system
performance characteristics are defined as [22]:
Z
Case 2
dE
Table 4
System parameters.
Generator
5
ð0:01 jDPe j þ 0:025 jDV dc j þ jDxjÞ tdt
0
ð31Þ
FD ¼ ðOS 1000Þ2 þ ðUS 3000Þ2 þ T 2s
where speed deviation (Dx), electrical power deviation (DPe), DC
voltage deviation (DVdc), overshoot (OS), undershoot (US) and settling time of speed deviation of the machine is considered for evaluation of the ITAE and FD indices. It is worth mentioning that the
lower the value of these indices is, the better the system response
in terms of time-domain characteristics. Numerical results of performance robustness for all system loading cases are listed in Tables
2 and 3. It can be seen that the values of these system performance
characteristics with the QPSO based tuned controller are much
smaller compared to PSO based tuned stabilizers. This demonstrates
that the overshoot, undershoot, settling time and speed deviations
of the machine are greatly reduced by applying the proposed QPSO
based tuned controller. Moreover, it can be concluded that the dE
based controller is the most robust controller.
5. Conclusions
The quantum-behaved particle swarm optimization algorithm
has been successfully applied to the robust design of UPFC based
damping controllers. The design problem of the robustly selecting
controller parameters is converted into an optimization problem
according to time domain-based objective function which is solved
by a QPSO technique which is a novel population based search
technique using a diversity control method. It has stronger global
search ability and more robust than PSO and other methods. The
effectiveness of the proposed UPFC controllers for improving transient stability performance of a power system are demonstrated by
a weakly connected example power system subjected to different
severe disturbances. The non-linear time-domain simulation results show the effectiveness of the proposed controller and their
ability to provide good damping of low frequency oscillations.
The system performance characteristics in terms of ‘ITAE’ and
‘FD’ indices reveal that the proposed QPSO based tuned stabilizers
demonstrates its superiority than PSO based tuned stabilizers at
various fault disturbances and fault clearing sequences.
M ¼ 8 MJ=MVA
X q ¼ 0:6 pu
Excitation system
Transformers
Transmission line
Operating condition
DC link parameter
UPFC parameter
T 0do ¼ 5:044 s
X 0d ¼ 0:3 pu
X d ¼ 1 pu
D¼0
K a ¼ 10
X T ¼ 0:1 pu
X B ¼ 0:1 pu
X L ¼ 1 pu
P ¼ 0:8 pu
V t ¼ 1:0 pu
V DC ¼ 2pu
mB ¼ 0:08
dE ¼ 85:35
Ks = 1
T a ¼ 0:05 s
X E ¼ 0:1 pu
V b ¼ 1:0 pu
C DC ¼ 1 pu
dB ¼ 78:21
mE ¼ 0:4
Ts = 0.05
Appendix A
The nominal parameters and operating condition of the system
are listed in Table 4.
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ID
764750
Title
TuningofdampingcontrollerforUPFCusingquantumparticleswarmoptimizer
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