Optimal STATCOM Design via Flower Pollination Approach for A
Multimachine Power System
E. S. ALI1, S. M. ABD ELAZIM2
1Electrical Department, Faculty of Engineering,
Jazan University, Jazan,
KINGDOM OF SAUDI ARABIA
2Computer Science Department, Faculty of Computer Science and Information System,
Jazan University, Jazan,
KINGDOM OF SAUDI ARABIA
Abstract: - A new metaheuristic method, the Flower Pollination Approach (FPA), based on the pollination
process of flowers is proposed in this article for the optimal design of a static synchronous compensator
(STATCOM) in a multimachine environment. The STATCOM parameter tuning process is converted to an
optimization problem which is solved by FPA. The performance of the proposed FPA-based STATCOM
(FPASTATCOM) is compared with Genetic Algorithm (GA) based STATCOM (GASTATCOM) under
various operating conditions and disturbances. The superiority of the proposed technique in damping
oscillations is confirmed via eigenvalues and time domain simulation results over the GA.
Key-Words: - Flower Pollination Approach, GA, STATCOM, Power System, Stability, Multimachine.
Received: October 7, 2022. Revised: September 23, 2023. Accepted: Ocotber 24, 2023. Published: November 28, 2023.
1 Introduction
The recent development of high-power electronics
presents the use of Flexible AC Transmission
Systems (FACTS) controllers in power systems, [1].
Subsequently, it has been demonstrated that variable
shunt compensation is highly effective in both
controlling power flow in the lines and hence the
system voltage profile and stability, [2], [3]. Static
synchronous Compensator (STATCOM) is a
member of the FACTS family that is connected in
shunt with the power system, [4]. By controlling the
magnitude of the STATCOM voltage, the reactive
power exchanges between the STATCOM and the
transmission line and hence the amount of shunt
compensation in the power system can be
controlled. In addition to reactive power exchange, a
properly controlled STATCOM can also provide
great damping to the power system oscillations, [3],
[4].
Recently, Artificial Intelligence (AI) techniques
have been discussed in the literature to solve
problems related to STATCOM design. Artificial
Neural Network (ANN) for designing STATCOM is
addressed in, [5], [6], [7], [8]. The ANN approach
has its own merits and demerits. The performance of
the system is improved by the ANN-based
controller, but the main problem of this controller is
the long training time, the selection of several
layers, and the number of neurons in each layer.
Another AI approach Fuzzy Logic Control (FLC)
has received much attention in control applications.
In contrast with the conventional techniques, FLC
formulates the control action of a plant in terms of
linguistic rules drawn from the behavior of a human
operator rather than in terms of an algorithm
synthesized from a model of the plant, [9], [10],
[11]. However, it can be designed based on
linguistic information obtained from the previous
knowledge of the control system and gives better
performance results than the conventional
controllers; hard work is inevitable to get effective
signals when designing FLC. Robust techniques,
[12], [13], [14], have been also used for STATCOM
design, but these methods are iterative and
sophisticated and the system uncertainties should be
carried out in a special format. On the other hand,
the order of the controllers is as high as that of the
plant. This gives rise to the complex structure of
such controllers and reduces their applicability.
Global optimization techniques have been
applied to the STATCOM design problem. The
optimal design of STATCOM via Genetic
Algorithm (GA) is developed in, [15], [16], [17],
[18], [19], but, it requires a very long run time
depending on the size of the system under study.
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DOI: 10.37394/232016.2023.18.29
E. S. Ali, S. M. Abd Elazim
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Also, it gives rise to repeat revisiting of the
same suboptimal solutions. STATCOM parameters
tuning using Particle Swarm Optimization (PSO) are
illustrated in, [20], [21], [22], [23], [24], but it pains
from the partial optimism. Moreover, the algorithm
cannot work out the problems of scattering and
optimization. Furthermore, the algorithm suffers
from slow convergence in the refined search stage,
and weak local search ability, and the algorithm
may lead to possible entrapment in local minimum
solutions. Artificial Bee Colony (ABC) was
developed in, [25], to design a STATCOM
controller, but it is slow to converge and the
processes of exploration and exploitation contradict
each other, so the two abilities should be well
balanced for achieving good optimization
performance. A relatively newer evolutionary
computation algorithm, called Bacteria Foraging
(BF) scheme has been established recently by, [26],
[27], [28], [29], [30], [31], [32]. The BF algorithm
depends on random search directions which may
lead to delay in reaching the global solution.
To overcome these drawbacks, FPA is proposed
in this article for the optimal design of STATCOM
parameters. The problem of a robust STATCOM
design is formulated as an objective optimization
problem and a CS algorithm is used to handle it.
The effectiveness of the proposed FPASTATCOM
is tested on a multimachine power system under
various operating conditions in comparison with
GASTATCOM and open loop STATCOM (without
supplementary signal) via eigenvalue and time
domain analysis. Results evaluation show that the
proposed algorithm attains good robust performance
for suppressing the low-frequency oscillations under
various operating conditions and disturbances
2 Problem Formulation
2.1 Power System Model
A multimachine system that consists of three
generators and nine buses, is considered here. The
system data and loading events are given in, [33].
Each generator is represented by the third-order
model and equipped with a static exciter (IEEE
type STI). The electromechanical swing equations,
the generator internal voltage equation, and the
exciter equation for one machine are given below:
1
.
(1)
D
e
T
m
T
j
.
(2)
td
I
do
d
X
d
X
q
E
fd
E
do
q
E
)(
)(
1
.
(3)
)(
1
.
t
V
ref
V
A
TA
K
fd
E
A
T
fd
E (4)
2.2 STATCOM Dynamic Model
The power circuit of STATCOM is composed of a
boosting transformer, three-phase GTO-based
VSCs, and a DC capacitor link, [34], [35]. c,
are
the amplitude modulation ratio and phase angle of
the control signal of each VSC respectively, which
are the input control signals to the STATCOM as
shown in Figure 1. The parameters of STATCOM
are given in Appendix.
The DC voltage dynamic equation is given below:
}sincos{
.
Lod
I
Loq
I
DC
C
c
DC
V (5)
DC Voltage Regulator
The DC voltage regulator controls the DC voltage
across the DC capacitor. Figure 2. shows the
dynamic model of the DC voltage regulator, which
adopts the PI controller. The DC voltage regulator
exchanges the active power between the STATCOM
and the power system, [36], [37], [38]. As
it
increases, more active power is sent to the power
system from the STATCOM. The DC voltage
regulator dynamic equation is given below:
VSC
C
DC
I
DC
V
DC
V
o
=cV
DC
sin(
t+
)
I
Lo
c
Control
P
Q
Transformer
Power System
Fig. 1: Active and reactive power control o
f
STATCOM.
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E. S. Ali, S. M. Abd Elazim
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))(
)1(
)(( DC
V
DCref
V
S
c
T
c
ST
S
dc
Ki
dc
Kp
(6)
Fig. 2: Dynamic model of DC voltage regulator.
AC Voltage Regulator with Supplementary Signal
The AC voltage regulator controls the reactive
power exchange with the power system. A
supplementary signal can be imposed on the AC
voltage control signal of the STATCOM as shown
in Figure 3, where the feedback signal for the
supplementary controller is the local speed
deviation, [34], [35], [36]. The function of the
supplementary signal is to counteract the negative
damping effect brought by the interaction of both
AC and DC regulators. The AC voltage regulator
dynamic equations are given below:
))(
)
1
1(
1
)(( S
V
L
V
Lref
V
S
c
T
c
ST
S
ac
Ki
ac
Kpc
(7)
))(
)1(
)(
4
1
3
1
)(
2
1
1
1
(
S
w
Tw
ST
ST
ST
ST
ST
K
S
V
(8)
Fig. 3: Block diagram of AC voltage regulator with
supplementary signal.
Bus 4 is the most sensitive bus due to the lowest
maximum loadability point and Hopf bifurcation,
[39], [40], [41], [42]. Moreover, it is the lower
voltage profile. Finally, this location agrees with
that obtained in, [29], [30].
3 Objective Function
A performance index can be defined by the Integral
of Time multiplied by the Absolute Error (ITAE) of
the speed deviation of each generator and DC
voltage link. The merit of this chosen performance
index is that minimal dynamic plant information is
required. Other indices, the Integral of Square Error
(ISE) and Integral of Time Multiply Squared Error
(ITSE) are very offensive criteria because squaring
the error creates unrealistic evaluation. Also, the
Integral of Absolute Error (IAE) is unqualified
compared with the ITAE which illustrates a more
realistic error-index, [43], [44].
Accordingly, the objective function J is set to be
t
sim
t
d
DC
V tJ
0
)
321
(9)
The values of the washout time constants
W
T ,
c
T
and
c
T 1are kept at 10, 8, and 8 seconds
respectively. The values of time constants 2
T and
4
T are fixed at a reasonable value of 0.05 second.
Typical ranges of the optimized parameters are [1-
100] for
K
,dc
Kp ,dc
Ki ,ac
Kp ,ac
Ki , and [0.06-
1.0] for 1
T and 3
T. Optimization problem based on
the objective function J can be stated as: minimize
J subjected to:
max
K K
min
K
max
1
T
1
T
min
1
T
max
3
T
3
T
min
3
T
max
ac
Kp
ac
Kp
min
ac
Kp
max
ac
Ki
ac
Ki
min
ac
Ki
max
dc
Kp
dc
Kp
min
dc
Kp
max
dc
Ki
dc
Ki
min
dc
Ki (10)
The optimization aims to search for the optimal
set of STATCOM parameters via CS that reflect the
settling time and overshoots of the system.
Furthermore, the aims are enhancing the damping
characteristics, acquiring a good performance under
different operating conditions, and improving the
voltage profile of the system.
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4 Overview of FPA
FPA was developed by, [45]. It is inspired by the
pollination process of flowers. Real-world design
problems in engineering are usually multiobjective.
These multiple objectives conflict with one another.
FPA has been adopted here to solve the problem of
STATCOM design.
4.1 Characteristics of Flower Pollination
The main purpose of a flower is reproduction via
pollination. Flower pollination correlates with the
transfer of pollen, which is often associated with
pollinators. Indeed, some flowers and insects have a
very specialized flower-pollinator sharing, [46].
Pollination can be achieved by self or cross-
pollination. In addition, bees and birds may follow
Lévy flight behavior in which they fly distance steps
obeying a Lévy distribution. Also, flower constancy
is considered as an incremental step using the
similarity of two flowers, [47]. The objective of
flower pollination is the survival of the fittest and
the optimal reproduction of plants. This can be
considered as an optimization process of plant
species. All of these factors created optimal
reproduction of the flowering plants.
4.2 Flower Pollination Algorithm
For FPA, the following four steps are used:
Step 1: Global pollination represented in biotic and
cross-pollination processes, as pollen-carrying
pollinators fly following Lévy flight, [45].
Step 2: Local pollination is represented in abiotic
and self-pollination as the process does not require
any pollinators.
Step 3: Flower constancy which can be developed
by insects, which is on par with a reproduction
probability that is proportional to the similarity of
the two flowers involved.
Step 4: The interaction of local and global
pollination is controlled by ]1,0[ p, lightly biased
toward local pollination.
The previous steps have to be converted to
suitable updating equations. For example at the
global pollination step, the pollinators carry the
flower pollen gametes, so the pollen can travel over
a long distance. Therefore, global pollination and
flower constancy step can be represented by:
))((
1t
i
xgL
t
i
x
t
i
x
(11)
Where
t
i
x
is the pollen i, and
gis the current best
solution found among all solutions at the current
generation. Here
is a scaling factor controlling
the step size.
The Lévy flights are based on step size that
corresponds to the strength of the pollination. Since
long distances can be covered by insects using
various distance steps, a Lévy flight can be used to
mimic this behavior. That is, 0L from a Lévy
distribution.
ss
s
L)0
0
(
1
12)/)sin((
~
(12)
)(
is the standard gamma function, and this
distribution is valid for large steps 0s.
For the local pollination, both Step 2 and Step 3
can be represented as
t
k
x
tj
x
t
i
x
t
i
x)(
1
(13)
where tj
x and t
k
xare pollen from different flowers
of the same plant species mimicking the flower
constancy in a limited neighborhood. For a local
random walk, tj
x and t
k
xcomes from the same
species and then
is drawn from a uniform
distribution as [0, 1].
Flower pollination activities can occur at all
scales. However, adjacent flower patches are more
likely to be pollinated by local flower pollen than
those far away. To mimic this, one can use a switch
probability to switch between common global
pollination to intensive local pollination. The
flowchart of FPA is given in Figure 4 (Appendix).
The data of FPA is shown in the appendix.
5 Results and Simulations
In this section, the superiority of the proposed FPA
algorithm in designing STATCOM compared with
optimized STATCOM with GA and open loop
STATCOM (DC and AC regulators) is illustrated.
Table 1, shows the system eigenvalues and damping
ratio of mechanical modes with three different
loading conditions. It is clear that the
FPASTATCOM shifts the electromechanical modes
to the left of the S-plane, and the values of the
damping factors with the proposed FPASTATCOM
are significantly enhanced for different loading
conditions. Also, the damping ratios corresponding
to FPASTATCOM controllers are larger than those
corresponding to GASTATCOM and open loop
STATCOM. Hence, compared with GASTATCOM
and open loop, FPASTATCOM provides good
robust performance and achieves superior damping
characteristics of electromechanical modes. Results
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of FPASTATCOM parameters set values based on
the proposed objective function using FPA and GA
are given in Table 2.
Table 1. Mechanical modes and
under different
loading conditions and controllers
Table 2. Parameters of STATCOM for different
algorithms
5.1 Response under Normal Load Condition
The validation of the system performance due to a
20% increase of mechanical torque for generator 1
as a small disturbance is verified. Figure 5 and
Figure 6, show the response of 12
,
and
13
due to this disturbance under normal loading
conditions. It can be seen that the system with the
proposed FPASTATCOM is more stabilized than
GASTATCOM and open loop. In addition, the
required mean settling time to mitigate system
oscillations is approximately 1.05 seconds with
FPASTATCOM and 1.6 seconds for
GASTATCOM.
01234567
-4
-3
-2
-1
0
1
2
3
x 10
-4
Time in second
C hange in w 12 (rad/second)
FPASTATCOM
GASTATCOM
Fig. 5: Change of 12
under normal condition.
0 1 2 3 4 5 6 7
-2
-1
0
1
2x 10
-4
Tim e in sec o nd
C hange in w13 (rad/second)
FPASTATCOM
GASTATCOM
Fig. 6: Change of 13
under normal condition.
5.2 Response under Light Load Condition
Figure 7 and Figure 8, show the system response
under light loading conditions with fixing the
controller parameters. It is clear from these figures,
that the proposed FPASTATCOM has good
damping characteristics to system oscillatory modes
and stabilizes the system rapidly. Also, the mean
settling time of oscillations is
s
T=1.46 and 2.6
seconds for FPASTATCOM and GASTATCOM
respectively. In addition, the system with open loop
STATCOM cannot reach a steady state value till 12
seconds. Hence, the proposed FPASTATCOM
outlasts GASTATCOM and the open loop controller
in attenuating oscillations effectively and minifying
settling time. Consequently, the proposed
FPASTATCOM extends the power system stability
limit.
FPA GA
DC
Regulator
dc
Kp
dc
Ki
18.0959
23.4575
12.0959
49.4575
AC
Regulator
ac
Kp
ac
Ki
55.3694
25.9627
65.3694
35.9627
Supplementary
Signal
K
1
T
3
T
49.4526
0.6875
0.4168
42.3005
0.2475
0.6801
GASTATCOM FPASTATCOM
Light
load
-1.43 6.53j,0.21
-1.09 6.92j,0.155
-1.4 5.6j,0.243
-1.13 6.92j,0.16
-2.16 6.05j,0.34
-1.51 5.68j,0.26
Normal
load -1.35 9.07j,0.147
-1.28 7.9j,0.16
-0.91 5.77j,0.156
-1.43 9.1j,0.155
-1.69 7.7j,0.21
-1.7 5.7j,0.29
Heavy
load -1.06 10.81j,0.1
-0.92 8.56j,0.11
-1.14 5.6j,0.2
-1.16 10.56j,0.11
-0.99 8.25j,0.12
-1.37 5.27j,0.25
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0 1 2 3 4 5 6 7 8 9 10
-5
-4
-3
-2
-1
0
1
2
3
x 10
-4
Time in second
C hange in w12 (rad/second)
FP A S TATCOM
GASTATCOM
Fig. 7: Change of 12
under light condition.
012345678910
-1.5
-1
-0.5
0
0.5
1
1.5 x 10
-4
Time in second
Change in w 13 (rad/second)
FPASTATCOM
GASTATCOM
Fig. 8: Change of 13
under light condition.
012345678910
-4
-3
-2
-1
0
1
2
3
4x 10
-4
Time in second
Change in w12 (rad/second)
FPASTATCOM
GASTATCOM
Fig. 9: Change of 12
under heavy condition.
5.3 Response under Heavy Load Conditions
Figure 9 and Figure 10, show the system response
under heavy loading conditions. These figures
indicate the superiority of the FPASTATCOM in
reducing the settling time and suppressing the power
system oscillations. Moreover, the mean settling
time of this oscillation is
s
T =1.0 and 2.43 seconds
for FPASTATCOM and GASTATCOM
respectively. Also, the system without
supplementary signal is suffered from sustained
oscillations. Hence, the FPASTATCOM controller
greatly improves the system stability and enhances
the damping characteristics of the power system.
Furthermore, the settling time of the proposed
controller is smaller than that in, [35], [41].
6 Conclusions
A new optimization algorithm known as FPA, for
optimal setting of STATCOM parameters is
proposed in this paper. The STATCOM parameters
tuning problem is formulated as an optimization
problem and the FPA algorithm is employed to seek
optimal parameters. A time domain objective
function involving the change of synchronous speed
of the generator and DC voltage is proposed to
alleviate power system oscillations and enhance
system performance in terms of settling time and
overshoots. Simulation results confirm the
robustness and superiority of the proposed
FPASTATCOM in providing good damping
characteristics to system oscillations over a wide
range of loading conditions compared with
GASTATCOM
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0 1 2 3 4 5 6 7 8 9 10
-2
-1
0
1
2
3
x 10-4
Time in second
Change in w23 (rad/sec ond)
FP A STATCOM
GASTATCOM
Fig. 10: Change of 23
under heavy condition.
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APPENDIX
a) DC link parameters (p.u): D
C
V=1.25; D
C
C=1.0.
b) STATCOM
and c parameters have been recalculated, at each loading condition.
c) Parameters of FPA: Maximum number of iterations = 500, population size = 20, probability switch =
0.8.
d) The parameters of GA are as follows: Max generation=100; Population size=50; Crossover
probabilities=0.75; Mutation probabilities =0.1.
Fig. 4: Flowchart of FPA.
If rand > p
Input population size, maximum iteration,
switch probability, number of units, B matrix,
u
pp
er and lower limits of units
,
and demand.
Start
Initialize a population
solution
Check the
condition is
satisfied?
Global pollination using Levy
fli
g
ht
Find the current best solution
Stop
Yes
No
Update current global best
Output the best solution
Do local
pollination
Evaluate new solutions
(outputs of generating units,
No
Yes
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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DOI: 10.37394/232016.2023.18.29
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Volume 18, 2023
