Optimal Stabilizer PID Parameters Tuned by Chaotic Particle Swarm Optimization for Damping Low Frequency Oscillations (LFO) for Single Machine Infinite Bus system (SMIB)

Abstract

In this paper, the Power system stabilizer (PSS) and (PID) are enhanced with a Chaotic Particle Swarm Optimization (CPSO) Damping Controller in order to suppression the Low-Frequency Oscillations (LFO) in a Single Machine Infinite Bus (SMIB) power system. Chaotic particle swarm optimization (CPSO) is used to tune the parameters of the PSS-PID. The design damping controller is an optimized lead-lag controller, which extracts the speed deviation of the generator rotor and generates the output feedback signal, which aims to modulate the reference values of the PSS-PID controller to achieve the best damping of LFO. In order to search the better damping option, the damping controller is applied to a series of the PSS-PID and the results are compared in two cases (PSS without PID and PSS with PID). The effectiveness of the proposed controller is achieved by time-domain simulation results in MATLAB environment, using three different operational conditions (Nominal, Light, and heavy). In addition, the results obtained from the PSS-PID were robust and more efficient compared to the PID only in terms of oscillations damping, overshoot minimizing and settling time reducing.

Full text

1 23
Journal of Electrical Engineering &
Technology
ISSN 1975-0102
Volume 15
Number 4
J. Electr. Eng. Technol. (2020)
15:1577-1584
DOI 10.1007/s42835-020-00442-5
Optimal Stabilizer PID Parameters Tuned
by Chaotic Particle Swarm Optimization
for Damping Low Frequency Oscillations
(LFO) for Single Machine Infinite Bus
system (SMIB)
Ayad Fadhil Mijbas, Bahaa Aldin Abas
Hasan & Hussein Ali Salah

1 23
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Vol.:(0123456789)
1 3
Journal of Electrical Engineering & Technology (2020) 15:1577–1584
https://doi.org/10.1007/s42835-020-00442-5
ORIGINAL ARTICLE
Optimal Stabilizer PID Parameters Tuned byChaotic Particle Swarm
Optimization forDamping Low Frequency Oscillations (LFO) forSingle
Machine Innite Bus system (SMIB)
AyadFadhilMijbas1· BahaaAldinAbasHasan2· HusseinAliSalah3
Received: 29 April 2019 / Revised: 11 December 2019 / Accepted: 28 April 2020 / Published online: 11 May 2020
© The Korean Institute of Electrical Engineers 2020
Abstract
In this paper, the Power system stabilizer (PSS) and (PID) are enhanced with a Chaotic Particle Swarm Optimization (CPSO)
Damping Controller in order to suppression the Low-Frequency Oscillations (LFO) in a Single Machine Infinite Bus (SMIB)
power system. Chaotic particle swarm optimization (CPSO) is used to tune the parameters of the PSS-PID. The design
damping controller is an optimized lead-lag controller, which extracts the speed deviation of the generator rotor and gener-
ates the output feedback signal, which aims to modulate the reference values of the PSS-PID controller to achieve the best
damping of LFO. In order to search the better damping option, the damping controller is applied to a series of the PSS-PID
and the results are compared in two cases (PSS without PID and PSS with PID). The effectiveness of the proposed control-
ler is achieved by time-domain simulation results in MATLAB environment, using three different operational conditions
(Nominal, Light, and heavy). In addition, the results obtained from the PSS-PID were robust and more efficient compared
to the PID only in terms of oscillations damping, overshoot minimizing and settling time reducing.
Keywords LFO· Heffron-philips· PSS-PID· CPSO
1 Introduction
“Low-frequency oscillation” is a generator rotor angle oscil-
lation having a frequency value between 0.1 and 2.0Hz.
This phenomenon involves the mechanical oscillation of the
phase rotation angle with each of them to a rotary frame.
Increasing the phase angle and decreasing at a low frequency
in the energy transmitted from the asynchronous machine
as the phase angle will be strong to the transmitted energy.
The high demand for energy to the extreme end of the
system, which forces the transfer of enormous energy
through a long transmission line, leading to fluctuations of
strength, is increasing. The LFO can be classified as local
and inter-area mode [10]. Low-frequency oscillation may
lead to system instability and even loss of synchronization
if a suitable damping device is not provided. An automatic
voltage regulator (AVR) has become more appropriate to
maintain a steady-state but is not useful for maintaining
stability during transient conditions. It was observed that
the effect of the excitation system always leads to increase
synchronization but reduces the damping torque and causes
instability due to LFO [15, 16].
Yet, to overcome this effect, the power system damping
device must be provided suitable for damping local mode of
small signal and decreasing effect AVR. Power system stabi-
lizer PSS was enhancing the dynamic stability and improve
the transfer stability of the power systems. PSS is installed
on the synchronous generator to provide the excitation sys-
tem enhancement feedback stabilizing signals in the excita-
tion system [15, 16].
* Hussein Ali Salah
husseinalali6@gmail.com
Ayad Fadhil Mijbas
Eaad.fadhil@gmail.com
Bahaa Aldin Abas Hasan
ba.hasan12@googlemail.com
1 Department ofElectrical Techniques, Technical
Institute-Suwaira, Middle Technical University, Baghdad,
Iraq
2 Department ofPower Mechanics, Technical
Institute-Suwaira, Middle Technical University, Baghdad,
Iraq
3 Department ofComputer Systems, Technical
Institute-Suwaira, Middle Technical University, Baghdad,
Iraq
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To improve the performance of power system stabilizer
many techniques have been proposed to design PSS param-
eter, for example, population-based such as Iteration Particle
Swarm Optimization (IPSO) algorithm to tune optimal gains
of a “Proportional Integral Derivative” (PID) type multiple
stabilizers [13], Particle Swarm Optimization Based PID
Power System Stabilizer [8]. Particle Swarm Optimization
(PSO) and Cat Swarm Optimization (CSO) based Power
System Stabilizer [11], design of the PSS is based on a
simplified single machine infinite bus (SMIB) model using
Particle Swarm Optimizat + ion and Genetic Algorithm
(Bhagat 2015), design of the PSS is based on a simplified
single machine infinite bus (SMIB) model using Particle
Swarm Optimization and Genetic Algorithm [9], A Robust
PID Power System Stabilizer Design of “Single Machine
Infinite Bus System” using Firefly Algorithm [6].
In this paper (PSS-PID) controller at different operational
conditions “Nominal, Light, and Heavy” was used.
Chaotic particle swarm optimization (CPSO) is used to
tune the parameters of the (PSS-PID) controller to damp-
ing low-frequency oscillations (LFO). (CPSO) based on the
min squared error objective function in the design of the
controllers proposed to achieve the optimal characteristics.
The aim of using (PID) is to minimize “low-frequency oscil-
lations (LFO)” of the electric power system under differ-
ent operating conditions and increase damping (LFO). To
ensure a better result of the stability for the power system,
the PID controller with PSS were used. (PSS-PID) has a
faster response, maximum damping of oscillations, shorter
settling time and minimum overshoot compared to their PID
controllers.
2 Mathematical Model
This section presents the small-signal model for a single
machine connected to an infinite bus system to analyze the
local mode of oscillations. “Single Machine Infinite Bus
System (SMIB)” is shown in Fig.1. The model consists of a
single machine with AVR, exciter, transmission line, infinite
bus and addition to PSS-PID controller [2].
The non-linear equations are as in (1–4) equations:
(1)
̇𝜔
=
T
m
−Te
M
(2)
̇
𝛿
=𝜔
0𝜔
(3)
̇
E
fd =
1
TA
(
KAEref −Vt−Efd
)
where δ is the rotor angle in rad, ω is the generator speed
in rad/s, E’q is the generator voltage in q-axis and Efd is
the output voltage of exciter., Tm and Te are the mechanical
and electrical torque respectively. xd, x’d, and xe is genera-
tor’s synchronous reactance transient reactance in d-axis and
transmission line reactance, Vt, Eref the terminal, reference
voltages respectively., TA and T’d0 are the time constants of
the exciter and generator model.
2.1 Modeling theSystems inHeron‑Philips Form
For analyzing of a performance of PSS-PID, the single
machine infinite machine (SMIB) system has been taken
into consideration. The Heffron-Philips model shown in
Fig.2 represents the linearized model of a synchronous
machine which is suitable for stability study. The param-
eters constants K1 to K6 represent the system parameters
(4)
̇
E
�
q=
1
T�
do [
Efd −xd+xe
x�
d
+x
e
E�
q+xd+xe
x�
d
+x
e
Vcos 𝛿
]
Fig. 1 Schematic diagram of Single Machine Infinite Bus system
(SMIB)
Fig. 2 Heffron Philips model structure with PSS-PID
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at a certain operation condition [1]. The expense of the
constants (K1 to K6) as shown:
where:
2.2 Power System Stabilizer (PSS)
“Power system stabilizer (PSS)” an auxiliary device
installed in an AVR excitation, it provides supplementary
feedback stabilizing signal in the excitation systems. It
also produces the electrical torque in phase with rotor
speed deviations. The block diagram of PSS consists of
the following blocks.
Gain It determines the amount of damping introduced
by the stabilizer.
Washout “It is a high pass filter that responds only to
oscillations in speed and prevents the dc offset. From the
view of the washout function, the value of Tw is generally
not critical and maybe in the range of (1 to 20) seconds”.
In this study, it is fixed to 10s.
Phase compensator It compensates for the phase lag
introduced by the AVR and the field circuit of the genera-
tor. The block diagram of the power system stabilizer is
shown in Fig.3 [5].
The transfer functions of the basic form of PSS
controller:
K
1=X3

Pe2
Pe2+(Qe +X1)2

+Qe +X1
K
2=X4Pe
Pe2+(Qe +X1)2
K
3=X2
K
4=X5Pe
Pe2+(Qe +X1)2
K
5=X4xePe
Vb2+Qexe X1+Qe
Pe2+(Qe +X1)2X6
K
6=

X7

Pe2+(Qe +X1)2
Vb2+Qexe

xe+

X1xq
X1+Qe
Pe2+(Qe +X1)2

X
1=

V
2
b

(Xe+Xq);X2=
(X
�
d+Xe)
Xd+Xe
X
3=Xq−X�
d
(Xe+X,
d)(X1);X4=Vb
Xe+X�
d
X
5=Xd−X�
d
Xe+X�
d;
X
6=X2
q−X�
dXq

X
e
+X
q
(X1);X7=Xe

X
e
+X�
d.
2.3 Structure PSS‑PID
Since the 1930s, three-mode controllers with proportional,
integral, and derivative (PID) actions became commercially
available and widely accepted in various industrial fields.
These types of control units are still the most commonly
used control in the process industries. That success is due
to many good features of this controller such as robustness,
simplicity, and wide applicability ability [12].
The general form PID controller is:
where, Kp is “proportional gain”, Ki is “the integral gain”,
and Kd is the “derivative gain”.
The PID controller includes three separate parameters;
the Integral, the derivative and the Proportional values. The
weighted sum of these three procedures is used to adjust the
process for obtaining the desired output [17].
The transfer functions of the basic form of PID controller:
The purpose of using the PID controller with PSS is to
provide a better response to the stability problem much more
efficiently than the power systems used. PID was connected
in series with PSS. The speed deviation Δω “is the input
signal of the proposed stabilizer” [4]. The block diagram of
power system stabilizer with PID is shown in Fig.4.
3 Objective Function
The following objective function min square error was
used for optimization in this study and increases the system
damping to electromechanical modes:
(5)
Upss
=K⋅
STw
(
1
+
STw
)
[
(1+ST1)⋅(1+ST3)
2
(
1
+
ST1
)⋅(
1
+
ST3
)
]Δω
(6)
u
(t)=Kpe(t)+Ki
∫t
0
e(t)dt +Kd
de
dt
(7)
G
(s)=KP+Ki
S
+KdS=KdS
2
+KpS+K
i
S
(8)
J=min(e)2
Fig. 3 Block diagram of power system stabilizer
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The optimization purpose to minimize the objective func-
tion bounded to following constraints.
Minimize J Subject to:
The above parameters of the controller are determined
by (CPSO) algorithm under the one objective function as
describe above.
4 Chaotic Particle Swarm Optimization
(CPSO)
Particle Swarm Optimization (PSO) technique was inspired
by the social behavior of bird swarms to adapt to their sur-
rounding environment in order to search for abundant food
sources and avert the risk of predators by applying an infor-
mation exchanging method among them. Each solution of
the optimization problem was represented randomly as a
(particle) in the identity D-dimension space, and each group
of particles includes a (population). The location arranged
for each particle in hyperspace is stocked in a save memory
called (Pbest) which is related to the fittest solution in each
experience. In addition, the location arranged related to the
best value obtained so far among all the particles in the pop-
ulation is saving in a memory called “Gbest”. The “Pbest”
and “Gbest” values are updated for each of the (PSO) algo-
rithm iterations. The PSO updates each particle’s velocity
and position and when the stopping criterion is achieved.
The equation of the velocity updating:
Kmin ≤
K
≤
K
max
K
min
p≤Kp≤K
max
p
K
min
d≤Kd≤K
max
d
K
min
i≤Ki≤Kmax
i
T
min
1≤T1≤Tmax
1
T
min
2≤T2≤Tmax
2
T
min
3≤T3≤Tmax
3
T
min
4
≤T
4
≤Tmax
4
The equation of the Weighting Function:
The equation of the position updating:
where, νik is the velocity of agent i at iteration k, k is the
number of iterations, w is the Weighting Function. (Inertia
weight factor), c1, c2 is the Weighting factor. (The cognitive
and asocial acceleration factors respectively), rand is the
random number between 0 and 1, Sik is the Current posi-
tion of agent i at iteration k. (particle position), Pbest is the
Pbest of agent i. Gbest is the Gbest of the group, Wmax is
the maximum inertia Weight, Wmin is the minimum inertia
Weight, itermax is the Maximum Iteration number, iter is the
Current iteration number.
Optimization algorithm describes an outstanding perfor-
mance under complex problems, but still sometimes faces
some problems [14]. Accordingly, has been the introduc-
tion of various improvements to solve problems faced by the
PSO. The first approach was the inertia weight, in order to
improve the performance of the PSO approach by controlling
the local and global exploration behavior of the population.
Then, various hybrid and innovative approaches were
introduced in order to get rid of the PSO barriers. One of the
main important solutions for obtaining the local optimum
of the PSO algorithm is the chaotic particle swarm optimi-
zation CPSO. The CPSO method relies on a well-known
chaotic theory as a very useful theory in many engineering
applications. One of the basic features of chaotic system is
that small changes in the parameters or data start values lead
to different behavior in the future, such as periodic oscil-
lation, bifurcations, and stable fixed points. Optimization
algorithms based on the chaotic theory are stochastic search
methodologies that differ from any of the existing evolution-
ary algorithms. In CPSO sequences are generated by the
logistic map rather than random parameters such as (r1 and
r2) in conventional PSO [3].
In this study, the logistic sequence equation adopted for
constructing the hybrid CPSO algorithm is described as the
following equation:
where μ is the control parameter with a real value between
(0 and 4), and β0 ∉ {0, 0.25, 0.5, 0.75, 1}. It shows depend-
ence on initial conditions, which is the basic characteristic
of chaos.
The new weight parameter wnew is defined by
(9)
𝜈(k+1)
i
=w⋅𝜈k
i
+c
1
⋅rand
1(
Pbest
i
−sk
i)
+c
2
⋅rand
2(
Gbest
i
−sk
i)
(10)
w
=

wmax

−
w
max
−w
min
itermax iter
(11)
S(k+1)
i
=S
k
i
+𝜈
(k+1)
i
(12)
𝛽k+1
=𝜇.𝛽
k(
1−𝛽
k)
Fig. 4 Block diagram of PSS with PID
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To improve global search capability in the PSO, we need
to introduce the new speed update equation as follows:
We have observed that the proposed new weight decreases
and oscillates simultaneously for total iteration, whereas the
conventional weight decreases monotonously from wmax to
wmin [7] (Fig.5).
5 Results andAnalysis
Heffron Phillip model is developed for Single Machine
Infinite Bus System (SMIB) using MATLAB program
version (R2015b). SMIB system is simulated under
three cases differential load condition with and without
PID. Case 1 “(Nominal Load, Pe = 0.8, Qe = 0.2), Case 2
(Light Load, Pe = 0.3, Qe = 0.1), and Case 3 (Heavy Load,
Pe = 1.2, Qe = 0.25)”. The parameters of the PSS-PID
(13)
wnew
=
w
𝛽
(k+1)
(14)
𝜈(k+1)
i
=w
new
⋅𝜈k
i
+c
1
⋅rand
1(
Pbest
i
−sk
i)
+c
2
⋅rand
2(
Gbest
i
−sk
i)
controllers will be optimized by using the CPSO algo-
rithm. Chaotic particle swarm optimization (CPSO) is
used to tune the parameters of the damping controllers
based on the min squared error objective function to
achieve the optimal characteristics.
Figures6, 7 and 8 show speed deviation, and power devi-
ation sequentially without a controlled. They also show that
the system is unstable under nominal, light, and heavy load
conditions. Figures9, 10 and 11 show speed deviation, and
power deviation sequentially with PSS control, and PSS-
PID control. CPSO algorithm is chosen to realize optimal
Fig. 5 Flowchart of the CPSO algorithm for the tuning parameters of
damping controllers
Fig. 6 Case 1 nominal load without control
Fig. 7 Case 2 light load without control
Fig. 8 Case 3 heavy load without control
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performance in the optimization method. Table1 shows the
final choice of the optimal parameters by using the CPSO
algorithm for three cases of load conditions, and that is con-
sidered the optimal choice in this study.
Finally, PSS-PID has a faster response, maximum damp-
ing of oscillations, shorter settling time and minimum over-
shoot compared to their PID controllers.
6 Conclusions
The PSS-PID controller was proposed to enhance the sta-
bility of the response in a “Single Machine Infinite Bus”.
“Chaotic Particle Swarm Optimization CPSO” was used
to tune the PSS-PID parameters. The results of this study
showed that chaotic particle swarm optimization (CPSO)
which was based on PSS-PID yields better dynamic per-
formance than traditional PSS performance. A significant
improvement in damping was achieved by using PSS-PID
on different operating conditions to control the excita-
tion of a synchronous machine. In this paper, the simula-
tion studies described that the performance of the system
response with PSS-PID is robust in terms of the overshoot
from using PSS only. Therefore, the proposed PSS–PID is
relatively simpler than other controllers to provide an opti-
mal solution. The aim to minimize “low-frequency oscilla-
tions (LFO)” of the electric power system under different
operating conditions and to increase damping LFO was
achieved by using PID. The better results of the stabil-
ity of the power system, faster response, shorter settling
time and minimum overshoot, and maximum damping of
low-frequency oscillations were obtained by using the PID
controller with PSS.
Fig. 9 Case 1 nominal load with control
Fig. 10 Case 2 light load with control
Fig. 11 Case 3 heavy load with control
Table 1 Optimal PID-PSS parameters for SMIB system
Parameter CPSO CPSO-PID
Case 1 (nominal) Case 2 (light) Case 3 (heavy) Case 1 (nominal) Case 2 (light) Case 3 (heavy)
Kp – – – 2.0585 2.0520 2.0472
Ki – – – 0.0426 0.0195 0.0397
Kd – – – 0.0250 0.0068 0.0148
K 7.7624 7.7704 7.7546 7.7678 7.7779 7.7693
Tw 10 10 10 10 10 10
T1 0.0061 0.0061 0.0060 0.0060 0.0060 0.0061
T2 0.0090 0.0090 0.0089 0.0089 0.0088 0.0092
T3 0.0021 0.0018 0.0024 0.0037 0.0023 0.0039
T4 0.1528 0.1602 0.1524 0.1250 0.1369 0.1279
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Appendix
See Tables2 and 3.
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Publisher’s Note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.
Ayad Fadhil Mijbas received the five-year B.Sc. degree in Electrical
Engineering Science in 1993 from Al-Technology University, Iraq. In
2004, he concluded a Master in Electrical Engineering Science/Control
from Al-Technology University, from 2006–2010 he has been as a head
of Electrical Department and Lecturer in Foundation of Technical Edu-
cation/Middle Technical University, Iraq. His main research interests
include Electrical control systems.
Bahaa Aldin Abas Hasan received in 2006 PhD in Automotive Mechan-
ical Engineering Design and Manufacture “Near Net Shape Processing
of Automotive Brake Lining Friction Materials”. The University of
Bradford, School of Engineering, Design and Technology, Bradford,
England. Sponsored by EPSRC (Engineering and Physical Sciences
Research Council in the UK) and TMD Friction Ltd (the Brake Friction
Materials Manufacturer). He had in 1998–1999 Lift Technology Certif-
icate (with Merit), one year course at University College Northampton,
England. The course sponsored by Contract Direct Lift Ltd—partner
of the Spanish lift’s manufacturer Electra Victoria. In 1994–1995, he
concluded MSc in Design and Manufacture, “Dimensional Variation
Modelling” The Manchester Metropolitan University, Department of
Table 2 Data for the SMIB system [17]
Parameter Value
Inertia constant, M8
Machine damping coefficient, D0
Open-circuit field time constant, T′do 5.044s
Gain of excitation system, KA 10
reactance of transmission line, xe 0.7 p.u
Transient reactance d-axis, x′d0.3 p.u
Synchronous reactance d-axis, xd 1 p.u
Time constant of excitation system, TA 0.05s
Synchronous reactance q-axis, xq 0.6 p.u
Generator electrical output power, Pe 0.8 p.u
Terminal voltage, Vt 1 p.u
Infinite bus voltage, Vb 1 p.u
Synchronous speed, ωb (rad/s) 377rad/s
Table 3 Parameters used for
CPSO algorithm CPSO control parameter Value
n40
Kmax 80
c11.5
c21.5
wmax 0.9
wmin 0.3
μ4
Β10.3
r11
r21
Author's personal copy

1584 Journal of Electrical Engineering & Technology (2020) 15:1577–1584
1 3
Mechanical Engineering, Design and Manufacture, Manchester, UK.
In 1993–1994, Post Graduate Diploma (PgD) in Automotive Engi-
neering Design and Manufacture, Coventry University, Coventry, UK.
He graduated from the Institute of Technology (HND), in 1977–1979,
Baghdad, Iraq. He is working now head of Power Mechanics Tech-
niques Department, since 1st of August 2018, Lecturer, Al Suwaira
Technical Institute, Middle Technical University, since 1st of August
2018, Member of the Committee of Experts of Technical Education
Authority Since 1/3/2019, Iraq. Worked Energy Consultant for Eon,
UK Energy, England from August 2008 until 1/05/2016. He worked
from 1/10/2006 to 30/07/2008 Energy Consultant with British Gas,
England. From 1999–2003 worked as a Researcher/PhD Scholarship
with the University of Bradford, England. He took the position of Tech-
nical Support Engineer/Project Management with Contract Direct Lift
Ltd 1997–1999, England. He worked as Technical Engineer with Bos-
ton Motor Company 1996–1997, England. He worked as Technical
Engineer with Gilbert Lowton VW & Audi 1995–1996, England.
Hussein Ali Salah received the four-year B.Sc. degree in Computer
Science in 2000 from Al-Rafidain University College, Iraq. In 2004, he
concluded a Master in Computer Science (MCS) from Baghdad Uni-
versity, College of Science. From 2006–2013 he has been as a head of
computer center, Supervision of Auto CAD laboratory and Lecturer in
Foundation of Technical Education/Middle Technical University, Iraq.
He received the Ph.D. degree in Computer Science IT in 2016 from
Politehnica’ University of Bucharest, Bucharest, Romania. His main
research interests include data mining and decision support system, and
cloud computing. He is the author and co-author of twelve international
journals and conferences (IEEE). He has an author id from Scopus and
ORCID id. He has been working as a programmer at Middle Technical
University, Iraq and then worked as a head of the Computer Systems
Department, Middle Technical University, Technical Institute-Suwaira,
Wasit/Iraq from 2016 until now. His main research interests include:
decision support systems, web design, intelligent DSS.
Author's personal copy