Tuning of PI and PID Controller withSTATCOM, SSSC and UPFC for
Minimizing Damping of Oscillation
Sobuj Kumar Ray
Department of Electrical and Electronic Engineering
Dhaka University of Engineering & Technology, Gazipur
October 2017
Tuning of PI and PID Controller withSTATCOM, SSSC and UPFC for
Minimizing Damping of Oscillation
A dissertation submitted in partial fulfilment of the requirements for thedegree of
Master of Engineering in Electrical and ElectronicEngineering
By
Sobuj Kumar Ray
Student No. 112261-P
Under Supervision of
Dr. Md. Raju AhmedProfessor and Head, Dept. of EEE, DUET, Gazipur
Department of Electrical and Electronic Engineering
Dhaka University of Engineering & Technology, Gazipur
October 2017
The project report entitled “Tuning of PI and PID Controller with STATCOM, SSSC andUPFC for Minimizing Damping of Oscillation” submitted by Sobuj Kumar Ray, Student ID:112261-P, Session: 2011-2012 has been accepted as satisfactory in partial fulfillment for thedegree of Master of Engineering in Electrical and Electronic Engineering on October 10,2017.
BOARD OF EXAMINIERS
…………………………………………………………..Prof. Dr. Md Raju Ahmed Head of the DepartmentDepartment of Electrical and Electronic EngineeringDhaka University of Engineering & Technology, Gazipur
Chairman(Supervisor)(Ex-officio)
…………………………………………………………..Dr. Md. Bashir UddinProfessorDepartment of Electrical and Electronic EngineeringDhaka University of Engineering & Technology, Gazipur
Member
…………………………………………………………..Dr. RumaProfessorDepartment of Electrical and Electronic EngineeringDhaka University of Engineering & Technology, Gazipur
Member
…………………………………………………………..Dr. Md. Arifur RahmanAssistant ProfessorDepartment of Electrical and Electronic EngineeringDhaka University of Engineering & Technology, Gazipur
Member
…………………………………………………………..Dr. Mohammad Jahangir AlamProfessorDepartment of Electrical and Electronic EngineeringBangladesh University of Engineering and Technology, Dhaka
Member(External)
Declaration
I declare that this thesis is my own work and has not been submitted in any form for another
degree or diploma at any university or other institute of tertiary education. Information
derived from the published and unpublished work of others has been acknowledged in the
text and a list of references is given.
Sobuj Kumar Ray Date: 10/10/2017
iii
Acknowledgements
All admiration is due to the Almighty, the creator of the universe who gave me theopportunity and strength to carry out this research work.
I would like to express my sincere gratitude to my honorable supervisor Prof. Dr. Md. RajuAhmed Head, Department of EEE, Dhaka University of Engineering and Technology,(DUET), Gazipur for his continuous and wholehearted support for my M. Engineering studyand research. His guidance helped me during all the time of my study and research. I amthankful to him for allowing me the freedom to pursue my own ideas and interests. I couldnot have imagined having a better advisor and mentor for my M. Engineering study.
I am obligated to pay my sincere gratitude to Dr. Md. Arifur Rahman, Assistant Professor,EEE, and DUET for his endless support in guiding me on my way during my M.Engineering thesis.
I am thankful to all the teachers and staffs of the Department of EEE of Dhaka University ofEngineering and Technology for their continuous support. I feel indebted to DhakaUniversity of Engineering and Technology, (DUET), Gazipur for providing a congenialenvironment for research as well as overall education.
My family members, specially my parents, wife and friends had a lot to do behind thisaccomplishment. I can never thank them enough for their sacrifice and appreciationthroughout my career.
Last but not the least, I am also thankful to the people, who have directly or indirectly helpedme and encouraged me to complete my thesis.
v
Abstract
In a power systems, when rotor step change is occurred then the voltage of the generator isreduced to a very low magnitude. When voltage magnitude falls below the desired voltagecalled voltage sag, which is one of the most severe problems to the power system and itcauses severe disruptions and results in substantial economic loss. To control andcompensate for the voltage drop, Flexible AC Transmission System (FACTs) is used.
This paper presents the comparative performance of PI and PID controller scheme withFlexible AC Transmission System (FACTs) devices, such as Static SynchronousCompensator (STATCOM), Static Synchronous Series Compensator (SSSC) and UnifiedPower Flow Controller (UPFC) in terms of improvements in transient stability, extenuationof system oscillations and furnishing voltage support in single machine infinite bus system(SMIB).
The performances of the system with PI and PID controllers which are the combination withSTATCOM, SSSC and UPFC are analyzed using matlab simulation software (Simulink).Rotor angle deviation and speed deviation has been analyzed for PI and PID with UPFC,SSSC and STATCOM. The performances of each combination are compared in term ofmaximum overshoot and settling time. Finally an optimal solution will be proposed based onthe simulation results.
vi
Abbreviations
PSS Power System Stabilizers
FACTs Flexible AC Transmission System
TSSC Thyristor Switched Series Capacitor
GTO Gate Turn-Off
ASD Aperiodic Small Disturbance
TSSC Thyristor Switched Series Capacitor
SVC Static Var Compensator
VSC Voltage Source Converters
TCSC Thyristor- Controlled Series Capacitor
TCPS Thyristor-Controlled Phase Shifter
STATCOM Static Synchronous Compensator
SSSC Static Synchronous Series Compensator
UPFC Unified Power Flow Controller
IPFC Interline Power Flow Controller
SMIBS Single Machine Infinite Bus System
PI Proportional Integral PID Proportional Integral and Derivative
DDC Direct Digital Control
DCS Distributed Control System
VSI Voltage Sourced Inverters
CSC Controlled Series Capacitor
TCR Thyristor Controlled Reactors
SSR Sub Synchronous Resonance
IPFC Interline Power Flow Controller
IPPC Inter Phase Power Controller
TCVL Thyristor-Controlled Voltage Limiter
vii
Contents
Acknowledgements v
Abstract viAbbreviations vii1 Introduction and Literature Review 1
1.1 Introduction 11.2 Literature Review 3
1.2.1 First Generation of FACTs 41.2.1.1 Static VAR Compensator (SVC) 41.2.1.2 Thyristor-Controlled Series Capacitor (TCSC) 41.2.1.3 Thyristor-Controlled Phase Shifter (TCPS) 51.2.2 Second Generation of FACTs 51.2.2 .1 A Static Compensator (STATCOM) 51.2.2 .2 Static Synchronous Series Compensator (SSSC) 51.2.2 .3 Unified Power Flow Controller (UPFC) 5
1.3 Objectives with Specific Aims and Possible Outcome 6 1.3.1 Objectives 6
1.3.2 Possible Outcomes 61.4 Outline of the Thesis 7
2 Optimizations of PI and PID Controllers 82.1 Introduction 82.2 PI Controller 82.3 PID Controller 92.4 Proportional Control 102.5 Integral Control 102.6 Derivative Control 112.7 Continuous PID 112.8 Tuning of PI Controller 122.9 Tuning of PID Controller 122.10 Conclusion 17
3 Single Machine Infinite Bus System for Stability Analysis 183.1 Introduction 183.2 Principle of Power Transmission 193.3 Power Flow Control Concepts 213.4 Single Machine Infinite Bus System 213.5 Stability Analysis 223.6 Swing Equation 233.7 Synchronous Machine Operation 233.8 Mathematical Representation of Single Machine Infinite Bus 253.9 Conclusion 26
4 Mathematical Representation of STATCOM 27
4.1 Introduction 274.2 Principle of Shunt Compensation 284.3 Static Synchronous Compensator 304.4 Mathematical Modeling of STATCOM 314.5 Block Diagram of STATCOM 33
4.6 Conclusion 345 Mathematical Representation of SSSC 35
5.1 Introduction 355.2 Principle of series compensation 355.3 Static synchronous series compensator (SSSC) 375.4 Mathematical Modeling of SSSC 385.5 Block Diagram of SSSC 405.6 Conclusion 41
6 Unified Power Flow Controller 426.1 Introduction 426.2 UPFC Construction 436.3 Methodology 446.4 Phase-shifter transformer 476.5 Inter phase Power Controller (IPC) 476.6 Modeling of UPFC 48
6.6.1 Block Diagram of UPFC 496.7 Conclusion 50
7 Simulation Result of STATCOM, SSSC and UPFC with PI and PID Controller 517.1 Introduction 517.2 Simulation Result without FACTs Controller 517.3 Simulation Result with STATCOM, SSSC and UPFC 527.4 Simulation Result with STATCOM, SSSC, UPFC and PI 567.5 Simulation Result with STATCOM, SSSC, UPFC and PID 607.6 Comparison of Simulation Result 637.7 Comparison of Simulation with the Previous Work 647.8 Conclusion 64
8 Conclusion and Future Work 658.1 Conclusion 658.2 Recommendation 66
References 66
List of FiguresFigure 2.1: A typical PID control structure 9Figure 2.2: Schematic of the PID controller - non-interacting form 10Figure 2.3: Schematic of the PID controller - non-interacting form 11Figure 2.4: PID tuning with actuator constraints using matlab 13Figure 3.1: Two-machine power system 19Figure 3.2: Power against angle 20Figure 3.3: A single-machine infinite-bus power system 22Figure 3.4: Single machine infinite bus systems 25Figure 3.5: Equivalent circuit of single machine infinite bus system 25Figure 4.1: Transmission system with shunt compensation: simplified model 29Figure 4.2: Transmission system with shunt compensation: phase diagram 29Figure 4.3: Corresponding steady-state power exchange diagram. 30Figure 4.4: Schematic diagram of the SMIB system with STATCOM 31Figure 4.5: Equivalent circuit of SMIB system with STATCOM 31Figure 4.6: Simulation diagram with STATCOM. 33Figure 5.1: Transmission system with series compensation: simplified model. 36Figure 5.2: Phasor diagram of series compensator 36
Figure 5.3: A series compensated transmission line. 38Figure 5.4: Schematic diagram of the SMIB system with SSSC. 39Figure 5.5: Equivalent circuit of SMIB system with SSSC 39Figure 5.6: Simulation diagram with SSSC. 40Figure 6.1: Schematic diagram of three phases UPFC connected to a transmission line 43Figure 6.2: Single line diagram of UPFC and phasor diagram of voltage and current 44Figure 6.3: Simulink simulation model. 45Figure 6.4: Block diagram of lab scale model. 45Figure 6.5: Thyristor-controlled phase shifting transformer for transmission angle control 46Figure 6.6: Schematic diagram of the SMIB system with UPFC 48Figure 6.7: Equivalent circuit of SMIB system with UPFC 48Figure 6. 8: Simulation diagram with UPFC. 49Figure 7.1: Rotor angle deviation without FACTs device 51Figure 7.2: Simulation of STATCOM, SSSC and UPFC. 52Figure 7.3: Rotor angle deviation with SSSC, STATCOM and UPFC controller 53Figure 7.4: Rotor speed deviation with SSSC, STATCOM and UPFC controller 54Figure 7.5: Injected current and voltage by SSSC, STATCOM and UPFC controller 55Figure 7.6: Simulation Result with STATCOM, SSSC, UPFC with PI Controller. 56Figure 7.7: Rotor angle deviation of SSSC, STATCOM and UPFC with PI controller 57Figure 7. 8: Rotor speed deviation of SSSC, STATCOM and UPFC with PID controller 58Figure 7.9: Injected current and voltage by SSSC, STATCOM and UPFC with PI controller 58Figure 7.10: Simulations of STATCOM, SSSC, UPFC and PID 60Figure 7.11: Rotor angle deviation of SSSC, STATCOM and UPFC with PID controller 61Figure 7.12: Rotor speed deviation of SSSC, STATCOM and UPFC with PID controller 62Figure 7.13: Injected current and voltage by SSSC, STATCOM and UPFC with PID controller 63
List of Tables
Table -2.1: PI controller gain parameter 12Table -2.2: PID controller gain parameter 13Table -2.3: Tuning parameter of STATCOM 14Table -2.4: Tuning parameter of SSSC 15Table -2.5: Tuning parameter of UPFC 16Table -7.1: Rotor angle deviation with SSSC, STATCOM and UPFC controller 53Table -7.2: Rotor speed deviation SSSC, STATCOM and UPFC controller 54Table -7.3: Rotor angle deviation of SSSC, STATCOM and UPFC with PI controller 57Table -7.4: Rotor speed deviation of SSSC, STATCOM and UPFC with PI controller 58Table -7.5: Rotor angle deviation of SSSC, STATCOM and UPFC with PID controller 61Table -7.6: Rotor speed deviation of SSSC, STATCOM and UPFC with PID controller 62Table -7.7: Rotor angle deviation comparision 63Table -7.8: Rotor speed deviation comparision 64
Chapter 1
Introduction and Literature Review
1.1 Introduction
Power system low-frequency oscillations are the electromechanical oscillations which occurred
in systems with oscillation frequency up to a pair of Hz. The oscillations may persist for a
while and then disappear, or continuously grow to cause system collapse. A power system
fluctuation can be triggered by unrelenting faults of system operation, such as a three-phase to-
earth, short circuit or tripping of a transmission line. Power system large-disturbance rotor
angle stability or small-disturbance rotor angle stability [1] occurred due to collapse of power
system. The power system is unstable in terms of system oscillation stability if an oscillation is
of a sustained continuously or increasing magnitude. If the oscillation diminishes rapidly with a
damping ratio greater than 0.1, it is said that the power system is steady as far as oscillation
stability is concerned and the oscillation is of excellent damping. If the low-frequency
oscillation sustains for a certain time (several to tens of seconds) and sets eventually, it is
identified that the oscillation stability of the power system is maintained but with poor
oscillation damping. In October, 1964 power system oscillations were first reported in Northern
American power network during a trial of interconnection of the Northwest Power Pool and the
Southwest Power Pool [2]. After then the connection during tie line, a power oscillation of 0.1
Hz was examined on the tie line which was tripped out later. Since then power system
oscillation incident data has been reported in power transmission networks of many
countries.In late 1970s and early 1980s, power oscillations were investigated in the power
transmission arena from Scotland to England in Great Britain power network. Operational
result indicated that those oscillations were associated with relatively high level of power
transfer from Scotland to England. A series of tests carried out between 1980 and 1985
confirmed that the oscillations occurred when the power transfer from Scotland to England
reached a certain level andthe typical frequency of oscillations was around 0.5 Hz. This
difficulty of power oscillations was successfully solved by installing Power System Stabilizers
(PSS) at various power plants in Scotland [3].It is now well recognized that the cause of power
system oscillations is the poor damping of the so-called “electromechanical oscillation modes”
in the power system.
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Poor damping could be caused by
(1) Large amount of long-distance power transmission;
(2) Weak inter-connection of large power sub-networks;
(3) Negative damping provided by fast-acting high-gainAVR.
Oscillation modes are classified into two types:-
(1) Local oscillation modes (or local modes) ;
(2) Inter-area oscillation modes (or inter-area modes).
Power system oscillations associated with local oscillation modes are the power oscillations of
one or a group of local generators against a large power network. Usually local generators send
power over a long distance to load centers in the large power network. Frequency of
oscillations often is about one or several Hz. Power oscillations related to interarea oscillation
modes are the power oscillations between two or more sub-networks in a power system. A
typical inter-area oscillation is the tie-line power oscillation between two weakly connected
areas in the power system. Inter-are an oscillations could involve many sub-networks to
oscillate against each other’s (referred to as intra-area oscillations in some literature). A power
system oscillation could be engaged by one oscillation mode only (local or inter-area oscillation
mode), the so-called “single-mode oscillation”. It could also participate by many oscillation
modes, typically local modes plus inter-area modes. This is the case of so-called “multimode
oscillations”. The trend of development of modern power systems is towards open access,
customer-driven planning and operation. This requires the system operation and control more
flexible and reliable. At the same time, due to the environmental considerations, conventional
ways to reinforce power systems to achieve flexibility and reliability are significantly
constrained. Power system researchers and engineers havelooked for new alternatives of
strengthening system operation and control without, for example, constructing new
transmission lines.
The National grid of Bangladesh failed after the transmission line experienced a "technical
glitch" that led to a cascade of failures throughout the national power grid, with power plants
and substations shutting down on 1st November 2014. In the year 2003, North America and
Europe have experienced a number of series blackouts [4-5]. These blackouts call for a novel
algorithm of controlling mechanism and minimizing the effect of failure for a safe and more
reliable power system operation. Such types of blackouts usually occur due to the disturbance
of rotor angle and corresponding instability of the turbines of generators. In order to reduce the
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effect of aperiodic small disturbance (ASD) [6] and large disturbance of rotor angle instability
[7], a number of approaches have been already deployed in many times.
The closed loop control system stables the single machine operating condition due to impact of
loss of generating unit and large sudden change in load. For the FACTS damping controllers of
the feedback signals are realized by evaluating the modal residues of each feedback signal to
the system input [8]. To stabilize the power system by damping interarea power oscillations and
by improving the transient stability of the system a thyristor switched series capacitor (TSSC)
has been incorporated [9]. Flexible ac transmission system (FACTS) devices are being applied
to improve power transfer capability of ac transmission networks and to enhance the
controllability of power flow and voltage thus augmenting power system stability due to
continuing developments in power electronic technologies.
1.2 Literature Review
There are two generations of power electronics-based FACTS controllers: the first generation
was conventional thyristor-switched capacitors and reactors, and quadrature tap-changing
transformers, the second generation employs gate tum-off (GTO) thyristor switched converters
as voltage source converters (VSCs). The Static Var Compensator (SVC), the Thyristor-
Controlled Series Capacitor (TCSC), and the Thyristor-Controlled Phase Shifter (TCPS) are
commonly used in first generation. The second generation has incorporated the Static
Synchronous Compensator (STATCOM), the Static Synchronous Series Compensator (SSSC),
the Unified Power Flow Controller (UPFC), and the Interline Power Flow Controller (IPFC).
The two groups of FACTS controllers have particularly different operating and performance
characteristics.The potential benefits of FACTS equipment are now widely recognized by
the power systems engineering and T&D communities. With respect to FACTS
equipment, voltage sourced converter (VSC) technology, which utilizes self-commutated
thyristor /transistors such as GTOs, Ws, IGCTs, and IGBTs, has been successfully applied in a
number of installations world-wide for Static Synchronous Compensators (STATCOM)
[10-14].For power system stability improvement, FACT devices multifariously are used in [15-
17]. For transient stability improvement and to compare among them
different methodology have been used with PI and PID controller [18-20].
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1.2.1 First Generation of FACT
1.2.1.1 Static VAR Compensator (SVC)
SVCs enhance the dynamic stability performance ofa power system by injecting appropriate
portion of a signal.For providing appropriate reactive power compensation the shunt type of
FACTS Controllers are used to either absorb or inject Vars into the system. The output of
SVCis adjusted to interchange capacitive or inductive current so as to maintain or control
specific parameters of the electrical power system. This is a general term for a thyristor
controlled reactor, and/or thyristor-switched capacitor or combination of both. SVC is based on
thyristors without the gate turn-off capability. It includes separate equipment for leading and
lagging vars; the thyristor-controlled or thyristor switched reactor for absorbing the reactive
power and thyristor-switched capacitor for supplying the reactive power. Static var
Compensator (SVC) which provides for reactive power compensation both during the leading
and lagging power factor conditions, hence the term hybrid.
1.2.1.2 Thyristor-Controlled Series Capacitor (TCSC)
Too mitigate the power system stability problem, Thyristor controlled series compensator
(TCSC) is a significant device in FACTs arena which is widely renowned as an effective and
efficient devices. TCSC controller can regulate the line impedance through the introduction of a
thyristor-controlled capacitor in series with the transmission line [23-29]. Series capacitors
compromise assured major advantages over the shunt capacitors. With shuntcapacitors, the
reactive power is proportional to the square ofbus voltage, whereas with series capacitors, the
reactive powerrises as the square of line current. For accomplishing same system benefits as
those ofseries capacitors, shunt capacitors required are three to six times more reactive power
rated than series capacitors. Furthermore shunt capacitors typically must be connected at the
midpoint, whereas no such requirement exists for series capacitors. A series capacitor is capable
of compensating for the voltage drop of the series inductance in a transmission line. During low
loading the system voltage drop is lower and at the same time the series compensation voltage
is lower. When loading increases and the voltage drop becomes higher, the contribution of
series compensation increases and therefore system voltage will be regulated as desired.
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1.2.1.3 Thyristor-Controlled Phase Shifter (TCPS)
A capacitive reactance compensator which consists of a series capacitive bank shunted by a
thyristor controlled reactor in order to provide smooth variation of series capacitive reactance.
1.2.2 Second Generation of FACTS
1.2.2.1 A Static Compensator (STATCOM)
Among the FACTS devices, the Static Synchronous Compensator (STATCOM) is able to
improve the transfer capability of a power system by enhancing voltage regulation and stability.
These can significantly provide smooth and for improving both damping of power oscillations
[30-32] and transient stability and rapid reactive power compensation for voltage support [33].
In addition the STATCOM carries a reactive current to regulate the voltage independently [34,
35, 36, 37] and control grid fault [38, 39].
1.2.2.2 Static Synchronous Series Compensator (SSSC)
The Static Synchronous Series Compensator (SSSC) comprises of a voltage source converter in
series with coupling transformer in the line. SSSC can inject a voltage with controllable
magnitude and phase angle at the line frequency and found to be more capable of handling
power flow control, improvements of transient stability and damping of oscillations [40-42].
1.2.2.3 Unified Power Flow Controller (UPFC)
There are two solid state voltage source converters (VSCs) in the unified power flow controller
(UPFC). The VSCs are colligated via a common DC link capacitor. One of the VSCs is
STATCOM which is shunt connected and the other is SSSC which is series connected. Both
VSCs injects a nearly sinusoidal current of variable magnitude. STATCOM injects current in
quadrature with the line voltage and at the point of association whereas SSSC injects current in
quadrature with the line current. STATCOM and SSSC exchange solely reactive power at their
terminal when they operate as standalone controllers with open dc link switch. At the point
when both of the VSCs works together with the dc link switch, the injected voltage which lies
in series with the line can take any angle with respect to the line current. As a result, the power
that is exchanged at the terminals of SSSC can take any form either real or reactive. The real
power can be exchanged by the SSSC with the line flows bi-directionally to the line through thePage | 5
STATCOM and the common dc link capacitor. The UPFC has been used widely to improve
damping and dynamic performance of the system [43-44]and also enhancing reliability of
power system [45]. To incorporate synchronous AC grid, UPFC is also used in the system [46]
1.3 Objectives with specific aims and possible outcome
1.3.1 Objectives
This paper presents the comparative performance of PI and PID controller scheme with
Flexible AC Transmission System (FACTS) devices, such as Static Synchronous Compensator
(STATCOM), Static Synchronous Series Compensator (SSSC) and Unified Power Flow
Controller (UPFC) in terms of improvements in transient stability, extenuation of system
oscillations and furnishing voltage support in single machine infinite bus system (SMIB).The
specific aims are summarized as follows:
(i) To study transient and steady-state behaviour of Flexible AC Transmission System
(ii) To analysis rotor angle deviation and speed deviation for PI and PID controller with
STATCOM, SSSC and UPFC.(iii) To compare the simulation results in term of maximum overshoot and settling time.
1.3.2 Possible Outcomes
This paper presents to enumerate the rotor angle deviation and speed deviation by using two-
step methodology. The suggested techniques first simulates the STATCOM, SSSC, and UPFC
and then incorporate PI and PID controller with STATCOM, SSSC and UPFC. The actions of
STATCOM, SSSC, and UPFC will improve transient performance of the power system but
combine effect of PI and PID controller will show tremendous improvement. The PID
controller will perform betterthan PI controllerin term of maximum overshoot and settling time.
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1.4 Outline of the Thesis
The thesis is organized in 8 chapters.
In chapter 1 a general overview of FACTS devices are presented with a briefdescription. In chapter 2 the fundamentals of PID and PI controller are discussed. In this chapter the
tuning parameters of PI and PID controllers obtained for the system. Based on this
tuning parameter 20 different cases have been analyzed to optimized the controller. In chapter 3 the single machine infinite bus system is studied. The principle of power
system, stability analysis, and swing equation also has been discussed. The
mathematical model of single machine infinite bus power system also develops for
controlling of the system. In chapter 4, 5 and 6 the principle and mathematical equation has been developed for
STATCOM, SSSC and UPFC respectively. In these chapters block diagram of
STATCOM, SSSC and UPFC with PI and PID controllers has been incorporated. In chapter 7 simulation using matlab software (Simulink) has been performed for PI and
PID controller with STATCOM, SSSC and UPFC. From the simulationresults the
comparative performances of the system have beenanalysis. Further, in chapter 8 superior controller have been proposed as conclusion.
Chapter 2
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Optimizations of PI and PID Controllers
2.1 Introduction
The first controllers with proportional, integral, and derivative (PID) feedback control action
became commercially available during the 1930s. The 1940s saw widespread acceptance in
industry of pneumatic PID controllers, and their electronic counterparts entered the market in
the 1950s. Digital hardware has been routinely used since the 1980s with significant impact on
process control. Even several decades after three-mode controllers were introduced; the vast
majority of controllers used in the chemical process industry are based on PI/PID models [48].
The popularity of these controllers has led to research on tuning methods, resulting in hundreds
of publications on this topic. Ziegler-Nichols tuning relations and Cohen-Coon tuning rules are
among the earliest published methods. Tuning relations based on error criteria are more recent
model-based tuning rules, which offer improvements over earlier tuning methods. Tuning rules
also exist for unstable processes as well as for tuning in the presence of plant model mismatch
[49].
2.2 PI Controller
PI controller has been used in recent years with the purpose of improving the transient and the
steady-state performance and also for rejection of disturbances caused by operation events
throughout startup [50-52].It comprises of proportional action and integral action. The
proportional controller dimineshes the system error by using proportion of system error to
control the system. However, this incorporate an offset error into the system. The integral
controller output is proportional to the amount of time there is an error present in the system.
The integral action eliminates the offset which is introduced by the proportional control but
incorporates a phase lag into the system.
2.3 PID Controller
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A typical structure of a PID control system is shown in Figure 1.2,where it has been seen that in
a PID controller , the error signal e(t) is used to generate the proportional, integral, and
derivative actions, with the resulting signals weighted and summed to form the control signal
u(t) applied to the plant model [53].
Figure 2.1: A typical PID control structure
A mathematical description of the PID controller is [4]
u (t )=KP [e (t )+1T i∫0
t
e (τ )dτ+T dde(t )dt ] (1 .1)
Where u(t) is the input signal to the plant model, the error signal e(t) is defined as
e(t) =r(t) − y(t),and r(t) is the reference input signal.
PID controller consists of Proportional Action, Integral Action and Derivative Action. It is by
far the most common control algorithm. PID controller’s algorithm is mostly used in feedback
loops [48]. PID controllers can be implemented in many forms. It can be implemented as a
stand-alone controller or as part of Direct Digital Control (DDC) package or even Distributed
Control System (DCS). The latter is a hierarchical distributed process control system which is
widely used in process plants such as pharmaceutical or oil refining industries [54]. The
schematic of the PID controller is explained in the following figure 2.2. Such set up is known
as non- interacting form or parallel form.
Page | 9
Disturbance d(t)
PID Controlleru(t) y(t)
e(t)r(t) PlantModel
Controller
-
Measurementnoise
Plant
P
I
Figure 2.2 : Schematic of the PID controller.
The behavior of the proportional, integral, and derivative actions will be demonstrated
individually.
2.4 Proportional Control
Proportional control is denoted by the P-term in the PID controller. The proportional controller
output uses a ‘proportion’ of the system error to control the system. However, this introduces an
offset error into the system.
Pterm=K P×e( t) (2. 2)
Where, is the error signal and KP is the gain of the P controller.
2.5 Integral Control
Integral control is denoted by the I-term in the PID controller and is used when it is required
that the controller correct for any steady offset from a constant reference signal value. Integral
control overcomes the shortcoming of proportional control by eliminating offset without the
use of excessively large controller gain but introduces a phase lag into the system.
Page | 10
++
ErrorInput+
_ Output
D
)(te
C(S)
)1
1( di
STST
K Plant
Iterm=K I×∫e (t )dt (2.3)
Where, KI is gain of the integral controller
2.6 Derivative Control
If a controller can use the rate of change of an error signal as an input, then this introduces an
element of prediction into the control action. Derivative control uses the rate of change of an
error signal and is the D-term in the PID controller. Derivative control is used to
reduce/eliminate overshoot and introduces a phase lead action that removes the phase lag
introduced by the integral action.
Dterm=K D×d {e( t)}dt (2. 4)
Where, KD is the gain of the derivative controller.
2.7 Continuous PID
The three controllers when combined together have been represented by the following transfer
function.
Gc ( s )=K (1+1sT i
+sT d) (2. 5)
This has been illustrated in Figure 2.3 in the following block diagram
Figure 2.3: Block diagram of continuous PID controller
Page | 11
R(S) +_
What the PID controller does is basically is to act on the variable to be manipulated through a
proper combination of the three control actions that is the P control action, I control action and
D control action. The P action is the control action that is proportional to the actuating error
signal, which is the difference between the input and the feedback signal. The I action is the
control action which is proportional to the integral of the actuating error signal. Finally, the D
action is the control action which is proportional to the derivative of the actuating error signal.
With the integration of all the three actions, the continuous PID has been realized. This type of
controller has been widely used in industries all over the world. In fact a lot of research, studies
and application have been discovered in the recent years.
2.8 Tuning of PI Controller
The PI controller tuning parameters and have been optimized by PID tuning with
actuator constraint.
Table 2.1PI Controller Gain Parameter
Parameters
Gain with actuator constraints for linear block 3.715 0.4762
Gain for simulation 3.715 0.4762
2.9 Tuning of PID Controller
The PID controller is a “three modes” controller. The value of three tuning parameters the
proportional, integral and derivative determine the performance and activity of these
controllers. The three control actions that are P control action, I control action and D control
action work together to get the continuous PID controller. PID controller has been developed in
order to improve transient performance and speed control of motor [56-57] generator. A
discrete PID controller is incorporated into the system for diminishing nonlinear damping [58].
The tuning value of gain (KP, KI, KD) may be obtained from Steepest Gradient Descent Method
(SDGM) [59] and as well as Genetic Algorithms Method [60] and also Ziegler–Nichols tuning
Page | 12
PK IK
PK IK
method. In the proposed controller, the gain parameter ( , and ) of PID controller has
been tuned by PID tuning with actuator constraint as shown in figure 2.4. This gain parameters
have been manupulated due to non-linear block present in the system which have been shown
in Table 2.
Figure 2.4: PID Tuning with Actuator Constraints Using Matlab.
Table 2.2PID Controller Gain Parameter
Parameters
Gain with actuator constraints for linear block 1.646
0.7671 0.4633
Gain for Proposed Methodology 15 0.01083
0.4673
Tuning parameters for STATCOM, SSSC and UPFC are summarized in the following table 2.3,
2.4 and 2.5.
Page | 13
PK IK DK
PK IK DK
Table 2.3 Tuning Parameter of STATCOM
Page | 14
Sl.
No
Maximum Overshoot Setting Time
Angle Speed Angle Speed
1 55 0.25 0.25 4 43 0.23 0.27
2 20 0.1 0.50 1.25 38 0.45 0.4
3 15 0.2 0.1 5.625 49 0.40 0.30
4 10 1 0.6 0.375 23 0.57 0.62
5 11 0.3 0.4 1.25 29 0.43 0.45
6 12 0.35 0.8 1.25 22 0.52 0.4
7 30 1 0.7 0.5 44 0.30 0.39
8 40 0.9 0.8 0.3125 47 0.25 0.19
9 35 0.1 0.2 1.25 62 0.23 0.22
10 45 0.3 0.1 0.75 81 0.90 0.17
11 50 0.98 0.01 6.25 90 16 0.16
12 50 0.30 0.25 6.25 72 0.11 0.16
13 13 0.19 0.15 25.625 9.6 0.44 0.38
14 140 0.27 0.33 6.25 110 0.46 0.18
15 100 0.39 0.36 6.25 90 0.40 0.17
16 110 0.45 0.73 4.25 85 0.25 0.21
17 90 0.38 0.74 6.25 70 0.23 0.2
18 200 0.56 0.19 5.8 95 0.25 0.2
19 300 0.86 0.43 6.25 96 0.21 0.18
20 250 0.9 0.2 6.25 82 0.25 0.19
From the above table 2.3 it has been found that for STATCOM the values of KP,KIand KDare 55
0.25 and 0.25 respectively. For these tuning parameters, maximum overshoot and settlingtime
of rotor angle deviation are 0.001 and 0.11respectively. For the same tuning
parameters,maximum overshoot and settling time of rotor speed deviation are 0.72 and
0.16respectivelyPage | 15
PK IK DK
Table 2.4Tuning Parameter of SSSC
Sl
No
Maximum Overshoot Setting Time
Angle Speed Angle Speed
1 20 0.01083 0.4673 1.875 43 0.27 0.30
2 10 0.2 0.50 1.25 27 0.40 0.44
3 30 1 1.3 6.50 34 0.23 0.25
4 35 0.9 1 6.25 44 0.3 0.26
5 5 0.8 0.4 0.125 18 0.6 0.65
6 10 1 0.7 4.30 23 0.32 0.35
7 15 0.9 0.75 6.25 28 0.35 0.4
8 12 0.8 0.6 0.625 27 0.3 0.42
9 18 0.1 0.3 5.625 48 0.37 0.3
10 42 2.3 0.5 6.25 50 0.25 0.25
11 45 2 0.5 1.875 67 0.27 0.2
12 50 2.5 0.123 6.25 88 0.22 0.19
13 40 1 0.9 6.67 42 0.20 0.2
14 60 0.5 0.9 6.25 63 0.19 0.23
15 70 1.6 0.55 1.25 84 0.30 0.18
16 11.5 0.5 0.5 1.875 29 0.4 0.41
17 33 0.65 0.76 6.25 28 0.27 0.47
18 13 0.35 0.28 5.625 42 0.45 0.43
19 18 0.97 0.16 10.625 52 0.44 0.46
20 24 0.72 0.61 1.25 43 0.33 0.34
From the above table 2.4 it is found that for SSSC the best tuning values of and
are40, 1 and 0.09 respectively. For these tuning parameters, maximum overshoot and settling
Page | 16
PK IK DK
PK IK DK
time ofrotor angle deviation are 0.001 and 0.25respectively. For the same tuning parameters,
maximum overshoot and settling time of rotor speed deviation are 0.50 and 0.25respectively.
Table 2.5 Tuning Parameter of UPFC
Sl
No
Maximum Overshoot Setting Time
Angle Speed Angle Speed
1 15 0.01083 0.4673 6.25 27 0.45 0.55
2 11 0.2 0.5 12.5 23 0.46 0.65
3 18 0.15 0.67 6.25 27 0.4 0.55
4 60 0.9 0.5 6.25 54 0.25 0.30
5 50 0.8 0.6 5.23 46 0.35 0.25
6 55 0.7 0.2 3.42 65 0.4 0.27
7 5 0.86 0.34 4.52 17 0.8 0.85
8 70 0.64 0.26 6.3 27 0.30 0.67
9 75 0.85 0.42 4.7 30 0.27 0.62
10 80 0.67 0.55 5.1 60 0.25 0.30
11 85 0.77 0.41 3.6 65 0.80 0.32
12 97 0.32 0.21 7.2 82 0.22 0.23
13 77 0.86 0.52 5.1 60 0.31 0.30
14 46 0.34 0.47 3 26 0.15 0.26
15 64 0.39 0.60 4.5 46 0.25 0.22
16 67 0.43 0.47 5.30 55 0.30 0.27
17 82 0.60 0.50 4.30 62 0.25 0.25
18 79 0.80 0.20 5.88 75 0.20 0.40
19 89 0.42 0.69 3.49 62 0.25 0.37
20 65 0.32 0.60 4.14 58 0.21 0.23
Page | 17
PK IK DK
From the above table 2.5 it has been found that for UPFC the values of and are46
0.34 and 0.47 respectively. For these tuning parameters, maximum overshoot and settling time
of rotor angle deviation are 0.001 and 0.15respectively. For the same tuning parameters,
maximum overshoot and settling time of rotor speed deviation are 0.46 and 0.22respectively.
2.10Conclusion
This paper proposes novel approaches for data driven of nonlinear system. Tuning methods for
PI and PID controllers are proposed such that the response of the compensated system has
overshoot below a prescribed value. All the development of the methodologies is simple and
relies solely on concepts introduced in a frequency-domain-based control system. The tuning
values of controller achieved first for linear part of system using actuator constraint which is
the iterative tuning method. Based on the tuning values twenty iterations completed
comprehensively for STATCOM, SSSC and UPFC to get the tuning parameter of PID
controller.
Page | 18
PK IK DK
Chapter 3
Single Machine Infinite Bus System for Stability
Analysis
3.1 Introduction
Small signal stability investigation is vital as the system outage due small signal perturbation
being unknown to the system operators. The small signal disturbance may be initiating event
for large system outage. The Single Machine Infinite Bus (SMIB) power system helps in tuning
the controllers at one machine without considering the effect of other machines in the power
system. The effect of disturbance seen by the machine being 100%, whereas, in interconnected
power system the effect gets distributed among different machines. Therefore, the controller
tuning with SMIB remains valid for multi-machine power system as well. Small signal stability
investigations usually involve the analysis of the linearized system governing equations that
define the power system dynamics. Whereas, transient stability of the power system deals with
system analysis, following a severe disturbance, such as a single or multi-phase shorts circuit or
a generator loss. Under these conditions, the linearized power system model does not remain
valid. A third term, dynamic stability, has been widely used in the literature as a class of rotor
angle stability. The stability criterion with respect to synchronous machine equilibrium has
been presented. The mathematical model presented for small scale stability state is a set of
linear time invariant differential equations [61]. P.M. Anderson and A.A. Fouad, had
mentioned, the stability under the condition of small load changes has been called steady state
stability [62]. The concepts of synchronous machine stability as affected by excitation control
and the phenomenon of stability of synchronous machines under small perturbations in the case
of single machine connected to an infinite bus through external reactance has been presented by
F.P.demello and C. Concordia. The analysis also develops insights into effects of thyristor type
excitation systems and establishes understanding of the stabilizing requirements for systems
Page | 19
[63]. These stabilizing requirements include the voltage regulator gain parameters as well as the
transfer function characteristics for a machine speed derived signal superposed on the voltage
regulator reference for providing damping machine oscillations [64]. Trends in design of power
system components have resulted in lower stability and led to increased reliance on the use of
excitation control to improve stability [62]. IEEE Committee Report (1981), the working group
of IEEE on computer modeling of excitation systems, in their report has discussed excitation
system models suitable for use in large scale stability studies [65]. Michael J. Basler Richard C.
Schaefer discusses power system instability and the importance of fast fault clearing
performance to aid in reliable production of power [66]. In the past decades, the utilization of
supplementary excitation control signals for improving the dynamic stability of power systems
has received much attention.
3.2 Principle of Power Transmission
To model the operation, a transmission line can be represented by a series reactance and with
the sending and receiving end voltages. This is shown in figure 3.1 for one phase of a three-
phase system. Therefore, all quantities such as voltages and currents are defined per phase.
V s and V r are the per-phase sending end voltage and receiving end voltage, respectively.
They represent Thevenin equivalents with respect to the midpoint. The equivalent impedance
(jX/2) of each Thevenin equivalent represents the ‘’short-circuit impedance’’ located on the
right or left side of that midpoint. For the sake for the simplicity, let us assume that the
magnitudes of the terminal voltages remain constant, equal to V. That is V s = V R =
V m =V [67].
Page | 20
IX/2X/2
2/ VVRMV2/ VVS
Figure 3.5: Two-machine power system
Figure 3.6: Power against angle
Active (real) power P is defined as
Equation 3-1
(3.1)
Reactive power Q is defined as(3.2)
Page | 21
Power
Angle
P
Q
2
MaxP
MaxQ
SinX
VP
2
)1(2
CosX
VQ
Active power P becomes the maximum at δ=900
, and reactive power Q becomes
the maximum at δ=1800
.The plots of the active power and reactive power Q
against the angle δ are shown in Figure 3.2. For a constant value of line reactance X, varying
angle δ can control the transmitted power P. However, any changes in active power also change
the reactive power demand on the sending and receiving ends. Power and current flow can be
controlled by one of the following means [67].
Applying a voltage in the midpoint can also increase or decrease the magnitude of power.
Applying a voltage in series with the line, and in phase quadrature with the current flow, can
increase or decrease the magnitude of current flow. Because the current flow lags the voltage
by 900
, there is injection of reactive power in series.
If a voltage with a variable magnitude and a phase is applied in series, then varying the
amplitude and phase angle can control both the active and reactive current flows. This requires
injection of active power and reactive power in series.
Increasing and decreasing the value of the reactance X cause a decrease and an increase of the
power height of the curves, respectively, as shown in Figure 3.2. For a given power flow,
varying X correspondingly varies the angle δ between the terminal voltages.
Power flow can also be controlled by regulating the magnitude of sending and receiving end
voltages V s and V r . The type of control has much more influence over the reactive power
flow than the reactive power flow.Therefore, we can conclude that the power flow in a
transmission line can be controlled by
(1) Applying a shunt voltage V m at the midpoint,
(2) Varying the reactance X, and
(3) Applying a voltage with a variable magnitude in series with line.
These are easily done by FACTS devices
Page | 22
X
VP
2
max
X
VQ
2
max 2
3.3 Power Flow Control Concepts
To control power flow, it is necessary to be able to maintain or change line impedances, bus
voltage magnitudes, or phase angle differences. In this work, a power flow control device refers
to any device that changes or maintains one or more of these parameters. Power flow control
devices can be coordinated to affect system states in a way which attains some objective. There
are many power flow control devices, including the well-studied FACTS devices. Power flow
control devices often work by changing an effective admittance or impedance. Effective
impedance can either be changed through the use of physical capacitors and inductors or
through the use of a voltage source to perform active impedance injection.
3.4 Single Machine Infinite Bus System
The configuration of a power system has been shown in figure 3.3 where a generator sends
power to a large network. Capacity of the large network is much greater than that of the
generator such that operation of the large network is not affected at all by any changes in the
part of the power system on the left-hand side of bus bar b in figure 3.3. This effectively means
that the voltage and frequency at bus bar b are constant when the focus of the study is the part
of the left-hand side of the power system. Thus, from the point of view of operation of the part
of right-hand side of the power system, capacity of the large network is “infinite”. Hence, bus
bar b is called the “infinite bus bar”, and the part of the power system on the left-hand side of
bus bar b is a “single-machine infinite-bus” power system. The single-machine infinite-bus
power system is an approximate representation of a kind of real power systems, where a power
plant with a generator or a group of generators are connected by transmission lines to a very
large power network.
Page | 23
tV
bVtX
A large network
bItP
busbar b
Figure 3.7: A single-machine infinite-bus power system
3.5 Stability Analysis
The tendency of a power system to develop restoring forces equal to or greater than the
disturbing forces to maintain the state of equilibrium is known as “STABILITY”.
The problem of interest is one where a power system operating under a steady load condition is
perturbed, causing the readjustment of the voltage angles of the synchronous machines. If such
an occurrence creates an unbalance between the system generation and load, it results in the
establishment of a new steady-state operating condition, with the subsequent adjustment of the
voltage angles. The perturbation could be a major disturbance such as the loss of a generator, a
fault or the loss of a line, or a combination of such events. It could also be a small load or
random load changes occurring under normal operating conditions. Adjustment to the new
operating condition is called the transient period. The system behavior during this time is called
the dynamic system performance, which is of concern in defining system stability. The main
criterion for stability is that the synchronous machines maintain synchronism at the end of the
transient period. So we can say that if the oscillatory response of a power system during the
transient period following a disturbance is damped and the system settles in a finite time to a
new steady operating condition, we say the system is stable. If the system is not stable, it is
considered unstable. This primitive definition of stability requires that the system oscillations
be damped. This condition is sometimes called asymptotic stability and means that the system
contains inherent forces that tend to reduce oscillations. This is a desirable feature in many
systems and is considered necessary for power systems. The definition also excludes
continuous oscillation from the family of stable systems, although oscillators are stable in a
mathematical sense. The reason is practical since a continually oscillating system would be
undesirable for both the supplier and the user of electric power. Hence the definition describes a
practical specification for an acceptable operating condition. The stability problem is concerned
with the behavior of the synchronous machines after a disturbance. For convenience of
analysis, stability problems are generally divided into two major categories-steady state
stability and transient state stability.
3.6 Swing Equation
Page | 24
Under normal operating conditions, the relative position of the rotor axis and the resultant
magnetic field axis is fixed. The angle between the two is known as the power angle or torque
angle. During any disturbance, rotor will decelerate or accelerate with respect to the
synchronously rotating air gap mmf, a relative motion begins. The equation describing the
relative motion is known as the swing equation.
3.7 Synchronous Machine Operation
Consider a synchronous generator with electromagnetic torque Te running at synchronous speed
ωsm.
During the normal operation, the mechanical torque
A disturbance occur will result in accelerating/decelerating torque ( if
accelerating, if decelerating).
By the law of rotation
(3.3)
Where J is the combined moment of inertia of prime mover and generator
is the angular displacement of rotor with respect to stationery reference frame on the stator
is the constant angular velocity
Taking the derivative of we obtain
Page | 25
em TT
ema TTT 0aT
0aT
emam TTT
dt
dJ
2
2
m
msmm t sm
m
(3.4)
Taking the second derivative of
(3.5)
Substituting into law of rotation-
Multiplying to obtain power equation (3.6)
(3.7)
Where and are mechanical power and electromagnetic power.
Swing equation in terms of inertial constant M
(3.6)
Relations between electrical power angle and mechanical power angle and electrical
speed and mechanical speed
Page | 26
dt
d
dt
d msm
m
m
2
2
2
2
dt
d
dt
d mm
emam TTT
dt
dJ
2
2
m
ememmmammm
m PPTTTdt
dM
dt
dJ
2
2
2
2
mP eP
eme
m PPdt
dM
2
2
m
1 2
Where p is pole number
Swing equation in terms of electrical power angle
(3.7)
Converting the swing equation into per unit system
(3.8)
Where H is the inertia constant
3.8 Mathematical Representation of Single Machine Infinite Bus
A generator connected to a substation whose bus voltage and frequency are constant through a
very long transmission line. The characteristic of bus voltage remains constant through the
power supplied or consumed by any device connected to it.
Figure 3.8: Single machine infinite bus systems
Page | 27
m
p 2
m
p 2
eme
m PPdt
dM
P
2
22
)()(2
22puepum
es
PPdt
dH
L
1
L
3
V tm VV t
L
4
L
2 Infinite
bus
The equivalent circuit of the system is shown in Figure 3, where represent the equivalent
reactance between machine internal bus and the impedance represent the equivalent
reactance between the bus m and the infinite bus.
Figure 3.5: Equivalent circuit of single machine infinite bus system
The magnitude of the machine internal voltage and the infinite bus voltage is represented by E’
and V, respectively. The equation describing the relative motion between rotor axis and the
magnetic field axis is known as the swing equation. Under normal condition, the rotor remains
to its original position but if the disturbance is created due to any fault or sudden load, the rotor
comes to a new operating power angle relative to the synchronous revolving field.
The swing equation can be express in term of inertia constant
(3.9)
(3.10)
Here δ= the rotor angle deviation,
= the rotor angle deviation,
M= moment of inertia,
Pm = input mechanical power, and
D= damping coefficient.
Page | 28
1X
2X
V m = V m <E’=E’<δV=V<0
jX
1
jX
2
dt
d
)(1
2
2
DPPMdt
d
dt
dem
The simplified form of power flow equation in Figure 3 can be written as
(3.11)
Where
(3.12)
3.9 Conclusion
Power industries are modernized to provide effective operation to more consumers at lower
prices and better power efficiency. Due to interconnectivity of power system the complexity of
the power systems has been mounting. Load demand also increases linearly with the increase in
users. Since stability phenomenon limits the transfer capability of the system, there is a need to
confirm stability and reliability of the power system due to economic reasons. With these
conditions, authorities and researchers were continually tasked to find simple, effective and
economical strategy of achieving stabilization of the power system, which is considered of
highest priority. Thus, because of the importance of the stability of the power systems,
stabilizing control techniques have been used for the single-machine power system with the
help of intelligent methods. The optimal sequential design for single-machine power systems is
very essential. As a result, serious consideration is now being given on the concern of
stabilization control. In recent times, the utilization of optimization techniques becomes
possible to deal with control signals in power system.
Chapter 4
Mathematical Representation of STATCOM
4.1 Introduction
Static VAR compensator (STATCOM) is a device whose capacitive or inductive current can be
controlled independently without affecting ac system voltage.It is well established that the
steady-state transmittable power can be improved and the voltage profile along the line
controlled parameter by appropriate reactive shunt compensation. The methodology of this
reactive compensation isto create it more hormonal situation to prevail load demand of power
Page | 29
SinPPe max
21
'
max XX
VEP
system. Thus, shunt connected, fixed or mechanically switched reactors are applied to minimize
line overvoltage under light load conditions, and shunt connected, fixed or mechanically
switched capacitors are applied to maintain voltage levels under heavy load conditions. To
maintain a constant DC voltagethe STATCOM capacitor bank is used for thevoltage-source
converter operation. Common STATCOM mayvary from six-pulse topologies up to forty-eight-
pulse topologies that consist of eight six-pulse converters operated froma common dc link
capacitor [68-69].TheSTATCOM is optimalsuitable device for voltage control since it may
swiftlyinject or absorb reactive power to stabilize voltage excursions [70-71] and has been
shown to perform very well inactual operation [69]. Several prototype STATCOM installations
are currently in operation [69], [72]. The ability of the STATCOMto maintain a pre-set voltage
magnitude with reactive powercompensation has also been shown to improve transient stability
[70] and sub synchronous oscillation damping [73-75].In this section, basic considerations to
enhance the transmittable power by ideal shunt-connected var compensation will be reviewed
in order to provide a foundation for power electronics-based compensation and control
techniques to meet specific compensation objectives. The ultimate objective of applying
reactive shunt compensation in a transmission system is to increase the transmittable power.
This may be prerequisite to develop the steady-state and transient transmission characteristics
as well as the stability of the system. The applications of reactive power compensators based on
voltage-sourced inverters (VSI), such as Static Synchronous Compensator (STATCOM) [76],
are increasing in different power levels.These devices have several advantages over
conventional thyristor-based converters solutions in terms of the speed of response, flicker
compensation, flexibility, and minimal interaction with the supply grid.
Reactive compensation has been used widely in the power industry in order to provide voltage
regulation as well as improve transient stability [77]. Compared with SVCs, the voltage
sourced converter (VSC) based STATCOM has better compensating capability, faster response,
less harmonics and smaller physical size, and thus becomes a serious competitive alternative to
conventional SVCs [78]. This is used for voltage regulation at a given bus against load
variations or voltage support during generation or line outages in power systems.
4.2 Principle of Shunt Compensation
The power system is connected in parallel with shunt FACT devices for shunt compensation.It
works as a controllable current source. Shunt compensation is of two types: Shunt capacitive
Page | 30
compensation this method is used to improve the power factor. When an inductive load is
connected to power system, power factor lags because of lagging load current. To compensate,
a shunt capacitor is connected which draws current leading the source voltage. The net result is
improvement in power factor. Shunt inductive compensation this method is used either when
charging the transmission line, or, when there is very low load at the receiving end. Due to very
low or no load, very low current flows through the transmission line, shunt capacitance in the
transmission line causes voltage amplification (Ferranti Effect). The receiving end voltage may
significantly increasethan the sending end voltage. To compensate, shunt inductors are
connected across the transmission line.The objectives of STATCOM are to provide fast acting
dynamic reactive compensation for voltage support during contingency events, providing
dynamic and flexible voltage and reactive power support at their Substation, improving
power system and voltage stabilization to increase power transfer opportunities [79]. Shunt-
connected reactors are used to reduce the line over voltages by consuming the reactive power,
while shunt-connected capacitors are used to maintain the voltage levels by compensating the
reactive power to transmission line.
A simplified model of a transmission system with shunt compensation is shown in Figure 4.1.
The voltage magnitudes of the two buses and the phase angle may consider V andδ
respectively. The transmission line is assumed lossless and represented by the reactance X L .
At the midpoint of the transmission line, a controlled capacitor C is shunt-connected. The
voltage magnitude is maintained as V at the bus of transmission line.
Page | 31
j XL2
V<
δ2
j XL2
Bus 2Bus 1 V<
−δ2
I2I1
CIC
Figure 4.9: Transmission system with shunt compensation: simplified model
Figure 4.10: Transmission system with shunt compensation: phase diagram
As discussed previously, the active powers at bus 1 and bus 2 are equal.
(4.1)
The injected reactive power by the capacitor to regulate the voltage at the mid-point of the
transmission line is calculated as:
(4.2)
From the power angle curve shown in Figure 4.3 the transmitted power can be significantly
increased, and the peak point shifts from δ=90º to δ=180º. The shunt compensation can
improve operation margin of power system and also system stability effectively. The voltage
support function of the midpoint compensation can easily be extended to the voltage support at
the end of the radial transmission, which will be proven by the system simplification analysis in
a later section.
4.3 Static Synchronous Compensator (STATCOM)
Static synchronous compensator (STATCOM) is a fast acting device which is the representative
of FACTS family. A promising technology has been used comprehensively for reactive power
Page | 32
V c
V<
−δ2
V<
−δ2
I2I1
2sin
22
21
LX
VPP
)2
cos1(42 L
C X
VQ
1 2
control of power system. It is also known as static synchronous condenser. It is a controlling
device used on AC electricity network. STATCOM is a power electronic device. If the SVS is
used strictly for reactive shunt compensation, like a conventional static var compensator, the dc
energy source can be a relatively small dc capacitor, as shown in Figure 4.4. By measuring the
ripple input current the specification or size of the capacitor of particular converter may design.
In this case, interchange of the steady-state power between the SVS and the alternating current
system can only be reactive. The converter maintains the voltage level by using reactive power
generation of SVS. This is accomplished by making the output voltages of the converter lag the
system voltage by a small angle. The convertor furnishes the desired voltage level by absorbing
real power form the ac system. For increasing and decreasing of the capacitor voltage similar
method can be used to control the var generation or absorption. The dc capacitor maintains an
energy balance during the dynamic fluctuation of the var output [79]
Figure 4.3: Corresponding steady-state power exchange diagram
4.4 Mathematical Modeling of STATCOM
STATCOM is a controlled shunt current source that current is in quadrature with its terminal
voltage.
Page | 33
At AC terminal
I qSupply Q
V> V TV AC
At DC terminal
I dc≅0+V dc≅0
Absorb QV> V T
L
3
L
1
VmV t
Figure 4.4: Schematic diagram of the SMIB system with STATCOM.
The STATCOM is placed in the bus m and is represented by a shunt reactive current source
as show in Figure 4 and Figure 5.
Figure 4.5: Equivalent circuit of SMIB system with STATCOM
Where
(4.3)
Positive and negative signs indicate for the inductive and capacitive respectively.
Here
Page | 34
Infinite bus
L
2
L
4
VSC
C
sI
V m = V m <E’=E’<δV=V<0
jX
1
jX
2
Is
)90( mjSS eII
(4.4)
With the STATCOM the output power of the machine can be written as
(4.5)
Where
(4.6)
is positive when δ oscillates in between zero and π. Equation of suggests that it can be
modulated by modulating the shunt reactive current . For enhancement of power system
damping the shunt reactive current can be modulated in propagation to the rotor speed
deviation ω. With this control signal can be expressed as
, (4.7)
Where, K1 is a positive constant.
Putting all the values in equation (4.5)
(4.8)
From Equation (4.3) in setting value of
Page | 35
)cos
sin(tan
2'
1
21
XEVX
EXm
eP
Se IfPP )(sin 1max
)sin()(21
2'
1 mXX
XEf
mP
sI
sI
1KI S maxmaxSSS III
121
2'
21
'
)sin()(
sin)(
KXX
XE
XX
EP me
eP
Output
D ω
(4.9)
From equation (4.9) we may draw the block diagram of the system with STATCOM as depicted
the following in Figure 4.9.
4.5 Block Diagram of STATCOM
Figure 4.8: Simulation diagram with STATCOM
Figure 4.9 represents the simulation model for dynamic analysis of power system with
STATCOM. represents the shunt reactive current modulated by the STATCOM in
proportion to speed deviation of the machine,
PID: Proportional Integral Derivative Controller
Page | 36
})sin()(
sin)(
{1
121
2'
21
'
DK
XX
XE
XX
EP
Mdt
dmm
Pe = Pmax Sinδ+f1(δ)
-Pe
ω δPm
-
I s
1KI s
: Step change in mechanical input to the turbine.
eP : Electrical power output of the machine.
M : Machine moment of inertia.
ω : Rotor speed deviation.
δ : Rotor angle deviation.
D : Damping coefficient.
4.6 Conclusion
In this paper, PID controller is proposed to control STATCOM for improving power system
transient stability and system damping. Input parameters of controller are chosen carefully to
provide to considerable damping of power system. The range of each controller chosen from
actuator constant for linear portion of controller and then the tuning parameter rectify for better
performance. The single machine infinite bus system has been controlled by above controllers.
The performance of comparison results depict that the STATCOM improves the stability of
power system consideration part but after incorporating PI and PID controllers’ improvement of
stability is tremendous.
Page | 37
mP
Chapter 5
Mathematical Representation of SSSC
5.1 Introduction
The ac power transmission over long transmission lines is primarily limited by the series
reactive impedance of the line. Though series capacitive compensation was used decades ago to
diminish a portion of the reactive line impedance and thereby increase the transmittable power.
Subsequently, within the FACTS initiative, it has been established that variable series
compensation is highly effective in both controlling power flow in the line and in improving
stability. Controllable series line compensation is a cornerstone of FACTS technology. It can be
used for proper utilization of transmission assets to control the power flow of transmission
lines. It can be applied to prevent loop flows, minimized the system disturbances and also
reduced stability requirement. The SSSC can be considered as an impedancecompensation
controller acting like a controlled seriescapacitor [80-82]. It contains a solid-state
voltagesource inverter (VSI) which can inject nearly sinusoidal voltage, of flexible magnitude,
in series with a transmissionline. It compensates the inductive voltage drop in theline by
inserting capacitive voltage in order to reducethe effective inductive reactance of the
transmission line. In compare to others series capacitor, the SSSC can maintain a continuous
Page | 38
compensating voltage in case of variable line current or controls the amplitude of the injected
compensating voltage independent of amplitude of line current. In this section the basic
approach of reactive series compensation will be reviewed to provide the necessary foundation
for the treatment of power electronics based compensators. The effect of series compensation
on the basic factors, determining attainable maximal power transmission, steady-state power
transmission limit, transient stability, voltage stability and power oscillation damping, will be
examined.
5.2 Principle of Series Compensation
In series compensation, the FACTS are connected in series with the power system. It works as a
controllable voltage source. Series inductance occurs in long transmission lines, and when a
large current flow it causes a large voltage drop. To compensate, series capacitors are
connected. Series compensation aims to directly control the overall series line impedance of the
transmission line. Tracking back to Equations, the AC power transmission is primarily limited by
the series reactive impedance of the transmission line. A series-connected can add a voltage in
opposition to the transmission line voltage drop, therefore reducing the series line impedance.
A simplified model of a transmission system with series compensation is shown in Figure 5.1.
The voltage magnitudes of the two buses are assumed equal as V, and the phase angle between
them is δ. The transmission line is assumed lossless and represented by the reactance XL. A
controlled capacitor is series-connected in the transmission line with voltage addition Vinj. The
phase diagram is shown in Figure 5.2.
Figure 5.11: Transmission system with series compensation: simplified model
Page | 39
V<
δ2
Bus 2Bus 1jX LIC V<
−δ2
V L
V C
Figure 5.12: Phasor diagram of series compensator
Defining the capacitance of C as a portion of the line reactance,
(5.1)
The overall series inductance of the transmission line is,
(5.2)
The active power transmitted is,
(5.3)
The reactive power supplied by the capacitor is calculated as,
(5.3)
In Figure 5.3, shows the power angle curve from which it can be seen that the transmitted
active power increases with k.
5.3 Static Synchronous Series Compensator (SSSC)
A static synchronous generator operated without an external electric energy source as a series
compensator whose output voltage is in quadrature with, and controllable independently of, the
line current for the purpose of increasing or decreasing the overall reactive voltage drop across
Page | 40
V CV L
V<0
V<
δ2
LC kXX
LCL XkXXX )1(
sin)1(
2
LXk
VP
)cos1()1(
22
2
L
C Xk
kVQ
the line and thereby controlling the transmitted electric power. The SSSC may include
transiently rated energy storage or energy absorbing devices to enhance the dynamic behavior
of the power system by additional temporary real power compensation, to increase or decrease
momentarily, the overall real (resistive) voltage drop across the line.
Series reactive power compensation is obtained by controlling the equivalent impedance of a
transmission line, as to regulate the power flow through the line. Series connection of
capacitors banks was the first method of series compensation. However, the impossibility to
control in real time the level of compensation and the risk of initiating potentially dangerous
resonances constitute serious drawbacks to this solution. As for shunt compensation, the
utilization of fully controllable devices based on power electronics converters, provides the
most flexible solution for series compensation. The SSSC can be defined as a static
synchronous generator which acts as a series compensator whose output voltage is fully
controllable, independent of line current and kept in quadrature with it, with the aim of
increasing or decreasing the voltage drop across the line, therefore controlling the power
flow.The basic structure of an SSSC and its connection with the network is reported in Figure
5.7.SSSC operation is illustrated by the equivalent circuit of a lossless transmission line of
power system.
Figure 5.3: A series compensated transmission line
Page | 41
V r =V
e− jδ /2
V S =V e jδ /2 V q V 1
1 2
A series compensated transmission linecompensation if leads Iby π/2rad:or inductive
compensation if lags I by π/2 rad: A relatively small active power exchange is required to
compensate for coupling transformer and switching losses, and maintain the required DC
voltage. It can be concluded that the SSSC increases the voltage drop across line inductance
and hence power flow, if it emulates capacitive compensation. Differently from series
compensation achieved by means of either fixed or switched reactors, the SSSC can inject a
voltage that is independent of line current, whose amplitude can be fully controlled. Indeed, the
SSSC can be controlled in two different operation modes: constant reactance mode and
constant quadrature voltage mode. If SSSC is in constant reactance mode of operation, active
power transfer over the transmission line of Figure 5.7 is
(5.4)
SSSC is operated inconstant quadrature voltage mode, assuming active power
transfer.
5.4 Mathematical Modeling of SSSC
Synchronous Series Compensator (SSSC) is a solid-state voltage source inverter which absorbs
or produces reactive power when the line voltage is in phase quadrature with the line current.
The SSSC can interchange both active and reactive power with the ac system by controlling the
angular position of injected voltage with respect to line current. It may use to control the power
flow, to improve the transient stability, to diminish power system oscillation and to dampen
sub-synchronous resonance.
Page | 42
qV
qV
sin)1(1 sx
VVP rs
VVV rs
mL
3
L
1
V t
Figure 5.4: Schematic diagram of the SMIB system with SSSC.
Figure 5.5: Equivalent circuit of SMIB system with SSSC.
Consider that a SSSC is placed near bus m in the system as shown in Figure 5.6 and Figure 5.7.
The SSSC is represented by a series voltage source.
The series voltage injected by the SSSC is given by
(5.5)
Where � is the angle of the line current and is given by
(5.6)
With the SSSC the machine power can written as
(5.7)
Page | 43
Infinite
bus
L
4
L
2
VSC
C
E’=E’<δV=V<0
+jX
1
jX
2
)2( j
SS eVV
)sin
cos(tan
'
'
E
EV
eP
Se VfPP )(sin 2max
Where
(5.8)
f2 (δ) is positive when δ oscillates in between 0 and π.
can be modulated by properly controlling the value of
Vscan be expressed as
, (5.9)
K2 is a positive constant.
(5.10)
(5.11)
From equation (5.11) we may draw the block diagram of the system with SSSC.
5.5 Block Diagram of SSSC
Page | 44
)cos2
sin()(
''
max2 2
VEE
Pf
eP sV
2KVS maxmaxSSS VVV
2''
21
'
21
'
)cos2
sin))(
(
(sin)(
2 KVEE
XX
E
XX
EPe
})cos2
sin))(
(
(sin)(
{1
2''
21
'
21
'
2
DKVEE
XX
E
XX
EP
Mdt
dm
Pe = Pmax Sinδ+f2(δ)
-Pe
ω δ1M
Pm 1S Output
1S
-
V s
D ω
Fig.5.6: Simulation diagram with SSSC
Figure 5.8 represents the simulation model for dynamic analysis of power system with SSSC.
represents the series voltage injected by the SSSC in proportion to speed deviation of
the machine,
: Step change in mechanical input to the turbine.
: Electrical power output of the machine.
M : Machine moment of inertia.
ω : Rotor speed deviation.
δ : Rotor angle deviation.
D : Damping coefficient.
5.6 Conclusion
The SSSC and PID controller’s devices not only damp the system oscillations
of the single machine system but also reduce the oscillations transient
periods accordingly. The transient state period of rotor speed responses is
longer than those of voltage responses hence. FACTS provide better
support to system voltages compared to other parameters like rotor angle.
To achieve steady state operating after disturbances, it’s evident that the
damping characteristics of the PID are superior to those of SSSC.
Page | 45
ss KV
mP
eP
Chapter 6
Unified Power Flow Controller
6.1 Introduction
A combination of static synchronous compensator (STATCOM) and a static series compensator
(SSSC) which are coupled via a common dc link, to allow bidirectional flow of real power
between the series output terminals of the SSSC and the shunt output terminals of the
STATCOM, and are controlled to provide concurrent real and reactive series line compensation
without an external electric energy source. The UPFC, by means of angularly unconstrained
series voltage injection, is able to control, concurrently or selectively, the transmission line
voltage, impedance, and angle or, alternatively, the real and reactive power flow in the line. The
UPFC may also provide independently controllable shunt reactive compensate
The previous two chapters deal with shunt compensation and series compensation technique.
The combination of shunt and series compensation technique provides more flexibility to the
transmission system. In this chapter, a particular type of shunt and series compensator, a unified
power flow controller (UPFC) will be discussed. Unified Power Flow Controller (UPFC) is
used to control the power flow in the transmission systems by controlling the impedance,
voltage magnitude and phase angle. The static and dynamic operation of power system can be
performed by this controller. The fundamental structure of the UPFC comprises of two voltage
source inverter (VSI); where each source connected series and parallel with the transmission
line.
Page | 46
6.2 UPFC Construction
The UPFC is represented by of two ideal voltage sources converters; series and shunt
converter, which are connected to each other with a common dc link. Series converter or Static
Synchronous Series Compensator (SSSC) is used to add controlled voltage magnitude and
phase angle in series with the line, while shunt converter or Static Synchronous Compensator
(STATCOM) is used to provide reactive power to the ac system, besides that, it will provide the
dc power required for both inverter. The basic hardware employment of UPFC composed
of six valves, operated from a joint DC link is shown figure 6.1[85].
Therefore, active power absorb by the shunt converter could be equal to the active power
generated by the series converter. Figure 6.1 shows the schematic diagram of the three phases
UPFC connected to the transmission line [86].
Figure 6.13: Schematic diagram of three phases UPFC connected to a transmission line
Control of power flow is achieved by adding the series voltage, with a certain amplitude,
and phase shift, φ to . This will gives a new line voltage with different magnitude and
Page | 47
V 0V pqV 01
Transmission Line
P settingQ SettingMeasureDCvoltage
Ref
Parameter
V 01
V pq
V 0
ZZ
UPFC Control
i Series TransformerShunt Transformer
SV
1V 2V
phase shift. As the angle φ varies, the phase shift δ between and also varies. Figure 6.2
shows the single line diagram of the UPFC and phasor diagram of voltage and current.
Figure 6.14: Single line diagram of UPFC and phasor diagram of voltage and current
With the presence of the two converters, UPFC not only can supply reactive power but also
active power. The equation for the active and reactive power is given as follows:-
(6.1)
(6.2)
6.3 Methodology
The focus of this work is to design a UPFC and simulate it using matlabsoftware (Simulink).
Based on the schematic diagram of the three phases UPFC in Figure 6.1, a simulation model of
a single phase UPFC is drawn in Simulink and is illustrated in Figure 6.3.
Page | 48
2V 3V
δV 2−V 3 cos¿
¿V 2¿
Q=¿
P=V 2V 3 sin δ
XV s
I
V 3
V 2
V 1
I
V dV q
- V S
VSC1
1
VSC1
1
I_SH transmission line
P ,QX
V 3V 2V 1
sin12
2112 X
VVP
cos12
2112 X
VVQ
Figure 6.15: Simulation model
A lab scale model is constructed using H-bridge voltage source inverter to act as SSSC. Figure
6.4 shows the block diagram of the lab scale model. Programmable Interface Controller (PIC)
is being programmed to generated PWM signals to the gate drive that will send the signals to
trigger the IGBTs. The comparator provides a reference signal to the PIC controller board to
generate triggering signals in synchronization with the supply voltage.
Figure 6.16: Block diagram of lab scale model
Page | 49
AC DC
Pulse
Load
SeriesTransformer
InverterRectifier
ShuntTransformer
AC supplyLoad
H-bridgeinverter
DCcapacitor
H-bridgerectifier TransformerTransformer
H-bridgeinverter
Comparator PIC
A program is used to find zero crossing and to generate the required pulses. The program
generates a pulsed signal of 50Hz with a switching frequency of 1.22 kHz. The desired
frequency at the output of the H-bridge inverter is 50Hz which is equivalent to the supply
frequency. The program is written to start triggering when it detects zero crossing of the ac
supply. In order to get a delay at the output of the inverter in comparison to the supply, delay
instruction is added into the program before starting the triggering signals.
6.4 Phase-shifter transformer
Figure 6.5 shows a thyristor-controlled phase-shifter transformer arrangement. It contains a
shunt-connected excitation transformer and a series insertion transformer. The basic function of
a phase shifter is to provide a means to control power flow in a transmission line. It can modify
the voltage phase angle by injecting a variable quadrature voltage in series with the
transmission line in power system. The phase of the output voltage can be varied relative to that
of the input voltage by simply varying the magnitude of the series quadrature voltage.
Figure 6.17: Thyristor-controlled phase shifting transformer scheme for transmission angle
control.
Historically, this has been accomplished by specially connected mechanical regulating
transformers; because the power flow on the transmission line is proportional to the since of the
Page | 50
seriestransformer
Measuredvariables
Referenceinput
Parametersetting
Thyristorswitcharrangement
Excitation transformer
transmision line
Control
angle across the line, the steady state power flow can he controlled by utilizing a phase-shifter
to vary the angle across the line. The effectiveness of traditional phase shifters in performing
this function is well demonstrated in practice. Just as traditional phase shifters can be employed
to alter steady-state power flow, they can be used to alter transient power flow during system
disturbances or outages, if the phase shifter angle can be changed rapidly. Rapid phase angle
control could be accomplished by replacing the mechanical tap changer of by a thyristor
switching network.
6.5 Inter phase Power Controller (IPC)
The Interphase Power Controller (IPC) controlled at high short-circuits environments. IPCs offer
passive solutions for normal andcontingency conditions. It is a series connected controller which has
inductive and capacitive branch to control active and reactive power. By adjusting phase shifter the
active and reactive power may set independently by IPC. In the specific situation where the inductive
and capacitive impedancemake a conjugate pair, the terminal of IPC acts as a current source
[87-88].This is a broad based concept of series Controller, which can be designed to provide
control of active and reactive power.
6.6 Modeling of UPFC
The amalgamation of a static series compensator (SSSC) and static synchronous compensator
(STATCOM) which are combined via a common dc link, to permit bidirectional flow of active
power between the series output terminals of the SSSC and the shunt output terminals of the
STATCOM, and are controlled to provide concurrent active and reactive series line
compensation without an external electric energy source. The UPFC is able to control,
concurrently or selectively, the transmission line voltage, impedance, and angle or,
alternatively, the active and reactive power flow in the line.
Page | 51
1 2
Figure 6.6: Schematic diagram of the SMIB system with UPFC
Figure 6.7: Equivalent circuit of SMIB system with UPFC.
The single line diagram and equivalent circuit are given in Figure 6.6. and Figure 6.7. The
mathematical expression of Static Synchronous Series Compensator (SSSC) and Static
Compensator (STATCOM) will be combined to show the damping improvement of the system
with UPFC. With the UPFC the machine power Pecan written as
(6.3)
Where, the value of Pmax, δ, f1 (δ) and f2 (δ) are given in
Page | 52
L
1L
3
V t
m
Infinite
bus
L
4
L
2
VSC
VSC
C
V=V<0V m = V m <E’=E’<δ
jX2jX1+
I
s
SSe VfIfPP )()(sin 21max
(6.4)
(6.5)
From equation (6.5) we may draw the block diagram of the system with UPFC.
6.6.1 Block Diagram of UPFC
Figure 6.8: Simulation diagram with UPFC
Figure 6.8 represents the simulation model for dynamic analysis of power system with UPFC.
With UPFC both the loops (shunt current modulation) and (series voltage
modulation are present).
Page | 53
2''
21
'
121
2'
21
'
)cos2
sin))(
(()sin(
)(sin
)(2 K
VEE
XXE
KXX
XE
XX
EP me
))cos2
sin))(
(()sin(
)(sin
)((
12''
21
'
121
2'
21
'
2
DKVEE
XX
E
KXX
XE
XX
EP
Mdt
dmm
Pe = Pmax Sinδ+f1(δ) I s +f2(δ)
Pe
-Output
δω1M
Pm 1S
1S
-V sK 2 ω
K1 ωDI s
1K 2K
6.7 Conclusion
The UPFC is the most adaptable and compound of the truths gadgets, joining the elements of
the STATCOM and the SSSC. The capacity of UPFC is to pass the genuine power stream bi-
directionally, supporting all around managed DC voltage, workability in the extensive variety
of working conditions and so on. One VSI is associated in arrangement to the transmission
framework by means of an arrangement transformer, while the other one is associated in shunt
through a shunt transformer. The DC terminals of the two VSCs are coupled and this makes a
way for dynamic power trade between the converters. Along these lines the dynamic power
provided to the line by the arrangement converter can be provided by the shunt converter.
Along these lines, a wide scope of control alternatives is accessible contrasted with STATCOM
or SSSC. The UPFC can be utilized to control the stream of dynamic and responsive power
through the transmission line and to control the measure of receptive power provided to the
transmission line at the purpose of establishment. To control dynamic and receptive power
streams on the transmission line, the arrangement inverter is utilized to infuse a symmetrical
three stage voltage arrangement of controllable greatness and stage. Thus, this inverter will
trade dynamic and responsive power with the line. The shunt inverter is actuated so as to
request this dc terminal power (positive or negative) from the line keeping the voltage over the
capacity capacitor steady. In this way, the net genuine power assimilated from the line by the
UPFC is equivalent just to the misfortunes of the inverters and their transformers. The rest of
the limit of the shunt inverter can be utilized to trade receptive power with the line so to give a
voltage direction at the association point. The two VSI's can work freely of each other by
isolating the dc side. So all things considered, the shunt inverter is working as a STATCOM
that produces or retains receptive energy to control the voltage size at the association point.
Rather, the arrangement inverter is working as SSSC that produces or ingests responsive energy
to direct the present stream, and henceforth the power streams on the transmission line. The
Page | 54
UPFC can likewise give synchronous control of all essential power framework parameters, viz.,
transmission voltage, and impedance.
Chapter 7
Simulation Result of STATCOM, SSSC and UPFC
with PI and PID Controller
7.1 Introduction
This work ensures system stability, in order to provide faster responses over a wide range of
power system operation, power system stability (PSS) of single machine infinite bus system
(SMIB) is developed and its parameters are tuned by PI, PID, STATCOM, SSSC and UPFC.
For Transient State Response, a Synchronous generator is taken having a suitable inertia
constant and transient reactance which is connected to an infinite bus through a purely reactive
circuit where the reactance’s are marked on a common system base.
7.2 Simulation Result without FACT Controller
The simulation perform by using matlab software (simulink) and model has been chosen [89]
for step change in the turbine mechanical input, ∆pm = 0.1 p.u. From Figure 7.1, it is clear that
there are sustained rotor angle oscillations and speed deviation with poor damping.
Page | 55
Figure 7.18: Rotor angle deviation without FACTS device
7.3 Simulation Result with STATCOM, SSSCand UPFC
Page | 56
Pm
Pm
Pm
3Output1
2Out1
1Output
angle
-C- V*X2
1*0.15
V*X1
1.2602
V*V3
1 V*V2
1.2602
V*V1 1
V*V
sin
TrigonometricFunction7
sin
TrigonometricFunction6
cos
TrigonometricFunction5
sin
TrigonometricFunction4
sin TrigonometricFunction3
sin
TrigonometricFunction2
cos
TrigonometricFunction1
cos
TrigonometricFunction
t
To Workspace4
y
To Workspace2
y1
To Workspace1
Switch1
Switch
Speed1
Speed
Scope9
Scope8
Scope6
Scope5
Scope4
Scope3
Scope2
Scope12
Scope11
Scope10
Scope1Scope
Product9
Product8
Product7
Product6
Product5
Product4
Product3
Product2
Product15
Product14
Product13Product12
Product11
Product10
Product1
Product
-C- Pmax1
-C- Pmax
Pe5 Pe4
Pe3
Pe2
Pe1
Pe
sqrt
MathFunction1
sqrt
MathFunction
.2
K4
2
K3
.2
K2
2
K1
1s
Integrator5
1s
Integrator4
1s
Integrator3
1s
Integrator2
1s
Integrator1
1s
Integrator
180/pi
Gain3
180/pi
Gain2
-K-
Gain1
3.7419
EV/X3 -C- EV/X2
3.7419
EV/X12
3.7419
EV/X1
-C- E*X3
2.2452
E*X2
0.16839
E*X1
Divide3
Divide2
Divide1
Divide
atan
Delta_m1
atan
Delta_m
0
D2
0
D1
0
D
0
Constant1
0
Constant
Clock3
Clock1
Clock
Add7Add6
Add5
Add4Add3
Add2Add1
Add
2.2452 2E*X2
11
1/M2
15.5
1/M1
15.5
1/M
sin cos
Figure 7.19: Simulation of STATCOM, SSSC and UPFC
The figure 7.2 is depicted the simulation of STATCOM, SSSC and UPFC using parameters
from [89].
Page | 57
0 1 2 3 4 5 6 7 8 90
0.5
1
1.5
2
2.5
3
Time (Second)
Rot
or A
ngle
Dev
iatio
n (D
egre
e)
STATCOMSSSCUPFC
Figure 7.20 Rotor angle deviation with SSSC, STATCOM and UPFC controller
Table 7.6Rotor angle deviationwith SSSC, STATCOM and UPFC controller
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM80 7
SSSC66 3.4
UPFC53 3.20
Page | 58
0 1 2 3 4 5 6 7 8 9-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time (Second)
Rot
or S
peed
Dev
iati
on P
er U
nit
STATCOMSSSCUPFC
Figure 7.4: Rotor speed deviation with SSSC, STATCOM and UPFC controller
Table 7.7Rotor speed deviationwith SSSC, STATCOM and UPFC controller
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM18 7
SSSC17 4.5
UPFC15 3.5
Page | 59
0 1 2 3 4 5 6 7 8 9-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time (Second)
Inje
cted
Vol
tage
/Cur
rent
Per
Uni
t
Injected Voltage by UPFC
Injected Voltage by SSSC
Injected Current by STATCOM
Injected Current by UPFC
Figure 7.5: Injected Current and Voltage by SSSC, STATCOM and UPFC Controller
From Figure 7.3 and Figure 7.4 the rotor angle deviation and speed deviation have been
demonstrated for STATCOM, SSSC and UPFC. We found that due to small disturbance of
turbine rotor angle oscillation overshoot varies 80, 66, 53 percent with settling time 7, 3.4 and
0.20 second respectively. Again, the rotor speed deviation diminishing within 7, 4.5, 3.5 second
respectively. From Figure 7.5 the maximum injected current by STATCOM is 0.3 per unit and
injected voltage by SSSC is 0.40 per unit. Again, the injected current and voltage by UPFC are
0.03 per unit.
Page | 60
7.4 Simulation Result with STATCOM, SSSC, UPFC and PI
Pm
Pm
Pm
3Output1
2Out1
1Output
angle
-C- V*X2
1*0.15
V*X1
1.2602
V*V3
1 V*V2
1.2602
V*V1 1
V*V
sin
TrigonometricFunction7
sin
TrigonometricFunction6
cos
TrigonometricFunction5
sin
TrigonometricFunction4
sin TrigonometricFunction3
sin
TrigonometricFunction2
cos
TrigonometricFunction1
cos
TrigonometricFunction
t
To Workspace4
r
To Workspace3
y1
To Workspace2
Switch1
Switch
Speed
Scope9
Scope8
Scope7
Scope6
Scope5
Scope4
Scope3
Scope2
Scope12
Scope11
Scope10
Scope1
Scope
Product9
Product8
Product7
Product6
Product5
Product4
Product3
Product2
Product15
Product14
Product13Product12
Product11
Product10
Product1
Product
-C- Pmax1
-C- Pmax
Pe5 Pe4
Pe3
Pe2
Pe1
Pe
PID
PID Controller2
PID
PID Controller1
PID
PID Controller
sqrt
MathFunction1
sqrt
MathFunction
.2
K4
2
K3
.2
K2
2
K1
1s
Integrator5
1s
Integrator4
1s
Integrator3
1s
Integrator2
1s
Integrator1
1s
Integrator
180/pi
Gain3
180/pi
Gain2
-K-
Gain1
3.7419
EV/X3 -C- EV/X2
3.7419
EV/X12
3.7419
EV/X1
-C- E*X3
2.2452
E*X2
0.16839
E*X1
Divide3
Divide2
Divide1
Divide
atan
Delta_m1
atan
Delta_m
0
D2
0
D1
0
D
0
Constant1
0
Constant
Clock3Clock1
Clock
Add7Add6
Add5
Add4Add3
Add2Add1
Add
2.2452 2E*X2
11
1/M2
15.5
1/M1
15.5
1/M
sin cos
Figure 7.6: Simulation result with STATCOM, SSSC, and UPFC with PI controller
Page | 61
The figure 7.6 is presented the simulation of STATCOM, SSSC and UPFC with PI Controller
using matlab software.
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
Time (Second)
Roto
r Ang
le D
evia
tion
(Deg
ree)
STATCOM
SSSC
UPFC
Figure 7.7: Rotor angle deviation of SSSC, STATCOM and UPFC with PI controller
Table 7.8Rotor angle deviation of SSSC, STATCOM and UPFC with PI controller
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM60 1.5
SSSC46 1
UPFC36 0.90
Page | 62
0 0.5 1 1.5 2 2.5-0.2
0
0.2
0.4
0.6
Time (Second)
Rot
or S
peed
Dev
iati
on P
er U
nit
SSSCSTATCOMUPFC
Figure 7.8: Rotor speed deviation of SSSC, STATCOM and UPFC with PI controller
Table 7.9Rotor speed deviation of SSSC, STATCOM and UPFC with PI controller
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM33 1.5
SSSC32 0.90
UPFC27 0.70
Page | 63
0 0.5 1 1.5 2 2.5-0.5
0
0.5
1
Time (Second)
Inje
cted
Cur
rent
/Vol
tage
Per
Uni
t
Injected Voltage by UPFCInjected Voltage by SSSCInjected Voltage by STATCOMInjected Current by UPFC
Figure 7.9 Injected current and voltage by SSSC, STATCOM and UPFC with PI controller
From Figure 7.7 and Figure 7.8, the rotor angle deviation and speed deviation have been
presented for STATCOM, SSSC and UPFC with PI controller. We analyzed that due to small
disturbance of turbine rotor angle oscillation overshoot varies 60, 46 and 36 percent with
settling time 1.50, 1.0 and 0.90 second respectively. Again, the rotor speed deviation
diminishing within 1.5 0.90 and 0.70 second with maximum overshoot33, 32, and
27respectively. From Figure 7.9, the maximum injected current by STATCOM is 0.50 per unit
and injected voltage by SSSC 0.70 per unit. Again, the injected current and voltage by UPFC
are 0.10 and 0.0.80 per unit respectively.
Page | 64
7.5 Simulation Result with STATCOM, SSSC, UPFC and PID
Page | 65
Pm
Pm
Pm
3Output1
2Out1
1Output
angle
-C- V*X2
1*0.15
V*X1
1.2602
V*V3
1 V*V2
1.2602
V*V1 1
V*V
sin
TrigonometricFunction7
sin
TrigonometricFunction6
cos
TrigonometricFunction5
sin
TrigonometricFunction4
sin TrigonometricFunction3
sin
TrigonometricFunction2
cos
TrigonometricFunction1
cos
TrigonometricFunction
t
To Workspace4
r
To Workspace3
y1
To Workspace2
Switch1
Switch
Speed
Scope9
Scope8
Scope7
Scope6
Scope5
Scope4
Scope3
Scope2
Scope12
Scope11
Scope10
Scope1
Scope
Product9
Product8
Product7
Product6
Product5
Product4
Product3
Product2
Product15
Product14
Product13Product12
Product11
Product10
Product1
Product
-C- Pmax1
-C- Pmax
Pe5 Pe4
Pe3
Pe2
Pe1
Pe
PID
PID Controller2
PID
PID Controller1
PID
PID Control ler
sqrt
MathFunction1
sqrt
MathFunction
.2
K4
2
K3
.2
K2
2
K1
1s
Integrator5
1s
Integrator4
1s
Integrator3
1s
Integrator2
1s
Integrator1
1s
Integrator
180/pi
Gain3
180/pi
Gain2
-K-
Gain1
3.7419
EV/X3 -C- EV/X2
3.7419
EV/X12
3.7419
EV/X1
-C- E*X3
2.2452
E*X2
0.16839
E*X1
Divide3
Divide2
Divide1
Divide
atan
Delta_m1
atan
Delta_m
0
D2
0
D1
0
D
0
Constant1
0
Constant
Clock3Clock1
Clock
Add7Add6
Add5
Add4Add3
Add2Add1
Add
2.2452 2E*X2
11
1/M2
15.5
1/M1
15.5
1/M
sin cos
Figure 7.10: Simulation result with STATCOM, SSSC, and UPFC with PID controller
Page | 66
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.5
1
1.5
2
Time (Second)
Rot
or A
ngle
Dev
iatio
n (D
egre
e)
UPFC with PID
SSSC with PID
STATCOM with PID
Figure 7.11: Rotor angle deviation of SSSC, STATCOM and UPFC with PID controller
Table 7.5Rotor angle deviation of SSSC, STATCOM and UPFC with PID controller
Page | 67
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM4 0.23
SSSC6.67 0.20
UPFC3.30 0.15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (Second)
Rot
or S
peed
Dev
iatio
n Pe
r U
nit
STATCOM with PID
SSSC with PID
UPFC with PID
Figure 7.12: Rotor speed deviation of SSSC, STATCOM and UPFC with PID
Table 7.6Rotor speed deviation of SSSC, STATCOM and UPFC with PID
Page | 68
Devices Maximum Overshoot (%) Settling Time(Sec)
STATCOM43 0.27
SSSC42 0.20
UPFC26 0.26
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (Second)
Inje
cted
Cur
rent
/Vol
tage
Per
Uni
t
Injected Voltage by UPFC
Injected Voltage by SSSC
Injected Current by STATCOM
Injected Current by UPFC
Figure 7.13: Injected Current and Voltage by SSSC, STATCOM and UPFC with PIDcontroller
From Figure 7.11 and Figure 7.12, the rotor angle deviation and speed deviation have been
depicted for STATCOM, SSSC and UPFC with PID controller at non-linear feedback path. We
found that due to small disturbance of turbine rotor angle oscillation overshoot varies 4, 6.67,
3.3 percent with settling time 0.23, 0.20 and 0.15 second respectively. Again, the rotor speed
deviation diminishing within 0.27, 0.20, 0.26 second respectively. From Figure 7.13, the
maximum injected current by STATCOM is 0.0.055 per unit and injected voltage by SSSC
0.088 per unit. Again, the injected current and voltage by UPFC are 0.09 and 0.03 per unit
respectively.
7.6 Comparison of Simulation Result
Table 7.10Rotor angle deviation comparision
Devices
FACT Devices
FACT Devices
with PI Controller
FACT Devices
with PID Controller
Maximum
Overshoot
(%)
Settling
Time
Maximum
Overshoot
(%)
Settling
Time
Maximum
Overshoot
(%)
Settling
Time
Page | 69
STATCOM 80 7 60 1.5 4 0.23
SSSC 66 3.4 46 1 6.67 0.20
UPFC 53 3.20 36 0.90 3.30 0.15
Table 7.8Rotor Speed Deviation
Devices
FACT Devices
FACT Devices
with PI Controller
FACT Devices
with PID Controller
Maximum
Overshoot
(%)
Settling
Time
Maximum
Overshoot
(%)
Settling
Time
Maximum
Overshoot
(%)
Settling
Time
STATCOM 18 7 33 1.5 43 0.27
SSSC 17 4.5 32 0.90 42 0.20
UPFC 15 3.5 27 0.70 26 0.26
7.7 Comparison of Simulation with the Previous Work
In [19], rotor speed deviation is analyzed and it has been settle in 2 to 2.2 sec. In this thesis,
rotor angle deviation as well as speed deviation is analyzed. From table 7.7, rotor angle
deviation settles in 0.15 to 0.23 sec. Again, from table 7.8, rotor speed deviation settle in 0.20
to 0.27 sec. So, we may summarize that UPFC with PID controller perform superior than other
controller.
7.8 Conclusion
At first the system is simulated with STATCOM, SSSC, and UPFC for step response. For step
change of mechanical input, UPFC quickly damps the oscillations compared to the SSSC and
STATCOM. Then PI and PID controller have been incorporated with the system including
STATCOM, SSSC and UPFC controller.
Page | 70
Chapter 8Conclusion and Future Work
8.1 Conclusion
This paper presents a systematic method of designing of PI and PID controllers for the FACTS
devices in single machine infinite bus system. The performance of the system is analyzed in
term of power handling capacity, improvement in transient stability and damping of oscillations
and compared for different types of controllers.
Initially the system is simulated with STATCOM, SSSC, and UPFC for step response. For step
change of mechanical input, UPFC quickly damps the oscillations compared to the SSSC and
STATCOM. Then PI and PID controller have been incorporated with the system including
STATCOM, SSSC and UPFC controller.
STATCOM, SSSC, and UPFC improved the transient performance of the power system, when
PI and PID controller is incorporated with STATCOM, SSSC, and UPFC the performance is
improved tremendously. However, the UPFC with PID controller diminished the maximum
overshoot and as well as minimized the settling time to stable the system more rapidly as
compared to the STATCOM and SSSC.
In previous works [20] PI, PID and fuzzy logic controllers have been used with SSSC for
power transmission line performance evaluation. In [12] only PI controller and STATCOM
have been used for only power factor improvement. In [19], STATCOM, SSSC and UPFC
Controllers have been demonstrated for transient stability
improvement.Very few researchers analyzed the power system stability using PI and PID
controller with SSSC, STATOM and UPFC thoroughly.
In this thesis the transient performance of power system is analyzed for change of mechanical
input power with STATCOM, SSSC and UPFC using PI and PID controller rigorously. It is
Page | 71
found that the UPFC with PID controller stabilized the system more rapidly than STATCOM
and SSSC.
In [19], rotor speed deviation is analyzed and it has been settle in 2 to 2.2 sec. In this thesis,
rotor angle deviation as well as speed deviation is analyzed. Rotor angle deviation settles in
0.15 to 0.23 sec. Again, Rotor speed deviation settle in 0.20 to 0.27 sec. So, we may summarize
that UPFC with PID controller perform superior than other controller.
8.2 Future Works
In this thesis, PI and PID controller are simulated with STATCOM, SSSC and UPFC for change
of mechanical input power. In future, further simulation can be performed for sudden load
change and during faulty condition forminimizing maximum overshoot and settling time. In
future, Lag-lead compensator, lag compensator can be used for more reliability and quick
damping of the system. It is seen that it would be better if the peak overshoot and the settling
time can be reduced to a lower value. For this purpose, some modern controller like fuzzy logic
controller can be added with FACTS devices for desired operation.
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Publication
[1] S. K. Ray, M. A, Rahman and M. R. Ahmed “Tuning of PI and PID Controller with STATCOM,
SSSC andUPFC for Minimizing Damping of Oscillation”, IOSR Journal of Electrical and
Electronics Engineering (IOSR-JEEE), Volume 12, Issue 1 Ver. II PP 30-44, Jan, 2017.
Page | 78
