pid designing

IMPLEMENTATION OF PID CONTROLLER

FOR POWER SYSTEM STABILIZATION

Project report submitted in partial fulfillment of the requirements

for the award of the degree BACHELOR OF TECHNOLOGY

By

G.Avinash (2210511220) B. Sugiani (2210511256)

M.Lalit Anand (2210511234) CH.Sai Praveen (2210511211)

Under the guidance of

Mr. P. Sivaramakrishna

Assistant Professor

Department of Electrical and Electronics Engineering

GITAM Institute of Technology (GIT)

GITAM UNIVERSITY, Hyderabad Campus

(Declared as Deemed to be University u/s 3 of the UGC Act., 1956,

Accredited by NAAC With A Grade)

2011-2015

GITAM UNIVERSITY

Hyderabad Campus, Rudraram

CERTIFICATE

This is to certify that the project report entitled “Implementation of PID

Controllers for Power System Stabilization” being submitted by G.AVINASH

(2210511220), SUGIANI.B (2210511256), M.LALIT ANAND (2210511234),

CH.SAI PRAVEEN (2210511211) in partial fulfillment for the award of the

Degree of Bachelor of Technology in EEE (2011-2015) to the GITAM University

is a record of bonafide work carried out by her under my guidance and

supervision.

The results embodied in this project report have not been submitted to any

other University or Institute for the award of any Degree.

Guide: Mr. P SivaRamaKrishna Dr. Chakravarthy M

Assistant Professor HOD

Department, EEE Department, EEE

GITAM UNIVERSITY, GITAM UNIVERSITY,

HYDERABAD HYDERABAD

ACKNOWLEDGEMENT

I humbly owe my gratitude and sincere regards to my respected guide Mr.

P. Sivaramakrishna, Assistant Professor, Electrical and Electronics Engineering

Department, GITAM University, Hyderabad under whose constant supervision,

meticulous guidance and encouragement, this work has been carried out to

completion. His valuable suggestions and keen interest throughout the

investigation have enabled me to make my work worthy of presentation.

I am grateful to Dr. Chakravarthy M, Head of Electrical and Electronics

Engineering department, GITAM University, Hyderabad for his support and

encouragement to carry out this dissertation work.

I express my deep sense of respect and gratitude to Prof. Siva Prasad N,

director of campus, GITAM University, Hyderabad for his constant

encouragement, continuous support and valuable suggestions.

Last but not the least, there are no words which can express my gratitude

towards My Parents for their constant support, unlimited patience, immense care,

faith in me and divine love towards me which made my dream come true.

G.AVINASH (2210511220),

B. SUGIANI (2210511256),

M.LALITANAND (2210511234),

CH. SAIPRAVEEN(2210511211)

DECLARATION

We, the undersigned, declare that the project entitled ‘IMPLEMENTATION

OF PID CONTROLLERS FOR POWER SYSTEM STABILIZATION’,

being submitted in partial fulfilment for the award of Bachelor of Technology

Degree in Electrical and Electronics Engineering, GITAM University, is the work

carried out by us.

G. Avinash B. Sugiani M. Lalit Anand Ch. Sai Praveen

(2210511220) (2210511256) (2210511234) (2210511211)

ABSTRACT

In this work, we are implementing a PID controller for stabilization of power system. The

property of a system to return to an acceptable working condition following a transient is

called transient stability which is a major problem in power system. We are considering a

Single Machine Infinite Bus (SMIB) system with swing equation model. The control

technique is implemented using a linear controller called PID and the actuator used is

Controllable Series Capacitor (CSC). The CSC is modeled by using injection model. We are

considering a short circuit fault occurs at far end of the transmission line.

The control objective is to implement a controller in such a way that the system is going to

stable equilibrium point on occurrence of a fault. We are planning to implement the above

stated work on MATLAB/SIMULINK platform.

CONTENTS

Chapter 1:

1 Introduction 1-7

1.1 Classification of power system stability 2

1.2 Modelling of power systems 5

Chapter 2: 8-11 2 Modelling of SMIB system with Controllable Series Capacitor 8

2.1 Introduction 8

2.2 Synchronous machine dynamics 8

2.3 System Model 8

2.4 Modelling of controllable series capacitor 11

2.5 SMIB system with controllable series capacitor4 11

Chapter 3: 13-17 3 Implementation of PID controllers 13

3.1 Introduction 13

3.2 PDI Controllers 13

3.3 Effects of PID controllers 14

3.4 Ziegler Nicholas method for Tuning of PID controllers 14

Chapter 4: 18-22 4 Simulation results 18

4.1 Resulting graphs 18

Conclusion and Scope for Future work 23

Bibliography 24

LIST OF FIGURES

S.No Figure

number

Name of the figure Page

number

1 1 Classification of Power system stability 4

2 1.1 A power system with N generators and N load

buses

6

3 2.1 Single machine infinite bus system 8

4 2.2 Single line diagram of single machine system 9

5 2.3 Equivalent diagram of system 9

6 2.4 SMIB system with Controllable Series Capacitor

12

7 3.2 PID control of a plant 13

8 3.4.1 Unit step response of a plant 14

9 3.4.2 Shaped response curve 15

10 3.4.3 Closed loop system with P controller 15

11 3.4.4 Sustained oscillation with period PC 16

12 4.1 & 4.2 Response Of SMIB system With PD controller 18

13 4.3 & 4.4 Response Of SMIB system With PI controller 19

14 4.5 & 4.6 Response Of SMIB system With PID controller 20

15 4.7 & 4.8 Response Of SMIB system With PID controller 21

IMPLEMENTATION OF PID CONTROLLERS FOR POWER SYSTEM STABILIZATION | 1

GITAM SCHOOL OF TECHNOLOGY, HYDERABAD

Chapter 1

Introduction:

The electrical energy is a primary prerequisite for economic growth. The demand for electrical

energy has greatly increased due to large-scale industrialization. Modern power system operates under

much stressed conditions because of growth in demand and deregulation of electric power system.

This leads to many problems associated with operation and control of power systems. The economics

of power generation has a major concern for the power utilities. Therefore, the power utilities always

need new technology to solve its problems. The complexity of power systems is continuously growing

due to the increasing number of generation plants and load demand. Power systems are becoming

heavily stressed due to the increased loading of the transmission lines and due to the difficulty of

constructing new transmission systems as well as the difficulty of building new generating plants near

the load centers. All of these problems lead to the voltage stability problem in the system. An

interconnected power system basically consists of several essential components. They are namely the

generating units, the transmission lines and the loads. During the operation of the generators, there

may be some disturbances such as sustained oscillations in the speed or periodic variations in the torque

that is applied to the generator. These disturbances may result in voltage or frequency fluctuation that

may affect the other parts of the interconnected power system. External factors, such as lightning, can

also cause disturbances to the power system. All these disturbances are termed as faults. When a fault

occurs, it causes the generators to lose synchronism. With these factors in mind, the basic condition

for a power system with stability is synchronism. Besides this condition, there are other important

conditions such as steady-state stability, transient stability, harmonic sand disturbance, collapse of

voltage and the loss of reactive power.

The stability of a system is defined as the tendency and ability of the power system to develop

restoring forces equal to or greater than the disturbing forces to maintain the state of equilibrium.

There are many major blackouts caused by instability of a power system which illustrates the

importance of this phenomenon. The stability has been acknowledged as an important problem for

secure system operation since the 1920‟s.

Damping of power system oscillation between interconnected areas is very important for the

system secure operation. Power System Stabilizer (PSS) is the most widely used device for resolving

oscillatory stability problems, and to enhance the power system damping. Traditionally, lead-lag

structures have been used as power system stabilizers. The PID controller is a well-established type

of controller and has been in use for a long time. Tuning PID controllers are traditionally tuned using

standard techniques such as the root locus, and classical PID controllers which tuned by “Ziegler

Nichols” methods.

This paper produces a design method for the stability enhancement of a single machine infinite

bus power system using PID-PSS which its parameters are tuned by “Ziegler Nichols” method. The

main advantage of this method is, it includes dynamics of whole process, which gives a more accurate

picture of how the system is behaving.



1.1 CLASSIFICATION OF POWER SYSTEM STABILITY

A typical modern power system is a high-order multivariable process whose dynamic response is

influenced by a wide array of devices with different characteristics and response rates. Stability is a

condition of equilibrium between opposing forces. Depending on the network topology, system

operating condition and the form of disturbance, different sets of opposing forces may experience

sustained imbalance leading to different forms of instability. In this section, we provide a systematic

basis for classification of power system stability.

A. Need for Classification

Power system stability is essentially a single problem; however, the various forms of

instabilities that a power system may undergo cannot be properly understood and effectively dealt with

by treating it as such. Because of high dimensionality and complexity of stability problems, it helps to

make simplifying assumptions to analyze specific types of problems using an appropriate degree of

detail of system representation and appropriate analytical techniques. Analysis of stability, including

identifying key factors that contribute to instability and devising methods of improving stable

operation, is greatly facilitated by classification of stability into appropriate categories Classification,

therefore, is essential for meaningful practical analysis and resolution of power system stability

problems.

B. Categories of Stability

The classification of power system stability proposed here is based on the following considerations:

• The physical nature of the resulting mode of instability as indicated by the main system variable in

which instability can be observed.

• The size of the disturbance considered which influences the method of calculation and prediction of

stability.

• The devices, processes, and the time span that must be taken into consideration in order to assess

stability.

Fig. 1 gives the overall picture of the power system stability problem, identifying its categories and

subcategories. The following are descriptions of the corresponding forms of stability phenomena.

B.1 Rotor Angle Stability:

Rotor angle stability refers to the ability of synchronous machines of an interconnected power system

to remain in synchronism after being subjected to a disturbance. It depends on the ability to

maintain/restore equilibrium between electromagnetic torque and mechanical torque of each



synchronous machine in the system. Instability that may result occurs in the form of increasing

angular swings of some generators leading to their loss of synchronism with other generators.

The rotor angle stability problem involves the study of the electromechanical oscillations inherent in

power systems. A fundamental factor in this problem is the manner in which the power outputs of

synchronous machines vary as their rotor angles change. Under steady-state conditions, there is

equilibrium between the input mechanical torque and the output electromagnetic torque of each

generator, and the speed remains constant. If the system is perturbed, this equilibrium is upset, resulting

in acceleration or deceleration of the rotors of the machines according to the laws of motion of a

rotating body. If one generator temporarily runs faster than another, the angular position of its rotor

relative to that of the slower machine will advance. The resulting angular difference transfers part of

the load from the slow machine to the fast machine, depending on the power-angle relationship. This

tends to reduce the speed difference and hence the angular separation. The power-angle relationship is

highly nonlinear. Beyond a certain limit, an increase in angular separation is accompanied by a

decrease in power transfer such that the angular separation is increased further. Instability results if the

system cannot absorb the kinetic energy corresponding to these rotor speed differences. For any given

situation, the stability of the system depends on whether or not the deviations in angular positions of

the rotors result in sufficient restoring torques. Loss of synchronism can occur between one machine

and the rest of the system, or between groups of machines, with synchronism maintained within each

group after separating from each other.

The change in electromagnetic torque of a synchronous machine following a perturbation can

be resolved into two components:

Synchronizing torque component, in phase with rotor angle deviation.

Damping torque component, in phase with the speed deviation.

System stability depends on the existence of both components of torque for each of the synchronous

machines. Lack of sufficient synchronizing torque results in aperiodic or non-oscillatory instability,

whereas lack of damping torque results in oscillatory instability.

For convenience in analysis and for gaining useful insight into the nature of stability problems,

it is useful to characterize rotor angle stability in terms of the following two subcategories:

Small-disturbance (or small-signal) rotor angle stability is concerned with the ability of the

power system to maintain synchronism under small disturbances. The disturbances are considered to

be sufficiently small that linearization of system equations is permissible for purposes of analysis

-Small-disturbance stability depends on the initial operating state of the system. Instability that may

result can be of two forms: i) increase in rotor angle through a non-oscillatory or a periodic mode due

to lack of synchronizing torque, or ii) rotor oscillations of increasing amplitude due to lack of sufficient

damping torque.

-In today’s power systems, small-disturbance rotor angle stability problem is usually associated with

insufficient damping of oscillations. The a periodic instability problem has been largely eliminated by

use of continuously acting generator voltage regulators; however, this problem can still occur when

generators operate with constant excitation when subjected to the actions of excitation limiters (field

current limiters).



Fig.1. Classification of power system stability.

Large-disturbance rotor angle stability or transient stability, as it is commonly referred to, is concerned

with the ability of the power system to maintain synchronism when subjected to a severe disturbance,

such as a short circuit on a transmission line. The resulting system response involves large excursions

of generator rotor angles and is influenced by the nonlinear power-angle relationship.

- Transient stability depends on both the initial operating state of the system and the severity of the

disturbance. Instability is usually in the form of a periodic angular separation due to insufficient

synchronizing torque, manifesting as first swing instability. However, in large power systems, transient

instability may not always occur as first swing instability associated with a single mode; it could be a

result of superposition of a slow inter area swing mode and a local-plant swing mode causing a large

excursion of rotor angle beyond the first swing. It could also be a result of nonlinear effects affecting

a single mode causing instability beyond the first swing.

- The time frame of interest in transient stability studies is usually 3 to 5 seconds following the

disturbance. It may extend to 10–20 seconds for very large systems with dominant inter-area swings.

As identified in Fig. 1, small-disturbance rotor angle stability as well as transient stability are

categorized as short term phenomena.

B.2 Voltage Stability:

Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the

system after being subjected to a disturbance from a given initial operating condition. It depends on

the ability to maintain/restore equilibrium between load demand and load supply from the power

system. In- stability that may result occurs in the form of a progressive fall or rise of voltages of some

buses. A possible outcome of voltage instability is loss of load in an area, or tripping of transmission

lines and other elements by their protective systems leading to cascading outages. Loss of synchronism

of some generators may result from these outages or from operating conditions that violate field current

limit



B.3 Basis for Distinction between Voltage and Rotor Angle Stability:

It is important to recognize that the distinction between rotor angle stability and voltage stability is not

based on weak coupling between variations in active power/angle and reactive power/voltage

magnitude. In fact, coupling is strong for stressed conditions and both rotor angle stability and voltage

stability are affected by pre-disturbance active power as well as reactive power flows. Instead, the

distinction is based on the specific set of opposing forces that experience sustained imbalance and the

principal system variable in which the consequent instability is apparent.

B.4 Frequency Stability:

Frequency stability refers to the ability of a power system to maintain steady frequency following a

severe system upset resulting in a significant imbalance between generation and load. It depends on

the ability to maintain/restore equilibrium between system generation and load, with minimum

unintentional loss of load. Instability that may result occurs in the form of sustained frequency swings

leading to tripping of generating units and/or loads.

1.2 Modeling of power systems

An electrical power system consists of power generating units interconnected with each other and with

the loads through transmission lines. Thus, many electrical machines and devices like transformers,

capacitors are connected together to form a complex system. These elements have dynamic interaction

which may affect the power system behavior. Here, we use the reduced network model to describe

the power system.

Figure 1.1 shows a multi machine power system having 2n + N nodes of which bus 1 to bus n are

generator internal buses, bus n + 1 to bus 2n are n generator terminal buses for respective generator

internal buses and bus 2n + 1 to 2n + N are N load buses. There may be loads connected to the

terminal buses. Each kth generator internal bus is connected to its respective (k + n)th terminal bus

through a lossless line with transient reactance of Xk .

Ek =Ek∠δk (k = 1, ....., n) is the internal machine voltage phasor behind the transient reactance xk .

Reduced network model (RNM): This is a simple mathematical model used to describe the dynamics

of a power system, and it is based on the following assumptions:



Figure1.1:A power system with N generators and N load buses

1. Each synchronous machine can be represented by a constant voltage source behind a

transient reactance.

2. Mechanical power in put is constant.

3. The mechanical angle of the synchronous machine rotor is assumed to coincide with the

electrical phase angle of the voltage phase or behind the transient reactance.

4. Saliency is neglected, that is, xdk =xqk.

5. The various network components are assumed to be insensitive to changes in frequency.

6. Stator and transmission line resistances are neglected.

7. Loads a represented by passive impedances.

Let Dk >0,Mk >0,PGk,Pk, be the damping constant, moment of inertia constant, power

injected into the system, and the mechanical power input, respectively, for the kth machine.



Let δk be the swing angle and ωk be the rotor speed deviation with respect to a

synchronously rotating reference for the kth machine. Now the dynamics of the kth

generator is given by the swing equation as

Mkδ̈k+Dkδ̇k+PGk−Pk = 0. (1.1)

By choosing δk and ωk =δ̇k as the state variables the dynamics of kth generator becomes can be written

as

δ̇ = ωk

𝜔�̇� =1

𝑀𝑘(𝑃𝑘 − 𝐷𝑘𝜔𝑘

− 𝑃𝐺𝑘) (1.2)



Chapter 2

Modeling of Single Machine Infinite Bus (SMIB) system with

Controllable Series Capacitor (CSC)

2.1 Introduction

The power system is a high order complex nonlinear system. In order to simplify the analysis

and focus on one machine, the multi-machine power system is reduced to the single machine infinite

bus (SMIB) system. In the SMIB system, the machine of interest is modelled in detail while the rest

of the power system is equated with a transmission line connected to an infinite bus. As shown in

Figure 2.1, Single machine is connected to infinite bus system through a transmission line having

resistance𝑟 and inductance 𝑥𝑒

Figure 2.1: Single machine infinite bus system

2.2. Synchronous machine Dynamics

Synchronous machines, i.e. practically all generators together with synchronous motors and

synchronous compensators, are the most important power system components in the analysis of

electro-mechanical oscillations in power systems. The oscillations are manifested in that the rotors of

the synchronous machines do not rotate with constant angular velocity corresponding to system

frequency, but superimposed are low frequency oscillations, typically 0.1 – 4 Hz. It is important that

this superimposed oscillations is not too large, because then the stability of the power system can be

endangered. A correct description of these oscillations requires often detailed models of many different

system components, but to get an understanding of and insight into the basic physical phenomenon

and processes that determine the stability it is often sufficient to employ the simple model

As the name electro-mechanical oscillations suggests, both electrical and mechanical

phenomena are involved, i.e. both currents in and voltages across deferent windings in the machines

but also the mechanical motion of the rotor. Therefore, models of both electrical and mechanical parts

of the synchronous machine are needed.

2.3 System Model

Consider the system (represented by a single line diagram) shown in Fig. 2.1. Here the single

generator represents a single machine equivalent of a power plant(consisting of several

generators).The generator G is connected to a double circuit line through transformer T. The

line is connected to an infinite bus through an equivalent impedance ZT. The infinite bus, by

definition, represents a bus with fixed voltage source. The magnitude, frequency and phase of

the voltage are unaltered by changes in the load (output of the generator). It is to be noted that

the system shown in Fig. 2.1 is a simplified representation of a remote generator connected to a

load center through transmission line.



Figure 2.2 Single line diagram of single machine system

The major feature In the classical methods of analysis is the simplified (classical) model of the

generator. Here, the machine is modelled by an equivalent voltage source behind an impedance.

The major assumptions behind the model are as follows

1. Voltage regulators are not present and manual excitation control is used. This implies that in

steady- state, the magnitude of the voltage source is determined by the field current which is

constant.

2. Damper circuits are neglected.

3. Transient stability is judged by the first swing, which is normally reached within one or two

seconds.

4. Flux decay in the field circuit is neglected (This is valid for short period, say a second,

following a disturbance, as the field time constant is of the order of several seconds).

5. The mechanical power input to the generator is constant.

6. Saliency has little effect and can be neglected particularly in transient stability studies. Based

on the classical model of the generator, the equivalent circuit of the system of Fig. 2.2 is shown

in Fig. 2.3. Here the losses are neglected for simplicity. Xe is the total external reactance viewed

from the generator terminals. The generator reactance, xg, is equal to synchronous reactance Xd

for steady-state analysis. For transient analysis, Xg is equal to the direct axis transient reactance

x~. In this case, the magnitude of the generator voltage Egis proportional to the field flux

linkages which are assumed to remain constant (from assumption 4)

Figure 2.3 Equivalent circuit of the system shown in Fig. 2.2

For the classical model of the generator, the only differential equation relates to the motion of the rotor

Let us consider a three-phase synchronous alternator that is driven by a prime mover. The

equation of motion of the machine rotor is given by



2.1

Where

J is the total moment of inertia of the rotor mass in kgm2

Tm is the mechanical torque supplied by the prime mover in N-m

Te is the electrical torque output of the alternator in N-m

θ is the angular position of the rotor in rad

Neglecting the losses, the difference between the mechanical and electrical torque gives the net

accelerating torque Ta . In the steady state, the electrical torque is equal to the mechanical

torque, and hence the accelerating power will be zero. During this period the rotor will move at

synchronous speed ωs in rad/s.

The angular position θ is measured with a stationary reference frame. To represent it with respect

to the synchronously rotating frame, we define

2.2

Where δ is the angular position in rad with respect to the synchronously rotating reference frame.

Taking the time derivative of the above equation we get

2.3

Defining the angular speed of the rotor as

We can write equation 2.3 as

2.4

We can therefore conclude that the rotor angular speed is equal to the synchronous speed only

when dδ / dt is equal to zero. We can therefore term dδ / dt as the error in speed. Taking

derivative of (2.3), we can then rewrite (2.1) as

2.5

Multiplying both side of (2.5) by ωm we get

2.6

Where Pm , Pe and Pa respectively are the mechanical, electrical and accelerating power in

MW.

We now define a normalized inertia constant as

2.7



Substituting (2.7) in (2.5) we get

2.8

In steady state, the machine angular speed is equal to the synchronous speed and hence we can

replace ωr in the above equation by ωs. Note that in (2.8) Pm ,Pe and Pa are given in MW.

Therefore dividing them by the generator MVA rating Srated we can get these quantities in per

unit. Hence dividing both sides of (2.8) by Srated we get

per unit

By converting in to state space we get

(𝑥1̇

�̇�2) = (

𝑥21

𝑀[𝑃 − 𝐷𝑥2 − 𝑏1𝑠𝑖𝑛𝑥1]

) + (0

−𝑏1

𝑀sin 𝑥1

) 𝑢

2.4 Modelling of controllable series capacitor

Generally, a Controllable Series Capacitor (CSC) can be considered as a continuously controllable

reactance (normally capacitive) which is connected in series with the transmission line. Figure

2.4shows a CSC is placed between buses i and j. The active electrical power transferred from the bus

i to bus j is given by

Where, Xl denote the effective reactance of the line in which the CSC is installed. Thus, Xl decides

the capacity of the transmission line to transfer the electrical power across the network. The injection

model of the CSC is derived in a single-phase positive sequence phasor frame and is given by

2.5 SMIB system with Controllable Series Capacitor (CSC)

In this section we synthesize a stabilizing control law based on PID for the SMIB system.

Consider the SMIB system with a CSC as shown in Figure 2.4. It consists of a synchronous generator



connected to the infinite bus or reference bus. The magnitude of the voltage and the frequency for

the infinite bus are assumed to be constant .The generator bus is numbered as 1 and the infinite

bus as 2. They are connected to each other through a series combination of the line reactance X12

And a CSC which is denoted by a reactance −jXc . We use the following notation δ is the rotor angle

and ω is the rotor angular speed deviation with respect to synchronously

Figure 2.4 SMIB system with Controllable Series capacitor (CSC)

Rotating reference for the generator. Let D>0,M>0andP>0be the damping constant, moment of

inertia constant and the mechanical power in put to the generator, respectively. The dynamics of

the synchronous generator is described by the swing equation model as,

(𝑥1̇

�̇�2) = (

𝑥21

𝑀[𝑃 − 𝐷𝑥2 − 𝑏1𝑠𝑖𝑛𝑥1]

) + (0

−𝑏1

𝑀sin 𝑥1

) 𝑢

Where x=δ and x2=ω are the state variables is the input to the CSC, x1 the open loop reactance

between buses 1 and 2 and b1=𝑒𝑣

𝑥𝑙∗ . We assume that the Domain of operation is

Control objective:

The open loop operating equilibrium point for the system is given by x∗ = (x1∗,0). We assume that

x∗ is known to us and synthesize a control a law u in order to make the system (2.8) asymptotically

stable at x∗.



Chapter 3

Implementation of PID controller

3.1 Introduction

A controller is a device, historically using mechanical, hydraulic, pneumatic or electronic techniques

often in combination, but more recently in the form of a microprocessor or computer, which monitors

and physically alters the operating conditions of a given dynamical system. Typical applications of

controllers are to hold settings for temperature, pressure, flow or speed.

A system can either be described as a MIMO system, having multiple inputs and outputs, therefore

requiring more than one controller; or a SISO system, consisting of a single input and single output,

hence having only a single controller. Depending on the set-up of the physical (or non-physical)

system, adjusting the system's input variable (assuming it is SISO) will affect the operating parameter,

otherwise known as the controlled output variable. Upon receiving the error signal that marks the

disparity between the desired value (set point) and the actual output value, the controller will then

attempt to regulate controlled output behavior. The controller achieves this by either attenuating or

amplifying the input signal to the plant so that the output is returned to the set point. For example, a

simple feedback control system, such as the one shown on the right, will generate an error signal that's

mathematically depicted as the difference between the set point value and the output value, r-y.

Figure 3.1.1. A simple feedback control system

A simple feedback control loop illustrates that the error signal is received by controller C, which then

either attenuate or amplify the input signal to the plant. This signal describes the magnitude by which

the output value deviates from the set point. The signal is subsequently sent to the controller C which

then interprets and adjusts for the discrepancy. If the plant is a physical one, the inputs to the system

are regulated by means of actuators.

3.2 PID CONTROLLERS

Figure 3.2.1 shows a PID control of a plant. If a mathematical model of the plant can be derived, then

it is possible to apply various design techniques for determining parameters of the controller that will

meet the transient and steady-state specifications of the closed-loop system. However, if the plant is

so complicated that its mathematical model cannot be easily obtained, then an analytical approach to

the design of a PID controller is not possible. Then we must resort to experimental approaches to the

tuning of PID controllers.

The process of selecting the controller parameters to meet given performance specifications is known

as controller tuning. Ziegler and Nichols suggested rules for tuning PID controllers (meaning to set

values Kp, T,, and T,) based on experimental step responses or based on the value of K, that results in

marginal stability when only proportional control action is used. Ziegler-Nichols rules, which are

briefly presented in



Figure 3.2.1 PID control of a plant.

the following, are useful when mathematical models of plants are not known. (These rules can, of

course, be applied to the design of systems with known mathematical models.) Such rules suggest a

set of values of Kp, Ti, and Td, that will give a stable operation of the system. However, the resulting

system may exhibit a large maximum overshoot in the step response, which is unacceptable. In such a

case we need series of fine tunings until an acceptable result is obtained. In fact, the Ziegler-Nichols

tuning rules give an educated guess for the parameter values and provide a starting point for fine tuning,

rather than giving the final settings for Kp, Ti, and Td in a single shot

3.3 Effects of PID Controller

The following table indicates the several effects of PID Controller

Cl Response Rise Time Overshoot Settling Time S-S Error

Kp Decrease increase Small Change Decrease

ki Decrease increase Increase Eliminate

kd Small Change decrease Decrease Small Change

Table 3.3.1 Effects of PID Controller

3.4 Ziegler-Nichols Rules for Tuning PID Controllers.

Ziegler and Nichols proposed rules for determining values of the proportional gainki integral timeTi

and derivative time Td based on the transient response characteristics of a given plant. Such

determination of the parameters of PID controllers or tuning of PID controllers can be made by

engineers on-site by experiments on the plant. (Numerous tuning rules for PID controllers have been

proposed since the Ziegler-Nichols proposal. They are available in the literature and from the

manufacturers of such controllers.) There are two methods called Ziegler-Nichols tuning rules: the

first method and the second method. We shall give a brief presentation of these two methods.

First Method. In the first method, we obtain experimentally the response of the plant to a unit step

input, as shown in Figure 3.4.1. If the plant involves neither integrator (~) nor dominant complex-

conjugate poles, then such a unit-step response curve may look S-shaped, as shown in Figure 3.4.2.This

method applies if the response to a step input exhibits an S-shaped curve. Such step-response curves

may be generated experimentally or from a dynamic simulation of the plant. The S-shaped curve may

be characterized by two constants, delay time L and time constant



T. The delay time and time constant are determined by drawing a tangent line at the inflection point of

the S-shaped curve and determining the intersections of the tangent line with the time axis and line c(t)

= K, as shown in Figure 3.4.2.

Fig 3.4.1.unit step response of a plant

Fig 3.4.2. S Shaped response Curve

Table 3.4.1 Ziegler-Nichols Tuning Rule Based on Step Response of Plant (First Method)

The transfer function C(s)/U(s) may then be approximated by a first-order system with a transport lag

as follows:

Ziegler and Nichols suggested to set the values ofKp, Ti, and Tdaccording to the formula

shown in Table 3.4.1.

Notice that the PID controller tuned by the first method of Ziegler-Nichols rules gives



Thus, the PID controller has a pole at the origin and double zeros at s = -1/L

Second Method. In the second method, we first set Ti = ∞ and Td = 0. Using the proportional control

action only (see Figure3.4.3), increase Kp, from 0 to a critical value Kcr at which the output first

exhibits sustained oscillations. (If the output does not exhibit sustained oscillations for whatever value

Kp, may take, then this method does not apply.) Thus, the critical gain

Kcr, and the corresponding period PCr, are experimentally

Fig 3.4.3.closed loop system with p controller

Fig 3.4.4Sustained oscillation with period PC

determined (see Figure 3.4.4 ). Ziegler and Nichols suggested that we set the values of

the parameters Kp, Ti, and Td according to the formula shown in Table 3.4.2.

Table 3.4.2 Ziegler-Nichols Tuning Rule Based on Critical Gain Kc, and Critical Period PC, (Second

Method)

Notice that the PID controller tuned by the second method of Ziegler-Nichols rules gives



Thus, the PID controller has a pole at the origin and double zeros at s = -4/Pcr. Note that if the system

has a known mathematical model (such as the transfer function), then we can use the root-locus method

to find the critical gain Kc, and the frequency of the sustained oscillations

wcr, where 2.rr/wC, = PC,. These values can be found from the crossing points of the root-locus

branches with the jw axis. (Obviously, if the root-locus branches do not cross the jw axis, this method

does not apply.)

Comments. Ziegler-Nichols tuning rules (and other tuning rules presented in the literature) have been

widely used to tune PID controllers in process control systems where the plant dynamics are not

precisely known. Over many years, such tuning rules proved to be very useful. Ziegler-Nichols tuning

rules can, of course, be applied to plants whose dynamics are known. (If the plant dynamics are known,

many analytical and graphical approaches to the design of PID controllers are available, in addition to

Ziegler-Nichols tuning rules.)



Chapter - 4

Simulation Results

We assume the following simulation parameters for the SMIB system as shown figure M=

8

100𝜋 ,

D=0.4

100𝜋, E=V=1(p u) , 𝑏1=2.5(pu) ,-

1

3≤ 𝑢 ≤ 1. To assess the performance of the proposed control laws

we assume that a short circuit fault at the far end of the transmission line at the time t=1 s for a duration

of 0.1 s. We use the following system parameters for the lightly loaded condition The operating

equilibrium point is x∗=(0.4556, 0) and P = 1.1 (p u). The values of the tuning parameters are chosen

for PID controller P=0.5, I=0.5,D=0.005, for PI controller P=0.1,I=0.001,for PD controller

P=0.1,D=0.001.From the simulations, we can observe the following: The open loop system(i.e.

without controller) exhibits heavy and sustained oscillations in x1 and x2 as shown in figures by dotted

lines. The closed-loop system (using PID controller) oscillations decay at a faster rate and settle

quickly .Further, we can observe that, in the case of using PD controller and using PI controller.

PD CONTROLLER USING:

For scope x1 (Rotor Angle (rad) vs Time (sec))

Figure 4.1



For Scope X2 (Speed (rad) vs Time (sec)):

Figure 4.2

Figure 4.1 & Figure 4.2 Response of SMIB system With PD controller: Dotted Line (Without

Controller) Dashed line (with PD controller P=0.1,D=0.001 parameters)

USING PI CONTROLLER:

For scope x1 (Rotor Angle (rad) vs Time (sec))

Figure 4.3




Figure 4.4

Figure 4.3 & Figure 4.4: Response Of SMIB system With PI controller: Dotted Line (Without

Controller) Dashed line (with PI controller P=0.1,I=0.001 parameters)

USING PID CONTROLLER:

For scope x1 (Rotor Angle (rad) vs Time (sec)):

Figure 4.5




Figure 4.6

Figure 4.5 & Figure 4.6: Response Of SMIB system With PID controller: Dotted Line (Without

Controller) Solid Line (with PID controller, P=0.5, I=0.5, D=0.05 parameters)

COMPARSION OF PID CONTROLLER WITH PI & WITHOUT CONTROLLER:

For scope x1 (Rotor Angle (rad) vs Time (sec)):

Figure 4.7




Figure 4.8

Figure 4.7 & figure 4.8: Response of SMIB system with PID controller: Dotted line (without controller)

Dashed line (PI controller P=0.1, I=0.001), Solid line (with PID controller P=0.5, I=0.5, D=0.05)

parameters.



Conclusion & Scope for Future Work

In this report we presented PID controller technique for stabilization of SMIB system with CSC

as actuator, and SMIB with CSC is modelled by using injection model.

From the simulation results we observed that using PI controller the system attains stability

within less time when compared to PD controller. But by using PID controller the system attains

stability within less time even when compared to PI controller.

Future scope:

The work proposed here could be extended to multi machine system (like two machine infinite

bus system TMIB) and we can also compare the proposed control technique with nonlinear controllers.

.



Bibliography

1. Nonlinear Control Synthesis for Asymptotic Stabilization of the Swing Equation using a

Controllable Series Capacitor via Immersion and Invariance by N S Manjarekar, R N Banavar

and R Ortega 47th IEEE Conference on Decision and control Cancun, Mexico, Dec. 9-11, 2008

2. A. Astolfi and R. Ortega, “Immersion and Invariance: A New Tool for Stabilization and Adaptive

Control of Nonlinear Systems,” IEEE Trans. on Automatic Control, vol. 48, pp. 590–606, April

2003.

3. Y. Wang, D. J. Hill, R. H. Middleton, and L. Gao, “Transient stability enhancement and voltage

regulation of power systems,” IEEE Trans. on Power Systems, vol. 8, pp. 620–627, May 1993.

4. P. Kundur, Power System Stability and Control. New York: McGraw-Hill, 1994.



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