pmu based relaying

-1- BE Final Year Project Report (Academic Year 2011-2012)

Dept. of Electrical & Electronics Engg, Birla Institute of Technology, Mesra, Ranchi

A THESIS On

A PMU BASED SYNCHRONIZED RELAYING SCHEME FOR

TRANSMISSION LINE PROTECTION

Guided By:

Mrs. Debomita Ghosh

Assistant Professor, Dept. OF EEE

Submitted By:

Manish Agarwal

Roll No. BE/1209/08

Rajan Kumar Dubey

Roll No. BE/1214/08

Biswajeet Choudhary

Roll No. BE/1189/08

In partial fulfillment of the requirements for the award of the degree of

BACHELOR OF ENGINEERING

IN

ELECTRICAL AND ELECTRONICS ENGINEERING

� DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

BIRLA INSTITUTE OF TECHNOLOGY (A deemed university U/s 3 of UGC Act. 1956)

Mesra, Ranchi – 835215, INDIA



DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING



Ranchi 03/05/2012

DECLARATION CERTIFICATE

This is to certify that the thesis entitled “A PMU BASED SYNCHRONIZED

RELAYING SCHEME FOR TRANSMISSION LINE PROTECTION” submitted is

a record of the bonafide work done by Manish Agarwal (Roll No. BE/1209/08), Rajan

Kumar Dubey (Roll No. BE/1214/08), Biswajeet Choudhary (Roll No. BE/1189/08) in

partial fulfillment of the requirements for the award of the Degree of Bachelor of

Engineering in Electrical and Electronics Engineering of Birla Institute of

Technology, Mesra, Ranchi, (A deemed university U/s 3 of UGC Act. 1956), during the

academic year 2011-12.

To the best of my knowledge, the content of this thesis does not form a basis for the

award of any previous degree to anyone else.

Date:

Mrs. Debomita Ghosh Assistant Professor EEE Dept. BIT, Mesra Ranchi

Dr. T. Ghose Head of Dept. EEE Dept. BIT, Mesra Ranchi



DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING



Ranchi 03/05/2012

CERTIFICATE OF APPROVAL The foregoing thesis entitled “A PMU BASED SYNCHRONIZED RELAYING

SCHEME FOR TRANSMISSION LINE PROTECTION”, is hereby approved as a

creditable study of research topic and has been presented in a satisfactory manner to warrant

its acceptance as prerequisite to the degree for which it has been submitted.

It is understood that by this approval, the undersigned do not necessarily endorse any

conclusion drawn or opinion expressed therein, but approve the thesis for the purpose for

which it is submitted.

(Internal Examiner) (External Examiner)

(Head of the Department)

Electrical and Electronics Engineering



ACKNOWLEDGEMENTS

During the course of our thesis preparation, we have received lot of support, encouragement,

advice and assistance from many people and to this end we are deeply grateful to them all.

It is with great pleasure that we express our cordial thanks and indebtedness to our admirable

Guides, Mrs. D. GHOSH, Professor, and Department of Electrical And Electronics

Engineering. His vast knowledge, expert supervision and enthusiasm continuously challenged

and motivated us to achieve our goal. We will be eternally grateful to him for allowing us the

opportunity to work on this project.

We also express our sincere gratitude to Dr T. Ghose, Professor and Head of Department,

Electrical and Electronics Engineering for his valuable help and suggestions and providing us

all research facilities that have made the work completed in time.

The present work certainly would not have been possible without the help of our friends, and

also the blessings of our parents.

Date:

MANISH AGARWAL

(BE/1209/2008)

RAJAN KUMAR DUBEY

(BE/1214/2008)

BISWAJEET CHOUDHARY

(BE/1189/2008)



CONTENTS

Topic Page No.

Abstract……………………………………………………………………………………....06

Abbreviations………………………………………………………………………………...07

List of Figures………………………………………………………………………………..08

Chapter 1

1.1- Introduction……………………………………………………………………..09

Chapter 2- Literature Review

2.1- Phasor……………………………………………………………………………12

2.2- Phasor Measurement Unit………………………………………………………14

2.3- Distance Relay Fundamentals…………………………………………………..20

2.4- Tripping Characteristics………………………………………………………....21

2.5- Principle of Operation…………………………………………………………..22

2.6- Zones of Operations…………………………………………………………….23

2.7- Symmetrical Components………………………………………………….……24

2.8- The Butterworth Low Pass Filter………………………………………………..29

2.9- Discrete Fourier Transform……………………………………………………...31

2.10- Mimic Filter……………………………………………………………………33

Chapter 3- Solution Techniques

3.1- PMU Installation………………………………………………………………...36

3.2- Filtering using Low Pass filter…………………………………………………..36

3.3- Removal of DC offset using mimic Filter……………………………………….37

3.4- Sampling and Phasor Estimation using DFT……………………………………37

3.5- Strategy for Optimal Placement of PMU for Fault Observability………………38

3.6- Detection of the area nearest to the fault & the faulted line…………………….39

3.7- The Proposed Algorithm for the detection of the Faulted Line…………………41

3.8- Asynchronous Tripping in Conventional Relaying Scheme…………………….42

3.9- The Proposed Pmu Based Relaying Schemes Zones……………………………43

3.10- Setting the relay to protect 80-90% of the Transmission Line………………...44

3.11- Proposed Algorithm for Synchronized Relaying………………………………45



Chapter 4- Case Study, Results and Discussions

4.1- Placement of the PMUs…………………………………………………………48

4.2- The SIMULINK model…………………………………………………………49

4.3- Details of the case study………………………………………………………...49

4.4- Results and Discussions…………………………………………………………50

4.5- Comparison of Asynchronous & Synchronous Tripping of Circuit Breakers......52

Chapter 5- Conclusion and Further Scope of Work

5.1- Scope for Further Work…………………………………………………………53 References…………………………………………………………………………………...54



ABSTRACT

The electricity supply industries need tools for dealing with system-wide disturbances that

often cause widespread catastrophic blackouts in power system networks. When a major

disturbance occurs, protection and control measures overtake a greatest role to prevent further

degradation of the system, restore the system back to a normal state, and minimize the impact

of the disturbance. Continuous technological development in Information and

Communication Technology, novel sensors and measurement principles in general has

promoted the utilization of Phasor Measurement Unit (PMU). According to recent studies,

the mal-operation or fail-to trip of protection is determined as one of the origins to raise and

propagate major power system disturbances. In the existed relay protection system, mal

operations of backup protection contribute a lot to system security and stability; furthermore,

they are main reasons to system cascade tripping.The conventional relaying schemes are

highly asynchronous ,PMU based relaying schemes are being developed which can provide

synchronous and coordinated operation of the relays.

In this work an efficient method to detect the faulted line and a synchronous relaying

algorithm based on PMU is presented. The work also covers a strategy for optimal placement

of PMU for a network based on the detection of the location of a fault on the transmission

line. The proposed method is implemented and investigated on a six bus network using

MATLAB/SIMULINK package.



ABBREVIATIONS

PMU : Phasor Measurement Unit

GPS : Global Positioning Satellite

CT : Current Transformer

PT : Potential Transformer

DFT : Discrete Fourier Transform

UTC : Universal Time Coordinate



LIST OF FIGURES

Figure 1: Convention for synchrophasor representation

Figure 2: A sinusoid with a period of T observed at instants which are multiples of T0 apart.

T0 is not an integer multiple of T.

Figure 3: Model 1690 Phasor Measurement Unit

Figure 4: Block Diagram of Phasor Measurement Unit

Figure 5: Typical PMU Installation at a Substation

Figure 6: GPS Satellite

Figure 7: The GPS satellites orbiting the earth

Figure 8: Principle of operation of distance relay

Figure 9: Illustration of 1+a

Figure 10: Positive Sequence Components

Figure 11: Negative Sequence Components

Figure 12: Central Protection Centre

Figure 13: Phasor Measurement unit Simulation Flow Chart

Figure 14: One bus spaced placement of PMU for fault observability

Figure 15: Six bus network

Figure 16: Voltage waveform during fault

Figure 17: Current waveform during fault

Figure 18: Algorithm for detection of faulted line.

Figure 19: Three zones of protection and the delays.

Figure 20: The proposed PMU based relaying scheme zones

Figure 21: Transmission line with PMU at one end

Figure 22: The six bus network undertaken for study.

Figure 23: Placement of the PMU on the 6 bus network.

Figure 24: The SIMULINK model of the 6 bus network

Figure 25: Comparison of positive sequence voltage magnitude from all the PMUs

Figure 26: Comparison of positive sequence voltage magnitude from all the PMUs

Figure 27: Status of the trip signal

Figure 28: Comparison between conventional relaying and the proposed scheme.



CHAPTER 1

1.1 Introduction

More recent technological advancements in microprocessor relays, combined with GPS

receivers for synchronization and accurate time stamping, is providing users advanced relay

systems with synchronized measurements, called synchrophasor measurements (IEEE Power

System Relaying Committee, 2002; Phadke, 2002; Marek, 2002). Synchrophasor

measurements together with advancements in digital communications, provides users with

the power system state at a rate of twenty times per second. Synchrophasor measurements

from different network locations when combined and processed in a central computer system

will provide users with the absolute phase angle difference between distant network buses

with an accuracy of tenths of an electrical degree. These types of central computer systems,

equipped with wide-area protection and control algorithms, will be able to better address

future system out-of-step conditions and other system problems because they will have a

better knowledge of what happens throughout the power system. In addition, knowledge of

online generation and load demand provided from synchrophasor measurement systems will

aid in balancing better the generation and load during islanding, as well as minimizing load

and generation shedding in order to preserve stability during major system disturbances.

Time synchronized phasor measurements provide a dynamic view of a power system,

combining these measurements in a central protection system (CPS); this capability is used to

set up a wide area control, protection and optimization platform by means of new

communication systems and (GPS), integrated application design is shown in Figure 1.

Figure 1 shows an integrated application design based on phasor measuring units. When the

system operates in extreme conditions, load shedding, generation shedding, or system

islanding must occur to prevent total system collapse (Thorp et al., 1988; Centen et al., 1993;

Guzman et al., 2002; Guzman et al., 2002). Typical causes of system collapse are voltage

instability or transient angle instability. These instabilities can occur independently or jointly.

In most cases, system wide-area disruptions begin as a voltage stability problem. Because of

a failure to take proper actions for the system to recover, this voltage stability problem

evolves into an angle stability problem.



New monitoring, protection, and communications technologies allow us to implement

economical local- and wide-area protection systems that minimize risk of wide-area system

disruptions or total system collapse.

This study proposes a technique based on wide-area measurements for a power system. The

study is very vital and needed in the current state regarding the electrical utility and the

society as well to face future expansion of the electrical grid and to cover the demand of the

increasing growth and solving the problem of peak period. The study is very beneficial also

from the stability and security of the grid viewpoint in case of interconnection with other

countries.

This study presents a new approach for fault detection for interconnected system using the

time synchronized phasor measurements. The scheme is depending on comparing positive

sequence voltage magnitudes for specified areas and positive sequence current phase

difference angles for each interconnected line between two areas on the network. The

Matlab/Simulink program is extensively used to implement the idea. It is used to simulate the

power system, phase measurement unit function, synchronization process, and fault detection.



Chapter 2

LITERATURE REVIEW

2.1 Phasor The pure sinusoidal waveform x(t)=Xmcos(�t + ø) is commonly represented as a phasor

X=Xr + jXi =(Xm/ )( where ø depends on the definition of the time scale.

For this Standard, this basic concept is adapted as the representation of power system

sinusoidal signals.

Synchrophasor

The synchrophasor representation X of a signal x(t) is the complex value given by

X=Xr + jXi

=(Xm/ )

=(Xm/ )(cosø + jsinø)

where (Xm/ ) is the rms value of the signal x(t) and ø is its instantaneous phase angle

relative to a cosine function at nominal system frequency synchronized to UTC. This angle is

defined to be 0 degrees when the maximum of x(t) occurs at the UTC second rollover (1 PPS

time signal), and -90 degrees when the positive zero crossing occurs at the UTC second

rollover. Figure illustrates this relationship.



Figure 1: Convention for synchrophasor representation

Off-nominal frequency signals:

The synchrophasor representation of a sinusoid is based on the nominal system frequency,

not the actual frequency of the system. Given the sinusoid x(t)=Xmcos(2�ft + ø) and a power

system frequency f0, the synchrophasor is based on the representation x(t)=Xmcos(2�(f0 +

�f)t + ø)=

x(t)=Xmcos(2�f0t + 2��ft + ø)) where f = f0 + �f and has a phasor representation

X=(Xm/ ) It is clear that the base phase angle f of the phasor is determined by

the starting time (t=0) of the sinusoid and the phasor angle will rotate as a function of the

difference (�f) between the actual frequency f of the signal and the system frequency (f0).

Consider that such a sinusoid is observed at intervals {0, T0, 2T0, 3T0,..,nT0, …} where T0,= 1/

f0, and the corresponding phasor representations are {X0, X1, X2, X3, …}. If the sinusoid

frequency f � f0, the observed phasor will have a constant magnitude, but the phase angles of

the sequence of phasors { X0, X1, X2, X3, …}will change uniformly at a rate 2�(f-f0)T0, where

f0 = 1/T0 as illustrated in Figure



Figure 2: A sinusoid with a period of T observed at instants which are multiples of T0

apart. T0 is not an integer multiple of T.

2.2 PHASOR MEASUREMENT UNIT:

A PMU is a device which measures the electrical waves on an electricity grid, using a

common time source for synchronization. Time synchronization allows synchronized real-

time measurements of multiple remote measurement points on the grid. In power engineering,

these are also commonly referred to as synchrophasors and are considered one of the most

important measuring devices in the future of power systems. A PMU can be a dedicated

device, or the PMU function can be incorporated into a protective relay or other device.

Figure 3: Model 1690 Phasor Measurement Unit



A PMU is an electronic device that uses state-of-the-art digital signal processors that can

measure 50/60Hz AC waveforms (voltages and currents) typically at a rate of 48 samples per

cycle (2880samples per second). The analog AC waveforms are digitized by an Analog to

Digital converter for each phase. A phase-lock oscillator along with a Global Positioning

System (GPS) reference source provides the needed high-speed synchronized sampling with

1 microsecond accuracy. Additionally, digital signal processing techniques are used to

compute the voltage and current phasors. Line frequencies are also calculated by the PMU at

each site. This method of phasor measurement yields a high degree of resolution and

accuracy. The resultant time tagged phasors can be transmitted to a local or remote receiver at

rates up to 60 samples per second.

Figure 4: Block Diagram of Phasor Measurement Unit

PMUs come in different sizes. Some of the larger ones can measure up to 10 phasors plus

frequency while others only measure from one to three phasors plus frequency. The

approximate cost of the larger PMUs can range in the $30 to $40 thousand of dollars while

the smaller ones cost considerably less.

PMU INSTALLATION AND CONNECTION:

Installation of a typical 10 Phasor PMU is a simple process. A phasor will be either a 3 phase

voltage or a 3 phase current. Each phasor will, therefore, require 3 separate electrical

connections (one for each phase). We are talking about 6 wires per phasor – 2 for each phase

of either voltage or current.The PMU will also measure the line frequency from a specific

voltage phasor (typically a major bus assigned by the user).



Typically an electrical engineer designs the installation and interconnection of a PMU at a

substation or at a generation plant. Substation personnel will bolt equipment rack to the floor

of the substation following established seismic mounting requirements. Then the PMU along

with a modem and other support equipment will be mounted on the equipment rack. They

will also install the GPS antenna on the roof of the substation per manufacturer instructions.

The antenna signal cable will be connected to the antenna and brought directly to the PMU.

Substation personnel will also install “shunts” in all Current Transformer (CT) secondary

circuits that are to be measured. Potential Transformer (PT) connections will not require the

installation of any additional equipment other than terminal blocks and fuses. They will have

to run wires from the CT shunts and the PTs to either an interface cabinet or directly to the

input connections of the PMU.

Each phasor (either Voltage or Current) will require three connections – one for each phase.

In addition to the CT and PT connections the PMU will also require the following

connections:

- Power connection – typically from station batteries.

- Station ground connection.

- Global Positioning Satellite (GPS) antenna connection.

- Communication circuit connection (Modem if using 4-wire connection or Ethernet for

network connection).

After all the connections are made, the PMU is configured and tested. This task is typically

performed by a substation Test Technician.

The utility’s IT department will play a key role will the phasor data connections phase of the

PMU installation. After the entire input channel configuration and testing is completed, the

PMU is connected to the utility’s Phasor Data Concentrator (PDC) via 4-wire Modem or

Ethernet connection depending on the bandwidth needs. They will also need to evaluate the

need to install additional communication equipment in order to provide the necessary circuit

connections between the PDC at the master site and the PC workstations at the client sites.



Figure 5: Typical PMU Installation at a Substation

Global Positioning System:

What is GPS?

The GPS is a space-based satellite navigation system that provides location and time

information in all weather, anywhere on or near the Earth, where there is an unobstructed line

of sight to four or more GPS satellites. It is maintained by the United States government and

is freely accessible to anyone with a GPS receiver.

The GPS program provides critical capabilities to military, civil and commercial users around

the world. In addition, GPS is the backbone for modernizing the global air traffic system.



Figure 6: GPS Satellite

The Global Positioning System (GPS) is a satellite-based navigation system made up of a

network of 24 satellites placed into orbit by the U.S. Department of Defense. GPS was

originally intended for military applications, but in the 1980s, the government made the

system available for civilian use. GPS works in any weather conditions, anywhere in the

world, 24 hours a day. There are no subscription fees or setup charges to use GPS.

How it works

GPS satellites circle the earth twice a day in a very precise orbit and transmit signal

information to earth. GPS receivers take this information and use triangulation to calculate

the user's exact location. Essentially, the GPS receiver compares the time a signal was

transmitted by a satellite with the time it was received. The time difference tells the GPS

receiver how far away the satellite is. Now, with distance measurements from a few more

satellites, the receiver can determine the user's position and display it on the unit's electronic

map.

A GPS receiver must be locked on to the signal of at least three satellites to calculate a 2D

position (latitude and longitude) and track movement. With four or more satellites in view,



the receiver can determine the user's 3D position (latitude, longitude and altitude). Once the

user's position has been determined, the GPS unit can calculate other information, such as

speed, bearing, track, trip distance, distance to destination, sunrise and sunset time and more.

How accurate is GPS?

Today's GPS receivers are extremely accurate, thanks to their parallel multi-channel design.

Garmin's 12 parallel channel receivers are quick to lock onto satellites when first turned on

and they maintain strong locks, even in dense foliage or urban settings with tall buildings.

Certain atmospheric factors and other sources of error can affect the accuracy of GPS

receivers. Garmin® GPS receivers are accurate to within 15 meters on average.

Newer Garmin GPS receivers with WAAS (Wide Area Augmentation System) capability can

improve accuracy to less than three meters on average. No additional equipment or fees are

required to take advantage of WAAS. Users can also get better accuracy with Differential

GPS (DGPS), which corrects GPS signals to within an average of three to five meters. The

U.S. Coast Guard operates the most common DGPS correction service. This system consists

of a network of towers that receive GPS signals and transmit a corrected signal by beacon

transmitters. In order to get the corrected signal, users must have a differential beacon

receiver and beacon antenna in addition to their GPS.



Figure 7: The GPS satellites orbiting the earth

The GPS satellite system

The 24 satellites that make up the GPS space segment are orbiting the earth about 12,000

miles above us. They are constantly moving, making two complete orbits in less than 24

hours. These satellites are travelling at speeds of roughly 7,000 miles an hour.

GPS satellites are powered by solar energy. They have backup batteries onboard to keep

them running in the event of a solar eclipse, when there's no solar power. Small rocket

boosters on each satellite keep them flying in the correct path.

Here are some other interesting facts about the GPS satellites (also called NAVSTAR, the

official U.S. Department of Defense name for GPS):

• The first GPS satellite was launched in 1978.

• A full constellation of 24 satellites was achieved in 1994.

• Each satellite is built to last about 10 years. Replacements are constantly being

built and launched into orbit.

• A GPS satellite weighs approximately 2,000 pounds and is about 17 feet across

with the solar panels extended.

• Transmitter power is only 50 watts or less.

2.3 Distance Relay Fundamentals

Distance relay is also called impedance relays, they are used to calculate line impedance by

measurement of voltages and currents on one single end. Impedance relays are better able to



discriminate (to distinguish) between conditions for which they should operate and conditions

for which they should not. Suppose �V=0.5(Vnormal) and �I=2(Inormal).

Before fault: normalnormal

normal ZIV

IV == .

After fault: faultnormal

normal

normal

normal ZIV

IV

IV ===

41

)(2)(5.0

From this, we can see that:

normalfault ZZ41= but normalfault II 2= .

Therefore, proportionally, a larger change is seen in impedance than current, and so faults are

easier to correctly detect when measuring impedance relative to measuring current.

2.4 Tripping characteristic

The simplest impedance relay is one that operates with the following logic:

tZIV ≤ � Trip

tZIV >

� Block

This logic can be illustrated in the impedance plane as in Fig



TRIP

BLOCK

|Zt|

2.5 Principle of operation

The basic principle as illustrated in figure 1, involves the division of the voltage at the

relaying point by the measured current. The apparent impedance is compared with the reach

point impedance. If the measured impedance is less than the reach point impedance, it is

assumed that a fault exists on the line between the relay and the reach point. The reach point

of the relay is the point along the line impedance locus that is intersected by the boundary

characteristics of the relay. Distance relay is the broader name of the different types of

impedance relay.

Figure 8: Principle of operation of distance relay



The relay is connected at position, R and receives a secondary current, iF, equivalent to a

primary fault current, IF. The secondary voltage, VF, is equivalent to the product of the fault

current “IF” and impedance of the line up to the point of fault, ZF. The operating torque of

this relay is proportional to the fault current “IF”, and its restraining torque is proportional to

the voltage “VF”. Taking into account the number of turns of each coil, there will be a

definite ratio of V/I at which the torque will be equal. This is the reach point setting of the

relay. The relay will operate when the operating torque is greater than the restraining torque.

Thus any increase in current coil ampere-turns, without a corresponding increase in the

voltage coil ampere-turns, will unbalance the relay. This means the V/I ratio has fallen below

the reach point. Alternatively if the restrain torque is greater than the operating torque, the

relay will restrain and its contacts will remain open. In this case the V/I ratio is above the

reach point. The reach of a relay is the distance from the relaying point to the point of fault.

Voltage on the primary of voltage transformer, VT, is:

V =EZF/(ZS+ZF)

The fault current, IF

I=E/(ZS+ZF)

The relay compare the secondary values of V and I, as to measure their ratio which is an

impedance Zm ,

Zm=(V/V.T Ratio) / (I/C.T Ratio)

Zm=ZF* (C.T Ratio / V.T Ratio)

Zm is the measured impedance called secondary impedance.

2.6 Zones of protection

Basic distance protection will comprise instantaneous directional Zone 1 protection and one

or more time delayed zones. Numerical distance relays may have up to five zones, some set



to measure in the reverse direction. Numerical relays usually have a reach setting of up to

85% of the protected line impedance for instantaneous Zone 1 protection. The resulting 15%

safety margin ensures that there is no risk of the Zone 1 protection over-reaching the

protected line due to errors in the current and voltage transformers, inaccuracies in line

impedance data provided for setting purposes and errors of relay setting and measurement of

the distance protection must cover the remaining 15% of the line. The reach setting of the

Zone 2 protection should be at least 120% of the protected line impedance. In many

applications it is common practice to set the Zone 2 reach to be equal to the protected line

section +50% of the shortest adjacent line. Zone 3 reach should be set to at least 1.2 times the

impedance presented to the relay for a fault at the remote end of the second line section.

Typical reach for a 3-zone distance protection are shown in Figure 2.

2.7 SYMMETRICAL COMPONENT Theorem: We can represent any unsymmetrical set of 3 phasors as the sum of 3 constituent

sets, each having 3 phasors:

� A positive (a-b-c) sequence set and

� A negative (a-c-b) sequence set and

� An equal set

These three sets we will call, respectively,



� Positive ( )111 ,, cba VVV

� Negative ( )222 ,, cba VVV

� zero ( )000 ,, cba VVV

Sequence components.

The implication of this theorem that any unsymmetrical set of 3 phasors Va, Vb, Vc can be

written in terms of the above sequence components in the following way:

210aaaa VVVV ++=

210bbbb VVVV ++=

210cccc VVVV ++=

We can write the equations of (9) in a more compact fashion, but first, we must describe a

mathematical operator that is essential.

The a-operator

To begin on familiar ground, we are all conversant with the operator “j” which is used in

complex numbers.

Remember that “j” is actually a vector with a magnitude and an angle:

°∠= 901j

In the same way, we are going to define the “a” operator as:

°∠= 1201a

It is easy to show the following relations:

°−∠= 12012a



°∠= 013a

aa =°∠= 12014

We also have that:

°∠=−=+ 6011 2aa

as illustrated in Fig.

1+a

a

1

Figure 9: Illustration of 1+a

Note that

°∠=°∠−=− 60124012a

Similarly, we may show that:

°−∠=−=+ 6011 2 aa

°−∠=− 3031 a

°∠=− 3031 2a

°∠=− 15031a

°−∠=− 150312a

And there are many more relations like this that are sometimes helpful when dealing with

symmetrical components. (See the text called “Analysis of faulted power systems” by Paul

Anderson, pg. 17.)

Symmetrical components: the math

We repeat equations (9) below for convenience:



210aaaa VVVV ++=

210bbbb VVVV ++=

210cccc VVVV ++=

We can relate the three different quantities having the same subscript.

� Zero sequence quantities: These quantities are all equal, i.e.,

000cba VVV ==

� Positive sequence quantities: The relation between these quantities can be observed

immediately from the phasor diagram and can be expressed using the a-operator.

a-b-c Vc1

Vb1

Va1

Figure 10: Positive sequence components

11

121

ac

ab

aVV

VaV

=

=

� Negative sequence quantities: The relation between these quantities can be observed

immediately from the phasor diagram and can be expressed using the a-operator.



a-c-b Vb2

Vc2

Va2

Figure 11: Negative sequence components

222

22

ac

ab

VaV

aVV

=

=

Now let’s use equations (22), (23), and (24) to express the original phasor Va, Vb, Vc in terms

of only the a-phase components

210 ,, aaa VVV ,

i.e., we will eliminate the b-phase components

210 ,, bbb VVV

And the c-phase components

210 ,, ccc VVV

This results in

210aaaa VVVV ++=

2120aaab aVVaVV ++=

2210aaac VaaVVV ++=

So we have written the abc quantities (phase quantities) in terms of the 012 quantities

(sequence quantities) of the a-phase. We can write this in matrix form as:



��

�

�

��

�

�

��

�

�

��

�

�

=��

�

�

��

�

�

2

1

0

2

2

11

111

a

a

a

c

b

a

V

V

V

aa

aa

V

V

V

Defining

��

�

�

��

�

�

=2

2

11

111

aa

aaA

we see that eq. (25) can be written as:

��

�

�

��

�

�

=��

�

�

��

�

�

2

1

0

a

a

a

c

b

a

V

V

V

A

V

V

V

We may also obtain the 012 (sequence) quantities from the abc (phase) quantities:

��

�

�

��

�

�

=��

�

�

��

�

�−

c

b

a

a

a

a

V

V

V

A

V

V

V1

2

1

0

where

��

�

�

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�

�

=−

aa

aaA2

21

11

111

31

2.8 The Butterworth Low Pass Filter

The frequency response of the Butterworth Filter approximation function is also often

referred to as "maximally flat" (no ripples) response because the pass band is designed to

have a frequency response which is as flat as mathematically possible from 0Hz (DC) until

the cut-off frequency at -3dB with no ripples. Higher frequencies beyond the cut-off point

rolls-off down to zero in the stop band at 20dB/decade or 6dB/octave. This is because it has a

"quality factor", "Q" of just 0.707. However, one main disadvantage of the Butterworth filter



is that it achieves this pass band flatness at the expense of a wide transition band as the filter

changes from the pass band to the stop band. It also has poor phase characteristics as well.

The ideal frequency response, referred to as a "brick wall" filter, and the standard

Butterworth approximations, for different filter orders are given below.

Ideal Frequency Response for a Butterworth Filter

Note that the higher the order and number of

cascaded stages the closer the filter is to the

ideal "brick wall" response. However, in

practice this "ideal" response is

unattainable.

The Butterworth low-pass filter has a magnitude response given by

Where A is the filter gain and �c is the 3 dB cut-off frequency and N is the order of the

filter.The design parameters of the butterworth filter are obtained by considering the low-pass

filter with the desired specifications as given below.

�1 |H(j�)| 1, 0 � �1

|H(j�)| �2, �2 �

The order of the filter N is given by

N=

Normalised Low Pass Butterworth Filter Polynomials



Butterworth produced standard tables of normalised second-order low pass polynomials

given the values of coefficient that correspond to a cut-off corner frequency of 1 radian/sec.

2.9 Discrete Fourier Transform (DFT)

In this approach the estimation is based on equation Z = v / i . The sampled current and

voltage signals are initially transformed in to phasor quantities (both direct and quadrature

components). The estimation approach includes estimation of the first harmonic; calculation

from equation Z = v / i the impedance as a quotient of voltage and current phasors. Based on

fault type, the resistance and reactance up to the relay point is calculated.

Mathematical Background

Signal at any given time may be described by a phasor. Phasor actually is a vector rotating in

the complex plane with a speed � radian/sec , a snap-shot in time, the signal at that time, x(t)

is given in rectangular form by

x(t) |t=T = (realcoordinate) + j(imaginarycoordinate)

x(t) = a + jb

And in polar form by

x(t) = Aej�t

Considering the initial value at t=0,

x(0) = Aej�

the general form of x(t)is;

x(t) = Aej(�+�)



ej�t = cos�t + j sin�t

cos�t = (ej�t + e-j�t)

sin�t = (ej�t - e-j�t)

Therefore, sine or cosine signal can be represented by two phasors form a conjugate pair, i.e

if, x(t) = Acos�t , then x(t)may be written as;

x(t) = (e( j�t + � ) + e( -j�t + � ))

The above discussion is related to a simple cosine or sine functions of a single frequency,

most signals are composed of many cosine and sine waves. Therefore any complex periodic

signal can be described as sum of many phasors. Fourier series assumes that a set of phasors

have frequencies which are multiples of some fundamental frequency, f0, i.e.

The individual frequency components are known as harmonics.

If the complex signal is not periodic the phasor frequencies are not related, thus the Fourier

general form may be written as;

�

In digital domain (discrete time), replace the continuous function, t, with a function

progresses in jumps of �0Ts, thus phasor description of single frequency signal would be;

x(n) = A



= cos(n�Ts) + jsin(n�Ts)

Where, Ts is the sampling interval.

A real signal can be described using Fourier in discrete domain called (Discrete Fourier

Series) as,

�

Which is a simple phasor model that describes a general discrete signal? The discrete Fourier

transform (DFT) is a digital filtering algorithm that computes the magnitude and phase at

discrete frequencies of a discrete time sequence. Fast Fourier transforms are computationally

efficient algorithms for computing DFTs. FFTs are useful if we need to know the magnitude

and/or phase of a number individual or band off frequencies. The DFT is ideal method of

detecting the fundamental frequency component in a fault signal. However, DFT, Least Error

Square LES and Walsh Function algorithms are among the most popular phasor estimation

techniques employed in numerical relays (Phadke & Thorp, 1990). As we are dealing with a

50 Hz signal that is sampled synchronously. This means that the sample interval is the inverse

of an integer multiple of 50 . We need to compute the DFT for the fundamental using

equation (1), where, k equal to one for the fundamental and n is the coefficient subscript. Two

digital filters are required, one to get the real part and one for the imaginary part.

2.10 Mimic Filter

After we obtain the samples of the faulted current & voltages , it is required to filter out the

other unnecessary components leaving behind the fundamental components. Thus to suppress

the undesirable DC offset over a wide range of time as in real systems, we use the popular

digital filters such as Mimic Filter.

The antialiasing filters cannot remove the decaying DC components and reject low frequency

components. This makes the phasors very difficult to be quickly estimated and affects the

performance of digital relaying. Therefore, we usually use mimic filter to remove the DC

offset components.



A mimic filter which can be implemented in analog or digital circuitry, and which removes

dc offset or other noise from an input signal using a pseudo-differentiation technique. The

input signal is adjusted by a feedback value, and the adjusted signal is amplified by a

proportional gain factor to generate an output signal. The feedback value is determined by

integrating the output signal and multiplying the integration by an integration gain factor. The

mimic filter avoids the generation of false signal spikes.

In real systems, the line relays which are to be used have a tendency to overreach in the

presence of the DC offset components in the fault current waveforms. Therefore the decaying

DC components have to be removed from the fault waveforms.

When we pass a current waveform through a mimic filter circuit consisting of a resistance in

series with an inductance or an impedance of the form

Then the exponential decaying component at the ouput will vanish.

The Gain Vs Frequency has been depicted in the figure. It is seen that the Gain diminishes to

zero for low frequency components resulting in the removal of DC components.

�

��

��

��

� � ��



CHAPTER 3

OVERVIEW OF THE PROTECTION SCHEME

1. Optimal placement of PMU on the basis for better fault observability.

2. A central protection centre is there which will analysze the data obtain from all the areas

where PMU are installed and take the required decisions.

3. Identification of the area nearest to the fault.

4. Identification of the faulted line connecting the faulted area with the neighbouring area.

5. Isolation of the faulted line with synchronous tripping of the circuit breakers using PMU

and a communication channel.

Figure 12: Central Protection Centre



3.1 PHASOR MEASUREMENT UNIT SIMULATION In order to study a given network and develop strategy for its protection using PMU, an

accurate model of PMU is needed to be developed and simulated. The flow chart for the

simulation of a PMU is given below:

Figure 13: Phasor Measurement unit Simulation Flow Chart The current and voltage waveforms is input from the CTs and PTs. Low pass filtering

removes the high pass frequency components present during the fault condition. The removal

of the DC offset components is done using mimic filtering algorithm. The sampling process

outputs discrete values. The Discrete Fourier Transform is performed to obtain the phasor

estimation of the fundamental component of the voltage and current. The common time

reference is provided by the clock of the Simulink which is same as the simulation time. The

positive sequence component of the voltage and current is computed (also negative and zero

sequence component if required).

In the PMU model we are assuming that the PMU has as many numbers of channels as the

number of connected lines to the bus it is installed.

3.2 Filtering using low pass filter The 8th order Butterworth filter with passband frequency of 314 rad/s was used.The

comparison has been made between filtered and normal signals.



3.3 Removal of DC offset using Mimic Filter

The mimic filter was used to remove DC offset component.

3.4 SAMPLING AND PHASOR ESTIMATION USING DFT In practical power systems the sampling is usually 4- 20 samples per cycle but as we are

using powerful SIMULINK/MATLAB package. Due to this reason the simple DFT is

preferred over FFT as the number of samples is less. However in our simulation we have

sampled at 32 samples per cycle for better accuracy in the results.



The phasor estimation is done using full cycle DFT. This gives us the amplitude and the

phase of the fundamental component of 50Hz for each cycle. The positive sequence

component is then obtained.

3.5 STRATEGY FOR OPTIMAL PLACEMENT OF PMU FOR FAULT OBSERVABILITY For observing a fault on the transmission line and controlling the tripping signal for isolation

of the line the best is to place the PMU at both the ends of a transmission line however the

economic considerations do not permit us to do so, therefore an optimal placement is desired

keeping in view the fault observability and protection from the fault.

One bus spaced strategy Every general transmission network can be broken down into the following one bus spaced

network:

Figure 14: one bus spaced placement of PMU for fault observability

For observing the fault location on the transmission lines PMU is required to be placed at one

end only. The constraint equations would be

F(x)=

=1 if PMU is placed at k

=0 if PMU is not placed at k

The purpose is to minimize subject to the constraints.



For the following six bus network:

Figure 15: six bus network

The constraint equations are:

+

+

+

+

+

+

Solving this optimization problem by ‘Branch and Bound method’ the results obtained for the

six bus network is

No of PMU= 3

Bus Location= 1, 3, 5 or 2, 4, 6

Applying the algorithm for the IEEE-14 bus network the optimized locations obtained are:

No of PMU= 8

Bus location= 2,3,4,7,8,9,11,13

3.6 Detection of the area nearest to the fault and the faulted line The proposed scheme uses synchronized phasor data obtained from the Phasor Measurement

Units. The technique is based on two events:

a) Voltage reduction due to fault: Whenever there is a fault on the transmission line the

voltage at the buses drop sharply as very high current flow during the fault to the faulted

point.



b) Change in the phase angle of current during fault: At the instant fault occurs there is a

sharp change in the phase angle of the current flowing in the lines. The current waveform

becomes highly unsymmetrical due to presence of harmonics, noise and the dc offset.

Figure 16: Voltage waveform during fault.

Figure 17: Current waveform during fault.



3.7 THE PROPOSED ALGORITHM FOR THE DETECTION OF THE FAULTED LINE

Figure 18: Algorithm for detection of faulted line.

At the central protection centre the data from all the areas where PMU are installed are

obtained. The positive sequence voltage magnitudes are compared and minimum value is

found out. The minimum value of the voltage will give the area nearest to the fault. After

analyzing the prefault and the post fault conditions, a threshold value of the voltage is set, if

the voltage drops to that threshold value, there is a fault in the power system.

To determine which line connected to that area is the faulted line, the absolute value of the

change in the phase angle at the instant of the fault is compared for all the lines connected to

that area and the maximum value is found out.

The line giving the maximum value is the faulted line.

The next step is to take decision to isolate the line by tripping the circuit breakers at the end

of the lines as per the relaying algorithm.



3.8 ASYNCHRONOUS TRIPPING IN CONVENTIONAL RELAYING SCHEME In the conventional relaying schemes without PMU there is a delay provided for different

zones of protection. Due to this delay the tripping of the circuit breakers at both the ends of

the transmission line is not synchronous this is a very big disadvantage as the fault should be

cleared as soon as possible to maintain power system stability.

Figure 19: Three zones of protection and the delays.

When the fault lies close to A, it will be detected in zone 1 of R1 and Zone 2 of R2. R1 will

trip instantaneously but R2 will trip after delay according to the zone 2 setting. Thus this

tripping will be asynchronous.

Using PMU and and a communication channel, this delay can be minimized and the tripping

of the circuit breakers can be made to synchronize as close as possible.



3.9 THE PROPOSED PMU BASED RELAYING SCHEMES ZONES

Figure 20. The proposed PMU based relaying scheme zones

When the fault is detected by the PMU at A to be within 80-90% of the line and the PMU at

B will report that the fault is beyond the 80-90% setting of line BC the line AC will be

isolated by sending the trip command to the circuit breakers at both ends of the line at the

same instance.

If the fault detected by the PMU at B is within its 80-90% setting and the PMU at B reports

that the fault is beyond its setting, the decision will be to trip the line BC.

If both the PMUs report that the fault is beyond their 80-90% setting, this will mean that the

fault is very close to the bus C, hence the decision made will be to isolate bolth the lines by

sending trip command to all the four circuit breakers.



3.10 SETTING THE RELAY TO PROTECT 80-90% OF THE TRANSMISSION LINE

Figure 21: Transmission line with PMU at one end

To set the relay at 1 to protect the 80-90% of the line it is required to obtain a threshold value

corresponding to the fault at 80-90 % of the transmission line length. We shall denote this

value by K. It is obtained by taking the ratio of positive sequence voltage magnitude to the

ratio of positive sequence current magnitude flowing through the line when the fault is

simulated at 80-90 % of the line.

After detection of the fault, this ratio is calculated at the bus 1 and compared with the value

K, if it is less than K; it means that the fault is within 80-90 % of the transmission line length.



3.11 PROPOSED ALGORITHM FOR SYNCHRONIZED RELAYING

Za= abs(Va positive sequence)/abs(Iac positive sequence) Zb= abs(Vb positive sequence)/abs(Ibc positive sequence)

Determine the faulted line connecting the area with the neighboring area.

Determine the Area nearest to the fault

Is Za<Ka��

Is Zb<Kb ?

Is Zb>Kb��

ISOLATE LINE A-C

ISOLATE LINE B-C

ISOLATE BOTH�LINES ERROR

��

��

��

��

��

��

��

��

��



After detecting the faulted line, the next step is to make decision regarding the tripping of the

lines. The relay at A is set to detect any fault within 80-90% of the line AC and the relay at B

is set to detect any fault within 80-90 % of the transmission line length of line BC. When the

fault is within 80-90% of any line it will check if the other PMU is reporting fault beyond 80-

90 % of its observed line. If it is true then the tripping of that particular line will take place. If

the fault is very close to the bus C, both the PMUs will report that the fault is beyond 80-90%

of both the lines hence the decision will be to isolate both the lines.

The circuit breakers at both the end of the lines will be given the trip command at the same

instance, however practically there will be some delay due to the communication channel

between the two PMUs. The channel may be wireless, optical fiber or cable; delays will be

different for each case.



CHAPTER 4

CASE STUDY, RESULTS AND DISCUSSION The following six bus network is taken for the case study. MATLAB/SIMULINK package is

used to simulate the network and the proposed algorithm is implemented and investigated.

Figure 22: The six bus network undertaken for study.



4.1 PLACEMENT OF THE PMUs

Figure 23: Placement of the PMU on the 6 bus network.

The placement of the PMU is based on the fault observability as discussed in chapter 3. Out

of the two solutions obtained we have taken the locations as 2, 4 and 6. The other placement

could be at the buses 1, 3, and 5.



4.2 THE SIMULINK MODEL

Figure 24: The SIMULINK model of the 6 bus network

4.3 DETAILS OF THE CASE STUDY

1) Three phase to ground fault is simulated.

2) Line 4-1 is the faulted line.

3) The PMU at bus 4 is nearest to the fault.

4) The fault is simulated within 90% range of PMU at 4.

5) The purpose is to detect and isolate line 4-1 and continue power flow through line 2-1.



4.4 RESULTS AND DISCUSSION The comparison of the positive sequence voltage magnitude is shown below.

Figure 25. comparison of positive sequence voltage magnitude from all the PMUs

The area nearest to the fault is the area 4. From the figure it can be seen that the PMU located

at 4 is showing the minimum voltage.

Next to identify the line connecting area 4 with the neighbouring area in which fault has

taken place, the absolute value of the difference of phase angles of the current through each

line connected to area 4 is made. There are two lines connected to the bus 4. The comparison

is shown is the following figure:

Figure 26: Comparison of the absolute difference of current phase angles of all the lines

connected to bus 4. The comparison clearly shows that the line 4-1 in which the fault has taken place is giving the

maximum change of phase angle.



Status of the trip signal The status of the signal to trip the lines 4-1 and 2-1 is shown in the figure:

Figure 27: Status of the trip signal

The proposed algorithm has successfully identified the faulted line as 4-1 and the trip signal

has been generated for isolating the same. The trip signal for the line 2-1 is still 0.



4.5 COMPARISON OF ASYNCHRONOUS AND SYNCHRONOUS TRIPPING OF CIRCUIT BREAKERS

Figure 28. Comparison between conventional relaying and the proposed scheme.

To compare the conventional relaying and the proposed synchronized relaying scheme, the

tripping of the circuit breakers at both the end of the line was also made according to the

conventional 3 zone protection scheme .The delay for the zone 2 operation is usually 0.2-0.4s

but the delay was scaled down to four cycles for the purpose of simulation in MATLAB.

From the comparison made, it can be seen that the tripping of one circuit breaker takes place

after the zone 2 delay, which a very big disadvantage is considering the stability of the power

system.

However when the relaying scheme is based on the PMU, this delay can be minimized and

limited to the delay caused by the communication channel.



CHAPTER 5

CONCLUSION The proposed scheme has successfully identified the faulted line on a large power

interconnected system. The idea is based on sharing the data from many PMUs. The scheme

has proposed an optimal placement of PMUs in a power system for better observation of fault

location. The proposed scheme is simple yet efficient and economical in application. The idea

is implemented and investigated using the powerful MATLAB/SIMULINK package. The

modeling for PMU was also done which can be used in modeling of any network in

SIMULINK .The power system configuration, fault detection; tripping and isolation of the

line were performed through MATLAB program.

5.1 SCOPE FOR FURTHER WORK Further work includes classification of the fault and identification of the faulted phase. The

effects of arcing phenomenon, power swings, and transients on the reliability of the proposed

scheme are yet to be studied.



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452, 1994.

[2] IEEE Standard for synchrophasor for Power Systems, IEEE Std 1344-1995 (R2001).

[3] A. G. Phadke, “ Synchronized phasor measurements in power systems,” IEEE Comput.

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[4] K.Mazlumi,H.Askarian Abyaneh,S.H.H.Sadeghi,and S.S.Geramian,"Determination of

Optimal PMU placement fo Fault-Location Observability",DRPT2008 6-9 April 2008

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[5] Moustafa, Mohammed Eissa and Masoud, Mohammed El-Shahat,” A Novel Wide Area

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[6] Thorp, J. S; Phadke A. G; Horowitz, S. W. & Begovic, M. M. (1988). Some Applications

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[7] Wang, et el. (2005). Design of a novel wide-area backup protection system, Proceedings

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[10] G. Benmouyal, “ Removal of Decaying DC in Current Waveforms Using Digital Mimic

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[14] Devesh Due, Sanjay Dambhare, Rajeev Kumar Gajbhiye and S.A.Soman,“ Optimal

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[15] Bei Xu, Ali Abur “ Optimal Placement of Phasor Measurement Units forState

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pmu based relaying

Documents

rajan kumar dubey

discrete fourier transform

decaying dc components

dc offset components

transmission line length

faulted line connecting

bus network undertaken

bus spaced placement