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VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY BURLA, ODISHA, INDIA DEPARTMENT OF ELECTRICAL ENGINEERING Lecture Notes on Power System Engineering II Subject Code:BEE1604 6th Semester B.Tech. (Electrical & Electronics Engineering)
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VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY BURLA, ODISHA, INDIA DEPARTMENT OF ELECTRICAL ENGINEERING

Lecture Notes on Power System Engineering II

Subject Code:BEE1604

6th Semester B.Tech. (Electrical & Electronics Engineering)

Disclaimer

This document does not claim any originality and cannot be used as a substitute for prescribed

textbooks. The information presented here is merely a collection by the committee members for

their respective teaching assignments. Various sources as mentioned at the end of the document

as well as freely available material from internet were consulted for preparing this document.

The ownership of the information lies with the respective authors or institutions. Further, this

document is not intended to be used for commercial purpose and the committee members are not

accountable for any issues, legal or otherwise, arising out of use of this document. The

committee members make no representations or warranties with respect to the accuracy or

completeness of the contents of this document and specifically disclaim any implied warranties

of merchantability or fitness for a particular purpose. The committee members shall be liable for

any loss of profit or any other commercial damages, including but not limited to special,

incidental, consequential, or other damages.

(6 SEMESTER)

POWER SYSTEM-II (3-1-0)

MODULE-I (10 HOURS)

Lines Constants: Resistance, inductance and capacitance of single and three phase lines with

symmetrical and unsymmetrical spacing transposition, charging current, skin effect and

proximity effect, Performance of transmission Lines: Analysis of short, medium and long lines,

equivalentcircuit, representation of the lines and calculation of transmission parameters, Power

flow through transmission line, Power circle diagram, Series and shunt compensation.

MODULE-II (10 HOURS)

Corona: Power loss due to corona, practical importance of corona, use of bundled conductors in

E.H.V. transmission lines and its advantages, Overhead line Insulators, voltage distribution in

suspension type insulators, string efficiency, grading. Sag and stress calculation of overhead

conductors, vibration dampers

Under Ground Cable: Type and construction, grading of cables, capacitance in 3 core cables and

dielectric loss in cables.

MODULE-III (10 HOURS)

Definition of the load flow problem, Network model formulation, A load flow sample

study,Computational aspect of the load flow problem. Gauss siedel and Newton Raphson method

for power flow fast decoupled load flow, On load tap changing transformer and block regulating

transformer, effects of regulating transformers.

MODULE-IV (10 HOURS)

Economic Operation of Power System: Distribution offload between units within a plant,

Transmission losses as function of plant generation, Calculation of loss coefficients, Distribution

of loads between plants with special reference to steam and hydel plants, Automatic load

dispatching. Introduction to Flexible AC Transmission System (FACTS), SVC, TCSC, SSSC,

STATCOM and UPFC

BOOKS

[1]. John J Grainger, W. D. Stevenson, “Power System Analysis”, TMH Publication

[2]. I. J. Nagrath & D. P. Kothari, “Power System Analysis”, TMH Publication

MODULE I

Transmission line

Conductors

Commonly used conductor materials:

The most commonly used conductor materials for over head lines are copper, aluminium, steel-

cored aluminium, galvanised steel and cadmium copper. The choice of a particular material will

depend upon the cost, the required electrical and mechanical properties and the local conditions.

All conductors used for overhead lines are preferably stranded in order to increase the

flexibility.In stranded conductors, there is generally one central wire and round this,

successive layers of wires containing 6, 12, 18, 24 ...... wires. Thus, if there are n layers,

the total number of individual wires is 3n(n + 1) + 1. In the manufacture of stranded

conductors, the consecutive layers of wires are twisted or spiralled in opposite directions so

that layers are bound together.

Types of Conductors

1. Copper. Copper is an ideal material for overhead lines owing to its high electrical

conductivity and greater tensile strength. It is always used in the hard drawn form as stranded

conductor. Although hard drawing decreases the electrical conductivity slightly yet it increases

the tensile strength considerably.

Copper has high current density i.e., the current carrying capacity of copper per unit of X-

sectional area is quite large. This leads to two advantages. Firstly, smaller X-sectional area of

conductor is required and secondly, the area offered by the conductor to wind loads is

reduced. Moreover, this metal is quite homogeneous, durable and has high scrap value. There is

hardly any doubt that copper is an ideal material for transmission and distribution of

electric power. However, due to its higher cost and non-availability, it is rarely used for these

purposes. Now-a-days the trend is to use aluminium in place of copper.

2. Aluminium. Aluminium is cheap and light as compared to copper but it has much

smaller conductivity and tensile strength. The relative comparison of the two materials is briefed

below:

(i) The conductivity of aluminium is 60% that of copper. The smaller conductivity of aluminium

means that for any particular transmission efficiency, the X-sectional area of conductor must be

larger in aluminium than in copper. For the same resistance, the diameter of aluminium

conductor is about 1·26 times the diameter of copper conductor. The increased X-section

of aluminium exposes a greater surface to wind pressure and, therefore, supporting towers must

be designed for greater transverse strength. This often requires the use of higher towers with

consequence of greater sag.

(ii) The specific gravity of aluminium (2·71 gm/cc) is lower than that of copper (8·9

gm/cc).Therefore, an aluminium conductor has almost one-half the weight of equivalent copper

conductor. For this reason, the supporting structures for aluminium need not be made so strong

as that of copper conductor.

(iii) Aluminium conductor being light, is liable to greater swings and hence larger cross-arms are

required.

(iv) Due to lower tensile strength and higher co-efficient of linear expansion of aluminium, the

sag is greater in aluminium conductors. Considering the combined properties of cost,

conductivity, tensile strength, weight etc., aluminium has an edge over copper. Therefore, it is

being widely used as a conductor material. It is particularly profitable to use aluminium

for heavy-current transmission where the conductor size is large and its cost forms a

major proportion of the total cost of complete installation.

3. Steel cored aluminium. Due to low tensile strength, aluminium conductors produce greater

sag. This prohibits their use for larger spans and makes them unsuitable for long

distance transmission. In order to increase the tensile strength, the aluminium conductor is

reinforced with a core of galvanised steel wires. The composite conductor thus obtained is

known as steel cored aluminium and is abbreviated as A.C.S.R. (aluminium conductor steel

reinforced).

Fig 1.1:ACSR Conductor

Steel-cored aluminium conductor consists of central core of galvanized steel wires surrounded by

a number of aluminium strands. Usually, diameter of both steel and aluminium wires is the same.

The X-section of the two metals are generally in the ratio of 1 : 6 but can be modified to 1 : 4 in

order to get more tensile strength for the conductor. Fig. shows steel cored aluminium conductor

having one steel wire surrounded by six wires of aluminium. The result of this

composite conductor is that steel core takes greater percentage of mechanical strength

while aluminium strands carry the bulk of current. The steel cored aluminium conductors

have the following advantages :

(i) The reinforcement with steel increases the tensile strength but at the same time keeps

the composite conductor light. Therefore, steel cored aluminium conductors will produce smaller

sag and hence longer spans can be used.

(ii) Due to smaller sag with steel cored aluminium conductors, towers of smaller heights can be

used.

TRANSMISSION LINE PARAMETER

An electric transmission line has four parameters, namely resistance, inductance,

capacitance and shunt conductance. These four parameters are uniformly distributed along

the whole line. Each line element has its own value, and it is not possible to concentrate

or lumped them at discrete points on the line. For this reason the line parameters are

known as distributed parameter, but can be lumped for the purpose of analysis on

approximate basis. However, the validity of assumption for the analysis on lumped basis may

fail if the line is very long.

Line Inductance:

When an alternating current flows through a conductor, a changing flux is set up which links

the conductor. Due to these flux linkages, the conductor possesses inductance.

Mathematically, inductance is defined as the flux linkages per ampere i.e.

I

L

where ψ = flux linkage in weber-turns

I = current in turns

Which shows that the self inductance of an electric circuit is numerically equal to the

flux linkage of the circuit per unit of current.

Flux Linkages:

As stated earlier, the inductance of a circuit is defined as the flux linkages per unit

current. Therefore, in order to find the inductance of a circuit, the determination of flux

linkages is of primary importance. We shall discuss two important cases of flux linkages.

1. Flux linkages due to a single current carrying conductor. Consider a long straight

cylindrical conductor of radius r metres and carrying a current I amperes (rms) as shown

in Fig.1.2(i). This current will set up magnetic field. The magnetic lines of force will exist inside

the conductor as well as outside the conductor. Both these fluxes will contribute to the

inductance of the conductor.

(i) Flux linkages due to internal flux. Refer to Fig.1.2 (ii) where the X-section of the conductor

is shown magnified for clarity. The magnetic field intensity at a point x metres from the centre is

given by;

x

IH x

x2

As Ir

xI x 2

2

Ir

xH X 22

AT/m

Fig 1.2: Internal flux linkage in a cylindrical conductor

If μ (=μ0μr) is the permeability of the conductor, then flux density at the considered point is given

by

xrx HB 0

2

0

2 r

xI

wb/m2 (μr=1 for non magnetic material)

Now, flux dφ through a cylindrical shell of radial thickness dx and axial length 1 m is given by

dxr

xIdxBd x 2

0

21

This flux links with the current Ix only. Therefore the flux linkages per unit length of the

conductor is

dxr

Ixd

r

xd

4

30

2

2

2

weber-turns

Total flux linkages from centre upto the conductor surface is

r

dxr

xI

0

4

30

int2

80 I

weber-turns per meter length

(ii) Flux linkages due to external flux. Now let us calculate the flux linkages of the

conductor due to external flux. The external flux extends from the surface of the

conductor to infinity. Referring to Fig. 4.5, the field intensity at a distance x metres (from

centre) outside the conductor is given by ;

Fig 1.3: External flux linkage in a conductor

x

IH x

2 AT/m

Flux density,X

IHB Xx

20

0 wb/m2

Now, flux dφ through a cylindrical shell of radial thickness dx and axial length 1 m is given by

dxx

IdxBd x

21 0

The flux dφ links all the current in the conductor once and only once.

dxx

Idd

20 Weber-turns

Total flux linkage of the conductor from surface to infinity

r

ext dxx

I

20 Weber-turns

Over all flux linkage

r

ext dxx

II

2800

int

rx

dxI

4

1

20

weber-turns/m length

Inductance of Single Phase Two Wire Line

A single phase line consists of two parallel conductors which form a rectangular loop of

one turn. When an alternating current flows through such a loop, a changing magnetic flux is set

up. The changing flux links the loop and hence the loop possesses inductance. It may appear

that inductance of a single phase line is negligible because it consists of a loop of one turn and

the flux path is through air of high reluctance. But as the X -sectional area of the loop is very

large, even for a small flux density, the total flux linking the loop is quite large and hence the

line has appreciable inductance.

Fig 1.4: Single phase two wire transmission line

Consider a single phase overhead line consisting of two parallel conductors A and B spaced d

metres apart as shown in Fig. 4.7. Conductors A and B carry the same amount of current (i.e. IA

= IB), but in the opposite direction because one forms the return circuit of the other.

IA+IB=0

In order to find the inductance of conductor A (or conductor B), we shall have to consider the

flux linkages with it. There will be flux linkages with conductor A due to its own current IA and

also due to the mutual inductance effect of current IB in the conductor B. Flux linkages with

conductor A due to its own current

r

A

x

dxI

4

1

20

Flux linkages with conductor A due to current IB

d

B

x

dxI

20

Total flux linkage with the with conductor A is

d

B

r

AA

x

dxI

x

dxI

24

1

200

BA IdIr lnlnlnln

4

1

20

dIrI

IBA

A lnln42

0

rIdI

IAA

A lnln42

0

r

dI

IA

A ln42

0

r

dI A ln4

1

20

Inductance of conductor A, A

AA

IL

r

dln

4

1

20

H/m

r

de lnln102 4

17

][ln1024

1

7

re

d

'

7 ln102r

d H/m

The radius r′ is that of a fictitious conductor assumed to have no internal flux but with the same

inductance as the actual conductor of radius r. The quantity e-1/4= = 0·7788 so that

r′ = r e-1/4= 0·7788 r

The term r′ (= r e-1/4) is called geometric mean radius (GMR) of the conductor.

Loop inductance = 2 LA = 2 × 2 × 10−7 log d/r′ H/m

Note that r′ = 0·7788 r is applicable to only solid round conductor.

Inductance of Three phase Overhead line:

Fig. 1.4 shows the three conductors A, B and C of a 3-phase line carrying currents IA, IB and IC

respectively. Let d1, d2 and d3 be the spacing between the conductors as shown. Let us further

assume that the loads are balanced i.e. IA + IB + IC = 0. Consider the flux linkages with conductor

A. There will be flux linkages with conductor A due to its own current and also due to the mutual

inductance effects of IB and IC.

Fig 1.4 Three phase Overhead line

Flux linkages with conductor A due to its own current

r

A

x

dxI

4

1

20

Flux linkages with conductor A due to current IB

14

1

20

d

B

x

dxI

Flux linkages with conductor A due to current IC

24

1

20

d

C

x

dxI

The total flux linkage with the conductor A is

214

1

24

1

24

1

2000

d

C

d

B

r

AA

x

dxI

x

dxI

x

dxI

As IA+ IB+IC=0

2

0 ln3lnln4

1

2dIdIIr CBAA

(i) Symmetrical Spacing:

If the three conductors A, B and C are placed symmetrically at the corners of an equilateral

triangle of side d, then, d1 = d2 = d3 = d. Under such conditions, the flux linkages with

conductor A become:

dIIIr CBAA ln)(ln

4

1

20

dIIr AAA lnln

4

1

20

r

dI AA ln

4

1

20

Inductance of conductor A,

r

d

IL

A

AA ln

4

1

20

H/m

putting the value of μ0=4π x 10-7 in the above equation

,

7 ln102r

dLA H/m

(ii)Unsymmetrical spacing

When 3-phase line conductors are not equidistant from each other, the conductor spacing is

said to be unsymmetrical. Under such conditions, the flux linkages and inductance of each

phase are not the same. A different inductance in each phase results in unequal voltage drops in

the three phases even if the currents in the conductors are balanced. Therefore, the voltage at the

receiving end will not be the same for all phases. In order that voltage drops are equal in all

conductors, we generally interchange the positions of the conductors at regular intervals along

the line so that each conductor occupies the original position of every other conductor over an

equal distance. Such an exchange of positions is known as transposition. Fig. 1.5 shows

the transposed line. The phase conductors are designated as A, B and C and the

positions occupied are numbered 1, 2 and 3. The effect of transposition is that each conductor

has the same average inductance.

Fig 1.5: Transposition of three phase conductor

Above fig.1.5 shows a 3-phase transposed line having unsymmetrical spacing. Let us assume that

each of the three sections is 1 m in length. Let us further assume balanced conditions i.e., IA + IB

+IC = 0.

The inductance per phase can be

,

33217 ln102

r

dddLA H/m

Electric potential

The electric potential at a point due to a charge is the work done in bringing a unit

positive charge from infinity to that point. The concept of electric potential is extremely

important for the determination of capacitance in a circuit since the latter is defined as the charge

per unit potential. We shall now discuss in detail the electric potential due to some important

conductor arrangements.

Fig 1.6 Potential of single conductor

(i) Potential at a charged single conductor. Consider a long straight cylindrical

conductor A of radius r metres. Let the conductor operate at such a potential (VA) that

charge QA coulombs per metre exists on the conductor. It is desired to find the expression for

VA. The electric intensity E at a distance x from the centre of the conductor in air is given

by

x

QE A

02 volts/m

As x approaches infinity, the value of E approaches zero. Therefore, the potential

difference between conductor A and infinity distant neutral plane is given by:

r

AA

x

dxQV

02

Capacitance of Single Phase Two Wire Line

Consider a single phase overhead transmission line consisting of two parallel conductors

A and B spaced d metres apart in air. Suppose that radius of each conductor is r metres.

Let their respective charge be + Q and − Q coulombs per metre length.

Fig 1.7: Single phase two wire transmission line

The total p.d. between conductor A and neutral “infinite” plane is

dr

Ax

dxQ

x

dxQV

00 22

r

dQln

2 0 Volts

Similarly, p.d. between conductor B and neutral “infinite” plane is

dr

Bx

dxQ

x

dxQV

00 22

r

dQln

2 0

Volts

Both these potentials are w.r.t. the same neutral plane. Since the unlike charges attract each

other, the potential difference between the conductors is

r

dQVV AAB ln

2

22

0

r

dV

QC

AB

AB

ln

0 F/m

Capacitance to neutral: Above equation gives the capacitance between the conductors of a

two wire line. Often it is desired to know the capacitance between one of the conductors and a

neutral point between them. Since potential of the mid-point between the conductors is

zero, the potential difference between each conductor and the ground or neutral is half

the potential difference between the conductors. Thus the capacitance to ground or capacitance

to neutral for the two wire line is twice the line-to-line capacitance.

r

dCCCC ABBNANN

ln

22 0

Capacitance of a 3-Phase Overhead Line

In a 3-phase transmission line, the capacitance of each conductor is considered instead of

capacitance from conductor to conductor. Here, again two cases arise viz., symmetrical

spacing and unsymmetrical spacing.

(i) Symmetrical Spacing. Fig. 1.8 shows the three conductors A, B and C of the 3-phase

overhead transmission line having charges QA, QB and QC per metre length respectively. Let the

Conductors be equidistant (d metres) from each other. We shall find the capacitance from

line conductor to neutral in this symmetrically spaced line. Referring to Fig.1.8 overall potential

difference between conductor A and infinite neutral plane is given by

Fig 1.8 Three phase symmetrically spaced transmission line

r d d

cBAA dx

x

Qdx

x

Qdx

x

QV

000 222

Assuming QA+QB+QC=0

r

dQV A

A ln2 0

Capacitance of conductor A with respect to neutral

r

dV

QC

A

AA

ln

2 0 F/m

Note that this equation is identical to capacitance to neutral for two-wire line. Derived in a

similar manner, the expressions for capacitance are the same for conductors B and C.

(ii) Unsymmetrical spacing. Fig.1.9 shows a 3-phase transposed line having unsymmetrical

spacing. Let us assume balanced conditions i.e. Q A+ QB+ QC = 0.

Fig 1.9: Unsymmetrically spaced transposed three phase line

r

dddQV A

A

3321

ln2

Capacitance from conductor to neutral is

r

dddV

QC

A

AA

3321

0

ln

2

Performance of Transmission Line

The transmission lines are categorized as three types-

1) Short transmission line– the line length is up to 80 km and the operating voltage is < 20 kV.

2) Medium transmission line– the line length is between 80 km to 160 km and the operating

voltage is > 20 kV and < 100kV

3) Long transmission line – the line length is more than 160 km and the operating voltage is >

100 kV

Whatever may be the category of transmission line, the main aim is to transmit power from one

end to another. Like other electrical system, the transmission network also will have some power

loss and voltage drop during transmitting power from sending end to receiving end. Hence,

performance of transmission line can be determined by its efficiency and voltage regulation.

Efficiency of transmission line=Power delivered at receiving end

Power sent from sending end×100%

Power sent from sending end – line losses = Power delivered at receiving end.

Voltage regulation of transmission line is measure of change of receiving end voltage from no-

load to full load condition.

% regulation=no load receiving end voltage-full load receiving end voltage

full load voltage×100%

Every transmission line will have three basic electrical parameters. The conductors of the line

will have electrical resistance, inductance, and capacitance. As the transmission line is a set of

conductors being run from one place to another supported by transmission towers, the parameters

are distributed uniformly along the line.

The electrical power is transmitted over a transmission line with a speed of light that is 3X108 m ⁄

sec. Frequency of the power is 50 Hz. The wave length of the voltage and current of the power

can be determined by the equation given below,

f.λ = v where f is power frequency, & λ is wave length and v is the speed of light.

Therefore λ =�

�=

����

��= 6 × 10�meter = 6000km

Hence the wave length of the transmitting power is quite long compared to the generally used

line length of transmission line.

For this reason, the transmission line, with length less than 160 km, the parameters are assumed

to be lumped and not distributed. Such lines are known as electrically short transmission line.

This electrically short transmission lines are again categorized as short transmission line (length

up to 80 km) and medium transmission line(length between 80 and 160 km). The capacitive

parameter of short transmission line is ignored whereas in case of medium length line the

, capacitance is assumed to be lumped at the middle of the line or half of the capacitance may be

considered to be lumped at each ends of the transmission line. Lines with length more than 160

km, the parameters are considered to be distributed over the line. This is called long transmission

line.

TWO PORT NETWORK

A major section of power system engineering deals in the transmission of electrical power from

one particular place (e.g. generating station) to another like substations or distribution units with

maximum efficiency. So it is of substantial importance for power system engineers to be

thorough with its mathematical modeling. Thus the entire transmission system can be simplified

to a two port network for the sake of easier calculations.

The circuit of a 2 port network is shown in the diagram below. As the name suggests, a 2 port

network consists of an input port PQ and an output port RS. Each port has 2 terminals to connect

itself to the external circuit. Thus it is essentially a 2 port or a 4 terminal circuit, having

Fig 1.10: Representation of Two port network

Supply end voltage=Vs

Supply end current=Is

Given to the input port P Q.

Receiving end voltage=VR

Receiving end current=IR

Given to the output port R S.

Now the ABCD parameters or the transmission line parameters provide the link between the

supply and receiving end voltages and currents, considering the circuit elements to be linear in

nature.

Thus the relation between the sending and receiving end specifications are given using ABCD

parameters by the equations below.

RRs BIAVV (1)

RRS DICVI (2)

Now in order to determine the ABCD parameters of transmission line let us impose the required

circuit conditions in different cases.

ABCD Parameters (When Receiving End is Open Circuited)

The receiving end is open circuited meaning receiving end current IR = 0.

Applying this condition to equation (1) we get,

�� = ��� + �0

�� = ��� + 0

� =��

��(�� = 0)

Thus it implies that on applying open circuit condition to ABCD parameters, we get parameter A

as the ratio of sending end voltage to the open circuit receiving end voltage. Since dimension

wise A is a ratio of voltage to voltage, A is a dimension less parameter.

Applying the same open circuit condition i.e. IR = 0 to equation (2)

D0+CV=Is R

�� = ��� + 0

� =��

��(�� = 0)

Thus its implies that on applying open circuit condition to ABCD parameters of transmission

line, we get parameter C as the ratio of sending end current to the open circuit receiving end

voltage. Since dimension wise C is a ratio of current to voltage, its unit is mho.

Thus C is the open circuit conductance and is given by C = IS ⁄ VR mho.

ABCD Parameters (When Receiving End is Short Circuited)

Receiving end is short circuited meaning receiving end voltage VR = 0

Applying this condition to equation (1) we get,

�� = �0 + �� �

RS BI+0=V

� =��

��(�� = 0)

Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter

B as the ratio of sending end voltage to the short circuit receiving end current. Since dimension

wise B is a ratio of voltage to current, its unit is Ω. Thus B is the short circuit resistance and is

given by

B = VS ⁄ IR Ω.

Applying the same short circuit condition i.e. VR = 0 to equation (2) we get

�� = �0 + �� �

�� = 0 + �� �

� =��

��(�� = 0)

Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter

D as the ratio of sending end current to the short circuit receiving end current. Since dimension

wise D is a ratio of current to current, it’s a dimension less parameter.

Short Transmission Line

The transmission lines which have length less than 80 km are generally referred as short

transmission lines.

For short length, the shunt capacitance of this type of line is neglected and other parameters

like electrical resistance and inductor of these short lines are lumped, hence the equivalent circuit

is represented as given below, Let’s draw the vector diagram for this equivalent circuit, taking

receiving end current Ir as reference. The sending end and receiving end voltages make angle

with that reference receiving end current, of φs and φr, respectively.

Fig.1.11 Representation of a short transmission line

As the shunt capacitance of the line is neglected, hence sending end current and receiving

end current is same, i.e.

Is = IR.

Now if we observe the vector diagram carefully, we will get,

Vs is approximately equal to

VR + IR.R.cosφR + IR.X.sinφR

That means,

Vs ≅ VR + IR.R.cosφR + IR.X.sinφR as it is assumed that φs ≅ φR

As there is no capacitance, during no load condition the current through the line is considered as

zero, hence at no load condition, receiving end voltage is the same as sending end voltage.

As per definition of voltage regulation of power transmission line,

%100%

R

Rs

V

VVregulation

%100sincos

XV

XIRI

R

RRRR

Any electrical network generally has two input terminals and two output terminals. If we

consider any complex electrical network in a black box, it will have two input terminals and

output terminals. This network is called two – port network. Two port model of a network

simplifies the network solving technique. Mathematically a two port network can be solved by 2

by 2 matrix.

A transmission as it is also an electrical network; line can be represented as two port network.

Hence two port network of transmission line can be represented as 2 by 2 matrixes. Here the

concept of ABCD parameters comes. Voltage and currents of the network can represented as,

RRs BIAVV

RRS DICVI

Where A, B, C and D are different constant of the network.

If we put IR = 0 at equation (1), we get,

0

RIR

S

V

VA

Hence, A is the voltage impressed at the sending end per volt at the receiving end when receiving

end is open. It is dimension less.

If we put VR = 0 at equation (1), we get

0

RVR

S

I

VB

That indicates it is impedance of the transmission line when the receiving terminals are short

circuited. This parameter is referred as transfer impedance.

0

RIR

S

V

IC

C is the current in amperes into the sending end per volt on open circuited receiving end. It has

the dimension of admittance.

0

RVR

S

I

ID

D is the current in amperes into the sending end per amp on short circuited receiving end. It is

dimensionless.

Now from equivalent circuit, it is found that,

Vs = VR + IRZ and Is = IR

Comparing these equations with equation (1) and (2) we get,

A = 1, B = Z, C = 0 and D = 1. As we know that the constant A, B, C and D are related for

passive network as,

AD − BC = 1.

Here, A = 1, B = Z, C = 0 and D = 1

⇒ 1.1 − Z.0 = 1

So the values calculated are correct for short transmission line

From above equation (1),

RRs BIAVV

When IR = 0 that means receiving end terminals is open circuited and then from the equation (1),

we get receiving end voltage at no load.

A

VV S

R '

and as per definition of voltage regulation of power transmission line,

Efficiency of Short Transmission Line

The efficiency of short line as simple as efficiency equation of any other electrical equipment,

that means

X100R3Iend receivingat receivedPower

end receivingat receivedPower y%efficienc

2R

R is per phase electrical resistance of the transmission line.

Medium Transmission Line

The transmission line having its effective length more than 80 km but less than 250 km, is

generally referred to as a medium transmission line. Due to the line length being considerably

high, admittance Y of the network does play a role in calculating the effective circuit parameters,

unlike in the case of short transmission lines. For this reason the modeling of a medium length

transmission line is done using lumped shunt admittance along with the lumped impedance in

series to the circuit.

These lumped parameters of a medium length transmission line can be represented using two

different models, namely-

1) Nominal Π representation.

2) Nominal T representation.

Let’s now go into the detailed discussion of these above mentioned models.

Nominal Π Representation of a Medium Transmission Line

In case of a nominal Π representation, the lumped series impedance is placed at the middle of the

circuit where as the shunt admittances are at the ends. As we can see from the diagram of the Π

network below, the total lumped shunt admittance is divided into 2 equal halves, and each half

with value Y ⁄ 2 is placed at both the sending and the receiving end while the entire circuit

impedance is between the two. The shape of the circuit so formed resembles that of a symbol Π,

and for this reason it is known as the nominal Π representation of a medium transmission line. It

is mainly used for determining the general circuit parameters and performing load flow analysis.

Fig.1.12: Nominal Π Representation of a Medium Transmission Line

As we can see here, VS and VR is the supply and receiving end voltages respectively, and

Is is the current flowing through the supply end.

IR is the current flowing through the receiving end of the circuit.

I1 and I3 are the values of currents flowing through the admittances. And

I2 is the current through the impedance Z.

Now applying KCL, at node P, we get

21 III S (1)

Similarly applying KCL, to node Q.

RIII 32 (2)

Now substituting equation (2) to equation (1)

RS IIII 31

RRS IVY

VY

22

(3)

Now by applying KVL to the circuit,

2ZIVV RS

)2

( RRR IY

VZV

RR ZIVY

Z )12

( (4)

Now substituting equation (4) to equation (3), we get

RRRRs IVY

ZIVZYY

I 2

])12

[(2

RR IZY

VZY

Y )12

()14

( (5)

Comparing equation (4) and (5) with the standard ABCD parameter equations we derive the

parameters of a medium transmission line as:

)12

(

)14

(

12

ZY

D

ZY

YC

ZB

ZY

A

Nominal T Representation of a Medium Transmission Line

In the nominal T model of a medium transmission line the lumped shunt admittance is placed in

the middle, while the net series impedance is divided into two equal halves and placed on either

side of the shunt admittance. The circuit so formed resembles the symbol of a capital T, and

hence is known as the nominal T network of a medium length transmission line and is shown in

the diagram below.

Fig.1.13: Nominal T representation of medium transmission line

Here also Vs and VR is the supply and receiving end voltages respectively, and

Is is the current flowing through the supply end.

IR is the current flowing through the receiving end of the circuit.

Let M be a node at the midpoint of the circuit, and the drop at M, be given by VM.

Applying KVL to the above network we get,

4

)(2

2/2/

YZ

VVV

Z

VVYV

Z

VV

RSM

RMM

MS

(6)

And the receiving end current

2/

)(2

Z

VVI RM

R

(7)

Now substituting VM from equation (6) to (7) we get

RRS IZY

ZVZY

V )14

(12

(8)

Now the sending end current is,

RMS IYVI (9)

Substituting the value of VM to equation (9) we get,

RRS IZY

YVI )12

( (10)

Again comparing equation (8) and (10) with the standard ABCD parameter equations, the

parameters of the T network of a medium transmission line are

)12

(

)14

(

)12

(

ZY

D

YC

ZY

ZB

ZY

A

Long Transmission Line

A power transmission line with its effective length of around 250 ms or above is referred to as

a long transmission line. Calculations related to circuit parameters (ABCD parameters) of such

a power transmission is not that simple, as was the case for a short transmission line or medium

transmission line. The reason being that, the effective circuit length in this case is much higher

than what it was for the former models (long and medium line) and, thus ruling out the

approximations considered there like.

Fig.1.14: Long line model

a) Ignoring the shunt admittance of the network, like in a small transmission line model.

b) Considering the circuit impedance and admittance to be lumped and concentrated at a point as

was the case for the medium line model.

Rather, for all practical reasons we should consider the circuit impedance and admittance to be

distributed over the entire circuit length as shown in the figure below.

The calculations of circuit parameters for this reason are going to be slightly more rigorous as we

will see here. For accurate modeling to determine circuit parameters let us consider the circuit of

the long transmission line as shown in the diagram below.

Fig.1.15: Modeling of long transmission line

Here a line of length l > 250km is supplied with a sending end voltage and current of VS and

IS respectively, where as the VR and IR are the values of voltage and current obtained from the

receiving end. Lets us now consider an element of infinitely small length Δx at a distance x from

the receiving end as shown in the figure 1.15 where.

V = value of voltage just before entering the element Δx.

I = value of current just before entering the element Δx.

V+ΔV = voltage leaving the element Δx.

I+ΔI = current leaving the element Δx.

ΔV = voltage drop across element Δx.

zΔx = series impedence of element Δx

yΔx = shunt admittance of element Δx

Where Z = z l and Y = y l are the values of total impedance and admittance of the long

transmission line.

Therefore, the voltage drop across the infinitely small element Δx is given by

xIzV

Now to determine the current ΔI, we apply KCL to node A.

ΔI = (V+ΔV)yΔx = V yΔx + ΔV yΔx (1)

Since the term ΔV yΔx is the product of 2 infinitely small values, we can ignore it for the sake of

easier calculation.

Therefore, we can write dI ⁄ dx = V y (2)

Now derivating both sides of eqn (1) with respect to x,

d2 V ⁄ d x2 = z dI ⁄ dx

Now substituting dI ⁄ dx = V y from equation (2)

d2 V ⁄ d x2 = zyV

or d2 V ⁄ d x2 − zyV = 0 (3)

The solution of the above second order differential equation is given by.

V = A1 ex√yz + A2 e

−x√yz (4)

Derivating equation (4) w.r.to x.

dV/dx = √(yz) A1 ex√yz − √(yz)A2e

−x√yz (5)

Now comparing equation (1) with equation (5)

YZXeAz

y

dX

dVI 1 (6)

Now to go further let us define the characteristic impedance Zc and propagation constant δ of a

long transmission line as

Zc = √(z/y) Ω

δ = √(yz)

Then the voltage and current equation can be expressed in terms of characteristic impedance and

propagation constant as

V = A1 eδx + A2 e

−δx (7)

I = A1/ Zc eδx + A2 / Zc e

−δx (8)

Now at x=0, V= VR and I= IR. Substituting these conditions to equation (7) and (8) respectively.

VR = A1 + A2 (9)

IR = A1/ Zc + A2 / Zc (10)

Solving equation (9) and (10),

We get values of A1 and A2 as,

A1 = (VR + ZCIR) ⁄ 2

And A1 = (VR − ZCIR) ⁄ 2

Now applying another extreme condition at x=l, we have V = VS and I = IS.

Now to determine VS and IS we substitute x by l and put the values of A1 and

A2 in equation (7) and (8) we get

VS = (VR + ZC IR)eδl ⁄ 2 + (VR −ZC IR)e−δl/2 (11)

IS = (VR ⁄ ZC + IR)eδl/2 − (VR / ZC − IR)e−δl/2 (12)

By trigonometric and exponential operators we know

sinh δl = (eδl − e−δl) ⁄ 2

And cosh δl = (eδl + e−δl) ⁄ 2

Therefore, equation(11) and (12) can be re-written as

VS = VRcosh δl + ZC IR sinh δl

IS = (VR sinh δl)/ZC + IRcosh δl

Thus comparing with the general circuit parameters equation, we get the ABCD parameters of a

long transmission line as,

A = cosh δl

B = ZC sinh δl

C = sinh δl ⁄ ZC

D = cosh δl

Skin Effect

The phenomena arising due to unequal distribution of current over the entire cross section of the

conductor being used for long distance power transmission is referred as the skin effect in

transmission lines. Such a phenomena does not have much role to play in case of a very short

line, but with increase in the effective length of the conductors, skin effect increases

considerably. So the modifications in line calculation needs to be done accordingly. The

distribution of current over the entire cross section of the conductor is quite uniform in case of a

DC system. But what we are using in the present era of power system engineering is

predominantly an alternating current system, where the current tends to flow with higher density

through the surface of the conductors (i.e. skin of the conductor), leaving the core deprived of

necessary number of electrons. In fact there even arises a condition when absolutely

no current flows through the core, and concentrating the entire amount on the surface region,

thus resulting in an increase in the effective electrical resistance of the conductor. This particular

trend of an AC transmission system to take the surface path for the flow of current depriving the

core is referred to as the skin effect in transmission lines.

Why Skin Effect Occurs in Transmission Lines?

Having understood the phenomena of skin effect let us now see why this arises in case of an AC

system. To have a clear understanding of that look into the cross sectional view of the conductor

during the flow of alternating current given in the diagram below.

Let us initially consider the solid conductor to be split up into a number of annular filaments

spaced infinitely small distance apart, such that each filament carries an infinitely small fraction

of the total current.

Like if the total current = I

Let us consider the conductor to be split up into n filament carrying current ‘i’ such that I = ni .

Now during the flow of an alternating current, the current carrying filaments lying on the core

has a flux linkage with the entire conductor cross section including the filaments of the surface as

well as those in the core. Whereas the flux set up by the outer filaments is restricted only to the

surface itself and is unable to link with the inner filaments. Thus the flux linkage of the

conductor increases as we move closer towards the core and at the same rate increases

the inductor as it has a direct proportionality relationship with flux linkage. This results in a

larger inductive reactance being induced into the core as compared to the outer sections of the

conductor. The high value of reactance in the inner section results in the current being distributed

in an un-uniform manner and forcing the bulk of the current to flow through the outer surface or

skin giving rise to the phenomena called skin effect in transmission lines.

Fig.1.16: Current distribution in a conductor

Factors Affecting Skin Effect in Transmission Lines

The skin effect in an ac system depends on a number of factors like:-

1) Shape of conductor.

2) Type of material.

3) Diameter of the conductors.

4) Operational frequency.

Proximity Effect:

Proximity means nearness in space or time, so as the name suggests, proximity effect in

transmission lines indicates the effect in one conductor for other neighbouring conductors.

When the alternating current is flowing through a conductor, alternating magnetic flux is

generated surrounding the conductor. This magnetic flux associates with the neighbouring wires

and generates a circulating current (it can be termed as ‘eddy current’ also). This

circulating current increases the resistance of the conductor and push away the flowing current

through the conductor, which causes the crowding effect.

When the gaps between two wires are greater the proximity effect is less and it rises when

the gap reduces. The flux due to central conductor links with right side conductor. In a

two wire system more lines of flux link elements farther apart than the elements nearest to

each other as shown above. Therefore, the inductance of the elements farther apart is more as

compared to the elements near to each other and hence the current density is less in the

elements farther apart than the current density in the element near to each other. As a result the

effective resistance of the conductor is increased due to non uniform distribution of

current. This phenomenon is actually referred as proximity effect. This effect is pronounced in

the case of cables where the distance between the conductor is small whereas proximity

effect in transmission lines in the case of overhead system, with usual spacing is negligibly

small.

Series and shunt compensation:

The demand of active power is expressing Kilo watt (kw) or mega watt (mw). This power should

be supplied from electrical generating station. All the arrangements in electrical pomes system

are done to meet up this basic requirement. Although in alternating power system, reactive power

always comes in to picture. This reactive power is expressed in Kilo VAR or Mega VAR. The

demand of this reactive power is mainly originated from inductive load connected to the system.

These inductive loads are generally electromagnetic circuit of electric motors, electrical

transformers, inductance of transmission and distribution networks, induction furnaces,

fluorescent lightings etc. This reactive power should be properly compensated otherwise, the

ratio of actual power consumed by the load, to the total power i.e. vector sum of active and

reactive power, of the system becomes quite less. This ratio is alternatively known as electrical

power factor, and fewer ratios indicates poor power factor of the system. If the power factor of

the system is poor, the ampere burden of the transmission, distribution network, transformers,

alternators and other equipments connected to the system, becomes high for required active

power. And hence reactive power compensation becomes so important. This is commonly done

by capacitor bank.

Let’s explain in details,

we know that active power is expressed =VIcosθ

where,cosθ is the power factor of the system. Hence, if this power factor has got less valve, the

corresponding current (I) increases for same active power P.

As the current of the system increases, the ohmic loss of the system increases. Ohmic loss

means, generated electrical power is lost as unwanted heat originated in the system. The cross-

section of the conducting parts of the system may also have to be increased for carrying extra

ampere burden, which is also not economical in the commercial point of view. Another major

disadvantage, is poor voltage regulation of the system, which mainly caused due to poor power

factor.

The equipments used to compensate reactive power.

There are mainly two equipments used for this purpose.

(1) Synchronous condensers

(2) Static capacitors or Capacitor Bank

Synchronous condensers, can produce reactive power and the production of reactive power can

be regulated. Due to this regulating advantage, the synchronous condensers are very suitable for

correcting power factor of the system, but this equipment is quite expensive compared to static

capacitors. That is why synchronous condensers, are justified to use only for voltage regulation

of very high voltage transmission system. The regulation in static capacitors can also be achieved

to some extend by split the total capacitor bank in 3 sectors of ratio 1: 2:2. This division enables

the capacitor to run in 1, 2, 1+2=3, 2+2=4, 1+2+2=5 steps. If still further steps are required, the

division may be made in the ratio 1:2:3 or 1:2:4. These divisions make the static capacitor bank

more expensive but still the cost is much lower them synchronous condensers.

It is found that maximum benefit from compensating equipments can be achieved when they are

connected to the individual load side. This is practically and economically possible only by using

small rated capacitors with individual load not by using synchronous condensers.

Static capacitor Bank.

Static capacitor can further be subdivided in to two categories,

(a) Shunt capacitors

(b) Series capacitor

Fig.1.17: Series and Shunt Capacitor bank

These categories are mainly based on the methods of connecting capacitor bank with the system.

Among these two categories, shunt capacitors are more commonly used in the power system of

all voltage levels. There are some specific advantages of using shunt capacitors such as,

a) It reduces line current of the system.

b) It improves voltage level of the load.

c) It also reduces system Losses.

d) It improves power factor of the source current.

e) It reduces load of the alternator.

f) It reduces capital investment per mega watt of the Load.

All the above mentioned benefits come from the fact, that the effect of capacitor reduces reactive

current flowing through the whole system. Shunt capacitor draws almost fixed amount of leading

current which is superimposed on the load current and consequently reduces reactive

components of the load and hence improves the power factor of the system.

series capacitor on the other hand has no control over flow of current. As these are connected in

series with load , the load current always passes through the series capacitor bank. Actually, the

capacitive reactance of series capacitor neutralizes the inductive reactance of the line hence,

reduces, effective reactance of the line. Thereby, voltage regulation of the system is improved.

But series capacitor bank has a major disadvantage. During faulty condition, the voltage across

the capacitor maybe raised up to 15 times more than its rated value. Thus series capacitor must

have sophisticated and elaborate protective equipments. Because of this, use of-series capacitor

is confined in the extra high voltage system only.

MODULE II

Corona

When an alternating potential difference is applied across two conductors whose spacing is large

as compared to their diameters, there is no apparent change in the condition of atmospheric air

surrounding the wires if the applied voltage is low. However, when the applied voltage exceeds a

certain value, called critical disruptive voltage, the conductors are surrounded by a faint violet

glow called corona.

The phenomenon of corona is accompanied by a hissing sound, production of ozone, power loss

and radio interference. Electric power transmission practically deals in the bulk transfer of

electrical energy, from generating stations situated many kilometers away from the main

consumption centers or the cities. For this reason the long distance transmission cables are of

utmost necessity for effective power transfer, which in-evidently results in huge losses across the

system. Minimizing those has been a major challenge for power engineers of late and to do that

one should have a clear understanding of the type and nature of losses. One of them being

the corona effect in power system, which has a predominant role in reducing the efficiency of

EHV(extra high voltage lines) which we are going to concentrate on, in this article. When an

alternating current is made to flow across two conductors of the transmission line whose spacing

is large compared to their diameters, then air surrounding the conductors (composed of ions) is

subjected to dielectric stress. At low values of supply end voltage, nothing really occurs as the

stress is too less to ionize the air outside. But when the potential difference is made to increase

beyond some threshold value of around 30 kV known as the critical disruptive voltage, then the

field strength increases and then the air surrounding it experiences stress high enough to be

dissociated into ions making the atmosphere conducting. This results in electric discharge around

the conductors due to the flow of these ions, giving rise to a faint luminescent glow, along with

the hissing sound accompanied by the liberation of ozone, which is readily identified due to its

characteristic odor. This phenomenon of electrical discharge occurring in transmission line for

high values of voltage is known as the corona effect in power system. If the voltage across the

lines is still increased the glow becomes more and more intense along with hissing noise,

inducing very high power loss into the system which must be accounted for.

Factors Affecting Corona Effect in Power System

As mentioned earlier, the line voltage of the conductor is the main determining factor for corona

in transmission lines, at low values of voltage (lesser than critical disruptive voltage) the stress

on the air is too less to dissociate them, and hence no electrical discharge occurs. Since with

increasing voltage corona effect in a transmission line occurs due to the ionization of

atmospheric air surrounding the cables, it is mainly affected by the conditions of the cable as

well as the physical state of the atmosphere. Let us look into these criterion now with greater

details :

Atmospheric Conditions for Corona in Transmission Lines

It has been physically proven that the voltage gradient for di-electric breakdown of air is directly

proportional to the density of air. Hence in a stormy day, due to continuous air flow the number

of ions present surrounding the conductor is far more than normal, and hence its more likely to

have electrical discharge in transmission lines on such a day, compared to a day with fairly clear

weather. The system has to designed taking those extreme situations into consideration.

Condition of Cables for Corona in Transmission Line.

This particular phenomena depends highly on the conductors and its physical condition. It has an

inverse proportionality relationship with the diameter of the conductors. i.e. with the increase in

diameter, the effect of corona in power system reduces considerably.

Also the presence of dirt or roughness of the conductor reduces the critical breakdown voltage,

making the conductors more prone to corona losses. Hence in most cities and industrial areas

having high pollution, this factor is of reasonable importance to counter the ill effects it has on

the system.

Spacing between Conductors

As already mentioned, for corona to occur effectively the spacing between the lines should be

much higher compared to its diameter, but if the length is increased beyond a certain limit, the

dielectric stress on the air reduces and consequently the effect of corona reduces as well. If the

spacing is made too large then corona for that region of the transmission line might not occur at

all.

Important Terms:

The phenomenon of corona plays an important role in the design of an overhead

transmission line. Therefore, it is profitable to consider the following terms much used in

the analysis of corona effects:

(i) Critical Disruptive Voltage: It is the minimum phase-neutral voltage at which corona

occurs. Consider two conductors of radii r cm and spaced d cm apart. If V is the phase-neutral

potential, then potential gradient at the conductor surface is given by:

r

dr

Vg

ln

Volts/cm

In order that corona is formed, the value of g must be made equal to the breakdown strength of

air. The breakdown strength of air at 76 cm pressure and temperature of 25ºC is 30 kV/cm (max)

or 21·2 kV/cm (r.m.s.) and is denoted by g0. If Vc is the phase-neutral potential required under

these conditions, then,

r

dr

Vg c

ln0

where go = breakdown strength of air at 76 cm of mercury and 25ºC

= 30 kV/cm (max) or 21·2 kV/cm (r.m.s.)

∴ Critical disruptive voltage, r

drgVc ln0

The above expression for disruptive voltage is under standard conditions i.e. at 76 cm of Hg and

25ºC. However, if these conditions vary, the air density also changes, thus altering the value

of go.The value of go is directly proportional to air density. Thus the breakdown strength of air at

a barometric pressure of b cm of mercury and temperature of tºC becomes δg0 where

δ = air density factor = t273

92.3

Under standard conditions, the value of δ = 1.

Critical disruptive voltage, r

drgVc ln0

Correction must also be made for the surface condition of the conductor. This is accounted for

by multiplying the above expression by irregularity factor mo.

Critical disruptive voltage,r

drmgVc ln00 kV/phase

where

mo = 1 for polished conductors

= 0·98 to 0·92 for dirty conductors

= 0·87 to 0·8 for stranded conductors

(ii) Visual critical voltage

It is the minimum phase-neutral voltage at which corona glow appears all along the line

conductors.

It has been seen that in case of parallel conductors, the corona glow does not begin at the

disruptive voltage Vc but at a higher voltage Vv, called visual critical voltage. The phase-

neutral effective value of visual critical voltage is given by the following empirical formula

r

d

rrgmV vv ln)

3.01(0

kV/phase

where mv is another irregularity factor having a value of 1·0 for polished conductors and 0·72 to

0·82 for rough conductors.

(iii) Power loss due to corona Formation of corona is always accompanied by energy

loss which is dissipated in the form of light, heat, sound and chemical action. When

disruptive voltage is exceeded, the power loss due to corona is given by:

25 2510241 cVV

d

rfP

kw/km/phase

Advantages and Disadvantages of Corona

Corona has many advantages and disadvantages. In the correct design of a high voltage

overheadline, a balance should be struck between the advantages and disadvantages.

Below are the Advantages and disadvantages of Corona.

Advantages

Due to corona formation, the air surrounding the conductor becomes conducting and hence

virtual diameter of the conductor is increased. The increased diameter reduces the electro-

static stresses between the conductors.

Corona reduces the effects of transients produced by surges.

Disadvantages

Corona is accompanied by a loss of energy. This affects the transmission efficiency of the

line.

Ozone is produced by corona and may cause corrosion of the conductor due to chemical

action.

The current drawn by the line due to corona is non-sinusoidal and hence non-sinusoidal

Voltage drop occurs in the line. This may cause inductive interference with neighboring

Communication lines.

Methods to reduce Corona Discharge Effect

Corona can be avoided

1. By minimizing the voltage stress and electric field gradient.: This is accomplished by

using utilizing good high voltage design practices, i.e., maximizing the distance between

conductors that have large voltage differentials, using conductors with large radii, and

avoiding parts that have sharp points or sharp edges.

2. Surface Treatments: Corona inception voltage can sometimes be increased by using a

surface treatment, such as a semiconductor layer, high voltage putty or corona dope.

3. Homogenous Insulators: Use a good, homogeneous insulator. Void free solids, such as

properly prepared silicone and epoxy potting materials work well.

4. If you are limited to using air as your insulator, then you are left with geometry as the

critical parameter. Finally, ensure that steps are taken to reduce or eliminate unwanted voltage

transients, which can cause corona to start.

5. Using Bundled Conductors: on our 345 kV lines, we have installed multiple conductors per

phase. This is a common way of increasing the effective diameter of the conductor, which in

turn results in less resistance, which in turn reduces losses.

6. Elimination of sharp points: electric charges tend to form on sharp points; therefore when

practicable we strive to eliminate sharp points on transmission line components.

7. Using Corona rings: On certain new 345 kV structures, we are now installing corona rings.

These rings have smooth round surfaces which are designed to distribute charge across a

wider area, thereby reducing the electric field and the resulting corona discharges.

8. Whether: Corona phenomena much worse in foul weather, high altitude

9. New Conductor: New conductors can lead to poor corona performance for a while.

10. By increasing the spacing between the conductors: Corona Discharge Effect can be

reduced by increasing the clearance spacing between the phases of the transmission lines.

However increase in the phase’s results in heavier metal supports. Cost and Space

requirement increases.

11. By increasing the diameter of the conductor: Diameter of the conductor can be increased to

reduce the corona discharge effect. By using hollow conductors corona discharge effect can

be improved.

Insulators

Electrical Insulator must be used in electrical system to prevent unwanted flow of current to the

earth from its supporting points. The insulator plays a vital role in electrical system. Electrical

Insulator is a very high resistive path through which practically no current can flow. In

transmission and distribution system, the overhead conductors are generally supported by

supporting towers or poles. The towers and poles both are properly grounded. So there must

be insulator between tower or pole body and current carrying conductors to prevent the flow

of current from conductor to earth through the grounded supporting towers or poles.

Insulating Material

The main cause of failure of overhead line insulator, is flash over, occurs in between line and

earth during abnormal over voltage in the system. During this flash over, the huge heat produced

by arcing, causes puncher in insulator body. Viewing this phenomenon the materials used for

electrical insulator, has to posses some specific properties.

Properties of Insulating Material

The materials generally used for insulating purpose is called insulating material. For successful

utilization, this material should have some specific properties as listed below-

1. It must be mechanically strong enough to carry tension and weight of conductors.

2. It must have very high dielectric strength to withstand the voltage stresses in High Voltage

system.

3. It must possesses high Insulation Resistance to prevent leakage current to the earth.

4. The insulating material must be free from unwanted impurities.

5. It should not be porous.

6. There must not be any entrance on the surface of electrical insulator so that the moisture or

gases can enter in it.

7. There physical as well as electrical properties must be less affected by changing temperature.

There are mainly three types of insulator used as overhead insulator likewise

1. Pin Insulator

2. Suspension Insulator

3. Strain Insulator

In addition to that there are other two types of electrical insulator available mainly for

low voltage application i.e. Stray Insulator and Shackle Insulator.

Pin Insulator

Pin Insulator is earliest developed overhead insulator, but still popularly used in power

network up to 33KV system. Pin type insulator can be one part, two parts or three parts type,

depending upon application voltage. In 11KV system we generally use one part type insulator

where whole pin insulator is one piece of properly shaped porcelain or glass. As the leakage path

of insulator is through its surface, it is desirable to increase the vertical length of the insulator

surface area for lengthening leakage path. In order to obtain lengthy leakage path, one, tower or

more rain sheds or petticoats are provided on the insulator body. In addition to that rain shed or

petticoats on an insulator serve another purpose. These rain sheds or petticoats are so designed,

that during raining the outer surface of the rain shed becomes wet but the inner surface remains

dry and non-conductive. So there will be discontinuations of conducting path through the wet pin

insulator surface.

Fig 2.1- Pin Insulator

In higher voltage like 33KV and 66KV manufacturing of one part porcelain pin insulator

becomes difficult. Because in higher voltage, the thickness of the insulator become more and a

quite thick single piece porcelain insulator cannot manufactured practically. In this case we use

multiple part pin insulator, where a number of properly designed porcelain shells are fixed

together by Portland cement to form one complete insulator unit. For 33KV tow parts and for

66KV three parts pin insulator are generally used.

Designing Consideration of Electrical Insulator

The live conductor attached to the top of the pin insulator is at a potential and bottom of the

insulator fixed to supporting structure of earth potential. The insulator has to withstand the

potential stresses between conductor and earth. The shortest distance between conductor and

earth, surrounding the insulator body, along which electrical discharge may take place through

air, is known as flash over distance.

1. When insulator is wet, its outer surface becomes almost conducting. Hence the flash over

distance of insulator is decreased. The design of an electrical insulator should be such that the

decrease of flash over distance is minimum when the insulator is wet. That is why the upper most

petticoat of a pin insulator has umbrella type designed so that it can protect, the rest lower part of

the insulator from rain. The upper surface of top most petticoat is inclined as less as possible to

maintain maximum flash over voltage during raining.

2. To keep the inner side of the insulator dry, the rain sheds are made in order that these rain

sheds should not disturb the voltage distribution they are so designed that their subsurface at

right angle to the electromagnetic lines of force.

Suspension Insulator

In higher voltage, beyond 33KV, it becomes uneconomical to use pin insulator because size,

weight of the insulator become more. Handling and replacing bigger size single unit insulator are

quite difficult task. For overcoming these difficulties, suspension insulator was developed.

In suspension insulator numbers of insulators are connected in series to form a string and the

line conductor is carried by the bottom most insulator. Each insulator of a suspension string is

called disc insulator because of their disc like shape.

Advantages of Suspension Insulator

(i) Suspension type insulators are cheaper than pin type insulators for voltages beyond 33 kV.

(ii) Each unit or disc of suspension type insulator is designed for low voltage,usually 11 kV.

Depending upon the working voltage, the desired number of discs can be connected in series.

(iii) If any one disc is damaged, the whole string does not become useless because the damaged

disc can be replaced by the sound one.

(iv) The suspension arrangement provides greater flexibility to the line. The connection at

the cross arm is such that insulator string is free to swing in any direction and can

take up the position where mechanical stresses are minimum.

(v) In case of increased demand on the transmission line, it is found more satisfactory to supply

the greater demand by raising the line voltage than to provide another set of

conductors. The additional insulation required for the raised voltage can be easily

obtained in the suspension arrangement by adding the desired number of discs.

(vi) The suspension type insulators are generally used with steel towers. As the conductors run

below the earthed cross-arm of the tower, therefore, this arrangement provides partial

protection from lightning.

Disadvantages of Suspension Insulator

1. Suspension insulator string costlier than pin and post type insulator.

2. Suspension string requires more height of supporting structure than that for pin or post

insulator to maintain same ground clearance of current conductor.

3. The amplitude of free swing of conductors is larger in suspension insulator system, hence,

more spacing between conductors should be provided.

Strain Insulator

When suspension string is used to sustain extraordinary tensile load of conductor it is referred

as string insulator. When there is a dead end or there is a sharp corner in transmission line, the

line has to sustain a great tensile load of conductor or strain. A strain insulator must have

considerable mechanical strength as well as the necessary electrical insulating properties.

Fig 2.2- Strain Insulator

Shackle Insulator or Spool Insulator

The shackle insulator or spool insulator is usually used in low voltage distribution network. It

can be used both in horizontal and vertical position. The use of such insulator has decreased

recently after increasing the using of underground cable for distribution purpose. The tapered

hole of the spool insulator distributes the load more evenly and minimizes the possibility of

breakage when heavily loaded. The conductor in the groove of shackle insulator is fixed with

the help of soft binding wire.

POTENTIAL DISTRIBUTION OVERA STRING OF SUSPENSION INSULATORS:

A string of suspension insulators consists of a number of porcelain discs connected in

series through metallic links. Fig. 2.3(i) shows 3-disc string of suspension insulators. The

porcelain portion of each disc is in between two metal links. Therefore, each disc forms a

capacitor C as shown in Fig.2.3(ii). This is known as mutual capacitance or self-capacitance.

If there were mutual capacitance alone, then charging current would have been the same through

all the discs and consequently voltage across each unit would have been the same i.e., V/3 as

shown in Fig. 2.3(ii). However, in actual practice, capacitance also exists between metal fitting

of each disc and tower or earth. This is known as shunt capacitance C1. Due to shunt

capacitance, charging current is not the same through all the discs of the string [See Fig

2.3(iii)]. Therefore, voltage across each disc will be different. Obviously, the disc nearest to

the line conductor will have the maximum voltage. Thus referring to Fig 2.3(iii), V3 will be

much more than V2 or V1.

The following points may be noted regarding the potential distribution over a string of

suspension insulators:

(i) The voltage impressed on a string of suspension insulators does not distribute itself

uniformly across the individual discs due to the presence of shunt capacitance.

(ii) The disc nearest to the conductor has maximum voltage across it. As we move

towards the cross-arm, the voltage across each disc goes on decreasing.

(iii) The unit nearest to the conductor is under maximum electrical stress and is likely to be

punctured. Therefore, means must be provided to equalize the potential across each unit.

(iv)The presence of stray capacitance causes unequal potential distribution over the string. The

end unit of the string (which is the closest to the line) takes maximum potential difference and

the upper units have a gradually decreased potential difference until the uppermost unit which

has the lowest potential difference. The next proof illustrates this concept.

Fig 2.3- Suspension Insulator string

String Efficiency:

As stated above, the voltage applied across the string of suspension insulators is not

uniformly distributed across various units or discs. The disc nearest to the conductor has much

higher potential than the other discs. This unequal potential distribution is undesirable and is

usually expressed in terms of string efficiency.

The ratio of voltage across the whole string to the product of number of discs and the voltage

across the disc nearest to the conductor is known as string efficiency i.e.

conductor near to disc across Voltagen

string theacross VoltageEfficiency String

Where n is the no. of discs in the string.

String efficiency is an important consideration since it decides the potential distribution along the

string. The greater the string efficiency, the more uniform is the voltage distribution. Thus 100%

string efficiency is an ideal case for which the voltage across each disc will be exactly the same.

Although it is impossible to achieve 100% string efficiency, yet efforts should be made

to improve it as close to this value as possible.

Mathematical expression. Fig. 2.3(iii) shows the equivalent circuit for a 3-disc string. Let us

suppose that self capacitance of each disc is C. Let us further assume that shunt capacitance C1 is

some fraction K of self capacitance i.e., C1 = KC. Starting from the cross-arm or tower, the

voltage across each unit is V1,V2 and V3 respectively as shown.

Applying kirchoff’s current law to node A

112 iII

1112 CVCVCV

KCVCVCV 112

)1(12 KVV

Applying kirchoff’s current law to node B

223 iII

12123 )( CVVCVCV

KCVVCVCV )( 2123

)1(213 KVKVV

)31( 213 KKVV

1003

%3

V

Vciencystringeffi

The following points may be noted from the above mathematical analysis:

(i) If K = 0·2 (Say), then we get, V2 = 1·2 V1 and V3 = 1·64 V1. This clearly shows that disc

nearest to the conductor has maximum voltage across it; the voltage across other discs decreasing

progressively as the cross-arm in approached.

(ii) The greater the value of K (= C1/C), the more non-uniform is the potential across the discs

and lesser is the string efficiency.

(iii) The inequality in voltage distribution increases with the increase of number of discs in

the string. Therefore, shorter string has more efficiency than the larger one

String Efficiency and methods to improve String Efficiency

The ratio of voltage across the whole string to the product of number of discs and the voltage

across the disc nearest to the conductor is known as string efficiency i.e.,

conductor near to disc across Voltagen

string theacross VoltageEfficiency String

where n = number of discs in the string.

String efficiency is an important consideration since it decides the potential distribution along the

string. The greater the string efficiency, the more uniform is the voltage distribution. Thus 100%

string efficiency is an ideal case for which the voltage across each disc will be exactly the same.

Although it is impossible to achieve 100% string efficiency, yet efforts should be made to

improve it

as close to this value as possible.

Methods of Improving String Efficiency

The maximum voltage appears across the insulator nearest to the line conductor and decreases

equalise the potential across the various units of the string i.e. to improve the string efficiency

progressively as the cross arm is approached. If the insulation of the highest stressed insulator

(i.e. nearest to conductor) breaks down or flash over takes place, the breakdown of other units

will take place in succession.

The various methods for improving the string efficiency are:

1. By using longer cross-arms. The value of string efficiency depends upon the value of K i.e.,

ratio of shunt capacitance to mutual capacitance. The lesser the value of K, the greater is the

string efficiency and more uniform is the voltage distribution. The value of K

can be decreased by reducing the shunt capacitance. In order to reduce shunt capacitance, the

distance of conductor from tower must be increased i.e., longer cross-arms should be used.

However, limitations of cost and strength of tower do not allow the use of very long cross-

arms. In practice, K = 0·1 is the limit that can be achieved by this method.

2. By grading the insulators. In this method, insulators of different dimensions are so chosen

that each has a different capacitance. The insulators are capacitance graded i.e. they are

assembled in the string in such a way that the top unit has the minimum capacitance,

increasing progressively as the bottom unit (i.e., nearest to conductor) is reached. Since

voltage is inversely proportional to capacitance, this method tends to equalise the potential

distribution across the units in the string. This method has the disadvantage that a large

number of different-sized insulators are required. However, good results can be obtained by

using standard insulators for most of the string and larger units for that near to the line

conductor.

3. By using a guard ring. The potential across each unit in a string can be equalised by using a

guard ring which is a metal ring electrically connected to the conductor and surrounding the

bottom insulator. The guard ring introduces capacitance between metal fittings and the line

conductor. The guard ring is contoured in such a way that shunt capacitance currents i1, i2

etc. are equal to metal fitting line capacitance currents i′1, i′2 etc. The result is that same

charging current I flows through each unit of string. Consequently, there will be uniform

potential distribution across the units.

Conductor Material

The most common conductor in use for transmission today is aluminum conductor steel

reinforced (ACSR). Also seeing much use is all-aluminum-alloy conductor (AAAC). Aluminum

is used because it has about half the weight of a comparable resistance copper cable (though

larger diameter due to lower fundamental conductivity), as well as being cheaper. Copper was

more popular in the past and is still in use, especially at lower voltages and for grounding. Bare

copper conductors are light green.

While larger conductors may lose less energy due to lower electrical resistance, they are more

costly than smaller conductors. An optimization rule called Kelvin's Law states that the optimum

size of conductor for a line is found when the cost of the energy wasted in the conductor is equal

to the annual interest paid on that portion of the line construction cost due to the size of the

conductors. The optimization problem is made more complex by additional factors such as

varying annual load, varying cost of installation, and the discrete sizes of cable that are

commonly made.

Since a conductor is a flexible object with uniform weight per unit length, the geometric shape of

a conductor strung on towers approximates that of a catenary. The sag of the conductor (vertical

distance between the highest and lowest point of the curve) varies depending on the temperature

and additional load such as ice cover. A minimum overhead clearance must be maintained for

safety. Since the temperature of the conductor increases with increasing heat produced by the

current through it, it is sometimes possible to increase the power handling capacity (uprate) by

changing the conductors for a type with a lower coefficient of thermal expansion or a higher

allowable operating temperature.

BUNDLE CONDUCTORS

For higher amounts of current, bundle conductors are used for several reasons. Due to the skin

effect, for larger conductors, the current capacity does not increase proportional to the cross-

sectional area; instead, it is only with the linear dimension. Also, reactance decreases only slowly

with size. But the cost and weight do increase with area. Due to this, several conductors in

parallel become more economical.

Bundle conductors consist of several parallel cables connected at intervals by spacers, often in a

cylindrical configuration. The optimum number of conductors depends on the current rating, but

typically higher-voltage lines also have higher current. There is also some advantage due to

lower corona loss. American Electric Power is building 765 kV lines using six conductors per

phase in a bundle. Spacers must resist the forces due to wind, and magnetic forces during a short-

circuit.

Advantages

At extra high voltage, the electric field gradient at the surface of a single conductor is high

enough to ionize air, which loses power and generates both audible noise

and interference with communication systems. The field surrounding a bundle of conductors is

similar to the field that would surround a single, very large conductor—this produces lower

gradients which mitigates issues associated with high field strength. When transmitting

alternating current, bundle conductors also avoid the reduction in capacity of a single large

conductor due to the skin effect. A bundle conductor also has lower reactance, compared to a

single conductor. Additionally, bundled conductors cool themselves more efficiently due to the

increased surface area of the conductors, further reducing line losses.

MECHANICAL DESIGN OF TRANSMISSION LINE

Sag in Overhead Transmission Line:

While erecting an overhead line, it is very important that conductors are under safe tension.

If the conductors are too much stretched between supports in a bid to save conductor material,

the stress in the conductor may reach unsafe value and in certain cases the conductor may break

due to excessive tension. In order to permit safe tension in the conductors, they are not fully

stretched but are allowed to have a dip or sag. The difference in level between points of supports

and the lowest point on the conductor is called sag. Following Fig. 8.1 shows a conductor

suspended between two equal level supports A and B. The conductor is not fully stretched but is

allowed to have a dip. The lowest point on the conductor is O and the sag is S.

Fig 2.4- Sag in a transmission line

The following points may be noted:

(i) When the conductor is suspended between two supports at the same level, it takes the shape

of catenary. However, if the sag is very small compared with the span, then sag-span curve is

like a parabola.

(ii) The tension at any point on the conductor acts tangentially. Thus tension T0 at the lowest

Point O acts horizontally as shown in Fig. (ii).

(iii) The horizontal component of tension is constant throughout the length of the wire.

(iv) The tension at supports is approximately equal to the horizontal tension acting at any point

on the wire. Thus if T is the tension at the support B, then T = T0.

Conductor sag and tension. This is an important consideration in the mechanical design of

overhead lines. The conductor sag should be kept to a minimum in order to reduce the conductor

material required and to avoid extra pole height for sufficient clearance above ground level. It is

also desirable that tension in the conductor should be low to avoid the mechanical failure

of conductor and to permit the use of less strong supports. However, low conductor tension

and minimum sag are not possible. It is because low sag means a tight wire and high

tension, whereas a low tension means a loose wire and increased sag. Therefore, in actual

practice, a compromise in made between the two.

Calculation of Sag: In an overhead line, the sag should be so adjusted that tension in the

conductors is within safe limits. The tension is governed by conductor weight, effects of wind,

ice loading and temperature variations. It is a standard practice to keep conductor tension less

than 50% of its ultimate tensile strength i.e., minimum factor of safety in respect of conductor

tension should be 2. We shall now calculate sag and tension of a conductor when (i) supports are

at equal levels and (ii) supports are at unequal levels.

When supports are at equal levels. Consider a conductor between two equilevel supports A

and B with O as the lowest point as shown in Fig.2.5. It can be proved that lowest point will be at

a conductor between two equilevel supports A and B with O as the lowest point as shown in

Fig. 2.5. It can be proved that lowest point will be at the mid-span.

Fig 2.5- Sag Clculation

A conductor between two equilevel supports A and B with O as the lowest point as shown in Fig.

2. It can be proved that lowest point will be at the mid-span.

Let l = Length of span

w = Weight per unit length of conductor

T = Tension in the conductor.

Consider a point P on the conductor. Taking the lowest point O as the origin, let the co-ordinates

of point P be x and y. Assuming that the curvature is so small that curved length is equal to its

horizontal projection (i.e., OP = x), the two forces acting on the portion OP of the conductor are :

(a) The weight wx of conductor acting at a distance x/2 from O.

(b) The tension T acting at O.

Equating the moments of above two forces about point O, we get,

2

xwxTy

T

wxy

2

2

The maximum dip (sag) is represented by the value of y at either of the supports A & B.

At supports A 2

lx and y=s

8T

wlS Sag

2

Effect of wind and ice loading- The above formulae for sag are true only in still air and at

normal temperature when the conductor is acted by its weight only. However, in actual practice,

a conductor may have ice coating and simultaneously subjected to wind pressure. The weight of

ice acts vertically downwards i.e., in the same direction as the weight of conductor. The force

due to the wind is assumed to act horizontally i.e., at right angle to the projected surface

of the conductor. Hence, the total force on the conductor is the vector sum of horizontal and

vertical forces as shown in

Fig 2.6- Effect of Ice and Wind

Total weight of conductor per unit length is

22)( wit wwww

Where w = weight of conductor per unit length

= conductor material density × volume per unit length

wi = weight of ice per unit length

= density of ice * volume of ice per unit length

= density of ice x 124

22 dtd

ww = wind force per unit length

= wind pressure per unit area × projected area per unit length

= wind pressure x 12 td

Vibration Damper

Aeolian vibrations mostly occur at steady wind velocities from 1 to 7 m/s. With increasing wind

turbulences the wind power input to the conductor will decrease. The intensity to induce

vibrations depends on several parameters such as type of conductors and clamps, tension, span

length, topography in the surrounding, height and direction of the line as well as the frequency of

occurrence of the vibration induced wind streams.

In the wake of wind power plants (up to 3 x diameter of the rotor behind the plant) the wind

velocity will be reduced up to 0,5 of the velocity of the free wind stream, so that lower

wind velocities could be expected more frequently here. That’s why the probability of a higher

stresses for the conductors caused by wind-induced vibrations will be greater than without wind

power plants.

On the other hand the intensity of turbulences will increase which will hinder the arising

of vibrations. The both important parameters for inducing vibrations, wind velocity and

turbulence intensity, depends on the distance to the rotor and the height of it.

The investigations showed an increasing of damage probability on OHTL due to the wake

of wind power plants of the factor 2,5 to 3,5 between one and three rotor diameters behind the

plant which will cause an equivalent decreasing of lifetime of conductors and earth wires.

Stringing chart: For use in the field work of stringing the conductors, temperature-sag and

temperature tension charts are plotted for the given conductor and loading conditions. Such

curves are called stringing charts. These charts are very helpful while stringing overhead lines.

Fig 2.7- Stringing Chart

Sag Template: A Sag Template is a very important tool with the help of which the

position of towers on the Profile is decided so that they conform to the limitations of vertical and

wind loads on any particular tower, and minimum clearances, as per I.E. Rules, required to be

maintained between the line conductor to ground, telephone lines, buildings, streets,

navigable canals, power lines, or any other object coming under or near the line.

Fig 2.8- Sag Template

A Sag Template is specific for the particular line voltage, the conductor used and the applicable

design conditions. Therefore, the correct applicable Sag Template should be used. A Sag

Template consists of a set of parabolic curves drawn on a transparent celluloid or a crylic clear

sheet duly cut in over the maximum conductor sag curve to allow the conductor curve to

be drawn and the lowest points of the conductor sag to be marked on the profile when the profile

is placed underneath it.

The set of curves in the sag template consists of:

a) Cold or Uplift Curve’ showing sag of conductor at minimum temperature (minus 2.5ºC) and

still wind.

b) Hot or Maximum Sag Curve’ showing maximum sag of conductor at maximum

temperature and still wind including sag tolerances allowed (normally 4%), if any, and under

maximum ice condition wherever applicable.

c) Ground Clearance Curve’ which is drawn parallel to the ‘Hot or Maximum Sag

Curve’ and at a distance equal to the specified minimum ground clearance for the

relevant voltage.

d) ‘Tower Footing Curve’ which is drawn parallel to the ‘Ground Clearance Curve’ and

separated by a minimum distance equal to the maximum sag at the basic design span.

INSULATED CABLES

Electric power can be transmitted or distributed either by overhead system or by

underground cables. The underground cables have several advantages such as less liable

to damage through storms or lightning, low maintenance cost, less chance of faults, smaller

voltage drop and better general appearance. However, their major drawback is that they have

greater installation cost and introduce insulation problems at high voltages compared with the

equivalent overhead system. For this reason, underground cables are employed where it is

impracticable to use overhead lines. Such locations may be thickly populated areas where

municipal authorities prohibit overhead lines for reasons of safety, or around plants and

substations or where maintenance conditions do not permit the use of overhead construction.

The chief use of underground cables for many years has been for distribution of electric power in

congested urban areas at comparatively low or moderate voltages. However, recent

improvements in the design and manufacture have led to the development of cables suitable for

use at high voltages. This has made it possible to employ underground cables for transmission of

electric power for short or moderate distances. In this chapter, we shall focus our attention on the

various aspects of underground cables and their increasing use in power system.

Underground Cables:-An underground cable essentially consists of one or more conductors

covered with suitable insulation and surrounded by a protecting cover. Although several types of

cables are available, the type of cable to be used will depend upon the working voltage

and service requirements. In general, a cable must fulfill the following necessary requirements:

(i) The conductor used in cables should be tinned stranded copper or aluminum of high

conductivity. Stranding is done so that conductor may become flexible and carry more current.

(ii) The conductor size should be such that the cable carries the desired load current without

overheating and causes voltage drop within permissible limits.

(iii) The cable must have proper thickness of insulation in order to give high degree of safety and

reliability at the voltage for which it is designed.

(iv) The cable must be provided with suitable mechanical protection so that it may withstand the

rough use in laying it.

(v) The materials used in the manufacture of cables should be such that there is

complete chemical and physical stability throughout.

Construction of Cables:-Figure shows the general construction of a 3-conductor cable. The

various parts are

Fig 2.9- Cable

Cores or Conductors. A cable may have one or more than one core (conductor)

depending upon the type of service for which it is intended. For instance, the 3 conductor

cable shown in Figure is used for 3-phase service. The conductors are made of tinned copper or

aluminum and are usually stranded in order to provide flexibility

to the cable.

(ii) Insulation. Each core or conductor is provided with a suitable thickness of insulation, the

thickness of layer depending upon the voltage to be withstood by the cable. The

commonly used materials for insulation are impregnated paper, varnished cambric or rubber

mineral compound.

(iii) Metallic sheath. In order to protect the cable from moisture, gases or other damaging

liquids (acids or alkalies) in the soil and atmosphere, a metallic sheath of lead or

aluminum is provided over the insulation as shown in Fig.

(iv) Bedding. Over the metallic sheath is applied a layer of bedding which consists of a

fibrous material like jute or hessian tape. The purpose of bedding is to protect the metallic

sheath against corrosion and from mechanical injury due to armouring.

(v) Armouring. Over the bedding, armouring is provided which consists of one or two

layers of galvanized steel wire or steel tape. Its purpose is to protect the cable from

mechanical injury while laying it and during the course of handling. Armouring may not be done

in the case of some cables.

(vi) Serving. In order to protect armouring from atmospheric conditions, a layer of fibrous

material (like jute) similar to bedding is provided over the armouring. This is known as serving.

It may not be out of place to mention here that bedding, armouring and serving are only applied

to the cables for the protection of conductor insulation and to protect the metallic sheath

from mechanical injury.

Insulating Materials for Cables:-The satisfactory operation of a cable depends to a great

extent upon the characteristics of insulation used. Therefore, the proper choice of insulating

material for cables is of considerable importance. In general, the insulating materials used in

cables should have the following properties:

(i) High insulation resistance to avoid leakage current.

(ii) High dielectric strength to avoid electrical breakdown of the cable.

(iii) High mechanical strength to withstand the mechanical handling of cables.

(iv)Non-hygroscopic i.e., it should not absorb moisture from air or soil. The moisture tends to

decrease the insulation resistance and hastens the breakdown of the cable. In case the insulating

material is hygroscopic, it must be enclosed in a waterproof covering like lead sheath.

(v) Non-inflammable.

(vi) Low cost so as to make the underground system a viable proposition.

(vii) Unaffected by acids and alkalies to avoid any chemical action. No one insulating material

possesses all the above mentioned properties. Therefore, the type of insulating material to be

used depends upon the purpose for which the cable is required and the quality of insulation to be

aimed at.

The principal insulating materials used in cables are rubber, vulcanized rubber, impregnated

paper and polyvinyl chloride.

1. Rubber: Rubber may be obtained from milky sap of tropical trees or it may be produced from

oil products. It has relative permittivity varying between 2 and 3, dielectric strength is about 30

kV/mm and resistivity of insulation is 1017 cm. Although pure rubber has reasonably high

insulating properties, it suffers from some major drawbacks viz., readily absorbs moisture,

maximum safe temperature is low (about 38ºC), soft and liable to damage due to rough handling

and ages when exposed to light. Therefore, pure rubber cannot be used as an insulating material.

2. Vulcanised India Rubber (V.I.R.). It is prepared by mixing pure rubber with mineral matter

such as zinc oxide, red lead etc., and 3 to 5% of sulphur. The compound so formed is rolled into

thin sheets and cut into strips. The rubber compound is then applied to the conductor and

is heated to a temperature of about 150ºC. The whole process is called vulcanisation and

the product obtained is known as vulcanised India rubber. Vulcanised India rubber has

greater mechanical strength, durability and wear resistant property than pure rubber. Its main

drawback is that sulphur reacts very quickly with copper and for this reason, cables using VIR

insulation have tinned copper conductor. The VIR insulation is generally used for low and

moderate voltage cables.

3. Impregnated paper. It consists of chemically pulped paper made from wood chippings and

impregnated with some compound such as paraffinic or naphthenic material. This type of

insulation has almost superseded the rubber insulation. It is because it has the advantages of low

cost, low capacitance, high dielectric strength and high insulation resistance. The only

disadvantage is that paper is hygroscopic and even if it is impregnated with suitable

compound, it absorbs moisture and thus lowers the insulation resistance of the cable.

4. Polyvinyl chloride (PVC). This insulating material is a synthetic compound. It is obtained

from the polymerization of acetylene and is in the form of white powder. For obtaining

this material as a cable insulation, it is compounded with certain materials known as

plasticizers which are liquids with high boiling point. The plasticizer forms a gell and

renders the material plastic over the desired range of temperature. Polyvinyl chloride has

high insulation resistance, good dielectric strength and mechanical toughness over a wide

range of temperatures. It is inert to oxygen and almost inert to many alkalies and acids.

Therefore, this type of insulation is preferred over VIR in extreme environmental conditions such

as in cement factory or chemical factory. As the mechanical properties (i.e., elasticity etc.) of

PVC are not so good as those of rubber, therefore, PVC insulated cables are generally used for

low and medium domestic lights and power installations.

Classification of Cables: -Cables for underground service may be classified in two ways

according to (i) the type of insulating material used in their manufacture (ii) the voltage

for which they are manufactured. However, the latter method of classification is generally

preferred, according to which cables can be divided into the following groups:

Fig 2.10- Cross section of Cables

(i) Low-tension (L.T.) cables — upto 1000 V

(ii) High-tension (H.T.) cables — upto 11,000 V

(iii) Super-tension (S.T.) cables — from 22 kV to 33 kV

(iv)Extra high-tension (E.H.T.) cables — from 33 kV to 66 kV

(iv) Extra super voltage cables — beyond 132 kV

A cable may have one or more than one core depending upon the type of service for which it is

intended. It may be (i) single-core (ii) two-core (iii) three-core (iv) four-core etc. For a 3-phase

service, either 3-single-core cables or three-core cable can be used depending upon the operating

voltage and load demand. Fig. 11.2 shows the constructional details of a single-core low tension

cable. The cable has ordinary construction because the stresses developed in the cable for low

voltages (up to 6600 V) are generally small. It consists of one circular core of tinned stranded

copper (or aluminium) insulated by layers of impregnated paper. The insulation is surrounded by

a lead sheath which prevents the entry of moisture into the inner parts. In order to protect the

lead sheath from corrosion, an overall serving of compounded fibrous material (jute etc.)

is provided. Single-core cables are not usually armoured in order to avoid excessive sheath

losses. The principal advantages of single-core cables are simple construction and availability of

larger copper section.

Cable for 3-phase

In practice, underground cables are generally required to deliver 3-phase power. For the purpose,

either three-core cable or three single core cables may be used. For voltages upto 66 kV, 3-core

cable (i.e., multi-core construction) is preferred due to economic reasons. However, for voltages

beyond 66 kV, 3-core-cables become too large and unwieldy and, therefore, single-core cables

are used. The following types of cables are generally used for 3-phase service:

1. Belted cables — upto 11 kV

2. Screened cables — from 22 kV to 66 kV

3. Pressure cables — beyond 66 kV

Dielectric Stress in Cable

Fig 2.11- Dielectric Stress in Cable

Under operating conditions, the insulation of a cable is subjected to electrostatic forces. This is

known as dielectric stress. The dielectric stress at any point in a cable is in fact the

potential gradient (or electric intensity) at that point. Consider a single core cable with core

diameter d and internal sheath diameter D. The electric intensity at a point x metres from the

centre of the cable is

x

QE

r

x 02

volts/m

By definition, electric intensity is equal to potential gradient. Therefore, potential gradient g at a

point x meters from the Centre of cable is

xEg

x

Eg

r 02 volts/m

Potential difference V between conductor and sheath is

d

DQV

r

ln2 0

volts

d

D

VQ r

ln

2 0

Substituting the value of Q, we get

d

Dx

Vg

ln

volts/m

It is clear from the above equation that potential gradient varies inversely as the distance x.

Therefore, potential gradient will be maximum when x is minimum i.e., when x = d/2 or at the

surface of the conductor. On the other hand, potential gradient will be minimum at x = D/2 or at

sheath surface.

Maximum potential gradient is

d

Dd

Vg

ln

2max volts/m

Minimum potential gradient is

d

DD

Vg

ln

2min volts/m

d

D

g

g

min

max

The variation of stress in the dielectric is shown in Fig.14. It is clear that dielectric stress is

maximum at the conductor surface and its value goes on decreasing as we move away from the

conductor. It may be noted that maximum stress is an important consideration in the design of a

cable. For instance, if a cable is to be operated at such a voltage that maximum stress is

5 kV/mm, then the insulation used must have a dielectric strength of at least 5 kV/mm, otherwise

breakdown of the cable will become inevitable.

Most Economical Size of Conductor

It has already been shown that maximum stress in a cable occurs at the surface of the conductor.

For safe working of the cable, dielectric strength of the insulation should be more than

the maximums tress. Rewriting the expression for maximum stress, we get,

d

Dd

Vg

ln

2max volts/m

The values of working voltage V and internal sheath diameter D have to be kept fixed at certain

values due to design considerations. This leaves conductor diameter d to be the only variable.

For given values of V and D, the most economical conductor diameter will be one for which

gmax has a minimum value. The value of gmax will be minimum when dln D/d is

maximum i.e.

0ln

d

Dd

dd

d

718.2 ed

D

Most economical conductor diameter is

718.2

Dd

and the value of gmax under this condition is

d

Vg

2max volts/m

Grading of Cables

The process of achieving uniform electrostatic stress in the dielectric of cables is known

as grading of cables. It has already been shown that electrostatic stress in a single core cable has

a maximum value (gmax) at the conductor surface and goes on decreasing as we move

towards the sheath. The maximum voltage that can be safely applied to a cable depends upon

gmax i.e., electrostatic stress at the conductor surface. For safe working of a cable having

homogeneous dielectric, the strength of dielectric must be more than gmax. If a dielectric of high

strength is used for a cable, it is useful only near the conductor where stress is maximum. But as

we move away from the conductor, the electrostatic stress decreases, so the dielectric will be

unnecessarily over strong. The unequal stress distribution in a cable is undesirable for two

reasons. Firstly, insulation of greater thickness is required which increases the cable size.

Secondly, it may lead to the breakdown of insulation. In order to overcome above disadvantages,

it is necessary to have a uniform stress distribution in cables. This can be achieved by

distributing the stress in such a way that its value is increased in the outer layers of dielectric.

This is known as grading of cables. The following are the two main methods of grading of

cables:

(i) Capacitance grading (ii) Intersheath grading

Capacitance Grading:

The process of achieving uniformity in the dielectric stress by using layers of different dielectrics

is known as capacitance grading.

Fig 2.12- Capacitance grading

In capacitance grading, the homogeneous dielectric is replaced by a composite dielectric.

The composite dielectric consists of various layers of different dielectrics in such a

manner that relative permittivity > r of any layer is inversely proportional to its distance

from the center. Under such conditions, the value of potential gradient any point in the

dielectric is constant and is independent of its distance from the center. In other words, the

dielectric stress in the cable is same everywhere and the grading is ideal one. However, ideal

grading requires the use of an infinite number of dielectrics which is an impossible task. In

practice, two or three dielectrics are used in the decreasing order of permittivity, the dielectric of

highest permittivity being used near the core. The capacitance grading can be explained

beautifully by referring to the above Figure. There are three dielectrics of outer diameter d1, d2

and D and of relative permittivity >1, >2 and >3 respectively. If the permittivity are such that

>1 > 2 > 3 and the three dielectrics are worked at the same maximum stress, then

23121 ddd

d

dd

gV 1max

1 ln2

1

21

max2 ln

2 d

dd

gV

2

2max

3 ln2 d

Dd

gV

Total p.d. between core and earthed sheath is

321 VVVV

2

2

1

21

1max lnlnln2 d

Dd

d

dd

d

dd

gV

Intersheath Grading: In this method of cable grading, a homogeneous dielectric is used, but it

is divided into various layers by placing metallic inters heaths between the core and lead sheath.

The inter sheaths are held at suitable potentials which are in between the core potential and earth

potential. This arrangement improves voltage distribution in the dielectric of the cable and

consequently more uniform potential gradient is obtained.

Fig 2.13- Intersheath grading

Consider a cable of core diameter d and outer lead sheath of diameter D. Suppose that two

intersheaths of diameters d1 and d2 are inserted into the homogeneous dielectric and maintained

at some fixed potentials. Let V1, V2 and V3 respectively be the voltage between core and

intersheath 1, between inter sheath 1 and 2 and between inter sheath 2 and outer lead sheath.

As there is a definite potential difference between the inner and outer layers of each inter

sheath, therefore, each sheath can be treated like a homogeneous single core cable Maximum

stress between core and inter sheath 1 is

Since the dielectric is homogeneous, the maximum stress in each layer is the same i.e.,

maxmax3max2max1 gggg

d

Dd

V

d

dd

V

d

dd

V

ln2

ln2

ln2

2

2

1

21

2

1

1

As the cable behaves like three capacitors in series, therefore, all the potentials are in phase i.e.

Voltage between conductor and earthed lead sheath is

321 VVVV

Inter sheath grading has three principal disadvantages. Firstly, there are complications in fixing

the sheath potentials. Secondly, the inter sheaths are likely to be damaged during

transportation and installation which might result in local concentrations of potential

gradient. Thirdly, there are considerable losses in the inter sheaths due to charging

currents. For these reasons, inter sheath grading is rarely used.

Measurement of capacitance of 3-core cables

In three-core cables, capacitance does not have a single value, but can be lumped as shown in

below figure.

Capacitance between each core and sheath = ��

Capacitance between cores = C

Fig 2.14- Cable Capacitance

These can be separated from measurements as described in the following section.

(a) Strap the 3 cores together and measure the capacitance between this bundle and the sheath as

shown in figure.

Measured value = Cm1 = 3 Cs

This gives the capacitance to the sheath as Cs = 3

1mC

Fig 2.15- Capacitance Measurement

(b) Connect 2 of the cores to the sheath and measure between the remaining core and the sheath.

Measured value Cm2= 2 C + Cs

i.e. C = (Cm2 – Cs)/2 = (3 Cm2 – Cm1)/6

Which gives the capacitance between the conductors.

Fig 2.16-Capacitance Measurement

The effective capacitance to neutral Co of any of the cores may be obtained by considering the

star equivalent. This gives

�� = �� + 3� =1

3�� 1 + 3

3��� − ��

6

�� =3

2��

� −1

6��

Fig 2.17-Calculation of C0

In the breakdown of actual 3-core belted cables, it is generally observed that charring occurs at

those places where the stress is tangential to the layers of paper. Thus for the insulation to be

effective, the tangential stresses in paper insulation should be preferably avoided. This can

usually be accomplished only screening each core separately (or by having individual lead

sheaths for each of the cores), so that the cable in effect becomes 3 individual cables laid within

the same protective covering.

MODULE III

LOAD FLOW STUDIES

Load flow studies are important in planning and designing future expansion of power systems.

The load flow gives us the sinusoidal steady state of the entire system voltages, real and

reactive power generated and absorbed and line losses. Generally, load flow studies are limited

to the transmission system, which involves bulk power transmission.

Through the load flow studies we can obtain the voltage magnitudes and angles at each bus in

the steady state. This is rather important as the magnitudes of the bus voltages are required to be

held within a specified limit. Once the bus voltage magnitudes and their angles are computed

using the load flow, the real and reactive power flow through each line can be computed. Also

based on the difference between power flow in the sending and receiving ends, the losses in a

particular line can also be computed. Furthermore, from the line flow we can also determine the

over and under load conditions. Load flow studies throw light on some of the important aspects

of the system operation, such as: violation of voltage magnitudes at the buses, overloading of

lines, overloading of generators, stability margin reduction, indicated by power angle differences

between buses linked by a line, effect of contingencies like line voltages, emergency shutdown

of generators, etc. Load flow studies are required for deciding the economic operation of the

power system. They are also required in transient stability studies. Hence, load flow studies play

a vital role in power system studies.

CLASSIFICATION OF BUSES

For load flow studies it is assumed that the loads are constant and they are defined by their real

and reactive power consumption. It is further assumed that the generator terminal voltages are

tightly regulated and therefore are constant. The main objective of the load flow is to find the

voltage magnitude of each bus and its angle when the powers generated and loads are pre-

specified. To facilitate this we classify the different buses of the power system as listed below.

1. Load Buses: In these buses no generators are connected and hence the generated real power

PGi and reactive power QGi are taken as zero. The load drawn by these buses are defined by

real power PLi and reactive power QLi in which the negative sign accommodates for the

power flowing out of the bus. This is why these buses are sometimes referred to as P-Q bus.

The objective of the load flow is to find the bus voltage magnitude Vi and its angle i.

2. Voltage Controlled Buses: These are the buses where generators are connected. Therefore

the power generation in such buses is controlled through a prime mover while the terminal

voltage is controlled through the generator excitation. Keeping the input power constant

through turbine-governor control and keeping the bus voltage constant using automatic

voltage regulator, we can specify constant PGi and Vi for these buses. This is why such

buses are also referred to as P-V buses.

3. Slack or Swing Bus: Usually this bus is numbered 1 for the load flow studies. This bus sets

the angular reference for all the other buses. Since it is the angle difference between two

voltage sources that dictates the real and reactive power flow between them, the particular

angle of the slack bus is not important. However it sets the reference against which angles

of all the other bus voltages are measured. For this reason the angle of this bus is usually

chosen as 0. Furthermore it is assumed that the magnitude of the voltage of this bus is

known.

Now consider a typical load flow problem in which all the load demands are known. Even if the

generation matches the sum total of these demands exactly, the mismatch between generation

and load will persist because of the line I2R losses. Since the I2R loss of a line depends on the

line current which, in turn, depends on the magnitudes and angles of voltages of the two buses

connected to the line, it is rather difficult to estimate the loss without calculating the voltages and

angles. For this reason a generator bus is usually chosen as the slack bus without specifying its

real power. It is assumed that the generator connected to this bus will supply the balance of the

real power required and the line losses.

REAL AND REACTIVE POWER INJECTED IN A BUS

For the formulation of the real and reactive power entering a bus, we need to define the

following quantities. Let the voltage at the ith bus be denoted by

iiiiii jVVV sincos

(3.1)

Also let us define the self admittance at bus-i as

iiiiiiiiiiiiiiii jBGjYYY sincos (3.2)

Similarly the mutual admittance between the buses i and j can be written as

ijijijijijijijij jBGjYYY sincos (3.3)

Let the power system contains a total number of n buses. The current injected at bus-i is given as

n

kkik

niniii

VY

VYVYVYI

1

2211

(3.4)

It is to be noted we shall assume the current entering a bus to be positive and that leaving the bus

to be negative. As a consequence the power and reactive power entering a bus will also be

assumed to be positive. The complex power at bus-i is then given by

n

kkkikikiikiik

n

kkkikikkikiii

n

kkikiiiii

jjjVVY

jjVYjV

VYVIVjQP

1

1

1

sincossincossincos

sincossincossincos

(3.5)

Note that

ikikikik

kikkikii

kkikikii

j

jj

jjj

sincos

sincossincos

sincossincossincos

Therefore substituting in (3.5) we get the real and reactive power as

n

kikikkiiki VVYP

1

cos (3.6)

n

kikikkiiki VVYQ

1

sin (3.7)

PREPARATION OF DATA FOR LOAD FLOW

Let real and reactive power generated at bus-i be denoted by PGi and QGi respectively. Also let us

denote the real and reactive power consumed at the ith bus by PLi and QLi respectively. Then the

net real power injected in bus-i is

LiGiinji PPP , (3.8)

Let the injected power calculated by the load flow program be Pi,calc. Then the mismatch between

the actual injected and calculated values is given by

calciLiGicalciinjii PPPPPP ,,, (3.9)

In a similar way the mismatch between the reactive power injected and calculated values is given

by

calciLiGicalciinjii QQQQQQ ,,, (3.10)

The purpose of the load flow is to minimize the above two mismatches. It is to be noted that

(3.6) and (3.7) are used for the calculation of real and reactive power in (3.9) and (3.10).

However since the magnitudes of all the voltages and their angles are not known a priori, an

iterative procedure must be used to estimate the bus voltages and their angles in order to

calculate the mismatches. It is expected that mismatches Pi and Qi reduce with each iteration

and the load flow is said to have converged when the mismatches of all the buses become less

than a very small number.

For the load flow studies we shall consider the system of Fig. 3.1, which has 2 generator and 3

load buses. We define bus-1 as the slack bus while taking bus-5 as the P-V bus. Buses 2, 3 and 4

are P-Q buses. The line impedances and the line charging admittances are given in Table 3.1.

Based on this data the Ybus matrix is given in Table 3.2. This matrix is formed using the same

procedure as given in Section 3.1.3. It is to be noted here that the sources and their internal

impedances are not considered while forming the Ybus matrix for load flow studies which deal

only with the bus voltages.

Fig. 3.1 The simple power system used for load flow studies.

Table 3.1 Line impedance and line charging data of the system of Fig. 3.1.

Line (bus to bus) Impedance Line charging (Y/2)

1-2 0.02 + j0.10 j0.030

1-5 0.05 + j0.25 j0.020

2-3 0.04 + j0.20 j0.025

2-5 0.05 + j0.25 j0.020

3-4 0.05 + j0.25 j0.020

3-5 0.08 + j0.40 j0.010

4-5 0.10 + j0.50 j0.075

Table 3.2 Ybus matrix of the system of Fig. 3.1.

1 2 3 4 5

1 2.6923

j13.4115

1.9231 +

j9.6154

0 0 0.7692 +

j3.8462

2 1.9231 +

j9.6154

3.6538

j18.1942

0.9615 +

j3.8077

0 0.7692 +

j3.8462

3 0 0.9615 +

j3.8077

2.2115

j11.0027

0.7692 +

j3.8462

0.4808 +

j2.4038

4 0 0 0.7692 +

j3.8462

1.1538

j5.6742

0.3846 +

j1.9231

5 0.7692 +

j3.8462

0.7692 +

j3.8462

0.4808 +

j2.4038

0.3846 +

j1.9231

2.4038

j11.8942

The bus voltage magnitudes, their angles, the power generated and consumed at each bus are

given in Table 3.3. In this table some of the voltages and their angles are given in boldface

letters. This indicates that these are initial data used for starting the load flow program. The

power and reactive power generated at the slack bus and the reactive power generated at the P-V

bus are unknown. Therefore each of these quantities are indicated by a dash (). Since we do not

need these quantities for our load flow calculations, their initial estimates are not required. Also

note from Fig. 3.1 that the slack bus does not contain any load while the P-V bus 5 has a local

load and this is indicated in the load column.

Table 3.3 Bus voltages, power generated and load – initial data.

Bus

no.

Bus voltage Power generated Load

Magnitude

(pu)

Angle

(deg)

P (MW) Q

(MVAr)

P (MW) P

(MVAr)

1 1.05 0 0 0

2 1 0 0 0 96 62

3 1 0 0 0 35 14

4 1 0 0 0 16 8

5 1.02 0 48 24 11

LOAD FLOW BY GAUSS-SEIDEL METHOD

The basic power flow equations (3.6) and (3.7) are nonlinear. In an n-bus power system, let the

number of P-Q buses be np and the number of P-V (generator) buses be ng such that n = np + ng +

1. Both voltage magnitudes and angles of the P-Q buses and voltage angles of the P-V buses are

unknown making a total number of 2np + ng quantities to be determined. Amongst the known

quantities are 2np numbers of real and reactive powers of the P-Q buses, 2ng numbers of real

powers and voltage magnitudes of the P-V buses and voltage magnitude and angle of the slack

bus. Therefore there are sufficient numbers of known quantities to obtain a solution of the load

flow problem. However, it is rather difficult to obtain a set of closed form equations from (3.6)

and (3.7). We therefore have to resort to obtain iterative solutions of the load flow problem.

In the Gauss-Seidel load flow we denote the initial voltage of the ith bus by Vi(0), i = 2, , n. This

should read as the voltage of the ith bus at the 0th iteration, or initial guess. Similarly this voltage

after the first iteration will be denoted by Vi(1). In this Gauss-Seidel load flow the load buses and

voltage controlled buses are treated differently. However in both these type of buses we use the

complex power equation given in (3.5) for updating the voltages. Knowing the real and reactive

power injected at any bus we can expand (3.5) as

niniiiiii

n

kkikiinjiinji VYVYVYVYVVYVjQP

22111

,, (3.11)

We can rewrite (3.11) as

ninii

i

injiinji

ii

i VYVYVYV

jQP

YV 2211

,,1 (3.12)

In this fashion the voltages of all the buses are updated.

Algorithm for GS method

1. Prepare data for the given system as required.

2. Formulate the bus admittance matrix YBUS. This is generally done by the rule of inspection.

3. Assume initial voltages for all buses, 2,3,…n. In practical power systems, the magnitude of the

bus voltages is close to 1.0 p.u. Hence, the complex bus voltages at all (n-1) buses (except slack

bus) are taken to be 1.0<0.This is normally referred as the flat start solution.

4. Update the voltages. In any k+1 iteration, the voltages are given by

n

ij

kjij

k

j

i

jijK

i

injiinji

ii

i VYVYV

jQP

YV

1

11

1*

,,

)(

1 for i=2,3,......n

Here note that when computation is carried out for bus-i, updated values are already available for

buses 2,3…....(i-1) in the current (k+1) iteration. Hence these values are used. For buses

(i+1)…..n, values from previous, kth iteration are used.

5. Continue the iteration till ki

ki

ki VVV 11 for i=2,3,......n Where,ε is the tolerance

value. Generally it is customary to use a value of 0.0001 pu.

6. Compute slack bus power after voltages have converged [assuming bus 1 is slack bus].

)(1

1*

111*1

n

jjjVYVjQPS

7. Compute all line flows.

8. The complex power loss in the line is given by Sik + Si. The total loss in the system is

calculated by summing the loss over all the lines.

Updating Load Bus Voltages

Let us start the procedure with bus-2. Since this is load bus, both the real and reactive power into

this bus is known. We can therefore write from (3.12)

0

525

0

424

0

3231210

2

,2,2

22

1

2

1VYVYVYVY

V

jQP

YV injinj (3.13)

From the data given in Table 3.3 we can write

25242321

22

1

2 02.105.11

62.096.01YYYY

j

YV

It is to be noted that since the real and reactive power is drawn from this bus, both these

quantities appear in the above equation with a negative sign. With the values of the Ybus elements

given in Table 3.2 we get V2(1) = 0.9927 2.5959.

The first iteration voltage of bus-3 is given by

0

535

0

434

1

2321310

3

,3,3

33

1

3

1VYVYVYVY

V

jQP

YV injinj (3.14)

Note that in the above equation since the update for the bus-2 voltage is already available, we

used the 1st iteration value of this rather than the initial value. Substituting the numerical data we

get V3(1) = 0.9883 2. 8258. Finally the bus-4 voltage is given by

0

545

1

344

1

2421410

4

,4,4

44

1

4

1VYVYVYVY

V

jQP

YV injinj (3.15)

Solving we get V4(1) = 0. 9968 3.4849.

Updating P-V Bus Voltages

It can be seen from Table 3.3 that even though the real power is specified for the P-V bus-5, its

reactive power is unknown. Therefore to update the voltage of this bus, we must first estimate

the reactive power of this bus. Note from Fig. 3.11 that

niniiiiii

n

kkikiinji VYVYVYVYVVYVQ

22111

, ImIm (3.16)

And hence we can write the kth iteration values as

11

2211

1

, Im

k

nin

k

iii

k

ii

k

i

k

inji VYVYVYVYVQ (3.17)

For the system of Fig. 3.1 we have

0

555

1

454

1

353

1

252151

0

1

1

,5 Im VYVYVYVYVYVQ inj (3.18)

This is computed as 0.0899 per unit. Once the reactive power is estimated, the bus-5 voltage is

updated as

0

454

1

353

1

2521510

5

1

,5,5

55

1

5

1VYVYVYVY

V

jQP

YV injinj (3.19)

It is to be noted that even though the power generation in bus-5 is 48 MW, there is a local load

that is consuming half that amount. Therefore the net power injected by this bus is 24 MW and

consequently the injected power P5,inj in this case is taken as 0.24 per unit. The voltage is

calculated as V4(1) = 1.0169 0.8894. Unfortunately however the magnitude of the voltage

obtained above is not equal to the magnitude given in Table 3.3. We must therefore force this

voltage magnitude to be equal to that specified. This is accomplished by

1

5

1

55

1

,5V

VVV corr (3.20)

This will fix the voltage magnitude to be 1.02 per unit while retaining the phase of 0.8894.

The corrected voltage is used in the next iteration.

Convergence of the Algorithm

As can be seen from Table 3.3 that a total number of 4 real and 3 reactive powers are known to

us. We must then calculate each of these from (3.6) and (3.7) using the values of the voltage

magnitudes and their angle obtained after each iteration. The power mismatches are then

calculated from (3.9) and (3.10). The process is assumed to have converged when each of P2,

P3, P4, P5, Q2, Q3 and Q4 is below a small pre-specified value. At this point the process

is terminated.

Sometimes to accelerate computation in the P-Q buses the voltages obtained from (3.12) is

multiplied by a constant. The voltage update of bus-i is then given by

1

,

1

,

1

,, 1

k

acci

k

i

k

acci

k

i

k

acci

k

acci VVVVVV (3.21)

where is a constant that is known as the acceleration factor. The value of has to be below 2.0

for the convergence to occur. Table 3.4 lists the values of the bus voltages after the 1st iteration

and number of iterations required for the algorithm to converge for different values of . It can

be seen that the algorithm converges in the least number of iterations when is 1.4 and the

maximum number of iterations are required when is 2. In fact the algorithm will start to

diverge if larger values of acceleration factor are chosen. The system data after the convergence

of the algorithm will be discussed later.

Table 3.4 Gauss-Seidel method: bus voltages after 1st iteration and number of iterations required

for convergence for different values of .

Bus voltages (per unit) after 1st iteration No of

iterations

for

convergence

V2 V3 V4 V5

1 0.9927 2.6 0.9883 2.83 0.9968 3.48 1.02

0.89

28

2 0.9874

5.22

0.9766 8.04 0.9918 14.02 1.02 3.39 860

1.8 0.9883 3.7 0.9785 6.8 0.9903 11.12 1.02 3.52 54

1.6 0.9893

3.17

0.9807 5.67 0.9909 8.65 1.02 2.74 24

1.4 0.9903

3.64

0.9831 3.62 0.9926 6.57 1.02 2.05 14

1.2 0.9915

3.11

0.9857 3.68 0.9947 3.87 1.02 1.43 19

SOLUTION OF A SET OF NONLINEAR EQUATIONS BY NEWTON-RAPHSON

METHOD

In this section we shall discuss the solution of a set of nonlinear equations through Newton-

Raphson method. Let us consider that we have a set of n nonlinear equations of a total number of

n variables x1, x2, , xn. Let these equations be given by

nnn

n

n

xxf

xxf

xxf

,,

,,

,,

1

212

111

(3.22)

where f1, , fn are functions of the variables x1, x2, , xn. We can then define another set of

functions g1, , gn as given below

0,,,,

0,,,,

0,,,,

11

21212

11111

nnnnn

nn

nn

xxfxxg

xxfxxg

xxfxxg

(3.23)

Let us assume that the initial estimates of the n variables are x1(0), x2

(0), , xn(0). Let us add

corrections x1(0), x2

(0), , xn(0) to these variables such that we get the correct solution of these

variables defined by

00

0

2

0

22

0

1

0

11

nnn xxx

xxx

xxx

(3.24)

The functions in (3.23) then can be written in terms of the variables given in (3.24) as

nkxxxxgxxg nnknk ,,1,,,,,000

1

0

11 (3.25)

We can then expand the above equation in Taylor’s series around the nominal values of x1(0),

x2(0), , xn

(0). Neglecting the second and higher order terms of the series, the expansion of gk, k =

1, , n is given as

0

0

0

2

0

2

0

1

0

1

00

11 ,,,,n

kn

kknknk

x

gx

x

gx

x

gxxxgxxg

(3.26)

where 0

ik xg is the partial derivative of gk evaluated at x2(0), , xn

(0).

Equation (3.26) can be written in vector-matrix form as

00

1

00

12

00

11

0

0

2

0

1

0

21

22212

12111

,,0

,,0

,,0

nn

n

n

nnnnn

n

n

xxg

xxg

xxg

x

x

x

xgxgxg

xgxgxg

xgxgxg

(3.27)

The square matrix of partial derivatives is called the Jacobian matrix J with J(0) indicating that

the matrix is evaluated for the initial values of x2(0), , xn

(0). We can then write the solution of

(3.27) as

0

0

2

0

1

10

0

0

2

0

1

nn g

g

g

J

x

x

x

(3.28)

Since the Taylor’s series is truncated by neglecting the 2nd and higher order terms, we cannot

expect to find the correct solution at the end of first iteration. We shall then have

001

0

2

0

2

1

2

0

1

0

1

1

1

nnn xxx

xxx

xxx

(3.29)

These are then used to find J(1) and gk(1), k = 1, , n. We can then find x2

(1), , xn(1) from an

equation like (3.28) and subsequently calculate x2(1), , xn

(1). The process continues till gk, k =

1, , n becomes less than a small quantity.

LOAD FLOW BY NEWTON-RAPHSON METHOD

Let us assume that an n-bus power system contains a total number of np P-Q buses while the

number of P-V (generator) buses be ng such that n = np + ng + 1. Bus-1 is assumed to be the slack

bus. We shall further use the mismatch equations of Pi and Qi given in (3.9) and (3.10)

respectively. The approach to Newton-Raphson load flow is similar to that of solving a system of

nonlinear equations using the Newton-Raphson method: at each iteration we have to form a

Jacobian matrix and solve for the corrections from an equation of the type given in (3.27). For

the load flow problem, this equation is of the form

p

p

pn

n

n

n

n

Q

Q

P

P

V

V

V

VJ

1

2

2

1

1

2

2

2

(3.30)

where the Jacobian matrix is divided into submatrices as

2221

1211

JJ

JJJ (3.31)

It can be seen that the size of the Jacobian matrix is (n + np 1) (n + np 1). For example for

the 5-bus problem of Fig. 3.1 this matrix will be of the size (7 7). The dimensions of the

submatrices are as follows:

J11: (n 1) (n 1), J12: (n 1) np, J21: np (n 1) and J22: np np

The submatrices are

n

nn

n

PP

PP

J

2

2

2

2

11 (3.32)

p

p

p

p

n

nn

n

n

n

V

PV

V

PV

V

PV

V

PV

J

1

1

2

2

1

21

2

22

12

(3.33)

n

nn

n

ppQQ

QQ

J

1

2

1

2

2

2

21

(3.34)

p

p

p

p

p

p

n

n

n

n

n

n

V

QV

V

QV

V

QV

V

QV

J

1

1

1

2

1

2

1

21

2

22

22

(3.35)

Load Flow Algorithm

The Newton-Raphson procedure is as follows:

Step-1: Choose the initial values of the voltage magnitudes V(0) of all np load buses and n 1

angles (0) of the voltages of all the buses except the slack bus.

Step-2: Use the estimated V(0) and (0) to calculate a total n 1 number of injected real power

Pcalc(0) and equal number of real power mismatch P(0).

Step-3: Use the estimated V(0) and (0) to calculate a total np number of injected reactive power

Qcalc(0) and equal number of reactive power mismatch Q(0).

Step-3: Use the estimated V(0) and (0) to formulate the Jacobian matrix J(0).

Step-4: Solve (3.30) for (0) and V(0)V(0).

Step-5: Obtain the updates from

001 (3.36)

0

001

1V

VVV (3.37)

Step-6: Check if all the mismatches are below a small number. Terminate the process if yes.

Otherwise go back to step-1 to start the next iteration with the updates given by (3.36) and

(3.37).

Formation of the Jacobian Matrix

We shall now discuss the formation of the submatrices of the Jacobian matrix. To do that we

shall use the real and reactive power equations of (3.6) and (3.7). Let us rewrite them with the

help of (3.2) as

n

ikk

ikikkiikiiii VVYGVP1

2cos (3.38)

n

ikk

ikikkiikiiii VVYBVQ1

2sin (3.39)

A. Formation of J11

Let us define J11 as

nnn

n

LL

LL

J

2

222

11 (3.40)

It can be seen from (3.32) that Mik’s are the partial derivatives of Pi with respect to k. The

derivative Pi (3.38) with respect to k for i k is given by

kiVVYP

L ikikkiik

k

iik

,sin

(3.41)

Similarly the derivative Pi with respect to k for i = k is given by

n

ikk

ikikkiik

i

iii VVY

PL

1

sin

Comparing the above equation with (3.39) we can write

iiii

i

iii BVQ

PL

2

(3.42)

B. Formation of J21

Let us define J21 as

nnn

n

ppMM

MM

J

2

222

21 (3.43)

From (3.34) it is evident that the elements of J21 are the partial derivative of Q with respect to .

From (3.39) we can write

kiVVYQ

M ikikkiik

k

iik

,cos

(3.44)

Similarly for i = k we have

iiii

n

ikk

ikikkiik

i

iii GVPVVY

QM

2

1

cos

(3.45)

The last equality of (3.45) is evident from (3.38).

C. Formation of J12

Let us define J12 as

p

p

nnn

n

NN

NN

J

2

222

12 (3.46)

As evident from (3.33), the elements of J21 involve the derivatives of real power P with respect

to magnitude of bus voltage V. For i k, we can write from (3.38)

kiMVVYV

PVN ikikikkiik

k

ikik

cos (3.47)

For i = k we have

iiiii

n

ikk

ikikkiikiii

n

ikk

ikikkikiiii

i

iiii

MGVVVYGV

VYGVVV

PVN

2

1

2

1

2cos2

cos2

(3.48)

D. Formation of J22

For the formation of J22 let us define

ppp

p

nnn

n

OO

OO

J

2

222

22 (3.49)

For i k we can write from (3.39)

kiLVVYVV

QVO ikikikkiiki

k

iiik

,sin (3.50)

Finally for i = k we have

iiiii

n

ikk

ikikkiikiii

n

ikk

ikikkikiiii

k

iiii

LBVVVYBV

VYBVVV

QVO

2

1

2

1

2sin2

sin2

(3.51)

We therefore see that once the submatrices J11 and J21 are computed, the formation of the

submatrices J12 and J22 is fairly straightforward. For large system this will result in considerable

saving in the computation time.

TAP-CHANGING AND REGULATING TRANSFORMERS

Transformers which provide a small adjustment of voltage magnitude, usually in the range o f ±

10%, and others which shift the phase angle of the line voltages are important components of a

power system. Some transformers regulate both the magnitude and phase angle.

Almost all transformers provide taps on windings to adjust the ratio of transformation by

changing taps when the transformer is deenergized. A change in tap can be made while the

transformer is energized and such transformers a recalled load-tap-changing (LTC) transformers

or tap-changing-under-load (TCUL) transformers. The tap changing is automatic and operated by

motors which respond to relays set to hold the voltage at the prescribed level. Special circuits

allow the change to be made without interrupting the current.

A type of transformer designed for small adjustments of voltage rather than large changes in

voltage levels is called a regulating transformer Each of the three windings to which taps are

made is on the same magnetic core as the phase winding whose voltage is 90° out of phase with

the voltage from neutral to the point connected to the center of the tapped winding. For instance,

the voltage

to neutral ��� is increased by a component ∆��� which is in phase or 180° out

of phase with ∆���.

Fig. 3.2 Regulating t/f for control of voltage magnitude

Fig 3.3 Regulating t/f for control of phase angle

PHASE-SHIFTING TRANSFORMER

The voltage drop in a transmission line is simulated in a line drop compensator, which senses the

remote secondary voltage and adjusts the voltage taps. The voltage taps, however, do not change

the phase angle of the voltages appreciably. A minor change due to change of the transformer

impedance on account of tap adjustment and the resultant power flow through it can be ignored.

The real power control can be affected through phase-shifting of the voltage. A phase-shifting

transformer changes the phase angle without appreciable change in the voltage magnitude; this is

achieved by injecting a voltage at right angles to the corresponding line-to-neutral voltage.

Fig. 3.4 (a) Voltage injection vector diagram of a phase shifting transformer; (b) schematic

diagram of phase-shifting transformer.

Consider the equivalent circuit representation of Fig. 13. Let the regulating transformer be

represented by an ideal transformer with a series impedance or admittance. Since it is an ideal

transformer, the complex power input equals the complex power output, and for a voltage

adjustment tap changing transformer we have already shown that

�� = ����� − ����

where n is the ratio of the voltage adjustment taps (or currents). Also,

�� = �(�� − ���)

EFFECTS OF REGULATING TRANSFORMERS

The transformer with the higher tap setting is supplying most of t h e reactive power to the load.

The real power is dividing equally between the transformers. If both transformers have the same

impedance, they would share both the real and reactive power equally if they had the same turns

ratio. When two transformers are in parallel, we can vary the distribution of reactive power

between the transformers by adjusting the voltage-magnitude ratios. When two paralleled

transformers of equal kilovolt amperes do not share the Kilovolt amperes equally because their

impedances differ, the kilovolt amperes may be more nearly equalized by adjustment of the

voltage-magnitude ratios through tap changing.

MODULE IV

ECONOMIC OPERATION OF POWER SYSTEM

INTRODUCTION

One of the earliest applications of on-line centralized control was to provide a central facility, to

operate economically, several generating plants supplying the loads of the system. Modern

integrated systems have different types of generating plants, such as coal fired thermal plants,

hydel plants, nuclear plants, oil and natural gas units etc. The capital investment, operation and

maintenance costs are different for different types of plants.

The operation economics can again be subdivided into two parts.

i) Problem of economic dispatch, which deals with determining the power output of each plant to

meet the specified load, such that the overall fuel cost is minimized.

ii) Problem of optimal power flow, which deals with minimum – loss delivery, where in the

power flow, is optimized to minimize losses in the system. In this chapter we consider the

problem of economic dispatch.

During operation of the plant, a generator may be in one of the following states:

i) Base supply without regulation: the output is a constant.

ii) Base supply with regulation: output power is regulated based on system load.

iii) Automatic non-economic regulation: output level changes around a base setting as area

control error changes.

iv) Automatic economic regulation: output level is adjusted, with the area load and area control

error, while tracking an economic setting.

Regardless of the units operating state, it has a contribution to the economic operation, even

though its output is changed for different reasons. The factors influencing the cost of generation

are the generator efficiency, fuel cost and transmission losses. The most efficient generator may

not give minimum cost, since it may be located in a place where fuel cost is high. Further, if the

plant is located far from the load centers, transmission losses may be high and running the plant

may become uneconomical. The economic dispatch problem basically determines the generation

of different plants to minimize total operating cost. Modern generating plants like nuclear plants,

geo-thermal plants etc, may require capital investment of millions of rupees. The economic

dispatch is however determined in terms of fuel cost per unit power generated and does not

include capital investment, maintenance, depreciation, start-up and shut down costs etc.

PERFORMANCE CURVES

INPUT-OUTPUT CURVE

This is the fundamental curve for a thermal plant and is a plot of the input in British thermal

units (Btu) per hour versus the power output of the plant in MW as shown in Fig.4.1

Fig.4.1: Input output curve

HEAT RATE CURVE

The heat rate is the ratio of fuel input in Btu to energy output in KWh. It is the slope of the input

– output curve at any point. The reciprocal of heat – rate is called fuel – efficiency. The heat rate

curve is a plot of heat rate versus output in MW. A typical plot is shown in Fig .

Fig.4.2: Heat Rate Curve

INCREMENTAL FUEL RATE CURVE

The incremental fuel rate is equal to a small change in input divided by the corresponding change

in output.

Incremental fuel rate =∆Input/∆Output

The unit is again Btu / KWh. A plot of incremental fuel rate versus the output is shown in

Fig.4.3

Fig 4.3: Incremental Fuel Rate Curve

Incremental cost curve

The incremental cost is the product of incremental fuel rate and fuel cost (Rs / Btu or $/Btu). The

curve in shown in Fig.4.4. The unit of the incremental fuel cost is Rs / MWh or $ /MWh.

Fig. 4.4: Incremental Cost curve

In general, the fuel cost Fi for a plant, is approximated as a quadratic function of the

generated output PGi.

Rs/hPcPbaF2

GiiGiiii

The incremental fuel cost is given by

Giii

Gi

i PcbdP

dF2 Rs/MWh

The incremental fuel cost is a measure of how costly it will be produce an increment of power.

The incremental production cost, is made up of incremental fuel cost plus the incremental cost of

labour, water, maintenance etc. which can be taken to be some percentage of the incremental fuel

cost, instead of resorting to a rigorous mathematical model. The cost curve can be approximated

by a linear curve. While there is negligible operating cost for a hydel plant, there is a limitation

on the power output possible. In any plant, all units normally operate between PGmin, the

minimum loading limit, below which it is technically infeasible to operate a unit and PGmax,

which is the maximum output limit.

ECONOMIC GENERATION SCHEDULING NEGLECTING LOSSES AND

GENERATOR LIMITS

In an early attempt at economic operation it was decided to supply power from the most efficient

plant at light load conditions. As the load increased, the power was supplied by this most

efficient plant till the point of maximum efficiency of this plant was reached. With further

increase in load, the next most efficient plant would supply power till its maximum efficiency is

reached. In this way the power would be supplied by the most efficient to the least efficient plant

to reach the peak demand. Unfortunately however, this method failed to minimize the total cost

of electricity generation. We must therefore search for alternative method which takes into

account the total cost generation of all the units of a plant that is supplying a load.

The simplest case of economic dispatch is the case when transmission losses are neglected. The

model does not consider the system configuration or line impedances. Since losses are neglected,

the total generation is equal to the total demand PD.

Consider a system with ng number of generating plants supplying the total demand PD. If Fi is the

cost of plant i in Rs/h, the mathematical formulation of the problem of economic scheduling can

be stated as follows:

Minimize

gn

iiT FF

1

Such that

gn

iDGi PP

1

Where FT= total cost

PGi= generation of plant i

PD= total demand

This is a constrained optimization problem, which can be solved by Lagrange’s Method.

LAGRANGE METHOD FOR SOLUTION OF ECONOMIC SCHEDULE

The problem is restated below:

Minimize

gn

iiT FF

1

Such that

gn

iGiD PP

1

0

The augmented cost function is given by

)(1

gn

iGiDT PPFL

The minimum is obtained when

0

GiP

L and

L0

0

Gi

T

Gi P

F

P

L

gn

iGiD PP

L

1

0

The second equation is simply the original constraint of the problem. The cost of a plant Fi

depends only on its own output PGi, hence

Gi

i

Gi

i

Gi

T

dP

dF

P

F

P

F

Using the above,

0

Gi

i

Gi dP

dF

dP

L i = 1, 2, -----------, ng

We can write Giii Pcb 2 i = 1, 2, -----------, ng

The above equation is called the co-ordination equation. Simply stated, for economic generation

scheduling to meet a particular load demand, when transmission losses are neglected and

generation limits are not imposed, all plants must operate at equal incremental production costs,

subject to the constraint that the total generation be equal to the demand.

ECONOMIC SCHEDULE INCLUDING LIMITS ON GENERATOR (NEGLECTING LOSSES)

The power output of any generator has a maximum value dependent on the rating of the

generator. It also has a minimum limit set by stable boiler operation. The economic dispatch

problem now is to schedule generation to minimize cost, subject to the equality constraint.

gn

iDGi PP

1

and the inequality constraint

PGi(min) ≤ PGi ≤ PGi(max) i = 1, 2, ……… ng

The procedure followed is same as before i.e. the plants are operated with equal incremental fuel

costs, till their limits are not violated. As soon as a plant reaches the limit (maximum or

minimum) its output is fixed at that point and is maintained a constant. The other plants are

operated at equal incremental costs.

ECONOMIC DISPATCH INCLUDING TRANSMISSION LOSSES

When transmission distances are large, the transmission losses are a significant part of the

generation and have to be considered in the generation schedule for economic operation. The

mathematical formulation is now stated as

Minimize

gn

iiT FF

1

Such that L

n

iDGi PPP

g

1

Where PL is the total loss

The Lagrange function is now written as

)(1

L

n

iGiDT PPPFL

g

The minimum point is obtained when

0)1(

Gi

L

Gi

T

Gi P

P

P

F

P

L i=1,2,...........ng

gn

iLGiD PPP

L

1

0

(same as the constraint)

Since Gi

i

Gi

T

dP

dF

P

F

Gi

L

Gi

i

dP

dP

dP

dF

Gi

LGi

i

dP

dPdP

dF

1

1

The term

Gi

L

dP

dP1

1 is called the penalty factor of plant i, Li. The coordination equations including

losses are given by

i

Gi

i LdP

dF i=1,2, ............,ng

The minimum operation cost is obtained when the product of the incremental fuel cost and the

penalty factor of all units is the same, when losses are considered.

A rigorous general expression for the loss PL is given by

GnmnGmnm

L PBPP

Where Bmn is called loss coefficient, depends on load composition.

For a two plant system

2222121111 2 GGGGL PBPBPPBP as B12=B21

AUTOMATIC LOAD DISPATCH

Economic load dispatching is that aspect of power system operation wherein it is required to

distribute the load among the generating units actually paralleled with the system in such a

manner as to minimize the cost of supplying the minute to minute requirements of the system. In

a large interconnected system it is humanly impossible to calculate and adjust such generations

and hence the help of digital computer system along with analogue devices is sought and the

whole process is carried out automatically; hence called automatic load dispatch. The objective

of automatic load dispatch is to minimise the cost of supplying electricity to the load points while

ensuring security of supply against loss of generation and transmission capacity and also

maintaining the voltage and frequency of the system within specified limits. Since the

interconnection is growing bigger and bigger in size with time, the control engineer has to make

adjustments to various parameters in the system. Hence automatic control of load dispatch

problem is required. The chosen control system is invariably based on a digital computer

working on-line.

The components for automatic load dispatching are

Computer-The computer predicts the load and suggests economic loading. It transmits

information to machine controller.

Fig.4.5: Schematic diagram of automatic load dispatching components

Data Input: The computer receives a lot of data from the telemetering system and from the paper

tape. Telemetering data comes to the computer either as analog signals representing line power

flows, plant outputs or as signal bits indicating switch or isolator positions. Paper tape stores all

the basic data required e.g. the system parameters, load predictions, security constraints, etc.

Console: It is the component through which the operator can converse with the computer. He can

obtain certain information required for some action to be taken under emergency condition or he

can put data into it if needed. The console has the facilities of security checking and load flows

for the network calculations.

Machine Controller: The computer sends information regarding the optimal generation to the

machine controller at regular intervals which in turn implements them. Control on each machine

is applied by a closed loop system which uses a measure of actual power generated and which

operates through a conventional speeder motor. These are referred to as controller power loops.

In the power frequency loop an error signal proportional to the difference between the derived

and actual frequency and power is developed. A summed error signal is formed from these two

components and is converted in the motor controller to a train of pulses that are applied to a

speed governor reference setting motor called the speeder motor. The duration and amplitude of

these pulses are fixed but the pulse rate is made proportional to the summed error signal. The

pulses are applied as raise or lower command to the speeder motor in accordance with the error

signal and thus the output of the generator is increased or decreased accordingly.

HYDROTHERMAL SCHEDULING LONG AND SHORT TERMS-

Long-Range Hydro-Scheduling:

The long-range hydro-scheduling problem involves the long-range forecasting of water

availability and the scheduling of reservoir water releases (i.e., “drawdown”) for an interval

of time that depends on the reservoir capacities. Typical long-range scheduling goes anywhere

from 1 week to 1 yr or several years. For hydro schemes with a capacity of impounding

water over several seasons, the long-range problem involves meteorological and statistical

analyses.

Short-Range Hydro-Scheduling

Short-range hydro-scheduling (1 day to 1 wk) involves the hour-by-hour scheduling of all

generation on a system to achieve minimum production cost for the given time period. In such a

scheduling problem, the load, hydraulic inflows, and unit availabilities are assumed known. A set

of starting conditions (e.g., reservoir levels) is given, and the optimal hourly schedule

that minimizes a desired objective, while meeting hydraulic steam, and electric system

constraints, is sought. Hydrothermal systems where the hydroelectric system is by far the

largest component may be scheduled by economically scheduling the system to produce the

minimum cost for the thermal system. The schedules are usually developed to minimize

thermal generation production costs, recognizing all the diverse hydraulic constraints that may

exist.

Fig. 4.6: Hydro Scheduling

The hydroplant can supply the load by itself for a limited time. That is, for any time period j,

loadjHj PP max j=1,2,.........jmax

The energy available from the hydroplant is insufficient to meet the load.

max max

1 1

j

j

j

jjloadjjHj nPnP nj is the no of hours in period j

max

1max

j

jj Tn = Total Interval

Steam plant energy required is

maxmax

11

j

jjHj

j

jjloadj EnPnP

Where

sN

jjsj nPE

1

Ns is the no of periods the steam plant is on

sN

jj Tn

1max

So the scheduling problem and the constraint are

Min

sN

jjsjT nPFF

1

)(

Subject to

sN

jjsj EnP

1

0

Lagrange function is

ss N

jjsj

N

jjsj nPEnPFL

11

)(

0)(

sj

sj

sj dP

PdF

P

L for j=1,2,...............Ns

sj

sj

dP

PdF )(

So steam plant should be run at constant incremental cost for the entire period it is on. Let this

optimum value of steam-generated power be Ps*, which is the same for all time intervals

the steam unit is on.

The total cost over the interval is

s sN

j

N

jssjsjsT TPFnPFnPFF

1 1

*** )()()(

Ts is the total run time for the steam plant

The total cost sssT TcPbPaF )( 2**

Also

s sN

j

N

jssjsjsj ETPnPnP

1 1

**

So *

s

sP

ET

))((*

2**

s

ssTP

EcPbPaF

Minimizing FT , we get c

aPs *

So the unit should be operated at its maximum efficiency point (Ps*) long enough to

supply the energy needed, E. Optimal hydrothermal schedule is as shown below:

Fig.4.7: Optimal Hydrothermal Scheduling

FACTS

The large interconnected transmission networks are susceptible to faults caused by

lightning discharges and decrease in insulation clearances. The power flow in a

transmission line is determined by Kirchhoff’s laws for specified power injections (both

active and reactive) at various nodes. While the loads in a power system vary by the time of the

day in general, they are also subject to variations caused by the weather (ambient temperature)

and other unpredictable factors. The generation pattern in a deregulated environment also tends

to be variable (and hence less predictable).

The factors mentioned in the above paragraph point to the problems faced in maintaining

economic and secure operation of large interconnected systems. The probles are eased if

sufficient margins (in power transformer) can be maintained. The required safe operating margin

can be substantially reduced by the introduction of fast dynamic control over reactive and active

power by high power electronic controllers. This can make the AC transmission network

flexible to adapt to the changing conditions caused by contingencies and load variations.

Flexible AC Transmission System (FACTS) is used as Alternating current transmission systems

incorporating power electronic-based and other static controllers to enhance controllability and

increase power transfer capability. The FACTS controller is used as a power electronic

based system and other static equipment that provide control of one or more AC transmission

system parameters like voltage, current, power, impedance etc.

Benefits of utilizing FACTS devices: The benefits of utilizing FACTS devices in

electrical transmission systems can be summarized as follows:

1. Better utilization of existing transmission system assets.

2. Increased transmission system reliability and availability.

3. Increased dynamic and transient grid stability and reduction of loop flows.

4. Increased quality of supply for sensitive industries.

FACTs controllers: Structures & Characteristics of following FACTs Controllers

The FACTS controllers can be classified as—

1. Shunt connected controllers

2. Series connected controllers

3. Combined series-series controllers

4. Combined shunt-series controller

Static Var Compensator (SVC)

Static Var compensator is a static Var generator whose output is varied so as to maintain or

control specific parameters (e.g. voltage or reactive power of bus) of the electric power

system. In its simplest form it uses a thyristor controlled reactor (TCR) in conjunction

with a fixed capacitor (FC) or thyristor switched capacitor (TSC). A pair of anti parallel

thyristors is connected in series with a fixed inductor to form a TCR module while the

thyristors are connected in series with a capacitor to form a TSC module. An SVC can control

the voltage magnitude at the required bus thereby improving the voltage profile of the

system. The primary task of an SVC is to maintain the voltage of a particular bus by

means of reactive power compensation (obtained by varying the firing angle of the

thyristors). It can also provide increased damping to power oscillations and enhance power

flow over a line by using auxiliary signals such as line active power, line reactive

power, line current, and computed internal frequency. Static VAR Compensator (SVC) is a

shunt connected FACTS controller whose main functionality is to regulate the voltage at a

given bus by controlling its equivalent reactance. Basically it consists of a fixed capacitor (FC)

and a thyristor controlled reactor (TCR).

Fig.4.8: Static Var Compensator

Thyristor Controlled Series Capacitor (TCSC)

A TCSC is a capacitive reactance compensator, which consists of a series capacitor bank

shunted by a thyristor controlled reactor in order to provide a smoothly variable series

capacitive reactance. Even through a TCSC in the normal operating range in mainly capacitive,

but it can also be used in an inductive mode. The power flow over a transmission line can

be increased by controlled series compensation with minimum risk of sub-synchronous

resonance (SSR).TCSC is a second generation FACTS controller, which controls the

impedance of the line in which it is connected by varying the firing angle of the thyristors. A

TCSC module comprises a series fixed capacitor that is connected in parallel to a thyristor

controlled reactor (TCR). A TCR includes a pair of anti-parallel thyristors that are connected in

series with an inductor. In a TCSC, a Metal Oxide Varistor (MOV) along with a bypass

breaker is connected in parallel to the fixed capacitor for overvoltage protection. A

complete compensation system may be made up of several of these modules. TCSC controllers

use thyristor-controlled reactor (TCR) in parallel with capacitor segments of series capacitor

bank. The combination of TCR and capacitor allow the capacitive reactance to be smoothly

controlled over a wide range and switched upon command to a condition where the bi-

directional thyristor pairs conduct continuously and insert an inductive reactance into the line.

TCSC is an effective and economical means of solving problems of transient stability,

dynamic stability, steady state stability and voltage stability in long transmission lines. A

TCSC is a series controlled capacitive reactance that can provide continuous control of power on

the ac line over a wide range.

Fig.4.9: Thyristor Controlled Series Capacitor

Static Synchronous Series Compensator (SSSC)

A SSSC is a static synchronous generator operated without an external electric energy source as

a series compensator whose output voltage is in quadrature with, and controllable

independently of the line current for the purpose of increasing or decreasing the overall

reactive voltage drop across the line and thereby controlling the transmitted electric power. The

SSSC may include transiently rated energy source or energy absorbing device to enhance the

dynamic behaviour of the power system by additional temporary real power

compensation, to increase or decrease momentarily, the overall real voltage drop across

the line.

A SSSC incorporates a solid state voltage source inverter that injects an almost sinusoidal

voltage of variable magnitude in series with a transmission line. The SSSC has the same

structure as that of a STATCOM except that the coupling transformer of an SSSC is connected in

series with the transmission line. The injected voltage is mainly in quadrature with the line

current. A small part of injected voltage, which is in phase with the line current, provides the

losses in the inverter. Most of injected voltage, which is in quadrature with the line

current, emulates a series inductance or a series capacitance thereby altering the transmission line

series reactance. This reactance, which can be altered by varying the magnitude of injected

voltage, favourably influences the electric power flow in the transmission line.

Fig.4.10: Static Synchronous Series Compensator

SSSC is a solid-state synchronous voltage source employing an appropriate DC to AC

inverter with gate turn- off thyristor. It is similar to the STATCOM, as it is based on a

DC capacitor fed VSI that generates a three - phase voltage, which is then injected in a

transmission line through a transformer connected in series with the system. In SSSC, the

resonance phenomenon has been removed. So SSSC is having more superior performance as

compare to TCSC. The main control objective of the SSSC is to directly control the

current, and indirectly the power, flowing through the line by controlling the reactive

power exchange between the SSSC and the AC system. The main advantage of this

controller over a TCSC is that it does not significantly affect the impedance of the

transmission system and, therefore, there is no danger of having resonance problem.

Static Synchronous Compensator (STATCOM)

A STATCOM is a static synchronous generator operated as a shunt connected static var

compensator whose capacitive or inductive output current can be controlled independent of the

ac system voltage. A STATCOM is a solid state switching converter capable of generating

or absorbing independently controllable real and reactive power at its output terminals, when it

is fed from an energy source or an energy storage device of appropriate rating. A STATCOM

incorporate a voltage source inverter (VSI) that produces a set of three phase ac output

voltages, each of which is in phase with, and coupled to the corresponding ac system

voltage via a relatively small reactance. This small reactance is usually provided by the per

phase leakage reactance of the coupling transformer. The VSI is driven by a dc storage

capacitor. By regulating the magnitude of the output voltage produced, the reactive power

exchange between STATCOM and the ac system can be controlled. The Static Synchronous

Compensator (STATCOM) is a power electronic-based Synchronous Voltage Generator (SVG)

that generates a three-phase voltage from a dc capacitor in synchronism with the

transmission line voltage and is connected to it by a coupling transformer.

Fig.4.11: Static Synchronous Compensator

By controlling the magnitude of the STATCOM voltage the reactive power exchange

between the STATCOM and the transmission line and hence the amount of shunt

compensation can be controlled. In STATCOM, the resonance phenomenon has been removed.

So STATCOM is having more superior performance as compared to SVC.

Unified Power Flow Controller (UPFC)

The UPFC, by means of angularly unconstrained series voltage injection, is able to control,

concurrently or selectively, the transmission line voltage, impedance, and angle or,

alternatively, the real and reactive power flow in the line. The UPFC may also provide

independently controllable shunt reactive compensation.

The UPFC is the most versatile and powerful FACTS device. UPFC is also known as the

most comprehensive multivariable flexible ac transmission system (FACTS) controller.

Simultaneous control of multiple power system variables with UPFC poses enormous

difficulties. In addition, the complexity of the UPFC control increases due to the fact that

the controlled and the variables interact with each other. The Unified Power Flow Controller

(UPFC) is used to control the power flow in the transmission systems by controlling the

impedance, voltage magnitude and phase angle. This controller offers advantages in terms of

static and dynamic operation of the power system. The basic structure of the UPFC consists of

two voltage source inverter (VSI); where one converter is connected in parallel to the

transmission line while the other is in series with the transmission line. The UPFC consists of

two voltage source converters; series and shunt converter, which are connected to each other

with a common dc link. Series converter or Static Synchronous Series Compensator (SSSC) is

used to add controlled voltage magnitude and phase angle in series with the line, while shunt

converter or Static Synchronous Compensator (STATCOM) is used to provide reactive power to

the ac system, beside that, it will provide the dc power required for both inverter. Each of the

branch consists of a transformer and power electronic converter. These two voltage source

converters share a common dc capacitor. The energy storing capacity of this dc capacitor

is generally small. Therefore, active power drawn by the shunt converter should be equal to the

active power generated by the series converter. The reactive power in the shunt or series

converter can be chosen independently, giving greater flexibility to the power flow

control. The coupling transformer is used to connect the device to the system.

Fig.4.11: Unified Power Flow Controller

References Books:

1. D.P. Kothari, I.J. Nagrath, “Power System Engineering” Second Edition, TMH Publication

2. C.L.Wadhwa, “Electrical Power Systems” Fifth Edition, New Age International Publications

3. J.B. Gupta, “A Course in Electrical Power” Kataria Publication

4. John J Grainger, W. D. Stevenson, “Power System Analysis”, TMH Publication

Lecture Notes

On

BEE 1711 POWER SYSTEM-III

A COURSE IN 7TH SEMESTER OF BACHELOR OF TECHNOLOGY PROGRAMME IN ELECTRICAL AND ELECTRONICS ENGINEERING

Department of Electrical & EEE Engineering

Veer Surendra Sai Institute of Technology, Burla,

Sambalpur- 768018

DISCLAIMER

This document does not claim any originality and cannot be used as a substitute

for prescribed textbooks. The matter presented here is prepared by the author for

their respective teaching assignments by referring the text books and reference

books. Further, this document is not intended to be used for commercial purpose

and the committee members are not accountable for any issues, legal or

otherwise, arising out of use of this document.

BEE 1711 POWER SYSTEM-III

Lecture Plan

Module No. Lecture

No. Topics

MODULE – I

1. Philosophy of protection, Nature, Causes and consequences of faults,

Zone of protection, Requirements of a protective scheme, Basic

terminology components of protection scheme.

2. Circuit Breakers: Formation of arc during circuit breaking.

3. Theories of arc Interruption.

4. Recovery and restriking voltage, interruption of capacitive and

inductive currents.

5. Current chopping, circuit breaker rating, Different types of circuit

breakers.

6. Air break and Air blast circuit breaker.

7. Plain break and controlled break all circuit breakers.

8. Minimum oil circuit breakers.

9. Vacuum circuit breaker

10. SF6circuit breaker. D.C. Circuit breaker

MODULE – II

11. Relay classification, Principle of different types of electromagnetic

relay.

12. General equation of phase and magnitude comparators, Duality of

comparators,

13. Electromagnetic relays

14. , over current relays Directional relays,

15. Distance relay- impedance,

16. Reactance and Mho type, Differential relays,

17. Concept of static and numerical relay.

18. Feeder Protection, Generator Protection,

19. Transformer Protection,

20. Bus Zone Protection

MODULE – III

21. Z bus Algorithm,

22. Z bus Algorithm,

23. Z bus Algorithm,

24. Symmetrical and unsymmetrical fault analysis for power system,

25. Symmetrical and unsymmetrical fault analysis for power system,

26. Symmetrical and unsymmetrical fault analysis for power system,

27. Z bus method in fault analysis.

28. Arrangement of Bus bar,

29. Arrangement of Circuit breaker and isolator.

30. Current limiting reactors in power system and their arrangement

calculation of fault MVA for symmetrical short circuits. Circuit

breaker capacity.

MODULE – IV

31. Power System Stability,

32. Power System Stability,

33. Steady State Stability, Transient stability,

34. Swing equation, Equal area criterion for stability,

35. Swing equation, Equal area criterion for stability,

36. Critical clearing angle,

37. point by point Methods of improvement of transient stability.

38. point by point Methods of improvement of transient stability.

39. Voltage stability, concept, causes and counter measures.

40. Load frequency control, PF versus QV control

Books:

[1]. Van C Warrington, “Protective Relays” Vol.-I & II

[2]. Ravindranath, M.Chander, “Power System Protection and SwitchGear”, Wiley Eastern

Ltd. New Delhi.

[3]. John J Grainger, W. D. Stevenson, “Power System Analysis”, TMH Publication

[4]. P. Kundur, “Power System Stability and Control”, TMH Publication

MODULE- I

Philosophy of Protection

The purpose of an Electric Power System is to generate and supply electrical energy to

consumers. The power system should be designed and managed to deliver this energy to the

utilization points with both reliability and economically

The capital investment involved in power system for the generation, transmission and

distribution is so great that the proper precautions must be taken to ensure that the equipment not

only operates as nearly as possible to peak efficiency, but also must be protected from accidents

The normal path of the electric current is from the power source through copper (or aluminium)

conductors in generators, transformers and transmission lines to the load and it is confined to this

path by insulation.

Nature of Faults

Short circuit fault- current

Open circuit fault- voltage

In terms of seriousness of consequences of a fault, short circuits are of far greater concern

than open circuits, although some open circuits present some potential hazards to personnel

Classification of short circuited Faults

• Three phase faults (with or without earth connection)

• Two phase faults (with or without earth connection)

• Single phase to earth faults

Classification of Open Circuit Faults

• Single Phase open Circuit

• Two phase open circuit

• Three phase open circuit

Causes of Faults

The insulation, however, may break down, either by the effect of temperature and age or by a

physical accident, so that the current then follows an abnormal path generally known as Short

Circuit or Fault

• Any abnormal operating state of a power system is known as FAULT.

• A fault in general consists of short circuits as well as open circuits.

• Open circuit faults are less frequent than short circuit faults, and often they are

transformed in to short circuits by subsequent event

Consequences of occurrence of Faults

• Expensive damage to the equipment due to abnormally large currents, unbalanced

currents, or low voltages produced by the short circuits

• Explosions which may occur in equipment containing insulating oil during short circuits

and which may cause fire resulting in serious hazard to personnel and to other equipment

• Sever drop in voltage which is likely to cause the individual generators in a power

station or a group of generators in different stations to loose synchronism and fall out of

step with consequent splitting of the system

• A risk of synchronous motors in large industrial premises falling out of step and tripping

out.

Zones of Protection

An electric power system is divided into zones of protection as shown in Fig. 1.1. Each

zone of protection contains one or more components of a power system in addition to two

circuit breakers.

For a fault with in the boundary of a zone, the protection system responsible for the

protection of the zone acts to isolate (by tripping CBs) everything with in that zone from

the rest of the system

Fig.1.1 Zones of Protections

The circuit Breakers are inserted between the component of of the zone and the rest of the

power system. Thus, the location of the CBs helps to define the boundaries of the zones

of protection.

The neighbouring zones of protection are made to overlap so as to ensure that no part of

the power system remains without protection. However, occurrence of fault with in the

overlapped region would trip more number of circuit breakers than the minimum

necessary to disconnect the faulty element

Protection System Requirements

• The fundamental requirements for a protection system areas follows:

– Reliability: the ability of the protection to operate correctly. It has two basic

elements-dependability, which is the certainty of a correct operation on the

occurrence of a fault, and security ,which is the ability to avoid incorrect

operation during faults.

– Speed: minimum operating time to clear a fault in order to avoid damage to

equipment.

– Selectivity: maintaining continuity of supply by disconnecting the minimum

section of the network necessary to isolate the fault. The property of selective

tripping is also called ”discrimination” and is achieved by two general methods:

• Time graded systems

• Unit systems

– Cost: maximum protection at the lowest cost possible

Primary and back-up Protection

• Primary Protection

– The primary protection scheme ensures quick and selective clearing of the faults

within the boundary of the circuit element it protects. Primary Protection as a

rule is provided for each section of an electrical installation.

Causes of Failure of Primary Protection

Primary Protection may fail because of failure in any of the following:

1. Current or voltage supply to the relay.

2. D.C.tripping voltage supply

3. Protective relays

4. Tripping circuit

5. Circuit Breaker

• Back-up Protection

Back-up protection is the name given to a protection which backs the primary protection

whenever the later fails in operation.

The back-up protection by definition is slower than the protection

The design of the back-up protection needs to be coordinated with the design of the

primary protection

Circuit Breaker

Circuit breakers provide a manual means of energizing and de-energizing a circuit and

automatic over current protection. Unlike fuses, which must be replaced when they open, a

circuit breaker can be reset once the over current condition has been corrected. Pushing the

handle to the “OFF” position then back to the “ON” position restores the circuit. If a circuit

reopens upon reset to the “ON” position, the circuit should be checked by a qualified electrician.

Circuit Breaker Operation

In the following illustration, an AC motor is connected through a circuit breaker to a voltage

source. When the circuit breaker is closed, a complete path for current exists between the voltage

source and the motor allowing the motor to run. Opening the circuit breaker breaks the path of

current flow and the motor stops. The circuit breaker automatically opens when it senses a fault.

After the fault has been cleared, the breaker can be closed, allowing the motor to operate.

Fig. 1.2 Circuit Breaker operation during open and closed condition.

Formation of arc during circuit breaking

During opening of current carrying contacts in a circuit breaker the medium in between

opening contacts become highly ionized through which the interrupting current gets low resistive

path and continues to flow through this path even the contacts are physically separated. During

the flowing of current from one contact to other the path becomes so heated that it glows. This is

called arc.

Arc in Circuit Breaker

Whenever, on load current contacts of circuit breaker open there is an arc in circuit breaker,

established between the separating contacts. As long as this arc is sustained in between the

contacts the current through the circuit breaker will not be interrupted finally as because arc is

itself a conductive path of electricity. For total interruption of current the circuit breaker it is

essential to quench the arc as quick as possible. The main designing criteria of a circuit breaker is

to provide appropriate technology of arc quenching in circuit breaker to fulfill quick and

safe current interruption. So before going through different arc quenching techniques employed

in circuit breaker, we should try to understand "e;what is arc"e; and basic theory of arc in circuit

breaker, let‟s discuss.

Thermal Ionization of Gas

There are numbers of free electrons and ions present in a gas at room temperature due to

ultraviolet rays, cosmic rays and radioactivity of the earth. These free electrons and ions are so

few in number that they are insufficient to sustain conduction of electricity. The gas molecules

move randomly at room temperature. It is found an air molecule at a temperature of 300°K

(Room temperature) moves randomly with an approximate average velocity of 500

meters/second and collides other molecules at a rate of 1010

times/second. These randomly

moving molecules collide each other in very frequent manner but the kinetic energy of the

molecules is not sufficient to extract an electron from atoms of the molecules. If the temperature

is increased the air will be heated up and consequently the velocity on the molecules increased.

Higher velocity means higher impact during inter molecular collision. During this situation some

of the molecules are disassociated in to atoms. If temperature of the air is further increased many

atoms are deprived of valence electrons and make the gas ionized. Then this ionized gas can

conduct electricity because of sufficient free electrons. This condition of any gas or air is called

plasma. This phenomenon is called thermal ionization of gas.

Ionization due to Electron Collision

As we discussed that there are always some free electrons and ions presents in the air or gas but

they are insufficient to conduct electricity. Whenever these free electrons come across a strong

electric field, these are directed towards higher potential points in the field and acquire

sufficiently high velocity. In other words, the electrons are accelerated along the direction of the

electric field due to high potential gradient. During their travel these electrons collide with other

atoms and molecules of the air or gas and extract valance electrons from their orbits. After

extracted from parent atoms, the electrons will also run along the direction of the same electric

field due to potential gradient. These electrons will similarly collide with other atoms and create

more free electrons which will also be directed along the electric field. Due to this conjugative

action the numbers of free electrons in the gas will become so high that the gas stars conducting

electricity. This phenomenon is known as ionization of gas due to electron collision.

Deionization of Gas

If all the cause of ionization of gas is removed from an ionized gas it rapidly come back to its

neutral state by recombination of the positive and negative charges. The process of

recombination of positive and negative charges is known as deionization process. In deionization

by diffusion, the negative ions or electrons and positive ions move to the walls under the

influence of concentration gradients and thus completing the process of recombination.

Role of Arc in Circuit Breaker

When two current contacts are just open, an arc bridges the contact gap through which the

current gets a low resistive path to flow so there will not be any sudden interruption of current.

As there is no sudden and abrupt change in current during opening of the contacts, there will not

be any abnormal switching over voltage in the system. If i is the current flows through the

contacts just before they open, L is the system inductance, switching over voltage during opening

of contacts, may be expressed as V = L.(di/dt) where di/dt rate of change of current with respect

to time during opening of the contacts. In the case of alternating current arc is monetarily

extinguished at every current zero. After crossing every current zero the media between

separated contacts gets ionized again during next cycle of current and the arc in circuit breaker is

reestablished. To make the interruption complete and successful, this re-ionization in between

separated contacts to be prevented after a current zero.

If arc in circuit breaker is absence during opening of current carrying contacts, there would be

sudden and abrupt interruption of current which will cause a huge switching

overvoltage sufficient to severely stress the insulation of the system. On the other hand, the arc

provides a gradual but quick, transition from the current carrying to the current breaking states of

the contacts.

Arc Interruption or Arc Quenching or Arc Extinction Theory

Arc Column Characteristics

At high temperature the charged particles in a gas are rapidly and randomly move, but in absence

of electric field, no net motion is occurred. Whenever an electric field is applied in the gas, the

charged particles gain drift velocity superimposed on their random thermal motion. The drift

velocity is proportional to the voltage gradient of the field and particle mobility. The particle

mobility depends upon the mass of the particle, heavier particles, lower the mobility. The

mobility also depends upon mean free paths available in the gas for random movement of the

particles. Since every time a particle collides, it losses its directed velocity and has to be re-

accelerated in the direction of electric field again. Hence net mobility of the particles is reduced.

If the gas is in highly pressure, it becomes denser and hence, the gas molecules come closer to

each other, therefore collision occurs more frequently which lowers the mobility particles. The

total current by charged particles is directly proportional to their mobility. Therefore the mobility

of charged particles depends upon the temperature, pressure of the gas and as well as nature of

the gas. Again the mobility of gas particles determines the degree ionization of gas.

So from above explanation we can say that ionization process of gas depends upon nature

of gas (heavier or lighter gas particles), pressure of gas and temperature of gas. As we said

earlier the intensity of arc column depend up on the presence of ionized media between separated

electrical contacts, hence, special attention should be given in reducing ionization or increasing

deionization of media between contacts. That is why the main designing feature of circuit

breaker is to provide different pressure control methods, cooling methods for different arc media

in between circuit breaker contacts.

Heat loss from Arc

Heat loss from arc in circuit breaker is taken place through conduction, convection as

well as radiation. In circuit breaker with plain break arc in oil, arc in chutes or narrow slots

nearly all the heat loss due to conduction. In air blast circuit breaker or in breaker where a gas

flow is present between the electrical contacts, the heat loss of arc plasma occurs due to

convection process. At normal pressure the radiation is not a significant factor but at higher

pressure the radiation may become a very important factor of heat dissipation from arc plasma.

During opening of electrical contacts, the arc in circuit breaker is produced and it is extinguished

at every zero crossing of the current and then it is again reestablished during next cycle. The final

arc extinction or arc quenching in circuit breaker is achieved by rapid increase of the dielectric

strength in the medium between the contacts so that reestablishment of arc after zero crossing

cannot be possible. This rapid increase of dielectric strength in between circuit breaker contacts

is achieved either by deionization of gas in the arc media or by replacing ionized gas by cool and

fresh gas.

There are various deionization processes applied for arc extinction in circuit breaker, let

us discussed in brief.

Deionization of Gas due to Increasing Pressure

If pressure of the arc path increases, the density of the ionized gas is increased which

means, the particles in the gas come closer to each other and as a result the mean free path of the

particles is reduced. This increases the collision rate and as we discussed earlier at every

collision the charged particles loss their directed velocity along electric field and again they are

re-accelerated towards field. It can be said that over all mobility of the charged particles is

reduced so the voltage required to maintain the arc is increased. Another effect of the increased

density of particles is a higher rate of deionization of gas due to the recombination of oppositely

charged particles.

Deionization of Gas due to Decreasing Temperature

The rate of ionization of gas depends upon the intensity of impact during collision of gas

particles. The intensity of impact during collision of particles again depends upon velocity of

random motions of the particles. This random motion of a particle and its velocity increases with

increase of temperature of the gas. Hence it can be concluded like that if temperature of a gas is

increased; its ionization process is increased and opposite statement is also true that is if the

temperature is decreased the rate of ionization of gas is decreased means deionization of gas is

increased. Therefore more voltage required to maintain arc plasma with a decreased temperature.

Finally it can be said that the cooling effectively increases the resistance of the arc.

The insulating material (may be fluid or air) used in circuit breaker should serve two important

functions. They are written as follows:

1. It should provide sufficient insulation between the contacts when breaker opens.

2. It should extinguish the arc occurring between the contacts when breaker opens.

The second point needs more explanation. To understand this point let us consider a situation if

there is some fault or short circuit in the system, the relay provides desired signals to the circuit

breaker so as to prevent system from ongoing fault. Now when circuit breaker opens its contacts,

due to this an arc is drawn. The arc is interrupted by suitable insulator and technique.

Methods of Arc Interruption

There are two methods by which interruption is done.

1. High resistance method,

2. Low resistance method or zero interruption method.

In high interruption method we can increase the electrical resistance many times to such a high

value that it forces the current to reach to zero and thus restricting the possibility of arc being

restruck. Proper steps must be taken in order to ensure that the rate at which the resistance is

increased or decreased is not abnormal because it may lead to generation of harmful

induced voltages in the system. The arc resistance can be increased by various methods like

lengthening or cooling of the arc etc.

Limitations of high resistance method: Arc discharge has a resistive nature due to this most of

the energy is received by circuit breaker itself hence proper care should be taken during the

manufacturing of circuit breaker like mechanical strength etc. Therefore this method is applied in

dc power circuit breaker, low and medium ac power circuit breaker. Low resistance method is

applicable only for ac circuit and it is possible there because of presence of natural zero of

current. The arc gets extinguished at the natural zero of the ac wave and is prevented from

restricting again by rapid building of dielectric strength of the contact space. There are two

theories which explain the phenomenon of arc extinction:

1. Energy balance theory,

2. Voltage race theory.

Before going in details about these theories, we should know the following terms.

Restriking voltage: It may be defined as the voltage that appears across the breaking

contact at the instant of arc extinction.

Recovery voltage : It may be defined as the voltage that appears across the breaker

contact after the complete removal of transient oscillations and final extinction of arc has

resulted in all the poles.

Active recovery voltage : It may be defined as the instantaneous recovery voltage at the

instant of arc extinction.

Arc voltage : It may be defined as the voltage that appears across the contact during the

arcing period, when the current flow is maintained in the form of an arc. It assumes low

value except for the point at which the voltage rise rapidly to a peak value and current

reaches to zero.

1. Energy Balance Theory: When the contact of circuit breaker are about to open,

restriking voltage is zero, hence generated heat would be zero and when the contacts are

fully open there is infinite resistance this again make no production of heat. We can

conclude from this that the maximum generated heat is lying between these two cases and

can be approximated, now this theory is based on the fact that the rate of

generation of heat between the contacts of circuit breaker is lower than the rate at which heat

between the contact is dissipated. Thus if it is possible to remove the generated heat by

cooling, lengthening and splitting the arc at a high rate the generation, arc can be

extinguished.

2. Voltage Race Theory: The arc is due to the ionization of the gap between the contacts of

the circuit breaker. Thus the resistance at the initial stage is very small i.e. when the contacts

are closed and as the contact separates the resistance starts increasing. If we remove ions at

the initial stage either by recombining them into neutral molecules or inserting insulation at

a rate faster than the rate of ionisation, the arc can be interrupted. The ionisation at

zero current depends on the voltage known as restriking voltage.

Let us define an expression for restriking voltage. For loss-less or ideal system we have, Here v

= restriking voltage.V = value of voltage at the instant of interruption. L and C are

series inductor and shunt capacitance up to fault point. Thus from above equation we can see that

lower the value of product of L and C, higher the value of restriking voltage. The variation of v

versus time is plotted in Fig. 1.3:

Fig. 1.3 Voltage across breaker contacts

Now let us consider a practical system, or assume there finite loss in the system. As shown in

Fig. 1.4, in this case the restriking voltage is damped out due to the presence of some

finite resistance. Here it is assumed that the current lags behind the voltage by an angle

(measured in degrees) of 90. However in practical situation angle may varies depending upon

time in cycle at which the fault is occurred.

Fig. 1.4 Restriking voltage across breaker contacts

Fig. 1.5 Restriking voltage across breaker contacts along with fault current

Let us consider the effect of arc voltage, if arc voltage is included in the system, there is an

increment in the restriking voltage. However this is offset by another effect of an arc

voltage which opposes the current flow and making change in the phase of current, thus bringing

it more into phase with the applied voltage. Hence the current is not at its peak value

when voltage passes through zero value. Rate of Rise of Restriking Voltage (RRRV): It is

defined as the ratio of peak value of restriking voltage to time taken to reach to peak value. It is

one of the most important parameter as if the rate at which the dielectric strength developed

between the contacts is greater than RRRV, and then the arc will be extinguishes.

Rating of Circuit Breaker

The rating of a circuit breaker includes,

1) Rated short circuit breaking current.

2) Rated short circuit making current.

3) Rated operating sequence of circuit breaker.

4) Rated short time current.

Short Circuit Breaking Current of Circuit Breaker

This is the maximum short circuit current which a circuit breaker can withstand before it. Finally

cleared by opening its contacts. When a short circuit flows through a circuit breaker, there would

be thermal and mechanical stresses in the current carrying parts of the breaker. If the contact area

and cross-section of the conducting parts of the circuit breaker are not sufficiently large, there

may be a chance of permanent damage in insulation as well as conducting parts of the CB.

As per Joule‟s law of heating, the rising temperature is directly proportional to square of short

circuit current, contact resistance and duration of short circuit current. The short

circuit current continuous to flow through circuit breaker until the short circuit is cleared by

opening operation of the circuit breaker. As the thermal stress in the circuit breaker is

proportional to the period of short circuit, the breaking capacity of electrical circuit breaker,

depends upon the operating time.

At 160°C aluminum becomes soft and losses its mechanical strength, this temperature may be

taken as limit of temperature rise of breaker contacts during short circuit.

Hence short circuit breaking capacity or short circuit breaking current of circuit breakeris

defined as maximum current can flow through the breaker from time of occurring short circuit to

the time of clearing the short circuit without any permanent damage in the CB. The value of

short circuit breaking current is expressed in RMS. During short circuit, the CB is not only

subjected to thermal stress, it also suffers seriously from mechanical stresses. So during

determining short circuit capacity, the mechanical strength of the CB is also considered. So for

choosing suitable circuit breaker it is obvious to determine the fault level at that point of the

system where CB to be installed. Once the fault level of any part of electrical transmission is

determined it is easy to choose the correct rated circuit breaker for this part of network.

Rated Short Circuit Making Capacity

The short circuit making capacity of circuit breaker is expressed in peak value not in rms value

like breaking capacity. Theoretically at the instant of fault occurrence in a system, the

fault current can rise to twice of its symmetrical fault level. At the instant of switching on

a circuit breaker in faulty condition, of system, the short circuit portion of the system connected

to the source. The first cycle of the current during a circuit is closed by circuit breaker, has

maximum amplitude. This is about twice of the amplitude of symmetrical

fault current waveform. The breaker‟s contacts have to withstand this highest value

of current during the first cycle of waveform when breaker is closed under fault. On the basis of

this above mentioned phenomenon, a selected breaker should be rated with short circuit making

capacity. As the rated short circuit making current of circuit breaker is expressed in

maximum peak value, it is always more than rated short circuit breaking current of circuit

breaker. Normally value of short circuit making current is 2.5 times more than short circuit

breaking current.

Rated Operating Sequence or Duty Cycle of Circuit Breaker

This is mechanical duty requirement of circuit breaker operating mechanism. The sequence of

rated operating duty of a circuit breaker has been specified as

O – t – CO – t‟ – CO

where O indicates opening operation of CB. CO represents closing operation immediately

followed by an opening operation without any intentional time delay.

„t‟ is time between two operations which is necessary to restore the initial conditions and / or to

prevent undue heating of conducting parts of circuit breaker. t = 0.3 sec for circuit breaker

intended for first auto re closing duty, if not otherwise specified. Suppose rated duty circle of a

circuit breaker is 0 – 0.3 sec – CO – 3 min – CO. This means, an opening operation of circuit

breaker is followed by a closing operation after a time interval of 0.3 sec, then the circuit breaker

again opens without any intentional time delay. After this opening operation the CB is again

closed after 3 minutes and then instantly trips without any intentional time delay.

Rated Short Time Current

This is the current limit which a circuit breaker can carry safely for certain specific time without

any damage in it.

The circuit breakers do not clear the short circuit current as soon as any fault occurs in the

system. There always some intentional and an intentional time delays present between the instant

of occurrence of fault and instant of clearing the fault by CB. This delay are because of time of

operation of protection relays, time of operation of circuit breaker and also there may be some

intentional time delay imposed in relay for proper coordination of power system protection. Even

a circuit breaker fails to trip, the fault will be cleared by next higher positioned circuit breaker. In

this case the fault clearing time is longer. Hence, after fault, a circuit breaker has to carry the

short circuit for certain time. The summation of all time delays should not be more than 3

seconds, hence a circuit breaker should be capable of carrying a maximum faulty current for at

least this short period of time.

The short circuit current may have two major affects inside a circuit breaker.

1. Because of the high electric current, there may be high thermal stress in the insulation and

conducting parts of C.B.

2. The high short circuit current, produces significant mechanical stresses in different

current carrying parts of the circuit breaker.

A circuit breaker is designed to withstand these stresses. But no circuit breaker has to carry a

short circuit current not more than a short period depending upon the coordination of protection.

So it is sufficient to make C.B capable of withstanding affects of short circuit current for a

specified short period.

The rated short time current of a circuit breaker is at least equal to rated short circuit

breaking current of the circuit breaker.

Rated Voltage of Circuit Breaker

Rated voltage of circuit breaker depends upon its insulation system. For below 400 KV systems,

the circuit breaker is designed to withstand 10% above the normal system voltage. For above or

equal 400 KV system the insulation of circuit breaker should be capable of withstanding 5%

above the normal system voltage. That means, rated voltage of circuit breaker corresponds to the

highest system voltage. This is because during no load or small load condition the voltage level

of power system is allowed rise up to highest voltage rating of the system.

A circuit breaker is also subject to two other high voltage conditions.

1) Sudden disconnection of huge load for any other cause, the voltage imposed on the CB and

also between the contacts when the CB is open, may be very high compared to higher system

voltage. This voltage may be of power frequency but does not stay for very long period as this

high voltage situation must be cleared by protective switchgear.

But a circuit breaker may have to withstand this power frequency over voltage, during its normal

life span. The Circuit Breaker must be rated for power frequency withstand voltage for a specific

time only. Generally the time is 60 seconds. Making power frequency withstand capacity, more

than 60 second is not economical and not practically desired as all the abnormal situations of

electrical power system are definitely cleared within much smaller period than 60 seconds.

2) Like other apparatuses connected to power system, a circuit breaker may have also to face

lighting impulse and switching impulses during its life span.

The insulation system of CB and contact gap of an open CB have to withstand these

impulse voltage waveform amplitude of this disturbance is very high but extremely transient in

nature. So a circuit breaker is designed to withstand this impulse peaky voltage for microsecond

range only

Fig. 1.6 Different types of Circuit Breakers

Air Circuit Breaker and Air Blast Circuit Breaker

This type of circuit breakers, is those kind of circuit breaker which operates in air at atmospheric

pressure. After development of oil circuit breaker, the medium voltage air circuit

breaker (ACB) is replaced completely by oil circuit breaker in different countries. But in

countries like France and Italy, ACBs are still preferable choice up to voltage 15 KV. It is also

good choice to avoid the risk of oil fire, in case of oil circuit breaker. In America ACBs were

exclusively used for the system up to 15 KV until the development of new vacuum and

SF6 circuit breakers.

Working Principle of Air Circuit Breaker

The working principle of this breaker is rather different from those in any other types of circuit

breakers. The main aim of all kind of circuit breaker is to prevent the reestablishment of arcing

after current zero by creating a situation where in the contact gap will withstand the system

recovery voltage. The air circuit breaker does the same but in different manner. For

interrupting arc it creates an arc voltage in excess of the supply voltage. Arc voltage is defined as

the minimum voltage required maintaining the arc. This circuit breaker increases the

arc voltage by mainly three different ways,

1. It may increase the arc voltage by cooling the arc plasma. As the temperature of arc plasma

is decreased, the mobility of the particle in arc plasma is reduced, hence

more voltage gradient is required to maintain the arc.

2. It may increase the arc voltage by lengthening the arc path. As the length of arc path is

increased, the resistance of the path is increased, and hence to maintain the same

arc current more voltage is required to be applied across the arc path. That means

arc voltage is increased.

3. Splitting up the arc into a number of series arcs also increases the arc voltage.

Types of ACB

There are mainly two types of ACB are available.

1. Plain air circuit breaker.

2. Air blast Circuit Breaker.

Operation of ACB

The first objective is usually achieved by forcing the arc into contact with as large an

area as possible of insulating material. Every air circuit breaker is fitted with a chamber

surrounding the contact. This chamber is called „arc chute‟. The arc is driven into it. If

inside of the arc chute is suitably shaped, and if the arc can be made conform to the

shape, the arc chute wall will help to achieve cooling. This type of arc chute should be

made from some kind of refractory material. High temperature plastics reinforced with

glass fiber and ceramics are preferable materials for making arc chute.

The second objective that is lengthening the arc path, is achieved concurrently with fist

objective. If the inner walls of the arc chute is shaped in such a way that the arc is not

only forced into close proximity with it but also driven into a serpentine channel

projected on the arc chute wall. The lengthening of the arc path increases the

arc resistance.

The third technique is achieved by using metal arc slitter inside the arc chute. The main

arc chute is divided into numbers of small compartments by using metallic separation

plates. These metallic separation plates are actually the arc splitters and each of the

small compartments behaves as individual mini arc chute. In this system the initial arc is

split into a number of series arcs, each of which will have its won mini arc chute. So

each of the split arcs has its won cooling and lengthening effect due to its won mini arc

chute and hence individual split arc voltage becomes high. These collectively, make the

over all arc voltage, much higher than the system voltage.

This was working principle of air circuit breaker now we will discuss in details the

operation of ACB in practice.

The air circuit breaker, operated within the voltage level 1 KV, does not require any arc

control device. Mainly for heavy fault current on low voltages (low voltage level above 1 KV)

ABCs with appropriate arc control device, are good choice. These breakers normally have two

pairs of contacts. The main pair of contacts carries the current at normal load and these contacts

are made of copper. The additional pair is the arcing contact and is made of carbon. When circuit

breaker is being opened, the main contacts open first and during opening of main contacts the

arcing contacts are still in touch with each other. As the current gets, a parallel low resistive path

through the arcing contact during opening of main contacts, there will not be any arcing in the

main contact. The arcing is only initiated when finally the arcing contacts are separated. The

each of the arc contacts is fitted with an arc runner which helps, the arc discharge to move

upward due to both thermal and electromagnetic effects as shown in the figure.

Fig. 1.7 Air Circuit Breaker

As the arc is driven upward it enters in the arc chute, consisting of splitters. The arc in

chute will become colder, lengthen and split hence arc voltage becomes much larger than

system voltage at the time of operation of air circuit breaker, and therefore the arc is quenched

finally during the current zero.

Although this type of circuit breakers have become obsolete for medium voltage application, but

they are still preferable choice for high current rating in low voltage application.

Air Blast Circuit Breaker

These types of air circuit breaker were used for the system voltage of 245 KV, 420 KV and

even more, especially where faster breaker operation was required. Air blast circuit breaker has

some specific advantages over oil circuit breaker which are listed as follows,

1. There is no chance of fire hazard caused by oil.

2. The breaking speed of circuit breaker is much higher during operation of air blast circuit

breaker.

3. Arc quenching is much faster during operation of air blast circuit breaker.

4. The duration of arc is same for all values of small as well as high currents interruptions.

5. As the duration of arc is smaller, so lesser amount of heat realized from arc to

current carrying contacts hence the service life of the contacts becomes longer.

6. The stability of the system can be well maintained as it depends on the speed of operation of

circuit breaker.

7. Requires much less maintenance compared to oil circuit breaker.

There are also some disadvantages of air blast circuit breakers-

1. In order to have frequent operations, it is necessary to have sufficiently high capacity air

compressor.

2. Frequent maintenance of compressor, associated air pipes and automatic control equipments

is also required.

3. Due to high speed current interruption there is always a chance of high rate of rise of re-

striking voltage and current chopping.

4. There also a chance of air pressure leakage from air pipes junctions.

As we said earlier that there are mainly two types of ACB, plain air circuit breaker and air blast

circuit breaker. But the later can be sub divided further into three different categories.

1. Axial Blast ACB.

2. Axial Blast ACB with side moving contact.

3. Cross Blast ACB.

Axial Blast Air Circuit Breaker

Fig. 1.8 Axial Blast ACB

In axial blast ACB the moving contact is in contact with fixed contact with the help of a spring

pressure as shown in the figure. There is a nozzle orifice in the fixed contact which is blocked by

tip of the moving contact at normal closed condition of the breaker. When fault occurs, the high

pressure air is introduced into the arcing chamber. The air pressure will counter the spring

pressure and deforms the spring hence the moving contact is withdrawn from the fixed contact

and nozzle hole becomes open. At the same time the high pressure air starts flowing along the

arc through the fixed contact nozzle orifice. This axial flow of air along the arc through the

nozzle orifice will make the arc lengthen and colder hence arc voltage become much higher than

system voltage that means system voltage is insufficient to sustain the arc consequently the arc is

quenched.

circuit breaker with side moving contact” title=”Axial Blast Air Circuit Breaker with side

moving contact” class=”alignleft”/>

Axial Blast ACB with Side Moving Contact

Fig. 1.9 Axial Blast side movement ACB

In this type of axial blast air circuit breaker the moving contact is fitted over a piston supported

over a spring. In order to open the circuit breaker the air is admitted into the arcing chamber

when pressure reaches to a predetermined value, it presses down the moving contact; an arc is

drawn between the fixed and moving contacts. The air blast immediately transfers the arc to the

arcing electrode and is consequently quenched by the axial flow of air.

Cross Blast Air Circuit Breaker

Fig. 1.10 Cross Blast ACB

The working principle of cross blast air circuit breaker is quite simple. In this system of air

blast circuit breaker the blast pipe is fixed in perpendicular to the movement of moving contact

in the arcing chamber and on the opposite side of the arcing chamber one exhaust chamber is

also fitted at the same alignment of blast pipe, so that the air comes from blast pipe can straightly

enter into exhaust chamber through the contact gap of the breaker. The exhaust chamber is spit

with arc splitters. When moving contact is withdrawn from fixed contact, an arc is established in

between the contact, and at the same time high pressure air coming from blast pipe will pass

through the contact gap and will forcefully take the arc into exhaust chamber where the arc is

split with the help of arc splitters and ultimately arc is quenched.

Minimum Oil Circuit Breaker or MOCB

These types of circuit breakers utilize oil as the interrupting media. However, unlike bulk oil

circuit breaker, a minimum oil circuit breaker places the interrupting unit in insulating

chamber at live potential. The insulating oil is available only in interrupting chamber. The

feature of designing MOCB is to reduce requirement of oil, and hence these breaker are

called minimum oil circuit breaker.

As the volume of the oil in bulk oil circuit breaker is huge, the chances of fire hazard in bulk oil

system are more. For avoiding unwanted fire hazard in the system, one important development in

the design of oil circuit breaker has been introduced where use of oil in the circuit breaker is

much less than that of bulk oil circuit breaker. It has been decided that the oil in the circuit

breaker should be used only as arc quenching media not as an insulating media. Then the concept

of minimum oil circuit breaker comes. In this type of circuit breaker the arc interrupting device

is enclosed in a tank of insulating material which as a whole is at live potential of system. This

chamber is called arcing chamber or interrupting pot. The gas pressure developed in the arcing

chamber depends upon the current to be interrupted. Higher the current to be interrupted causes

larger the gas pressure developed inside the chamber, hence better the arc quenching. But this

put a limit on the design of the arc chamber for mechanical stresses. With use of better insulating

materials for the arcing chambers such as glass fiber, reinforced synthetic resin etc,

the minimum oil circuit breaker are able to meet easily the increased fault levels of the

system.

Working Principle or Arc Quenching in Minimum Oil Circuit Breaker

Fig. 1.11 Minimum Oil Circuit Breaker

Working Principle of minimum oil circuit breaker or arc quenching in minimum oil circuit

breaker is described below. In a minimum oil circuit breaker, the arc drawn across

the current carrying contacts is contained inside the arcing chamber.

Hence the hydrogen bubble formed by the vaporized oil is trapped inside the chamber. As the

contacts continue to move, after its certain travel an exit vent becomes available for exhausting

the trapped hydrogen gas. There are two different types of arcing chamber is available in terms

of venting are provided in the arcing chambers. One is axial venting and other is radial venting.

In axial venting, gases (mostly Hydrogen), produced due to vaporization of oil and

decomposition of oil during arc, will sweep the arc in axial or longitudinal direction.

Let‟s have a look on working principle Minimum Oil Circuit Breaker with axial venting arc

chamber. The moving contact has just been separated and arc is initiated in MOCB.

The ionized gas around the arc sweep away through upper vent and cold oil enters into the arcing

chamber through the lower vent in axial direction as soon as the moving contact tip crosses the

lower vent opening and final arc quenching in minimum oil circuit breaker occurs the cold oil

occupies the gap between fixed contact and moving contact and the minimum oil circuit

breaker finally comes into open position. Whereas in case of radial venting or cross blast, the

gases (mostly Hydrogen) sweep the arc in radial or transverse direction. The axial venting

generates high gas pressure and hence has high dielectric strength, so it is mainly used for

interrupting low current at high voltage. On the other hand radial venting produces relatively

low gas pressure and hence low dielectric strength so it can be used for low voltage and

high current interruption. Many times the combination of both is used in minimum oil circuit

breaker so that the chamber is equally efficient to interrupt low current as well as high current.

These types of circuit breaker are available up to 8000 MVA at 245 KV.

Vacuum Circuit Breaker or VCB

A vacuum circuit breaker is such kind of circuit breaker where the arc quenching takes place in

vacuum. The technology is suitable for mainly medium voltage application. For

higher voltage vacuum technology has been developed but not commercially viable. The

operation of opening and closing of current carrying contacts and associated arc interruption take

place in a vacuum chamber in the breaker which is called vacuum interrupter. The vacuum

interrupter consists of a steel arc chamber in the centre symmetrically arranged ceramic

insulators. The vacuum pressure inside a vacuum interrupter is normally maintained at 10 – 6

bar.

The material used for current carrying contacts plays an important role in the performance of

the vacuum circuit breaker. CuCr is the most ideal material to make VCB contacts. Vacuum

interrupter technology was first introduced in the year of 1960. But still it is a developing

technology. As time goes on, the size of the vacuum interrupter is being reducing from its early

1960‟s size due to different technical developments in this field of engineering. The contact

geometry is also improving with time, from butt contact of early days it gradually changes to

spiral shape, cup shape and axial magnetic field contact. Thevacuum circuit breaker is today

recognized as most reliable current interruption technology for medium voltage switchgear. It

requires minimum maintenance compared to other circuit breaker technologies.

Advantages of Vacuum Circuit Breaker or VCB

Service life of vacuum circuit breaker is much longer than other types of circuit breakers. There

is no chance of fire hazard as oil circuit breaker. It is much environment friendly than SF6 Circuit

breaker. Beside of that contraction of VCB is much user friendly. Replacement of vacuum

interrupter (VI) is much convenient.

Operation of Vacuum Circuit Breaker

The main aim of any circuit breaker is to quench arc during current zero crossing, by establishing

high dielectric strength in between the contacts so that reestablishment of arc after current zero

becomes impossible. The dielectric strength of vacuum is eight times greater than that of air and

four times greater than that of SF6 gas. This high dielectric strength makes it possible to quench

a vacuum arc within very small contact gap. For short contact gap, low contact mass and no

compression of medium the drive energy required in vacuum circuit breaker is minimum. When

two face to face contact areas are just being separated to each other, they do not be separated

instantly, contact area on the contact face is being reduced and ultimately comes to a point and

then they are finally de-touched. Although this happens in a fraction of micro second but it is the

fact. At this instant of de-touching of contacts in a vacuum, the current through the contacts

concentrated on that last contact point on the contact surface and makes a hot spot. As it is

vacuum, the metal on the contact surface is easily vaporized due to that hot spot and create a

conducting media for arc path. Then the arc will be initiated and continued until the

next current zero.

At current zero this vacuum arc is extinguished and the conducting metal vapor is re-condensed

on the contact surface. At this point, the contacts are already separated hence there is no question

of re-vaporization of contact surface, for next cycle of current. That means, the arc cannot be

reestablished again. In this way vacuum circuit breaker prevents the reestablishment of arc by

producing high dielectric strength in the contact gap after current zero. There are two types of arc

shapes. For interrupting current up to 10 kA, the arc remains diffused and the form of vapor

discharge and cover the entire contact surface. Above 10 kA the diffused arc is constricted

considerably by its own magnetic field and it contracts. The phenomenon gives rise over heating

of contact at its center. In order to prevent this, the design of the contacts should be such that the

arc does not remain stationary but keeps travelling by its own magnetic field. Specially designed

contact shape of vacuum circuit breaker make the constricted stationary arc travel along the

surface of the contacts, thereby causing minimum and uniform contact erosion.

SF6 Circuit Breaker

A circuit breaker in which the current carrying contacts operate in sulphur hexafluoride

or SF6 gas is known as an SF6 circuit breaker. SF6 has excellent insulating property. SF6 has

high electro-negativity. That means it has high affinity of absorbing free electron. Whenever a

free electron collides with the SF6 gas molecule, it is absorbed by that gas molecule and forms a

negative ion. The attachment of electron with SF6 gas molecules may occur in two different

ways,

(1.1)

These negative ions obviously much heavier than a free electron and therefore over all

mobility of the charged particle in the SF6 gas is much less as compared other common gases.

We know that mobility of charged particle is majorly responsible for conducting current through

a gas.

Fig. 1.12 A SF6 Circuit Breaker

Hence, for heavier and less mobile charged particles in SF6 gas, it acquires very high

dielectric strength. Not only the gas has a good dielectric strength but also it has the unique

property of fast recombination after the source energizing the spark is removed. The gas has also

very good heat transfer property. Due to its low gaseous viscosity (because of less molecular

mobility) SF6 gas can efficiently transfer heat by convection. So due to its high dielectric

strength and high cooling effect SF6gas is approximately 100 times more effective arc quenching

media than air. Due to these unique properties of this gas SF6 circuit breaker is used in

complete range of mediumvoltage and high voltage electrical power system. These circuit

breakers are available for the voltage ranges from 33KV to 800KV and even more.

Disadvantages of SF6 CB

The SF6 gas is identified as a greenhouse gas, safety regulation are being introduced in

many countries in order to prevent its release into atmosphere. Puffer type design of SF6 CB

needs a high mechanical energy which is almost five times greater than that of oil circuit breaker.

Types of SF6 Circuit Breaker

There are mainly three types of SF6 CB depending upon the voltage level of application-

1. Single interrupter SF6 CB applied for up to 245 KV(220 KV) system.

2. Two interrupter SF6 CB applied for up to 420 KV(400 KV) system.

3. Four interrupter SF6 CB applied for up to 800 KV(715 KV) system.

Working of SF6 Circuit Breaker

The working of SF6 CB of first generation was quite simple it is some extent similar to

air blast circuit breaker. Here SF6 gas was compressed and stored in a high pressure reservoir.

During operation of SF6 circuit breaker this highly compressed gas is released through the arc

in breaker and collected to relatively low pressure reservoir and then it pumped back to the high

pressure reservoir for re utilize.

The working of SF6 circuit breaker is little bit different in modern time. Innovation of

puffer type design makes operation of SF6 CB much easier. In buffer type design, the arc energy

is utilized to develop pressure in the arcing chamber for arc quenching. Here the breaker is filled

with SF6 gas at rated pressure. There are two fixed contact fitted with a specific contact gap. A

sliding cylinder bridges these to fixed contacts. The cylinder can axially slide upward and

downward along the contacts. There is one stationary piston inside the cylinder which is fixed

with other stationary parts of the SF6 circuit breaker, in such a way that it cannot change its

position during the movement of the cylinder. As the piston is fixed and cylinder is movable or

sliding, the internal volume of the cylinder changes when the cylinder slides.

During opening of the breaker the cylinder moves downwards against position of the

fixed piston hence the volume inside the cylinder is reduced which produces compressed SF6gas

inside the cylinder. The cylinder has numbers of side vents which were blocked by upper fixed

contact body during closed position. As the cylinder move further downwards, these vent

openings cross the upper fixed contact, and become unblocked and then compressed SF6 gas

inside the cylinder will come out through this vents in high speed towards the arc and passes

through the axial hole of the both fixed contacts. The arc is quenched during this flow of SF6 gas.

During closing of the circuit breaker, the sliding cylinder moves upwards and as the

position of piston remains at fixed height, the volume of the cylinder increases which introduces

low pressure inside the cylinder compared to the surrounding. Due to this pressure difference

SF6 gas from surrounding will try to enter in the cylinder. The higher pressure gas will come

through the axial hole of both fixed contact and enters into cylinder via vent and during this

flow; the gas will quench the arc.

D.C circuit breakers

Miniature circuit breakers available for use in direct current

Nowadays we use more commonly miniature circuit breaker or MCB in low voltage electrical

network instead of fuse. The MCB has some advantages compared to fuse.

1. It automatically switches off the electrical circuit during abnormal condition of the network

means in over load condition as well as faulty condition. The fuse does not sense but miniature

circuit breaker does it in more reliable way. MCB is much more sensitive to over current than

fuse.

2. Another advantage is, as the switch operating knob comes at its off position during tripping,

the faulty zone of the electrical circuit can easily be identified. But in case of fuse, fuse wire

should be checked by opening fuse grip or cutout from fuse base, for confirming the blow of fuse

wire.

3. Quick restoration of supply cannot be possible in case of fuse as because fuses have to be

replaced for restoring the supply. But in the case of MCB, quick restoration is possible by just

switching on operation.

4. Handling MCB is more electrically safe than fuse.

Because of too many advantages of MCB over fuse units, in modern low voltage electrical

network, miniature circuit breaker is mostly used instead of backdated fuse unit. Only one

disadvantage of MCB over fuse is that this system is more costly than fuse unit system.

Working Principle Miniature Circuit Breaker

There are two arrangement of operation of miniature circuit breaker. One due to

thermal effect of over current and other due to electromagnetic effect of over current. The

thermal operation of miniature circuit breaker is achieved with a bimetallic strip whenever

continuous over current flows through MCB, the bimetallic strip is heated and deflects by

bending. This deflection of bimetallic strip releases mechanical latch. As this mechanical latch is

attached with operating mechanism, it causes to open the miniaturecircuit breaker contacts. But

during short circuit condition, sudden rising of current, causes electromechanical displacement of

plunger associated with tripping coil or solenoid of MCB. The plunger strikes the trip lever

causing immediate release of latch mechanism consequently open the circuit breaker contacts.

This was a simple explanation of miniature circuit breaker working principle.

Miniature Circuit Breaker Construction

Miniature circuit breaker construction is very simple, robust and maintenance free. Generally

a MCB is not repaired or maintained, it just replaced by new one when required. A

miniature circuit breaker has normally three main constructional parts. These are:

Frame of Miniature Circuit Breaker

The frame of miniature circuit breaker is a molded case. This is a rigid, strong, insulated

housing in which the other components are mounted.

Operating Mechanism of Miniature Circuit Breaker

The operating mechanism of miniature circuit breaker provides the means of manual

opening and closing operation of miniature circuit breaker. It has three-positions “ON,” “OFF,”

and “TRIPPED”. The external switching latch can be in the “TRIPPED” position, if the MCB is

tripped due to over-current. When manually switch off the MCB, the switching latch will be in

“OFF” position. In close condition of MCB, the switch is positioned at “ON”. By observing the

positions of the switching latch one can determine the condition of MCB whether it is closed,

tripped or manually switched off.

Trip Unit of Miniature Circuit Breaker

The trip unit is the main part, responsible for proper working of miniature circuit

breaker. Two main types of trip mechanism are provided in MCB. A bimetal provides

protection against over load current and an electromagnet provides protection against short-

circuit current.

Operation of Miniature Circuit Breaker

There are three mechanisms provided in a single miniature circuit breaker to make it

switched off. If we carefully observe the picture beside, we will find there are mainly one bi –

metallic strip, one trip coil and one hand operated on – off lever. Electric current carrying path of

a miniature circuit breaker shown in the picture is like follows. First left hand side power

terminal – then bimetallic strip – then current coil or trip coil – then moving contact – then fixed

contact and – lastly right had side power terminal. All are arranged in series.

If circuit is overloaded for long time, the bi – metallic strip becomes over heated and

deformed. This deformation of bi metallic strip causes, displacement of latch point. The moving

contact of the MCB is so arranged by means of spring pressure, with this latch point, that a little

displacement of latch causes, release of spring and makes the moving contact to move for

opening the MCB. The current coil or trip coil is placed such a manner, that during short circuit

fault the mmf of that coil causes its plunger to hit the same latch point and make the latch to be

displaced. Hence the MCB will open in same manner. Again when operating lever of the

miniature circuit breaker is operated by hand, that means when we make the MCB at off position

manually, the same latch point is displaced as a result moving contact separated from fixed

contact in same manner. So, whatever may be the operating mechanism, that means, may be due

to deformation of bi – metallic strip, due to increased mmf of trip coil or may due to manual

operation, actually the same latch point is displaced and same deformed spring is released, which

ultimately responsible for movement of the moving contact. When the the moving contact

separated from fixed contact, there may be a high chance of arc.

MODULE- II

Relay Classification

Protection relays can be classified in accordance with their construction, the incoming signal and

function

Construction

• Electromechanical

• Solid State

• Microprocessor

• Numerical

Incoming Signal

• Current

• Voltage

• Power

• Frequency

• Temperature

• Pressure

• Speed

• Others

Function

• Overcurrent

• Directional Overcurrent

• Distance

• Over voltage

• Differential

• Reverse Power

• Others

Electromechanical Relays

These relays are constructed with electrical, magnetic & mechanical components & have an

operating coil & various contacts, & are very robust & reliable. Based on the construction,

characteristics, these are classified in three groups.

Attraction Relays

Attraction relays can be AC & DC and operate by the movement of a piece of iron when it is

attracted by the magnetic field produced by a coil. There are two main types of relays:

1. The attracted armature type

2. Solenoid type relay

Attracted Armature Relays

• Consists of a bar or plate (made of iron) that pivots when it is attracted towards the coil.

• The armature carries the moving part of the contact, which is closed or opened, according

to the design, when the armature is attracted to the coil.

Fig. 2.1 Hinged Armature Relay

Solenoid Type Relays

In this a plunger or a piston is attracted axially within the field of the solenoid. In this case, the

piston carries the moving contacts.

Fig. 2.2 Solenoid-type Relay

The force of attraction =

Where, K1 depends on

• The number of turns of the coil

• The air gap

• The effective area

• The reluctance of the magnetic circuit

K2 is the restraining force, usually produced by spring

For threshold or balanced condition, the resultant force is zero.

𝐼 = 𝐾1

𝐾2 (2.1)

In order to control the value of current at which relay operates, the parameters K1 and K2 may

adjusted. Attraction relays effectively have no time-delay and are widely used when

instantaneous operation is required

Relays with Movable Coils

This type of relay consists of a rotating movement with a small coil suspended or pivoted with

the freedom to rotate between the poles of a permanent magnet.

2

1 2KI K

2

1 2KI K

The coil is restrained by two special springs which also serve as connections to carry

the current to the coil

Fig. 2.3 Moving-coil relay

The torque produced in the coil is

(2.2)

where,

T= Torque, B= flux density, l= length of the coil, a= distance between the two sides of the coil

i=current flowing through the coil , N=number of turns in the coil

• The relay has inverse type characteristic

Induction Relays

• An induction relay works only with AC

• It consists of an electromagnetic system Which operates on a moving conductor,

generally in the form of a DISC or CUP

Production of Actuating Torque

Various quantities are shown at instant when

• Both fluxes are directed downward

T BlaNi

• Are increasing in magnitude

Let

It may be assumed with negligible error that the paths in which rotor current flow have negligible

self inductance.

(2.2)

Since sinusoidal flux waves are assumed, we may substitute the rms values of the fluxes for the

crest values in the above equation.

• It may be noted that the net force is same at every instant.

• The net force is directed from the point where the leading flux process the rotor towards the

point where the lagging flux pierces the rotor.

• Actuating force is produced in the presence of out of phase fluxes.

• Maximum force is produced when θ=90o

Classification Of Induction Relays

1. Shaded pole relay

2. Watt-hour- meter type relay

3. Cup type relay

• The air gap flux produced by the current flowing in a single coil is split into two out of phase

components by a so called „Shading Ring‟ generally of copper, that encircles part of the pole

face of each pole at the air gap.

1 1() sin( )mt t

2 1F F F

Fig.2.3 Shaded-pole induction relay

• The shading ring may be replaced by coils if control of operation of the shaded pole relay is

desired.

• The inertia of the disc provides the time delay characteristics.

Watt Hour –Meter Structure

Fig.2.4 Watt-hour meter relay

• This structure gets its name from the fact that it is used in watt hour meters.

• It contains two separate coils on two different magnetic circuit, each of which produces one of two

necessary fluxes for driving the rotor, which is also a disc

Induction-Cup

• This type of relay has a cylinder similar to a cup which can rotate in the annular air gap between the poles

& the fixed central core.

• The operation of this relay is similar to that of an induction motor with salient poles for the windings of

the stator

Fig.2.5 Induction-cup type relay

• The movement of the cup is limited to a small amount by the contact & the stops.

• A special spring provides restraining torque.

• The cup type of relay has a small inertia & is therefore principally used when high speed operation is

required, for example in instantaneous units.

Over-current Relays

• Protection against excess current was naturally the earliest protection systems to evolve

• From this basic principle has been evolved the graded over current system, a discriminate fault protection.

• “Over current” protection is different from “over load protection”.

• Overload protection makes use of relays that operate in a time related in some degree to the thermal

capability of the plant to be protected.

• Over current protection, on the other hand, is directly entirely to the clearance of the faults, although with

the settings usually adopted some measure of overload protection is obtained.

Types of over current Relays

• Based on the relay operating characteristics , over current relays can be classified into three groups

– Definite current or instantaneous

– Definite time

– Inverse time

Definite-Current Relays

• This type of relay operates instantaneously when the current reaches a predetermined value.

Definite Time Current Relays

• This type of relay operates after a definite time when the current reaches a pre-determined value.

Inverse Time Relays

• The fundamental property of these relays is that they operate in a time that is inversely

proportional to the fault current. Inverse time relays are generally classified in accordance with

their characteristic curve that indicates the speed of operation.

• Inverse-time relays are also referred as inverse definite minimum time or IDMT over-current

relays

Setting the Parameters of Time Delay Over-current Relay

Pick-up setting

• The pick-up setting, or plug setting, is used to define the pick-up current of the relay, and fault

currents seen by the relay are expressed as multiples of plug setting.

• Plug setting multiplier (PSM) is defined as the ratio of the fault current in secondary Amps to the

relay plug setting.

• For phase relays the pick-up setting is determined by allowing a margin for overload above the

nominal current, as in the following expression

Pick-up setting = (OLF x Inom) / CTR

where,

OLF = Overload factor that depends on the element being protected.

Inom = Nominal circuit current rating

CTR = CT Ratio

Time dial setting

• The time-dial setting adjusts the time –delay before the relay operates whenever the fault

current reaches a value equal to, or greater than the relay setting.

• The time-dial setting is also referred to as time multiplier setting (TMS)

Discrimination by Time

In this method an appropriate time interval is given by each of the relays controlling the CBs

in a power system to ensure that the breaker nearest the fault opens first.

A simple radial distribution system is considered to illustrate this principle

Fig. 2.6 A radial distribution system with time-discrimination

• The main disadvantage of this method of discrimination is that the longest fault clearance

time occurs for faults in the section closest to the power source, where the fault level is

highest.

Discrimination by Current

• Discrimination by current relies on the fact that the fault current varies with the position

of the fault , because of the difference in impedance values between the source and the

fault .

• The relays controlling CBs are set to operate at suitably tapered values such that only the

relay nearest the fault trips its circuit breaker.

Inverse time over current relay characteristic is evolved to overcome the limitations imposed by

the independent use of either time or over current coordination.

Directional over-current Relays

1. When fault current can flow in both directions through the relay location, it is necessary

to make the response of the relay directional by introduction of directional control

elements.

2. These are basically power measuring devices in which the system voltage is used as a

reference for establishing the relative phase of the fault current.

Basically, an AC directional relay can recognize certain difference in phase angle between

two quantities, just as a D.C. directional relay recognize difference in polarity

The Polarizing Quantity of a Directional Relay

1. It is the reference against which the phase angle of the other quantity is compared.

Consequently the phase angle of the polarizing quantity must remain fixed when other

quantity suffers wide change in phase angle.

2. The voltage is chosen as the “polarizing” quantity in the current-voltage induction type

directional relay.

3. Four pole induction cup constructions is normally used.

Distance relay

Distance relay is used for the protection of transmission line

In a distance relay, instead of comparing the local line current with the current at far end

of line, the relay compares the local current with the local voltage in the corresponding

phase or suitable components of them

Principle of Operation of Distance Relay

1. The basic principle of measurement involves the comparison of fault current seen by the

relay with the voltage at relaying point; by comparing these two quantities.

2. It is possible to determine whether the impedance of the line up to the point of fault is

greater than or less than the predetermined reach point impedance

There are two types of torques

1. Restraining torque

2Fr VT

2. Operating torque

2F0 IT

The relay trips when T0 greater than Tr

The constant K depends on the design of the electromagnets.

Types of Distance Relay

Distance relays are classified depending on their operating characteristic in the R-X

plane

• Impedance Relay

• Mho Relay

• Reactance Relay

Disadvantage of Impedance Relay

1. It is not directional.

2. It is affected by the Arc resistance

3. It is highly sensitive to oscillations on the power system, due to large area covered by its

circular characteristic

Operating Characteristic of Mho Relay

The Mho relay combines the properties of impedance and directional relays. Its characteristic is

inherently directional and the relay only operates for faults in front of the relay location.

Operating Characteristic of Reactance Relay

1. The reactance relay is designed to measure only reactive component of the line reactance.

2. The fault resistance has no affect on the reactance relay

Differential Relay

• The most positive method of protecting a circuit is to arrange relays to compare the

currents entering and leaving it, which should be the same under normal conditions and

during an external fault. Any difference current must be flowing in to a fault within the

protected circuit

Differential Protection current balance

2 2

F FKI V

• When this system is applied to electrical equipment (Generator stator windings,

Transformer, Bus bars etc.) it is called differential current protection.

• When it is applied to lines and cables it is called pilot differential protection because pilot

wires or an equivalent link or channel is required to bring the current to the relay from the

remote end of the line.

The CTs at both ends of the protected circuit connected so that for through load or through fault

conditions current circulates between the interconnected CTs. The over-current relay is normally

connected across equipotential points and therefore doesn‟t operate.

• Circulating current balance methods are widely used for apparatus protection where CTs

are within the same substation area and interconnecting leads between CTs are short (e.g.

generator stator windings, Transformer, Bus bars etc.)

• The circulating current balance method is also called longitudinal differential protection

or Merz-Price differential protection system.

• The current in the differential relay would be proportional to the phasor difference

between the currents that enter and leave the protected circuit. If the current through the

relay exceeds the pick-up value, then the relay will operate.

Static Relays

Advantages of Static Relays

• Due to the amplification of energizing signals obtainable, the sources need only provide

low power. Therefore the size of the associated current and voltage transformers could be

reduced.

• Improved accuracy and selectivity.

• Fast operation of relays and hence fast clearance of faults.

• Flexibility of circuitry would allow new and improved characteristics.

• The relays would be unaffected by the number of operations.

Basic Circuits Employed

• Timers

• Phase comparators

• Level detectors

• Integrators

• Polarity detectors

High reliability operational amplifiers are used for realizing the basic components of static relays

Numerical Protection

Numerical relays are technically superior to the conventional type relays. Their general

characteristics are:

• Reliability

• Self diagnosis

• Event and disturbance records

• Adaptive Protection

• Integration of Digital Systems

Typical Architecture of Numerical Relays

Numerical relays are made up from modules with well defined functions.

Fig. 2.7 Numerical Relay Architecture

Digial Relay Logic

• The digital relay does not record the analog signal,but only samples of the signal, which

are spread in time.

• the mathematics of discrete signal processing is used.

• The relay is programmed to apply various forms of digital signal processing algorithms to

the observed samples and based on the results of these computations,the decision to trip

is made.

Protection of Feeders

Media used for Protection Signaling

• Power - line - carrier circuits

• Pilot Wires

Power Line Carrier

• The signal propagation medium is power line itself, communication between ends of the

power line being effected by means of a superimposed carrier, carrier frequency signal

carried by the power circuit conductors.

• The band of frequencies employed for the carrier frequency signal is 70-700khz.

• 2. Power level is 1-2 w for continuous signaling.

• 3. 10-20 w for short -time signaling

Fig. 2.8 Over-current Protection and Earth Faults

Generator Protection

• The range of size of generators extends from a few hundred KVA to more than 500MVA

• Small and Medium sized sets may be directly connected to the distribution system

A larger unit is usually associated with an individual transformer, through which the set is

coupled to the EHV transmission system. No switchgear is provided between the generator and

transformer, which are treated as a unit. The neutral point of the generator is usually earthed, so

as to facilitate the protection of the stator winding and associated system

• Impedance is inserted in the earthing lead to limit the magnitude of the earth fault current.

• Severe arcing to the machine core burns the iron at the point of fault and welds the

laminations together. The welding of laminations would most likely result in local

overheating.

• In case of severe damage to the core, it may require rebuilding of the core, which would

involve expensive rebuilding of the windings

• Practice as to the degree of fault current limitation varies from approximately rated

current on one hand to comparatively low values on the other

• Sometimes, it is asserted that if fault current is limited to 5A, burning of the core will not

occur readily.

• Generators which are directly connected to the transmission or distribution system are

usually earthed through a resistance which will pass approximately rated current to a

terminal earth fault

• In case of generator-transformer unit, the generator winding and primary winding of a

transformer can be treated as an isolated system which is not influenced by the earthing

requirements of the transmission system

• Modern practice is to use a large earthing transformer (5-100 KVA) – the secondary

winding which is designed for 100-500V is loaded with a resistor of a value, which when

referred through the transformer ratio, will pass a suitable fault current the resistor is

therefore of low value and can be of rugged construction

• The equivalent resistance in the stator circuit should not exceed the impedance as system

frequency of the total summated capacitance of the three phases

• The resistance component of the fault current should not be less than the residual

capacitance current, that is 3 Ico

Transformer Protection

• The power transformer is one of the most important links in a power transmission and

distribution system.

• It is a highly reliable piece of equipment. This reliability depends on

• adequate design

• careful erection

• proper maintenance

• Application of protection system.

Protection Equipment Includes

1. Surge diverters

2. Gas relay: It gives early warning of a slowly developing fault, permitting shutdown and repair

before severe damage can occur.

3. Electrical relays.

• The choice of suitable protection is also governed by economic considerations. Although

this factor is not unique to power transformers, it is brought in prominence by the wide

range of transformer ratings used( few KVA to several hundred MVA)

• Only the simplest protection such as fuses can be justified for transformers of lower

ratings.

• For large transformers best protection should be provided.

Types of Faults Affecting Power Transformer

• Through Faults

a) Overload conditions.

b) External short-circuit conditions.

The transformer must be disconnected when such faults occur only after allowing a

predetermined time during which other protective gears should have operated.

• Internal Faults

The primary protection of a power transformer is intended for a condition which arises as

a result of faults inside the protection zone.

1. Phase-to-earth fault or phase- to- phase fault on HV and LV external terminals

2. Phase-to-earth fault or phase-to- phase fault on HV and LV windings.

3. Interturn faults of HV and LV windings.

4. Earth fault on tertiary winding or short circuit between turns of a tertiary windings.

Nature & Effect of Transformer Faults

A faults on transformer winding is controlled in magnitude by

a) Source & neutral earthing impedance

b) Leakage reactance of the transformer

c) Position of the fault on the winding.

Bus Zone Protection

The protection scheme for a power system should cover the whole system against all probable

type s of fault.

Unrestricted forms of line protection such as over current and distance systems, meet this

requirement, although faults in the Bus bar zone are cleared only after some time delay.

If unit protection is applied to feeder and plant the bus bars are not inherently protected.

Bus bars have been left without specific protection for one or more of the following reasons:

– The bus bars and switchgear have high degree of reliability, to the point of being

regarded as intrinsically safe.

Bus-bar Faults

• Majority of bus faults involve one phase and earth, but faults arise from many causes and

a significant number are inter-phase clear of earth.

• With fully phase-segregated metal clad gear, only earth faults are possible, and a

protective scheme need have earth fault sensitivity only.

• For outdoor bus-bars , protection schemes ability to respond to inter-phase faults clear of

earth is an advantage

Types of Protection Schemes

• System protection used to cover bus bars

• Frame –earth protection

• Differential protection

System Protection

• A system protection that includes over current or distance systems will inherently give

protection cover to the bus bars.

• Over current protection will only be applied to relatively simple distribution systems, or

as a back-up protection set to give considerable time delay. Distance protection will

provide cover with its second zone.

• In both cases, therefore ,the bus bar protection so obtained is slow

Frame-Earth Protection

• This is purely an earth fault system, and, in principle, involves simply measuring the fault

current flowing from the switchgear frame to earth. To this end a current transformer is

mounted on the earthing conductor and is used to energize a simple instantaneous relay.

MODULE-IV

Stability of power system is its ability to return to normal or stable operating condition after been

subjected to some of disturbance. Instability means a condition representing loss of synchronism

or fall out of step.

The instability of power system is divided into two parts

1. Steady state stability

2. Transient stability

Increase in load is a kind of disturbance to power system. If the increase in load takes place

gradually and slowly in small steps and the system withstand this change in load and operates

satisfactorily then this system phenomena is said to be STEADY STATE STABILITY.

Cause of transient disturbances

1. Sudden change of load.

2. Switching operation.

3. Loss of generation.

4. Fault.

Due to the following sudden disturbances in the power system, rotor angular difference, rotor

speed and power transfer undergo fast changes whose magnitude are dependent upon the severity

of disturbances.

If the disturbance is so large that the angular difference increases so much which can cause the

machine out of synchronism. This kind of instability is denoted as transient instability. It is a

very fast phenomenon it occurs within one second for the generating unit closer to the

disturbance.

Dynamics Of A Synchronous Machine

The kinetic energy of the rotor at synchronous machine is

MJJKE sm

62 102

1 (4.1)

J =rotor moment of inertia in kg-m2

sm

=synchronous speed in rad (mech)/s

s

= sm

P

2=rotor speed in rad(elect/s)

P =number of machine poles

sss MP

JKE 2

110

2

2

1 6

2

(4.2)

Where

6

2

102

s

PJM =Moment of inertia MJ-s/elect. rad

now inertia constant h be written as

sMKEGH 2

1 mj (4.3)

g =machine rating(base)in mva(3-phase)

h =inertia constant in mj/mva or mw-s/mva

so,

f

GHGHM

s

2MJ-s/elect.rad (4.4)

f

GH

180 MJ-s/elect.rad (4.5)

Taking G as base, the inertia constant in pu is

f

HM

s

2/elect.rad (4.6)

f

HM

180 s

2/elect.degree (4.7)

Swing Equation

The differential equation that relates the angular momentum M, acceleration power Pa and the

rotor angle is known as swing equation. Solution of swing equation shows how the rotor angle

changes with respect time following a disturbance. The plot Vs t is known as swing curve. The

differential equation governing the rotor dynamics can then be written as.

emm TT

dt

dJ

2

2 (4.8)

where,

J = rotor moment of inertia in kg-m2, m

= angle in radian (mech.)

Fig. 4.1 Electrical and mechanical power flow in motor

While the rotor undergoes dynamics as per Equation (9), the rotor speed changes by

insignificant magnitude for the time period of interest (1s)

Equation (4.8) can therefore be converted into its more convenient power form by assuming the

rotor .speed (ωsm). Multiplying both sides of Equation (4.8) by ωsm we can write

emm

sm PPdt

dJ 6

2

2

10

MW (4.9)

Where,

Pm= mechanical power input in MW

Pe=electrical power output in MW; stator copper loss is assumed neglected.

Rewriting Equation (4.9)

MWPPdt

d

PJ em

es

2

26

2

102

(4.11)

eme PP

dt

dM

2

2MW (4.12)

Where

ϴe =angle in rad.(elect.)

As it is more convenient to measure the angular position of the rotor with respect to a

synchronously rotating frame of reference.

Let us assume,

tse (4.13)

δ is rotor angular displacement from synchronously rotating reference frame, called

Torque Angle/Power Angle.

From Equation (4.9)

2

2

2

2

dt

d

dt

d e (4.14)

Hence Equation (4.11) can be written in terms of 𝛿 as

MWPPdt

dM em

2

2 (4.15)

Using Equation (4.11) we can also write

MWPPdt

d

f

GHem

2

2

(4.16)

Dividing throught by G, the MVA rating of the machine

em PPdt

dpuM

2

2

)(

(4.17)

Where

f

HpuM

)( , em PP

dt

d

f

H

2

2

pu

Equation (4.17) is called as swing equation and it describes the rotor dynamics for a synchronous

machine (generating/motoring). It is a second-order differential equation where the damping

term (proportional todt

d ) is absent because of the assumption of a loss less machine and the

fact that the torque of damper winding has been ignored. Since the electrical power Pe depends

upon the sine of angle the swing equation is a non-linear second-order differential equation.

Multi-Machine System

In a multi-machine system a common system base must be chosen

Let

Gmach=machine rating (base)

Gsystem=system base

Equation(18) can then be written as

system

mach

em

mach

system

mach

G

GPP

dt

d

f

H

G

G)(

2

2

Or em

systemPP

dt

d

f

H

2

2

pu in system base. (4.18)

Where

system

machmachsystem

G

GHH (4.19)

Consider the swing equations of two machines or a common system base.

112

1

2

1

em PPdt

d

f

H

pu (4.20)

222

2

2

2

em PPdt

d

f

H

pu (4.21)

Since the machine rotors swings together (coherently or in unison)

21

Adding Equation (4.20) and (4.21)

em

eqPP

dt

d

f

H

2

2

(4.22)

Where

21 mmm PPP

21 eee PPP

21 HHHeq

The two machines swinging coherently are thus reduced to a single machine as in Equation (4.

22), the equivalent inertia in (4.22) can be written as

system

machmach

system

machmacheq G

GH

GG

HH 22

11 (4.23)

The above results are easily extendable to any number of machines swinging coherently. To

solving the swing equation (Equation (4.23), certain simplifying assumptions are usually made.

These are:

1. Mechanical power input to the machine (Pm) remains constant during the period of

electromechanical transient of interest. In other words, it means that the effect of the turbine

governing loop is ignored being much slower than the speed of the transient. This assumption

leads to pessimistic result-governing loop helps to stabilize the system.

2. Rotor speed changes are insignificant-these have already been ignored in formulating the

swing equation.

3. Effect of voltage regulating loop during the transient is ignored, as a consequence the

generated machine emf remains constant. This assumption also leads to pessimistic results-

voltage regulator helps to stabilize the system.

Before the swing equation can be solved, it is necessary to determine the dependence of the

electrical power output (Pe) upon the rotor angle.

Simplified Machine Model

For a non-salient pole machine, the per-phase induced emf-terminal voltage equation under

steady conditions is.

qdqqdd XXIjXIjXVE ; (4.24)

Where

gd III

Under transient condition

ddd XXX

dq XX

Since the main field is on the d-axis

qd XX

;

Equation (4.24) during the transient modifies to.

dddq

qqdd

IjXIIjXV

IjXIjXVE

)( (4.25)

dqdd IXXjIjXV )()(

(4.26)

The phasor diagram corresponding to Equation (4.25) and (4.26) is drawn in Fig. 4.2. Since

under transient condition, dd XX

but dX remains almost unaffected, it is fairly valid to

assume that

dd XX

Fig. 4.2 Phasor diagram of a salient pole machine

Fig.4.3 Simplified machine model.

The machine model corresponding to Eq. (4.26) is drawn in Fig. (4.3) which also applies to a

cylindrical rotor machine where ///

sqd XXX (transient synchronous reactance).

Power Angle Curve

For the purposes of stability studies E , transient emf of generator motor remains constant or is

the independent variable determined by the voltage regulating loop but V, the generator

determined terminal voltage is a dependent variable. Therefore, the nodes (buses) of the stability

study network to the ernf terminal in the machine model as shown in Fig.4.4, while the machine

reactance )( dX is absorbed in the system network as different from a load flow study. Further,

the loads (other than large synchronous motor) will be replaced by equivalent static admittances

(connected in shunt between transmission network buses and the reference bus).

Fig. 4.4 Simplified Machine studied Network

Fig 4.5 Power Angle Curve

This is so because load voltages vary during a stability study (in a load flow study, these remain

constant within a narrow band). The simplified power angle equation is

sinmaxPPe (4.27)

Where

X

EEP

21

max

(4.28)

The graphical representation of power angle equation (4.28) is shown in Fig. 4.5. The swing

equation (4.27) can now be written as

em PPdt

d

f

H

2

2

pu (4.29)

It is a non linear second-order differential equation with no damping.

Machine Connected to Infinite Bus

Figure 4.6 is the circuit model of a single machine connected to infinite bus through a line of

reactance Xe. In this simple case

edtransfer XXX

From Eq (4.30) we get

sinsin maxPX

VEP

transfer

e

(4.30)

Fig. 4.6 Machine connected to infinite bus bar

The dynamics of this system are described in Eq. (4.15 ) as

em PPdt

d

f

H

2

2

pu (4.31)

Two Machine Systems

The case of two finite machines connected through a line (Xe) is illustrated in Fig. 5

where one of the machines must be generating and the other must be motoring. Under steady

condition, before the system goes into dynamics and the mechanical input/output of the two

machines is assumed to remain constant at these values throughout the dynamics (governor

action assumed slow).During steady state or in dynamic condition, the electrical power output of

the generator must be absorbed by the motor (network being lossless).

Fig. 4.7 Two machine system

Thus at all time

mmm PPP 21 (4.32)

eeme PPP 21 (4.33)

The swing equations for the two machines can now be written as

11

11

2

1

2

H

PPf

H

PPf

dt

d emem

(4.34)

And

11

22

2

2

2

H

PPf

H

PPf

dt

d meem

(4.35)

Subtracting Eq. (36) from Eq. (35)

)()(

21

21

2

21

2

em PPHH

HHf

dt

d

(4.36)

Or em

eqPP

dt

d

f

H

2

2

(4.37)

Where 21

21

21

HH

HHH eq (4.38)

The electrical power interchange is given by expression.

sin21

21

ded

eXXX

EEP

(4.39)

The swing equation Eq. (4.35) and the power angle equation Eq. (4.39) have the same form as

for a single machine connected to infinite bus. Thus a two-machine system is equivalent to a

single machine connected to infinite bus. Because of this, the single-machine (connected to

infinite bus) system would be studied here.

Steady State Stability

The steady state stability limit of a particular circuit of a power system is defined as the

maximum power that can be transmitted to the receiving end without loss of synchronism.

Consider the simple system of Fig. 4.7 whose dynamics is described by equations

MWPPdt

dM em

e 2

2 (4.40)

f

HM

in pu system (4.41)

And,

sinsin maxPX

VEP

d

e (4.42)

For determination of steady state stability, the direct axis reactance (Xd) and, voltage behind Xd

are used in the above equations. Let the system be operating with steady power transfer of

Pe0=Pm with torque angle 0 as indicated in the figure. Assume a small increment P in the

electric power with the input from the prime mover remaining fixed at Pm (governor response is

slow compared to the speed of energy dynamics), causing the torque angle to change to

)( 0 . Linearizing about the operating point Q0 (Pe0, 0 ) we can written as.

0

ee

PP

The excursions of are then described by

0

0

)(

0

2

0

2

2

02

2

e

e

eeem

PMp

or

P

dt

dM

or

PPPPdt

dM

(4.43)

Where

dt

dp

The system stability to small change is determined from the characteristic equation.

00

2

ep

Mp

Its two roots are

2

1

M

p

p

e

As long as 0

ep it positive, the roots are purely imaginary and conjugate and the system

behaviour is oscillatory about 0 . Line resistance and damper windings of machine, which have

been ignored in the above modelling, cause the system oscillations to decay. The system is

therefore stable for a small increment in power so long as

00

ep (4.44)

When 0

ep , is negative, the roots are real, one positive and the other negative but of equal

magnitude. The torque angle therefore increases without bound upon occurrence of a small

power increment (disturbance) and the synchronism is soon lost. The system is therefore unstable

for

00

ep (4.45)

0

ep is known as synchronizing coefficient. This is also called stiffness (electrical) of

synchronous machine.

Assuming |E| and |V| to remain constant, the system is unstable, if

0cos 0 X

VE

900 (4.46)

The maximum power that can be transmitted without loss of stability (steady state) occurs for

900 (4.47)

X

VEP max (4.48)

If the system is operating below the limit of steady stability condition (Eq.4.48), it may

continue to oscillate for a long time if the damping is low. Persistent oscillations are a threat to

system security. The study of system damping is the study of dynamical stability.

The above procedure is also applicable for complex systems wherein governor action and

excitation control are also accounted for. The describing differential equation is linerized about

the operating point. Condition for steady state stability is then determined from the

corresponding characteristic equation (which now is of order higher than two).

It was assumed in the above account that the internal machine voltage |E| remains

constant (i.e., excitation is held constant). The result is that as loading increases, the terminal

voltage |Vt| dips heavily which cannot be tolerated in practice. Therefore, we must consider the

steady state stability limit by assuming that excitation is adjusted for every load increase to keep

|Vt| constant. This is how the system will be operated practically. It may be understood that we

are still not considering the effect of automatic excitation control.

Some Comment on Steady State Stability

Knowledge of steady state stability limit is important for various reasons. A system can

be operated above its transient stability limit but not above its steady state limit. Now, with

increased fault clearing speeds, it is possible to make the transient limit closely approach the

steady state limit.

As is clear from Eq. (4.50), the methods of improving steady state stability limit of a

system are to reduce X and increase either or both |E| and |V|. If the transmission lines are of

sufficiently high reactance, the stability limit can be raised by using two parallel lines which

incidentally also increases the reliability of the system. Series capacitors are sometimes

employed in lines to get better voltage regulation and to raise the stability limit by decreasing the

line reactance. Higher excitation voltages and quick excitation system are also employed to

improve the stability limit.

Transient Stability

The dynamics of a single synchronous machine connected to infinite bus bars is governed by the

nonlinear differential equation

sin

sin

max2

2

max

2

2

PPdt

dM

or

PP

where

PPdt

dM

m

e

em

(4.49)

As said earlier, this equation is known as the swing equation. No closed form solution

exists for swing equation except for the simple case Pm = 0 (not a practical case) which involves

elliptical integrals. For small disturbance (say, gradual loading), the equation can be linearised

leading to the concept of steady state stability where a unique criterion of stability 0 ep

could be established. No generalized criteria are available for determining system stability with

large disturbances (called transient stability). The practical approach to the transient stability

problem is therefore to list all important severe disturbances along with their possible locations

to which the system is likely to be subjected according to the experience and judgement of the

power system analyst. Numerical solution of the swing equation (or equations for a multi-

machine case) is then obtained in the presence of such disturbances giving a plot of Vs t called

the swing curve. If starts to decrease after reaching a maximum value, it is normally assumed

that the system is stable and the oscillation of around the equilibrium point will decay and

finally die out. As already pointed out in the introduction, important severe disturbances are a

short circuit or a sudden loss of load.

For ease of analysis certain assumptions and simplifications are always made (some of

these have already been made in arriving at the swing equation (Eq. 4.49). All the assumptions

are listed, below along with their justification and consequences upon accuracy of results.

1. Transmission line as well as synchronous machine resistance is ignored. This leads to

pessimistic result as resistance introduces damping term in the swing equation which helps

stability.

2. Damping term contributed by synchronous machine damper windings is ignored. This also

leads to pessimistic results for the transient stability limit.

3. Rotor speed is assumed to be synchronous. In fact it varies insignificantly during the course of

the stability transient.

4. Mechanical input to machine is assumed to remain constant during the transient, i.e.,

regulating action of the generator loop is ignored. This leads to pessimistic results.

5. Voltage behind transient reactance is assumed to remain constant, i.e., action of voltage

regulating loop is ignored. It also leads to pessimistic results.

6. Shunt capacitances are not difficult to account for in a stability study. Where ignored, no

greatly significant error is caused.

7. Loads are modelled as constant admittances. This is a reasonably accurate representation.

Note: Since rotor speed and hence frequency vary insignificantly, the network parameters remain

fixed during a stability study.

A digital computer programme to compute the transient following sudden disturbance

can be suitably modified to include the effect of governor action and excitation control.

Preset day power system are so large that even after lumping of machines (Eq.(24)), the

system remains a multi-machine one. Even then, a simple two machine system greatly aids the

understanding of the transient stability problem. It has been shown in that an equivalent single

machine infinite bus system can be found for a two- machine system (Eq. 4.45) to (Eq. 4.49)

Upon occurrence of a severe disturbance, say a short circuit, the power transfer between

machines is greatly reduced, causing the machine torque angles to swing relatively. The circuit

breakers near the fault disconnect the unhealthy part of the system so that power transfer can be

partly restored, improving the chances of the system remain stable. The shorter the time to

breaker operating, called clearing time, the higher is the probability of the system being stable.

Most of the line faults are transient in nature and get cleared on opening the line. Therefore, it is

common practice now to employ auto-reclose breakers which automatically close rapidly after

each of the two sequential openings. If the fault still persists, the circuit breakers open and lock

permanently till cleared manually. Since in the majority of faults the first reclosure will be

successful, the chances of system stability are greatly enhanced by using autoreclose breakers.

The procedure of determining the stability of a system upon occurrence of a disturbance

followed by various switching off and switching on action called a stability study. Steps to be

followed in stability study are outlined below for single- machine infinite bus bar system shown

in fig. 6. The fault is assumed to be transient one which is cleared by the time of first reclosure.

In the case of a permanent fault, this system completely falls apart. This will not be the case in a

multi-machine system. The steps listed, in fact, apply to a system of any size.

1. From prefault loading, determine the voltage behind transient reactance and the torque

angle 0 of the machine with reference to the infinite bus.

2. For the specified fault, determine the power transfer equation )(eP during fault. In this

system Pe = 0 for a three-phase fault.

3. From the swing equation starting with 0 as obtained in step 1, calculate as a function

of time using a numerical technique of solving the nonlinear differential equation.

4. After clearance of the fault, once again determine )(eP and solve further for )(t . In

this case, 0)( eP as when the fault is cleared, the system gets disconnected.

5. After the transmission line is switched on, again find )(eP and continue to calculate

)(t .

6. If )(t goes through a maximum value and starts to reduce, the system is regarded as

stable. It is unstable if )(t continues to increase. Calculation is increased after a suitable

length of time.

Equal Area Criteria for Stability

In a system where one machine is swinging with respect to an infinite bus, it is possible

to study transient stability by means of a simple criterion, without resorting to the numerical

solution of a swing equation.

Consider the equation

aem PPPdt

dM

2

2 (4.50)

Pa =accelerating power

lf the system is unstable continues to increase indefinitely with time and the machine

loses synchronism. On the other hand, if the system is stable, )(t performs oscillations

(nonsinusoidal) whose amplitude decreases in actual practice because of damping terms (not

included in the swing equation).These two situations are shown in fig. 6. Since the system is no-

linear, the nature of its response1 [ )(t ] is not unique and it may exhibit instability in a fashion

different from that indicated in Fig. 6, depending upon the nature and severity of disturbance.

However, experience indicates that the response )(t in a power system generally falls in the

two broad categories as shown in the figure. It can easily be visualized now (this has also been

stated earlier) that for a stables system, indication of stability will be given by observation of the

first swing where will go to a maximum and will start to reduce.

Fig. 4.8 Plot of δ vs t for stable and unstable system.

This fact can be stated as a stability criterion, that the system is stable if at some time

0dt

d (4.51)

And is unstable, if

0dt

d (4.52)

The stability criterion for power systems stated above can be converted into a simple and easily

applicable form for a single machine infinite bus system. Multiplying both sides of the swing

equation by

dt

d2 , we get

dt

d

M

P

dt

d

dt

d a 22

2

2

Integrating, both sides we get

2

1

2

0

0

2

2

dPMdt

d

or

dPMdt

d

a

a

(4.53)

Where 0 is the initial rotor angle and it begins to swing due to disturbances in the system. From

Eqs. (4.53) and (4.54), the condition for stability can be written as

0

02

0

0

2

1

dP

or

dPM

a

a

(4.54)

Fig.4.9 Pe- δ diagram for sudden increase in mechanical input

The condition of stability can therefore be stated as: the system is stable if the area under Pa

(accelerating power) - curve reduces to zero at some value of . In other words, the positive

(accelerating) area under Pa - curve must equal the negative (decelerating) area and hence the

name „equal area‟ criterion of stability. To illustrate the equal area criterion of stability, we now

consider several types of disturbances that may occur in a single machine infinite bus bar system.

Figure 4.9 shows the transient model of a single machine tied to infinite bus-bar. The electrical

power transmitted is given by

sinsin maxPX

VEP

d

e

Under steady operating condition

0max00 sinPPP em

This is indicated by the point a in the Pe - diagram of Fig. 4.8.

Let the mechanical input to the rotor be suddenly increased to Pm1 (by opening the steam

valve). The accelerating power ema PPP 1 causes the rotor speed to increase )( s and

so does the rotor angle. At angle 1 , 0sin 1max1 PPPP ema (state point at b) but the rotor

angle continues to increase as )( s .Pa now becomes negative (decelerating), the rotor speed

begins to reduce but the angle continues to increase till at angle2 , )( s once again (state

point at c. At c), the-decelerating area A2 equals the accelerating area A1, (areas are shaded), i.e,

0

0

dPa

Since the rotor is decelerating, the speed reduces below s and the rotor angle begins to

reduce. The state point now traverses the eP Vs curve in the opposite direction as indicated by

arrows in Fig. 8.It is easily seen that the system oscillates about the new steady state point b

)( 1 with angle excursion up to 0 and 2 on the two sides. These oscillations are similar to

the simple harmonic motion of an inertia-spring system except that these are not sinusoidal.

As the oscillations decay out because of inherent system damping (not modelled), the

system settles to the new steady state where

1max1 sinPPP em

From Fig. 12.20, areas A1=A2 are given by

dPPA

or

dPPA

me

em

0

0

0

0

)(

)(

11

11

For the system to be stable, it should be possible to find angle 2 such that A1=A2. As Pm1 is

increased, a limiting condition is finally reached when A1 equals the area above the Pm1 line as

shown in Fig 4.10.Under this condition, 2 acquires the maximum value such that

max

11

1max2 sinP

Pm (4.55)

Any further increase in Pm1, means that the area available for A2 is less than A1, so that the excess

kinetic energy causes to increase beyond point c and the decelerating power changes over to

accelerating power, with the system consequently becoming unstable.

Fig. 4.10 Limiting case of transient stability with mechanical input suddenly increased

It has thus been shown by use of the equal area criterion that there-is an upper limit to sudden

increase in mechanical input ( 01 mm PP ), for the system in question to remain stable'

It may be noted from Fig. 9 that the system will remain stable even though the rotor may

oscillate beyond90 , so long as the equal area criteria is met. The condition of

90 is

meant for use in steady state stability only and does not apply to the transient stability case.

Effect of Clearing Time on Stability

Let the system of Fig. 4.9 be operating with mechanical input Pm at a steady angle of

(Pm=Pe) as shown by the point a on the Pe Vs diagram of Fig. 4.10. If a 3-phase fault occurs at

the point P of the outgoing radial line, the electrical output of the generator instantly reduces to

zero, i.e., Pe = 0 and the state point drops to b. The acceleration area A1 begins to increase and so

does the rotor angle while the state point moves along bc. At time tc corresponding to angle c ,

the faulted line is cleared by the opening of the line circuit breaker. The values of tc and c are

respectively known as clearing time and, clearing angle. The system once again becomes

healthy and transmits sinmaxPPe i.e. the state point shifts to d on the original Pe Vs curve.

The rotor now decelerates and the decelerating area A2, begins while the state point moves

along de. If an angle 1 can be found such that A2=A1, the system is found to be stable. The

system finally settles down to the steady operating point a in an oscillatory manner because of

inherent damping.

Fig. 4.10 Limiting case of transient stability with critical angle

The value of clearing time corresponding to a clearing angle can be established only by

numerical integration except in this simple case. The equal area criterion therefore gives only

qualitative answer to system stability as the time when the breaker should be opened is hard to

establish.

As the clearing of the faulty line is delayed, A1 increases and so does 1 , to find A2=A1

till max1 as shown in Fig. 4.10. For a clearing time (or angle) larger than this value, the

system would be unstable as A2<A. The maximum allowable value of the clearing time and angle

for the system to remain stable are known respectively as critical clearing time and angle.

For this simple case (Pe=0 during fault), explicit relationships for c (critical) and tc

(critical) are established below. All angles are in radians.

It is easily seen from Fig.4.10

0max (4.56)

0max sinPP

and

m (4.57)

)()cos(cos

)sin(

)()0(

maxmax

max2

01

max

0

crmmcr

m

crmm

PP

dPPA

and

PdPA

Now

cr

cr

For the system to be stable, A2=A1 which gives

max0max

max

cos)(cos P

Pmcr (4.58)

Where

cr =critical clearing angle.

Substituting Eq. (58) and (59) in Eq.(60), we get

]cossin)2[(cos 000

1

cr (4.59)

During the period the fault is persisting, the swing equation is

;2

2

mPH

f

dt

d where 0eP (4.60)

Integrating twice

0

2

2

tP

H

fm

Or 0

2

2

crmcr tP

H

f (4.61)

Where

tcr =critical clearing time.

cr =critical clearing angle

From Eq. (4.61)

m

crcr

Pf

H

..

)(2 0

(4.62)

Where cr , is given by the expression of Eq. (4.62)

An explicit relationship for determining tcr is possible in this case as during the faulted

condition Pe =0 and so the swing equation can be integrated in closed form. This will not be the

case in most other situations.

Consider now a single machine tied to infinite bus through two parallel lines as in Fig. 4.11a

circuit model of the system is given in Fig. 4.11b.

Let us study the transient stability of the system when one of the lines is suddenly

switched off with the system operating at a steady road. Before switching off, power angle curve

is given by

sinsin max

21

I

d

eI PXXX

VEP

Immediately on switching off line 2, power angle curve is given by

sinsin max

21

II

d

eII PXXX

VEP

Fig. 4.11 Single machine tied to infinite bus through two parallel lines

Fig. 4.12 Equal area criterion applied to the opening of one of the two lines in parallel

Both these curves are plotted in Fig. 4.12, wherein PmaxII < PmaxI as )||()( 211 XXXXX dd

.The system is operating initially with a steady power transfer Pe=Pm at a torque angle 0 on

curve I. Immediately on switching off line 2, the electrical operating point shifts to curve II

(point b). Accelerating energy corresponding to area A1 is put into rotor followed by decelerating

energy for 01 . Assuming that an area A2 corresponding to decelerating energy (energy out of

rotor) can be found such that A1 = A2, the system will be stable and will finally operate at c

corresponding to a new, rotor angle 11 . This is so because a single line offers larger

reactance and larger rotor angle is needed to transfer the same steady power.

It is also easy to see that if the steady load is increased (line Pm is shifted upward in Fig. 4.12, a

limit is finally reached beyond which decelerating area equal to A1 cannot be found and

therefore, the system behaves as an unstable one, For the limiting case of stability, 1 has

maximum value given by

c max1

This is the same condition as in the previous example.

We shall assume the fault to be a three-phase one. Before the occurrence of a fault, the power

angle curve is given by

sinsin max

21

I

d

eI PXXX

VEP

This is plotted in fig. 16

Upon occurrence of a three-phase fault at the generator end of line 2 (see Fig. 15a), the

generator gets isolated from the power system for purposes of power flow as shown by Fig. 15b.

Thus during the period the fault lasts,

PeII=0

The rotor therefore accelerates and angle increases. Synchronism will be lost unless

the fault is cleared in time.

The circuit breakers at the two ends of the faulted line open at time tc (corresponding to

angle c ), the clearing time, disconnecting the faulted line.

The power flow is now restored via the healthy line (through higher line

reactance X2 in place of Xl || X2), with power angle curve

sinsin max

21

II

d

eII PXXX

VEP

Fig. 4.13 Equal area criteria applied to the system, I system is normal, II fault applied, III faulted

line isolated.

Obviously, PmaxII < PmaxI. The rotor now starts to decelerate as shown in Fig. 4.13. The system

will be stable if a decelerating area A2 can be found equal to accelerating area A1 before

reaches the maximum allowable value max .As area A1 depends upon clearing time tc

(corresponding to clearing angle c ), clearing time must be less than a certain value (critical

clearing time) for the system to be stable. It is to be observed that the equal area criterion helps to

determine critical clearing angle and not critical clearing time. Critical clearing time can be

obtained by numerical solution of the swing equation

It also easily follows that larger initial loading (Pm.) increases A1 for a given clearing angle (and

time) and therefore quicker fault clearing would be needed to maintain stable operation. The

power angle curve during fault is therefore given by

sinsin max II

II

eII PX

VEP

PeI , PeIII and PeII as obtained above are all plotted in Fig.4.14. Accelerating area A1

corresponding to a given clearing angle is less in this case then in case a giving a better

chance for stable operation. Stable system operation is shown in Fig. 4.14, wherein it is possible

to find an area A2 equal to A1 for max2 . As the clearing angle c is increased, area A1

increases and to find A2 = A1, 2 increases till it has a value max , the maximum allowable for

stability This case of critical clearing angle is shown in Fig. 4.15

Fig. 4.14 Fault on middle of one line of the system with δ c< δcr

Fig.4.15 Fault on middle of one line of the system of, case of critical clearing angle

Applying equal area criterion to the case of critical clearing angle of Fig. 4.15 we can write

max

0

)sin()sin( maxmax

cr

cr

dPPdPP mIIIIIm

where

III

m

P

P

max

1

max sin (4.63)

Integrating, we get

or

PP

PP

or

PPPP

crIIIcrm

crIIcrm

mIIIIImcr

cr

0)cos(cos

)cos(cos

0)cos(cos

maxmaxmax

0max0

maxmax

max

0

IIIII

IIIIImcr

PP

PPP

maxmax

maxmax0max0max coscoscos

(4.64)

Critical clearing angle can be calculated from Eq. (4.64) above. The angles in the equation are in

radians. The equation modifies as below if the angle are in degrees.

IIIII

IIIIIm

crPP

PPP

maxmax

maxmax0max0max coscos180cos

If the circuit breakers of line 2 are reclosed successfully (i.e., the fault was a transient one and

therefore vanished on clearing the faulty line), the power transfer once again becomes

sinmax IeIeIV PPP

Since reclosure restores power transfer, the chances of stable operation improve. A case

of stable operation is indicated by Fig. 4.16. For critical clearing angle

I

m

P

P

max

1

max1 sin

max

0

)sin()sin()sin( maxmaxmax

rc

rc

cr

cr

dPPdPPdPP mImIIIIIm

Fig. 4.16 fault in middle of a line of the system

Point To Point Method of Improvement of Transient Stability

In most practical systems, after machine lumping has been done, there are still more than

two machines to be considered from the point of view of system stability. Therefore, there is no

choice but to solve the swing equation of each machine by a numerical technique on the digital

computer. Even in the case of a single machine tied to infinite bus bar, the critical clearing time

cannot be obtained from equal area criterion and we have to make this calculation numerically

through swing equation. There are several sophisticated methods now available for the solution

of the swing equation including the powerful Runge-Kutta method. Here we shall treat the point-

by-point method of solution which is a conventional, approximate method like all numerical

methods but a well tried and proven one. We shall illustrate the point-by-point method for one

machine tied to infinite bus bar. The procedure is, however, general and can be applied to every

machine of a multi-machine system. Consider the swing equation

GHM

M

PPP

Mdt

d a

m

)sin(1

max2

2

Or in p.u f

HM

The solution )(t is obtained at discrete intervals of time with interval spread of At uniform

throughout. Accelerating power and change in speed which are continuous functions of time are

discretized as below:

1. The accelerating power Pa computed at the beginning of an interval is assumed to remain

constant from the middle of the preceding interval to the middle of the interval being considered

as shown in Fig. 4.17.

2.The angular rotor velocity ω= dδ/dt (over and above synchronous velocity ωs) is assumed

constant throughout any interval, at the value computed for the middle of the interval as shown

in fig . 4.17

Fig. 4.17 Point-by-point solution of swing equation

In Fig.4.17, the numbering on t/∆t axis pertains to the end of intervals At the end of the (n-1)th

interval, the acceleration power is

1max)1( sin nmna PPP (4.65)

Where δn-1 has been previously calculated. The change in velocity (ω=dδ/dt), caused by the P(n-

1), assumed constant over ∆t from (n-3/2) to (n-1/2) is

)1(2/32/1 )/( nann PMt (4.66)

The change in δ during the (n-1)th interval is

2/321 nnnn t (4.67)

And during the nth interval

2/11 nnnn t (4.68)

Subtracting Eq. (4.67) from Eq. (4.68) and using Eq. (4.65), we get

)1(

2

1

nann P

M

t (4.69)

Using this, we can write

nnn 1 (4.70)

The process of computation is now repeated to obtain Pa(n),∆δn+1.and δ n+1. The time solution in

discrete form is thus carried out over the desired length of time, normally 0.5 s. Continuous form

of solution is obtained by drawing a smooth curve through discrete values as shown in Fig. 4.17.

Greater accuracy of solution can be achieved by reducing the time duration of intervals.

The occurrence or removal of a fault or initiation of any switching event causes a

discontinuity in accelerating power Pa. lf such a discontinuity occurs at the beginning of an

interval, then the average of the values of Pa before and after the discontinuity must be used.

Thus, in computing the increment of angle occurring during the first interval after a fault is

applied at t = 0, Eq. (4.69) becomes

2

)( 02

1

aP

M

t

Where (Pa0+) accelerating power after fault. Immediately before the fault the system is in

steady state, so that Pa0- = 0 and δ0 is a known value. If the fault is cleared at the beginning of the

nth interval, in calculation for this interval one should use for Pa(n-1) the value ½[Pa(n-1)_

+ Pa(n-

1)+], where Pa(n-1)

_is the accelerating power immediately before clearing and Pa(n-1)

+ is that

immediately after clearing the fault. If the discontinuity occurs at the middle of an interval, no

special procedure is needed. The increment of angle during such an interval is calculated, as

usual, from the value of Pa at the beginning of the interval.

Voltage Stability

Power transmission capacity has traditionally been limited by either rotor angle (synchronous)

stability or by thermal loading capabilities. The blackout problem has been linked with transient

stability. Luckily this problem is now not that serious because of fast short circuit clearing,

power excitation systems, and other special stability controls. Electrical companies are now

required to squeeze the maximum possible power through existing networks owing to various

constraints in the construction of generation and transmission facilities.

Voltage (load) stability, however, is now a main issue in planning and operating electric

power systems and is a factor reading to limit power transfers. Voltage stability is concerned

with the ability of a power system to maintain acceptable voltages at all buses in the system

under normal conditions and after being subjected to a disturbance. A power system is said to

have entered a state of voltage instability when a disturbance results in a progressive and

uncontrollable decline in voltage

Inadequate reactive power support from generators and transmission lines leads to

voltage instability or voltage collapses, which have resulted in several major system failures in

the world. They are:

(i) South Florida, USA, system disturbance of 17 May 1985,

(ii) French system disturbances of December 19, 1978 and January 12, 1987, (longer term).

(iii) Swedish system disturbance of December 27, 1983 (longer term, 55 sec).

(iv) Japanese( Tokyo) system disturbance of July 23, 1987 (longer term, 20 min).

(v) NREB grid disturbance in India in 1984 and 1987.

(vi) Belgium, Aug 4, 1982 (longer term, 4.5 min).

(vii) Baltimore, washington DC, USA, 5th July 1990 (longer term, insecure for hours).

Hence, a full understanding of voltage stability phenomena and designing mitigation schemes to

prevent voltage instability is of great value to utilities. Consequently over the last ten years,

utility engineers, consults and researchers have thoroughly studies voltage stability.

Voltage stability covers a wide range of phenomena. Because of this, voltage stability means

different things to different engineers. Voltage instability and voltage collapse are used

somewhat interchangeably by many researchers. Voltage instability or collapse is a faster

dynamic-process. As opposed to angle

Voltage instability or collapse is a faster dynamic-process. As opposed to angle stability,

the dynamics mainly involves the loads and the means for voltage control.

Effective Counter Measures to Prevent or Contain Voltage Instability

(i) Generator terminal voltage should be raised.

(ii) Generator transformer tap value may be increased.

(iii) Q-injection should be carried out at an appropriate location.

(iv) Load-end OLTC (on-load tap changer) should be suitably used.

(v) For under voltage conditions, strategic load shedding should be resorted to.

System reinforcement may be carried out by installing new transmission lines between

generation and load centers. Series and shunt compensation may be carried out and SVCs (static

VAR compensation) may be installed. Practical aspects of Q-flow problems leading to voltage

collapse in EHV lines:

(i) For long lines with uncontrolled buses, receiving end or road voltages increase for light load

conditions and decrease for heavy load conditions.

(ii) For radial transmission lines, if any loss of a line takes place, reactance goes up, I2X loss

increases resulting in increase in voltage drop. This should be suitably compensated by local Q

injection. Of course this involves cost. If there is a shortage of local Q sources, then import of Q

through long line may have to be resorted to. However, this is not desirable

Only the operating points above the critical points represent satisfactory operating

conditions. At the 'knee' of the V-P curve, the voltage drops rapidly with an increase in load

demands. Power-flow solution fails to converge beyond this limit indicating instability.

Operation at or near the stability limit is impractical and a satisfactory operating condition is

ensured by permitting sufficient "power margin".

Voltage Collapse

Voltage collapse is the process by which the sequence of events accompanying voltage

instability leads to unacceptable voltage profile in a significant part of the power system. It may

be manifested in several different ways. Voltage collapse may be characterized as follows:

(i) The initiating event may be due to variety of reasons: Small gradual system change such as

natural increase in system load, or large sudden disturbance such as loss of a generating unit or a

heavily loaded line.

(ii) The crux of the problem is the inability of the system to meet its reactive demands. When

transport of reactive power from neighboring areas is difficult, any change that requires

additional reactive power support may eventually lead to voltage collapse.

(iii) The voltage collapse generally manifests itself as a slow decay of voltage. It is the result of

an accumulative process involving the actions and interactions of many devices, controls, and

protective systems. The time frame of collapse in such cases would be of the order of several

minutes. Voltage collapse is strongly influenced by system conditions and characteristics.

(iv)Reactive compensation can be made most effective by the judicious choice of a mixture of

shunt capacitors, static VAR compensator and possibly synchronous condensers.

Methods of Improving Voltage Stability

i. Voltage stability can be improved by adopting the following means:

ii. Enhancing the localised reactive power support (SVC) is more effective and C-banks are

more economical. FACTS devices or synchronous condenser may also be used,

iii. Compensating the line length reduces net reactance and power flow increases.

iv. Additional transmission line may be erected. I t also improves reliability.

v. Enhancing excitation of generator, system voltage improves and Q is supplied to the

system.

vi. HVDC tie may be used between regional grids.

vii. By resorting to strategic load shedding, voltage goes up as the reactive burden is reduced.


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