chapter02 transients

7/27/2019 Chapter02 Transients

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Chapter 2

Theoretical principle concern

2.1 Transient Overvoltage in Power System2.1.1 Characteristic of Overvoltage in Power System

Electromagnetic transient overvoltage is voltage stresses which directly

effective to equipment in power system and especially to insulation. It is severe to the

system in case of stored energy in the line such as trapped charge in capacitor. The

overvoltage can be classified into two groups; the first group is external overvoltage

such as lightning. This causes from natural events. The second group is internal

overvoltage due to switching and temporary overvoltage as show in table: 2.1[4], [5].

Table: 2.1 Cases and shapes of overvoltage Standard voltage shapes and

standard withstand tests [16].


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2.1.2 Switching Overvoltage in Power System

Switching overvoltage is one of the internal overvoltages which generate

many changes in the operating conditions of network. There are a great variety of

events that would initiate a switching surge in a power network, whenever a switch in

an electric circuit is opened or closed; this is true for transmission as well as

distribution circuits. The interruption by switching operations of a circuit having

inductance and capacitance may result in transient oscillations that can cause

overvoltage on the systems. The switching operations of greatest relevance to

insulation design can be classified as following: [4], [5], [16]

Line energization Line re-energization Switching off of small capacitive currents Switching off of small inductive currents Fault initiation Fault clearing

As can be seen in table: 2.2, there are different ranges of switching overvoltage

classified by causes of overvoltages for EHV system.

Table: 2.2 Cases of switching overvoltage without protective device [6].

p.u on phase-to-ground base

Cause of overvoltages Value of maximum SOV (p u)

Closing ( line energization) 2.4 2.8

Re- Closing ( Re- energization ) 3.5 4.0

Single phase to ground 1.5 1.7

Double phase to ground 1.5 1.7

Fault clearing 1.4 1.8


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2.1.2.1 Line Energization Overvoltage in Power System

( )c

V tsin[ ( )]SV t T +

Figure 2.1 Diagram of line energization switching transient [16].

In the Figure 2.1 the inductance L represents the leakage inductance of

transformer, and the inductance of line. The resistance R includes all series resistance

of the line and transformer. The voltage across the capacitor C represents the voltage

at the open circuit end of the line which is included in the scope of study.

The circuit performance after switch on can be expressed as:

( ) 1( ) . ( ) ( )

S

di tV t R i t L i t dt

dt C= + + , (2.1)

The apply voltage ( )S

V t beyond the switching instant is:

( ) sin( )S S

V t V t T = + , (2.2)

The expression for voltage across the line capacitance is:

1( ) sin( ) sin( )t

C CV t V t T Ae t

= + + , (2.3)

Where:

2 2( . 1/ . )

SC

VV

C R L C =

+ , (2.4)

tan. 1/ .

t R

L C

=

, (2.5)

0

1

LC = , (2.6)

2 2

1 0 12 .f = + = , (2.7)


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2

R

L= , (2.8)

1 1 sin( )tancos( ) sin( )

T

T T

= +

. (2.9)

As we can see from above expression the voltage across at opened end ( )C

V t is

oscillation wave form with damped-decay. However the maximum value is the most

interesting value for design and safe operation [17].

2.1.2.2 Switching Overvoltage with Capacitive and Inductive Currents

1) Switching of capacitive currents: This includes capacitor banks,

unloaded overhead lines and cables. It involves interruption of small capacitive

currents at peak voltage. The recovery overvoltage may reach 1.5 p.u. across the

contacts of the circuit breaker. Half a cycle later, when the voltage of the feeding side

attains its maximum, a voltage of 2.5 p.u. is then established across the circuit breaker

contacts which may lead to restrike of the circuit breaker [28].

2) Switching of inductive current: When interrupting the small

inductive currents of unloaded transformers and shunt reactors, current shopping may

occur with the current forced to zero before natural current zero. The high di/dt

associated with current shopping results in high induced voltage in the inductive

circuit. This type of operation produces overvoltages of 2 to 3 p.u. in modern

transformer; however, with transformers loaded with shunt reactors, value up to 5 p.u.

may be reached which necessitates the use of surge arresters for protection [17].

2.1.2.3 Switching Overvoltage with Fault Initiation and Clearing

Initiation and closing of system faults: the most frequent fault on

power systems is the short circuit phase to earth which is often accompanied by anincrease of neutral potential. If the fault occurs at peak voltage, then up to 2.7 p.u

overvoltages can be generated. Reducing of ratio ( X0/X1 ), however, will

significantly limit the overvoltage: e.g. for a configuration having a ratio equal to 1,

no overvoltage has been observed. The single phase fault which causes an asymmetry

is therefore the most dangerous fault. The clearing of a fault by circuit breakers, in

particular a three phases fault, will also generate crest overvoltages of up to 3 p.u. as

shown in Figure 2.2 [17].


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CV C

CBL

cosm

SourceV V t =

Fault

Fault

CB

Figure 2.2 Equivalent circuit of transient recovery voltage when a circuit

breaker clears a fault [18].

The simplest circuit that can be chosen to illustrate this phenomenon is that

shown in Figure 2.2. It is assumed that load being fed through the circuit breaker is

suddenly isolated by the occurrence of a fault and that fault is a dead short circuit.

Where:

L is all the inductance limiting the current to the point of fault.

Cis the natural capacitance of the adjacent to the circuit breaker.

In the circuit of Figure 2.2 the current is assumed to be symmetrical and will be

completely reactive since it is limited entirely by inductance. This means that at the

instant of current zero, the circuit voltage will be at a maximum value, but the voltage

at the switch contacts, and therefore across the capacitor C, will be arc voltage. The

relative importance of the arc voltage varies.In this analysis, time will be measured from the instant of interruption when the

fault current has just come to zero. Sine the source voltage is a sinusoidally varying

quantity and is at its peak at the moment, it is expressed as cosm

V t . The circuit

equation is therefore

cosc m

dIL V V t

dt+ = , (2.10)

There are two unknowns, I and VC , so another relationship between them is

required. This is


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cdV

I Cdt

= , (2.11)

after the switch has cleared, the only path for current is into the capacitor. The

combination of these equations gives

2cos

2c c m

d V V V t

LC LCdt+ = , (2.12)

Let2

01/LC = , and transform Equation 2.12:

2 ' 2 2

0 0

2 2

( ) (0) (0) ( )c c c c m

ss v s sV V v s V

s

+ =

+,

or

'2

0 2 2 2 2 2 2 2 2

0 0 0

(0)( ) (0)

( )( )

cc m c

Vs sv t V V

s s s s

= + +

+ + + + (2.13)

If we neglect are voltage the second term on the right is zero. The third term is also

zero because, from Equation 2.11, '(0)

(0) 0c

IV

C= = ,

Therefore only the first term remains. Now

2 2 2 2 2 2 2 2 2 2

0 0 0

1( )

( )( )

s s s

s s s s =

+ + + +,

Therefore

2

0

2 2 2 2 2 2

0 0

( ) ( )c ms s

v s Vs s

=

+ +,

and

2

0

02 20

( ) (cos cos )c m

V t V t t

=

, (2.14)

Equation 2.13 is the voltage appearing across the switch contacts after current

zero. It is the classical transient recovery voltage described by Park and Skeats [18].

Almost invariably 0 >>, so that2 2 2

0 0/ ( ) 1 . Thus to a very close

approximation,

0( ) (cos cos )c mV t V t t = , (2.15)

Indeed, it often happens that over the period of interest (the time for switch the


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natural frequency oscillation persists), there is little change in the power frequency

term. In this case equation 2.14 can be further reduced to give

0( ) [1 cos ]c mV t V t = . (2.16)

This is very evident from Figure 2.3 which shown as oscillogram of the current

interruption period. In this case the transient recovery voltage oscillation (lower trace)

lasts for about 600 s . The decline of the current to zero can be seen in the upper

trace. It will be noted that transient recovery voltage begins with a small excursion of

the opposite polarity to the instantaneous system voltage. This indicates some current

chopping [18].

Figure 2.3 Characteristic of restriking voltage [18].

2.1.3 Temporary Overvoltage in Power System

Temporary overvoltage is characterized by amplitude and durations,

typically from a few cycles to a few seconds. These overvoltages differ from transient

switching overvoltages in that they last longer. They take the form of undamed or

slightly damped oscillation at a frequency equal or close to the power frequency. The

classification of temporary overvoltages as distinct from transient switchingovervoltages is due mainly to the fact that responses of the power network insulation

and surge arresters to their shapes are different. Some of the most important events

leading to the generation of temporary overvoltages are discussed briefly as

following: [4], [5], [17]

Ferranti effect ( Long line effect ) Load rejection

Transformer energization Ground faults


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2.1.3.1 Ferranti Effect Overvoltage in Power System

ES

XS R

X 0S

U

RU

( )xU

E

l

Figure 2.4 Equivalent of the Ferranti effect rise voltage at opened line [17].

From Figure 2.4 the Ferranti effect of an uncompensated transmission line is

given by

cosh sinhS R R C

U U l I Z l = + , (2.17)

sinh coshRS RC

UI l I lZ = + , (2.18)

No load in line 0R

I =

coshS

R

Ul

U= , (2.19)

where:

RU and

SU are the receiving end and the sending end voltages,

respectively; cZ is impedance of line and lis line length in km.

is the phase shift constant of the line per unit length. It is equal to the

imaginary part of 1/2( )YZ , where Z and Y are impedance and admittance

of the line per unit length.

Obviously for uncompensated transmission line the highest overvoltage will

appear at the receiving end.

For a losses line:

LC = , (2.20)


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where:

Land Care inductance and capacitance of the line per unit length.

has a value of about 6per 100 km at the normal power frequency.

When the impedance of sourceEbe consider and the shunt reactor was installed

at the receiving end of the line [17].

The voltage rise at the receiving end is:

cos . cos

cos( )

RU

E l

=

+ +, (2.21)

Where:

RX the reactance of shunt reactor,

SX is the transient reactance of

generator in series with the transformer reactance and lis line length in km.

tan SX

Z= , (2.22)

tanR

Z

X= . (2.23)

2.1.3.2 Load Rejection Overvoltage in Power System

E

X

CX V

Figure 2.5 Equivalent circuits during load rejection [17].

From Figure 2.5 when the transmission line or large inductive load that is fed

from power station is suddenly switched off, the generator will speed up and busbar

voltage will rise.

The amplitude of the overvoltage can be evaluated approximately by

C

C

XV E

X X=

. (2.24)

where:


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E is voltage behind the transient reactance, which is assumed to be

constant over the subtransient reactance of the generator in series with the

transformer reactance [17].

X is the transient reactance of generator in series with the transformer

reactance

CX is the equivalent capacitive input reactance of the system.

2.1.3.3 Inrush Transient by Switching on Transformer

Transformer energization creates transient inrush currents, when the

transformers core becomes over fluxed or saturation. Transformer inrush currents can

have a high magnitude containing a significant harmonic content. The harmonic rich

transformer inrush currents interact with harmonic resonances of power system.

The inrush is most severe when the transformer is switched on the instant the

voltage goes through zero with such polarity that flux increases in the direction of

residual flux is shown in Figure 2.6 [18].

Figure 2.6 Equivalent circuit of a transformer.

For condition above, we may write:

2 sin dd

v V t N s s dt dt

= = = , (2.25)

The value of the flux is then found by integration:

0

2sin (0)

t

sV tdtN

= + , (2.26)


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where 0(0) = is the residual flux, thus

0 02 (1 cos ) coss mV t tN

= + = + +

, (2.27)

Representing winding and core losses, the periodic component 0m + , is

obtained as a constant quantity. However, due to these losses, the aperiodic term

decays very slowly according to the large time constant of magnetizing circuit.

Then, at t = ( a period after switching) the instantaneous flux will be

max 02 m = + , (2.28)

The magnetic flux density under steady-state conditions is 1.3mB T . If

0 is assumed to 0.6 m , then the maximal flux density, which in a transformer

is directly proportional to the flux, will be

max (2 0.6)1.3 3.4B T T= + . (2.29)

The typical curve of an inrush current for a transformer switched at zero

instantaneous voltage is shown in Figure 2.7 [19].

Since a magnetic flux density is the ratio of magnetic flux to a given area with

passes through equation 2.28 can be recast of following:

max 0(2 )c mA B B = + , (2.30)

Bm and BO are the peak steady state and residual magnetic flux density

magnitudes, and Ac is sectional area of the transformer core. Equation 2.30 assumes

that the flux lines are perpendicular toAc.

Using Amperes Law, wherea

H dl iN= and a aB H= , we can compute the

inrush current magnitude as follow:

0(2 ),a c

inrush m Sat

a

H l A lI B B B

N NA= = + + (2.31)

where lis the mean length of the transformer leg and winding, Nis the number of the

turns in winding and is the flux linkages. It should be noted that the inrush current

magnitude estimate is the maximum theoretical value as shown in Figure 2.7.


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Figure 2.7 (A) Magnetizing curve, (B) Inrush current of transformer [18].

2.2. Determination of Transient Overvoltages

At present, computer is an important equipment used for analyzing the

overvoltage in power system because of its high accuracy, speed and convenient to

change the parameters. There are four main methods for analyzing the

electromagnetic transient overvoltage in the transmission line which are Lattice

Diagram, Fourier Transform, Transient Network Analysis (TNA) and

Electromagnetic Transient Program (EMTP). The detail of each method could be

explained as follows:

2.2.1 Lattice Diagram Method

Lattice Diagram is an excellent method of keeping track of the various

reflections as they occurred. By applied reflection theory the voltage at the receiving

end can be plotted. But the method is not suitable for actual system, because there are

many transmission lines connect together. For study of transient in single line this

method is rather suitable [20].

(A)

(B)


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2.2.2 Fourier Transform Method

This method is applies in the frequency domain analysis and convert in the

time domain in final state. The output results are more accurate than Lattice Diagram

method. But the Fourier Transform is not convenient for complicated or network

systems [21].

2.2.3 Transient Network Analysis (TNA) Method

This method is simulator device for power system or substation. The

Transient Network Analysis can be used to study transient switching surge level that

take place at the substation. It is suitable for specified model with all equipments are

not change, because must re-arrange modeling which take the time and cost. The

results may be used to determine and coordinate proper impulse insulation and

switching surge strength required in substation apparatus [21].

2.2.4 Electromagnetic Transient Program (EMTP) Method

Generally in electromagnetic transient simulations, there are two main

ways to represent transmission lines. The most familiar method is Pi sections model.

The other method is a distributed transmission line, which is most suited for transient

line response modeling using digital computer [22].

Using transient studies in the Electromagnetic Transient Program is very popular

in the world. This simulator not only can simulate the transient in power systems, but

also simulate steady state solutions and Transient Analysis of Control Systems

(TACS). If there is any change in equipment, it is very easy to modify the model and

re-simulate as user requirement [20], [23].

2.2.4.1 Equipment Modeling

There are many types of equipment models in the PSCAD/EMTDC program library. This thesis used the equipment models for the 500 kV

transmission line Nam Theun 2 Roi Et 2 from program library as shown in table 2.3.


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Table: 2.3 Equipments modeling of 500 kV transmission system [20], [23].

List

Transmission

line / Equipment Modeling of equipment

1 Transmission line Traveling wave parameter frequency dependent model

2 Transformer Lumped linear elements, Type short circuit impedance

3 Generator Non-linear elements, Type three phase (X)-matrix

4 Surge Arrester Non-linear elements, Type metal oxide arrester

5 Circuit Breaker Lumped linear elements for pre-insert resistor, Ordinary switches

6 Shunt Reactor Lumped linear elements

7 Load Lumped linear elements

2.2.4.2 Transmission Line

There are three basic transmission line modeling techniques in

PSCAD/EMTDC: Pi section model, the Bergeron model, and the frequency

dependent line models. The requirements for this research will determine which one

of three models will be suitable [22].

2.2.4.2.1 The Pi Section Model

Equivalent Pi section is shown in Figure 2.8. There are

two Pi line section components: normal Pi line model and coupled Pi line model. One

Pi section is equal 15 km of transmission line length. If the line is longer than 15 km,

then two or more Pi sections should be cascaded in series, a maximum of 10 Pi

sections for a long line is adequate. This model is usually quite short line and it is use

at power frequency, where R, L and C is resistance, inductance and capacitance of

line per unit length [22-24].

1[C]

2

1[ ]

2C

Figure 2.8 The transmission line model Pi-circuit [25].


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2.2.2.4.2 The Bergeron Model

The Bergeron model is based on a distributed LC

parameter traveling wave line model with lumped resistance. It should generally be

chosen over a Pi model, lines over 15 km could be represented by Bergeron model.

The model produces a constant surge impedance and is essentially a single frequency

model, it is roughly equivalent to using an infinite number like of Pi Section except

that resistance is lumped by inserting R/2 in the middle of line and R/4 at each end

of the line. The Bergeron model can be used for any general fundamental frequency

impedance studies, such as relay testing or matching load-flow result.

A line model will be represented as shown in Figure 2.9 (A) and (B) with 0Z for

the characteristic or surge impedance [] and for travel time of the line [s]. The

travel time of the line and the characteristic impedance 0Z can be related to

inductance and capacitance of the transmission line [22-24].

1

4

R 1

4

R1

2

R

(B)

Figure 2.9 (A) Lossless line [6], (B) Equivalent impedance network [22].

2.2.2.4.3. The Frequency Dependent Line Model

The frequency dependent line model represents the

frequency dependence of all parameters R, L and C. This model should be used for all

k m

( )kV t ( )mV t 0

Z 0Z

( )kI t

( )mI t

,k mi

,m ki mk

(A)


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studies that require frequency other than the fundamental to be represented accurately

such as transient overvoltage, harmonic analysis etc. There are two models: the

frequency dependent phase model is the most accurate, as it presents the frequency

dependence of internal transformation matrices, whereas the frequency dependent

mode model assumes a constant transformation. The line is divided into two sections,

each section of transmission line has characteristic impedance. The voltages and

currents at one end of the line at the time ( t ) may be represented in terms of the

voltage and current at the other end at the time ( t- ), and related in terms of sources

( )kb t and ( )mb t . The Bergeron model and frequency dependent model are basically

distributed parameters traveling wave models. This model can be solved using the

more advantage phase domain techniques. The thesis is used this model for

representing equipment models for transmission line, because it is more accurate and

suitable for analysis of switching and temporary overvoltage. The frequency

dependent line model is shown in Figure 2.10 [6], [22-23].

Figure 2.10 Traveling wave frequency dependent line model (Matrix) [6], [9].

2.2.4.3 Transformer

Transformer is device that transfers energy from one circuit to

another by means of a common magnetic field. In all cases except autotransformers,

there is no direct connection from one circuit to the other.

Transformer model in Electromagnetic Transient Program is presented through

one of two fundamental methods. Simulation of transformers requires an

understanding of some of their basic properties involving both core and winding

configuration. This is complicated by the fact that the core of the transformer is prone


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to saturation leading to the phenomena of the inrush current, remanence geomagnetic

current effect and Ferro resonance. The two mutually couple winding is shown in

Figure 2.11.

Figure 2.11 Two mutually couple winding.

Where:

11L : Self inductance of winding 1

12L : Mutual inductance between winding 1 and 2

22L : Self inductance of winding 2

The voltage across the first winding is 1Vand the voltage across the second

winding is 2V . The following equation describes the voltage and current relationship

for two coupled coil [22].

1

2

V

V

=11

12

L

L

12

22

L

L

.1

2

Id

Idt

. (2.32)

2.2.4.4 Generator

In electricity generation, an electrical generator is a device that

converts mechanical energy to electrical energy, generally using electromagnetic

induction. The reverse conversion of electrical energy into mechanical energy is done

by a motor, and motors and generators have many similarities. A generator forces

electric charges to move through an external electrical circuit, but it does not create

electricity or charge, which is presented already in the wire of its windings.

Synchronous machines are simply represented as voltage sources. Switches arenot needed for the connection of these sources since they are connected to the network


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at all times. However, sources parameters ( StartT and StopT ) are employed to model the

period during which the source is in effect. Therefore, the source functions are zero

between 0 < t Stop

T . The source functions are evaluated at discrete

time step t t= , 2 t ,. only. Linear interpolation is assumed by the program to be

in-between. The following option is adopted for the sinusoidal function

representation:

max 0( ) cos( ( ) )startv t V t T = + , (2.33)

wheremaxV , 0 ( in degrees), startT ( in second ) must be supplied. The value 0startT < is

used to get AC steady state solution. Before entering the transient solution, negative

value ofstart

T are set to zero and treated as zero in the equation 2.33 [26].

2.2.4.5 Surge Arrester

The arrester equipments used in the transmission line are Metal-

Oxide and Zinc-Oxide. The resistance property of arrester equipment is non-linear, it

is normal practice in the 500 kV transmission line between Nam Theun 2 and Roi Et 2

to install surge arresters to protect transmission system equipments from the damage

by lightning. A bank of surge arrester is connected to one end of a three phases

distributed parameter transmission line. The non-linear current voltage characteristic

of a metal oxide arrester ( MOA) is shown in equation 2.34.

/ .k k

I V C

= (sign of kV ) , k= 1,2,,m, (2.34)

where m = 3 for three phase

= is constant.

C = difference voltage.

These equations are solved simultaneously with the rest of the network, which is

represented by the three phase Thevenin equivalent circuit

[ ] [ ] [ ][ ]open THEV

V V R i= . (2.35)

In each time step. Since the equations are nonlinear, a solution can only be

obtained iteratively. Newtons method is used to solve these equations for the voltage.

The accuracy of the convergence is determined according to a predefined tolerance

V . It is shown in Figure 2.12 [26].


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1k 2k 3k

1m 2m 3m

Figure 2.12 Equivalent circuit of surge arrester [6].

2.2.4.6 Circuit Breaker

In general, there are five basic switch types in electromagnetic

transient program which are modeled as ideal switches. In this thesis the time

controlled switch is used for modeling transmission line circuit breakers, as well as

for fault representation. The switch is originally open, and close atclose

T . It opens

again afteropen

T ( if maxopenT Tp ), where maxT is the maximum time for the transient

simulation, either as soon as the absolute value of the switch current falls below a user

defined current margin, or as soon as the current goes through zero. 0close

T p signal to

the program that switch is normally closed. The switching operation due to fault

inception and/or fault clearing is modeled as shown in Figure 2.13 [26].

R

2

switch R

2

switch

Figure 2.13 Equivalent of circuit breaker.

2.2.4.7 Shunt Reactor

Shunt reactor has been employed on power to partially compensate

the capacitive charging currents of long high voltage AC overhead lines or high

voltage cable systems. The technical advantages they provide include:

- Control of voltage rise at the ends of long high voltage lines at periods of high

load or following load rejection.

- Prevention of self-excitation of generators on leading power factor load.


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- Reduction of overvoltage due to line to ground fault.

- Reduction of switching overvoltage due to the initial charging of lines.

Shunt reactor compensation has a two fold effect when situated at the

transmission line receiving end, both respects of which contribute to a reduction in the

severity of the transient overvoltages. The reactor reduces the magnitude of the

Ferranti rise long line by negating the effect of portion of the line shunt capacitance

and presents a line termination other than an open circuit to any traveling waves from

the transmission line sending end as shown in Figure 2.14 [27].

Neutral reactors is compensated in additional to ensuring that the design of the

main reactors will satisfactory for single phase recloser, it is necessary to eliminate

the risk of an arc being maintained by capacitance coupling after this phase on with

the fault occurred has been disconnected by circuit breaker operation. This can be

achieved by connection a neutral reactor between the star point of the phase reactor

and earth [20].

, ( )k mi t t

2LR

t=

( )k

V t ( )m

V t

, ( )k mi t

Figure 2.14 Equivalent circuit shunt reactor using lumped elements [22].

2.3 Control Transient Overvoltages in Power System

The adverse effects of overvoltages on power networks can be reduced in two

ways: by using protective devices such as surge arrester or by reducing their

magnitudes wherever the surge originates. The latter way is commonly known

overvoltage control. The techniques employed to control switching surges and

temporary overvoltages are outlined briefly below.


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2.3.1 Pre-Insertion Resistor in Circuit Breaker Devices

This is one of the most common methods for reducing energization

overvoltages. It is effected by initially applying the voltage to the line, normally

between one-third or one- half of a cycle, the pre-insertion is short circuit, allowing

the full apply voltage to be applied to the line. The initial amplitude of the

energization surge when the pre-insertion resistor of value R is used would be only

0 0/( )Z R Z+ of reached in the absence of the resistor. It is shown in Figure 2.15,

where 0Z is surge impedance of the line. When the resistor is short at the end of the

pre-insertion period, another surge will develop. If R is too small, control of the first

surge become ineffective; if it is too large, the second surge become dangerous. An

optimal value of T would normally be a fraction of 0Z , and depend on transmission

line length [16].

Figure 2.15 Diagram of circuit breaker with pre-inserted resistor.

( R Pre-inserted resistor, 1K - Arcing contract and 2K - Main contract )

It is effected by initially applying the apply voltage to the line through a resistor.

By the end of the pre-insertion period, the magnitude of the energization surge is

usually is much reduced by the effect of the system damping.

2.3.2 Use of Shunt Reactor

Shunt reactors are used on many high voltage transmission lines as a

means of shunt compensation to improve the performance of the line, which would

otherwise draw large capacitive currents from the supply. The additional advantage of

shunt reactor is to decrease the transient surge magnitudes. This is accomplished

mainly by reduction in temporary overvoltages, as will be seen in the next section.

R 1

K

2K


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The shunt reactors can effectively control the temporary particularly the Ferranti

voltage rise.

2.3.3 Use of Surge Arrester

Surge arresters are used to control transient overvoltages effect on power

system, particularly the Zinc Oxide arrester, as shown in Figure 2.16.

Figure 2.16 Typical voltage-current characteristic of surge arrester [24].

Surge arresters are used of protective of power system equipment against surge

ovevoltages because they offer low protection levels and permit the decreasing of

insulation levels, which has a substantial effect on the cost of high voltage equipment.

2.4 Statistical Switching Studies

Circuit breaker closing in power systems can produce transient overvoltages

whose maximum peaks depend on several factors such as network configuration on

the source side of the circuit breaker and the amount of trapped charge in reclosing

operations of transmission lines. Therefore, statistical switching studies are used to

determine the maximum switching overvoltages along the transmission line [28].

Current ( A)

Voltage in (p.u) of rate voltage ( Crest value )


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Since all switching surges are products of circuit breaker actions, the random

variation in switching surges is attributed primarily to the performance of these

devises, as well as the network circumstances at the time of switching. Random

angles of switching are mainly responsible for this variation. The following factors

contribute to the randomness in switching angle:- The mechanical movement of circuit breaker contacts produces fluctuations

about the aiming angle of interruption or closure.

- Circuit closure may be prematurely effected following a breakdown betweenthe breakers contacts.

- Arc interruption, whose timing is relevant to the production of recoverytransient voltages, involves a number of physical processes, many of which

are inherently random.

In Figure 2.17 shows the closing and the delay times of circuit breaker. When

the operator closes the circuit breaker at time = t. Each phase of the circuit breaker

does not close immediately since the delay time of mechanical equipment. Normally,

each phase does not close at the same time. Therefore, in this work, it should be

assumed that circuit breaker phases a, b and c are closed at t+ta, t+tb and t+tc

respectively [16], [28], [29].

Figure 2.17 Circuit breaker closing and delay times [6].

The closing angles of the three breaker poles are the phase angles of the source

side voltages at the instant of electrical closure of the contract. The angles have a

strong influence on the line closing and reclosing overvoltages as they determine the

initial conditions for the transients. For transients, when they are not controlled,

undesired closing instants of the three poles many occur, but only within the limits of


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the circuit breakers pole span. The pole span is the time between the first and the last

pole to close. When all the three breaker poles close simultaneously, the overvoltages

are smaller than those of random closing.

If pre-insertion resistors are used to mitigate switching overvoltages, the closing

times of both main and auxiliary contacts are statistically determined. The closing

times can be determined assuming that main contacts aim at the same closing time

and both switches have a normal distribution. If statistical switches are used to normal

present a circuit breaker with pre-insertion resistors, the closing time of the auxiliary

contact is determined as follow [28]:

( ) ( )close slave close master off set T T T= + , (2.36)

whereoffset

T is now a constant value.

Therefore, the transient overvoltages depend upon the instant on the voltage

waveform at which the circuit breaker contacts close electrically. A statistical

switching case study typically consists of 100 or more separate simulations, each

using different set of circuit breaker closing times shown in Figure 2.18. The statistic

can be used to process the peak overvoltages from all the simulations. Normally, the

2% value on the cumulative frequency distribution curve is used to design

overvoltages. This thesis selects a numerically 200 times closing poles of circuit

breaker [6], [16], [28].


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-3

T

T

3

T

+

2

T

+

T

+-

2

T

-

T

6

Figure 2.18 Breaker pole random closing orders for the simulation of SOV during

line energization and reclosing [16].

In the transient overvoltage study, the breaker trip order is given at a precisetime during the simulation since the system separation time has a minor impact on the

near steady state overvoltage. During line energizing or single phase reclosing tests,

the breaker pole closing orders are generated as follows [16]:

- The _

T angle is first randomly selected recording to an even distribution

between 0and 360of period of the fundamental frequency.

- Afterwards, the closing time of the three breaker poles auxiliary contacts is

selected according to normal distribution around point _T truncated at

3 (3 2 )ms = . The operation simulates breaker three poles closing time

dispersion.

- Finally, the closing time of the breaker three main interrupting heads is

delayed by 10 ms with respect to point _

T with a standard deviation of

2 ms normally distribute around this point (3 2 )ms= . The operation is to

simulate the insertion time of the reclosing resistors. This procedure is

illustrated in the following Figure2.18 [4], [16].


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chapter02 transients

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