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EXPERT SYSTEMS AND SOLUTIONS

Email: expertsyssol@gmail.com

expertsyssol@yahoo.com

Cell: 9952749533www.researchprojects.info

PAIYANOOR, OMR, CHENNAI

Call For Research Projects Final

year students of B.E in EEE, ECE, EI,

M.E (Power Systems), M.E (Applied

Electronics), M.E (Power Electronics)

Ph.D Electrical and Electronics.

Students can assemble their hardware in our

Research labs. Experts will be guiding theprojects.

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Electrical Transients in Power System

January 2009

Mehdi Vakilian

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Text Books:

1-Transients in Power Systems

by: Lou van der Slius, 2001

2- Electrical Transients in Power Systemby: Allan Greenwood, 1991

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COURSE OUTLINE

Fundamental Notions About Electrical Transients

Basic Concepts and Simple Switching Transients

Damping Effect on Switching Transients

Abnormal Switching Transients

Testing ofCircuit Breakers

Transient Analysis of3Ph Power Systems

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Course Outline ..continued

Transient Analysis of3Ph Power Systems

Traveling Waves and OtherTransients on

Transmission Line

Modeling PowerEquipments forTransients

Numerical Simulation ofElec. Transients

Lightning and its Induced Transients

Insulation Coordination

Protection Against Over Voltages

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Evaluation System

Assignments 10%

Mid Term One (items 1 to 4) : 10%

Mid Term Two (items 5 to 7) : 10% Final : 60%

Class Project : 10%

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Chapter One : Fundemental Notions

about Electrical Transients Time Scale in Power System Studies:

planning, Load Flow, Dynamic Stability

Switching, external disturbancesFrequency Content

Differential Equations Solution

Distributed and Lumped ParametersCalculatable,Controllable, Preventable

Tools for Study

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CCT Parameters

In Steady State and

Transient

Mathematical

Presentation & Physical

Interpretation

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Simple RCCircuit, Closing Ideal Sw.

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Equations ofRCCircuit

1dQ dV I C

dt dt

! !

11

dVV RC V

dt

!

1

1

dV dt

V V RC

!

1V IR Idt

C

!

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RCCircuit Response

/1

t RCV V Ae

!

/1 1[ (0)] t RCV V V V e!

.)ln( 1 ConsRC

tVV !

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RCCircuit Discharge

11 0

dV RC V

dt !

/1 1(0) t RCV V e!

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Capacitor Voltage ofRCCCT

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Simple Circuits Characteristic

(th

umbprint)RC , RL , LC Circuits

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Thumbprints:

RC CCT: Time

Constant ; RC

RL CCT : Time

Constant ; L/R LC CCT : Period of

Oscillation ;

2 LCT

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Principle of Superposition

Ifstimulus s1 produces R1

& s2 produces R2

applying s1+ s2 simultaneouslyresponds R1+R2 in Linear System

Linear System: responseproportional to :

stimulus

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S.P. Application in Switching

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CCT Detail I1: Pre-opening current

I2: Superposed currentto simulate current cease

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S.P. application in Closing switch

V1 : voltage across contacts pre-closing

Therefore:

-V1fictitious stimulus superposedsimulating the closing action

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The LaplaceTransform Method

0

, 0

( ) ( )

lim ( )

st

st

a

F t F t e dt

F t e dtX

^

g

pg p

!

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Laplace Transform Continued

1 2 1 2

( ) ( )

( ) ( )

( ) ( )

[ ( ) ( )] ( ) ( )

s j

t f s

I t i s

V t v s

t t t t

W [

^

^

^

^ ^ ^

!

!

!

!

!

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Transform of Simple Functions

00 0

'

'' ' '

2

0 0

.

( )

st

st st

st st

consV

e VV V e dt V e dt Vs s

I t I t

II t I t e dt I t e dts

^

^

! ! ! !

!

! ! !

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Laplace Transform continued

sin2

j t j t e et

j

[ [

[

!

2 2

1 1 1sin ( )

2t j s j s j s

[

^ [ [ [ [! !

2 2cos st s^ [

[

!

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Laplace Transform Application

' ( ) ( ) (0)F t s F t F ^ ^!

'' 2 '( ) ( ) (0) (0) F t s F t sF F ^ ^!

( ) 1 2 ' 1( ) ( ) (0) (0) ... (0)n n n n nF t s F t s F s F F ^ ^ !

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Laplace Transform Continued

01 1

[ ( ) ] ( ) ( )

t

t dt t d s s

^ ^ X X

!

0

1 1[ ( ) ] ( ) ( ) ( )

t

I t dt I t I t dt ts s

^ ^ ^g g

! !

( ) (0)[ ( ) ] ( )

t

i sI t dt q ss s

^g

! !

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SolvingRC problem with Lap. Trans.

In terms of I in the

CCT:

Applying L.P. :

0d I I

d t R C !

( )( ) (0) 0

i s si s I

RC

!

(0 )(0 ) c

V VI

R

!

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ContinuingRC CCT solution

The L.T. solution:

The time solution:

( 0 ) 1( )

1cV Vi s

R sR C

!

(0)( ) [ ]

t

c RC

V VI t eR

!

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RL CCT excited by Battery V

Solving for I in CCT

The L.T. ofEq.:

The response:

dIRI L V

dt !

( ) ( ) (0)V

Ri s L si s LIs

!

1( ) ........ (0) 0

[ ]

Vi s I

RL s sL

! !

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RL Time solution

1 1 1 1[ ]( ) s s s sE E E

!

1 1 1 [1 ]

( )

te

s s

E^

E E

!

( ) [1 ]R t

LV

I t eR

!

(0) 0, : (0)tR

L I add I e

{

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Example: 377 MVA Gen field winding

L=0.638H, Exciter noload:1.2 MW(480V) Energy stored in F.W.:

6

1.2 10 2500480

I Av! !

2 2 61 10.638 2.5 10 1.994

2 2E L I ! ! v v v !

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How must the exciter voltage be changed

to reduce the field current to zero in 5 Sec

. .

4 8 00 .1 9 2

2 5 0 0f WR ! ! ;

0.638

3.3230.192

L

sRX ! ! !

53.323(5) 2500 (1 ) 0( )

0.192

exciter

VI e V V

! ! !

617......V Volts( !

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Example on LCCC T Transient

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Two energy stored elements

Second order O.D.E.

c

d IL V V

d t !

1d IL Id t V d t C

!

(0)( )( ) (0) c

Qi s VL si s LI

sC sC s !

(0 ): (0 )c c

Qw h e r e V

C!

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LCCCT solution Ass. I(0)=0

2 2

(0) 1( ) (0)1 1( ) (

)

cV V si s IL s s

LC LC

!

12 020 2 2

0

1(0) 0, ( ) ( )cCV i s V

LC L s

[

[

[

! ! p !

12

0( ) ( ) sinC

I t V t L[!

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LCCCT cont. solving for Vc

Surge Imp. 12

0 ( )L

ZC

!

2

2 2

0 02c c

d VV V

dt[ [ !

2

2 2 '0

0

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

V s v s sV V

s

[[ !

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If I(0)=0 then: V`c(0)=0 and Vc(0)

2

0

2 2 2 2

0 0

(0)

( ) ( )

c

c

V sV

v s s s s

[

[ [!

2

1 002 2

0

1 cos( )

ts s

[^ [[

!

0 0 0( ) (1 cos ) (0)cos [ (0)]cosc c cV t V t V t V V V t[ [ [! !

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Vc characteristic

Vc Osc. Amp depend on V-Vc(0)

Vc starts at Vc(0) as expected

Response for :

1-Vc(0)=-V

2-Vc(0)=0

3-Vc(0)=+V/2

Voltage and Current Relation

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Solution of an RL CCT Stimulated

by an Exp. Drive (Ass. I(0)=0)

( ) tU t V e E!

( ) ( ) (0)

VR

i s Lsi s LI s E !

( )( )( )

Vi s

R Ls s E!

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Exp. Stimulated RL CCT, Cont.

If /R LP !

1 1( ) ( )( )

Vi s L s sE E

!

( ) ( )( )

t tV

I te e

L

P E

E P

!