Power System Engineering Lecture 11

8/3/2019 Power System Engineering Lecture 11

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Review of Last Lecture

Lossless transmission line Surge impedance loading

Power flow through the transmission line


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Lossless Transmission Line

In loss less line, resistance is assumed to be zero

RRx

RCRx

IxVZc

xI

IxZVxV

coshsinh

sinhcosh

C

LZ

C ljl

RRx

RCRx

IxVZc

xjI

IxjZVxV

cossin

sincos

=0

and


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Surge Impedance Loading

RRCx

RCRx

IxVxZjI

IxjZVxV

cossin1

sincos

R

RCRCR

I

VZIZV

lj

RS

lj

RS

eII

eVV

xRCRxRCR eIZV

eIZV

V

22

If the line is terminated with surge impedanceZc , the

power transferred to load is called surge impedance

loading


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Power Transfer Through Transmission

Line

SV 0

RV

RRR jQPS SSS jQPS

Gen Load

B

AV

B

VIBIAVV RSRRRS

BBAA andLet

B

VA

B

VI

RS

R

ABCD

B

VA

B

VI

RS

R

0


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Power Flow Through Transmission Line

Complex power VRIR* at receiving end:

BVA

BVI RSR

*

BVA

B

VVjQPIV

RRS

RRRR

2

*

Real Part:

Imaginary Part:

coscos

2

B

VA

B

VV

P

RRS

R

sinsin2

B

VA

B

VVQ

RRS

R

Separating real and imaginary parts


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Power Flow Through Transmission Line

Maximum power will get transferred, if=

cos2

max_

B

VA

B

VVP

RRS

R

sin2

max_B

VAQ

R

R

Real Part:

Imaginary Part

coscos2

B

VA

B

VVPRRS

R

sinsin2

B

VA

B

VVQ

RRS

R


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Receiving End Circle Diagram

B

VV RSB

VAR

2

RR IV

R

BVA

B

VVIV

RRS

RRR

2

W

Var


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Maximum Power in Short Line

Approximation

For Short lineA=1,B=Z, C=0,D=1

ZRCZBDA /cos,0,,01

RZ

V

Z

VV

Z

V

Z

VVP

RRSRRS

R 2

22

max_ cos

cos2

max_BVA

BVVP RRSR

sin2

max_B

VAQ

R

R


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With large X/R Ratio

jXZXR thenGenerally,

sinXVVP RSR

,0,90,01 CXBDA

X

VVP

RS

R max_

X

V

X

VVQ

RRS

R

2

cos VX

VVV

X

VQ

R

RS

R

R

Real Part:

Imaginary Part

coscos2

BVA

BVVP RRSR

sinsin2

B

VA

B

VVQ

RRS

R


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Steady State Stability Limit


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Power Transfer Capability

Thermal Limit Voltage drop limit Stability limit

lSIL

lZ

V

B

VVP

c

RRS

R

sin

sinsin

sinsin

2

Actual Design


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Sending End Power

RRS DICVI

B

V

B

DVI

B

BCADVVB

D

VB

DAV

B

DCVI

RS

S

RS

RSRS

BAV

BVI RSR but

Complex power VSIS* at receiving end:

BBADA andLet


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Sending End Power

B

VV

B

VAjQPIV

RSS

SSSS

2

*

Real Part:

Imaginary Part

coscos2

B

VV

B

VAP

RSS

S

sinsin2

B

VV

B

VAQ

RSS

S

Separating real and imaginary parts

B

V

B

VA

B

V

B

VD

IRSRS

S

0


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Overhead Transmission Lines

Mechanical Design, Insulators, Electrical Design


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Main Objectives

Choice of voltage, choice of conductor, spacing between

conductors

Calculation line constants, regulation and efficiency

Calculation of Corona Loss

Choosing number and type of insulators Choice of method of grounding

Calculation of radio interference

Stability considerations

Electrostatic and electromagnetic effect

Insulation coordination

Protective system


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Main Components of Overhead Line

Conductors Copper

Aluminum: ACSR, AAAR, AAC, Expanded ACSR

Support Structure (Towers)

Galvanized steel (for high voltage) Wood, concrete, steel (for low voltage)

Insulators

Porcelain

Glass

Polymer insulation


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Mechanical Design

Main Factors Selection of line route

Types of tower or pole

Right of way

Ground and conductor clearance Tower spacing, span length

Mechanical loadings

Weight of conductor per unit length

Load due to wind, ice, snow, etc. Temperature

Conductor tension

Distance between the supports (Span length)


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Sag and Tension:

Maximum sag so thatclearance to ground

and other conductors

can be maintained.

Maximum tension sothat structures can be

designed to withstand

it.

Minimum sag to

control structure uplift

problems.


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Calculation of Sag and Tension

L =Span length

O is the lowest point on the wire

ws =weight per unit length

H= tension at point O

T= tension at point P


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Integrating

Atx=0, s=0, therefore c1=0


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Also


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Integrating

Aty=0,x=0, therefore


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For tension at point P,

We know


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Support at Same Heights

If the towers at same height and span is 2l, i.e. half span is l


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Supports at Different Heights

ya

yb

2l

2l-x1


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Supports at Different Heights

For towerB

For towerA

Therefore, difference in tower heights


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Approximate Formulae for Sag and Tension

and

and

Power System Engineering Lecture 11

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