Performance of Transmission Line

Line Parameters-Part 2

Introduction

Performance Parameters

Efficiency

Regulation

VoltageloadFull

VoltageloadFullVoltageLoadNo

RIP

P

LossesOutput

OutputEfficiency

r

Regulation%

1003

100%2

FLR

FLRNLR

V

VV

_

__

Distributed and Lumped Parameters

Transmission line with uniformly distributed line parameters (R, L, C, G)

Small section ∆x

I(x)z ∆x

y ∆x V(x)

V(x+ ∆x)

I(x+ ∆x)

Vs

Is

Vr

Ir

z = Series impedance /unit length/phase

y = Shunt admittance / unit length/phase

l = Length of transmission line Z = Total series impedance/

phase Y = Total shunt impedance/

phase

Transmission Line Models

Short line : Length less than 80 km. Shunt admittance is neglected Lumped parameter model

Medium line: Length between 80 km to 200 km. Shunt admittance needs to be considered Lumped parameter model

Nominal π model Nominal T model

Long line: Length longer than 200 km. Distributed parameter model Shunt admittance effect is important Equivalent π or T equivalent can be derived

ABCD Parameters of Transmission Line

R

R

S

S

I

V

DC

BA

I

V

Matrix Format

DA

BCAD

1

Passive, Linear, bilateral

Short Transmission Line

R

R

S

S

I

VZ

I

V

10

1Matrix Format

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

Regulation of Short Transmission Line

I=IR=IS

VS

VR

IR

IXIZ

ϕ

22sincos XIVRIVV RRS

sin2sinsin2cos 22222222 XIVXIVRIVRIVV RRRRS

2222 sin2sin2 XRIIXVIRVVV RRRS

2

222sin2sin21

RRRRS V

XRI

V

IX

V

IRVV

Small quantity

Regulation of Short Transmission Line

RRRS V

IX

V

IRVV

sin2sin21

.......1682

1132

xxx

x

RRRS V

IX

V

IRVV

sinsin1

sinsin IXIRVV RS

RR

R

RS

V

XI

V

RI

V

VV

sinsinRegulation

Regulation

1003

%2

RIP

P

Medium Transmission Line

Medium transmission lines are modelled with lumped series impedance and shunt admittance.

Nominal π Representation

Nominal T Representation

Nominal π Representation

Nominal π Representation

Therefore A, B, C, D parameters

Nominal T Representation

MMRRM YVIIZ

VV and2

IM

RRRRRS II

ZVY

ZI

ZVV

222

Nominal T Representation

Therefore A, B, C, D parameters

Long Line Model

x 0

x 0

Long Line Model

And

Again differentiating with respect to x

Solution of the differential Eqn.

Long Line Model

Differentiating with respect to x

We know that

Therefore

Long Line Model

Long Line Model

At x = 0.

V = VR and I = IR

And

Solving for A1 and A2

Long Line Model

R

ll

R

ll

CS

R

ll

CR

ll

S

Iee

Vee

ZI

Iee

ZVee

V

22

1

22

We are interested in terminal conditions: x = l we have V = Vs and I = IS

Long Line Model

R

ll

R

ll

CS

R

ll

CR

ll

S

Iee

Vee

ZI

Iee

ZVee

V

22

1

22

RRC

S

RCRS

IlVlZ

I

IlZVlV

coshsinh1

sinhcosh

Long Line Model

RRC

S

RCRS

IlVlZ

I

IlZVlV

coshsinh1

sinhcosh

The ABCD parameters of the long transmission line