TRANSMISSION LINESPARAMETERS

To develop models of transmission lines, we first need to determine the TL parameters.

CAPACITANCE OF A SINGLE PHASE

TWO-WIRE LINE

The capacitance between conductors is:

If r1 = r2 = r

2

• k ≡ Permittivity in farads/m (())

• k ≡ kr ko

• ko≡ Permittivity of free space (8.85410-12 F/m)

CAPACITANCE OF A SINGLE PHASE

TWO-WIRE LINE

Capacitance to neutral:

3

Charging Current:

Vab ≡ the applied voltage of single phase supply

CAPACITANCE OF A THREE-PHASE LINE WITH EQUILATERAL SPACING

Capacitance to neutral:

The charging current in each phase:

Van ≡ Phase Voltage

4

CAPACITANCE OF A THREE-PHASE LINE WITH UNSYMMETRICAL SPACING

TRANSPOSED

Capacitance to neutral:

5

CAPACITANCE FOR BUNDLED CONDUCTORS

Capacitance to neutral:

GMD

GMR

6

ACSR TABLES Because ACSR conductors are stranded, actual resistance,

inductance, and capacitance needs to be determined from tables.

7

Inductance and Capacitance assume a geometric mean distance Deq of 1 ft.

GMR is equivalent toeffective radius r’

ACSR TABLES

8

Term independent of conductor, but with spacing Dm in feet.

Term from table, depending on conductor type,but assuming a one foot spacing

TRANSMISSION LINESREPRESENTATION

9

After determining the TL parameters, we can develop models of transmission lines

TL MODEL

= r + j wL

= j wC

10

r wL r wL r wL r wL

C C C C

Sending End Receiving End

Is Ir

Short TL

Neglect the Shunt Capacitance

Medium TL

Lumped-parameter representation

TL MODEL

Lumped-parameter representation

Π model T model

Long TL

Distributed-parameters is required to get high degree of accuracy

11

SHORT TL

12

%100

R

RS

V

VVVR

SHORT TL

13

0 1 CZBDAThese ABCD constants are sometimes called the generalized circuit constants of the TL. A and D are dimensionless and equal each other if the line is the same when viewed from either end. The dimensions of B and C are ohms and mhos, respectively.

MEDIUM TL (NOMINAL Π)Lumped Parameters

14

MEDIUM TL (NOMINAL Π)

Check:

15

Check:

%100

R

RS

V

VAVVR

To get voltage Regulation, IR = Zero. Hence, no load

receiving end voltage VR0 = VS / A

MEDIUM TL (NOMINAL T)

Report:

Find the ABCD matrix model for a T-modeledmedium transmission line. In a T-modeledmedium transmission line, the line capacitancesare lumped together and placed in the middle of

16

are lumped together and placed in the middle ofthe line as one capacitor. The line seriesimpedance is divided into two equal parts placedbefore and after the line capacitance so that theline’s equivalent circuit looks like letter “T”.

LONG TL

Self Study

17Characteristic Impedance

Propagation Constant