D

COMPUTATION OF TRANSMISSION LINE PARAMETERS

Aim:

To compute the series inductance and shunt capacitance per phase per km of a three phase single circuit OH transmission line with solid, bundled conductors.

Theory:

The transmission line has the following important parameters:

1. Resistance2. Inductance3. Capacitance4. Conductance

The inductance and capacitance are due to the effect of magnetic and electric fields around the conductors. The shunt conductance characterizes the leakage current through inductors which is very small and can be neglected. The parameters R,L and C are essential for the development of the transmission models to be used in power system analysis both during planning and operation.

Inductance:

It is computed from the flux linkages per ampere. In the case of three phase lines, the inductance of each phase is not the same if conductors are not spaced equilaterally. A different inductance in each phase results in unbalanced circuit. Conductors are transposed in order to balance the inductance of the phases and the average inductance per phase is given by simple formula which depends on the conductor configuration and conductor radius.

The general formula for computing inductance per phase in mH of a transmission line is given by,

L=0 .2 ln [DmD s ]where, Dm-Geometric Mean Distance (GMD)

Ds – Geometric Mean Radius (GMR)

The expressions of GMD and GMR for different arrangement of conductors of transmission lines are given below:

a. Single phase Two wire system:

GMD=D and GMR=re-1/4 =r’ where r – radius of the conductor

b. Three phase symmetrical spacing:

D

D

D

D

D

D

D D

D

D D

D

D

D

GMD=D; GMR=re-1/4 =r’ where r – radius of the conductor

c. Three phase asymmetrical spacing:

GMD=Geometric mean of the three distances of asymmetrically placed conductorsGMD= (DabDbcDca)GMR=re-1/4 =r’ where r – radius of the conductor

d. Bundled conductors:EHV lines are constructed with bundled conductors to improve power transfer and reduces corona loss, radio interference and surge impedance.

GMR for 2 sub-conductor D sb=(D sXd )

12

GMR for 3 sub-conductor D sb=(Ds Xd2)

13

GMR for 3 sub-conductor D sb=1 .09(Ds Xd3)

14

where, Ds is the GMR of each sub conductor and d is the bundle spacing

e. Three phase double circuit transposed:Double circuit of three phase circuits consists of two identical three phase circuits. The phases are a, b and c are operated with a1-a2, b1-b2 and c1-c2 in parallel respectively. The GMD and GMR are computed considering that identical phase forms a composite conductor. For example, a phase conductors a1 and a2 for a composite conductor and similarly for other phases.Relative phase position a1b1c1-c2b2a2. It can also be a1b1c1- a2b2 c2.

H12

H23

S11

S22

S33

a1

b1

c1

c2

b2

a3

The inductance per phase in mH per km is

L=0 .2 ln ( GMDGMRL ) mH /km

Where, GMD is the equivalent GMD per phase; GMD=[DABDBCDCA]1/3

Where, DAB , DBC and DCA are GMD between each phase group A-B, B-C & C-A which are given by,

DAB=[Da 1b 1Da 1b 2Da 2 b2 ]1/4

DBC=[Db1 c1Db 1c 2Db 2c 2]1/4

DCA=[Dc1 a 1Dc2 a1Dc 2a 2 ]1 /4

GMRL is equivalent geometric mean radius and is given by, GMRL=(DSADSBDSC )1/3

where, DSA=[DsbDa 1 a2 ]1/2

DSB=[D sbDb 1b 2]1/2

DSC=[D sb Dc1 c2 ]1/2

Where, D sb

-GMR of bundled conductor if conductor a1,a2,… are bundled conductors

D sb=ra1

' =rb1' =rc1

'=ra2' =rb2

' =rc2'

if a1,a2,… are not bundled conductors

Capacitance:

A general formula for evaluating capacitance per phase in µF per km of a transmission line is given by,

C=0 .0556 ln(GMDGMR ) μF /km

Where GMD is the geometric mean distance which is same as that defined for inductance under various cases.

GMR is the geometric mean radius and is defined case by case below:

a. Three phase symmetrical spacing:

GMD=D

GMR=’r’ – in case of solid conductor

= Ds in the case of stranded conductor to be obtained from manufacturers’ data.

b. Three phase double circuit transposed:

C= 0 .0556

ln ( GMDGMRC )GMD is same for inductance

GMRC is the equivalent GMR which is given by, GMRC=[ rA rB rC ]13

where, rA , rB∧rC are GMR of each phase group obtained as,

rA=[rbDa1 a 2] 1/2rB=[rb Db1 b 2] 1/2rC=[ rbDc 1c2 ] 1/2

where, rb- GMR of bundle conductor.

Algorithm:

1. Read Z2. Check the value of Z.3. If Z value is equal to 1 then read the D12, D23, D31 and r.4. Calculate inductance and capacitance per phase5. Print the values of inductance and capacitance6. If the Z value is not equal to 1, then to read the D12, D23, D31 and r.7. Calculate GMD.8. If n=4 or n1=4 then calculate GMRC and GMRL.9. Calculate inductance and capacitance per phase10. Print the values of inductance and Capacitance