**AIM :**

(i) To determine the positive sequence line parameters L and C per phase per kilometre of a three

phase single and double circuit transmission lines for different conductor arrangements.

(ii) To understand modeling and performance of medium lines.

**SOFTWARE REQUIRED:**

MATLAB 5.3

**THEORY:**

Transmission line has four parameters – resistance, inductance, capacitance and

conductance. The inductance and capacitance are due to the effect of magnetic and electric fields

around the conductor. The resistance of the conductor is best determined from the manufactures

data, the inductances and capacitances can be

evaluated using the formula.

**EXERCISE-1:**

A three-phase transposed line composed of one ACSR, 1,43,000 cmil, 47/7 Bobolink

conductor per phase with flat horizontal spacing of 11m between phases a and b and

between phases b and c. The conductors have a diameter of 3.625 cm and a GMR of 1.439

cm. The line is to be replaced by a three-conductor bundle of ACSR 477,000-cmil, 26/7

Hawk conductors having the same cross sectional area of aluminum as the single-conductor

line. The conductors have a diameter of 2.1793 cm and a GMR of 0.8839 cm. The new line

will also have a flat horizontal configuration, but it is to be operated at a higher voltage and

therefore the phase spacing is increased to 14m as measured from the center of the bundles.

The spacing between the conductors in the bundle is 45 cm.

(a) Determine the inductance and capacitance per phase per kilometer of the above two

lines.

(b) Verify the results using the MATLAB program.

**PROGRAM:**

[GMD, GMRL, GMRC] = gmd;

L = 0.2*log(GMD/GMRL)

C = 0.0556/log(GMD/GMRC)

**EXERCISE-2:**

A three phase overhead line 200km long R = 0.16 ohm/km and Conductor diameter of 2cm with

spacing 4,5,6m transposed.Find A,B,C,D constants ,sending end voltage,current ,power factor and

power when the line is delivering full load of 50MW at 132kV ,0.8 pf lagging , transmission

efficiency , receiving end voltage and regulation.

**PROGRAM:**

ab=input('value of ab');

bc=input('value of bc');

ca=input('value of ca');

pr=input('receving end power in mw');

vr=input('receving end voltage in kv');

pfr=input('receving end powerfactor');

l=input('length of the line in km');

r=input('resistance/ph/km');

f=input('frequency');

D=input('diameter in m');

rad=D/2;

newrad=(0.7788*rad);

deq=(ab*bc*ca)^(1/3);

L=2*10^(-7)*log(deq/newrad);

C=(2*pi*8.854*10^-12)/log(deq/rad);

XL=2*pi*f*L*l*1000;

rnew=r*l;

Z=rnew+i*(XL);

Y=i*(2*pi*f*C*l*1000);

A=1+((Y*Z)/2);

D=A;

B=Z;

C=Y*(1+(Y*Z)/4);

vrph=(vr*10^3)/1.732;

irold=(pr*10^6)/(1.732*vr*10^3*.8);

k=sin(acos(pfr));

ir=irold*(pfr-(j*k));

vs=((A*vrph)+(B*ir));

is=((C*vrph)+(D*ir));

angle(vs);

angle(is);

f=angle(vs);

u=angle(is);

PFS=cos(f-u);

eff=((pr*10^6)/(3*abs(vs)*abs(is)*PFS))*100;

reg=(((abs(vs)/abs(A))-abs(vrph))/abs(vrph))*100;

L

C

rnew

A

B

C

abs(vs)

abs(is)

angle(vs)*180/pi

angle(is)*180/pi

PFS

eff

reg

**RESULT:**

Thus the the positive sequence line parameters L and C per phase per kilometre of a three

phase single and double circuit transmission lines for different conductor arrangements are determined and the modeling & performance of medium lines understood.

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