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.
(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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