Question 1-
a) A single phase 132 kV, 50 Hz overhead transmission line is shown in Fig.Q1a. The radius of each sub-conductor is 0.67 cm. Find the equivalent representation of the line and capacitance between the lines (h= 0.0866 m, D=6 m, and d=10 cm).
b) A three phase 500 kV, 50 Hz, 400 km transposed uncompensated line has two Pheasant 1,272,00 cmil 54/3 ACSR conductors per bundle. Each conductor has a diameter of 4.4755 cm, with 50 cm between conductors in the bundle. The horizontal spacings between bundles centres are 10, 10, and 20 m.
Assuming positive-phase sequence, calculate
i. Inductive reactance Ω/km and capacitive reactance F/km of the line (For resistance, from table of characteristic for ACSR, assume a 50°C conductor temperature);
ii. ABCD constants of the line (Assume a 50°C conductor temperature);
iii. Compare the equivalent and nominal π-model for the line;
iv. At the full load the line delivers 800 MW at 0.9 leading power factor and at 480 kV to the receiving end load. Calculate voltage regulation and efficiency of the line.
v. To improve the line performance, identical series capacitors are installed at both ends in each phase of the transmission line, providing 40% compensation. Determine the compensated ABCD constants and maximum power that this compensated line can deliver and compare with the uncompensated one.
Question 2- A three generator power supply system is connected to a bus network operating at a common voltage of 220 kV. The network is shown in Figure Q2a and Q2b.
The neutral of each generator is grounded through a j0.045 p.u. reactor. The generators are not loaded and are running at rated frequency and voltage. The system sequence impedance data on a common base of 220 kV and 100 MVA are given in Table. I.
A double line to ground fault occurs, between the phases detailed in Table. II and ground, at the bus shown in Figure Q2, through a fault impedance of j0.035 p.u.. Assuming the pre-fault bus voltages as 1 p.u., calculate
1. The 10 x 10 admittance matrices for the zero, positive and negative sequence circuits;
ii. Zkk for each of the zero, positive and negative sequence., where k is the number of the bus on which the fault occurs.
iii. The fault current;
iv. The current delivered during the fault by the generator detailed in Table. II; and
v. The current in the line detailed in Table. II during the fault.
TABLE I. System Parameters
|
Equipment
|
Voltage (kV)
|
x° (p.u.)
|
Xl. (p.u.)
|
X2 (p.u.
|
|
G1
|
25
|
0.036
|
0.072
|
0.101
|
|
G2
|
25
|
0.041
|
0.081
|
0.113
|
|
G3
|
25
|
0.038
|
0.076
|
0.106
|
|
T1
|
25/220
|
0.091
|
0.091
|
0.091
|
|
T2
|
25/220
|
0.093
|
0.09S
|
0.093
|
|
T3
|
25/220
|
0.111
|
0.111
|
0.111
|
|
Line 4-5
|
220
|
0.438
|
0.125
|
0.125
|
|
Line 4-7
|
220
|
0.581
|
0.160
|
0.166
|
|
Line 4-9
|
220
|
0.543
|
0.155
|
0.155
|
|
Line 4-10
|
220
|
0.305
|
0.087
|
0.087
|
|
Line 5-6
|
220
|
0.459
|
0.131
|
0.131
|
|
Line 6-7
|
220
|
0.473
|
0.135
|
0.135
|
|
Line 6-10
|
220
|
0.235
|
0.067
|
0.067
|
|
Line 7-8
|
220
|
0.427
|
0.122
|
0.122
|
|
Line 8-9
|
220
|
0.504
|
0.144
|
0.144
|
TAELE II. System Parameters
|
Fault
phase
|
Fault
bus
|
Gen
Current
|
Inter-bus
Current
|
Bus
p
|
Bus
q
|
Bus
r
|
Bus
x
|
Bus
v
|
Bus
z
|
|
c
|
8
|
1
|
6, 10
|
3
|
2
|
1
|
4
|
5
|
6
|
N.B.: Show full working and submit all code used in Your calculations.
Attachment:- ACSR.rar