Questions on long transmission lines

1. Long Transmission Lines
1. A 132 kv transmission line, having constants A,B,C, D is preceded and terminated by 132/33kV
transformers. The short circuit impedances of the transformers measured on their 33kV sides
are Z1 for the input transformers and Z2 for the output transformer. Neglecting the magnetizing
currents of the transformers, calculate the constants A, B, C, and D representing the complete
system. [(A+16Z1), (AZ2+B/16+16CZ1Z2+DZ1), 16C, (16CZ2+D)]
2. In a 3 phase transmission line with 132kV at the receiving end the following are the transmission
constants: A = D = 0.98 |_3°, B = 110|_75°, C = 0.0005|_88°Siemens(S). if the load at the
receiving end is 50MVA at 0.8 lagging pf determine the voltage, current and pf at the sending
end. [95.37|_11.346°KV, 196.88|_-24.41°, 0.8115(lagging)]
3. A 3 phase transmission line has the following circuit constants: A1= 0.97|_0.6°, B1 = 60|_70°. If a
second line ahving the constants A2 = 0.97|_0.4°; B2 = 50|_76° is connected in parallel with the
first line, determine the sending-end voltage when delivering 50MW at 132KV and 0.8 lagging pf
at the receiving end. [80.081|_3.626°V]
4. A transmission circuit is represented by a symmetrical π network in which the series impedance
is 120|_60°Ω, and each shunt admittance is 2.5x10-3|_90°S. calculate (a) the value of the general
circuit constants ABCD, and (b) the characteristic impedance of the circuit.
[0.7552|_11.456°, 120|_120°, 4.3665x10-3|_94.927° ; 165.78|_-17.46°]
5. A 2 port resistive network has input terminals A and B, and output terminals C and D. the
resistances measured across AB when terminals CD are first short-circuited and then open-
circuited are, respectively, 720Ω and 1240Ω. The resistance measured across CD with AB open-
circuited is 910Ω. Determine the equivalent T- network. [552.1 Ω, 222.1 Ω, 687.9 Ω]