Questions on short and medium lines

1. Short and Medium Lines
1. A single phase load of 200KVA is delivered at 2500V over a transmission line having R = 1.4 Ω, X
= 0.8 Ω. Calculate the current, voltage and pf at the sending end when the pf of the load is (a)
unity, (b)0.8 lagging lagging, and (c) 0.8 leading.
[2.612|_1.393°KV, 80|_o°A, 0.9997lagging;
2.627|_-0.3463°KV, 80|_-36.87°A, 0.8036 lagging ; 2.553|_2.6371°KV, 80|_36.87°A, 0.82676
leading]
2. 1500KVA is received at 33KV at 0.85 pf lagging over an 8km 3 phase OH line. Each line has R =
0.29 Ω/km, and X = 0.65 Ω/km. calculate (b)the voltage at the sending end (b) the power factor
at the sending end, (c) the regulation, and (d) the efficiency of the transmission line.
[20.31|_2.37°KV, 0.8275 lagging, 6.58%, 96.38%]
3. A 3 phase line, 10km long, delivers 5MW at 11KV, 50Hz, 0.8pf lagging. The power loss in the line
is 10% of the power delivered. The line conductors are situated at the corners of an equilateral
triangle of 2m side. Calculate the voltage and pf at the sending end. Assume resistivity of
copper to be 1.774µΩcm. [7.535|_5.266°KV, 0.7416 lagging]
4. A three phase, 50Hz, transmission line, 40 km long delivers 36MW at 0.8pf lagging at
60KV(phase). The line constants per conductor are, R = 2.5 Ω, L = 0.1H, C = 0.25µF. shunt leakage
may be neglected. Determine the voltage, current, pf, active power and reactive VA at the
sending end. Also, determine the efficiency and regulation of the line. Use (a)Nominal T method,
(b) Nominal pi method.
[65.4|_5.183°KV, 246.89|_-35.99°A,0.7527 lagging, 36.46MW31.89VAR]
5. A 3 phase 50Hz, 150km line operates at 110KV between the lines at the sending end. The total
inductance and capacitance per phaseare 0.2H and 1.5µF. Neglecting losses calculate the value
of receiving –end load having a pf of unity for which the voltage at the receiving end will be the
same as that at the sending end. Assume one-half of the total capacitance of the line to e
concentrated at each end. [173.275A]
6. A 3 phase 132KV transmission line is connected to a 50MW load at a power factor of 0.85
lagging. The line constants of the 80km long line are Z = 96|_78°Ω and Y = 0.0001|_90°S. Using
nominal T-circuit representation, calculate : (a)A, B, C, D constants of the line; (b) Sending end
voltage; (c) Sending end current; (d) Sending end pf; (e) efficiency of transmission line.
[0.9531 |_0.6°, 93.75|_78.29°Ω, 0.001|_90°; 91.08|_11.56°KV;
215.82|_-13.6°; 0.9051 lagging; 93.67%]