Power Systems Analysis

Problem 1
A 30-km, 34.5-kV, 60 Hz, three-phase line has a positive-sequence series impedance z=0.19+j0.34 Ω/km.
The load at the receiving end absorbs 10 MVA at 33 kV.
Assuming a short line,
(a) Find the ABCD parameters,
(b) Find the sending-end voltage for a load power factor of 0.9 lagging,
(c) Find the sending-end voltage for a load power factor of 0.9 leading,
(d) Find the series impedance of the nominal π-equivalent circuit and draw the equivalent circuit.
Problem 2
A 200-km, 230-kV, 60-Hz, three-phase line has a positive-sequence series impedance ? = 0.08 + ?0.48
Ω/km and a positive-sequence shunt admittance ? = ?3.33 × 10−6S/km. At full load, the line delivers
250 MW at 0.99 pf lagging and at the receiving end voltage 220 kV .
(a) Find the nominal π equivalent circuit
(b) Using the π equivalent circuit, calculate the ABCD parameters,
(c) Calculate the sending-end voltage and current,
(d) Calculate the percent voltage regulation.
Problem 3
A 500-km, 500-kV, 60-Hz, uncompensated three-phase line has a positive=sequence series impedance
? = 0.03 + ?0.35Ω/km and a positive-sequence shunt admittance ? = ?4.4 × 10−6S/km.
(a) Calculate characteristic impedance ?? and propagation constant ?,
(b) Calculate the exact ABCD parameters for this line,
(c) Calculate the series impedance ?′and shunt admittance ?′of the nominal π equivalent circuit,
(d) Assuming the line is lossless, find the surge impedance loading SIP and theoretical maximum
power the line can transfer.
(e) Based on the St. Clare curve, find the practical line loadability.
Problem 4
The following parameters are based on a preliminary line design: ? ? = 1.0 pu, ?? = 0.9 pu, ? =
5000km, ?? = 320 Ω, ? = 36.8°. A three-phase power of 700 MW is to be transmitted to a substation
located 315 km from the source of power.
(a) Determine a nominal voltage level for the three-phase transmission line, based on the practical
line loadability curve in Figure 5.12 of the textbook pp. 269,
(b) For the voltage level calculated in (a), find the maximum power the line can transmit under the
given condition in this problem based on equation (5.4.29) of the textbook pp. 269.
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