EEE F312 Power Systems
Tutorial – 3
(PU systems and representation of transmission lines)
1. A 3-ph, star-connected synchronous generated is rated at 6.25 kVA, 220 V
having a reactance of 8.4 Ω/ph. Using generator ratings as base values,
determine the pu reactance. Then, refer the pu value to 230 V, 7.5 kVA base
values.
Fig. 1
2. A 100 MVA, 33 kV 3-phase generator has a subtransient reactance of 15%. The
generator is connected to the motors through a transmission line and
transformers as shown in Fig. E1.1a. The motors have rated inputs of 30 MVA,
20 MVA and 50 MVA at 30 kV with 20% subtransient reactance. The 3-phase
transformers are rated at 110 MVA, 32 kV, Δ/110 kV Y with leakage reactance
8%. The line has a reactance of 50 ohms. Selecting the generator rating as the
base quantities in the generator circuit, determine the base quantities in other
parts of the system and evaluate the corresponding p.u. values.
Fig. 2
3. For the power system network shown in Fig. 2, the data is given below,
In the above data, the powers specified are 3-phase, voltages are line-to-line rms,
and reactances per phase (assuming star circuits). Draw the impedance diagram
of the above power system network. Consider Gen 1 rating as base MVA, find
the pu values of reactances of generators, transmission line and transformers.
Draw the equivalent pu reactance diagram.
4. A 3-phase load of 2000 kVA, 0·8 p.f. is supplied at 6·6 kV, 50 Hz by means of
a 33 kV transmission line 20 km long and 33/6·6 kV step-down transformer.
The resistance and reactance of each conductor are 0·4 Ω and 0·5 Ω per km,
respectively. The resistance and reactance of the primary transformer are 7.5 Ω
and 13.2 Ω, while those of the secondary is 0.35 Ω and 0.65 Ω respectively.
Find the voltage necessary at the sending end of the transmission line when 6.6
kV is maintained at the receiving end. Determine also the sending end power
factor and transmission efficiency.
5. A (medium) single-phase transmission line 100 km long has the following
constants :
Resistance/km = 0·25 Ω ; Reactance/km = 0·8 Ω
Susceptance/km = 14 × 106 Siemen ; Receiving end line voltage = 66,000 V
Assuming that the total capacitance of the line is localised at the receiving end
alone, determine (i) the sending end current (ii) the sending end voltage (iii)
regulation and (iv) supply power factor. The line is delivering 15,000 kW at 0.8
power factor lagging. Draw the phasor diagram to illustrate your calculations.
6. A 3-phase, 50 Hz transmission line 100 km long delivers 20 MW at 0·9 p.f.
lagging and at 110 kV. The resistance and reactance of the line per phase per km
are 0·2 Ω and 0·4 Ω respectively, while capacitance admittance is 2·5 X 10 6
siemen/km/phase. Calculate (i) the current and voltage at the sending end and (ii)
the transmission efficiency. Use nominal T and nominal π methods.
7. A single circuit 50 Hz, 3-phase transmission line has the following parameters
per km:
R = 0.2 ohm, L = 1.3 mH and C = 0.01 µF
(i) If the line is 120 km long and delivers 40 MW at 132 kV and 0.8 pf lagging,
determine the efficiency of the line.
(ii) Determine the ABCD parameters of the line and verify the results of (i) using
ABCD parameters.
(iii) Assume the line is open at the receiving end, then find the incident and
reflected voltages at the receiving end as well as at 120 km from the
receiving end.
8. Determine the sending end voltage current, power and power factor for a 160 km
section of 3-phase long-line delivering 50 MVA at 132 kV and p.f. 0.8 lagging.
Also find the efficiency and regulation of the line. Resistance per line 0.1557 ohm
per km, spacing 3.7 m, 6.475 m, 7.4 m transposed. Evaluate the A, B, C, D
parameters also. Diameter 1.956 cm.