Download EEE307 Electromechanical Energy Conversion Homework I (Due

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Electromechanical Energy Conversion
Homework I (Due on March 24th 2015)
1. An inductor of the form given below has dimensions:
Cross-sectional area Ac = 3.6 cm2 ; Mean core length lc = 15 cm ; N = 75 turns.
Assuming a core permeability µ= 2100µ0 and neglecting the effects of leakage flux and fringing
fields, calculate the air-gap length required to achieve an inductance of 6.0 mH.
2. Draw the magnetic circuit for the system given below:
3) The nameplate on a 9.2-kV:460-V, 46-kVA, single-phase transformer indicates that it has a
series reactance of 10 percent (0.10 per unit).
a) Calculate the series reactance in ohms as referred to (i) the low-voltage terminal and (ii) the
high-voltage terminal.
b) If three of these transformers are connected in a three-phase Y-Y connection, calculate (i) the
three-phase voltage and power rating, (ii) per unit impedance of the transformer bank, (iii) the
series reactance in ohms referred to the high-voltage terminal, and (iv) the series reactance in
ohms as referred to the low-voltage terminal.
Electromechanical Energy Conversion
Homework I (Due on March 24th 2015)
c) Repeat part (b) if the three transformers are connected in ∆ on the high-voltage side and Y on
their low-voltage terminal.
4) A 15-kV: 150-kV, 150-MVA, 60-Hz single-phase transformer has primary and secondary
impedances of 0.0095 + j0.063 per unit each. The magnetizing impedance is j148 per unit. All
quantities are in per unit on the transformer base. Calculate the primary and secondary
resistances and reactances and the magnetizing inductance (referred to the low-voltage side) in
ohms and henrys.
5) A 50-kVA, 2400/240-V, 60-Hz single phase transformer has a short-circuit test performed on
its high-voltage side. The following test results are obtained:
Voltage (V)
Current (A)
Short-Circuit (LV shorted)
Open-Circuit (HV open)
a) Draw the transformers equivalent circuit.
b) Determine its voltage regulation, and efficiency at rated load, 0.8 power factor lagging, and rated
voltage at the secondary terminals.