Q1: Intro to Power conversion. (20%)
A ferromagnetic core with a relative permeability of 1600 is shown below. The dimensions are as
shown in the diagram, and the depth of the core is 5 cm. The air gaps are 0.1 cm each. Because
of fringing effects, the effective area of the air gap is 5 % larger than their physical size. There are
200 turns in the coil wrapped around the center leg of the core and the current in the coil is 5A.
Calculate the flux values for the left, center, and right legs of the core.
Q2: Transformer. (30%)
Q2. Short circuit and open-circuit tests were performed on a 4000 VA transformer, rated 680 V
(Primary side)-110 V (Secondary side), with the results below.
(a) Find the equivalent circuit of this transformer referred to the secondary side of the
(b)Determine the transformer’s efficiency at rated current load with 0.9 Power factor lagging.
Q3: Synchronous Generator. (30%)
A 13.8 kV, 50 MVA, 0.85 power factor lagging, 60 Hz, 4 pole Y-connected synchronous generator
has a synchronous reactance (Xs) of 2 and armature resistance (RA) of 0.3 . At 60 Hz, its
friction and windage losses are 0.5 MW, and its core losses are 1.5 MW. Assume no stray loss.
The field circuit has a DC voltage of 200 V, and the maximum field current If is 10 A. The current
of the field circuit is adjustable over the range from 0 to 10 A. The open circuit characteristics
(OCC) of this generator is shown in below.
(a) What is the internal generated voltage EA of this machine at rated conditions? (10%)
(b) How much field current is required to make the terminal voltage VT equal to 13.8 kV
when the generator is running at rated conditions? (5%)
(c) Assuming the field current is supplied by an extra battery, how much steady-state power
and torque must be generator’s prime mover be capable of supplying to handle the rated
(d) What is the torque angle δ of the generator when supplying rated current at unity power