Exercise 1:
Three single-phase transformers, marked: S = 10 kVA , 460:120V , 60Hz are connected to
form a 3-fase transformer 460:208V. The equivalent impedance, referred to the high voltage
side is: ZH = 1,0 + j2,0 Ω. The transformer supplies 20kW at a power factor of 0,8 leading.
a) Draw a schematic diagram of the transformer connection
b) Determine the current flowing in the transformer windings
c) Determine the primary voltage
d) Determine the voltage regulation.
Exercise 2:
A single–phase transformer, marked 10kVA, 7500:250V, 60Hz, has an equivalent impedance
of, Zeq =0,015 + j0,06 pu, Rc =60 pu, & Xm =20 pu.
a) Determine the equivalent circuit model in machine values, referred to the secondary side.
b) The high voltage side is connected to an infinite bus of 7500 V, and a load of 5∠-90 is
connected to the low voltage side. Determine the voltage over the load and the current
flowing in it.
c) Determine the voltage regulation.
Exercise 3:
A 3 - phase transformer is marked: S = 630 kVA, 20/0.4 kV , connection phase angle
indicator Dy5, insulation class B.
The following test results are available:
Phase resistance at 18 deg. C: R1 = 8.62Ω & R2 = 1.01 mΩ
No load test: U0 = 20 kV, I0 = 0,32 A, P0 = 1,27 kW
Short circuit test: Usc = 820 V, Isc = 18.2 A, Psc = 5.41 kW
The tests were performed on the high voltage side, delta-connected.
1a) Determine the equivalent circuit parameter values and draw an approximate equivalent
circuit model, with a reference temperature of 75 deg.C.
1b) Determine the secondary voltage at full load current and apparent power (S), at: a) cosϕ
= 0 inductive., b) cosϕ = 0 capacitive. og c) cosϕ = 1.
Exercise 4:
Two three - phase transformers, both marked 10/0.4 kV and having connection phase angle
indicator Yy0 are connected to common bus-bars. The following information is available:
TR1: S = 100 kVA, usc = 3,6 %, cosϕ = 0.485.
TR2: S = 250 kVA, usc = 4,4 %, cosϕ = 0.325
2a) What is the accumulated load of the two transformers when one of them reaches full load?
2b) What current flows in each transformer when the accumulated load is 350 kVA?
Exercise 5:
The electrical machine shown in the figure has an open-circuited rotor, i.e. i2=0 A. The
inductance of the stator winding is given by:
Lss = 0.1 − 0.3cos(2θ ) − 0.2cos(4θ )
H
If a current of 10 A rms. Flows in the stator winding
1. Determine the speed of rotation ωm , where the average torque is different from zero
2. Determine the maximum torque and power on the shaft at all speeds.
3. determine the maximum torque at zero speed
Exercise 6:
A rotating electrical machine as shown above has the following machine constants:
Lss = 0.15 H, Lrr = 0,06 H; Lsr = 0.08cosθ.
The rotor turns at 3600 rpm. A current of 5 A at 60 Hz flows in the stator. If the rotor is opencircuited, determine the instantaneous voltage and the rms value of the voltage induced in the
rotor winding and the frequency of this voltage.
Assume that the stator and rotor coils are connected in series and a current of 5 A rms at 60
Hz flows in them. Determine the speed of the rotor at which the average torque is different
from zero. Determine the maximum torque developed by the machine at any speed.