1.

a)   Briefly explain the excitation system in brushless synchronous generators and contrast them with brushed machines. (2.5 Marks)

b)  Consider a synchronous generator acting alone. Briefly describe with the aid of phasor diagrams, the impact of increased loading on the terminal voltage for (i) Lagging loads and (ii) Leading loads. Describe the impact of the load increase on the power factor, the internal EMF and the torque angle. (2.5 Marks)

c)  You have just tested a 3 phase, 4-pole, 50 Hz, delta-connected synchronous machine at its rated field current of 15 A. You measured an open circuit line-to-line terminal voltage of 650 V anda short circuit line current of 950 A at the rated field current under synchronous speed. You also measured a DC current of 80 A after applying a DC voltage  of  10  V between  2  of the  3  stator  phases.  Assume  that  the  open  circuit characteristic relating the rotor current to the no-load terminal voltage is linear.

(i)  Calculate the machines  synchronous  speed, the per-phase armature resistance, the internal EMF and the synchronous reactance. Sketch the per-phase equivalent circuit of this synchronous machine.

(ii) Assume the machine has a synchronous reactance of 1.17 Ω, negligible armature resistance and is to operate as a synchronous motor at 0.8 Power Factor leading from a 3 phase AC supply with a line-to-line voltage of 400 VRMS. Calculate the internal EMF, output torque and load angle required for the machine to drive a 70 hp load if it is  95%  efficient.  Sketch  the  phasor  diagram  of the  machine  under  steady-state conditions (1 hp = 746 Watts). (10 Marks)

d)  The synchronous machine in (c) is now to act as a generator with a 400 VRMS  line-to line terminal voltage supplying 95 kW of electrical power.

(i)   Determine the rotor  current and torque angle required for this machine to deliver electrical power at 0.8 PF lagging recalling that the open circuit terminal voltage is 650 Vat the rated rotor current of 15 A and that the open circuit characteristic is linear.

(ii)  If the rotor current is doubled with the electrical load remaining unchanged, sketch the impact of this on the phasor diagram of the synchronous generator and calculate the new terminal current and power factor. (10 Marks)

(Total:  25 Marks)

2.   a)

(i)   Briefly  explain  “Armature  Voltage”  and  “Field  Current”  control  in  a  separately excited DC motor. Explain what is meant by “Field Weakening” .

(ii)  Explain the difference between separately excited and self-excited DC machines. (iii) Explain the difference between a series and shunt DC motor. (5 Marks)

b)  You have just performed no-load and locked rotor tests on a 3-phase, 600 V, 50 Hz,

star-connected induction motor and obtained the set of results shown in Table Q2.

You have also done DC measurements by supplying 20 V between 2 stator phases of the induction motor and recording a DC current 500 A. Based on these measurements, derive the per-phase IEEE recommended equivalent circuit of the induction motor. (10 Marks)

c)    A 400 V, 3-phase, star-connected, 50 Hz, 8-pole induction motor has a rotational speed of 700 rpm under full load conditions. The IEEE recommended equivalent circuit has the following per-phase parameters.

R1=0.2 Ω,       R2’=0.15 Ω,    X1=0.25 Ω,     X2’=0.33 Ω      and    Xm=40 Ω

The frictional and windage (rotational) losses of the machine are 5 kW and the core

losses can be considered to be negligible. Calculate:

(i)        The input power and power factor under full-load conditions with 400 V line- to-line voltage at the input.

(ii)       The air-gap power and converted power under full load conditions.

(iii)      The induced torque under full load conditions.

(iv)      The output power and efficiency under full load conditions.(10 Marks)

(Total:  25 Marks)

4.   The nameplate of a three-phase  squirrel cage induction machine contains the following data: the rated shaft power is 3 kW, the rated  line-to-line voltage is 380 V, the rated efficiency is 0.8, the rated power factor is 0.86, the synchronous velocity is 3000 rpm and the rated velocity is 2900 rpm.

a) Compute the following parameters of the motor:

(i)        Rated angular velocity in rad/s.

(ii)       Rated phase voltage.

(iii)      Rated stator current.

(iv)      Rated torque.

(v)       Rated slip. (5 Marks)

b) The machine is fed from a controlled voltage source which provides V/f = const ratio, leading to a constant rated critical torque of 25 N m. In a steady state, the frequency of the supplied voltage is 40 Hz, the machine’s angular velocity is 246 rad/s and the load torque is 10 N m. The number of pole pairs is equal to one. Compute the steady state values of

(i)        The no load angular velocity. (1 Mark)

(ii)       The slip. (1 Mark)

(iii)      The critical slip using the simplified Kloss formula. (3 Marks)

c) The vector control of the motor’s angular velocity is implemented in the d-q frame aligned with the rotor flux linkage vector in the d axis according to the block diagram in Figure Q4(a). The control system includes an Angular Velocity PI-Controller (AVC), a rotor Flux Linkage PI-Controller (FLC), two Current PI-Controllers (CC1 and CC2), a Compensation Block (CB), a Flux Sensor (FS) and a Vector Computation block (VC). At specific moment in time, the rotor flux linkage vector magnitude is 1 Wbandits angle with respect to stator axis a is 30 degrees. The instantaneous values of the stator currents in phases U, Vand Ware 2 A, 2 A and –4 A, respectively. The instantaneous values of the stator voltages in phases U, Vand Ware 100 V, 110 V and –210 V, respectively. For this moment in time compute:

(i)        The d and q axes stator currents. (3 Marks)

(ii)       The d and q axes stator reference voltages. (4 Marks)

d) Space Vector PWM modulation of the stator voltage vector is used in the system in Figure Q4(a). The modulation is implemented according to Figures Q4(b) and Q4(c), where E=600 V. For the moment in time and stator voltages specified in part c: