Alexandria University
Faculty of Engineering
Electromechanical Engineering
EME 308
emf equation
Sheet 1 (Synchronous machine)
1. A three phase, 8 pole synchronous generator is star connected. The stator has 168 slots with 9
conductors per slot. If the rotor speed is 750 rpm, estimate the flux required in the air gap to generate
an e.m.f. of 1000V between lines (Winding factor=0.96)
2. A 3-phase, 10 poles, star connected alternator runs at 600 rpm. It has 120 slots in the stator with 8
conductors per slot and the conductors of each phase are connected in series (one parallel path).
Determine the phase and the line e.m.f. s, if the flux per pole is 56 mWb. Assume full pitch coils.
3. A 3-phase, 10 poles alternator has 90 slots, each containing 12 conductors. If it runs at 600 rpm, and
the flux per pole is 0.1 Wb, calculate the line e.m.f. when the phases are i) star connected, ii) Delta
connected. (Assume sinusoidal distributed flux, and 0.96 winding factor.)
4. The no-load voltage of a 6-pole, 72 slot, 1200 rpm, three phase Y connected, synchronous generator is
1732 V. If there are 10 conductors per slot, determine the frequency of the induced emf and the flux
per pole.
5. A three phase, 8-poles synchronous generator is star connected. The stator has 168 slots with 9
conductors per slot. If the rotor speed is 750 rpm, estimate the flux required in the air gap to generate
an emf of 1000 V between lines. If the field current was 1 A, what would be the field current to reduce
the generated emf to 900 V? If the speed is allowed to be changed, what would be the new speed to
bring the emf back to its initial value? How does that affect the frequency of the generated voltage?
Comment! (Neglect saturation and take winding factor = 0.96).
.
Alexandria University
Faculty of Engineering
Electromechanical Engineering
EME 308
Equivalent circuit, phasor, power
Sheet 2 (Synchronous machine)
1. In a 50 KVA, star connected, 440 V, 3-phase, 50 Hz alternator, the armature resistance is 0.25  per
phase. The armature reactance is 3.7  per phase. Determine the induced emf per phase and the
voltage regulation at rated load and unity power factor. Sketch the phasor diagram.
2. A 9 KVA, 208 V, three phase, Y connected, synchronous generator has a winding resistance and a
synchronous reactance of 0.1 /phase and 5.6 /phase respectively. Determine the voltage regulation
when the power factor of the load is (a) 80% lagging, (b) unity, and (c) 80% leading.
3. A 3-phase, star connected alternator is rated at 1600 kVA, 13500 V. The armature effective resistance
and synchronous reactance are 1.5 ohm, and 30 ohm respectively per phase. Calculate the percentage
voltage regulation for a load of 1280 kW at (a) 0.8 leading power factor, and (b) 0.8 lagging power
factor.
4. A 100 kVA, 3 kV, 50 Hz, 3-phase, Y-connected alternator has effective armature resistance of 0.2 ohm
/ phase. A field current of 40 A produces short circuit current of 200 A and an open circuit voltage of
1040 V (line value). Calculate the full load percentage regulation at 0.8 lagging power factor. How
would the regulation be affected if the alternator delivers its full load at 0.8 leading power factor?
5. A 3-phase star connected, 6-pole synchronous generator is driven at 1200 rpm. It has an armature
resistance and synchronous reactance of 0.4/phase and 4/phase respectively. The machine supplies
a load of 100kW at 0.8 lagging power factor and 2kV terminal voltage between lines. The machine
has 100 turns per phase and winding distribution factor of 0.9, Calculate
a.
Generated emf per phase
b.
Voltage regulation
c.
Load angle 
d.
Average flux per pole
6. A 3-phase star connected alternator is rated at 5 kW, 110 V, 29 A lagging pf, 50 Hz and 1000 rpm.
The stator resistance and reactance per phase are 0.1  and 1.53  respectively.
a. Find the no load induced emf, voltage regulation and the number of poles
b. The field current is reduced to 90% of its value while speed is kept constant. What would be
the load voltage if the generator is supplying the same load current with the same pf.
c. If the speed, load current and field current are kept constant while the power factor became 0.8
leading, what would be the terminal voltage?
7. A three-phase, star connected, 6 pole synchronous generator supplies a three-phase load of 100kW,
0.8 leading power factor, at 60Hz, 2KV line voltage. The machine per phase armature resistance and
reactance are 0.4Ω and 4Ω respectively. Find:
a) Voltage regulation
b) Efficiency, if constant losses are 10% of copper losses
Alexandria University
Faculty of Engineering
EME 308
tests, parallel operation, motor
Sheet 3 (Synchronous machine)
Electromechanical Engineering
1. the results of a dc test performed on a 3-phase synchronous machine were V dc = 5V, Idc = 10A find the
armature resistance per phase if the test was performed between terminals
a. U and w
b. U and V
c. U and V
U
V
W
U
V
W
U
V
W
w
u
v
w
u
v
w
u
v
2. With terminal connection of figure in question 1 a. the no load tests was performed to give the
following results between terminals U and w
If
0.2
0.4
0.6
0.8
1.0
1.2
1.4
A
Vo.c.
70
140
200
240
255
260
261
V
0.05 A field current was necessary to circulate 10A short circuit current. If the armature resistance per
phase is 0.7 ,
a. Find the synchronous impedance and synchronous reactance when the excitation current is 0.2A.
b. Repeat part a. when the no load phase voltage is 140V.
c. Repeat part a. when the open circuit phase voltage is 260V.
d. Does the synchronous reactance increase or decrease at high excitation? Explain your answer.
e. what would be the expected maximum value of the synchronous reactance
3. Two 15kVA, 400V, three phase alternators are connected in parallel to supply a load of 25kVA at 0.8
lagging power factor. If one alternator shares half the load at unity power factor, determine the power
factor and kVA shared by the other alternator.
4. Two similar 6600V, three phase alternators are running on constant voltage and frequency bus bars.
Each has an equivalent resistance and reactance of 0.05 and 0.5 respectively and supplies one half
of a total load of 10Mw at a 0.8 lagging power factor. The two machines are similarly excited. If the
excitation of one machine is adjusted until the armature current is 438A and the steam supply to the
turbine remains unchanged, find the armature current, the generated e.m.f. and the p.f. of the other
alternator.
5. Two alternators are connected in parallel to supply a load of 1MVA at 0.7 lagging power factor. The
two generating units have the following linear external characteristics.
Unit A
Unit B
Power in KW
No load
400
No load
600
Frequency in Hz
52
48
51
48
Find the operating frequency and the power delivered by each generator
6. A 3-phase, 4-pole, 380V, 50Hz, Y connected synchronous machine has armature resistance of
0.5/phase and synchronous reactance of 2/phase. The machine is used as a synchronous capacitor
to modify the power factor of a small industrial plant. When the machine is connected to the supply it
absorbs 330W at unity power factor when the field current was 0.5A.
a. Find the speed and the developed torque of the machine.
b. What would be the machine field current if the machine is to compensate 33kVAR.
c. If the machine is to drive a fan with a developed torque of 21Nm. Find the field current when the
machine runs at unity power factor, and the field current if the machine is to compensate the same
33kVAR. Compare between the two field currents and comment on your results.
Alexandria University
Faculty of Engineering
Electromechanical Engineering
EME 308
Equivalent circuit, power flow
Sheet 4 (Asynchronous machine)
1. A three phase, four poles, 380V, 50Hz, Y connected induction motor has the following parameters:
r1=1
r2’=1.2
x1=1.5
x2’=1.5
Rc=880
xm=440, mechanical losses
66 W. if the motor runs at 1410 rpm, find:
i – Synchronous speed
ii – slip
iii – core losses power
iv - Stator copper losses
v – air gap power
vi – rotor copper losses
vii - developed power
viii - input current
ix - input power
x - output power
xi – efficiency
xii – developed torque
xiii – output torque
xiv- power factor
xv - draw the power flow diagram
Ns=1500 rpm, s=0.06, Pc=165W, SCL=322.6W, Pg=6453W, RCL=387.2W, Pd=6066W, I1=10.7A
Pin=6940.6W, Pout=6000W, =86.4%,Td=41N.m., Tout=40.6N.m., pf=0.98 lagging
2. Repeat problem 1 if the motor runs at a slip of 0.06, find also the rotor speed.
3. In problem 1 find the input current and power factor at slip of 0.2 comment on how the current and
power factor change with the slip.
4. Repeat problem 1 at zero speed (starting condition)
5. Repeat problem 1 at no load condition neglecting the mechanical losses (N = 1500r.p.m.)
6. For the motor described in problem 1, find the slip at which the motor develops its maximum torque
(break down slip). Find the speed of the motor and the value of the maximum torque (break down
torque).
7. For the motor described in problem 1, find the slip at which the motor develops its maximum power.
Find the speed of the motor and the value of the maximum developed power.
8. A three phase, 380V, 50Hz, 4-pole, star connected induction motor runs at 1440 rpm. If the magnetic
core losses, stator copper losses, rotor copper losses and mechanical losses are 500W, 750W, 750W,
and 500W respectively, find:
i-The synchronous speed
ii-The slip
iii-The gap power
iv-The developed power
v-The net output power
vi-The output torque
vii-The input power
viii-The motor efficiency
9. Write the MatLab code (m-file) to plot the torque slip (Td – s) for s changing from 1 to 0 with 0.05
steps characteristics for the motor described in problem 1
10. A three phase, four poles, 380V, 50Hz, Y connected, wound rotor induction motor has negligible
stator impedance and rotor impedance of 0.04+j0.16 /phase at standstill. Determine the breakdown
slip and the breakdown torque. What is the starting torque developed by the motor? If the starting
torque of the motor has to be 80% of the maximum torque, determine the external starting resistance
that has to be added in series with the rotor.