[EEE3002]






NEWCASTLE UNIVERSITY
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SEMESTER 1 2019/2020
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ELECTRICAL MACHINES


Time allowed - 1 hour 30 minutes
Candidates must answer any TWO questions
All questions carry equal marks.
[Marks shown in sub-sections are indicative only]
It is desirable to show the method of calculation and the steps
taken to achieve the results.
A formula sheet of trigonometric and geometrical relationships
is provided.

[Turn over]

2019 [EEE3002]
Page 2 of 8
Question 1
a) An electrical machine is used to drive an elevator hoist. The
mechanical system has the parameters shown below:
Electrical torque developed Te = 2000 - 100ω Nm
Machine inertia Je = 0.5 kgm2
Load torque Tm = 1250 Nm
Load inertia Jm = 49.5 kgm2
Total drag torque Tc = 50ω Nm

Assume that the connecting shaft is rigid and has zero inertia;
i) Sketch a free body diagram of this system.
ii) Derive the mechanical system equation, including all
torques, inertias and losses acting upon this system.
iii) Calculate the steady state speed and mechanical time
constant of this system.
iv) Derive an equation relating speed and time assuming the
machine starts from rest.
v) Carefully plot (to scale in your answer booklet) the
transient response of this machine and load.
vi) Calculate the time taken to reach 95% of the steady state
speed.
[30 marks]

2019 [EEE3002]
Page 3 of 8

b) If the electrical machine drives a pulley wheel of radius
250mm, calculate the time taken to raise the elevator vertically
20m from rest. You may use the parameters and your results
from part a) and ensure you state any approximations made.
[20 marks]


2019 [EEE3002]
Page 4 of 8
Question 2

a) Figure 1 shows three variants of the magnet arrangement for
a permanent magnet synchronous machine rotor. In all cases
the rotor core is constructed from laminated steel, with the 8-
pole magnets arranged as indicated.
i) Rank the three rotors below in order of increasing magnetic
saliency? Explain your reasoning.
ii) Which of the three rotor types will be most suitable for a
high-speed application? Explain your reasoning.


Rotor 1:
Interior PM rotor in
a V formation
Rotor 2:
Surface mounted
radial magnets
Rotor 3:
Inset radial
magnets
Figure 1. Three permanent magnet rotor topologies
[15 marks]

2019 [EEE3002]
Page 5 of 8
b) A permanent magnet synchronous machine is being used in
an automotive drive. Its per-phase rated parameters at the
corner point speed are as follows;
Corner point 4000 rpm Ef 0.75 per-unit
Rated current 50 A Ra 0 per-unit
Rated Voltage 500 V Xd 0.3 per-unit
Xq 0.5 per unit
i) In your answer booklet, draw to a scale of 1 per-unit =
10cm the voltage phasor diagram when the machine is
motoring at rated speed and rated current, with a current
angle, β=45o.
ii) From your phasor diagram, or otherwise, determine the
phase voltage and power factor.
iii) Derive the equation for the power delivered as a function of
the current angle, β.
iv) Derive the current angle, β, at which the output power is
maximised at the rated speed.
v) Calculate the maximum speed achievable within the
voltage and current limit.
[35 marks]

2019 [EEE3002]
Page 6 of 8
Question 3:
a) The equivalent circuit parameters of an induction machine are
obtained from a series of standard tests. A 3-phase, star
connected 50Hz, 8-pole induction machine is subject to these
tests and the results shown in table 1 are measured;

Table 1. Induction machine test results.
a) Measurement b) DC test c) Blocked rotor test
d) (ωr=0)
e) No-load test
f) (ωr= ωs)
g) Total power not measured 2000 W 20 W
Line voltage 4.0 VDC 120 Vrms 120 Vrms
Line current 15 ADC 30 Arms 1.5 Arms

i) Sketch the per-phase equivalent circuit diagram.
ii) From the DC test calculate the equivalent circuit parameter
R1.
iii) From the blocked rotor test calculate the equivalent circuit
parameters R2, X1 and X2. You may assume X1 = 0.5X2.
iv) From the no-load test calculate the equivalent circuit
parameters R0 and X0.
[25 marks]

2019 [EEE3002]
Page 7 of 8

b) The torque developed by an induction machine is described
by the equations;
=





+
and =



ℎ =



For a 50Hz, 8 pole, wound rotor induction machine with the
electrical parameters E2=120V R2=1Ω X2=5Ω
i) Accurately plot the torque-slip curve for this machine from
standstill to synchronous speed.
ii) Calculate the steady state speed when the machine is used
to drive a constant load of 15 Nm.
iii) If the load is increased to 30 Nm, calculate the additional
external resistance in series with R2, required to ensure the
machine starts and operates in a condition to avoid
overheating.
[25 marks]





[END of examination]

2019 [EEE3002]
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