UNIVERSITI TEKNOLOGI MALAYSIA PEPERIKSAAN AKHIR

SEMESTER 1 SESI 2016/2017

KOD MATAPELAJARAN : SEE 3433

MATA PELAJARAN : MESIN ELEKTRIK

PENSYARAH : ABD JAAFAR SHAFIE (JB) NIK DIN MUHAMAD (KL)

KURSUS : SEE

SEKSYEN :

MASA : 2 JAM 30 MINIT

TARIKH :

ARAHAN KEPADA CALON

:

JAWAB EMPAT (4) SOALAN SAHAJA. SEMUA PENGIRAAN HENDAKLAH DITUNJUKKAN DENGAN JELAS.

KERTAS SOALAN INI TERDIRI DARIPADA 9 (SEMBILAN) MUKA SURAT SAHAJA

SULIT

-2- SKEE4633/SEE3433

Question 1 (a) A magnetic circuit, which includes a movable plunger, is shown in Figure Q1(a). Assume

that the permeability of the core is infinite and with negligible leakage and fringing. The

dimensions of magnetic circuit are: a = 2.6 cm, b = 2.8 cm, c = 2.5 mm, d = 3.5 cm

(thickness of the magnetic core) and the numbers of turn of winding, N, is 2000 turns.

(i) Obtain expressions for the reluctance, , and inductance, L, of the magnetic circuit as a

function of x, o, N, a, b, c and d. [6 marks]

(ii) Obtain the expression for the force acting on movable plunger, fm, as a function of

variable x. [4 marks]

(iii) Determine the value of force, fm, for i = 5 A at x = 5 cm. [4 marks]

Figure Q1(a)

(b) An elementary two-pole cylindrical rotating machine with a uniform air gap has the

mutual inductance between the rotor and the stator given by

cos712 L H

An AC current source, )20100cos(71 ti A is applied to the stator and a DC current

source A72 i is applied to the rotor. Let mt + and = 60, where is the angle

between the magnetic axis of the stator and rotor windings, m is the angular velocity of

the rotor, and is the rotor position at t = 0.

(i) Obtain the expression for the instantaneous torque, T. [5 marks]

(ii) Determine the average torque developed by the machine, at m = 100 rad/s and 0

rad/s, respectively. [6 marks]

Moveable plunger

µ ∞

µ b

a

x N

i

Frictionless nonmagnetic sleeve with permeability µo

and width c

c

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Question 2

(a) Starting from the equation for the induced voltage in a single conductor with a length of l,

moving linearly at a constant speed of v, in a magnetic field density of B, show that the total

induced voltage in the armature winding of a DC generator in volt can be given by

E a Np

am

where N is total number of turns, p is number of poles, a is number of parallel paths, is

flux per pole and m is mechanical speed. [6 marks]

(b) A 21 kW, 210 V, 1800 rpm, Ra = 0.1 DC machine operated as shunt generator has a

magnetization characteristic at 1800 rpm as shown in Figure 2(c) in Attachment Q2(c). The

shunt field winding resistance Rfw = 80 and the number of turns Nf = 1000 turns per pole.

The effect of armature reaction at full-load, If(AR), is 0.10 A.

(i) Determine the maximum generated voltage. [4 marks]

(ii) The machine is operated as a shunt generator at 1800 rpm and the no-load terminal

voltage is adjusted to 210 V. Determine the full load terminal voltage with and

without armature reaction effect. [5 marks]

(iii) The no-load terminal voltage is the same as in (ii) but the load is reduced to 75% of

the full load. Determine the terminal voltage with and without armature reaction

effect. Assume the effect of armature reaction is proportional to Ia. [5 marks]

(iv) Determine the maximum value of the armature current that the generator can supply

and the corresponding value of the terminal voltage. Assume that If(AR) = 0.125 A at

the maximum armature current. [5 marks]

You must submit Attachment Q2(c) with your answer booklet

-4- SKEE4633/SEE3433

Question 3

(a) Explain the necessity for the use of starter with a DC motor. Explain how the starting

methods can be achieved. [6 marks]

(b) A 240 kW, 200 V, 1800 rpm, Ra = 0.1 DC machine operated as shunt self-excited motor

has a magnetization characteristic at 1800 rpm as shown in Figure 3(c) in Attachment

Q3(c). The shunt field winding resistance, Rfw = 100 and the number of turns, Nf = 1200

turns/pole. The machine is connected to a 200 V DC supply. At no load condition, the

motor runs at 1800 rpm and the armature draws 10 A.

(i) Find the back emf Ea, field current If, and field resistance, Rf at no load condition.

[4 marks]

(ii) Find the speed of the motor when the rated current flows in the armature. Neglect the

armature reaction effect. [4 marks]

(iii) Find the rotational losses and efficiency of the motor when rated current flows in the

armature. Neglect the armature reaction effect and assume that rotational loss does not

change with speed. [5 marks]

(iv) Find the speed of the motor when the rated current flows in the armature. Consider the

effect of armature reaction at full-load is If(AR) = 0.15 A. Then, calculate the percentage

reduction of flux in the machine due to armature reaction.

[6 marks]

You must submit Attachment Q3(c) with your answer booklet

-5- SKEE4633/SEE3433

Question 4

(a) Draw the approximate per phase equivalent circuit of three-phase induction motor using.

Derive the steady-state torque equation generated by the induction motor, in term of

supply voltage V1, synchronous speed s, slip s and parameters of induction motor which

are 2R , R1, '2X and X1.

[6 marks]

(b) The parameters for a 3-phase star-connected, 415 V, 50 Hz, 1450 rpm four poles wound

rotor induction motor are as follows:

R1 = 0.20 2R = 0.25

X1 = 0.7 '2X = 0.7 Xm = 100

(i) Determine the synchronous speed, slip and the slip speed of the motor.

[4 marks]

(ii) To enable maximum torque produced at the motor starting, determine how much

external resistor/phase should be connected at the rotor side. Determine the motor

starting current. [6 marks]

(iii) The motor drives a constant load of 100 Nm at its rated speed. Calculate the

external rotor resistor/phase needed if the speed to be decreased from motor rated

speed to a speed of 1300 rpm. How much mechanical power is needed under this

condition? Assume no friction and windage loss. [6 marks]

(iv) Sketch the torque-speed characteristics of the motor and load to represent the

condition (iii) and also at its original rated condition.

[3 marks]

-6- SKEE4633/SEE3433

Question 5

(a) Sketch the per phase equivalent circuit of synchronous machine which consists of

armature resistance, Ra, and synchronous reactance, Xs, Label all circuit parameter and

electrical variables. Based on the equivalent circuit, draw the phasor diagram of the

synchronous generator and motor when it is supplying power at leading power factor.

[5 marks]

b) An 11.7 kV, 3-phase, four pole, 50 Hz, delta-connected synchronous generator has

negligible stator winding resistance and synchronous reactance of 30 Ω per phase at rated

terminal voltage. The generator is connected to constant voltage, constant frequency

infinite busbars.

(i) The generator is delivering 9 MW at power angle of 55 to busbars. Determine

per phase excitation voltage, line current, power factor and reactive power

supplied by generator. Draw a phasor diagram for this operating condition.

[5 marks]

(ii) The power output of the generator is increased to 12 MW by increasing the

steam supply and the excitation voltage is increased by 30%. Determine the

MVA, power angle, line current and power factor at which the machine now

works. [5 marks]

(iii) With the excitation voltage maintain at the same value as in part (ii) mechanical

power input (i.e. steam supply) is further increased until the generator is operating

at power factor of 0.9 leading. Determine the output power, reactive power,

current and power angle. [5 marks]

(vi) Draw the phasor diagram of (ii) and (iii) to indicate the change in generator steam

supplied with respect to the changes in excitation voltage.

[5 mark]

-7- SKEE4633/SEE3433

Attachment Q2(c)

Name: …………………………………………………………………………………………..

Figure Q2(c)

-8- SKEE4633/SEE3433

Attachment Q3(c)

Name: ………………………………………………………………………………………….

Figure Q3(c)

-9- SKEE4633/SEE3433

Potentially Useful Formulae

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B A H

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A

lR

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a

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W f idl0

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ags

PT1

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RTh2 (Xth X2)2[ ]

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sin

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rotationalmout PPP )1()1(22

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constant

l

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m

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sin(x)sin(y) cos(x y)

2

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sin(x)cos(y) sin(x y)

2

sin(x y)

2

fm i2

2

d

dxL(x) cos(x)cos(y)

cos(x y)

2

cos(x y)

2

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dxL(x)

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RR

s

R ext

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1