This slide is about 3 phase apparatus.

1. 3-PHASE POWER
APPARATUS
BY: MUBAREK KURT
Mubarek Kurt

2. BASIC CONCEPT
-MAGNETIC FIELD-
Ampere’s Law – the basic law governing the
production of a magnetic field by a current:
Where H is the magnetic field intensity produced by
the current Inet and dl is the differential element of
length along the path of integration.
netIdlH 
mean path length, lc
I

N turns
CSA
c
c
Hl Ni
Ni
H
l

 
Mubarek Kurt

3. BASIC CONCEPT
-MAGNETIC FIELD-
• H is known as the effort to induce a magnetic
field. The amount of H is depend on
permeability of the material to form flux
density B.
HB 
B = magnetic flux density (webers per square meter,
Tesla (T))
µ= magnetic permeability of material (Henrys per
meter)
H = magnetic field intensity (ampere-turns per
meter)
r
o



 where: o – permeability of free
space (4π x 10-7 H/m)Mubarek Kurt

4. BASIC CONCEPT
-MAGNETIC FIELD-
Measuring the total flux in the core
B = H =
Now the total flux in a given area is given by
Where: A – cross sectional area
Assuming the flux density in the core is constant
cl
Ni
A
BdA  
BA 
c
NiA
l

 Mubarek Kurt

5. ROTATING MACHINE
-GENERAL-
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6. ROTATING MACHINE
• Rotor is a moving component of an
electromagnetic system. Its rotation is
due to the interaction between the
windings and magnetic fields which
produces torque around the rotor’s
axis.
• Stator is the stationary part of a rotary
system. The main use of the stator is
to keep the field aligned.
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7. ROTATING MACHINE
• Armature Winding: the winding that carries only
load current.
• Field Winding: the winding that carries only
magnetizing current.
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8. ROTATING MACHINE
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9. ROTATING MACHINE
-APPLICATION-
• Could be
Generators
Alternator
Motors
Transmission gears
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10. AC MACHINE
-STRUCTURE-
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11. AC MACHINE
-STRUCTURE-
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12. AC MACHINE
-STRUCTURE-
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13. AC MACHINE – 3-PHASE
-STRUCTURE-
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14. DC MACHINE
-STRUCTURE-
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15. DC MACHINE
-STRUCTURE-
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16. AC MACHINERY FUNDAMENTALS
• AC machines are generators that
convert mechanical energy.
• The fundamentals principles of ac
machines are very simple, but
unfortunately, they are somewhat
obscured by the complicated
construction of real machines.
• There are two major classes of ac
machines
i. Synchronous MachinesMubarek Kurt

17. A SIMPLE LOOP IN A
UNIFORM MAGNETIC FIELD
• We will start our study of ac machines
with a simple loop of wire rotating
within a uniform magnetic field.
• A loop of wire in a uniform magnetic
field is the simplest possible machines
that produces a sinusoidal ac voltage.
• This case is not representative of real
ac machines, since the flux in real ac
machines is not constant in either
magnitude or direction.
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18. THE VOLTAGE INDUCED IN A
SIMPLE ROTATING LOOP
• If the rotor of this machine is rotated,
a voltage will be induced in the wire
loop.
• To determine the magnitude and
shape of the voltage, examine figure
below
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19. Total induced voltage on the
loop eind = eba + ecb + edc + ead
= vBl sin θab + vBl sin θcd
= 2 vBL sinθ, note that
v=velocity
=2rωBLsinθ, where v=rω
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20. MOTOR
-INDUCED TORQUE-
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21. 


sin2
sinsin
rilB
rilBrilB cdab
dacdbcabind



The total induced torque on the loop:
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22. INDUCED VOLTAGE AND TORQUE
As a conclusion, the induced voltage is
dependent upon:
a. Flux level (the B component)
b. Speed of Rotation (the v component)
c. Machine Constants (the l component and
machine materials)
Also for the torque is dependent upon:
a. Strength of rotor magnetic field
b. Strength of stator magnetic field
c. Angle between the 2 fields
d. Machine constantsMubarek Kurt

23. RELATIONSHIP BETWEEN
FREQUENCY AND SPEED
Since one electrical cycle is 360 electrical
degrees, and mechanical motion is 180
mechanical degrees, the relationship between
the electrical angle θe and the mechanical θm in
this stator is
θe = 2 θm
Thus, for a four pole winding, the electrical
frequency of the current is twice the mechanical
frequency of rotation:
fe = 2 fm
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24. 2
2
2
e m
e m
e m
P
P
f f
P
 
 



60
120
m
m
m
e
n
since f where n is the number of rotation
n
f P

 
Therefore the general format will be as follows:
Also,
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25. INDUCED VOLTAGE IN 3-PHASE
The induced voltages at each phase will be
as follows:
'
'
'
sin
sin( 120 )
sin( 240 )
aa
o
bb
o
cc
e N t V
e N t V
e N t V
 
 
 

 
 
The maximum induced voltage is when sin has a value
of 1, hence,
max
max
, since 2 ,
2
E N f
E N f
  
 
 
 Mubarek Kurt

26. Therefore, the rms voltage at the 3 phase
stator:
2AE N f 
Note: These are induced voltages at each
phase, as for the line-line voltage values; it will
depend upon how the stator windings are
connected, whether as Y or D.
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27. INDUCED TORQUE IN 3-PHASE
sinind r s r sKH B KH B   
ind r skB B  
 ind r net r r netkB B B kB B     
sinind r netkB B 
Therefore the torque equation may be represented in the following form:
Note that K is a constant value.
Since BR= HR,
The constant k is a value which will be dependent upon the permeability
of the machine’s material. Since the total magnetic field density will be the
summation of the BS and BR, hence:
If there is an angle  between Bnet and BR,
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28. EXAMPLE 1
The simple loop is rotating in a uniform magnetic field shown in
Figure has the following characteristics:
B = 0.5 T to the right r = 0.1 m
l = 0.5 m ω = 103 rad/s
(a) Calculate the voltage e t tot( )induced in this rotating loop.
(b) Suppose that a 5 Ω resistor is connected as a load across the
terminals of the loop. Calculate the current that would flow
through the resistor.
(c) Calculate the magnitude and direction of the induced torque
on the loop for the conditions in (b).
(d) Calculate the electric power being generated by the loop for
the conditions in (b).
(e) Calculate the mechanical power being consumed by the loop
for the conditions in (b). How does this number compare to the
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29. Mubarek Kurt

30. EXAMPLE 2
A three-phase four-pole winding is installed in 12
slots on a stator. There are 40 turns of wire in each
slot of the windings. All coils in each phase are
connected in series, and the three phases are
connected in Δ. The flux per pole in the machine is
0.060 Wb, and the speed of rotation of the magnetic
field is 1800 r/min.
(a) What is the frequency of the voltage produced in
this winding?
(b) What are the resulting phase and terminal voltages
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31. AC MACHINE POWER FLOWS AND
LOSSES
• AC generators take in mechanical power and
produce electric power, while AC motors take
in electric power and produce mechanical
power.
• In either case, not all the power input to the
machine appears in useful form at the other
end-there is always some loss associate with
the process.
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32. THE LOSSES IN AC MACHINES
• The losses that occur in ac machines can be
divided into 4 basic categories:
a) Electrical or Copper losses (I2R losses)
b) Core losses
c) Mechanical losses
d) Stray Load losses
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33. (A) COPPER LOSSES
• Copper losses are the resistive heating losses
that occur in the stator (armature) and rotor
(field) winding of the machine.
• The stator copper losses (SCL) in 3 phase ac
machine
Where IA is armature current and RA is the
resistance of each armature phase.
AASCL RIP
2
3
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34. (A) COPPER LOSSES CONT.
• The rotor copper losses (RCL) of a synchronous
ac machine ac are given by
Where IF is field current and RF is the resistance
of field winding.
FFRCL RIP
2
3
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35. (B) CORE LOSSES
• The core losses are the hysteresis losses and
eddy current losses metal occurring in the
metal of the motor.
• Both hysteresis and eddy current losses cause
heating in the core material.
• Since both losses occur within the metal of the
core, they are usually lumped together and
called core losses.
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36. (C) MECHANICAL LOSSES
• The mechanical losses in an AC machine are the
losses associated with mechanical effects.
• There are two basic types of mechanical losses:
friction and windage.
• Friction losses are losses caused by the friction of
the bearing in the n between machine.
• Windage losses are caused by the friction between
the moving parts of the machine and the air inside
the motor’s casing.
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37. (C) MECHANICAL LOSSES CONT.
• The Mechanical and Core losses of a machine are
often lumped together and called the no-load
rotational loss of the machine.
• At the no load, all the input power must be used to
overcome these losses.
• Therefore, measuring the input power to the stator
of an AC machine acting as a motor at no load will
give approximate values of these losses.
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38. (D) STRAY LOSSES
• Stray or miscellaneous losses are losses that
cannot be placed in one of the previous
categories.
• No matter how carefully losses are accounted
for, some always escape inclusion in one of the
above categories.
• All such losses are lumped into stray losses.
• For most machines, stray losses are taken by
convention to be 1 percent of full load.Mubarek Kurt

39. THE POWER FLOW DIAGRAM
• One of the most convenient techniques for
accounting for power losses in a machine is the
power-flow diagram.
Pconv=the remaining
power converted from
Mechanical to
Electrical and vice
versa
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40. EFFICIENCY
• The efficiency of an AC machine is defined by
the equation
%100
Pin
Pout

%100


Pin
PlossPin

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41. VOLTAGE REGULATION
• Generators are often compared to each other
using a figure of merit called voltage
regulation.
• Voltage Regulation (VR) is a measure of ability
of a generator to keep a constant voltage at its
terminals as load varies.
%100


fl
flnl
V
VV
VR
Mubarek Kurt

42. SPEED REGULATION
• Similarly, motors are often compared to each
other by using a figure of merit called speed
regulation.
• Speed Regulation (SR) is a measure of the
ability of a motor to keep a constant shaft
speed as load varies.
%100


fl
flnl
n
nn
SR %100


fl
flnl
SR


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43. GENERATOR
-TESTING-
• Insulation test
• Test of dielectric withstanding voltage (DWV)
• Impulse test
• Partial discharge test
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44. MOTOR
-TESTING-
• Insulation test
• Voltage test
• Current test
• Impulse test
• Continuity test
• Impedance test
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