1 ELECTRICAL MACHINES - II Emf induced in the armature conductors: The voltage induced in the conductors is an alternating one and is converted into DC using commutator segments as shown in the figure. The brush 1 always makes contacts with a conductor moving under north pole and the brush 2 makes contact with the conductor moving under south pole and hence the emf collected across brushes 1 and 2 is always of unipolar nature as given below: When there are four conductors (making two turns ) we have four commutator segments as shown below :
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ELECTRICAL MACHINES - II
Emf induced in the armature conductors:
The voltage induced in the conductors is an alternating one and is converted into DC using
commutator segments as shown in the figure.
The brush 1 always makes contacts with a conductor moving under north pole and the brush 2
makes contact with the conductor moving under south pole and hence the emf collected across
brushes 1 and 2 is always of unipolar nature as given below:
When there are four conductors (making two turns ) we have four commutator segments as shown
below :
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As the number of conductors and the commutator segments increases, the DC output emf also
increases and becomes more and more smoother. The emf induced in the armature is always an
AC emf. Using commutator segments, the DC emf is collected and AC emf is collected using slip
rings.
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UNIT – I : SYNCHRONOUS GENERATORS
Each brush makes contact with the ring which is permanently connected to a particular conductor.
As the conductor moves through north and south poles the voltage collected through the brushes
becomes AC emf.
For every pair of poles, one cycle of AC emf is induced.
For the above case two cycles of voltage is induced. Hence the frequency of emf induced is
120/PNf c/s
where N is speed in rpm.
1 Deg. Mechanical = P/2 Deg. Electrical.
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Constructional details of synchronous machines:
The armature power handling capacity is always high in synchronous machines compared to dc
machines.Moreover field windings require less DC power.Hence in synchronous machines
armature winding is placed in stator and the field winding is placed in the rotor getting its supply
through slip rings. If the armature winding is in the rotor the following problems arise :
Higher electro dynamic forces
Higher mechanical losses
Large power at nearly high current and voltage has to be taken through slip rings
Sparking and higher contact losses
Hence the armature is placed in stator and the field is made rotating in synchronous machines.
Rotor winding in synchronous machines:
DC machine
Stator- Field poles
Rotor -Armature windings
Syn. machines
Stator-Armature windings
Rotor -Field poles
Rotor field
Salient poles -projecting pole
rotor
wound rotor -non salient pole
rotor
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Emf equation of alternator:
Let φ The total flux per pole in weber varying sinusoidally as φmsinωt
P No. of Poles
T No. of turns/ phase
f The frequency
Emf induced/turn = e = - mdt
dd
dtsin ωt
Emf/turn = ω Φm cosωt volts
Emf/phase = ω T Φm cosωt volts
Erms/phase = 2πfT Φm /√2 = 4.44 π f T volts
Erms/phase =4.44 π f T volts
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The above equation is complete provided all the conductors are in the same slot and there is no
short pitch in the coil.
But, the windings are distributed over the different slots and are not concentrated. Moreover the
coil pitch is not always π degrees but it is short pitched . Hence we have to take distribution
factor(kd) and the pitch factor (kp) into account:
Distribution factor:
Assume,
g - no. of slots/pole/phase
p- no. of poles
α- slot angle ( slot pitch )
Arithmetic sum of the voltage in g slots
=g*e=(R sin2
) *2*g =2Rg sin 2
Vector sum of voltage in g slots =2[R sin (g 2
)]
Distribution factor= Voltage induced in the distributed winding /Voltage induced in the
concentrated winding
Kd=
2sin2
)2
sin(2
Rg
gR
=
2sin
)2
sin(
g
g
For nth order harmonic emf, Kdn=
2sin
)2
sin(
ng
gn
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Pitch factor : Emf in short pitched coil /Emf of full pitched coil
The pitch of the winding=(π-ρ)
Short chorded angle= ρ
Pitch factor, k p =e
e
2
2cos2
=cos2
For nth harmonic emf, the pitch factor kpn
kpn= cos2
n
In addition to distribution factor and pitch factor one other factor (i.e.)skew factor also should be
taken into account, when the winding is skewed.
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Hence the complete emf equation in alternate is ,
E1=4.44φ1fTkd1kp1ks1 volts
.
.
.
En=4.44φn (nf)Tkdnkpnksn volts
For flux waveform given below,
Φ=φ1sinωt+ φ3sin3ωt+ φ5sin5ωt+……. Φnsinnωt
The emf equation is as follows:
e= E1msinωt+ E3msin3ωt+ E5msin5ωt+……. Enmsinnωt
Erms= 2 2 2 2
1 3 5 nE rms + E rms + E rms +.......+E rms .Though the induced emf in the individual
phases contain harmonics , we can get almost pure sinusoidal emf as output in the following
ways:
By connecting the winding in star, the third harmonic and multiples of third harmonics
are eliminated.
By short chording the windings by 360 , the fifth harmonic and multiples of fifth are
eliminated
i.e., Kp5=cos (5*36/2)=cos 900=0
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By properly distributing the winding, 7th harmonic can be eliminated
Kd7=2
7sin
27
sin
g
g
=0
(i.e.) 2
7 g=1800
By properly skewing , 11th harmonic can be eliminated.
Next order of harmonics is only from 13th
The 13th order flux will be almost = φ1/(13)2 = φ1/169
which is less than 1 percent in magnitude and is insignificant hence the emf becomes pure
sinusoidal even though the flux is not exactly sinusoidal.
Alternate method to derive the emf equation:
The emf equation for alternator can also be derived from the average voltage induced in armature
as in the case of DC.
The speed of alternator - N rpm
Flux/pole - φ Wb.
No. of poles - p
No. of turns / phase - T
Average emf per conductor =
pN60
=
60
pN
Average emf per turn = 60
2 pN =
60*2
4 pN volts
The rms value of emf per phase = 120
**11.1*4 TpN
(where 1.11 is the form factor for sinusoidal wave)
E1 = 120
**44.4 TpN = 4.44 φfT volts
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En = 4.44φn(nf)T volts
Taking into account the winding factors kpn,kdn,ksn.,
En = 4.44φn(nf)T kdnkpn,ksn volts
=4.44φn(nf)T kwn volts
where,
Kwn is the winding factor ; kwn= kdnkpnksn
Regulation of Alternators:
Regulation of alternators is defined as the change in the terminal voltage from no load to full
load at a given power factor the field current kept constant,expressed in terms of rated terminal