Synch Generators
Copyright © by L.R.Linares
Dedicatory
• To those three masters of life as it looks
when you take your time to realize what all
the serious matters really are.
Dedicatory
• To those three masters of life as it looks
when you take your time to realize what all
the serious matters really are.
Synch Motors
a
b
C
B
c
A
• We put a set of coils on the stator
Synch Motors
• We put a set of coils on the stator
• Run a set of three phase currents through them
iA (t ) = 2 I sin(t )
iB (t ) = 2 I sin(t − 2 / 3)
iC (t ) = 2 I sin(t − 4 / 3)
Synch Motors
• We put a set of coils on the stator
• Run a set of three phase currents through them
• This creates a Rotating Magnetic Field (RMF) in
the air gap between the stator and the rotor
Synch Motors
• We put a set of coils on the stator
• Run a set of three phase currents through them
• This creates a Rotating Magnetic Field (RMF) in
the air gap between the stator and the rotor
2 f1
o =
p
Synch Motors
• We put a set of coils on the stator
• Run a set of three phase currents through them
• This creates a Rotating Magnetic Field (RMF) in
the air gap between the stator and the rotor
• A magnet, is set in the middle of the RMS in
such a way that it can rotate, will try to follow the
RMS at the same speed! A synchronous motor!
• The speed of a synchronous motor is
determined by the frequency of currents in the
stator, and the number of poles
In revolutions per second: f1 / p (p is the # pairs of poles)
In revolutions per minute: n=60f1 / p (p is the # pairs of poles)
In rad per sec: o = 2 f1 / p (p is the # pairs of poles)
A magnet, eh?
• Yes, a rotating magnet … first try!
A
a
c
C
N
S
b
B
A better magnet!
• A rotating electromagnet!
A
a
c
C
A DC current
in the electromagnet, so the N
pole is always the
N pole, etc.
N
F1
F2
S
b
B
Slip rings
• To feed the electromagnet from outside!
A
a
c
C
N
F1
DC
power
supply
F2
S
b
B
Slip rings
• To feed the electromagnet from outside!
A
a
c
C
N
F1
DC
power
supply
F2
S
b
B
More than two poles (p>1)
A
b
S
C
a
c
N
B
a
N
B
C
S
b
c
A
More than two poles (p>1)
A
b
c
C
B
S
N
a
a
N
B
C
S
b
c
A
More than two poles (p>1)
A
b
B
N
C
c
S
a
a
S
B
C
N
b
c
A
Self excited!
Synchronous speed
• In a synchronous motor with p pairs of
poles, and fed from currents of f1 hertz
– In revolutions per second (rps): ns = f1
If f=60Hz and p=1 ns = 60 rps
p
60 f1
– In revolutions per minute (rpm): n = 60ns =
p
If f=60Hz and p=1 n = 3600 rpm
2

f
1
– In rad/s: o = 2 ns =
p
2 60
If f=60Hz and p=1 o =
= 377 rad / s
1
Torque
• The RMF created by the stator …
• … and the magnetic field of the rotor EM
• … interact to produce a torque
T = Brmf Brotor sin 
Brotor

Brmf
With the resulting field
• The net RMF created by the combined
effect of stator currents and rotor MMF
• … interact to produce a torque
T = Bres Brotor sin 
Brotor

Bres
Rubber Band
Analogy

N
As the load increases, the angle delta
increases as well, stretching the
“flux lines” in a rubber band fashion,
increasing the torque.
S
S
Torque angle (load angle)
N
T = Brmf Brotor sin 
The bigger , the more torque
If the rotor is leading
• Let’s leave the stator three coils open…
• Then we apply a current to the rotor
electromagnet, to create a field in the gap
• Next, we apply a torque to the rotor to
make the electromagnet rotate…
• … we have a rotating magnetic field!
• This field “cuts” the three coils in the stator
and induces three sine voltages… out of
phase by 120 degrees!
If the rotor is leading
• Let’s leave the stator three coils open…
• Then we apply a current to the rotor
electromagnet, to create a field in the gap
• Next, we apply a torque to the rotor to
make the electromagnet rotate…
• … we have a rotating magnetic field!
• This field “cuts” the three coils in the stator
and induces three sine voltages… out of
phase by 120 degrees!
A synchronous generator!
A
a
c
C
N
F1
F2
S
b
B
Who moves the rotor?
Who moves the rotor?
Steam Turbine
Wind turbines
Who applies the torque?
•
•
•
•
•
A hydro turbine
A steam turbine
A diesel motor
A gasoline motor
A wind turbine
What is the input power?
• It’s the mechanical power applied by the
turbine.
Pin = 
• And the output power? Electric power!
Pout = 3Vline I line cos( )
Model of the synch machine
• The rotor contains the coil that creates the
field, so it’s called the “field coil”.
• The current in the rotor, in the synch
machine, is the “field current”.
• The coils where the voltages are induced,
what we used to call the “armature” in the
DC machine, are stationary in the S.M., so
• The stator coils are called the “armature”.
Model of the synch machine
Ra
jXa
A
Ea
Ra
jXa
F1
Rf
a
B
Ea
F2
b
Ra
jXa
C
Ea
c
The armature model
Z
Zy =
3
Model of the
Coil Aa
Eay =
Ea 
3
Model of the synch machine
If
DC
Power
supply
Ra
Rf
Ea
jXa
Ia
LOAD
Phase Aa of a Wye connected armature
So, If generates Ea
Synchronous speed!
Ea = k
Ea = 4.44 fNa max
If
Open Circuit Characteristic (OCC) of the machine
Rectifying…
Rectifying…
Rectifying…
Voltage at the load
It is not DC
It contains some DC
At least, it’s not
alternating
It has a “ripple”!
Rectifying 3-phase
blue=A, green=B, red=C
10
8
6
4
volts
2
0
-2
-4
-6
-8
-10
0
0.005
0.01
0.015
0.02
seconds
0.025
0.03
0.035
The voltage in
The load is not
alternating
It is pulsating
It has a lot of DC
It has less ripple
Self excited generator
• The output of the generator (3ph) is rectified and
…
• … put to a stationary coil (stationary magnetic
field)
• On the rotor three rotating coils “cut” the
stationary DC field… three phase AC voltages
are induced…
• Those rotor coils are connected to a rectifier,
which feeds the electromagnet field coils of the
generator rotor proper.
Self excited generator
3ph coils
DC field
coil
3ph AC to DC
rectifier
3ph AC to DC
rectifier
Electromagnet
Rotor
Coils (DC current)
3ph AC coils
Loaded synch generator
jXa
Ea
Pconv = 3Ea I a cos 
Ra
Sload = 3Vay I a = 3Va I a
Ia
load
S(kVA)
p.f.
Ea
Converted
power
Ohmic losses
In the armature
Ia
Va
Vd
VX
VR
Power Flow in the S.G.
Where is the Pconv … ?
A video from “Learn Engineering”
END OF SET
B(T )
1.7
1.3
H (A/m)
300
5000
Ea (V)@1200 rpm
290
270
0.7
1.4
i*f (A)
12
12
35
gap = 1.5
34
12
12
70
12
70
12
ROSARIO A LAS 9 PM
EN ESPAñol
Hoy martes 6 de diciembre
tinyurl.com/rosario-olos
5
2 I1
Rth
V th
jX th
ZX