No-Load SM Characteristic
Rotor flux magnitude
Induced stator voltage magnitude
EA
k
Characteristic of the
iron (stator and rotor)
Rotor field current
Rotor field current
Effect of saturation: for large field currents the no-load
armature voltage magnitude scales sub-proportionally with IF
and the voltage waveform becomes non sinusoidal (distorted).
Fundamentals of Power Systems
Lecture 12
1
SM Armature Reaction I
Unloaded generator at
arbitrary rotor position
Phase-A induced voltage
can be represented by a
space vector EA which
aligns with rotor field
vector BR
y
EA
x
Rotor field
axis
The time evolution of
phase-A voltage and
current is the projection of
the respective space
vector onto the y-axis
Phase A
Fundamentals of Power Systems
Lecture 12
Page 1
2
SM Armature Reaction II
Generator with lagging
load current (balanced)
Phase-A current space
vector IA is rotated (in
space) out of the rotor BR
axis by the load phase
angle
y
EA
x
IA
It will require the time /
for the IA space vector to
reach the rotor axis
The phase-A current
produces a magnetic
excitation in the x-axis
only
Fundamentals of Power Systems
Lecture 12
3
SM Armature Reaction II
The balanced 3-phase
stator current system
generates a rotating
magnetic field BS which
is another 90 behind
the phase-A current
space vector
Reasoning: BS points in xdirection when when iA(t)
is at its peak, i.e. when IA
reaches the y-direction
BS itself induces voltages
Estat in the stator
Fundamentals of Power Systems
Lecture 12
Page 2
y
EA
x
IA
90
Estat
4
SM Armature Reaction II
y
The resulting terminal
voltage the of machine is
V
EA
EA
x
Estat
Which aligns with the
resulting (net) magnetic
field B
BB
net
IA
R
-jX
S
Since Estat is proportional
to IA the relationship in
phasor quantities becomes
V
EA
Estat
X is a factor
jXI A
-j accounts for the -90 rotation
Lecture 12
Fundamentals of Power Systems
5
SM Single-Phase Equivalent Circuit Model
Armature reaction
Armature (self) reactance
V
EA
jX
jX A
V
EA
jX S
Synchronous reactance
EA
RA I A
RA I A
Armature resistance
kI F
(below saturation)
Fundamentals of Power Systems
Lecture 12
Page 3
6
SM 3-Phase Equivalent Circuit Model
Y-connection
-connection
Neutral
possible
VT terminal (line-line) voltage
IL line current
Fundamentals of Power Systems
Lecture 12
7
SM Phasor Diagrams (incl. RA), Generator
EA V
Same active current
component => same
active power P
jX S
RA I A
Unity PF
Lagging
Leading
Same terminal voltage
Fundamentals of Power Systems
Lecture 12
Page 4
8
Measuring Machine Parameters
Parameters required for machine model
EA = f(IF)
XS
RA
Losses (other than I2RA)
Lecture 12
Fundamentals of Power Systems
9
Open Circuit Test
Air gap line (linear)
EA, rated
Saturation
IA = 0 !
Rotor field
current
Fundamentals of Power Systems
Lecture 12
Page 5
Results:
EA = kF,OCIF (only in
linear region)
No-load losses
(windage, core &
bearing)
10
Short Circuit Test
IA
VA = 0 !
Results:
IA = kF,SCIF
Load losses
(windage, copper &
bearing)
IA, rated
EA ( I F )
I A (IF )
XS
Rotor field
current
Fundamentals of Power Systems
IF
Lecture 12
Page 6
RA
RA
XS
jX S
EA
IA
11