ECE 576 – Power System
Dynamics and Stability
Lecture 12: Exciters
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
overbye@illinois.edu
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Announcements
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Homework 3 is due now
Homework 4 is on the website and is due on March 6
Read Chapter 4
Midterm exam is on March 13 in class
– Closed book, closed notes
– You may bring one 8.5 by 11" note sheet
• You do not need to write down block diagrams or the
detailed synchronous machine equations; I'll give you
what you need here
– Simple calculators allowed
2
Wind Cut-outs, 2/17/14
Plot-0
105
102
MW
103
HMW
28
MPH
80
60
40
20
0
-20
2/17/2014 12:00:00 AM
PAL_WIND-PWD - AVA GEN MW - AGC PRIMARY
PAL_WIND-35KV GEN MW - POTENTIAL MAX GEN
PAL_WIND-INSTANTANEOUS AVG WIND SPEED
24.00 hours
2/18/2014 12:00:00 AM
Graph provided by Tracy Rolstad, Avista
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GenRou, GenTPF, GenTPJ
Figure compares gen 4 reactive power output for the
0.1 second fault
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Voltage and Speed Control
P, 
Q,V 
Exciters, Including AVR
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Exciters are used to control the synchronous machine
field voltage and current
– Usually modeled with automatic voltage regulator included
A useful reference is IEEE Std 421.5-2005
– Covers the major types of exciters used in transient stability
simulations
– Continuation of standard designs started with "Computer
Representation of Excitation Systems," IEEE Trans. Power
App. and Syst., vol. pas-87, pp. 1460-1464, June 1968
Another reference is P. Kundur, Power System Stability
and Control, EPRI, McGraw-Hill, 1994
– Exciters are covered in Chapter 8 as are block diagram basics
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Functional Block Diagram
Image source: Fig 8.1 of Kundur, Power System Stability and Control
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Types of Exciters
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None, which would be the case for a permanent magnet
generator
– primarily used with wind turbines with ac-dc-ac converters
DC: Utilize a dc generator as the source of the field
voltage through slip rings
AC: Use an ac generator on the generator shaft, with
output rectified to produce the dc field voltage;
brushless with a rotating rectifier system
Static: Exciter is static, with field current supplied
through slip rings
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Brief Review of DC Machines
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Prior to widespread use of machine drives, dc motors
had a important advantage of easy speed control
On the stator a dc machine has either a permanent
magnet or a single concentrated winding
Rotor (armature) currents are supplied through brushes
and commutator
The f subscript refers to the field, the
Equations are
a to the armature;  is the machine's
v f  if Rf  Lf
di f
dt
dia
va  ia Ra  La
 Gmi f
dt
speed, G is a constant. In a
permanent magnet machine the field
flux is constant, the field equation
goes away, and the field impact is
embedded in a equivalent constant
to Gif
Taken mostly from ECE 330 book, M.A. Pai, Power Circuits and Electromechanics
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Types of DC Machines
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If there is a field winding (i.e., not a permanent magnet
machine) then the machine can be connected in the
following ways
– Separately-excited: Field and armature windings are
connected to separate power sources
• For an exciter, control is provided by varying the field
current (which is stationary), which changes the armature
voltage
– Series-excited: Field and armature windings are in series
– Shunt-excited: Field and armature windings are in parallel
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Separately Excited DC Exciter
(to sync
mach)
ein1  r f 1iin1  N f 1
a1 
1
1
 f1
d f 1
dt
1 is coefficient of dispersion,
modeling the flux leakage
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Separately Excited DC Exciter
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Relate the input voltage, ein1, to vfd
f 1
v fd  K a11a1  K a11
1
N f 1 1
N f 1 f 1 
v fd
K a11
d f 1 N f 1 1 dv fd
Nf1

dt
K a11 dt
N f 1 1 dv fd
ein  iin rf 1 
K a11 dt
1
Assuming a constant
speed 1
1
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Separately Excited DC Exciter
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If it was a linear magnetic circuit, then vfd would be
proportional to in1; for a real system we need to account
for saturation
v fd
iin1 
 f sat v fd v fd
K g1
Without saturation we
can write
Kg1
K a11

L f 1us
N f 1 1
Where L f 1us is the
unsaturated field inductance
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Separately Excited DC Exciter
ein  r f 1iin1  N f 1
1
d f 1
dt
Can be written as
rf 1
L f 1us dv fd
ein 
v fd  r f 1 f sat v fd v fd 
K g1
K g1 dt
1
 
This equation is then scaled based on the synchronous
machine base values
X md
X md v fd
E fd 
V fd 
R fd
R fd VBFD
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Separately Excited Scaled Values
KE

sep
rf 1
K g1
L f 1us
TE 
K g1
X md
VR 
ein1
R fd VBFD
 
 VBFD R fd

S E E fd  r f 1 f sat 
E fd 
 X

md


Thus we have
TE
dE fd
dt
 


  KE
 S E E fd  E fd  VR


sep


Vr is the scaled
output of the
voltage
regulator
amplifier
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The Self-Excited Exciter
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When the exciter is self-excited, the amplifier voltage
appears in series with the exciter field
TE
dE fd
dt
 


  KE
 S E E fd  E fd  VR  E fd


sep


Note the
additional
Efd term on
the end
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Self and Separated Excited Exciters
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The same model can be used for both by just modifying
the value of KE
TE
dE fd
dt


  K E  S E  E fd  E fd  VR


KE
 KE
 1  typically K E
 .01


self
sep
self


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Saturation
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A number of different functions can be used to
represent the saturation
The quadratic approach is now quite common
S E ( E fd )  B ( E fd  A) 2
An alternative model is S E ( E fd ) 
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B ( E fd  A) 2
E fd
Exponential function could also be used
S E  E fd   Ax e
Bx E fd
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Exponential Saturation
KE  1
S E E fd   0.1e
0.5 E fd
.5 E fd

Steady state VR  1  .1e

 E
 fd
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Exponential Saturation Example
Given:
K E  .05


S E  E fd
  0.27
max 



S E  .75 E fd
  0.074
max 

VR
 1.0
max
Find:
E fd max  4.6
Ax , Bx and E fd max
S E  Axe
Bx E fd
Ax  .0015
Bx  1.14
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Voltage Regulator Model
Amplifier
dVR
TA
 VR  K AVin
dt
VRmin  VR  VRmax
VR
Vref  Vt  Vin 
KA
K A  Vt  Vref
In steady state
Big
Modeled
as a first
order
differential
equation
There is often a droop in regulation
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Feedback
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This control system can often exhibit instabilities, so
some type of feedback is used
One approach is a stabilizing transformer
N2
dIt1
Ltm
Large Lt2 so It2  0 VF 
N1
dt
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Feedback
dIt1
E fd  Rt1It1   Lt1  Ltm 
dt

dVF
Rt1
N 2 Ltm dE fd 
  VF 


 Lt1  Ltm  
dt
N1 Rt1 dt 

1
TF

KF
IEEE T1 Exciter
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This model was standardized in the 1968 IEEE
Committee Paper with Fig 1 shown below
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IEEE T1 Evolution
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This model has been subsequently modified over the
years, called the DC1 in a 1981 IEEE paper (modeled
as the EXDC1 in stability packages)
Note, KE in the
feedback is the
same as
the 1968
approach
Image Source: Fig 3 of "Excitation System Models for Power Stability Studies,"
IEEE Trans. Power App. and Syst., vol. PAS-100, pp. 494-509, February 1981
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IEEE T1 Evolution
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In 1992 IEEE Std 421.5-1992 slightly modified it,
calling it the DC1A (modeled as ESDC1A)
Same model is in 421.5-2005
Image Source: Fig 3 of IEEE Std 421.5-1992
VUEL is a
signal
from an
underexcitation
limiter,
which
we'll
cover
later
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