brushless exciter
TRANSCRIPT
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Brushless exciter model
S.M.L.
Kabir
R. Shuttleworth
Indexing term s: Exciter , Power system beh aviour, Simulation
Abstract: The IEEE model of a brushless exciter
can be found in many software packages for the
simulation of power system behaviour. Yet the
model is simplistic and does not represent the
exciter alternator accurately. This paper describes
the reasons for the inaccuracy of the IEEE repre-
sentation and proposes an alternative model.
Goo d agreement is obtained between results from
a micromachine test system and the alternative
model.
1
Introduction
Generator exciters and automatic voltage regulator
play an important part in determining power system sta-
bility during transients. Nevertheless, general purpose
computer models describing their performance over a
wide range of operating conditions have not yet emerged.
This is because interactions between AVRs, exciters and
generators are complicated and not thoroughly under-
stood.
In
1968
an IEEE working party published a set of
excitation system models for use in large scale stability
studies. These mod els were devised in an attem pt to
establish a unified approach to power system analysis. In
1981,
the set was updated with the publication of a
second paper
[l]
reflecting changes in excitation tech-
nology and modelling methods. These models have
become widely used in industry, as was intended, to the
point where they are now considered a standard in the
specification and testing of excitation equipment as well
as in power system analysis.
Unfortunately the form of the IEEE models makes
them inappropriate for the universal role gradually being
forced upon them. This is evident from some of the con-
flicting results they yield in practice. These arise mainly
from misuse, since the models, designed for small signal
analysis are frequently used in the pred iction of response
following a large disturbanc e. H owever, the lim its of
applicability remain unknown as there has been no
precise guidance from the working party or any other
published source.
This indeterminate situation has led to unnecessary
conflicts between the users and suppliers of equipment.
The former are tending to apply IEEE models, often
embedded in standard software packages, to check
on
the
IEE, 1994
Paper
9704C (PlO),
first received 1st October 1992 and in revised
form
17th May 1993
S.M.L . Kabir is with B.U.E.T. ,Bangladesh
R. Shuttleworth is with the Electrical Engineering Laboratories, The
University, Manchester
M13 9PL,
nited Kingdom
I E E Proc.-Gener. Transm . Distrib.,
Vol.
141,
No.
January 1994
specification of equipment supplied by the latter a nd to
predict its response to large scale disturbances. One of
the commonest excitation systems, the brushless exciter,
is particularly badly simulated by the IEEE model and
has caused confusion.
For
this reason the authors have
addressed the problem of brushless exciter modelling.
This paper describes a model which, whilst based on the
IEEE arrangement, takes better account of exciter behav-
iour and is able to predict responses more accurately.
2
In essence a brushless exciter is, as shown in Fig. 1, an
inside-out three-phase synchronous generator, the field
winding of which is mounted on the stator housing, the
The brushless exciter ecti fi er system
generotor
e x c i te r
f i e l d
winding
a
f i e l d
w l n d l n g g e n e r a t o r
t h r e e - p h a s e
e x c i te r thr e e -pha s e
i n d 3
k
rotating
s e c t
ion
F ig . 1 Brushless exciter-generator
three-phase windings being attached to the rotor. The
three-phase outp ut voltage is rectified by diodes mo unted
on the rotating shaft and applied directly to the main
generator field winding. Thereby, sliprings and brushes
are eliminated, and maintenance costs reduced. In most
cases the rectifier is a three-phase full wave bridge.
2.1 Effect of rect i f icat ion on the exci ter
It is generally known that, as a consequence of source
inductance, rectifying systems suffer from overlap. The
inductance in each phase of the supply opposes transfer
of current from rectifier to rectifier creating temporary
phase to phase short circuits, or overlaps, during the
cycle. The overall effect of these repetitive intervals of
overlap, each occurring for an angular duration
U,
is to
reduce the mean ou tput voltage of the rectifying system.
For
a
three-phase bridge rectifier supplying an induct-
ive load, the rectification process can be divided into
The authors wish to thank Dr. R.D.M. Whitelaw
and Mr.
B.
Aranyos of CEC-Alsthom Turbine
Generators Ltd., and Prof. D.W. Auckland of
Manchester University, for their help and suppo rt.
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three distinct modes,
1,
2, and 3, which occur in numeri-
cal sequence as load current increases from zero.
A
full
description of the phenomenon is given by Gayek
[Z]
and Witzke et
al. [3].
In brief, mode
1
is characterised by intervals of no
overlap, where two diodes conduct, interspaced with
intervals of overlap and the conduction of three diodes.
As the rectifying system output current increases, so does
the overlap angle U, until U reaches
60',
which occurs at
the point of transition from mode 1 to mode 2. At this
transition point overlap becomes continuous and thus
three diodes are always conducting. In mode 2,
U
remains
constant at 60 , and a delay angle, known as Y, appears
which retards the start of each overlap period. The angle
ct
increases from
0
to 30 as the rectifying system moves
through mode 2 owing to increasing load current. When
ct
equals 30 , which signifies the transition from mode 2
to mode 3, an increase in load current will again increase
U,
while ct remains fixed at
30 .
However as
U
increases, so
intervals of three-phase short circuits occur during the
overlap process. Increasing the load current causes both
U
and the intervals of three-phase short circuit to
increase, until at the end of mode 3, a complete three-
phase short circuit is imposed upon the source, and U is
equal to
120 .
Thus for this level of load current and for
higher levels, the b ridge becom es, for the load, a free-
wheeling path. This final short circuit condition will be
referred to as m ode
4.
It follows that, as rectifier load current increases from
zero,
so
the power factor impressed upon the AC source
worsens, moving from almost unity at the beginning of
mode 1 to zero lagging at the end of mode 3 and
throughout mode
4.
3
The
IEEE model
Fig.
2
shows the exciter and rectifier components of the
IEEE model. The voltage applied to the field winding of
the exciter is represented by V, on the left of the diagram
whereas
E,,
is the voltage applied to the main generator
field winding on the right of the mod el.
t
K E ' 5 E
NMCm lVE
:L
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applied to a rectifier bridge simulation which performs
the necessary logic to determine the connections of the
phases to the
DC
load as follows.
At
the end of every time step a comm utation integer is
set with a value which indicates the state of the rectifier.
The values assigned to the integer indicate which phases,
if any, are being subjected
to
commutat ion, or, alterna-
tively, if a three-phase short circuit is occurring.
O n the following time step this integer is used to
connect the load to the correct phases of the Canay
model. After calculating the new parameters a check is
made
to
see if the co mm utatio n integ er has change d. If
i t
has not,
I ,
and
I ,
are returned to the alternator model.
If, however, a change has occurred, then the com-
mutation integer, and hence load connection, is updated,
and the recalculated values of
I ,
and
I ,
are returned to
the alternator model. The program is slow in operation,
as it must, for accuracy, be time stepped at
0.1
ms inter-
vals for a 50
Hz
alternator. Typically it takes some
3 hours to simulate seconds of exciter operation using
an IBM compatible PC. No doubt the model could be
improved in speed of operation, but this was not
attempted as its purpose was to give a benchmark for
development
of
the faster model
to
be described in the
next Section.
~
10
5 Simple
digital
model
Fig. 4s a block diagram of the model.
As
in the complex
model, a Canay representation of alternator behaviour is
used, but terms for rate of change
of
direct and quadra-
ture axis flux are omitted. Thus direct current terms in
the stator current cannot be simulated, but the model can
be time stepped with longer periods than the previous
model.
An assumption m ade is that rectifier operation,
although highly nonlinear, can be treated as a steady
state phenomenon since the repetitive line-to-line short
O f A 1
and
81
.
l D a n d 10 mode mode I F
-
.
81 U .O: calculat ion
of
-
l o X Q
I
circuiting due to comm utation oc curs equally to all three
phases.
The Canay alternator simulation has applied to it, at
each time step, values of
I , , I ,
and input voltage V,,
from which terminal voltages U , and U, are calculated.
Commutating reactance is assumed to be equal to sub-
transient reactance [4] and the phasor values of voltage
behind this, U, , and U , , , are thus determined as shown
in Fig. 5. The per unit alternator output voltage, V,,
follows. The sim ple rectifier simulation pro posed by the
IEEE is used, with the inclusion of a fourth mode
of
operation which accounts for freewheeling of generator
field currents through the bridge rectifier, as explained in
Section
2.
Fig. 5 Phasor diagram
I ,
and I , can be determined from the real and reactive
currents, A I and B1, taken by the rectifier, providing
these can be determined. Formulas for calculating
A 1
and B1 can be found in the literature [2,
8,
91 but only
for modes
1
and 2. Mode 3 has been neglected in the
literature with the exception of Ferguson et
al
[4] who
provide a graphical solution for a machine of particular
subtransient reactance. In order to obtain a mathemati-
Fig.4 Simple digital model
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Proc-G ener. Transm. Distrib . , Vol
141,
N o . I
January
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cal representation, suitable for use in a computer,
of
real
and reactive currents in mode 3, it was necessary to
perform a Fourier analysis
of
the alternating current
taken by the rectifier. This analysis was based upon the
description
of
mode 3 operation given by Witzke et al.
[3]
The formulas derived for mode 3 are unlike the
equivalent formulas for modes 1 and
2
as they include the
terms
V,/X,
as
a
result of the repetitive three-phase short
circuits.
Having determined A 1 an d E1 for three modes
of
rec-
tifier operation,
I ,
a n d
I ,
can be found from the phasor
diagram
of
Fig.
5
as U D 0 ,U Q o and
VE
are known. In the
case of
mode
4
he alternator supplies reactive current to
the short circuiting rectifier so that A1 = 0 and E1
=
V,/X,.
A complete list
of
the formulas used is given in
Appendix 11.1.
6
Testsystem
Obtaining test results from
a
brushless exciter
is
of
course
difficult as it is an integral part
of
the main generator.
For this reason, two microalternators were used to simu-
late a brushless exciter and main generator, as shown in
Fig.
6
The machines were rated at
220 V, 3
kVA and
50 Hz,
an d were driven by DC motors.
I I
round rotor
machine
h
MOSFETrectiiier
sirnulotion
shadow
winding
Fig.6
Diagram ojmicromuhin e tes t system
The first microalternator had a salient pole rotor with
wound direct and quadrature axis damper circuits and
was used to represent the brushless exciter alternator.
The second machine had
a
round rotor with wound
direct and quadrature axis damper circuits an d was used
to simulate the field winding of the main generator.
So
as
to minimise the complexity
of
the physical model, the
damper circuits of the second microalternator were open-
circuited, thereby ensuring the field winding represented
a single time con stant load. It was thus possible a t a la ter
stage to reconnect the damper circuits and simulate a
complete brushless exciter-generator system. This
allowed the impact
of
disturbances at the main generator
terminals on the exciter rectifier system to be invest-
igated.
Because the two microalternators had identical ratings
it was necessary t o ope rate the salient pole machine with
a low field current to avoid over exciting the round rotor
machine. At this current level brush drop is significant
and so the graphite brushes of the salient pole micro-
alternator were replaced by low voltage drop copper
loaded brushes. Losses in the field brushes of the round
rotor machine were minimised by the same method.
Standard silicon diodes were not used in the bridge
rectifier as their voltage drop is significant. Instead rec-
64
tifying elements comprising two power
MOSFETs in
bilateral configuration driven by an operational amplifier
clamp circuit were used. These introduced a low resist-
ance of
0.1 R
which is about
2.5%
of the load resistance.
It is usual for microalternator windings to be fitted
with time constant regulating equipment (TCRs) [lo,
1 I].
Although TCRs were available for the salient pole
machine it was decided not to use these as their band-
width
of
100H z, which is adequate for normal power
system studies, would cause undue attenuation
of
the rec-
tifier induced harmonic currents. However, it was neces-
sary to enhance the natural time constant of the round
rotor field circuit as this, being about looms, was
untypical of
a
large generator. A continuously acting
TCR was used to increase this time constant by a factor
of
50.
The amplifier used had a gain
of 50
and a band-
width of
2
kHz, which calculations showed was enough
bandwidth to ensure adequate time constant com-
pensation for harmonics. This was proven by tests at a
lower amplifier gain
of
10 performed with
10
k H z a n d
2 kHz bandwidths which produced identical results,
validating the choice of
2
kHz.
7
Test results
A step inpu t of 1 p.u. excitation voltage was applied to
the field winding of the salient pole alternator and the
consequent variations in field and load current were
recorded. These results were plotted and the responses
of
the two digital models, and the standard
I E E E
model,
compared with them.
The parameters used in the digital models were deter-
mined from
a
three-phase sudden short circuit test per-
formed on the salient pole machine at a current level
approximately equal to that used in the step test above.
Th e parame ters are given in Appendix 11.2. A flux
linkage versus current plot for the field winding
of
the
round rotor machine, from zero to the appropriate
current level and back to zero, is shown in Fig.
7.
For
increasing current, the curve has, approximately, a slope
current
Fig.
7
Flux
linkage versus current plotfor
the DC
load
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equal
to
an inductance
of
2 5 . 6 H .
Fig.
8
compares the
responses of the two computer models with the step test
described. Despite the simplifications involved in the
simple model it follows closely the results of the comp lex
model.
/
0 - .
. .
, I
1 I I
0
0 5
1 0 1 5 2 0
2 5
3 0
3 5
4 0 4 5
5 0
time, s
Fig. 8
held
uoltage
a
field current
of
simple model
field current ofcomplex model