yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Pulse-width modulation wikipedia, lookup

Power factor wikipedia, lookup

Coilgun wikipedia, lookup

Current source wikipedia, lookup

Chirp compression wikipedia, lookup

Power engineering wikipedia, lookup

Resistive opto-isolator wikipedia, lookup

Stray voltage wikipedia, lookup

Ground (electricity) wikipedia, lookup

Electric machine wikipedia, lookup

Islanding wikipedia, lookup

Chirp spectrum wikipedia, lookup

Electrical substation wikipedia, lookup

Opto-isolator wikipedia, lookup

Buck converter wikipedia, lookup

Power inverter wikipedia, lookup

Voltage optimisation wikipedia, lookup

Mains electricity wikipedia, lookup

Rectifier wikipedia, lookup

Switched-mode power supply wikipedia, lookup

History of electric power transmission wikipedia, lookup

Variable-frequency drive wikipedia, lookup

Mercury-arc valve wikipedia, lookup

Induction motor wikipedia, lookup

Power electronics wikipedia, lookup

Inductor wikipedia, lookup

Stepper motor wikipedia, lookup

Earthing system wikipedia, lookup

Transformer wikipedia, lookup

Alternating current wikipedia, lookup

Three-phase electric power wikipedia, lookup

O.W. Andersen, Senior Member IEEE
Norwegian Inst. of Technology, N-7034 Trondheim, Norway
Abstract - The transformers described here are in the multimegawatt range. They are rapidly becoming more important and
have characteristics and features that are different in many ways
from those of normal power transformers. Information about
them has been incomplete, scattered and hard to find in the
Harmonics are of prime importance in these transformers.
Their appearance and suppression are explained with an emphasis on making it easy to understand.
Different winding arrangements are presented and their
characteristics explained. Cores with gaps to limit inrush currents are also discussed.
Starting with six pulse loads, the line currents are analyzed
for their harmonic content. It is explained how transformers
can be used to increase the number of pulses and how this
eliminates certain harmonics and reduces others. The relative
merits of different winding arrangements are discussed.
It is also explained how filter windings can be arranged for
optimum filter performance, with further reduction of the
harmonic content.
Results of theoretical analysis of harmonics are confirmed,
using numerical circuit analysis.
The theory assumes that the three phase primary voltages
are sinusoidal and balanced and that firing angles are precisely the same in all the phases. In practice, there will always
be deviations from these assumptions, and measured
harmonic content can be significantly different from that
predicted by the theory.
Two types of six pulse loads are investigated here, a three
phase rectifier bridge as shown in Fig. 1, and a triac or back
to back thyristor controlled three phase reactor, as shown in
Fig. 2. The rectifier can have either diodes or thyristors, with
very similar behavior with respect to harmonic currents. In the
reactor, the harmonic content is increased as the firing angle
is increased beyond 90 degrees, where the currents are
sinusoidal and the reactive power maximum. In the rectifier,
the harmonic content is less when the commutation angle is
large, but it is always substantial.
Even harmonics are absent due to the symmetry between
negative and positive half cycles. Triple harmonic line currents, if present, would have the same instantaneous values in
all three phases. Since they don't have any return paths, they
also become zero. In general, all the other harmonics are
present, and the 5th and the 7th harmonics will usually have
the largest amplitudes.
Typical six pulse line currents are shown in figures 3 and
4, together with their harmonic spectra. They have been
calculated with program PECAN (Power Electronic Circuit
Analysis), which is described in [1]. In the harmonic spectra,
lengths of vertical bars are proportional to harmonic content.
The term six pulse refers to the number of times per cycle
conduction starts in a switching element. They are 60 degrees
To get twelve pulse connections with lower harmonic content, two six pulse loads are usually supplied through a transformer with two secondary windings, one Y-connected and
one D-connected. The loads have the same rated voltage and
current, and rectifier loads can be connected in series or in
parallel. The 30 degree phase shift of line currents from the
two windings gives the twelve pulses.
A possible winding arrangement is shown in Fig. 5. The
two parts of the often Y-connected primary winding, H1 and
H2, are in parallel. Reactances between the high voltage
winding and each of the two low voltage windings will be
equal, and forces are reasonably under control for a short
circuit in either LY or LD.
Fig.1. Rectifier.
Fig. 3. Line current with harmonic spectrum.
Fig. 5. Twelve pulse transformer.
Fig. 2. Reactor.
Fig. 4. Line current with harmonic spectrum.
Firing angle 113.5.
Fig. 6. Line currents.
The phase angles of the currents in LY and LD can be
explained with reference to Fig. 6. A line current from the LD
winding is here displaced +30 with respect to the corresponding line current from LY. However, the corresponding
phase currents line up, and add directly into the primary high
voltage winding. Therefore, 30 must be subtracted from the
angle of the line current in LD to get the angle of the phase
current. This applies regardless of frequency, therefore not
only for the fundamental, but also for the higher frequency
Between phases 1 and 2 there is a 120 displacement for
the fundamental, and 5x120=600 for the 5th harmonic.
Between phases 1 and 3 the displacement is 5x240=1200.
Subtracting multiples of 360 from 600 and 1200 gives anglesFi
240 and 120 for the 5th harmonic, and the phase sequence
is negative.
With +30 displacement of fundamental line current in LD,
the displacement is -5x30=-150 for the 5th harmonic line
current, and for the phase current, the displacement is -15030=-180. Consequently, 5th harmonic phase currents are in
direct phase opposition between LY and LD, and induce
opposing circulating currents in H1 and H2. Theoretically, the
5th harmonic line current in the high voltage winding will be
A similar investigation of the 7th harmonic reveals that the
phase sequence is positive, the line current in LD is displaced
+210, and the phase current 210-30=180. Again, phase
opposition prevents the harmonic from being transferred as
primary line current.
The lowest order harmonics that will appear in the high
voltage line currents are the 11th and the 13th. Analyzed in a
similar way, they are found to add directly from LY and LD.
Of the harmonic currents that appear in a six pulse connection, those that are eliminated in a twelve pulse connection
are of orders 5-7-17-19-29-31 and so on, and those that
remain unchanged are of orders 11-13-23-25-35-37.
The fairly large gap between the windings at the radial
centerline in Fig. 5 is there to avoid excessive eddy current
losses due to radial magnetic leakage fields set up by harmonic currents, which are in phase opposition between LY
and LD.
The transformer can be supplied with an additional winding
connected to filters, to reduce the harmonics further. The
winding arrangement can be as shown in Fig. 7. Like the high
voltage winding, also the filter winding has two permanently
parallel connected parts, F1 and F2.
Core leg
Fig. 7. Transformer with filter winding
The transformer now has an equivalent circuit for the
reactances, as shown in Fig. 8. Since XY = XD due to the
symmetry, there are four reactances that must be determined
from four short circuit calculations, H-F, H-LY, F-LY and
Fig. 8. Equivalent circuit
For the efficiency and the design of the filters, it is highly
desirable that XF comes out as zero. It is remarkable that with
the winding arrangement in Fig. 7, that seems to follow
automatically within very narrow tolerances, as evidenced
from the analysis of several transformers of this type, in sizes
up to 137 MVA. In five 54 MVA rectifier transformers that
were built and tested in Norway, the reactance XF was calculated and tested as zero within a tenth of a percent.
The calculations of reactances are complicated by the fact
that circulating currents and current distribution between
parallel connected windings are not known at the outset.
A flux plot from a finite element reactance calculation HLY is shown in Fig. 9. The winding arrangement is the same
as that of Fig. 7. The LY winding is short circuited, while LD
is open. The filter winding is also open, but a circulating
current flows between the two parts F1 and F2. Power is
supplied to the primary winding, with H1 and H2 connected
in parallel.
The normal 24 pulse connection has two transformers in
parallel, each with an LY and LD secondary winding, and
with primary phase shift windings with voltages displaced 7.5 and +7.5. Between the four secondary windings, voltages are displaced 15 degrees.
The two transformers have twelve pulse connections by
themselves, with the same harmonics eliminated as described
earlier. The 15 degree displacement betwen them reduces
substantially also harmonics of orders 11-13-35-37, and only
those of orders 23-25 (and 47-49) remain essentially
The 11th harmonic has negative phase sequence, and
11x15=-165 displacement of a line current in LD. With 30
subtracted to get the angle of the phase current, it becomes 195. Current vectors of unit length adding under this angle
give a vectorial sum equal to 2 x sin 7.5, whereas the
algebraic sum is 2. The reduction in per unit is therefore sin
7.5 = 0.131.
Harmonics of orders 13-35-37 are found to have the same
reduction factor 0.131.
Fig. 9. Flux plot for transformer reactance H-LY
It is known that for +100% current in LY, the sum of the
currents in H1 and H2 must be -100%, and the currents in F1
and F2 must be equal with opposite signs. Because of the
parallel connections, flux linkages must be equal in H1 and
H2, and also in F1 and F2.
A first initial calculation has -100% current in H1 and zero
in H2 and F1. A second calculation has -90% current in H1, 10% in H2 and zero in F1. A third calculation has
current in H1, zero in H2 and -10% in F1. Correct currents in
H2 and F1 can now be determined from the linear
relationships between currents and flux linkages based on the
three initial calculations, with the flux linkages equalized.
Current distributions and circulating currents will always
adjust themselves to give minimum magnetic field energy.
The accuracy of the calculated currents can therefore be
checked by observing how the magnetic energy changes with
small deviations from the calculated currents. The changes
should always be positive. When the calculations are right, it
never fails.
With this winding arrangement and +100% current in LY,
approximately -50% flows in H1, H2 and F1, and +50% in
Also the reactance calculations F-LY and LY-LD require
three initial calculations, in order to find unknown currents.
Only the calculation H-F is straightforward, with all the currents known in advance.
Fig. 10. 12 and 24 pulse rectifier line currents
Fig. 11. 12 and 24 pulse reactor line currents. Firing angle 113.5
12 and 24 pulse line currents for rectifiers and reactors are
shown in figures 10 and 11, as analyzed with PECAN.
Fourier analysis can be performed very easily with this
program, and the reduction of 11th and 13th harmonics to
13.1% is confirmed with great accuracy. The reduction of
harmonics of orders 35-37 is also confirmed, but the accuracy
is not quite as good, due to numerical errors.
12 pulse currents are shown as dashed lines in the figures,
and their 24 pulse sums are shown as solid lines. For the
reactor, the 113.5 firing angle corresponds to half rated
reactive power. The 24 pulse line current remains reasonably
sinusoidal down to about 15% power.
48 pulse connections are also used occasionally, and have
an additional reduction factor of sin 3.75 = 0.0654 for the
23rd and 25th harmonics.
With the highest pulse connections, rated voltages are
often very low, and LY and LD can have as few as 4 and 7
turns. In such cases, the currents are so large that LY and LD
must be on the outside of the primary phase shift winding.
Three possible phase shift windings are shown schematically in Fig. 12. There is no good reason for using the
polygon or hexagon connection for this purpose, so it is only
mentioned here as a possibility.
In Fig. 13, the connections are shown differently. The two
parts of each phase winding which are concentric on the
same core leg are shown above each other.
A possible winding arrangement is shown in Fig. 14.
H1,S1 and H2,S2 are connected in parallel at the terminals.
In the zig-zag or Z-connection, the currents in the two
concentric windings on one core leg are 60 displaced in
phase. In the extended delta connection, the displacement is
only 30.
With the small displacements of line voltages, as required
by 24 and 48 pulse connections, extended delta has significant
advantages. For 7.5 displacement, the phase shift only adds
2.6% to the sum of the kVAs for the H and S windings,
compared with 6.7% for the zig-zag connection. The smaller
phase displacement of currents also gives better conditions for
the magnetic leakage field, with a tendency of lower eddy
current losses and short circuit forces. In addition, the smaller
windings S1 and S2 will get proportionally more copper in
them, and be better capable of withstanding the short circuit
The Z-connection is used occasionally, where tap connections are required at the neutral. However, when the voltage is regulated, the phase shift also changes, and will not
always be ideal for harmonic suppression.
Fig. 12. Phase shift connections
Fig. 13. Phase shift connections
Fig. 14. Winding arrangement
In transformers for twelve pulse loads, 5th and 7th harmonics flow in phase opposition in the LY and LD windings.
Their magnetic leakage fields are essentially radial, and set up
circulating currents between the parallel connected parts of
both the primary winding and a possible filter winding. The
calculation of harmonic losses involves finding these
circulating currents, which can be done following a similar
procedure as explained for the reactances. Primary line
currents are theoretically zero.
The 11th and the 13th harmonics are in phase in LY and
LD. Their magnetic leakage fields are essentially axial, as for
the fundamental. No circulating currents flow due to these
harmonics. If a filter winding is present, they will ideally be
balanced by opposing currents in this winding due to low
impedance filter loads, and then also here primary line
currents will be close to zero.
In wire windings, eddy current losses are proportional to
(fdB)2, where d is conductor dimension perpendicular to the
flux density B, and f is the frequency. Even though flux
density may be low for the harmonics, frequency is high, and
harmonic eddy current losses are often higher than for the
fundamental. There is no practical way to find these losses
from factory tests, and a designer has to rely almost entirely
on numerical calculations.
Harmonic currents have been found here in two very simple
circuits in Fig. 1 and 2, in order to explain the basic concepts.
Practical applications will always be more complicated and
warrant a more detailed analysis.
An interesting feature of this arrangement is that a short
circuit test no longer gives reliable information about load
losses under normal operating conditions.
During the short circuit test the core flux is only large
enough to balance the leakage flux. In per unit, for rated
currents the flux equals the short circuit impedance.
Ampereturns in the two windings are essentially balanced,
and the leakage flux follows paths largely unaffected by the
core gaps.
Under normal operating conditions, however, the magnetizing current is significant, and the much higher core flux
fringes out into the inner winding and produces eddy current
losses which can be much higher than those tested at short
circuit. This is especially important when the inner winding
L1-L2 is a sheet winding. The losses will be highest at zero
powerfactor, when the magnetizing current is in phase with
the load current.
This adverse effect of core gaps is counteracted to some
extent by having gaps also in the windings, as shown in Fig.
High pulse harmonic suppression is very effective, and has
been analyzed here both analytically and numerically. For
additional suppression of harmonics, transformers can be
equipped with windings connected to filters, where the filter
winding reactance in the equivalent circuit is close to zero.
Transformers for power electronic loads sometimes have
cores with gaps in the middle of each core leg, as shown in
Fig. 15. A core gap can be quite large, typically of about 10
mm length.
The purpose of this is to limit remanent flux and keep
magnetizing reactance reasonably constant. This in turn limits
inrush currents and thereby protects the power electronic
Fig. 15. Transformer with core gaps
[1] O.W. Andersen, "Time Domain Circuit Analysis", IEEE
Computer Applications in Power, April 1992, pp. 34-38.
[2] O.W. Andersen, "Magnetic Leakage Fields in Rectifier
Transformers", Conference Proceedings ICEM, Paris September 1994, pp. 738-740.
Odd W. Andersen has been Professor of
Electric Power Engineering at the Norwegian
Institute of Technology since 1964. Before that
time, he was a synchronous machine designer
with Canadian General Electric. He has been
on sabbatical leave three times in the United
States, where he has worked for the General
Electric Company in the Turbine Generator
Department in Schenectady and in the
Transformer Department in Pittsfield, and has
been a visiting professor at Rensselaer
Polytechnic Institute in Troy and at the
University of Minnesota.
He made his first computer program in
1957, and it has been an ongoing activity ever
since. Most of the programs are for optimized
design of rotating machines and transformers,
finite element field calculations and circuit