Cost Effective Multi - Pulse Transformer Solutions
For Harmonic Mitigation in AC Drives
Gary L. Skibinski Nick Guskov Dong Zhou
Rockwell Automation Drives Division
6400 W. Enterprise Drive Mequon, WI 53092
Tel: 262-512-7151 Fax: 262-512-8300 Email: glskibinski@ra.rockwell.com
Abstract – More and more ac drive installations are requiring
manufacturer’s to improve line side harmonics to ultimately meet
IEEE Harmonic Std 519-1992 on site [1]. This paper reveals several
patented transformer topologies for such an effort. Compared with
other harmonic solutions, auto and isolated transformers possess
advantages as being simple, reliable, minimal line resonance
problems and relatively cost effective. The proposed nine and
twelve-phase auto-transformers can be viewed as a polygon winding
type, where besides achieving an improved input current
harmonics, junction points among various windings along the
polygon can be wired out for step- down, unity and step-up voltage
transfers. When electrically isolated primary windings are added,
unlimited transfer ratio is available for every application.
Application of these new industrial transformer devices, along with
simple power diode energy conversion methods, result in a robust
and reliable system that provides good DC bus regulation for AC
drives utilizing a common DC bus configuration. The proposed
topologies also provide a high AC input power factor and minimize
harmonic currents to the Utility Interface. The paper provides
technical analysis and field site data on the new topologies, as well
as per unit metric comparison to other harmonic mitigation
techniques versus horsepower size.
I. INTRODUCTION
Standard AC drive topologies utilize AC-DC-AC power
conversion with a three phase rectifying bridge for the AC-DC
function. A three-phase diode or SCR bridge generates 6 pulse
type current that is ~ 32% rich in total harmonic current
distortion [2]. As ac drives proliferate, equipment system
specifications limiting the amount of harmonic current injected
into the grid are becoming more common and thus solicit cost
effective harmonic mitigation solutions.
System specifications are often written so measured total
harmonic distortion at the Point of Common Coupling (PCC) in
Fig. 1 complies with the maximum low voltage total harmonic
distortion levels (THDV) and system classification of IEEE 519
Table 10.2 and current distortion limits of Table 10.3. The PCC
is usually at the power metering point (PCC1) where other
customers connect to the common line voltage but may also be
at (PCC2) or (PCC3) within a plant where linear and non-linear
loads are connected. System classification and (THDV) options
are Special Application @ 3%, Dedicated System @ 10 % and
most specified option of General System @ 5%. Current
harmonic distortion (THDI) of a single non-linear load is defined
as the square root of the sum of the squares of all harmonic
currents divided by the fundamental component of the non-linear
load. However, Table 10.3 defines total harmonic current
distortion limits in a system as Total Demand Distortion (TDD).
TDD limiting values are dependent on the ratio of short circuit
current (ISC) at the PCC to the maximum demand load current
(IL) supplied by the user. There are five classifications of (ISC/IL),
but worst case TDD limit of 5% for an (ISC/IL)< 20 is often used.
IEEE 2003 Industry Application Society (IAS) conference
utility
transformer
distribution
transformer
PCC1
Drive
600m of
cable
PCC2
PCC3
AC
AC
2500kVA
5.75%Z
480Vsec
250kVA
5.75%Z
480Vsec
Linear
Load A
Linear
Load B
Other
Customer
Fig. 1 One line showing various harmonic distortion measurement points
TDD =
h=n 2
∑ Ih
h=2
Eq. (1)
IL
Fig. 2 shows THDI of available solutions applied at PCC3.
Only the 18 pulse, active filter and synchronous converter front
end solutions are able to meet IEEE TDD limit of 5% at PCC3
and PCC1. The passive LC type has a typical THDI ~9% and is
regarded as cost effective [3]. However, it is well known to
have problems of resonance and leading power factor at noload condition [4]. The LC filter requires a detailed harmonic
analysis to determine if a TDD limit of 5% is possible at PCC3
in the installation. Active shunt, series and even hybrid filters
are promising but remain expensive and questionable in
reliability [5]. Analysis of Harmonic Canceling Reactors [6] or
Line-side Inter-phase Transformer (LIT) [7] shows their
effectiveness but does not prove their cost competitiveness.
An Auto-transformer solution is investigated in this paper as
a preferred embodiment because it does not introduce
resonance in power system, is reliable and relatively cost
effective. Integrating power switching devices with an autotransformer may reduce size, but sacrifices the optimum cost
target [8]. Traditional pure-passive auto-transformers may be
potentially more cost effective, but they also pose a problem in
sharing bridge currents in such multi-pulse application.[9]
In this paper, various patented topologies [10-12] of new
auto and isolation transformers are proposed for harmonic
mitigation, that inherently solve the diode current balancing,
and are proven with test results and product in the field.
Typical (THD_I), %
1
10
100
Basic Drive without dc link choke
Addition of dc link choke
Addition of 3% line reactor
Addition of passive filter
12 pulse auto transformer
18 pulse auto transformer
IEEE 519
Active filter
IEEE 519
Synchronous converter
IEEE 519
Fig. 2. Summary of harmonic mitigation solutions
1000
11
II. PRIOR ART OF MULTI-PULSE TRANSFORMER CIRCUITS
18-pulse isolation transformers that convert three-phase to
nine-phase AC power are well known but have several
shortcomings. First, isolation transformers must be rated for the
full power required on both primary and secondary windings.
Second, as a result of separate primary and secondary windings,
isolation transformers are relatively large. When isolation
between a utility supply and a rectifier is not required,
employing an auto-transformer, consisting of a plurality of series
and common windings, may advantageously reduce the size,
weight and cost of the 3-phase to 9-phase converter.
Fig. 3 shows an exemplary 3-phase to 9-phase autotransformer topology [13]. Three phase AC input lines are linked
to three input nodes (1,2,3) and nine output nodes (1-3, A-F)
provide voltage to three separate six pulse bridges. 18-pulse
operation is obtained with +/- 20 degree phase shift around
nodes 1,2 and 3. One problem is an inherent impedance
mismatch in the topology since one bridge is fed directly form
the line and the other two bridges are fed through the short
transformer windings which are characterized by a certain
amount of leakage reactance. This results in looping currents
among the 3 bridges, which further requires relatively bulky and
expensive inter-phase transformer hardware to correct.
Secondly, current-sharing problems among the three bridges is
exacerbated when irregular and unpredictable pre-existing AC
line harmonics occur as different source harmonics that
substantially change bridge current sharing.
One solution to the looping and sharing current problems is
to provide an autotransformer that equally spaces output
voltages in phase. Thus, where nine outputs are required, the
outputs can be phase shifted from each other by 40 degrees each.
In Fig. 4a this is accomplished in a step-down autotransformer
with three coils, having serial windings that form a delta and
stub windings magnetically coupled with the serial winding from
the same coil [14]. Three phase AC inputs are linked to the apex
nodes (11,12,13). Direct output nodes (14,17,19) and indirect
output nodes (15,16,18,19,21,22) all have identical voltage
magnitude vectors with the required 40-degree phase shift. The 6
leaf secondary windings solely process secondary power.
Fig. 4 shows other nine-phase step-down autotransformer
configurations investigated. A step-down version is needed to
compensate for a 14% increase in dc bus voltage that occurs
from 3-phase to 9-phase conversion. Fig. 4b and Fig. 4c contain
even more secondary leaf windings. Fig. 4d uses only 3
secondary leaf windings resulting in more efficient usage of
14
22
15
24
25
21
40° 40°
16
23
20
13
12
17
19
18
(a) Reference [14]
200
210
211
218
221
220
212
218
40° 40°
219
213
202
217
201
214
(b) Reference [14]
215
300
310
311
318
320
312
321
317
40° 40°
319
302
313
316
301
315
314
(c) Reference [15]
500
510
518
520
511
521
517
20° 20°
519
512
516
502
501
515
513
514
(d) Reference [16]
600
610
611
618
620
630
602
40° 40°
617
631
622
619
632
621
601
613
616
603
614
Fig. 3 Prior art 9-phase unity-gain autotransformer topology with +/20 degree phase shift between output voltages [13]
615
(e) Reference [17]
Fig. 4 Prior art 9-phase step-down autotransformer topology with 40
degree phase shift between output voltages
IR
H1
X1
H6
R2
R1
X2
X9
h6
x1
θ
R
3 Phase
AC
Source
S
40°
X3
40°
X8
T
O
H4
H3
X4
X7
R3
X5
R4
H2
DC
Output
R5
+
-
H5
X6
Fig. 6 Proposed nine-phase 18 pulse autotransformer in a step-down ac-dc system topology
material. However, the calculated step-down ratio may be
difficult to achieve. Fig. 4e has main windings in Y connection,
Y connected leaf windings and a separate non-power isolated
delta winding loop needed for circulating non sinusoidal
currents.
Fig. 5 shows other nine-phase unity-gain autotransformer
configurations. A 6-pulse drive guarantees 460V Output with
480V AC input. A unity-gain autotransformer version, with an
inherent 18-pulse higher DC bus voltage value, is sometimes
desirable for applications requiring 460V Output under low line
conditions of the 480V AC input.
While staggering the transformer outputs by 40o essentially
eliminates the looping and sharing current problems, the stub
winding requirement in each of the prior art renditions results
in increased kVA requirements, increased winding and core
material and increased physical size.
Thus, the next section proposes 3-phase to 9-phase
autotransformer solutions that do not have looping and sharing
current problems, are relatively inexpensive to construct, that
can be utilized as step-down or unity gain and that can have an
optional primary winding to accommodate any voltage transfer
ratio desired.
III. PROPOSED MULTI-PULSE TRANSFORMER CIRCUITS
A. 9-Phase Step-down & Unity Phase Shifting Autotransformer
100
101
One design objective is to develop a single auto transformer
topology that can be utilized as a step-down or unity-gain
transformer. This feature enables a manufacturer to reduce
102
40° 40°
design and manufacturing cost as one transformer is used for
107
two different applications. Fig. 6 shows a nine-phase auto109
transformer topology incorporated in a step down ac-dc power
conversion system [10]. The transformer is wound on a regular
103
106
three-pole core with 15 windings, where each phase has five
windings. For example phase R consists of windings R1-R5. On
each pole all windings are wound such that their polarities are in
104
105
(a) Reference [14]
the same direction. This polarity alignment assures inductance in
each winding is added up along the magnetic path length.
A second design objective is to provide 18-pulse
performance at lowest cost. To this end, the proposed
autotransformer only includes serial windings and does not
require leaf windings, which solely process one side power.
These results in better material utilization than prior art designs
for the same transformation results. The plurality of the series
windings is arranged to form a polygon.
The step-down transformation objective of Fig. 6 has
winding junction points H1-H6 and X1-X9 wired for
input/output, respectively. Since X1-X9 has equal magnitude
(b)Reference [15]
and equal 40ophase shift, they serve as a nine-phase voltage
Fig. 5 Prior art 9-phase unity-gain autotransformer topology with 40
degree phase shift between output voltages
output for rectification and DC output. Such DC output has 18108
400
401
408
410
402
40° 40°
407
409
406
403
404
405
pulse low ripple performance. Utility line RST input power
connections, with their 120o phase shift set, can be connected to
two sets of nodes; either [H1_H2_H3] or [H4_H5_H6] for a
same step-down ratio.
A third design objective is to eliminate the looping and
sharing current problems. This is accomplished by the equal
X1-X9 secondary voltage magnitudes which are separated by
equal 40o phase shift angles.
The step-down magnitude between primary and secondary
voltages can be analyzed by viewing Fig. 6 as a voltage plane
where distance between nodes represents voltage magnitude
Lines can be drawn between nodes and the Origin (O). The
angle between two lines represents a phase shift angle of two
node voltages. For example, the phase angle between nodes X1
and X2 is 400. A nine-phase autotransformer requires nine
output nodes X1-X9 whose voltages are identical and spaced
apart 400 on the dotted unit line circle of Fig.6. Nodes X1-X9
serve as output secondary voltages. It is seen that the voltage
magnitudes at the step-down input set (H1_H2_H3) of Fig. 6
are greater than the voltage magnitudes at the output set (X1X9). Step-down voltage magnitude will be proportional to the
length of vector X1 (i.e. output vector length) to the length of
vector H6 (i.e. supply vector length). The following equations
are formulated from the trigonometric relationship in Fig.6.
 cos 20o (1 − cos 40o ) 
o
θ = tan −1 
Eq.2
 sin o + cos o sin o  ≈ 13.08
20
40 
 20
V sec
V pri
=
X1
H6
= cos ( 40o − θ ) ~ 0 .8916
Eq.3
Thus, the step-down magnitude is 10.84 %. Fig. 6 can also be
used to identify the lengths of windings R1 through R5 with
respect to the supply voltage magnitude vector H6. From Fig. 6
the following relationships can be developed:
R1= R 2 = sin ( 40o − θ ) H 6 ≈ 0 .4527 * H 6
Eq.4
R 4 = 2 sin ( 20o ) cos ( 40o − θ ) H 6 ≈ 0 .6099 * H 6
Eq.5
R 5 = R3 = sin ( 20o + θ ) H 6 − 0.5 * R 4 ≈ 0 .2409 * H 6
Eq.6
The lengths expressed in Eq.4 – Eq.6 are proportional to the
turns ratios of windings R1 through R5. Thus, for windings R1
through R5 the turns ratios are:
R1 : R 2 : R3 : R 4 : R5 = 1: 1 : 0.5321:1.3472 : 0.5321
X1
R1
X2
R2
X9
H6
H1
x1
H1
h6
40°
X3
X8
R1
40°
T1
O
40°
H2
H3
H4
H3
S1
H5
H2
X4
X7
R5
R3
(b)
R4
X5
X6
(a)
Fig. 7 Proposed nine-phase autotransformer in a step-up ac-dc system
seen the output voltage vector lengths and magnitudes are
identical on the unit circle with the required 400 phase shift
angle, while the input voltage vector magnitudes are identical
in length to the output voltage vectors.
B. 9-Phase Step-up & Unity Phase Shifting Autotransformer
Winding re-arrangement of the 15 nine-phase auto-transformer
windings in Fig. 6 gives an alternate in Fig. 7a, capable of
x1
= 1.28 [11]. Unity three
unity and step up with a ratio of
h6
phase to nine phase voltage transformation is realized by
connecting the primary three phase source to either node sets
of [X1_X4_X7], [X2_X5_X8] or [X3_X6_X9] while the
secondary output nine phases are taken from X1 to X9. There
are three sets of parallel windings. One phase set in Fig. 7a
consists of R1 through R5. Thus, each phase set has five
windings wound on one pole of a conventional three-pole
magnetic core.
When either set of [H1_H2_H3] or [H4_H5_H6] nodes are
used to connect to the primary power source, this topology is
capable of step-up voltage transformation. The ratio is defined
by the trigonometric relationship as:
V sec
V pri
Eq.7
=
X1
H6
=
[
1
]
~1.28
Although non-integer numbers of winding turns can be
achieved, integer number of turns is preferred for ease of
manufacturing. Table 1 lists possible winding turn
combinations to achieve the turns ratios of Eq. 7. A maximum
error introduced because of integral winding turn numbers is
shown. Combination 3 has the lowest maximum error and is
preferred.
Again, each winding turns can be calculated in lengths:
Table 1
_______________________________________________________________
Consequently,
Combination #
1
2
3
4
R1
R2
R3
R4
R5
15
28
32
43
15
28
32
43
8
15
17
23
20
38
43
58
8
15
17
23
Max Error
0.77 %
0.31 %
0.07 %
0.25 %
Fig. 6 topology also meets the unity voltage transfer design
objective when RST are connected to either one of
[X1_X4_X7], [X2_X5_X8] or [X3_X6_X9] sets of nodes. It is
Eq.8
2
2
(sin 50o ) + tan (30o ) (1 − sin 50o)
[
]


R1 = R 2 =  (cos 50o ) − tan (30o ) (1 − sin 50o)  * X 1 ≈ 0.5077 * X 1


 1 − sin 50o 
 * X 1 ≈ 0.2701* X 1
R3 = R5 = 
 cos 30o 


o
R 4 = 2 * sin 20 * X 1 ≈ 0.6840 * X 1
(
Eq.9
Eq.10
)
Eq.11
R1 : R 2 : R3 : R 4 : R5 = 1: 1 : 0.5321:1.3472 : 0.5321
Eq. 12
Possible turns for each winding are summarized in Table 2
Table 2
_______________________________________________________________
Combination #
1
2
3
4
R1
R2
R3
R4
R5
Max Error
15
17
21
23
15
17
21
23
8
9
11
12
20
23
28
31
8
9
11
12
0.77 %
0.29 %
0.71 %
0.52%
H1
R1
X1 R2
R3
X12
H6
Y1
X11
X2
x1
h6
x12
6 Phase
Y6
Y4
Rectifier
o
30
X3
Module
X10
DC
Out
#1
H3
H4
6 Phase
X4
Rectifier
X9
o
30
o
15
Y2
Module
Y3
#2
X5
R
X8
Y5
S
Three
Phase
AC
Power
T
H2
R4 X6
R5
X7
R6
H5
Source
Fig. 8 Proposed twelve-phase 24 pulse autotransformer in a step-down ac-dc system topology
C. 9-PhasePolygon Secondary for Isolation Transformer
The autotransformer topology of Fig. 6 or Fig. 7a can be
utilized as a secondary of an isolation transformer. Addition of
three more windings electrically isolated from the fifteen
polygon windings, shown delta connected in Fig. 7b, converts
the entire topology into an isolation transformer with arbitrary
voltage transfer ratio. The delta primary winding can be added
to Fig. 6 in a similar manner.
With electrically isolated primary windings, unlimited
voltage transfer ratio is available for every application, such as
medium/low voltage transformation with medium voltage
feeders to eliminate the need for an interface step-down utility
transformer. For example, an 800 HP isolation transformer
with 4.2 kV primary / 600 V step-down polygon secondary was
manufactured and installed. This eliminated the need for a 1.5
MVA 4.2 kV primary / 600 V step-down utility transformer
that would normally have fed a 600V/600V polygon
autotransformer design.
D. 12-Phase Step-down/up & Unity Phase Shifting Autotransformer
Fig. 8 shows a twelve-phase auto-transformer configured as
step-down in a 24-pulse ac-dc conversion system [12]. A
twelve-phase 24-pulse rectifier system requires 30 degree
phase shift between the 12 output voltage nodes to eliminate
circulating and sharing current problems.
There are eighteen windings are arranged into a hexagon
where all winding junctions can be utilized for various voltage
transfer functions. These 18 windings are divided into three
groups wound on three magnetic poles of a transformer core.
Each pole phase has six windings that are interconnected with
the same polarity. The polarity alignment assures inductance in
each winding is added up along the magnetic path. Each phase
consists of six windings (R1-R6 for phase R). Secondary
voltages are supplied from equal magnitude points X1 to X12.
Voltage transformation is determined by the trigonometry
illustrated in Fig. 8. Figure 8 can be viewed as a voltage plane
where distance between nodes represents voltage magnitude.
The voltage vector of each output phase is represented by a line
from the origin node to its output node, such as X1. This line
length represents voltage magnitude of the output phase. It is
desirable for all output phases to have equal voltage
magnitudes, so all output nodes X1 to X12 are on a circle with
phase difference between phases of 30o. The twelve secondary
outputs are connected to two six-phase rectifiers and their
results are summed for a much lower ripple DC output.
Step-down autotransformer operation occurs when primary
voltages RST are connected to a set of [H1_H2_H3] or
[H4_H5_H6]. The step-down ratio is thus 0.8966.
V sec
V pri
=
X7
H2
=
cos (30 o)
~ 0 .8966
cos (15 o)
Eq. 13
Unity-gain autotransformer operation occurs when primary
voltages RST are connected to a set of [X1_X5_X9],
[X2_X6_X10], [X3_X7_X11] or [X4_X8_X12].
Step-up autotransformer operation occurs when primary
voltages RST are connected to a set of [Y1_Y2_Y3] or
[Y4_Y5_Y6]. The step-up ratio is thus 1.035.
V sec
V pri
=
X7
Y5
=
1
cos (15o)
~ 1.035
Eq.14
The turns ratio among set R1 – R6 is thus:
R1: R 2 : R3 : R 4 : R5 : R6 = 1: 1.733 :1 :1: 1.733 :1
Eq.15
E. 9-Phase / 12 phase Autotransformer kVA Rating, Size & Cost
An equivalent autotransformer VA rating assists in
comparing cost and size of the autotransformer topologies to
that of a conventional isolated transformer. Equivalent rating is
based upon the sum of all products of the sinusoidal equivalent
voltage across the windings and relevant rms current through
the windings [18]. Winding voltage is near sinusoidal but
current waveforms are not. The VA rating was computed with
simulation waveforms. Subsequent kVA rating calculation with
respect to the DC output is 2.3 for a conventional isolated 18
pulse transformer, 0.84 for the 18-pulse nine-phase auto-xfmr
Utility
Tr ansfo rmer
Iload
90
80
70
Volume,
Cub. Ft 60
50
T1
300
KVA
40
Iharm
30
VFD
10
18 pulse
AC Drive
100 HP
149 Amps
480 Vac
~
0
~
18p Isolation XFMR
100
200
400
Ratings, HP
18p AutoXFMR
600
Iharm
DC Drive
Harmonic
Analyzer
20
50
T2
300
KVA
6 pulse
DC D rive
180 Amps
500 Vdc
~
=
800
Fig. 9 Cubic volume of 18-pulse auto-xfmr vs. conventional 18-pulse
isolated transformer vs. HP rating
Load:100%
Fig. 12 Test setup used to test a 100 hp 18-pulse phase shifting step down
autotransformer.
8
7
t
6
18 pulse Isolation XFMR
200
5
150
4
18 pulse Auto XFMR
100
3
Amps
50
2
0.00
12.11
24.22
36.32
48.43
0
1
-50
0
0
100
200
300
400
500
600
700
800
-100
Transformer Rating [hp]
-150
Fig. 10 Relative cost of 18-pulse auto-xfmr vs. conventional 18-pulse
isolated transformer vs HP rating
500 hp DC bus Inverter
Input Bay
mSec
-200
(a) RST Input current waveform of 100 hp 18-pulse phase shifting step
down auto-xfmr @THDI =4.8% measured with Fluke 41 Power Analyzer
200
VFD
DC Bus
choke
100
18 pulse
rectifier
0A
Input LR
5% Z
-100A
18 pulse
auto
Xfmr.
Fig. 11 Proposed 9-phase 18-pulse step-down autotransformer @ 500 hp
and 0.74 for the 24-pulse twelve-phase auto-xfmr. These
calculations verify the cost and size advantages of the new
auto-xfmr topologies in Fig.9 and Fig.10 over existing isolation
transformer methods. Fig.11 shows an 18-pulse auto-xfmr and
Rectifier Bridge is about ½ the cubic volume of the 500 HP
inverter.
IV. HARMONIC PERFORMANCE OF MULTI-PULSE CIRCUITS
-200A
100m
I(Rr)
105m
110m
115m
120m
125m
130m
135m
140m
145m
150m
Time
(b) RST Input current waveform of 100 hp 18-pulse phase shifting step
down auto-xfmr @THDI =3.5% using P Spice circuit simulation
20
18
Input
Current 16
THD, %
14
Tested Total THD = 4.6%
Simulated Total THD = 3.5%
12
10
8
6
4
2
A.
9-Phase 18-pulse Autotransformer Simulation & Test Results
0
1
Fig. 12 shows a test setup used to test a 100 hp 18-pulse phase
shifting step-down autotransformer. Load to the AC drive
motor was a dc motor connected to the shaft.
Fig. 13 shows harmonic mitigation performance of 18-pulse
autotransformer with test and simulation results. The RST input
3
5
7
9
11
13
15
17
19
21
23
25
27
29 31
Harmonic number
Simulation
Test
(c) RST Input current harmonic spectrum of 100 hp 18-pulse phase
shifting step down auto-xfmr from simulation & test
Fig. 13 Harmonic mitigation performance of 18-pulse autotransformer –
Test and simulation
100
6-pulse _ 75 hp
6-pulse _ 75 hp + Harmonic Filter
10
12-pulse _ 650 hp
autotransformer
18-pulse _ 250 hp
autotransformer
Fig. 14 Simulated Phase R input Current and X1-X9 Output current
current waveform of Fig. 13(a) is nearly sinusoidal with a
measured THDI =4.8 %. The simulated RST current waveform
of Fig. 13(b) has a calculated THDI =3.5%. Simulated
harmonic current spectrum results in Fig. 13(c) show the
classic dominant 18 +/- 1 (17th & 19th) harmonics at ~ 2% of
fundamental, with the 5th, 7th 11th and 13th virtually eliminated.
Tested harmonic current spectrum results in Fig. 13(c) show
agreement with the (17th & 19th) harmonics, but contain a 3rd,
5th, 7th 11th and 13th components. The reason is attributed to
unbalanced input line voltages. Presence of unbalanced
negative sequence voltage in the power source does not effect
multi-pulse dc output but causes a third harmonic in the
converter line current [18]. A similar reason is attributed to the
5th and 7th components that appear only in measurement.
Fig. 14 shows simulated Phase R input line current along
with secondary X1- X9 line currents. Discrete positive and
negative rectifier conduction pulses of current in each line is
seen line with current magnitudes that are perfectly balanced.
The discrete line pulse magnitudes indicate there is no current
sharing problem and also no circulating current problem.
B.
12-Phase 24-pulse Autotransformer Simulation & Test Results
Fig. 15 shows harmonic mitigation performance of Fig.8 24pulse autotransformer with test and simulation results. The
Phase R input current waveform of Fig.15(a) is also nearly
sinusoidal with a measured THDI =4.1 %. The simulated RST
current waveform of Fig.15(b) has a calculated THDI =2.4 %.
Fig.15a Input current of 24 pulse AC Drive with input voltage THD =
0.9% (on test floor) and Current THD = 4.1%
1
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Load, %
Fig. 16 Current THD at input terminals for various front end topologies
under varying load
6
12-pulse _ 650 hp
autotransformer
5
6-pulse _ 75 hp + Harmonic Filter
4
6-pulse _ 75 hp
3
18-pulse _ 250 hp
autotransformer
2
1
0
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Load, %
Fig. 17 Voltage THD at input terminals for various front-end topologies
under varying load
C. 18-pulse AutoXFMR Comparison to Other Mitigation Techniques
Input current and voltage THD of 75 hp, 250 hp and 650 hp
drives is compared for various front-end topologies:
•
•
•
•
6-pulse drive with 6 SCR Bridge converter attached to PWM inverter
12-pulse phase shift autotransformer with diode bridge & PWM inverter
18-pulse phase shift autotransformer with diode bridge & PWM inverter
6-pulse drive with hybrid harmonic tuned filter [3]
The drives utilize the same inverter and control board. Loading
was similar to the test dyne setup of Fig.12. Tests were
performed at different hp test cells on the manufacturing floor
depending on drive size tested. Fig. 16 & Fig. 17 data is
presented as providing insight on different harmonic mitigation
techniques and not absolute since harmonic currents and
voltages are largely dependent on system impedance’s within
the power distribution system.
V. METRICS OF NEW MULTI-PULSE AUTOTRANSFORMERS
In a similar fashion other metrics are investigated in Table 3
with the various front-end topologies of Section IV.C. These
include power factor, displacement factor, K-factor and
efficiency.
Fig. 15b Input current of 24 pulse AC Drive with balanced input voltage
(simulation) and Current THD =2.4%.
Table 3
_______________________________________________________________
Category
6-Pulse
12-Pulse
18-Pulse
Current THD
30 – 35 %
6.5– 9.5 %
4.5– 5 %
Power factor
0.92 – 0.95
0.97 – 0.98
0.98 – 0.99
Displacement Factor 0.95 – 0.97
0.96 – 0.98
0.98 – 0.99
K – factor
3.0 – 5.0
2.0 – 3.0
1.0 – 2.0
Efficiency
96.5 – 97.5 % 97.0 – 98.0 % 97.5 – 98.0 %
______________________________________________________________
1.000
Distortion PF
0.990
=sqrt(1/(1+THD2))
0.980
0.970
0.960
0.950
0.940
0.930
0.920
A. Power Factor
0.910
0.900
0.890
Definitions are in order when discussing power factor of nonlinear converters.
Total Power Factor (pf total): the ratio for the total power input,
in watts to the total volt-ampere input to the converter.
Displacement Power Factor (pf disp): the displacement
component of power factor. The ratio of the active power of
the fundamental wave, in watts, to the apparent power of
the fundamental wave, in volt-amperes.
Distortion Power Factor (pf dist): the ratio of the root-meansquare of the harmonic content to the root-mean-square of
the fundamental component, expressed as a percent of
fundamental.
Equation 16 (set of equations)
For Three-Phase, Non-Sinusoidal, Balanced Systems
(the following approximations apply when V(THD)
< 5%)
pf total = true pf = pf disp * pf dist = Ireal / Itotal = P/S
pf disp = cos (angle between Ireal and Ifund) = Ireal / Ifund = P/S1
pf dist = cos (angle between Ifund and Itotal) = Ifund / Itotal = S1/S
THID = Iharm / Ifund
pf dist = sqrt(1/(1+THD_I2 ))
2
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
% I(THD)
Fig. 19 Distortion power factor vs. THDI
Fig.
20
Simulation of 480V 18-pulse nine -phase step-down
autotransformer line-neutral 400 Vpk voltage and phase R line
current of 400 Apk. Total power factor approaches unity.
Fig. 20 shows the proposed 18-pulse autotransformer topology
has a near unity total power factor from simulation, as also
shown Table 3. Fig. 21 shows measured total power factor of
the proposed 18-pulse autotransformer compared with the other
various front-end topologies. Fig. 22 shows measured
displacement power factor of proposed 18-pulse auto-xfmr
compared with the other various front-end topologies.
True Apparent Power = S = V*Itotal (kVA)
Apparent Power = S1 = V*Ifund (kVA)
Real Power = P = V*Ireal (kW)
True Reactive Power = Qt = V*sqrt(Ireact2 + Iharm2)
Reactive Power = Q = V*Ireact (kVAR)
Harmonic Power = D = V*Iharm (kVAR)
S = sqrt(P2 + Q2 + D2) = sqrt(P2 + Qt2)
2
0.880
2
1
18-pulse _ 250 hp
autotransformer
0.9
12-pulse _ 650 hp
autotransformer
0.8
6-pulse _ 75 hp
0.7
Itotal = sqrt(Ireal + Ireact + Iharm )
Itrue react = sqrt(Ireact 2 + Iharm2)
0.6
These relationships are best visualized by the power cube
representation in Fig. 18 [19]. Fig. 19 plots the pf dist equation.
This plot can be used with the THDI values in Table 3 to
generate Table 3 displacement factor for various multi-pulse
topologies or filter with known THDI values.
REACTIVE
Current
6-pulse _ 75 hp + Harmonic Filter
0.5
0.4
0%
50%
60%
70%
80%
90%
100%
18-pulse _ 250 hp
autotransformer
6-pulse _ 75 hp
end
12-pulse _ 650 hp
autotransformer
0.94
Ireact
Itrue react
0.92
Q
0.9
Qt
0.88
0.86
Ifund
S1
40%
0.96
D
S
30%
Fig. 21 Total power factor at input terminals for various front
topologies under varying load
1
Itotal
20%
Load, %
0.98
Iharm
10%
6-pulse _ 75 hp + Harmonic Filter
(0.34 @ 25% load)
0.84
Ireal
P
0.82
REAL
Current
0.8
0%
(in phase with line voltage, V)
HARMONIC
Current
Fig. 18 Power Cube relationship of power factor definitions
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Load, %
Fig. 22 Displacement factor at input terminals for various front end
topologies under varying load
B.
VI. MULTI-PULSE OPERATION WITH NON-IDEAL INPUT POWER
K- Factor
K – Factor is a calculation used to determine transformer derating in the presence of excessive current harmonic heating in
the primary/secondary coils [20-22]. K – Factor is defined as:
k=
h = h max
∑
h =1
2 h
Ih
2
Eq.17
where Ih = rms current at harmonic h , in per unit of rated rms load current
Table 3 shows the 18-pulse and 24 pulse autotransformer
topologies have the lowest value. Larger K-factor means larger
size and cost.
Thus, due to the lower fundamental input current with total
pf ~1 and lower harmonic currents, there is capital equipment
savings in the feed transformer cost with 18-p and 24-p systems
that offset original purchase cost. Also, $ cost savings is similar
for cables, fuses and breakers. These is also an operating $
savings in power factor penalty cost for very large kVA
systems with dedicated 18 pulse inputs with pf ~1.
C. Efficiency
This section calculates the input-output efficiency of a ninephase autoxfmr, 18 diode rectifier, pwm inverter and ac motor
compared to a 6 SCR rectifier, DC link choke, pwm inverter
and ac motor. Fig. 24 shows that 18-pulse system efficiency
may be equal or better than for a 6-pulse system. Some
differences may be the SCR forward voltage drop at higher
input current vs. a diode drop at lower input current in the 18pulse system. DC link power and output kVA to the motor
were made equal in Fig. 23 in both cases. Table 4 data for rated
100 hp load shows measured results with a FLUKE 41 Power
Analyzer that measured VLL and Iline .
Table 4
_______________________________________________________________
Drive Vin Iin kVA in kWin PF THDv THD I Vdc Idc kWdc
6 pulse 480 129.6 107.6 101.1 0.94 1.5 32.6 648 151.4 98.11
18 pulse 480 121.6 100.98 99.9 0.99 1.2
4.5 670 146.4 98.09
______________________________________________________________
_______________________________________________________________
Drive Eff Conv Vout Iout kVAout kWout Eff. inv Eff drive system
6 pulse 97.0%
18 pulse 98.1%
460 138 109.8
460 138 109.8
AC/DC
Pin
97.74
97.74
99.6%
99.6%
Pdc
DC Link
Converter
96.8%
97.8%
DC/AC
Pout
Inverter
Non-ideal power source characteristics may cause current
unbalance (up to 80% seen) and increased THDI in prior art
Auto-XFMR circuits with parallel bridge converters.
Pre-existing voltage harmonics is one contributor to current
unbalance. Pre-existing 5th harmonic voltage induced on the
desired PCC connection may be due to 6-pulse VFD (5th, 7th
dominate) operation at a distant location in Fig.1 plant one-line
diagram. A pre-existing 5th harmonic voltage of 2.5% is used for
analysis based on best field data to date.
Utility source voltage unbalance is another contributor to
current unbalance. ANSI C84.1-1982 [23] defines 3-phase %
voltage unbalance in Eq. 18. A value of 1% covers ~ 70% of all
field sites according to [23] and is thus a worst case design
criteria.
% V unbalance =
(
3 V max − V min
V a +V b + V c
) *100
Eq.18
THDI comparison at the input terminals to a drive with an 18pulse phase-shifting Autotransformer was simulated with a 300
kVA 480V line under the following Type I – Type III
combinations of utility Power Source input conditions.
Type I - Balanced Input Line Voltage & No pre-existing Harmonics
Type II - Imbalance (1%) Input Line Voltage & No pre-existing Harmonics
Type III - Imbalance (1%) Input Line Voltage & 2.5 % 5th Harmonic Voltage
Test
- Obtained on test Floor
Fig.25 shows a Type I power source results in a THDI = 3.25%
at full load and just over 5% at ¼ load. Type II power, with 1%
line unbalance, raises THDI to 4.8% at full load and 9% at ¼
load. However, IEEE-519 TDD limit of 5% at full load is still
met at drive input terminals. Test floor 1% unbalance
conditions match Type II simulation results very well with load.
Type III power with 1% unbalance lines and 2.5 % pre-existing
5th harmonic voltage causes the highest THDI at 7% for full
load. Higher THD is a result of the 5th harmonic voltage phase
angle causing a slight dc voltage unbalance in the rectifier
output and thus some current unbalance, as explained in [18].
However, converter bridge and autotransformer can still
operate continuously under this condition. Also, if the 18-pulse
THDI of 7% is combined with even a small linear load at the
PCC, then IEEE-519 TDD limit of 5% may still be met.
Pre-existing 5th harmonic condition was tested by removing
the dc drive isolation transformer in Fig.12, so that the dc drive
6-pulse current harmonics presented a THDV of 7.4% at the 18pulse autotransformer line inputs as shown in Fig.26. The
resulting current waveform simulation and test results of Fig.26
also show general agreement.
THD_I
%
Fig. 23 Loss model of AC Drive system to calculate input-output efficiency
15.0
18p VFD THD (PS I), %
18p VFD THD (PS II), %
18p VFD THD (PS III), %
18p VFD THD (Test), %
12.5
Efficiency, %
100.00
10.0
95.00
18 pulse System Efficiency,
7.5
90.00
5.0
85.00
6 pulse system Efficiency, %
80.00
2.5
75.00
0.0
70.00
0
20
40
60
80
VFD Load, %
100
Fig. 24 Efficiency comparison of nine-phase auto-xfmr with 6-pulse system
25
50
75
100
Load, %
Fig. 25 Harmonic mitigation performance of 18-pulse VFD with phase
shifting Auto-xfmr under different input line conditions
(a) test input voltage THD=7.3% at input terminals to 18-pulse autoXFMR
input current harmonics, various winding junction points along the
polygon can be wired out for various step down, unity and step up
voltage transfer ratios. With electrically isolated primary windings,
unlimited ratio is available for every application, such as medium/low
voltage transformation with medium voltage feeders to eliminate
needs for step-down utility transformer.
Working units at industrial field sites, ranging in hp sizes from 50
hp to 800 hp, are based on these topology patents [8-11]. The paper
provided technical analysis and field site data on the new topologies,
as well as comparison to other harmonic mitigation techniques versus
horsepower size.
Acknowledgement:
Authors wish to thank B. Eisenbrown, J. Simons, K.
Phillips of RA for support, R. Hoadley for engineering assistance, and K.
Jurkowski, G. Zenke and B. Hachey for producing the multi-pulse product line.
(b) Test floor input current THD=8.7% at input of 18-pulse autoXFMR
(c) Simulated input current THD=6.4% at input of 18-pulse autoXFMR
Fig. 26 Test results and simulation of new 18-pulse VFD / AutoXFMR at
full load but under adverse line voltage THD of 7.3% that exceeds
IEEE 519 General System voltage limit of 5%
Fig.27 shows a test harmonic mitigation comparison between
the new 18-pulse VFD / AutoXFMR vs. 6-pulse VFD with a
Hybrid Tuned Harmonic Filter [3] operated at different loads.
Type II 18-pulse curve is re-plotted from Fig.25. The THDI 6pulse with filter curve exceeds the 18-pulse curve at most loads
but is 7% at full load. However, at full load dc bus voltage is
well below rated, so that rated inverter output voltage cannot be
obtained. This is due to the large %Z input reactors of the tuned
filter acting as commutating reactor voltage drops. Thus, while
input harmonic current is reduced with hybrid tuned filters,
output rated voltage and output torque is likewise reduced.
THD_1
[%]
15 0
12.5
6p + Harmonic Filter,
10.0
7.5
5.0
18p VFD THD,
2.5
0
0
20
40
60
80
100
Load, %
Fig. 27 Tested harmonic mitigation performance of 18-pulse VFD /
AutoXFMR vs. 6-pulse VFD + Harmonic filter @ different loads
VII. CONCLUSION
This paper proposed several nine and twelve-phase autotransformers topologies to meet standard IEEE 519. Compared with
other solutions, autotransformers possess such advantages as being
simple, reliable, no resonance problem and relatively cost effective, as
well as small physical size. The proposed AC/DC converter
topologies utilizing these transformers were shown to not have current
sharing problems.
The proposed nine- and twelve-phase auto-transformers can be
viewed as polygon type, where besides achieving much improved
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