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Published in IET Power Electronics
Received on 1st February 2008
Revised on 15th May 2008
doi: 10.1049/iet-pel.2008.0039
ISSN 1755-4535
24-pulse ac –dc converter for harmonic
mitigation
V. Garg B. Singh G. Bhuvaneswari
Department of Electrical Engg, I.I.T. Delhi, New Delhi 110016, India
E-mail: vipin123123@gmail.com
Abstract: A new harmonic mitigator based on 24-pulse ac –dc conversion is proposed to feed voltage source inverter
supplying squirrel-cage induction motor drive. The proposed converter consists of a newly designed hexagonconnected autotransformer with reduced magnetics rating and having simplicity in design and manufacturing.
The proposed 24-pulse ac – dc converter is found capable of suppressing less than 23rd harmonic in the supply
current. The power factor is also improved to near unity in the wide operating range of the vector-controlled
induction motor drive (VCIMD). Moreover, the design of the autotransformer is modified to make it suitable for
applications, where presently a 6-pulse diode bridge rectifier is used. A laboratory prototype of the proposed
autotransformer-based 24-pulse ac –dc converter feeding a VCIMD is developed and test results are presented to
validate the developed design procedure and the simulation models of this ac – dc converter under varying loads.
1
Introduction
There has been an enormous increase in the number of variable
frequency induction motor drives (VFIMDs) being used for
various industrial applications such as air-conditioning,
blowers, fans, pumps for wastewater treatment plants, cement
industry and ship propulsion [1]. These VFIMDs are generally
operated in the vector control mode [2] owing to their inherent
advantages such as energy conservation and reduction in inrush
current. The power supply interface feeding voltage source
inverter (VSI) of an induction motor drive consists of diode
rectifiers (because of their reliability and economy) and this
arrangement results in the injection of harmonics in ac mains,
thereby polluting the power quality at the point of common
coupling (PCC). This has led to the publication of different
international standards. The most relevant and useful standard
IEEE 519-1992 [3] was issued in 1992 to maintain
restrictions on these harmonic-producing equipments.
Different techniques have been proposed for harmonic
mitigation in the literature [4, 5]. In alleviating the harmonics
effectively and efficiently, multipulse converters have gained
importance because of their robustness, efficiency and
simplicity in control. Many researchers have used different
configurations based on 12-pulse and 18-pulse rectification
[6–14]. The 12-pulse ac–dc converter based configurations
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do not meet IEEE standard-519 in terms of different power
quality indices. Recently, an 18-pulse ac–dc converter has
been reported to reduce the harmonics [13], but the THD of
ac mains current has been around 8.6% only, which may
deteriorate further as the load is reduced. Similarly, to reduce
the THD of ac mains current further, a 28-step current
shaper has been proposed [15], but even with this
configuration, the THD of ac mains current at full load is
6.54%, which is also not within IEEE Standard 519 limits.
This paper presents a 24-pulse ac – dc converter based on a
hexagon-connected autotransformer feeding a vectorcontrolled induction motor drive (VCIMD). Further, the
design of autotransformer is modified to make it suitable
for applications where a 6-pulse rectifier is being used. The
present approach results in a compact, cost-effective,
rugged and reliable converter configuration with a flexibility
to vary and adjust transformer output voltages as per the
requirement. The VCIMD is implemented by using a
dSPACE 1104 processor. Various tests are conducted on
the developed prototype of the proposed converter feeding
a VCIMD. The experimental results validate the
simulation results for the proposed 24-pulse ac – dc converter.
Different power quality parameters such as total harmonic
distortion (THD) and crest factor (CF) of ac mains current,
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
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eliminated from the line currents by choosing F equal to
308. This results in a 12-pulse converter based rectification.
The same concept can be extended to achieve 24-pulse
converter based rectification by choosing F equal to 158.
This results in elimination of 5th, 7th, 11th, 13th, 17th
and 19th harmonics in the supply current. It requires the
generation of four sets of ac voltages phase shifted through
an angle of 158. Two sets of voltages are at an angle of
+7.58 and other two sets of voltages are at an angle of
+22.58 with respect to the supply voltages.
3 Analysis and design of the
proposed 24-pulse ac –dc converter
Figure 1 Schematic diagram of 6-pulse diode rectifier-fed
vector-controlled induction motor drive (Topology ‘A’)
power factor (PF), displacement factor (DPF), distortion factor
(DF) and THD of supply voltage at PCC, ripple factor (RF) are
compared with that of a 6-pulse converter fed system as shown
in Fig. 1 and referred as Topology ‘A’.
2 Principle of harmonic
mitigation
An autotransformer-based n-pulse ac – dc converter operates
on the principle of harmonic elimination. The minimum
order of harmonics is nK + 1, where K is a positive integer
and n is the number of rectification pulses per cycle of the
fundamental voltage. The principle of harmonic elimination
is explained as follows.
For harmonic elimination, the required minimum phase
shift is given by [4]
Phase shift ¼ 608=number of 6-pulse converters
(1)
In a phase-shifting transformer, the fundamental output
current is shifted through an angle F as it passes through
the transformer. The harmonic currents are also moved
through an angle of either þ F or 2 F, depending on the
phase sequence. The negative and positive sequence sets of
5th, 7th, 11th, 13th, 17th and 19th harmonics are phase
shifted as they pass through the transformer. The negative
sequence shifts through an angle opposite to that of the
positive sequence. For example, considering the 5th
harmonic, it is shifted through an angle 25F (being a
negative sequence vector). Thus, the 5th harmonic current
is at an angle 6F with respect to the fundamental
component of current. Similarly, the 7th harmonic current,
being a positive sequence vector, is shifted through 7F.
Therefore it is again at an angle of 6F with respect to the
fundamental. Both 5th and 7th harmonic currents can be
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For achieving 24-pulse ac – dc conversion, it requires the
generation of four sets of phase-shifted voltages as
explained earlier. Fig. 2 shows the circuit diagram of the
proposed hexagon-connected autotransformer-based 24pulse ac– dc converter. It is divided into three main parts.
3.1 Design of hexagon-connected
autotransformer
Fig. 3a shows the winding diagram of the proposed hexagonconnected autotransformer. The hexagon-connected
autotransformer is designed such that when it is fed from
three-phase input voltages (Va , Vb , Vc) displaced at 1208
with respect to each other, it produces four sets of balanced
three-phase voltages, namely (Va1 , Vb1 , Vc1), (Va2 , Vb2 , Vc2),
(Va3 , Vb3 , Vc3) and (Va4 , Vb4 , Vc4), all displaced through an
angle of 158 desired for the 24-pulse converter operation.
For achieving the condition of 158 phase shift as per (1),
voltages (Va1 , Vb1 , Vc1) are at an angle of þ7.58 with
respect to supply voltages. Similarly, the set of voltages
(Va2 , Vb2 , Vc2) is at þ22.58, voltages (Va3 , Vb3 , Vc3) are at
27.58 and voltages (Va4 , Vb4 , Vc4) are at 222.58, as shown
in phasor diagram in Fig. 3b.
The number of turns required for achieving these phase
shifts among different phase voltages is calculated as
follows. Consider phase ‘a’ voltages in Fig. 3a as
Va1 ¼ Va þ K1 Vc K2 Vb
(2)
Va2 ¼ Va þ K3 Vc K4 Vb
(3)
Va3 ¼ Va þ K1 Vb K2 Vc
(4)
Va4 ¼ Va þ K3 Vb K4 Vc
(5)
Consider the following set of voltages
Va ¼ V /08, Vb ¼ V /1208, Vc ¼ V /1208
Va1 ¼ V /7:58, Vb1 ¼ V /112:58, Vc1 ¼ V /127:58
Va2 ¼ V /22:58, Vb2 ¼ V /97:58, Vc2 ¼ V /122:58
(6)
(7)
(8)
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Figure 2 Schematic diagram of proposed autotransformer-based 24-pulse converter-fed VCIMD (Topologies ‘B’ and ‘C’)
Figure 3 Autotransformer connection
a Proposed autotransformer winding connection diagram
b Phasor diagram of voltages in the proposed autotransformer connection
The phase-shifted voltages for phase ‘a’ are
Va3 ¼ V /7:58, Vb3 ¼ V /127:58, Vc3 ¼ V /112:58
(9)
Va4 ¼ V /22:58, Vb4 ¼ V /142:58, Vc4 ¼ V /97:58
(10)
where V is the rms value of phase voltage.
Using these equations, K1 , K2 , K3 and K4 can be calculated.
These equations result in K1 ¼ 0.08391, K2 ¼ 0.06679,
K3 ¼ 0.2971 and K4 ¼ 0.14474 for the desired phase shift
in autotransformer.
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Va1 ¼ Va þ 0:08391Vc 0:06679Vb
(11)
Va2 ¼ Va þ 0:2971Vc 0:14474Vb
Va3 ¼ Va þ 0:08391Vb 0:06679Vc
(12)
(13)
Va4 ¼ Va þ 0:2971Vb 0:14474Vc
(14)
This configuration is referred as Topology ‘B’. To make the
proposed ac–dc converter suitable for retrofit applications, the
autotransformer design is modified to make the dc link
voltage same as that of a 6-pulse diode bridge rectifier. Fig. 4
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
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Figure 5 Schematic diagram of interphase transformer
Figure 4 Phasor diagram of voltages in the proposed
autotransformer connection for retrofit arrangement
shows the generalised diagram of different phase voltages for
achieving different voltage ratios from the autotransformer by
varying the tap positions in the proposed autotransformer.
This ensures that the output voltages still have the required
phase shift of 158 (for achieving the 24-pulse converter
operation).
For retrofit design, the new constants are obtained as
K 10 ¼ 0.1389, K 20 ¼ 0.0027, K 30 ¼ 0.3393 and K 40 ¼ 0.076,
where K 10 , K 20 , K 30 and K 40 are the new constants for
achieving the same dc link voltage as that of a 6-pulse
diode bridge rectifier.
Thus, by simply changing the transformer winding
tapping, as shown in Fig. 4, the same dc link voltage as
that of a 6-pulse diode bridge rectifier is obtained. This
configuration is referred here as Topology ‘C’.
interphase transformers to ensure the independent
operation of the rectifier circuits. Fig. 5 shows the winding
configuration of the proposed interphase transformer. This
arrangement ensures symmetrical conduction of each diode
bridge. The interphase transformer consists of a central
core having four legs and all legs are excited in the same
direction so that the main portion of the dc ampere turns is
absorbed along the return path of the magnetic flux outside
the core. This prevents the transformer from entering the
saturation. Each winding of the IPT absorbs the difference
between the voltage across the dc circuit. The voltage
across the dc circuit at any instant is the mean value of all
four direct voltages and it fluctuates with 24-pulse ripple. A
small degree of saturation is inevitable and it may be
avoided by the following methods:
i. Using a core having an air gap will reduce the peak of
exciting current under unbalance, but it increases the
exciting current under balance conditions, as the air gap
needs additional excitation.
ii. Use of a higher rating IPT will reduce the exciting current
under unbalance condition as well as under balance
condition, but it is an expensive solution.
The best method, however, is to use a combination of
both, that is, using slightly higher rating IPT along with an
air gap core.
The kVA rating of the transformer is calculated as [4]
kVA ¼ 0:5
X
Vwinding Iwinding
(15)
where Vwinding is the voltage across one winding and Iwinding is
the current flowing through each winding. The kVA rating of
the interphase transformer is also calculated by using the
above relationship.
3.2 Design of interphase transformer
The four sets of voltages produced by the autotransformer are
given to four diode rectifier bridges, which rectify these
voltages. These obtained dc voltages are also phase shifted
through an angle of 158. These voltages are applied to the
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
4 Simulation and
experimentation
To illustrate the performance of the proposed ac– dc
converter, this 24-pulse ac – dc converter fed VSI supplying
to an induction motor drive is simulated in MATLAB
environment using Simulink and power system blockset
toolboxes as shown in Fig. 6. Fig. 7 shows the MATLAB
model of the proposed autotransformer, consisting of three
single-phase transformers. The simulated results have been
verified on a test bench consisting of the newly designed
and developed autotransformer along with small rating
interphase transformer. The VCIMD is implemented using
dSPACE 1104 processor. The details of design and
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Figure 6 MATLAB block diagram of proposed 24-pulse converter fed VCIMD (Topologies ‘B’ and ‘C’)
Figure 7 MATLAB block diagram of proposed autotransformer
development of different components of the proposed system
are described next.
4.1 Design and development of
autotransformer
Three single-phase identical transformers are developed to
realise the proposed converter configuration, as shown in
Fig. 8. The design details of the proposed autotransformer
are given as follows [16, 17]:
Flux density ¼ 1 Tesla, current density ¼ 2.3 A/mm2,
core
size
no. ¼ 8.
Area
of
cross-section
of
core ¼ 3225 mm2 (50.8 mm 63.5 mm). E-laminations:
length ¼ 184.1 mm, width ¼ 171.4 mm. I-laminations:
length ¼ 171.4 mm, width ¼ 50.8 mm. Number of turns
per volt ¼ 1. Accordingly, different windings (shown in
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Fig. 2) of different cross-section for the proposed 24-pulse
converter are wound for all three single-phase
autotransformers. It is observed that certain pre-calculated
number of turns in different windings help in obtaining
phase-shifted voltages of equal magnitude.
4.2 Design and development of
interphase transformer
To realise the interphase transformer, eight identical
windings are wound on a core. The design details of the
interphase transformer shown in Fig. 9 are as follows:
The flux density is taken as 0.8 Tesla and the current density
is considered as 2.3 A/mm2. The interphase transformer is
wound using a core of size no. 3 with E-I laminations of size
(76 mm 127 mm) and (127 mm 19 mm), respectively.
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
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Figure 8 Pictorial
autotransformer
view
of
hexagon
connected
three-phase 10-hp induction motor coupled to a dc
generator. Two-phase currents of the motor, namely ias and
ibs , are sensed using Hall effect current sensors of ABB
make (EL50P1BB). The current sensor gives an output
voltage signal, which is proportional to the sensed current.
The turn ratio of these current sensors is 1/1000. The VSI
consists of three legs of Semikron make half bridge IGBT
modules (SKM100GB128DN) mounted on heat sink to
constitute a VSI. This module is suitable for up to 20 kHz
switching frequency and is having in-built thermal
protection.
Various tests are carried out at three-phase line voltage of
230 V ac input and with a 10 hp VCIMD load and test
results are given in Figs. 12 and 13. The recording of test
results have been carried out using Agilent make digital
storage oscilloscope 54624A, with frequency of 100 MHz
Figure 10 Dynamic response of 6-pulse diode rectifier-fed
VCIMD with load perturbation (Topology ‘A’)
Figure 9 Realization of interphase transformer
Based on the voltage across different windings, the number of
turns are calculated and based on the current flowing through
different windings, the gauge of wire is calculated. The
number of turns in each winding of IPT is 75 and the gauge
of wire used is 12.
4.3 Development of VCIMD
The real-time implementation of the vector control of a
three-phase 10-hp induction motor drive is carried out
using a hardware platform dSPACE DS1104 processor.
The developed work bench of VCIMD mainly consists of
dSPACE DS 1104 processor, interfacing circuits namely
the speed and current sensing and scaling circuits,
PWM pulse isolation and amplification circuit, VSI and a
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
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Figure 11 AC mains current waveform of VCIMD fed by
6-pulse diode rectifier along with its harmonic spectrum
at full load (Topology ‘A’)
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Figure 12 Response of 10-hp vector controlled induction motor drive in 24-pulse converter configuration. Channel 1, 800 V/
div; channel 2, 15 A/div; channel 3, 5000 rpm/div; channel 4, 15 A/div
a During application of load
b During steady-state under load
c During removal of load
and 200 M samples/s and Fluke make power analyser model
43B on the developed prototypes.
5
Results and discussion
To demonstrate the improvement in performance of the
proposed autotransformer-based 24-pulse ac–dc converter,
a 6-pulse converter feeding a VCIMD is also studied and
its performance is presented.
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5.1 Performance of 6-pulse ac – dc
converter fed VCIMD
The dynamic performance of the drive along with load
perturbation on the VCIMD fed by a 6-pulse diode bridge
rectifier, referred as Topology ‘A’ is shown in Fig. 10. The
set of curves consists of supply voltage vs , supply current is ,
rotor speed ‘vr’ (in electrical rad/s), three-phase motor
currents iabcs , motor developed torque ‘Te’ (in N-m) and dc
link voltage vdc (V). The waveform of ac mains current
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
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Figure 13 AC mains current waveform alongwith its harmonic spectrum in simulation as well as experimentation for 24-pulse
converter configuration
a At full load
b At light load
along with its harmonic spectrum is shown in Fig. 11
showing the THD of ac mains current at full load as
31.3% and at light load as 62.2% as shown in Table 1. The
PF under these conditions is 0.935 and 0.807, respectively.
It shows that the power quality indices are not within the
limits of IEEE standard 519 [3].
current at full load is 3.56% and under light load is 5.35%,
as given in Table 1. The design of the autotransformer is
modified for retrofit applications, resulting in Topology ‘C’.
This topology is similar to Topology ‘B’ except the
difference in number of turns in the windings to produce
the same dc link voltage.
5.2 Performance of the proposed
24-pulse ac – dc converter fed VCIMD
The dynamic performance of the drive along with load
perturbation on the VCIMD fed by the proposed 24-pulse
ac– dc converter is shown in Fig. 12. It shows both
simulated as well as experimental results under different
conditions such as application of load, steady state under
load and removal of load. The experimental results show a
close agreement with the simulated results, thus validating
the design of the transformer. Fig. 13 shows the supply
The hexagon-connected autotransformer-based 24-pulse
ac– dc converter feeding VCIMD load is simulated and
referred here as Topology ‘B’. In this topology, the dc link
voltage is higher than that of a 6-pulse diode bridge
rectifier, as given in Table 1. The THD of ac mains
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
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Table 1 Comparison of power quality parameters of a VCIMD fed from different ac – dc converters
Sr. Topology
No.
Is, A
THD
against
(%) full
load
THD of Is, %
DF
DPF
PF
DC link
voltage, V
Average
Full
load
Light
load
(20%)
Full
load
Light
load
(20%)
Full
load
Light
load
(20%)
Full
load
Light
load
(20%)
Full
load
Light
load
(20%)
Full
load
Light
load
(20%)
31.3
62.20
0.95
0.849
0.97
0.95
0.93
0.807
546
555
1
A
6.76
14.3
4.35
2
B
2.48
11.6
2.36
3.56
5.35
0.99
0.998
1.00
0.991
0.99
0.99
572
581
3
C
2.50
11.7
2.38
3.55
5.21
0.99
0.986
0.99
0.994
0.988
0.989
545
553
Table 2 Variation of power quality indices of the proposed 24-pulse ac – dc converter (Topology ‘C’) fed VCIMD under varying
loads
Load, %
THD, %
CF of Is
DF
DPF
PF
RF, %
Vdc , V
Is
Vt
20
5.21
1.20
1.42
0.998
0.991
0.989
2.48
553
40
4.80
1.56
1.42
0.999
0.990
0.989
2.19
551
60
4.08
1.87
1.42
0.999
0.990
0.989
1.71
549
80
3.92
2.18
1.42
0.999
0.989
0.988
1.15
547
100
3.55
2.42
1.42
0.999
0.989
0.988
0.70
546
current waveform of the proposed 24-pulse ac–dc converter
(Topology ‘C’) in simulation as well as in experimentation
under different loading conditions. At full load, the THD
of ac mains current is observed as 3.55% in simulation and
3.7% in measurements and the PF obtained is 0.988. At
light load condition, the THD of ac mains current is
5.21% in simulation and 4.6% in experimentation, as
shown in Fig. 13b. The PF under this condition is
observed as 0.989, as given in Table 1. The dc link voltage
is almost the same as that of a 6-pulse diode bridge
rectifier system.
To study the effect of load variation on different power
quality indices, the load is varied on the VCIMD. The
different power quality indices are tabulated in Table 2. It
can be observed from Table 2 that the THD of ac mains
current is always within IEEE Standard limits [3] for
systems with SCR .20. The PF is always above 0.988 in
the wide operating range of the drive.
On magnetics front, the proposed configuration needs
only two main windings per phase, resulting in
autotransformer rating of 2.21 kVA, and small interphase
reactors of 0.66 kVA, totalling to magnetics of 2.87 kVA,
which is only 27.5% of the drive rating.
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6
Conclusions
A new hexagon-connected autotransformer-based 24-pulse
ac–dc converter has been designed, simulated and developed
to demonstrate its behaviour for feeding a 10 hp VCIMD.
The proposed autotransformer-based ac–dc converter has
resulted in elimination of less than 23rd harmonic in the
supply current. The design technique of the proposed
converter has shown the flexibility to design the
autotransformer suitable for retrofit applications. The low
volt–ampere rating autotransformer has resulted in a circuit
of lower cost, weight, volume and space when compared with
the conventional 12-pulse ac–dc converter. There has been
drastic improvement in the THD and CF of ac mains current
as well as the PF with almost close to unity in the wide
operating range of the drive. Thus, the proposed 24-pulse
ac–dc converter can easily replace the existing 6-pulse
converter without much alteration in the existing system
layout and equipments.
7
References
[1] BOSE B.K.: ‘Recent advances in power electronics’, IEEE
Trans. Power Electronics, 1992, 7, (1), pp. 2 – 16
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
www.ietdl.org
[2] VAS P.: ‘Sensorless vector and direct torque control’
(Oxford University Press, 1998)
[3] ‘IEEE guide for harmonic control and reactive
compensation of static power converters, IEEE Standard
519-1992
[4] PAICE D.A.: ‘Power electronic converter harmonics:
multipulse methods for clean power’ (IEEE Press,
New York, 1996)
[5] PAICE D.A.: ‘Multipulse converter system’. U.S. Patent
No. 4876634, 24 October 1989
[6] HAMMOND P.W. : ‘Autotransformer’. U.S. Patent No.
5619407, 8 April 1997
[17] GARG V.: ‘Power quality improvements at ac mains in
variable frequency induction motor drives’. Ph.D. thesis,
Indian Institute of Technology, Delhi, New Delhi, India,
May 2006
8
Appendix
8.1 Motor and controller specifications
Three-phase squirrel-cage induction motor 210 hp
(7.5 kW), three-phase, 4-pole, Y-connected, 415 V, 50 Hz,
Rr ¼ 0.76 V,
rated
current ¼ 14.5 A,
Rs ¼ 1.0 V,
Xls ¼ 0.77 V, Xlr ¼ 0.77 V, Xm ¼ 18.84 V, J ¼ 0.1 kg-m2
PI speed controller: Kp ¼ 7.0, Ki ¼ 0.1.
DC link parameters: Ld ¼ 0.002 H, Cd ¼ 2200 mF.
[7] PAICE D.A. : ‘Transformers for multipulse AC/DC
converters’. US Patent No. 6101113, 8 August 2000
Magnetics ratings: autotransformer rating 2.21 kVA,
interphase transformer 0.66 kVA.
[8] SINGH B., BHUVANESWARI G., GARG V.: ‘Multipulse improved
power quality ac-dc converters for vector controlled
induction motor drives’, IEE Proc. Electric Power Appl.,
2006, 153, (1), pp. 88– 96
8.2 Modelling of vector-controlled
induction motor drive
[9] KAMATH G.R., RUNYAN B., WOOD R.: ‘A compact
autotransformer based 12-pulse rectifier circuit’. Proc.
IEEE IECON Conf., 2001, pp. 1344– 1349
[10] SINGH B., BHUVANESWARI G., GARG V.: ‘Harmonic mitigation
using twelve-pulse ac-dc converter for vector controlled
induction motor drives’, IEEE Trans. Power Delivery, 2006,
21, (3), pp. 1483– 1492
[11] SINGH B., BHUVANESWARI G., GARG V.: ‘Harmonic mitigation in
ac-dc converters for vector controlled induction motor drives’,
IEEE Trans. Energy Conversion, 2007, 22, (3), pp. 637–646
[12] OGUCHI K., YAMADA T. : ‘Novel 18-pulse diode rectifier
circuit with non-isolated phase shifting transformers’, IEE
Proc. Electr. Power Appl., 1997, 14, (1), pp. 1 – 5
[13] DE SEIXAS F.J.M., BARBI I.: ‘A 12 kW three-phase low THD
rectifier with high frequency isolation and regulated dc
output’, IEEE Trans. Power Electronics, 2004, 19, (2),
pp. 371– 377
[14] DE SEIXAS F.J.M., GONCALVES V.A.: ‘Generalization of the deltadifferential autotransformer for 12 and 18-pulse converters’.
Proc. IEEE PES Conf. ’05, June 2005, pp. 460–466
Fig. 1 shows the schematic diagram of an indirect vectorcontrolled induction motor drive. To realise the vector
control of an induction motor, two currents of motor
phases, namely ias and ibs , and the motor speed signal (vr)
are sensed. The closed-loop PI speed controller compares
the reference speed (vr) with motor speed (vr) and
(after limiting it to a
generates reference torque T (n)
suitable value).
¼ T(n1)
þ Kp {we(n) we(n1) } þ Ki we(n)
T(n)
(16)
and T (n21)
are the output of the PI controller
where T (n)
(after limiting it to a suitable value) and ve(n) and ve(n21)
refer to speed error at the nth and (n 2 1)th instants. Kp
and Ki are the proportional and integral gain constants.
are fed to the
The flux control signal (imr) along with T (n)
vector controller, which computes the flux producing
), torque component of current
component of current (i ds
(iqs), slip speed (v2) and the flux angle (c) as follows
ids
Dimr
¼ imr þ tr
Dt
iqs
¼
w2 ¼
T
kimr
iqs
(17)
(18)
(19)
[15] CHEN C.L., HORNG G.K.: ‘A new passive 28-step current
shaper for three-phase rectification’, IEEE Trans. Ind.
Electronics, 2000, 47, (6), pp. 1212– 1219
Y(n) ¼ Y(n1) þ (w2 þ wr )Dt
[16] SINGH B., BHUVANESWARI G., GARG V.: ‘Polygon connected
autotransformer based 24-pulse converter for harmonic
mitigation’. Pending Indian Patent, filed January 2006
C(n) and C(n21) are the value of rotor flux angles at nth and
(n 2 1)th instants, respectively, and Dt is the sampling time,
which is taken as 100 ms.
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039
tr imr
(20)
373
& The Institution of Engineering and Technology 2009
www.ietdl.org
These currents (ids
, iqs) in synchronously rotating frame are
, ibs, ics)
converted to stationary frame three-phase currents (ias
as follows
ias
¼ iqs
sin Y þ ids
cos Y
pffiffiffi
1
ibs
¼ {cos Y þ 3 sin Y }ids
2
pffiffiffi
1
þ { sin Y þ 3 cos Y }iqs
2
ics ¼ ias þ ibs
374
& The Institution of Engineering and Technology 2009
, ibs
and ics
)
These three-phase reference currents (ias
generated by the vector controller are compared with the
sensed motor currents (ias , ibs and ics). The calculated
current errors are
(21)
ike ¼ iks
iks , where k ¼ a, b, c
(22)
(23)
(24)
These current errors are amplified and fed to the PWM
current controller, which controls the duty ratio of different
switches in VSI. The VSI generates the PWM voltages
being fed to the motor to develop the torque required to
maintain the rotor speed equal to the reference speed.
IET Power Electron., 2009, Vol. 2, Iss. 4, pp. 364– 374
doi: 10.1049/iet-pel.2008.0039