three-dimensional flux vector modulation of
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Three-Dimensional Flux Vector Modulation of
Four-Leg Sinewave Output InvertersDhaval C. Patel, Rajendra R. Sawant, Member, IEEE, and Mukul C. Chandorkar, Member, IEEE
AbstractThe time-integral of the output voltage vector ofa three-phase inverter is often termed as the inverter fluxvector. This paper addresses the control of a three-phase four-leg sinewave output inverter having an LC filter at its output,by controlling the flux vector in three dimensions. Flux vectorcontrol has the property that the output filter resonance isactively damped by the output voltage control loop alone. Further,the inverter switching action inherently regulates the outputvoltage rapidly against dc bus voltage variations. Flux vectorcontrol of sinewave output inverters finds several applicationsin three-phase four-wire systems. This paper presents the fluxmodulation method for three-phase four-leg inverters feeding
unbalanced and nonlinear loads. All the necessary steps for thedigital implementation of the flux modulator are presented. Theswitching behavior of the modulator has been evaluated, whichis useful for variable fundamental frequency applications of theinverters. To provide experimental validation, the modulator isimplemented as a part of the control system for a stand-alonethree-phase four-leg inverter with an LC filter at its output.Control system details are also provided. Experimental resultsindicate the effectiveness of the modulator and the control systemin providing balanced voltages at the output of the LC filtereven under highly unbalanced conditions with nonlinear loads.The resonance damping and voltage regulation properties of themodulator are also apparent from the experimental results.
Index TermsIntegral space vector modulation, Flux modula-tion, Four-leg inverter.
I. INTRODUCTION
CONVENTIONAL three-phase three-wire inverters are
suitable for supplying three-phase balanced loads such
as induction motors. For unbalanced three-phase loads such
as those formed by unequal single-phase loads connected to
the three-phase system, inverters should be able to provide
a path for the neutral current. There are two main ways for
doing this with three-phase inverters.
Inverters with split dc link capacitors [1] Inverters with fourth (neutral) leg [2][6] (see Fig. 1)
The higher dc link utilization, requirement of smaller dc link
capacitors and flexibility in control are inherent advantages of
four-leg inverters over split dc link capacitor inverters. Four-
leg inverters can be used for applications such as stand-alone
sinewave output inverters for non-linear unbalanced loads,
Manuscript submitted on February 10, 2009; revised May 22, 2009.Accepted for publication on July 14, 2009.
Copyright c2009 IEEE. Personal use of this material is permitted. How-ever, permission to use this material for any other purposes must be obtainedfrom the IEEE by sending a request to [email protected]
Dhaval C. Patel, Rajendra R. Sawant, and Mukul C. Chandorkar arewith Department of Electrical Engineering, Indian Institute of Technol-ogy Bombay, Mumbai 400076 INDIA e-mail: ([email protected]; [email protected]; [email protected])
Snp Sap Sbp
Snn San Sbn
Scp
Scn
AB
C
N
abc
n
Vdc
Ln
+
-
Linear/NonlinearBalanced/Unbalanced
Load
Four-Leg VSI
LC Filter
Fig. 1. Four-leg sinewave output voltage inverter
distributed generation interfaces, microgrids, neutral currentcompensators and active filters [6].
Space vector modulation methods for four-leg inverters have
been presented in [2][6]. Space vector modulation for four-leg
inverters is complex [2], [6]. However, it has advantages such
as low output distortion, suitability to digital implementation,
constant switching frequency and good dc bus utilization [7].
The inverter flux vector is the time-integral of the inverter
switching voltage vector. Inverter switching based on the
control of the flux vector has several advantages in the control
of sinewave output inverters having LC output filters. In
contrast to voltage modulation control methods, the output
voltage control loop alone with a flux modulator is sufficient
to actively damp the output filter resonance [8]. Further,the inverter switching inherently regulates the output voltage
against dc bus voltage variations. The method also lends itself
to easy digital implementation on a processor or a field-
programmable gate array (FPGA).
Two-dimensional flux vector modulation of three-leg invert-
ers was presented in [8], [9]. Grid connected applications of
three-leg sinewave output inverters using flux vector modula-
tion were discussed in [8]. A flux vector modulator for a fuel
cell inverter was presented in [10]. An application for active
filter was discussed in [11].
An undesirable feature of flux modulators is the variable
inverter switching frequency that results from the tracking of
the flux reference vector using inverter switching within ahysteresis band. The switching frequency characteristics of the
flux modulator for a three-leg inverter were discussed in [8].
A solution to the problem of variable switching frequency was
presented in [12], [13], which resulted in constant switching
frequency.
Charge modulator for current source inverter, an analogy of
the flux modulator, was presented in [14]. A flux modulator
designed in the synchronous reference frame was employed in
[14][16]. A comparison of different modulators for inverter
control was presented in [14]. An analysis of a flux modulator
was presented in [17]. A voltage modulation index in the
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3
V1
V4
V5
V6
V7
V14
q
d0Reference Flux Vector
Actual Flux Vector
Fig. 3. Graphical representation of reference flux tracking
III. FLU X MODULATION FOR FOU R-L EG INVERTER
A. Principle of the Flux Modulator
The inverter flux vector is defined as
(t) =
t0
V d + (0) (2)
In this, V is the inverter output voltage vector (Fig. 2.)In three-dimensional flux vector modulation, the vector
is made to track a reference vector
by choosing anappropriate sequence of inverter output voltage vectors. An
inverter voltage vector is selected on the basis of the error
between and , so that moves towards . Fig. 3 showsthe actual flux vector tracking the reference flux vector
in the three-dimensional qd0 space. The flux vector erroris sampled at regular intervals T, and the the inverter outputvoltage vector is chosen so as to keep the vector error within
a tolerance band. This is detailed in the next section.
B. Implementation of the Flux Modulator
The flux modulator is implemented in discrete-time on a
digital signal processor (DSP). The sampling time step for
the discrete-time implementation is T. This is the time stepat which the error between the reference and the actual flux
vector, , is sampled for corrective action. In order torealize flux modulator for a four-leg inverter it is necessary to
1) identify the sector on the q d plane in which qd, theq d plane projection of the reference flux vector ,is located, as shown in Table II and Fig. 4
2) generate the error bits for the q, d and 0axiscomponent errors as shown in Table III
3) select the inverter voltage vector that reduces the errors
in the q, d and 0axis components as shown inTables IV and V.
1) Sector identification: The location of qd identifies oneof six sectors (I. . .VI) on the q d plane. This is shownin Table II and Fig. 4. The sector is identified by limits
to the slope of the tangent to the trajectory of qd. Theselimits are given in Table II. It is important to note that,
depending on the application, the trajectory of qd may ormay not be a circle. In applications with balanced loads, the
trajectory would typically be a circle. However, if the inverter
has to produce balanced output voltages when unbalanced and
nonlinear loads are present, the trajectory of qd will not bea circle. Both situations are shown in Fig. 4. In Fig. 4, the
tangents are denoted as T1. . .T6 and the sectors as I. . .VI.
TABLE IISEC TOR WITH C OR RESPONDING LIMITS OF TANGENT SLOPE
Limits of tangent slope Sectors
/3 T < 2/3 I2/3 T < II
T < 4/3 III4/3 T < 5/3 IV5/3 T < 2 V
0 T < /3 VI
T1
T1
T2T2
T3T3
T4
T4
T5T5
T6 T6
II
IIII
III
III
IV
IV
VVVI
VI
qd
(a) (b)
q q
ddFlux Vector Trajectory
Fig. 4. Sector identifi cation for (a) balanced and (b) unbalanced fluxtrajectories
2) Error bits generation: The errors in the q, d and0axis flux vector components are q q, d d and0 0. These errors are used to determine three bits Sq,Sd and S0 as shown in Table III. In this table, the subscript xstands for one of q, d and 0. The error tolerance band is h.
3) Inverter voltage vector selection: The sector information
and error bits determined above are used to select an appropri-
ate inverter voltage vector for output during the current time
step. The selected vector reduces the error during thetime step.
There are eight possible inverter voltage vectors which can
be selected for any given sector. These are given in Table IV.
Further, there are eight possible combinations of the three error
bits Sq, Sd and S0. Each possible vector can correct for a
TABLE IIIER R OR B ITS GENER ATION
Comparison of Vectors Error Bit Next Action
x x h Sx = 1 Increase xx
x h Sx = 0 Decrease
x
h < x x < h Sx = Sx No Change
TABLE IVPO S S I B L E S W I T C H I N G V E C TO R S F O R E A C H S E C T OR
Sector Possible Vectors
I V0 V1 V4 V5 V12 V13 V14 V15II V0 V1 V4 V5 V6 V7 V14 V15III V0 V1 V2 V3 V6 V7 V14 V15IV V0 V1 V2 V3 V10 V11 V14 V15V V0 V1 V8 V9 V10 V11 V14 V15VI V0 V1 V8 V9 V12 V13 V14 V15
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Fundamental frequency f (Hz)
Switchingfrequencyfsw
(Hz) 1.50nom
1.25nom
1.00nom
0.75nom
0.50nom
0.25nom
00
200
400
600
800
1000
1200
1400
1600
1800
2000
10 20 30 40 50 60 70 80 90 100
Fig. 7. Switching frequency characteristics for different
Normalized output frequency f/fnom
Normalizedswitchingfrequencyfsw
/f
h = 0.01nom
0.015nom
0.02nom
0.025nom
0.03nom
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10
20
30
40
50
60
70
80
90
100
Fig. 8. Normalized switching characteristics
The maximum possible value of reference flux to getoperation in the linear region is given by
max = nomnom
VdcVdc,nom
(7)
The flux reference vector must be contained in a sphere
of radius max centered at the origin. Here, Vdc,nom isthe nominal dc-bus voltage, which can produce the nominal
inverter output voltage at the nominal frequency and nominal
flux reference magnitude nom. The maximum flux referencecan be calculated using (7) on the basis of the dc-bus voltage
feedback Vdc and the desired output frequency [8].Simulations of switching frequency characteristics are pre-
sented here for a nominal frequency fnom = 50 Hz andnominal angular velocity nom = 2fnom. The dc bus voltageis assumed to be at its nominal value.
Change of the switching state from ON to OFF and OFF
to ON are considered as separate events in the counting of
switching in all four legs. The number of switching events is
averaged over five fundamental cycles.
Fig. 6 shows the averaged switching frequency fsw as afunction of the output frequency f, with the hysteresis bandh as the parameter. For Fig. 6, the integration time step is set
as T = 20 s. The flux reference magnitude is set as
=
nom, if nom maxmax, if nom >
max
(8)
where nom and max are calculated by (6) and (7), respec-
tively. (8) ensures that the modulator remains in the linear
region, over entire range of the fundamental frequency f. Thecurves of Fig. 6 are independent of the dc-bus voltage Vdcbecause the tolerance h is represented as a fraction of thenominal flux nom.
Fig. 7 shows the averaged switching frequency fsw as afunction of the output frequency f, with the reference fluxmagnitude as the parameter. The hysteresis band value isfixed at h = 0.01nom and integration time step T = 20s.
Fig. 8 shows normalized switching characteristics derived
from the variable hysteresis band characteristics shown in
Fig. 6. These plots are useful during variable fundamental
frequency applications of the inverter, as they permit the
implementation of a variable hysteresis band to keep the
switching frequency constant.
V. FOU R-L EG SINEWAVE OUTPUT INVERTER CONTROL
Fig. 9 shows the closed loop control system for a stand-
alone four-leg sinewave output inverter with an LC filter. The
inverter and filter are required to supply regulated and balanced
sinusoidal voltages to unbalanced and nonlinear loads. As
shown in Fig. 9, the reference voltage vector components are
denoted by Eeqref, Eedref and E0ref. The superscript e denotes
quantities in the synchronously rotating qe de referenceframe. These are derived through transformation of phase
reference voltages from the a b c frame.
The q d plane component vector of the reference voltagevector is Eqd. This vector component is controlled by the two-dimensional flux control method detailed in [8]. The gains of
the q and daxis synchronous frame PI controllers shownin Fig. 9 are computed accordingly. The control of the 0axisvoltage is given below.
The model of an LC filter in q d 0 coordinate isVqd0 = Lqd0
ddt
iqd0 + Eqd0 (9)
Lqd0 =
Lf 0 00 Lf 0
0 0 Lf + 3Ln
(10)
Vqd0, iqd0 and Eqd0 are inverter voltage, inverter output currentand filter terminal voltage respectively. The state equations of
the inverter and filter for the 0axis components areE0
e0
=
0 2f01 0
E0
e0
+
2f0 1Cf
0 0
v0
i0
(11)
Equation (11) remains unchanged in synchronous reference
frame. The frequency f0 =1
Cf (Lf+3Ln). The flux compo-
nent e0 is associated with the 0axis voltage component
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6
+
+
+
+
Eeqref
Eedref
E0ref
PI
PI
PI
controller
controller
controller
eqref
edref
0ref
qref
dref
Eeq
Eed
Eq
Ed
E0
ejt
ejt
Ln
n
Lf
Cf
Vabc iabc
Eabc
Eabc
Switching Pulses
FLUX
MODULATOR
FOUR LEGINVERTER
abcto
qd0
Load
Fig. 9. Stand-alone four-leg sinewave output inverter system
across the filter capacitor, and v0 is associated with the
0axis voltage component at the inverter terminals.With a PI regulator, the close loop state equations for the
0axis component are E0e0
v0
=
0
2f0
2f0
1 0 0ki0 kp02f0 kp02f0
E0e0
v0
+
0 0
1Cf
0 0 0ki0 kp0 kp0
1Cf
E0refE0ref
i0
(12)
The characteristic polynomial for this system is
Fs = s3 + kp0
2f0s
2 + 2f0 (1 + ki0) s (13)
This can be used to determine the PI regulator gains for a
specified dynamic response.
V I . EXPERIMENTAL RESULTS
To provide experimental validation, the flux modulator and
voltage control system described above was implemented
to control a stand-alone four-leg sinewave output inverter.
The power circuit was built with four insulated gate bipolar
transistor (IGBT) legs. The IGBT assembly was rated for 35 Arms current and 1200 V dc bus with 850 F/1200 V dc linkcapacitors. The LC filter components values were Lf = 3mH, Ln = 3 mH and Cf = 200 F. The entire control
system including the flux modulator was implemented on aplatform with a Texas Instruments 32-bit floating point DSP
TMS320VC33 with a 13.3 ns instruction cycle. The samplingtime for the control system was T = 20 s.
The synchronous reference frame PI controller gains for
controlling Eqd were set at Kpq = 0.0023, Kiq = 0.175,Kpd = 0.000346, and Kid = 0.538. The gains for the 0-axiscontroller were Kp0 = 0.1 and Ki0 = 0.08. The suffixes pand i stand for proportional and integral gains respectively.The suffixes q, d and 0 stand for the q d 0 coordinates.
Fig. 10 shows the phase voltage VCN and the line voltageVBC at the inverter terminals (Fig. 1.) These were obtained
VCN
VCN
VBC
VBC200 V/div
200 V/div
2 ms/divTime
Fig. 10. Experimental phase and line voltage at inverter terminals
with only the flux modulator, for a 50 Hz output frequency,with balanced flux references. The q and daxis flux refer-ences each had a magnitude of 0.5 Vs, and the 0axis fluxreference was 0 Vs. The value of the tolerance band h = 0.01Vs. The inverter dc bus voltage was 320 V.
Experiments were performed to test different load condi-
tions, such as balanced/unbalanced and linear/nonlinear three-
phase loads. Here the waveforms for two different load con-
ditions are shown.Fig. 11 shows waveforms for a three-phase diode bridge
rectifier load on the inverter. The dc side of the rectifier has
a filter capacitor and a resistive load. The upper three traces
show phase voltages and the corresponding phase currents.
The lowest trace shows the inverter dc link voltage. Initially
the rectifier was not connected to the inverter. It was switched
on to the inverter at a certain time. Fig. 11 shows the no-
load, transient, and loaded steady state performance of the
system. The high quality sinewave voltage output under no
load shows the effectiveness of the active damping of the LC
filter resonance.
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7
VdcVdc
iaia
ibib
icic
EaEa
EbEb
Ec
Ec
Time
40 V/div
40 V/div
40 V/div
50 V/div
8 A/div
8 A/div
8 A/div
20 ms/div
Fig. 11. Experimental waveforms with three-phase rectifi er load
VdcVdc
inin
iaia
ibib
icic
EaEa
EbEb
EcEc
Time
40 V/div
40 V/div
40 V/div
50 V/div
8 A/div
8 A/div
8 A/div
3.3 A/div
20 ms/div
Fig. 12. Experimental waveforms with unbalanced linear load and three-phase rectifi er
VphVph
Vdc
Vdc
50 V/div
50 V/div
200 ms/divTime
Fig. 13. Experimental result of voltage regulation of flux modulator
Load
currentsia
,ib
,ic(A)
Time (s)
ia ib ic
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
20
10
10
20
Fig. 14. Experimental load currents for unbalanced linear and nonlinear load
Magnitude(%
offundamental)
Frequency (Hz)
Fundamental (50 Hz) = 112.4 V peakTotal Harmonic Distortion (THD) = 4.20 %
100
80
60
40
20
00
200 400 600 800 1000 1200 1400 1600 1800 2000
Fig. 15. Harmonic spectrum of the load voltage Ea
Fig. 12 shows waveforms with unbalanced linear load and
balanced nonlinear loads connected to the inverter. The upper
three traces show phase voltages and the corresponding phase
currents. The next trace shows the neutral current supplied bythe inverter to the unbalanced load. The lowest trace shows
the inverter dc link voltage. As in the previous experiment,
the inverter was operated on no load initially. The load was
switched on to the inverter subsequently.
Voltage regulation of the flux modulator is shown in Fig. 13.
Here the flux modulator was operated without the output
voltage control loop. The reference flux magnitudes were set as
a = 0.4, b = 0.4 and c = 0.4. The upper trace shows theoutput phase voltage across the LC filter capacitor. The lower
trace shows the inverter dc link voltage. In the experiment, the
dc link voltage was reduced from 330 V to 250 V. It is apparentthat there is no change in the output voltage amplitude even
after the dc link voltage is reduced.The performance of the four-leg inverter controlled by the
control system shown in Fig. 9 is shown here by means of
oscillograms and harmonic spectrum plots. Combinations of
balanced and unbalanced, linear and nonlinear loads were
connected to the inverter. The load on the inverter consisted of
three single-phase diode bridge rectifiers with unequal dc-side
resistances, in parallel with unbalanced linear (resistance in
series with inductance) load. This was a case of severe load
unbalance, both for the linear and the nonlinear load. The peak
of the distorted load current was about 20 A. Fig. 14 showsthe three-phase load current oscillogram. The highly distorted
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8
VoltagesEe q
,Ee d
,E0
(V)
Time (s)
Eeq
EedE0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
120
100
80
60
40
20
0
020
Fig. 16. Experimental load voltages in the synchronous reference frame
q (Vs)d (Vs)
0
(V
s)
0.1
0.2
0.20.2
0.4
0.4
0
00
0.1
0.2
0.2 0.20.40.4
Fig. 17. Experimental inverter flux vector locus for unbalanced linear andnonlinear load
and unbalanced nature of the load is apparent from this.
Fig. 15 shows the load voltage harmonic spectrum. It is
apparent that all harmonics are negligibly small compared to
the fundamental. Fig. 16 shows the load voltages Eeq , Eed
and E0 in the synchronous reference frame (refer Fig. 9.)The references were set to be Eeqref = 110 V, E
edref = 0
V and E0ref = 0 V. It is apparent that E0 is controlledclose to zero, indicating that the zero sequence load voltage
component is negligibly small. The control system orients the
load voltage vector so that the daxis voltage component Eedis zero on average, and the qaxis component Eeq has thedesired magnitude.
In order to achieve balanced sinusoidal load voltages in thepresence of such severe load nonlinearity and unbalance, the
inverter flux vector locus needs to deviate substantially from
a circle lying in the qd plane. The inverter flux vector locusis shown in Fig. 17.
VII. CONCLUSION
A flux vector modulation method has been proposed for
the control of a sinewave output four-leg inverter. Digital
processor implementation of the flux modulator for a four-leg
inverter is simple. This paper has described the implementation
details of the modulator. The switching behavior described
here is useful for a variable hysteresis band operation of the
modulator. This paper has also described the implementation
of a voltage control system to regulate the output sinewave
voltages feeding unbalanced and nonlinear loads using the flux
modulator. The paper has presented experimental validation
of the modulator and control system. The results show that
the flux modulator proposed here works satisfactorily under
balanced and unbalanced, linear and nonlinear load conditions
on the inverter.
REFERENCES
[1] N.-V. Nho, M.-B. Kim, G.-W. Moon and M.-J. Youn, A novel carrierbased PWM method in three phase four wire inverters, in Proc. of IEEE
Ind. Electron. Society Conf., 2004, pp. 1458-1462.[2] R. Zhang, D. Boroyevich, V. H. Prasad, H. Mao, F. C. Lee and S.
Dubovsky, A three-phase inverter with a neutral leg with space vectormodulation, in Proc. IEEE APEC, 1997, pp. 857-863.
[3] V. H. Prasad, D. Boroyevich and R. Zhang, Analysis and comparison ofspace vector modulation schemes for a four-leg voltage source inverter,in Proc. IEEE APEC, 1997, pp. 864-871.
[4] R. Zhang, V. H. Prasad, D. Boroyevich and F. C. Lee, Three-dimensionalspace vector modulation for four-leg voltage-source converters, in IEEETrans. Power Electron., vol. 17, no. 3, May 2002, pp. 314-326.
[5] M. G. Villalva and E. Ruppert F., 3-D space vector PWM for three-leg four-wire voltage source inverters, in Proc. IEEE PESC, 2004, pp.3946-3951.
[6] R. R. Sawant and M. C. Chandorkar, A multifunctional four-leg grid-connected compensator, in IEEE Trans. Ind. Appl., vol. 45, no. 1, Jan/Feb2009, pp. 249-259.
[7] D. Shen, P. W. Lehn, Fixed-frequency space-vector-modulation controlfor three-phase four-leg active power fi lters, in IEE Proc.- Electric Power
Appl., vol. 149, no. 4, July 2002, pp. 268-274.[8] M. Chandorkar, New techniques for inverter flux control, in IEEE Trans.
Ind. Appl., vol. 37, no. 3, May/June 2001, pp. 880-887.[9] A. M. Trzynadlowski, M. Bech, F. Blaabjerg and J. Pedersen, An
integral space-vector PWM technique for DSP-controlled voltage-sourceinverters, in IEEE Trans. Ind. Appl., vol. 35, no. 5, Sept./Oct. 1999, pp.1091-1097.
[10] F. Jurado, Novel Fuzzy Flux Control for Fuel-Cell Inverters, in IEEETrans. Ind. Electron., vol. 52, no. 6, Dec. 2005, pp. 1707-1710.
[11] S. Bhattacharya, A. Veltman, D. M. Divan and R. D. Lorenz, Flux-based active fi lter controller, in IEEE Trans. Ind. Appl., vol. 32, no. 3,May/June 1996, pp. 491-502.
[12] B. Shi, M. Chandorkar and G. Venkataramanan, Modeling and Designof a Regulator for Three Phase PWM Inverters with Constant SwitchingFrequency, in European Power Electron. Conf., Toulouse, France, 2003.
[13] P. C. Loh and D. G. Holmes, A multidimensional variable band fluxmodulator for four-phase-leg voltage source inverters, in IEEE Trans.Power Electron., vol. 18, no. 2, March 2003, pp. 628-635.
[14] P. C. Loh and D. G. Holmes, A variable band universal flux/chargemodulator for VSI and CSI modulation, in IEEE Trans. Ind. Appl., vol.38, no. 3, May/June 2002, pp. 695-705.
[15] P. C. Loh and D. G. Holmes, Flux modulation for multilevel inverters,in IEEE Trans. Ind. Appl., vol. 38, no. 5, Sept./Oct. 2002, pp. 1389-1399.
[16] P. C. Loh and G. H. H. Pang, High performance flux-based two-degree-of-freedom uninterruptible power supply, in IEE Proc.- Electric Power
Appl., vol. 152, no. 4, July 2005, pp. 915-921.[17] M. Morimoto, S. Sato, K. Sumito and K. Oshitani, Voltage modulation
factor of the magnetic flux control PWM method for inverter, in IEEETrans. Ind. Electron., vol. 38, no. 1, Feb. 1991, pp. 57-61.
[18] M. Morimoto, S. Sato, K. Sumito and K. Oshitani, Single-chip mi-crocomputer control of the inverter by the magnetic flux control PWMmethod, in IEEE Trans. Ind. Electron., vol. 36, no. 1, Feb. 1989, pp.42-47.
[19] D. T. W. Liang and J. Li, Flux vector modulation strategy for a four-switch three-phase inverter for motor drive applications, in Proc. IEEEPESC, 1997, pp. 612-617.
[20] H. Xie, L. Angquist and H.-P. Nee, Novel flux modulated positive andnegative sequence deadbeat current control of voltage source converters,in IEEE Power Engg. Society General Meeting, 2006, pp. 1-8.
[21] D. C. Patel, R. R. Sawant and M. C. Chandorkar, Control of four-legsinewave output inverter using flux vector modulation, in Proc. of IEEE
Ind. Electron. Society Conf., 2008, pp. 629-634.
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Dhaval C. Patel received the B.E. degree in PowerElectronics Engineering from the Saurashtra Univer-sity, India in 2002 and the M.E. degree in ElectricalEngineering with specialization in Power Electronicsand Drives from the Gujarat University, India in2004. Currently he is working toward the Ph.D.degree at the Department of Electrical Engineering,Indian Institute of Technology - Bombay, India. Hiscurrent research interests are in the area of diagnosisand analysis of electical machines, power converters
and modulation techniques for inverters.
Rajendra R. Sawant (M2000) was born in Ma-harashtra State, India on February 19, 1968. Hereceived B. E. degree in Electrical Engineering fromMarathwada University, Aurangabad, MaharashtraState in 1988, M. Tech. and Ph. D. degree from
Power Electronics and Power Systems group, de-partment of Electrical Engineering, Indian Instituteof Technology-Bombay, India, in 1996 and 2009,respectively.
He was involved in the development of ResonantConverter based Induction Heating Systems as a
Power Electronics Consultant and Researcher from 1996 to 2002 with differentsmall scale industries in Mumbai, India. He is involved in teaching PowerElectronics and different basic subjects in Electrical Engineering for the last18 Years in Mumbai University at the undergraduate and graduate level.Presently, he is working as a Professor and Head with the Dept. of Electronicsand Telecom. at Rajiv Gandhi Institute of Technology, University of Mumbai,India. His research interest are active power fi lters and power conditioners,grid connected converter control, converters for distributed generations andmicro-grid, resonant converters for induction heating systems, simulation ofelectric circuits and systems, etc.
Mukul C. Chandorkar (M84) received the B.Tech. degree from the Indian Institute of Technology- Bombay, the M. Tech. degree from the IndianInstitute of Technology - Madras, and the Ph.D.degree from the University of Wisconsin-Madison,in 1984, 1987 and 1995 respectively, all in electricalengineering.
He has several years of experience in the powerelectronics industry in India, Europe and the USA.During 1996-1999, he was with ABB CorporateResearch Ltd., Baden-Daettwil, Switzerland. He is
currently a professor in the electrical engineering department at the IndianInstitute of Technology - Bombay. His technical interests include electricpower quality compensation, drives, and the real-time simulation of electricalsystems.