Mr.B.Ravi and Mr.E.Narasimhulu
8
Comparison of Performance Characteristics of
Five-Leg and Four-Leg Inverters Fed to Two
Different Induction Motor Drives
Mr.B.Ravi and Mr.E.Narasimhulu
Abstract—Dual three-phase voltage source inverter (Three-
VSI) system to drive two three-phase ac motors independently
is generally used. The system connects one motor to one threeVSI and requires dual Three-VSIs. Recently, for the sake of
low cost, saving space, and reduction of inverter losses to
reduce switching device counts, four-switch inverter to drive
one motor, a four-leg inverter(FLI), a five-leg inverter and sixleg inverter to drive two three phase AC motors independently
has been studied. In particular, the four leg inverter consists of
four legs and two capacitors connected in a series. One phase of
both motors is shared and connected to the neutral point of
two- sprit capacitors in common. The four leg inverter requires
eight switching devices. Finally, the four leg inverter can
decrease four switches compared with dual three-VSI systems.
Also, the pulse width modulation technique in three phases VSI
is not directly applicable for the four leg inverter because only
two phases must be modulated. The four leg inverter is a single
inverter that can drive two three-phase ac motors
independently. The inverter consists of four legs and two
capacitors connected in a series. The U and V phases of both
motors are connected in each leg, respectively, whereas the W
phase of both motors is connected in the neutral point of twosprit capacitors. Then, this work also analyzes about the
neutral point potential of two-sprit capacitors and inverter
output voltage. Simulation of this project can be carried out by
using MATLAB/Simulink.
can be said that a five-leg inverter is the similar inverter. In
this inverter, the w phase of both motors is connected to one
leg in common. Therefore, the five-leg inverter has a
problem that the switching losses in this leg are increased
compared with the other legs. The four-leg inverter can
solve this problem by using a capacitor instead of a
switching device. The four-leg inverter is a single inverter
that can drive two motors independently. We show the
structure of the four-leg inverter to fig.1. The four-leg
inverter consists of four legs and two sprit capacitors. The u
and v phases of a motor1 are connected in a leg1 and a leg2
respectively, those of a motor2 is connected in a leg3 and a
leg4 and w phase of both motors are connected in the neutral
point of the two sprit capacitors.
Moreover, this paper also analyzes about potential in the
neutral point of two-sprit capacitors and inverter output
voltage. This paper presents the simulation results of the
independent driving characteristics of two induction motors
(IMs) fed by the four leg inverter and five leg inverter
simulation results comparing, the PWM technique, and the
validity of those analytic result
2. Main Circuit Of FLI
Index Terms— five-leg inverter, FLI, PWM, sprit-capacitors.
1.Introduction
At present, most of AC motors are driven with a three-leg
inverter. But two or more alternating current (AC) motors
cannot be independently driven with a three-leg inverter.
Recently, a single inverter for driving two AC motors
independently has been studied for aiming a low-cost,
saving space and reduction of inverter losses. For example,
four-leg inverter and five-leg inverter so on. It
Fig. 1.
1
Mr.B.Ravi PG-Student, Department of Electrical and Electronics Engg.
RGMCET, Nandyal, India,
E-Mail: bravi240@gmail.com
2
Mr.E.Narasimhulu, Assist. Professor, Department of Electrical and
Electronics Engg. RGMCET, Nandyal, India,
E-Mail: narasimha206366@gmaill.com
IRET Transaction on Power Electronics and Drives (ITPED)
Main circuit of an FLI.
Fig. 1 shows the structure of the FLI to supply two threephase ac motors [1]–[2]. The inverter consists of four legs
and two capacitors connected in a series. Inverter U1 and V1
phases are connected to U and V phases of IM1,
respectively. Inverter U2 and V2 phases are connected to U
and V phases of IM2, respectively, whereas the W phase of
both motors is shared and connected to the neutral point of
two-sprit capacitors in common. vUNi, vVNi, and vWNi are
the phase voltages in the IM i (i = 1, 2). vxO (x = U1, V1,
U2, V2, W) is the inverter x phase
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Mr.B.Ravi and Mr.E.Narasimhulu
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select capacitance of capacity in the range that the motor
may drive.
TABLE 1
DESCRIPTION OF THE SYMBOLS
Phase voltage in the IM
i(i=1,2)
Inverter x phase voltage
The neutral point
potentional of two-sprit
capacitors
Phase current in the IM i
Inverter phase current
Magnitude of the DC-bus
voltage
Capacitance of two-sprit
capacitors
B. Inverter output voltage
We analyze the output voltage of the FLI to use a switching
function. Equation (2) defines a switching function. The
voltage source and connects inductive loads (for example,
RL loads, ac motors, and so on) fed to the FLI . Therefore,
they should not make the open circuit path load currents to
the leg. In other words, the switches of one leg must not be
simultaneously closed or opened. The switching constraints
discussed earlier can be expressed by
VUNi, VVNi ,VWNI
VXO
(x=U1,V1,U2,V2,W)
Vwo
iUi, iVi, iWi
iw
Switching function
E
Sji=1, switch is closed
Sji=0, switch is opened (j=1,2,3,4; i=1,2
C
(2)
Switching restriction
voltage. vWO indicates the neutral point potential of twosprit capacitors. iUi, iVi, and iWi are the phase currents in the
IM i, and iW is the inverter phase current. E expresses the
magnitude of the dc-bus voltage. C is the capacitance of
two-sprit capacitors. Table I presents the description of the
symbols. In this paper, a based point is chosen to the
negative side of dc-bus for the simplicity of analysis.
Sj1+Sj2=1
(3)
Employing the switching function and (1), the inverter phase
voltage can be expressed by the following equation:
VUiO = S2i-11E
VViO=S2i1E
(4)
Vwo = E/2 + ΔVwo
The output line voltage level of the FLI differs from the
three-VSI because the modulation in W phase cannot be
impossible in the FLI. Therefore, the output line voltage can
be defined as follows from(4):
3. Characteristics Of FLI
A. Neutral point potential of two-sprit capacitors
VUVi = VUiO−VViO = (S2i-11−S2i1) E
VVWi = VViO−VWiO = (S2i1−1/2) E − ΔVwo
VWUi = VWiO−VUiO = (1/2−S2i-11) E + ΔVwo
(5)
Where VUVi, VVWi and VWUi are the U−V,V−W and W−U line
voltages in the motor i, respectively.
TABLE II
OUTPUT VOLTAGE LEVEL
Fig 2. Equivalent circuit of the four-switch inverter.
U−V line
voltage
VUVi
−E,0,E
3 level
V−W line
voltage
VVWi
−E/2− ΔVwo, E/2−ΔVwo
2 level
(superposition of ΔVwo)
W−U line
voltage
VWUi
−E/2+ ΔVwo, E/2+ ΔVwo
2level
(superposition of ΔVwo)
VWO is given by the following equation:
Vwo=E−
∫(iw1+iw2)dt
E+ΔVwo
(1)
Where Δvwo is the fluctuating component of vwo.
From (1) vwo changes around E/2. The fluctuated
component depends on the fundamental wave frequency and
peak value of both motor currents. In other words, it will be
able to decrease when the motors are driven at lighter load
and higher speed condition and be also decrease by the
capacitor with larger capacitance. Finally, it is necessary to
IRET Transaction on Power Electronics and Drives (ITPED)
Substituting (2) into (4), the output voltage level in both
motors is obtained as table II. The VUVi is three levels.
Otherwise, the VVWi, VWUi are two levels. It must be noted that
– ΔVwo and + ΔVwo will be added to VVW and VWU
respectively.
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Mr.B.Ravi and Mr.E.Narasimhulu
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V*Vi = ZiVi − ZiWi + ΔVWO
iUi + iVi + iWi = 0.
4. PWM Technique Of FLI
A. ETAM
Since inverter W phase is constructed in the two-sprit
capacitors, the modulation in the phase is impossible.
Therefore, the PWM technique in three-phase VSI is not
directly applicable for the FLI. To obtain a balanced threephase ac voltage, only the U and V phases must be
modulated in the FLI. Then, we apply an expanded two-arm
modulation (ETAM) known as a modulation method of a
five-leg inverter [4]. In the ETAM, inverter U (V) phase
voltage command in the IM i can be expressed as follows:
V*Ui = V*UNi − V*WNi
V*Vi = V*VNi − V*WNi
(6)
*
Where V ki is inverter k phase voltage command in the IM. i
“*” is the command value. V*kNi can be defined as follows:
(9)
From (9), iUi, iVi and iWi follow that
iUi =
iVi =
(10)
iWi =
substituting (1) and (8) into(10), it follows that
iui=
sin(
iui=
sin(
iui=
sin(
(11)
V*UNi = M*i E sin(ω* i t – φ*i)
V*VNi = M*i E sin(ω* i t −
V*VNi =
M*i E
*
sin(ω i t −
– φ*i)
–
(7)
φ*i)
Where M*i and ω* i are the modulation index and
fundamental angular frequency in the IM i, respectively. φ*i
is the initial phase angular to phase voltage in the IM i.
Substituting (6) into (7), we obtain
V*Ui =
M*i E sin(ω* i t −
– φ*i)
V*Vi =
M*i E sin(ω* i t −
– φ*i).
(8)
The connection method in the FLI is equivalent to the
V−connection of a transformer for one motor. In the
V−connection of a transformer, if the phase differences of
each phase voltage command are π/3 each other, we get a
balanced three-phase voltage. As can be seen from (8), the
phase difference between V*Ui and V*Vi is π/3. Therefore,
employing the ETAM, it is possible to obtain a balanced
three-phase voltage in the FLI.
B. Neutral point potential of two-sprit
Capacitor compensation
When we analyze the FLI, we had better consider
one motor to understand it easily. For one motor, it is
possible to think that the FLI connecting two motors is
equivalent to the four-switch inverter as shown in Fig.2.
From this reason, we use a model of the four-switch inverter
to analyze the characteristic of the FLI [3],[4].
Because only output voltage of the motors are remarkable
values to be analyzed , each phase of the motor can
approximate to a load having impedance Z. Ni is the neutral
point of the load. Applying Kirchhoff’s voltage law to Fig.2,
it follows that
Fig 3.Block diagram of carrier-based PWM
Employing the ETAM, the phase current in the IMi
becomes unbalanced three-phase current. To obtain
unbalanced three-phase current, it is necessary to
compensate.
As a compensation, is added to v* ki. V* ki follows that
(12)
Substituting (1) and (12) into (10), it follows that
(13)
Adding v*ki to Δvwo, the phase current in the IMi becomes a
balanced three-phase current [5].
V*Ui = ZiUi − ZiWi + ΔVWO
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Mr.B.Ravi and Mr.E.Narasimhulu
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C. Neutral Point Potential of Two-Sprit Capacitor
Compensation
Fig. 3 shows the block diagram of PWM technique in FLI.
The PWM strategy may apply carrier-based PWM. It is
noted that the amplitude of carrier signal is often chosen as
one in the carrier-based PWM. In the FLI, defining the
reference signal of U (V) phase voltage in the IM i
compared with the carrier signal as e∗ U(V)si can be
expressed as follows:
(14)
To obtain a balanced three-phase current, ΔvWO must be
added to reference signals in each phase (“unbalanced
compensation” in Fig. 3). vWO is detected with a voltage
sensor. ΔvWO is calculated from (1). “ΔvWO drift
compensation” in Fig. 3 shows the control block diagram to
restrain the drift of ΔvWO in steady state. Zero command is
given because the drift must be restrained to zero.
The error between the command and ΔvWO is
inputted to proportional–integral (PI) controller. Δvdrift_Comp,
which is the output value of PI controller, is the value to
compensate the drift. The drift is compensated with the
addition of Δvdrift_Comp to reference signal as shown in (14). It
must be noted that the drift will be able to compensate with
only the PI controller because it has a dc component in
steady state. Comparing the reference signal in (14) with the
carrier signal, inverter U and V phases are modulated. If the
drift is not compensated, over modulation may be caused in
consideration that ΔvWO is added to each reference signal. As
a result, the VUF will be reduced, and it will be necessary to
restrain the drift.
Fig 4. Independent V/F control system in the FLI.
Fig 5. Block diagram of V/F control.
Where Mimax expresses the maximum modulation index.
When the amplitude of the carrier signal is chosen as one,
the constraint must be satisfied as
| e*usi | ≤ 1
| e*vsi | ≤ 1.
(16)
5. Dc-Bus VUF
To evaluate the inverter capacity, it is important to
calculate the VUF. The VUF is defined as the ratio of the
maximum output voltage to the inverter and the dc-bus
voltage. In the carrier-based sinusoidal PWM, this way,
defining the VUF with the maximum modulation index has
the advantage that can investigate the VUF more easily. To
connect two motors in the FLI, it should be noted that the
VUF must be defined for each motor. From the definition of
the VUF, the VUF of the motor, which is VUFi, can be
expressed by
Fig.6.Equivalent circuit of IM without a load
Substituting (7) and (14) into (16), we obtain
Mimax =
-
|ΔvWOmax|
(17)
where |ΔVwomax| is the magnitude of maximum ΔVwo.
Substituting (17) into (15), the VUF of FLI is understood to
become 50% or less.
6. Independent Constant Volts Per Hertz Control
TABLE III
Ratings and parameters of tested IM
IRET Transaction on Power Electronics and Drives (ITPED)
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Mr.B.Ravi and Mr.E.Narasimhulu
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Rated output
The number of poles
0.75
4
Rated output voltage
200 vrms
Rated current
Rated frequency
3.1 A
50 Hz
Rated speed
1410 r/min
3.8 Ω
Stator resistance
Rotator resistance
Stator inductance
sprit capacitors. The drift phenomenon of vWO cannot be
almost observed at starting time and load change compared
with no compensation. Moreover, the potential in steady
state can be maintained at 141 V = E/2. Figs. 26 and 27
show the reference signal waveforms of the IM1 and IM2 at
C = 9900 μF and C = 3300 μF with compensation. The
central point of the reference signals of and V phases can be
maintained at zero.
4.0 Ω
254.6 mH
Rotator inductance
Inertia ( IM + Load)
251.0 mH
12.05 mkgm2
Fig. 4 shows the independent constant volts per hertz (V/f)
control system of the FLI. Another V/f controller for each
IM is employed to realize two IM independent control. Fig.
5 shows the block diagram of V/f control. The V/f control
system is the system to control the frequency fi in the IM i.
Fig. 6 shows the equivalent circuit of IM without a load,
where V is the phase voltage in IM. Io is the excitation
current, Rs is the stator resistance, ls is the stator inductance,
E1 is the internal induced voltage, and M is the mutual
inductance. From Fig. 5, it follows that
=
ω ) 0+
Fig 7. FLI Of Three-phase current waveforms of the IM1
(18)
1
where ω is the fundamental angular frequency in the IM. “•”
represents phasor. When the size of both sides is squared, it
follows that
2
2
2
V = (RsIo) + (ωlsIo + E1)
(19)
where E1 = kfn. fn is the rated frequency. Solving for k, we
obtain
where Vn is the rated voltage. Solving for modulation
*
indexM i in the IM i, we obtain
Fig 8. FLI Of Three-phase current waveforms of the IM2
(21)
*
where f i is the frequency command in the IM .
7. Simulation Results
In order to demonstrate the independent driving
characteristics of two IMs, an FLI to supply two three-phase
squirrel-cage IMs has been implemented. Table III shows
the ratings and parameters of tested IMs. Both IMs are
driven by V/f control. The ratings and parameters of both
IMs are identical. The dc bus voltage is 282 V. C is 9900 μF,
and the carrier frequency is 5 kHz.The frequency commands
in the IM1 and IM2 are 20 Hz in the direction of order
rotation and 16 Hz in the direction of reverse rotation,
respectively. Fig.9 shows the neutral point potential
waveform of two-sprit capacitors with no compensation.
The drift phenomenon of vWO can be observed at starting
time and load change. The potential in steady state is 149 V.
The drift magnitude (ΔvWO−drift) is 149 − E/2 = 8 (V). Figs.
23,27 shows the neutral point potential waveform of two
IRET Transaction on Power Electronics and Drives (ITPED)
Fig 9. FLI Of W phase current waveforms
Vol. 1, Issue. 1, Oct. 2013
Mr.B.Ravi and Mr.E.Narasimhulu
Fig 10. FLI Of Speed of IM1 (f*1 = 20 Hz in the direction
of order rotation)
Fig 11. Five-Leg Inverter Of Three-phase current
waveforms of the IM1
13
Fig 14. Five-Leg Inverter Of Speed of IM1 (f*1 = 20 Hz in
the direction of order rotation)
Fig 15. FLI Of Speed of IM2 (f*2 = 16 Hz in the direction
of reverse rotation)
Fig 12. Five-Leg Inverter Of Three-phase current
waveforms of the IM2
Fig 16. FLI Of U–V phase line voltage of the IM1
Fig 13. Five-Leg Inverter Of W phase current waveforms
Fig 17. FLI Of V–W phase line voltage of the IM1
IRET Transaction on Power Electronics and Drives (ITPED)
Vol. 1, Issue. 1, Oct. 2013
Mr.B.Ravi and Mr.E.Narasimhulu
Fig 18. FLI Of W–U phase line voltage of the IMl
14
Fig 22. Five-Leg Inverter Of W–U phase line voltage of the
IMl
Fig 19. Five-Leg Inverter Of Speed of IM2 (f*2 = 16 Hz in
the direction of reverse rotation)
Fig 23. FLI of Neutral point potential of two capacitors
Fig 20. Five-Leg Inverter Of U–V phase line voltage of the
IM1
Fig 24. FLI of Reference signal Wwaveforms of induction
motor 1 at c = 9900 µF
Fig 21. Five-Leg Inverter Of V–W phase line voltage of the
IM1
IRET Transaction on Power Electronics and Drives (ITPED)
Fig 25. FLI of Reference signal Wwaveforms of induction
motor 2 at c = 9900 µF
Vol. 1, Issue. 1, Oct. 2013
Mr.B.Ravi and Mr.E.Narasimhulu
Fig 26. FLI of Reference signal Wwaveforms of induction
motor 1 at c = 3300 µF
Fig 27. Five-Leg Inverter of Neutral point potential of two
capacitors
Fig 28. Five-Leg Inverter of Reference signal Wwaveforms
of induction motor 1 at c = 9900 µF
Fig 29. Five-Leg Inverter of Reference signal Wwaveforms
of induction motor 2 at c = 9900 µF
IRET Transaction on Power Electronics and Drives (ITPED)
15
Fig 30. Five-Leg Inverter of Reference signal Wwaveforms
of induction motor 1 at c = 3300 µF
Fig 31. FLI of Reference signal Wwaveforms of induction
motor 2 at c = 3300 µF
Fig 32. Five-Leg Inverter of Reference signal Wwaveforms of
induction motor 2 at c = 3300 µF
8. Conclosion
This paper has also analyzed about the neutral point
potential of two-sprit capacitors and inverter output voltage.
Next, a modulation technique in the FLI has been also
shown. The simulation results demonstrated the
characteristics of two IM independent drives and the validity
of those analytic results. The simulation results of the
independent driving characteristics of two IMs fed by the
FLI and the validity of the PWM technique and those
analytic results have been also demonstrated.
Vol. 1, Issue. 1, Oct. 2013
Mr.B.Ravi and Mr.E.Narasimhulu
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B.Ravi was born in anantapur,in india.
He received the B.Tech (Electricl and
Electronics Engineering) degree from
Jawaharlal
Nehru
Technological
University, Anantapur in 2010 and
pursuing M.Tech (Power Electronics)
from RGM College of Engineering and Technology
(Autonomous), Nandyal, Jawaharlal Nehru Technological
University Anantapur. His area of interesting power
electronic industrial drives.
(Email:bravi240@gmail.com)
Mr.E.Narasimhulu was born in Kurnool,
in india. He received the B.Tech(Electricl
and
Electronics
Engineering)
srivenkateswara university, Thirupathi in
2009 and received the M.Tech in NITK
Surathkal,manglore in 2011. His area of
interesting
power
electronic
industrial
drives.
(Email:narasimha206366@gmail.com)
Vol. 1, Issue. 1, Oct. 2013