ISSN 2348–2370
Vol.07,Issue.09,
August-2015,
Pages:1502-1507
www.ijatir.org
Analysis of Independent Two Induction Motors Drive Fed by A Four-Leg Inverter
B. MALLIKA REDDY1, K. RAVI KUMAR2
1
2
PG Scholar, Dept of EEE, Vasavi College of Engineering, Hyderabad, India, Email: mallika.mythri@gmail.com
Assoc Prof, Dept of EEE, Vasavi College of Engineering, Hyderabad, India, Email: ravikadali12345@rediffmail.com
Abstract: AC Induction motors plays key role in industries
due to its advantages. To make the induction motor drives
cost efficient, the paper presents the analyses of the
independent two three-phase Induction Motors (IMs) fed
by a Four-Leg Inverter (FLI). The FLI is a single inverter
that can drive two three-phase ac induction motors
independently. The inverter consists of four legs and two
capacitors connected in series. The U and V phases of both
motors are connected in each leg of the inverter and the W
phase of both motors is connected to the neutral point of
two-split capacitors. The pulse-width modulation technique
in three-phase voltage source inverter is not directly
applicable for the FLI because only two phases can be
modulated. The modulation technique for the FLI,
Expanded Two-Arm Modulation (ETAM) has been
implemented and the two induction motors are
independently controlled by V/f control. This paper also
analyzes about the neutral point potential of two-split
capacitors and its effect on the inverter output voltage. The
proposed
model
has
been
analyzed
using
MATLAB/SIMULINK and the results have been validated
with the theoretical results.
motors independently. This paper presents the simulation
results of the FLI fed two induction motor drive and they are
validated with the analytical results.
Keywords: Four Leg Inverter (FLI), Expanded Two-Arm
Modulation (ETAM), Two Induction Motors (IM) drives.
Figure1. Main circuit architecture of FLI.
I. INTRODUCTION
Induction motor also known as asynchronous motor is
now ruling the industries with many advantages. To control
the speed of the Induction motor as required, we adopt the
power electronic devices. Much advancement has been
seen in the controlling of Induction motor drive. For the
sake of cost reduction, less inverter losses and low space
the switches of the inverter which is fed to the induction
motor has been reduced. A four switch inverter [1]-[7] for
one motor, five-leg inverter [8]-[9], four-leg inverter(FLI)
[10]-[11] for controlling two induction motor have been
studied. In this paper, we are analyzing the FLI fed two
induction motors drive. FLI consists of four legs with two
switches in each leg and two capacitors connected in the
fifth leg. One phase of two induction motors is shared and
connected to the neutral point of two split capacitors. As
the pulse width modulation technique is not applicable
directly to FLI, we have adopted Expanded two-arm
modulation (ETAM) for controlling the FLI. Moreover in
this paper we are analyzing the neutral point voltage of the
two split capacitors and controlling the two induction
II. FLI FED TWO INDUCTION MOTORS CIRCUIT
ARCHITECTURE
TABLE 1: DESCRIPTION OF SYMBOLS
Figure 1 shows the circuit of FLI fed two induction motors.
The FLI has four legs and two capacitors connected in series.
The U1, V1, U2, V2 phases of the inverter are connected to
Copyright @ 2015 IJATIR. All rights reserved.
B. MALLIKA REDDY, K. RAVI KUMAR
the U, V phases of two induction motors respectively. The
shown in table 2. It is to be noted that
is three levels and
W phase of two induction motors is shared and connected
,
are two levels.
commonly to the neutral point of split capacitors. And the
table 1 shows the notation of voltages and currents,
Table II. Output Voltage Level
description of different symbols used.
III. NEUTRAL POINT POTENTIAL OF TWO-SPLIT
CAPACITORS
The neutral point potential of two split capacitors
is
given by the following equation,
(1)
Where,
is the fluctuating component of
.
From (1) it is clear that the
is changing around /2.
The fluctuating component depends on the peak value of
both the W phase currents of IM and it is inversely
proportional to the capacitance. This drift phenomenon is
observed at the starting of the motor, motor load and speed
change conditions. This drift is reducing the voltage utility
factor (VUF) of FLI. So, it is necessary to restrain this drift
which is analyzed theoretically.
IV. FLI OUTPUT VOLTAGE
Equation (2), (3) defines the switching strategy of
switches in each leg of FLI. The switches in the same leg
should not open or close simultaneously to make path to
load currents and to prevent the over currents respectively.
= 1, Switch is closed
= 0, Switch is opened
V. CONTROLLING TECHNIQUE OF FLI
A. ETAM
The pulse width modulation of three phase voltage source
inverter cannot be directly used here for FLI since only two
phases can be modulated. So, we apply Expanded two arm
modulation technique (ETAM) [9] in which the U and V
phases are modulated. In the ETAM, inverter U (V) phase
voltage command in the IM I are as follows,
(6)
Where
is the inverter phase voltage command for the
IM .
is the actual phase voltage command of the IM .
“*” is the command value.
can be defined as follows,
(2)
(7)
( = 1, 2, 3, 4; =1, 2)
Equation (3) shows the switching restriction in each leg
of FLI,
=1
(3)
Where
and
are the modulation index and fundamental
angular frequency of the IM respectively.
is the initial
phase angle to phase voltage of IM . Substituting (7) into (6),
we obtain
By following the above switching functions and equation
(1), the inverter phase voltages are given by equation (4),
(4)
The output line voltage of the inverter to the IM are
obtained from the inverter phase voltages as follows,
(5)
Where,
,
,
are the U-V, V-W and W-U
line voltages in the motor i. By substituting (2) in (4), the
output line voltages of FLI for both IMs are obtained and
(8)
Thus, the phase voltage commands ( ,
) are obtained
and it is to be noted that the phase difference between the two
phase voltage commands is .
B. Unbalanced Compensation
To analyze the FLI, it’s better to consider one motor for
easy understanding. For one motor, the following figure 2
shows the equivalent circuit of four-switch inverter. In the
figure 2, the motor is approximated to a star connected load
with impedance Z.
is the neutral point of the load.
Applying Kirchhoff’s voltage law to figure 2, it follows as
International Journal of Advanced Technology and Innovative Research
Volume.07, IssueNo.09, August-2015, Pages: 1502-1507
(9)
Analysis of Independent Two Induction Motors Drive Fed by A Four-Leg Inverter
and this compensation is known as Drift
compensation. If the drift is not compensated then over
modulation may be caused. The reference signals
are
as shown in equation (14)
(14)
These reference signals are to be compared with the
carrier signal whose amplitude is chosen as one and frequency
is 5 kHz. The figure 3 shows block diagram of the ETAM
technique in FLI.
Figure 2. Equivalent circuits for four-switch inverter.
Solving the equation (9) and obtain the induction motor
three-phase currents as follows,
(10)
Substituting (1), (8) in equation (10), it is obtained as
(11)
It is to be noted that the three-phase currents in IM with
ETAM are unbalanced currents. To obtain balanced threephase currents, it is necessary to do unbalanced
compensation, As an unbalanced compensation,
component is added to
as follows,
(12)
Figure3. Block diagram of carrier based ETAM.
VI. VUF OF FLI
VUF has to be calculated to understand the capacity of
inverter. The VUF is defined as the ratio of maximum output
voltage of inverter to the dc-bus voltage. The VUF of one
motor is expressed as,
(15)
Where,
is the maximum modulation index. To
avoid over modulation the constraint that must be satisfied is,
Substituting (1) and (12) into (10), it is obtained as
(16)
(13)
Substituting (7) and (14) into (16), it is obtained as
Thus, the three phase balanced currents are obtained with
unbalanced compensation.
C. Drift Compensation
The drift component,
has been added to
for
obtaining the three-phase balanced currents. The drift of
the
component in the steady state has to be
eliminated from the reference signals. This is done by
passing the error between the command signal which is
taken as zero command and
to the proportionalintegral (PI) controller. The output of the PI controller is
(17)
Where,
| is the maximum magnitude of
. So
to increase the VUF of FLI, it is needed to decrease the value
of
|.
VII. CONSTANT V/F CONTROL
Figure 4 shows the equivalent circuit of IM without a load.
In the figure 4, V is the phase voltage of IM.
is the
excitation current, Rs is the stator resistance, is the stator
inductance,
is the internal induced voltage, and M is the
International Journal of Advanced Technology and Innovative Research
Volume.07, IssueNo.09, August-2015, Pages: 1502-1507
B. MALLIKA REDDY, K. RAVI KUMAR
mutual inductance. The KVL equation for figure 4 is as
TABLE III: Ratings and Parameters of Tested IM
follows,
(18)
Figure 4. Equivalent circuit of IM without a load.
Where
is the fundamental angular frequency in the
IM. “•” indicates phasor. Squaring on the both sides to the
equation (18), it is obtained as
(19)
Where,
the value of
.
is the rated frequency. Solving for
,
The dc voltage is 282 V. The value of capacitor is 9900
μF. The frequency command of the IM1 is accelerated up to
20 Hz in the direction of order rotation in 0 s, 20 Hz in the
direction of order rotation from 2.0 s to 4.0 s, and decelerated
to 17 Hz in the direction of order rotation in 4.0 s, and 17 Hz
in the direction of order of rotation from 5.0 s. The frequency
command of the IM2 is accelerated up to 16 Hz in the
direction of reverse rotation in 0 s, 16 Hz in the direction of
reverse rotation from 2.0s to 7.0s, decelerated to 12 Hz in the
direction of reverse rotation in 7.0 s, and 12 Hz in the
direction of reverse rotation from 8.0 s. Figure 6 shows the
reference signal waveforms of IM1 and IM2.
(20)
Where,
is rated voltage. Solving for the modulation
index from (19) and (20), it is obtained as [11]
(21)
Where,
is the frequency command in the IM . Figure 5
shows the block diagram of V/F control.
Figure 6. Reference signal waveforms of both IMs.
It is to be noted that the U and V phases are unbalanced
because
is added to them which is shown in (14). Figure
7 shows the rotor speeds of IM1 and IM2. It is to be noted that
Figure 5: Block diagram of V/F control.
both the actual and command speeds are matching and two
IMs are driving independently. Figure 8 and 9 shows the three
VIII. EXPERIMENTAL RESULTS
phase current waveforms of IM1 and IM2 respectively. It is
A. FLI characteristics
noted that balanced three phase currents are obtained for both
In order to demonstrate the independent driving
IMs. Figure 10 shows the U-V, V-W and W-U line voltages of
characteristics of two IMs, an FLI fed two induction
IM1. U-V line voltage has three voltage levels which are –E,
motors drive has been implemented in MATLAB simulink.
0, E. V-W and W-U line voltages have two voltage levels
Table 3 shows the ratings and parameters of two IMs
which are –E/2 and E/2. The validity of table 2 has been
which are identical.
confirmed and IM2 has identical line voltages like IM1.
International Journal of Advanced Technology and Innovative Research
Volume.07, IssueNo.09, August-2015, Pages: 1502-1507
Analysis of Independent Two Induction Motors Drive Fed by A Four-Leg Inverter
Figure10. Line voltages of IM1.
Figure 7. Speeds of IM1 and IM2.
B. Characteristics in Capacitor Change
The purpose to change the capacitance is to investigate the
change in drift with change in capacitance. Figures 11 and 12
shows the neutral point potential waveform of two split
capacitors at C = 9900 μF and C = 3300 μF respectively
without compensation. It is to be noted that the drift has been
increased in C = 3300 μF compared with C = 9900 μF. The
drift is seen at the starting time and when speed changes.
Figure 8. Three phase current waveforms of IM1.
Figure11. Neutral point potential of two capacitors for C=
9900 μF without compensation.
Figure 9. Three phase current waveforms of IM2.
Figure 12: Neutral point potential of two capacitors for C=
3300 μF without compensation.
International Journal of Advanced Technology and Innovative Research
Volume.07, IssueNo.09, August-2015, Pages: 1502-1507
B. MALLIKA REDDY, K. RAVI KUMAR
Figures 13 and 14 shows neutral point potential of two
X. REFERENCES
split capacitors at C = 9900 μF and C = 3300 μF with
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with the compensation. As shown in (1), the drift is
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inversely proportional to the capacitance. The drift has
[2] Tuyen D. Nguyen, Hong-Hee Lee and Hoang M. Nguyen,
been clearly increased from C = 9900 μF to C = 3300 μF.
“Adaptive Carrier-based PWM for a Four-Switch Three-Phase
However, the potential in the steady state has almost
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maintained 141 V i.e., half of the dc bus voltage.
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[3] FredeBlaabjerg, Dorin O. Neacsu, John K. Pedersen,
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Figure 13. Neutral point potential of two capacitors for
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Figure 14: Neutral point potential of two capacitors for
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IX. CONCLUSION
September/October 2011.
In this paper, a FLI fed two induction motors drive has
been modeled using MATLAB/SIMULINK. With the FLI
fed two induction motors drive, the cost of the drive, the
complexity of the control strategy and the inverter losses
have been reduced by making use of less number of
switches of FLI. The neutral point potential of two split
capacitors has been analyzed and compensated using the
compensation techniques. The modulation technique
(ETAM) to the FLI has been implemented. With
consideration of V/F control strategy, the two induction
motors are independently controlled. Thus, the theoretical
equations have been validated with simulation results of
the proposed model.
International Journal of Advanced Technology and Innovative Research
Volume.07, IssueNo.09, August-2015, Pages: 1502-1507