A Quick-Simulation Tool for Induction Motor
Drives Controlled Using Advanced
Space-Vector-Based PWM Techniques
V. S. S. Pavan Kumar Hari1 and G. Narayanan2
Department of Electrical Engineering, Indian Institute of Science, Bangalore 560 012, INDIA
Email: pavan@ee.iisc.ernet.in1 , gnar@ee.iisc.ernet.in2
Abstract— Space-vector-based pulse width modulation (PWM)
for a voltage source inverter (VSI) offers flexibility in terms of
different switching sequences. Numerical simulation is helpful
to assess the performance of a PWM method before actual
implementation. A quick-simulation tool to simulate a variety
of space-vector-based PWM strategies for a two-level VSI-fed
squirrel cage induction motor drive is presented. The simulator
is developed using C and Python programming languages, and
has a graphical user interface (GUI) also. The prime focus being
PWM strategies, the simulator developed is 40 times faster than
MATLAB in terms of the actual time taken for a simulation.
Simulation and experimental results are presented on a 5-hp ac
motor drive.
I. I NTRODUCTION
Voltage source inverter (VSI)-fed induction motor stands
among the most sought-after industrial drive configurations. A
two-level VSI realized with IGBTs is shown in Fig. 1. Pulse
+
S1
C
VDC
S3
function for R-phase is defined as
mR = 0.5 +
S5
(3)−+−
D1
D3
D5
R
Y
B
++−(2)
II
III
S4
S6
D4
S2
D6
D2
–
α
q
VREF
+−−(1)
(0)−−−
1.0
IV
VI
V
(5)−−+
This work was supported by the Department of Heavy Industry, Government
of India, under a project titled “Off-line and Real-time Simulators for Electric
Vehicles / Hybrid Electric Vehicle Systems”.
I
(7)+++
(4)−++
Fig. 1.
Two-level voltage source inverter using insulated gate bipolar
transistors.
width modulation (PWM) of the switches is required to control
the output voltage and frequency of a VSI, for a given DC bus
voltage VDC .
Generation of PWM waveforms by comparing three-phase
sinusoidal modulating waves (mR , mY and mB ) against a
common triangular carrier wave is popularly known as sine
triangle PWM (STPWM) [1]. Considering a unipolar triangular carrier with peak value Vp , the sinusoidal modulating
(1)
where Vm is the peak value of sinusoid. Modulating signals
mY and mB are phase shifted by 120◦ and 240◦ , respectively,
with respect to mR .
Addition of third harmonic to the sinusoidal modulating
functions increases the highest possible ac voltage output of
the VSI. The DC bus utilization with such third harmonic
injection PWM (THIPWM) is maximum when the amplitude
of the third harmonic added is one sixth of the fundamental amplitude. This DC bus utilization is matched by the
space-vector-based PWM (SVPWM) strategies [1]. Further,
THIPWM also reduces the total harmonic distortion (THD)
in the output current of the VSI. The THD is minimum if the
third harmonic amplitude is 25% of the fundamental amplitude
[2]. Conventional space vector PWM (CSVPWM) results in
THD, which is quite close to this [1], [2]. Bus-clamping PWM
O
C
Vm
sin ωt
2Vp
ωt = 0◦ d
+−+(6)
Fig. 2. Voltage vectors of a voltage source inverter. Magnitudes of the vectors
are normalized with respect to DC bus voltage VDC . I, II, III, IV, V and VI
are sectors [2].
(BCPWM) methods yield lower THD than CSVPWM at high
modulation indices for a given average switching frequency
[3]. Advanced bus-clamping PWM (ABCPWM) techniques,
proposed recently, outperform BCPWM methods in terms of
THD at high modulation indices [4]. ABCPWM methods have
also been shown to have other advantages such as reduced
pulsating torque [5], improved converter efficiency [2],[6] and
low acoustic noise [7] under various operating conditions.
SR
Tz 12 T1
T2
1
2 T1
Tz 12 T2
T1
1
2 T2
1
2 T1
Tz 12 T1
T2
1
1
2 T2 Tz 2 T2
T1
0
−
−
−
2
+
+
−
1
+
−
−
7
+
+
+
1
+
−
−
2
+
+
−
1
+
−
−
0
−
−
−
2
+
+
−
2
+
+
−
1
+
−
−
1
+
−
−
SR
1
SY
SY
0
0
Vp
SB
cR
1
1
0
Vp
cR
cB
SB
1
SR
1
SY
0
Vp
7
+
+
+
2
+
+
−
1
0
SB
1
Vp
cR
cB1
cB2
cR1
cR2
cY
cY
cY 2
cY 2
cB
0
1
SY 1
1
SY 2
0
SY 1
0
SY 2
SY = SY 1 ⊕ SY 2
0
cB
0
SR1
SR2
SR = SR1 SR2
SY = SY 1 SY 2
(a)
(b)
(c)
0
1
0
SB1
0
SB2
1
SB = SB1 ⊕ SB2
(d)
21
Generation of switching functions for different ABCPWM sequences (a) 0121, (b) 7212, (c) 1012 and (d) 2721 in sector I.
27
12
72
27
01
0121
(a) CSVPWM
(b) Advanced
Clamp PWM
Fig. 4.
30◦
27
01
1012
(c) Hybrid PWM
PWM techniques considered.
Most SVPWM methods synthesize the desired voltage reference vector VREF (see Fig. 2) by applying the two nearest
active vectors and the zero vector. For the reference vector
shown in Fig. 2, the active vector 1 and the active vector 2
are applied for durations T1 and T2 , respectively, as given
by (2) [8], [9],
sin(60◦ − α)
Ts = mR − mY
(2a)
sin 60◦
sin α
T2 = VREF
Ts = mY − mB
(2b)
sin 60◦
where Ts is the duration of a sub-cycle, and α is the angle of
reference vector from the start of a sector. The zero vector is
applied for the rest of sub-cycle duration as given below.
T1
SR
1
+
−
−
SY
SB
cY 1
cY 1
Fig. 3.
2
+
+
−
= VREF
Tz = Ts − T1 − T2
(3)
CSVPWM applies the voltage vectors in a sequence starting
with one zero state and ending with the other zero state in
each sub-cycle; the two zero states are applied for 0.5Tz each
[1]. The switching sequences 0-1-2-7 and 7-2-1-0 are applied
in alternate sub-cycles in sector I [see Fig. 4(a)]. ABCPWM
schemes apply only one zero state for the entire duration
Tz , but apply an active state twice as illustrated in Fig. 3(a)
to Fig. 3(d). The ABCPWM method, shown in Fig. 4(b),
employs sequences 0-1-2-1 and 1-2-1-0 in alternate sub-cycles
in the first half of sector I. Sequences 7-2-1-2-2-1-2-7,... are
applied in the second half [4], [10]. Fig. 4(c) shows a hybrid
PWM method which employs sequences 1012 and 2721 along
with the conventional sequence 0127. Here, sequence 1012 is
applied for 0◦ < α < 14◦ , 0127 is applied for 14◦ < α < 46◦
and 2721 is applied for the remaining duration in sector I.
To simulate an induction motor drive fed from a pulse width
modulated two-level VSI, the switching function needs to be
generated for each switch in the inverter. This reduces to
generation of switching functions for the three legs (SR , SY
and SB ) since the two switches in each leg are complementary
in nature.
The switching functions corresponding to continuous PWM
schemes (STPWM, THIPWM and CSVPWM) and BCPWM
schemes can easily be generated by comparing three-phase
modulating signals with triangular carrier. However, generating SR , SY and SB is quite involved in case of ABCPWM
strategies. A method for determining the switching functions
for ABCPWM schemes in discussed in section II.
A tool for simulation of VSI-fed induction motor drive, controlled with different PWM methods, is developed in this work.
This tool is capable of simulating continuous PWM methods,
BCPWM methods and a variety of ABCPWM methods. The
details of the simulator developed are discussed in section III.
While there are commercial and open-source tools available
(e.g. MATLAB[11], Octave[12] and SEQUEL[13]) for simulating a wide range of dynamic systems, the tool developed
R-ph stator current (A)
0.2
0.4
0.6
0.8
1.0
120
100
80
60
40
20
0
20
400.0
0.2
0.4
0.6
0.8
1.0
1600
1400
1200
1000
800
600
400
200
00.0
0.2
0.4
0.6
0.8
1.0
Speed (RPM)
80
60
40
20
0
20
40
600.0
Torque (N-m)
(a) Screenshot of the simulator developed.
(b) Simulation results: Direct on-line start of a 5hp induction motor.
Fig. 5.
4
2
0
2
4
6
8
1.45
1.46
1.47
1.48
Time (sec)
1.49
4
2
0
2
4
6
1.45
1.50
6
R-ph stator current (A)
R-ph stator current (A)
1.46
(a)-(1)
2
0
2
4
1.47
1.48
Time (sec)
1.49
8
1.45
1.50
(a)-(2)
1.46
1.47
1.48
Time (sec)
1.49
1.50
(a)-(3)
6
6
4
Current (A)
4
Current (A)
4
6
2
0
−2
4
2
Current (A)
R-ph stator current (A)
8
6
8
6
0
−2
−2
−4
−4
−4
−6
1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5
Time (sec)
2
0
−6
−6
1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5
Time (sec)
1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5
Time (sec)
(b)-(1)
(b)-(2)
(b)-(3)
(c)-(1)
(c)-(2)
(c)-(3)
Fig. 6. Motor line current waveforms at a fundamental frequency of 40Hz with different PWM techniques: (a) Simulated with matra, (b) Simulated with
MATLAB and (c) Experimentally measured. (1)-CSVPWM, (2)-Advanced 30◦ clamp PWM and (3)-Hybrid PWM. Average switching frequency fsw is 1kHz.
here is focused on PWM-VSI-fed induction motor drives.
This tool is shown to be quicker than MATLAB in carrying
out simulations of motor drive. Simulation results obtained
from this tool are compared with those from MATLAB and
also with experimental results on a 5hp motor drive (see
section IV).
II. S PACE V ECTOR BASED PWM : R EALIZATION
The first step to realize a space vector PWM is identification
of the sector where VREF falls in. When the magnitude
and angle of VREF are available, the sector can easily be
determined from the angle. However, the reference is rarely
available in magnitude-angle form. On the other hand, the
voltage reference is usually provided by the controller as daxis and q-axis reference in the synchronous reference frame,
or as α-axis reference and β-axis reference in the stationary
reference frame, or as three-phase voltage references. The
voltage reference is assumed to be available as a three-phase
quantity here. (Even otherwise, the voltage references can be
transformed to three-phase quantities.)
The sector can be identified by comparing mR , mY and
mB . For example, mR > mY > mB indicates that VREF
is in sector I. Quite often, a sector may be divided into a
number of sub-sectors, each employing a different switching
sequence [see Fig. 4(b) and Fig. 4(c)]. Boundaries separating
the different sub-sectors in a sector need to be represented in
terms of mR , mY and mB . Once the sub-sector is identified,
the switching sequence is known. For the four ABCPWM
sequences, the switching functions can be determined as
discussed below.
Consider the sequence 0121 in Fig. 3(a). PWM pulse of the
single-switching phase SR can be generated by comparing one
modulating function cR against the carrier. Two modulating
functions cY 1 and cY 2 corresponding to Y-phase generate
the PWM pulses SY 1 and SY 2 , respectively. The final PWM
output of Y-phase SY is an XOR function of SY 1 and SY 2 . Bphase gets clamped to negative DC bus in sector I (i.e. SB = 0)
with the sequence 0121. Similar procedure can be followed for
the remaining sequences [Fig. 3(b) to Fig. 3(d)]. For instance,
double-switching of R-phase with 1012 can be achieved by
generating the pulses SR1 and SR2 (see Fig. 3(c)) and passing
them through an XNOR function. All the modulating functions
(cR , cR1 , cY , cY 2 etc.) can be expressed in terms of the
dwell-times of inverter states. The dwell-times are functions
of mR ,mY and mB as shown by (2). For example, cB2 =
(0.5T2 ) + Tz for the sequence 2721 [see Fig. 3(d)].
600
0
200
400
600
1.475
1.480
1.485
1.490
Time (sec)
1.495
Peak magnitude normalized w.r.t. VDC
1000
2000
3000
4000
Frequency (Hz)
5000
400
200
0
200
400
600
1.475
1.500
(a)-(1)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.00
Line-to-line voltage vRY (V)
200
600
1.480
1.490
Time (sec)
1.495
1000
2000
3000
4000
Frequency (Hz)
5000
200
0
200
400
600
1.475
1.500
(a)-(2)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.00
(b)-(1)
0.8
0.7
0.7
0.4
0.3
0.2
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Magnitude of Peak (p.u.)
0.8
0.5
1.490
Time (sec)
1.495
1.500
1000
2000
3000
4000
Frequency (Hz)
5000
(b)-(3)
0.7
0.6
1.485
(a)-(3)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.00
0.8
0
1.480
(b)-(2)
Magnitude of Peak (p.u.)
Magnitude of Peak (p.u.)
1.485
400
Peak magnitude normalized w.r.t. VDC
Line-to-line voltage vRY (V)
400
Peak magnitude normalized w.r.t. VDC
Line-to-line voltage vRY (V)
600
0.6
0.5
0.4
0.3
0.2
0.1
0
Frequency (kHz)
(c)-(1)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Frequency (kHz)
(c)-(2)
4.0
4.5
5.0
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Frequency (kHz)
(c)-(3)
Fig. 7. (a) Motor line-to-line voltage, (b) and (c) Harmonic spectra of line-to-line voltage at a fundamental frequency of 40Hz with different PWM techniques:
(a) and (b) Simulated with matra, (c) Experimentally measured [PWM of R-phase minus PWM of Y-phase]. (1)-CSVPWM, (2)-Advanced 30◦ clamp PWM
and (3)-Hybrid PWM. Average switching frequency fsw is 1kHz.
III. S IMULATION T OOL D EVELOPED
The squirrel cage induction machine is a sixth order system
when stator and rotor are modelled in their respective coordinate systems [14]. Thus, numerical simulation of an open-loop
induction motor drive can be viewed as solving of a system
of six ordinary differential equations (ODE) at each time step.
A large number of numerical methods are available to solve
a system of ODEs. In general, reduced step-size improves the
accuracy of solution; Runge-Kutta methods are shown to be
stable for smaller step sizes [15]. The simulator developed
uses the Explicit Runge-Kutta 4th Order method to solve the
system of ODEs. The simulator does not provide any option
to the user to choose the ODE solver method. Further, the
maximum integration step-size is limited to 1µs.
A screenshot of the simulation tool developed, “matra”, is
shown in Fig. 5(a). The single-window graphical user interface
(GUI) is written in PyGTK [16]. Details of the induction
machine and VSI and other simulation parameters have to be
entered by the user. The user has to select one among the three
PWM methods, namely, STPWM, THIPWM and SVPWM.
In case of SVPWM, total number of switching sequences in
a sector has to be specified, which is same as the number
of sub-sectors. Boundaries separating the sub-sectors have to
be given in terms of angle. Finally, the sequence employed in
each sub-sector has to be specified. The simulation data can be
loaded from and saved to a text file. The text file is taken as an
input to the main simulation routine, written in C programming
language [17]. Output of the C program is plotted using
NumPy and Matplotlib of the Python programming language
[18]. The plotting window of Matplotlib has basic features
such as x-axis zoom, y-axis zoom and rectangular zoom.
Further, the plot can be saved in many formats including PNG,
SVG, EPS, PDF, JPEG and EMF.
IV. S IMULATION A ND E XPERIMENTAL R ESULTS
Configuration of the computer used for testing the simulation tool is Intel Core i3-3120 3.2 GHz processor with 4
TABLE I
C OMPARISON OF matra WITH MATLAB
PWM method
CSVPWM
Advanced 30◦ clamp PWM
Hybrid PWM
Actual time taken for a simulation
of 1.5s with 500ns time-step
matra
MATLAB R2013a
(sec)
(sec)
5.393
226.43
5.632
282.88
5.638
295.1
threads, 4GB 1333MHz DDR3 RAM and Fedora 19 Linux
operating system. The experimental setup consists of a 10kVA
IGBT-based two-level VSI connected to a 5hp, 400V, 50Hz,
4-pole squirrel-cage induction motor. The PWM techniques
are implemented on ALTERA Cyclone II field programmable
gate array (FPGA)-based digital controller [19].
Fig. 5(b) shows the simulation results when the 5hp induction motor is started direct on-line. The simulation step-size
is 1µs, and the simulation end time is 1s. The actual time
taken for simulation is 7.12 seconds. The total number of time
points in the simulation above is 106 . When only steady-state
results are of interest (as in the case of comparing different
PWM schemes), only the last significant data points need to
be stored. This results in reduced time for simulation.
Simulation of the PWM methods, shown in Fig. 4, is carried
out with matra and MATLAB R2013a. Measured parameters
of the induction machine are given as inputs. The fundamental
frequency is 40Hz, and the average switching frequency fsw
is 1kHz. Simulation step size is 500ns, and the simulation
end time is 1.5s. Only the last 105 data points are stored to
improve the simulation speed. Actual time taken for simulation
by matra and MATLAB are tabulated in Table I. It can be
observed that the simulator developed performs 40 times faster
than MATLAB.
Motor line current waveforms with matra and MATLAB
are presented in Fig. 6(a) and Fig. 6(b), respectively, for
different PWM techniques. Further, experimental motor current waveforms under the same conditions are presented in
Fig. 6(c). The simulation results from matra are in excellent
agreement with those from MATLAB and also with experimental observations.
Simulated waveforms of line-to-line voltage (vRY ) of the
motor are shown in Fig. 7(a) for different PWM methods.
Fig. 7(b) shows harmonic spectra of vRY simulated with
matra. The measured harmonic spectra of line-to-line voltage
are presented in Fig. 7(c). The simulated harmonic spectra are
close to their experimental counterparts. Thus, the accuracy of
the simulator is verified and the fastness is evaluated.
V. C ONCLUSIONS
A quick simulation tool for VSI-fed induction motor drives
with a variety of PWM techniques is developed. The PWM
techniques include continuous PWM methods, discontinuous
or bus-clamping PWM methods, and advanced bus-clamping
PWM methods. Generation of switching functions in case of
ABCPWM schemes is explained. Simulation results from the
tool developed, those from MATLAB, and experimental results
on a 5-hp motor drive are presented. The simulation speed of
the developed tool is 40 times that of MATLAB. The simulator
developed has a simple GUI and is useful for the study of
various PWM techniques.
ACKNOWLEDGMENT
Pavan Kumar Hari would like to thank V. Seshadri Sravan
Kumar, Department of Electrical Engineering, Indian Institute
of Science and Arvind Iyer, Department of Aerospace Engineering, Indian Institute of Science for their valuable inputs
towards programming in C and Python.
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