A Quick-Simulation Tool for Induction MotorDrives Controlled Using Advanced

Space-Vector-Based PWM TechniquesV. S. S. Pavan Kumar Hari1 and G. Narayanan2

Department of Electrical Engineering, Indian Institute of Science, Bangalore 560 012, INDIAEmail: 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 ofdifferent switching sequences. Numerical simulation is helpfulto assess the performance of a PWM method before actualimplementation. A quick-simulation tool to simulate a varietyof space-vector-based PWM strategies for a two-level VSI-fedsquirrel cage induction motor drive is presented. The simulatoris developed using C and Python programming languages, andhas a graphical user interface (GUI) also. The prime focus beingPWM strategies, the simulator developed is 40 times faster thanMATLAB in terms of the actual time taken for a simulation.Simulation and experimental results are presented on a 5-hp acmotor drive.

I. INTRODUCTION

Voltage source inverter (VSI)-fed induction motor standsamong the most sought-after industrial drive configurations. Atwo-level VSI realized with IGBTs is shown in Fig. 1. Pulse

S1

S4

D1

D4

R

S3

S6

D3

D6

Y

S5

S2

D5

D2

B

–

+

VDC

C

C

O

Fig. 1. Two-level voltage source inverter using insulated gate bipolartransistors.

width modulation (PWM) of the switches is required to controlthe output voltage and frequency of a VSI, for a given DC busvoltage VDC .

Generation of PWM waveforms by comparing three-phasesinusoidal modulating waves (mR, mY and mB) against acommon triangular carrier wave is popularly known as sinetriangle PWM (STPWM) [1]. Considering a unipolar trian-gular carrier with peak value Vp, the sinusoidal modulating

This work was supported by the Department of Heavy Industry, Governmentof India, under a project titled “Off-line and Real-time Simulators for ElectricVehicles / Hybrid Electric Vehicle Systems”.

function for R-phase is defined as

mR = 0.5 +Vm2Vp

sinωt (1)

where Vm is the peak value of sinusoid. Modulating signalsmY and mB are phase shifted by 120◦ and 240◦, respectively,with respect to mR.

Addition of third harmonic to the sinusoidal modulatingfunctions increases the highest possible ac voltage output ofthe VSI. The DC bus utilization with such third harmonicinjection PWM (THIPWM) is maximum when the amplitudeof the third harmonic added is one sixth of the fundamen-tal amplitude. This DC bus utilization is matched by thespace-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 thethird harmonic amplitude is 25% of the fundamental amplitude[2]. Conventional space vector PWM (CSVPWM) results inTHD, which is quite close to this [1], [2]. Bus-clamping PWM

+−−(1)

++−(2)(3)−+−

(4)−++

(5)−−+ +−+(6)

q

d

VREFα(7)+++

(0)−−−

I

II

III

IV

V

VI

ωt = 0◦

1.0

Fig. 2. Voltage vectors of a voltage source inverter. Magnitudes of the vectorsare normalized with respect to DC bus voltage VDC . I, II, III, IV, V and VIare sectors [2].

(BCPWM) methods yield lower THD than CSVPWM at highmodulation indices for a given average switching frequency[3]. Advanced bus-clamping PWM (ABCPWM) techniques,proposed recently, outperform BCPWM methods in terms ofTHD at high modulation indices [4]. ABCPWM methods havealso been shown to have other advantages such as reducedpulsating torque [5], improved converter efficiency [2],[6] andlow acoustic noise [7] under various operating conditions.

−−−+−−

++−

+−−

0 1 2 1

Tz12T1 T2

12T1

1SR

0SY

SB 0

cR

cY 1

cY 2

cB 0

Vp

1SY 1

1SY 2

SY = SY 1⊕SY 2

(a)

+++

++−

+−−++−

7 2 1 2

Tz12T2 T1

12T2

SR 11

SY

0SB

cB

cY 1

cY 2

cR Vp

0

0SY 1

0SY 2

SY = SY 1�SY 2

(b)

+−−−−−

+−−++−

1 0 1 2

12T1 Tz

12T1 T2

1SR

1SY

SB 0

cR1

cR2

cY

cB 0

Vp

0SR1

0SR2

SR = SR1 � SR2

(c)

++−

+++

++−

+−−

2 7 2 1

12T2Tz

12T2 T1

SR 1

0SY

1SB

cB1

cB2

cY

cR Vp

01

SB1 1

SB2

SB = SB1⊕SB2

(d)

Fig. 3. Generation of switching functions for different ABCPWM sequences (a) 0121, (b) 7212, (c) 1012 and (d) 2721 in sector I.

0127

(a) CSVPWM

01217212

(b) Advanced 30◦Clamp PWM

0127

1012

2721

(c) Hybrid PWM

Fig. 4. PWM techniques considered.

Most SVPWM methods synthesize the desired voltage ref-erence vector VREF (see Fig. 2) by applying the two nearestactive vectors and the zero vector. For the reference vectorshown in Fig. 2, the active vector 1 and the active vector 2are applied for durations T1 and T2, respectively, as givenby (2) [8], [9],

T1 = VREFsin(60◦ − α)

sin 60◦Ts = mR −mY (2a)

T2 = VREFsinα

sin 60◦Ts = mY −mB (2b)

where Ts is the duration of a sub-cycle, and α is the angle ofreference vector from the start of a sector. The zero vector isapplied for the rest of sub-cycle duration as given below.

Tz = Ts − T1 − T2 (3)

CSVPWM applies the voltage vectors in a sequence startingwith one zero state and ending with the other zero state ineach 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 appliedin alternate sub-cycles in sector I [see Fig. 4(a)]. ABCPWM

schemes apply only one zero state for the entire durationTz , 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-cyclesin the first half of sector I. Sequences 7-2-1-2-2-1-2-7,... areapplied in the second half [4], [10]. Fig. 4(c) shows a hybridPWM method which employs sequences 1012 and 2721 alongwith the conventional sequence 0127. Here, sequence 1012 isapplied 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 begenerated for each switch in the inverter. This reduces togeneration of switching functions for the three legs (SR, SY

and SB) since the two switches in each leg are complementaryin nature.

The switching functions corresponding to continuous PWMschemes (STPWM, THIPWM and CSVPWM) and BCPWMschemes can easily be generated by comparing three-phasemodulating signals with triangular carrier. However, generat-ing SR, SY and SB is quite involved in case of ABCPWMstrategies. A method for determining the switching functionsfor ABCPWM schemes in discussed in section II.

A tool for simulation of VSI-fed induction motor drive, con-trolled 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. Thedetails 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 simu-lating a wide range of dynamic systems, the tool developed

(a) Screenshot of the simulator developed.

0.0 0.2 0.4 0.6 0.8 1.060

40

20

0

20

40

60

80

R-ph

sta

tor c

urre

nt (A

)

0.0 0.2 0.4 0.6 0.8 1.040

20

0

20

40

60

80

100

120

Torq

ue (N

-m)

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

1000

1200

1400

1600

Spee

d (R

PM)

(b) Simulation results: Direct on-line start of a 5hp induction motor.

Fig. 5.

(c)-(1) (c)-(2) (c)-(3)

1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5

−6

−4

−2

0

2

4

6

Time (sec)

Cur

rent

(A

)

1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5Time (sec)

−6

−4

−2

0

2

4

6

Cur

rent

(A

)

1.45 1.455 1.46 1.465 1.47 1.475 1.48 1.485 1.49 1.495 1.5Time (sec)

−6

−4

−2

0

2

4

Cur

rent

(A

)

(b)-(1) (b)-(2) (b)-(3)

1.45 1.46 1.47 1.48 1.49 1.50Time (sec)

8

6

4

2

0

2

4

6

8R-

ph s

tato

r cur

rent

(A)

1.45 1.46 1.47 1.48 1.49 1.50Time (sec)

8

6

4

2

0

2

4

6

8

R-ph

sta

tor c

urre

nt (A

)

1.45 1.46 1.47 1.48 1.49 1.50Time (sec)

6

4

2

0

2

4

6

R-ph

sta

tor c

urre

nt (A

)

(a)-(1) (a)-(2) (a)-(3)

Fig. 6. Motor line current waveforms at a fundamental frequency of 40Hz with different PWM techniques: (a) Simulated with matra, (b) Simulated withMATLAB 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 carryingout simulations of motor drive. Simulation results obtainedfrom this tool are compared with those from MATLAB andalso with experimental results on a 5hp motor drive (seesection IV).

II. SPACE VECTOR BASED PWM : REALIZATION

The first step to realize a space vector PWM is identificationof the sector where VREF falls in. When the magnitudeand angle of VREF are available, the sector can easily bedetermined from the angle. However, the reference is rarelyavailable in magnitude-angle form. On the other hand, thevoltage reference is usually provided by the controller as d-axis and q-axis reference in the synchronous reference frame,or as α-axis reference and β-axis reference in the stationaryreference frame, or as three-phase voltage references. Thevoltage reference is assumed to be available as a three-phasequantity here. (Even otherwise, the voltage references can betransformed to three-phase quantities.)

The sector can be identified by comparing mR, mY andmB . 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 switchingsequence [see Fig. 4(b) and Fig. 4(c)]. Boundaries separatingthe different sub-sectors in a sector need to be represented interms of mR, mY and mB . Once the sub-sector is identified,the switching sequence is known. For the four ABCPWMsequences, the switching functions can be determined asdiscussed below.

Consider the sequence 0121 in Fig. 3(a). PWM pulse of thesingle-switching phase SR can be generated by comparing onemodulating function cR against the carrier. Two modulatingfunctions cY 1 and cY 2 corresponding to Y-phase generatethe PWM pulses SY 1 and SY 2, respectively. The final PWMoutput of Y-phase SY is an XOR function of SY 1 and SY 2. B-phase gets clamped to negative DC bus in sector I (i.e. SB = 0)with the sequence 0121. Similar procedure can be followed forthe remaining sequences [Fig. 3(b) to Fig. 3(d)]. For instance,double-switching of R-phase with 1012 can be achieved bygenerating the pulses SR1 and SR2 (see Fig. 3(c)) and passingthem through an XNOR function. All the modulating functions(cR, cR1, cY , cY 2 etc.) can be expressed in terms of thedwell-times of inverter states. The dwell-times are functionsof mR,mY and mB as shown by (2). For example, cB2 =(0.5T2) + Tz for the sequence 2721 [see Fig. 3(d)].

Frequency (kHz)

Magnitudeof

Peak(p.u.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Frequency (kHz)

Magnitudeof

Peak(p.u.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Frequency (kHz)

Magnitudeof

Peak(p.u.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

(c)-(1) (c)-(2) (c)-(3)

0 1000 2000 3000 4000 5000Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Peak

mag

nitu

de n

orm

aliz

ed w

.r.t.

V DC

0 1000 2000 3000 4000 5000Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Peak

mag

nitu

de n

orm

aliz

ed w

.r.t.

V DC

0 1000 2000 3000 4000 5000Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Peak

mag

nitu

de n

orm

aliz

ed w

.r.t.

V DC

(b)-(1) (b)-(2) (b)-(3)

1.475 1.480 1.485 1.490 1.495 1.500Time (sec)

600

400

200

0

200

400

600Li

ne-to

-line

vol

tage

vRY

(V)

1.475 1.480 1.485 1.490 1.495 1.500Time (sec)

600

400

200

0

200

400

600

Line

-to-li

ne v

olta

ge v

RY (V

)

1.475 1.480 1.485 1.490 1.495 1.500Time (sec)

600

400

200

0

200

400

600

Line

-to-li

ne v

olta

ge v

RY (V

)

(a)-(1) (a)-(2) (a)-(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 PWMand (3)-Hybrid PWM. Average switching frequency fsw is 1kHz.

III. SIMULATION TOOL DEVELOPED

The squirrel cage induction machine is a sixth order systemwhen stator and rotor are modelled in their respective coordi-nate systems [14]. Thus, numerical simulation of an open-loopinduction motor drive can be viewed as solving of a systemof six ordinary differential equations (ODE) at each time step.A large number of numerical methods are available to solvea system of ODEs. In general, reduced step-size improves theaccuracy of solution; Runge-Kutta methods are shown to bestable for smaller step sizes [15]. The simulator developeduses the Explicit Runge-Kutta 4th Order method to solve thesystem of ODEs. The simulator does not provide any optionto the user to choose the ODE solver method. Further, themaximum integration step-size is limited to 1µs.

A screenshot of the simulation tool developed, “matra”, isshown in Fig. 5(a). The single-window graphical user interface(GUI) is written in PyGTK [16]. Details of the inductionmachine and VSI and other simulation parameters have to be

entered by the user. The user has to select one among the threePWM methods, namely, STPWM, THIPWM and SVPWM.In case of SVPWM, total number of switching sequences ina sector has to be specified, which is same as the numberof sub-sectors. Boundaries separating the sub-sectors have tobe given in terms of angle. Finally, the sequence employed ineach sub-sector has to be specified. The simulation data can beloaded from and saved to a text file. The text file is taken as aninput to the main simulation routine, written in C programminglanguage [17]. Output of the C program is plotted usingNumPy and Matplotlib of the Python programming language[18]. The plotting window of Matplotlib has basic featuressuch 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. SIMULATION AND EXPERIMENTAL RESULTS

Configuration of the computer used for testing the simu-lation tool is Intel Core i3-3120 3.2 GHz processor with 4

TABLE ICOMPARISON OF matra WITH MATLAB

Actual time taken for a simulationPWM method of 1.5s with 500ns time-step

matra MATLAB R2013a(sec) (sec)

CSVPWM 5.393 226.43Advanced 30◦ clamp PWM 5.632 282.88

Hybrid PWM 5.638 295.1

threads, 4GB 1333MHz DDR3 RAM and Fedora 19 Linuxoperating system. The experimental setup consists of a 10kVAIGBT-based two-level VSI connected to a 5hp, 400V, 50Hz,4-pole squirrel-cage induction motor. The PWM techniquesare implemented on ALTERA Cyclone II field programmablegate array (FPGA)-based digital controller [19].

Fig. 5(b) shows the simulation results when the 5hp induc-tion motor is started direct on-line. The simulation step-sizeis 1µs, and the simulation end time is 1s. The actual timetaken for simulation is 7.12 seconds. The total number of timepoints in the simulation above is 106. When only steady-stateresults are of interest (as in the case of comparing differentPWM schemes), only the last significant data points need tobe stored. This results in reduced time for simulation.

Simulation of the PWM methods, shown in Fig. 4, is carriedout with matra and MATLAB R2013a. Measured parametersof the induction machine are given as inputs. The fundamentalfrequency is 40Hz, and the average switching frequency fswis 1kHz. Simulation step size is 500ns, and the simulationend time is 1.5s. Only the last 105 data points are stored toimprove the simulation speed. Actual time taken for simulationby matra and MATLAB are tabulated in Table I. It can beobserved that the simulator developed performs 40 times fasterthan MATLAB.

Motor line current waveforms with matra and MATLABare presented in Fig. 6(a) and Fig. 6(b), respectively, fordifferent PWM techniques. Further, experimental motor cur-rent waveforms under the same conditions are presented inFig. 6(c). The simulation results from matra are in excellentagreement with those from MATLAB and also with experi-mental observations.

Simulated waveforms of line-to-line voltage (vRY ) of themotor are shown in Fig. 7(a) for different PWM methods.Fig. 7(b) shows harmonic spectra of vRY simulated withmatra. The measured harmonic spectra of line-to-line voltageare presented in Fig. 7(c). The simulated harmonic spectra areclose to their experimental counterparts. Thus, the accuracy ofthe simulator is verified and the fastness is evaluated.

V. CONCLUSIONS

A quick simulation tool for VSI-fed induction motor driveswith a variety of PWM techniques is developed. The PWMtechniques include continuous PWM methods, discontinuousor bus-clamping PWM methods, and advanced bus-clampingPWM methods. Generation of switching functions in case ofABCPWM schemes is explained. Simulation results from the

tool developed, those from MATLAB, and experimental resultson a 5-hp motor drive are presented. The simulation speed ofthe developed tool is 40 times that of MATLAB. The simulatordeveloped has a simple GUI and is useful for the study ofvarious PWM techniques.

ACKNOWLEDGMENT

Pavan Kumar Hari would like to thank V. Seshadri SravanKumar, Department of Electrical Engineering, Indian Instituteof Science and Arvind Iyer, Department of Aerospace Engi-neering, Indian Institute of Science for their valuable inputstowards programming in C and Python.

REFERENCES

[1] D. G. Holmes and T. A. Lipo, Pulse width modulation for powerconverters: Principles and practice, Hoboken, NJ: IEEE Press and JohnWiley Interscience, 2003.

[2] Di Zhao, V. S. S. P. K. Hari, G. Narayanan and R. Ayyanar, “Space-vector-based hybrid pulsewidth modulation techniques for reduced har-monic distortion and switching loss”, IEEE Trans. Power Electron.,vol. 25(3), pp. 760-774, March 2010.

[3] H. Khan, E. Miliani, K. E. K. Drissi, “Discontinuous random spacevector modulation for electric drives: A digital approach”, IEEE Trans.Power Electron., vol. 27(12), pp. 4944-4951, December 2012.

[4] T. Bhavsar and G. Narayanan, “Harmonic analysis of advanced bus-clamping PWM techniques”, IEEE Trans. Power Electron., vol. 24(10),pp. 2347-2352, October 2009.

[5] K. Basu, J. S. S. Prasad, G. Narayanan, H. K. Krishnamurthy andR. Ayyanar, “Reduction of torque ripple in induction motor drivesusing an advanced hybrid PWM technique”, IEEE Trans. Ind. Electron.,vol. 57(6), pp. 2085-2091, June 2010.

[6] J. S. S. Prasad and G. Narayanan. “Minimum switching loss pulsewidth modulation for reduced power conversion loss in reactive powercompensators”, IET Power Electron., 2013.

[7] A. C. Binojkumar, J. S. S. Prasad and G. Narayanan, “Experimentalinvestigation on the effect of advanced bus-clamping pulsewidth modu-lation on motor acoustic noise”, IEEE Trans. Ind. Electron., vol. 60(2),pp. 433-439, February 2013.

[8] D-W. Chung, J-S. Kim and S-K. Sul, “Unified voltage modulationtechnique for real-time three-phase power conversion, IEEE Trans. Ind.Appl., vol. 34(2), pp. 374-380, March/April 1998.

[9] A. Cataliotti, F. Genduso, A. Raciti and G. R. Galluzzo, “GeneralizedPWM-VSI control algorithm based on a universal duty-cycle expression:Theoretical analysis, simulation results and experimental validations”,IEEE Trans. Ind. Electron., vol. 54(3), pp. 1569-1580, June 2007.

[10] G. Narayanan, Di Zhao, H. K. Krishnamurthy, R. Ayyanar and V. T. Ran-ganathan, “Space vector based hybrid PWM techniques for reducedcurrent ripple”, IEEE Trans Industrial Electronics, vol. 55(4), pp. 1614-1627, April 2008.

[11] http://www.mathworks.in/products/matlab[12] http://www.gnu.org/software/octave[13] http://www.ee.iitb.ac.in/ sequel[14] Werner Leonhard, “Control of Electric Drives”, Springer International

Edition, 2003.[15] M. B. Patil, V. Ramanarayanan and V. T. Ranganathan, Simulation of

Power Electronic Circuits, Narosa Publishing House, Delhi, 2009.[16] http://www.pygtk.org[17] B. W. Kernighan, D. M. Ritchie, The C Programming Language,

Tsinghua University Press / Prentice-Hall, 1988.[18] http://www.python.org, http://www.numpy.org, http://matplotlib.org[19] S. Venugopal and G. Narayanan, “Design of FPGA based digital

platform for control of power electronics systems”, Proc. NPEC ’05,National Power Electronics Conference, Indian Institute of Technology,Kharagpur, December 2005.