Random Space Vector Modulation for ElectricDrives: A Digital Approach

Hamid KHAN*,**, Youssef TOUZANI*, Khalil El Khamlichi DRISSI**

* IFP, Rueil-Malmaison, France, e-mail: hamid.khan@ifp.fr, youssef.touzani@ifp.fr** UBP, LASMEA, Clermont-Ferrand, France, e-mail: drissi@lasmea.univ-bpclermont.fr

Abstract — SVM, with its many advantages over PWM, isgaining popularity. However, only Deterministic-SVM exist.Whereas Randomised-PWM with their cleaner harmonic-spectrum, are gaining interest for industrial applicationsrequired to meet EMC-Standards. Here we present,Randomised-SVM intended for Electric-Drive orientedHEV, which has the advantages of SVM & clean harmonic-spectrum of Randomised-PWM.

Keywords — SVM, RSVM, PWM, Harmonics, HEV, VectorControl, VSI, FOC, Electrical Drives, Variable speed drive,Brushless Motor, Power converters for EV, EMC/EMI, DSP.

I. INTRODUCTION

The issue with Electric/HEV is the weak autonomy; toimprove that, the battery should be used efficiently and thepower conversion system must be as light as possible. Theobjectives of RSVM are : reducing the weight bylightening the filtering effort to meet the EMC/EMIstandards, optimal use of the battery voltage and minimalswitching losses. Moreover we can place the electroniccomponents at proximity with the power circuit andreduce the volume of the power conversion chain andcould avoid using a faraday cage to curb the radiated noise(Weight, volume and cost constraints). The electrictraction drive under consideration consists of a PermanentMagnet Synchronous Motor (PMSM) fed by a 3-phaseinverter. The Field Oriented Control (FOC) is used toregulate the torque.

A. Space Vector Modulation

SVM is a digital Power Converter PWM techniquewhere the duty cycle of inverter switches are calculateddirectly using mathematical transformations [1]. Fig. 1depicts the vectors representing all possible 3-phaseinverter states that form a circle on the αβ-plane. The three bit binary subscript denotes the state of upper switch ofthe inverter leg corresponding the three phases 'a, b and c'in the same order. '0' and '1' represent the off and on staterespectively. The upper and lower switch states of a legare complimentary to avoid short circuiting the voltagesource. The voltage space vectors circle is divided in 6sectors in a way to make the duty cycle calculations assimple as possible.

SVM was chosen over ordinary PWM techniques forthe following reasons: better DC voltage utilization [2]and decreased switching losses. Reduced switching lossescan be explained by the freedom that one has ingenerating the pulses when the duty cycles are known

before hand. The idea is to use only the zero vector V0 atthe beginning and end of the period.

Fig. 1. Voltage Space Vectors

Whereas PWM techniques are based on comparison ofthe reference signals and the carrier signal, one cannotavoid the insertion of the vector V7 at the middle of theperiod [3]. This would be clear from Fig. 2; switchingfunction of leg A, when only the vector V0 is used tocomplete the modulation period, remains zero during one-third of the fundamental cycle. Which explains 33.3%reduction in the switching losses i.e. only 4 commutationsinstead of 6 per modulation period [4]. It can be seen as anintrinsically or naturally discontinuous-PWM techniquei.e. without having to add a zero sequence voltage to thereference. An analogy can be drawn with the GeneralizedDiscontinuous Modulator (GDPWM) where the zerosequence voltage is given by following expression:

0 min2dcV

u v (1)

Where * * *min min ( , , )a b cv v v v . So the new reference

signals become:

** *0x xv v u (2)

For a balanced three phase sinusoidal system:

*

*

*

sin ( )

sin ( 2 )3

sin ( 4 )3

a

b

c

A

v

v

v

(3)

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The new reference signals would be saturated to

2dcV

for 120 i.e. one-third of the fundamental period

and out of phase by 23

, this technique is also known as

DPWMMIN.

Fig. 2 shows the switching function for maximumutilization of the DC bus, i.e. maximum achievable value

of the reference voltage is3

dcVand not

2dcV in the linear

zone, as explained in the next section. Therefore 'da' is the

image of Va in percentage3

dcV .

Fig. 2. SVM: Switching Function leg A

The modulation index is defined as:

stepsixlfundamenta

PWMlfundamenta

iV

Vm

(4)

Fig. 3 shows an increase of 15.47% in phase voltagescompared to ordinary PWM techniques. There existtechniques such as harmonic injection (3rd and itsmultiple), to increase the linearity of PWM techniques [4].However these techniques are not possible for dynamicsystems where the fundamental frequency varies with timerandomly. Furthermore in vector control, instantaneousvalues are treated and the complete form of the referencesignal has no significance.

Fig. 3. Increased linearity of Modulation Index (adv of SVM)

B. EMC/EMI Problem

In spite of all the advantages of SVM, its drawback isthe harmonics at the switching frequency. RPWM iscommonly used to tackle this problem. The concept is torandomize the modulation function parameters, like thepulse position [5], the switching frequency to spread thefrequency spectrum around the switching frequency andhence remain under the permissible EMI limit.

There are quite a few papers on RPWM. The mostcommon RPWM is the randomization of the switchingfrequency, which improves the voltage and currentharmonics [6]. There are other techniques such as dualrandomization [7], which may spread the spectrum a littlebit more, whereas only randomizing the pulse position isnot very effective and has a discontinuous PowerSpectrum Density (PSD) [8].

II. RSVM

A. Random Space Vector Modulation

Random Space Vector Modulation (RSVM), a newsolution is proposed to conserve the advantages of SVMwhile adding those of the RPWM. The proposed methodis to vary the switching frequency randomly andcalculating the corresponding duty cycles.

There are many random distribution laws; it has beenshown that the uniform distribution, which is the simplestrandom distribution, is as good as any other complexdistribution law that can be used for harmonic ditheringlinked to switching frequency [9].

B. RSVM Switching Function

The switching (or modulating) function shouldcorrespond to the randomly generated frequency at everycycle. Fig. 4 and Fig. 5 show the variation of themodulation function after every random SVM-period.

It can be seen that completing the time period withvectors V0 and V7 or just by V0 does not change theaverage value of the resultant vector generated. “da-db”gives the image of the line voltage which is conserved inboth the cases, as is clear from the two figures.

Fig. 4. RSVM: Switching Function (using V7 and V0)

dcV3

1dcV

2

1

mi

Vx

Ov

erm

odul

atio

nPWM

SVM

0.907

0.785

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Fig. 5. RSVM: Switching Function (using only V0)

C. State of the Art

There are about half a dozen papers on RSVM; readingthem thoroughly we find contradictions in basic principlesof SVM. [10] Proposes a 3-level inverter with RSVM toreduce acoustic noise, however the generation of gatesignals is done through comparison of the reference signalby a triangular carrier signal, and this technique iscommonly known as PWM. [11] Proposes a random SVMtechnique, which is not really random, only two switchingfrequencies are used with scalar control, however thepulse generation remains ambiguous. Similarly there areother papers such as [12], [13] that treat the problem in asimilar way, which in our opinion are required to betreated further, which is the purpose of the paper to draw aline between RSVM and RPWM.

III. SIMULATION RESULTS

All the simulations are done on MATLAB/SIMULINK.The inverter, the Permanent Magnet SynchronousMachine (PMSM) and the DC source are taken from the“SimPowerSystems” library.

A. Open-loop Simulations

Three sine-waves of 20 Hz out of phase to form abalanced 3-phase system are taken as reference signals.The open loop results are shown in this section. Theswitching frequency for SVM is kept constant at 1 kHz,whereas for RSVM it is varied randomly between 0.75and 1.25 kHz and therefore has an expected meanfrequency of 1 kHz.

Fig. 6. Frequency Spectrum Contrast (Open Loop)

Frequency spectrum of the two signals are shown inFig. 6. We can see a peak at 1 kHz for SVM and for

RSVM we see a small hump around 1 kHz while the restremains the same. The peak value of the switchingharmonics is 10 times lower than the peak value for anSVM at a constant frequency.

SVM intrinsically adds third-order harmonics in thephase voltages, which could be seen in Fig. 6 marked byf3, f6. Higher multiples are not marked but can be seen onthe chart. These are zero sequence harmonics andtherefore disappear from the line voltage. The simulationresult validates the concept in open loop as we can see thelow frequency spectrums perfectly superimpose eachother. The open loop test consists of measuring the phasevoltages with respect to the DC mid point at no load.

B. Closed-loop Simulations

A torque drive is simulated using a PMSM supplied bya battery via a 3 phase inverter. The control strategy usedis Field Oriented Control (FOC), with the proposedmodulation technique RSVM and SVM. The simulationmodels are completely discretized, with the simulationstep being 10µs and a torque of 3 Nm is commanded inboth the cases. The modulating frequency varies between0.75 and 1.25 kHz for RSVM. In both cases it wasobserved that the torque generated at the motor shaftfollows the torque reference, hence the two controlstrategies are validated. Now that the models are validatedwe continue our analysis on the stator currents andvoltages. Fig. 7 and Fig. 8 show the stator current evolutionin the - plane for SVM and RSVM respectively. We getanticipated results. The curve for the RSVM is a littleblurry and wavy (darker inner circle) which represents therandomness added to the system.

Fig. 7. SVM: Stator Current Evolution

Fig. 8. RSVM: Stator Current Evolution

The outer circle represents the starting of the motor,when it draws in the maximum current and the inner mostcircles represent low currents when the machine reaches

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its steady state and draws only the load current and a partto meet the mechanical losses.

The frequency spectrum of the line voltage ‘Vab’ is shownin Fig. 9 and Fig. 10, SVM in red and RSVM in blue. Thefirst peak represents the evolution of the fundamentalfrequency till it reaches its steady state at 19 Hz, whichcorresponds to the steady-state speed of 570 rpm for a 4pole electric machine.

Fig. 9. Frequency Spectrum Contrast (Closed Loop)

The peaks in red and the humps in blue represent theharmonics at the switching frequency and its multiples.Fig. 10 is a zoom around fs (1 kHz) and it's multiple. Wecan see the harmonic peak for RSVM is five times smallerfor a frequency range of 500 Hz.

Fig. 10. Switching Harmonics (RSVM and SVM)

Satisfactory results were obtained for simulationscarried out for higher switching frequencies, 10 kHz andabove. However to stay coherent throughout the documentwe've worked with 1 kHz.

IV. EXPERIMETAL SETUP

A. System Description

The experimental setup consists of a 15 kW, 3-phase 2-level IGBT inverter works on 400 V DC with current andvoltage sensors for stator current and voltagemeasurement, 3 kW PMSM with an incremental encoder(4096 points), a 300 MHz Floating-Point DSP“TMS320C6727”, high speed acquisition system, a buffercard for gate signal conditioning with incorporated deadtime. The Fig. 11 shows the schematic diagram of thesystem. The RSVM algorithm is validated on SIMULINKin open and closed loop.

Fig. 11. Schematic Diagram- Complete System

All the calculations (time sector) and generation of arandom frequency are done on the DSP. The randomlygenerated frequency would synchronize reading data fromthe Acquisition system buffers and would also determinethe execution of the control algorithm and in turn the dutycycle calculation and pulse generation. The gate signalswould be fed to the “Pulse Conditioning + Drivers” blockwhere the signals of 0 and +3.3V are brought to a certainvoltage level to ensure safe commutations (-7 and +15Vrespectively) i.e. to avoid accidental commutations.

B. Test Bench

The test bench consists of two identical machinesmechanically coupled, Fig. 12, along with the rest of theapparatus mentioned in system description. One that ispart of the system under observation is controlled and theother acts as a load.

Fig. 12. Test Bench

C. Experimental Results

Open-loop test results are shown in Fig. 13 and Fig. 14for SVM and RSVM respectively, for a balanced 3-phasesystem with fundamental frequency at 20 Hz and theswitching frequency at 1 kHz for SVM and a randomlyvarying switching frequency between 0.75 and 1.25 kHzfor RSVM.

The experimental results are completely coherent withsimulation results for open loop, with switchingharmonics 10 times smaller in both cases.

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Fig. 13. Frequency Spectrum SVM

Fig. 14. Frequency Spectrum RSVM

Due to some technical glitches closed loopexperimental results could not be included. Neverthelesswe intend to present it in the conference.

V. CONCLUSION AND FUTURE WORK

The RSVM concept was validated with harmonics 5times smaller in closed loop for an electric drive with highdynamic over a frequency range of 500 Hz while reducingthe number of commutations by 33.3% for a givenswitching frequency. We have a custom-madeexperimental setup capable of testing the functionality,feasibility and practicality of the technique. We could alsoanalyze the different inverter and electric motor variables(electrical and mechanical) like the phase currents andvoltages, torque and speed.

We plan to quantify the reduction of ElectromagneticEmissions using RSVM in a reverberating chamber; treatthe problem of torque ripple produced by the harmoniccontent of the stator current as well as different acquisitiontechniques that could be used when the data is not fed at afixed frequency to the control block, such as using anti-aliasing filters, oversampling techniques etc. Finallyvalidating it on a IFP HEV prototype.

REFERENCES

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[2] Stefan Laurentiu CAPITANEANU, “Optimisation de la fonctionMLI d’un onduleur de tension deux-niveaux", PhD Thesissubmitted to the Institut National Polytechnique De Toulouse,pp.30-44, November 2002.

[3] Keliang Zhou, Danwei Wang, “Relationship between space-vectormodulation and three-phase carrier-based PWM: a comprehensiveanalysis [three-phase inverters] ", Industrial Electronics, IEEETransactions, Sch. of Electr. & Electron. Eng., Nanyang Technol.Univ., vol. 49 pp. 186-196, Feb 2002.

[4] Michael M. Bech, “Analysis of Random Pulse-Width ModulationTechniques for Power Electronic Converters", PhD Thesissubmitted to the Faculty of Engineering & Science at AalborgUniversity, pp.22-26, August 2002.

[5] S. Mahdavi, J. Agah, “Application of Random PWM Techniquefor Reducing the Conducted Electromagnetic Emissions in ActiveFilters”, Industrial Electronics, IEEE Transactions, vol. 54 pp.2333 - 2343, Aug. 2007.

[6] V. Blasko, M. Bech, “A new hybrid random pulse widthmodulator for industrial drives", Applied Power ElectronicsConference and Exposition, IEEE 2000, New Orleans, LA, USA.vol. 2 pp.932-938, 2000.

[7] K. El Khamlichi Drissi, P.C.K. Luk, B. WANG and J. Fontaine,“A Novel Dual-Randomization PWM Scheme for PowerConverters”, 34th IEEE Power Electronics Specialists Conference(PESC), vol. 2, pp. 480-484, 15-19 June 2003, Acapulco, Mexico.

[8] N. Boudjerda, M. Melit, B. Nekhoul, K. El Khamlichi Drissi andK. Kerroum, “Spread spectrum in DC-DC full bridge voltageconverter by a dual randomized PWM scheme", ElectromagneticCompatibility - EMC Europe, 2008, Hamburg, pp. 181-186,September 2008.

[9] K. El Khamlichi Drissi, P.C.K. Luk and B. Wang, “Effects ofsymmetric distribution laws on spectral power density inrandomized PWM ", Power Electronics Letters, IEEE, vol. 1pp.41-44, June 2003.

[10] Antônio S. de Oliveira Jr., Edison R. da Silva, “Random SpaceVector Modulation for 3-Level Power Inverters and InductionMotor Drives Current Control ", Power Electronics SpecialistsConference, vol. 36 pp.987-993, June 2005.

[11] M. Zigliotto, A. M. Trzynadlowski, “Effective Random SpaceVector Modulation for EMI Reduction in Low-Cost PWMInverters", Power Electronics and Variable Speed Drives 1998,IEEE, pp.163-168, Sep 1998.

[12] S. Bolognani, R. Conton, “Experimental Analysis of the EMIReduction in PWM Inverters Using Random Space vectorModulation", Industrial Electronics, IEEE, 1996, vol. 1 pp. 482 -487, Jun 1996.

[13] Yen-Shin Lai, “Random space vector modulation technique forhigh switching frequency inverter control ", Electronics Letters1997, IEEE, vol. A4 pp.108-117, September 2008.

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