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A Nov el Implementation of SVP WM A lgorithm an d Its Application toThree-phase Power ConverterXiaowei Zhang*, Yongdong Li, Wensen Wang

Department of Electrical EngineeringTsinghua University Beijing China 1 00084

Fax: 8610-62783 057, Phone: 8610-627862 30E-mail:liyd@mail.tsinghua.edu.cn

Abstract- In this pa per a novel implementation methodof the space voltage vector PW M algorithm for three-phase power converter is proposed. The theoreticalprinciples of this implementation method are discussed.The results of its application using digital signalprocessor TMS320F240 are shown.Key words: SVP WM algorithm

1. IntroductionIn most industrial system, such as variable speed AC

drive system and three-phase PWM converter, the sine-triangle PWM strategy is widely used due to itssimplicity. The space vector pulse-width modulation(SVPWM) [l-31 is another popular PWM strategy inwhich higher DC bus utilization and less harmonicdistortion compared to sine PWM can be obtained.Although it is well suitable for digital implementation,the SVPW M technique is som ewhat complex for somehigh performance variable speed AC drive system.

In this paper, a novel implem entation method basedon SV PWM appro ach is proposed, and the principles ofsymmetric PWM waveforms generation is described.Such algorithm is conceptually simple and easy to beimplemented for open loop or close-loop three-phase

* The author Xiaowei Zhang is an associate professorof the Southwest Institute of Technology, Mianyang,Sichuan, China. Now she is the visiting scholar ofTsinghua University Beijing C hina.

I1l q 0 10 ):y.................4.E..........,,,119 1

Fig 1 Space voltage vectors an d a reference vectorpower conversion system in a DSP. Throughexperiments the characteristic of the proposedimplement method is verified.

2. A N ovel Algorithm PrinciplesThe SVPWM technique of three-phase inverter

desc ribed by H,W.Broeck[ 11 becom es very popu larrecently. In this section we will describe a novelalgorithm principle.

In Fig. 1 the eight available different switchingvectors of the power converter are depicted in a-Pcoordinate. If a reference volta.ge vector V* is given inthe hexagon area, as shown in Fi gl, this vector can becomposed by the nearest two active vectors and zerovector as follows by assuming Ts (PWM carrier period)very short and the change of i'' is relatively small.

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I+T,T,P' = jv*= T l v ,+ T 2 v 2+ To~o(OOOorl1 )

I

The reference vector is composed at equal intervalsof time Ts. T1 and T2 are the duration of the activevectors. In high pe rformance variable-speed AC driveand three-phase PWM converter, stationarytransformation from three-phase to a-p coordinate isgenerally used. In this case, the a-p components ofreference voltage vector can be easily obtained by theoutput of close-loop controller. In open-loop control, thereference voltage vector va and vpare obtained bymapping the desired three-phase output voltage to the a-p coordinate. Now, ?@nd Tf lhave been given, we canfocus on the algorithm and software implementationissues. And a novel implementation of SVP WM byTMS 320F24 0 DSP is given below.2.1 Reference voltage vector f *

In the close-loop controller, the voltagevectorsp and p have been obtained, the magnitude ofreference voltage vector should be calculated as follows:

a P

P*2= v,2+v; (1 )Then, we can determine which sector P' is located

according to the sign of the v, and v , hat is:B

V* is in sector I.

In the open-loop controller, reference voltagevector r* hould be the desired value of three-phaseoutput voltage.2.2 Switching time duration

In order to avoid overflow in micro-con troller, it isassumed that the norm alized value of 7' is:

Th e a-p components become:A * A *v, = v cosa (4)Qi Ts i n a

Where, a s the angle between a-axis and referencevector ;C;*

a

a

v;Fi g 2 Relationship of reference vector in a-P planeAccording to the relation between the reference

vector and its components as shown in Fig.2, theduration of active vectors T1, T2 and z ero vec tor TO insector I can be calculated.

FITl+ V2T2cos 60"= V*T ,cos aV2T2 in 60"= V*T,sin a

( 5 )

This gives the switching time of activevectors.

1 - 1 -C Z T , ~ - V , T , = (?U - - V ; ) T S2 J5-sin 60 O

P*is in sector VI- 1105 -

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The switching time expression in the sector I - ector VIcan be given in a general form as follows:

2 q IC .* IC a *T, = -[sin(-k)V, - os(-k)Vp]J 5 3 3J5 3 3

IC A + IC A iT2 = -{-sin[-(kT, - )]V, + cos[-(k - ) ]Vp )

where k=l, , ...6 (sector number)After T I, T2, TO are obtained, the switching time

for each bridge can be g iven by following forms:141 14 2

T, =-ToTb =-To +-T ,

2.3 Switching PatternsFig.3 shows the three-phase symmetrical

modulation switching patterns. Now, the switching timefor each bridge o f three-phase power converter has to becalculated. We use space vector PWM waveformgenerator- of- TMS320F240 DSP to generate .spacevector PWM outputs. It greatly simplifies the generationof symmetric space vector PWM waveforms. Theswitching time is calculated in every carrier PWMperiod Ts. In different sectors, different switchingpatterns are output respectively.

. . .. .. . .

Fig 3 Switching patterns of SVPWM at sector I

The selection of active states and zero states in all sixsectors can be summarized as:table I

Degree sector choice active states and zero states0-60 I 000 100 110 1 1 1 110 100 00060-120 I1 000 010 110 1 1 1 110 010 000120-180111 000 001 101 1 1 1 101 001 000180-2401V 000 001 011 1 1 1 011 001 000240-300V 000 010 011 1 1 1 011 010 000300-36OVI 000 100 101 1 1 1 101 100 000

3. Experimental resultsTo verify the proposed nasvel SVPWM algorithm,

experiments are performed for PWM inverter by usingTMS320F2 40. The prototype used is 2.2 W, 220V,50Hz,three-phase induction motor drive fed from IGBT-based2KVA inverter with a DC bus voltage of 310V. Thedrive schemes have been implemented for switchingfrequency 1OKHz and fundamental frequency 50Hz.The waveforms for the proposed novel implementationSVPWM algorithm are'shown i n Fig4 -Fig7. Fig 4 andFig5 give the waveforms of phase voltage and linevoltage on open loop. Fig6 and Fig7 give the waveformsa phase current. Fig 8 is the waveform of the phasevoltage and current using the sine-triangle strategy. Fig9 is the FFT analysis for the SVPWM algorithm. Fromthese waveform, we can see thi3t through this method,the harmonic components can be reduced greatly,specially the 31h and Sh, omparing to the sine-trianglestrategy. There is less spikes in the current waveform.And the FFT analysis shows tliat the high frequencycomponent can be restrained obviously. Some otherexperiments have been done in different fundamentalfrequency to verify the performance of the proposedalgorithm.

4. ConclusionA novel SVPWM algorithm has been described. It

has been implemented for PWM converter using digitalsignal processor TM S320F240. Th e experimental resultsindicate that converter that ad opt the proposed algorithmcan achieve satisfactory performance. This algorithmhas good characteristic. Either in open-loop control orclose-loop-control-the proposed SVPW M algorithms canbe applied with the TMS320F24O 50ns per instruction

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(20MIPS). Very complex control algorithms, such asspeed sensor-less vector control of induction motors canbe realized. The program of vector control algorithm canbe completed with 1 OKHz sampling frequency. After theSVPWM algorithm programs have been made in theopen-loop controller, the programs for the close-loopcontroller can be archived easily. So , novel SVPWMalgorithm is very simple and easy to be used in differentcontrol systems.

B k m U 1 oo k s l s I O A WI? ' " ' ' ' , " ~ I ' , " " "---T----h

6 Mar 200021 SI 39Fig 4 Waveform of the phase voltage

6 MW 100019 SI 4 1m

Fig 5 Waveform of the line voltage

Fig 7 Waveform of the phase voltage and current

Fig 8 Waveform of the voltage and current using thesine-triangle strategy.

Fig 9 the FFT analysis resultReferences

[I ] H. W. Vander Broeck and H. C. Skudelny, "Analysis andrealization of a pulse width modulator based on voltage spacevectors" IEEE Trans. 1988, IA-24, ( I ) .[2] Dae-Woong Chung, Joohn-Sheok Kim, Seung-Ki SUI,"Unified voltage Modulation T echnique for Real-time Three-phase Power Conversion" IEEE Trans. 1998, IA-34.PP 374-380.

PP 142-150.

[3] GNarayanan and V.T.Ranganathan "Synchronised PW Mstrategies based on space vector approach. Part 1: Principles ofwaveform generation" IEE Proc-Elecre. Power. Appl. Vol.146,No.3, May 1999

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