PEDS 2007

New Space Vector Control Approach for Four

Switch Three Phase Inverter (FSTPI)

Phan Quoc Dzung*, Le Minh Phuong*, Pham Quang Vinh**,

Nguyen Minh Hoang***, Tran Cong Binh** Faculty of Electrical & Electronic Engineering, HCMC University of Technology, Ho Chi Minh City, Vietnam

* * Siemens AG Presentation, Ho Chi Minh City, Vietnam* * * NARC, Ulsan University, Korea

Abstract--This paper is to present a space vector PWMalgorithm for four switch three phase inverters (B4, FSTPI)based on the one for six switch three phase inverters (B6,SSTPI) (principle of similarity) where the cX plan is dividedinto 6 sectors and the formation of the required referencevoltage space vector is done in the same way as for B6 byusing effective (mean) vectors. This facilitates thecalculation for B4 and some studies on B6 can be applied forB4 as well through this proposed similarity, e.g. the problemwith PWM in the overmodulation zone due to thecomplicated non-linear character there. Matlab/ Simulink isused for the simulation of the proposed SVPWM algorithmfor undermodulation, overmodulation mode 1 and 2. ThisSVPWM approach is also validated experimentally usingcontrol board TMS eZDSP2812 (Texas Instrument Co.).

Index Terms-- B4 (Four Switch Three Phase Inverter), B6(Six Switch Three Phase Inverter), Low-cost inverter,overmodulation, Pulse-Width- Modulation, Space vector,undermodulation.

I. INTRODUCTIONThree phase variable speed drives for asynchronous

motors have been used more and more, especially inenergy saving drive applications for fans, pumps, aircompressors... In many cases, the cost reduction is animportant target for the drive. Hence, a reduced numberof inverter switches is a promising solution. Severalinverter schemes with reduced number of switches havebeen proposed. Among them the four switch three phaseinverter (B4) (fig.1) was introduced with four IGBTswitches instead of six (B6) in a conventional three phaseinverters [1-8, 10].

In spite of the B4's drawbacks like a higher DC sidecapacitor voltage and unsymmetrical scheme exposed tothe unbalanced capacitor voltage, this inverter has thefollowing advantages over B6 [2]:

- The number of switches is reduced by a third;driving circuits are only two as only twobranches are controlled.

- In spite of the switch's higher withstand-ablevoltage in B4 the cost is still lower thanks to theprice ratio ofB4 to B6 usually lower than 3/2.

- B4's maximum common mode voltage is just2/3 ofB6's.

This work was supported by Vietnamese Ministry of Science andTechnology (MOST).

An 11

X 1

(+Td-/2 S 2S S3

Fig. 1. Four switch three phase inverter (FSTPI)

Despite rather comprehensive study SVPWM's, as

proposed by the researchers and based on the formation

of the required voltage vectors from the 4 base vectors [2-

5, 7, 8, 10], have not yet set up the link with B6's

SVPWM\, therefore the results well known for B6 are not

exploited.The content of this paper is aimed at presenting a

SVPWM\ for B4 inverter (FSTP) modeled on the basis of

a B6 by using the principle of similarity and revealing

perspective solution for the PWM\ in the zone of

overmodulation when the PWM\ is quite complicated due

to the nonlinear character of modulation in this extended

zone. This issue has not been approached in the above

mentioned papers.

ANALYSIS OF SPACE VOLTAGE VECTORS AND STATOR

FLUX

According to the scheme in fig. the switching status

is represented by binary variables SI to S4, which are set

to "1" when the switch is closed and "0" when open. In

addition the switches in one inverter branch are

controlled complementary (1 on, off), therefore:

S1±S2=S3±S4 (1)

Phase to common point voltage depends on the turning

off signal for the switch:

V = (2S -i). Vdc; VbO = (2s3 dc). = 0; (2)

2 2

Combinations of switchingSt-S4 result in 4 general

space vectors -f th(Table 1), components [2-of the

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1-4244-0645-5/07/$20.00©2007 IEEE 1002

voltage vectors are gained from abc voltages by usingClark's transformation:

LVa] 2[ A -V (3)0 -0= 2 2 Vb1 3

where Va, Vb, V, : phase voltages on the load (Yconnection), defined by:

1VI = 3 (2Vao bo )

31

V= (2VbO -Va);

Vc =-I KO + VbO )1 (4)

In order to form the required voltage space vector -Fwe can use 3 or 4 vectors in one sampling interval Ts. Theconstant value 0 (zero) vectors can be formed by dividingto (duration of zero vector) among 2 opposite vectors

(VI,V3) or (V2,V4 ) [2, 7].For three phase induction motors the stator flux

linkage vector can be represented as follows [2, 10]:Cy = fV(t't (5)

In case of the sinusoidal voltage source the standardstator flux linkage vector can be defined:v V-eC 2) (6)

Thus the flux linkage vector locus will describe a

circle with the radius r =Vm0t)

TABLE 1COMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS

S1 S3 PV V, +VjVj

V1 = 3e

33 2Vd, eJ3

o i F~~~~~~4Vde5 6

~~~~~~~~3

p

a

I .

Fig. 3. Sectors used in conventional SVPWM methods for B4

In case the motor is fed from a B4 inverter the fluxlinkage vector is:

v 1 (7)where n = 1.4 ; t11: duration of V1.

If the switching algorithms can ensure the bestapproximation by minimizing the discrepancy betweenvector loci 'P andv , the stator voltage performance willbe optimized. Thus the design of the algorithm for PWMsamples in the inverter phases based on this rule has avery important role. This approach is used with successfor B6 inverters.

The performance index used for evaluating the outputvoltage is the Total Harmonic Distortion factor THD%,defined as follows [2]:

V,2

THD% =2A3( ) 100% (8)V,

where n : harmonic number.

III. NEW SVPWM APPROACH FOR B4 INVERTER

SVPWM methods presented in papers [2, 3, 7, 8, 10]are based on the formation of the reference vector on theplan c4x which is divided into four sectors (sector I.IV).The active vectors and their duration in one samplinginterval are selected and calculated on the basis of therequired Vref location respective for these sectors (fig.3).SVPWM method proposed in this paper is based on the

principle of similarity of the one for B6 inverters, whereplan cx3 is divided into 6 sectors and the formation of Vrefis done similarly as for B6. This facilitates the calculationfor B4 and some issues for B6 can be applied for B4thanks to this proposed approach.To simulate 6 non-zero vectors in B6, in this proposed

method, beside the two V1 and V3, we use the effectivevectors V23M, V34M, V41M and V12M. These vectors areformed as follows:

123M = 2 + '3= 3 e"; 134M2 3

Fig. 2. Voltage space vectors in the plan ixf

2 ()9=)1I ( ) Vdcj r4

I ( v v ) Vd -j-To 2 3 2 3

To simulate zero vectors of B6, we use the effective Vom:

1003

I _ibk

i

V34

V1V41 M V23M\VV3X \~~*-,''e ,'5 ,#\\Om\

\1/2 \ / XX \V2

\A d , \A dhA \ / /nQAV12 n

Fig. 4SVW mehdpooefo 4othprnilofsimlait of/B6X' "

\\

-

Fig. 5. Basic space vectors in B6 inverter.

TABLE 2SIMILARITY BETWEEN SPACE VECTORS OF B4 AND B6

Base voltage space vectors Voltage space vectors ofB4ofB6V1 V23MV2 V3V3 V34MV4 V41MV5 V1V6 V12M

VO, V7 VOM

-' (V orVOM =2 2 (V 0)The similarity between space vectors of B4 (Fig.4) and

B6 (Fig.5) is presented in Table 2. The base vectors ineach sector used to form the required space vector Vref ispresented in Table 3.

Below we will describe the space vector modulationfor B4 inverter based on the modulation for B6 with theprinciple of similarity.

A. Under modulation (0 <M < 0.90 7)In this zone the required voltage space vector rotates in

a hexagon. The space vector modulation in this zone isbased on the formation of three voltage vectors insequence in one sampling interval Ts so that the average

output voltage meets the requirement. The calculations ofthe switching states in B6 and B4 are as follows for 1/2 Ts[9]:tx = MT, sin(i/ 3 - a);

ty =-MT, sin(a); (1

= T, /2 -tx -ttywhere:t, - duration for vector Vxty - duration for vector Vytz - duration for vector VIM - the index ofmodulation M V /V1sw (V* - amplitudeof the required voltage vector, V1sw - peak value of sixstep voltage).

However in B4 inverter since mean vectors tXyM andzero vectors toM are formed from the two base vectors theduration of base vectors is equal to 1/2 as for the abovementioned mean and zero vectors.

In order to ensure the closest following and theminimized discrepancy between 'P and 'P* loci, theapproach shall be done in a symmetrical way from bothsides.

It can be used, for example, the effective vectors V23M,V3, VOM for sector I, where V23M, VOM are defined as (11):

tx = A=MTf sin(i/ 3 -a);t= t31= AXI7 sin(a);

tz = tof = TS I2t23r -t3f;

t23ft2m 2 ' t3m 223 t_o2 ' 3Z- 2 ' tiz

to22

(12)Thus the total durations for base vectors V1, V2, V3

are:tv1 = t1;tV2 = t2m;tV3 t3f + t3f + t3

Similarly we can calculate the space vector modulationfor the other sectors. The calculation results are shown inTable 4.

B. Overmodulation in mode 1 (0.907 <M< 0.952)Similarly as for B6, this mode starts when the required

Vref goes beyond the circle inscribing the hexagon andreached its sides. When sliding on the hexagon side(M=0.952) the value of t, is equal to zero:

~3cosa- sina T 0T14tX CO X-Snz s ; t = s _tx t 0= (14)tX 3cos a+ sin a 2 2As for the undermodulation, effective vectors tXyM and

TABLE 3VECTORS USED IN THE SPACE VECTOR MODULATION B6 & B4Sector B6 (VX, VY, VZ) B4 (VX, VY, VZ)

I_________ V1,V2,VZ V23M, V3, VOMII__________ | V2,V3,VZ | V3,V34M,VOMIII | V3, V4, VZ V34M, V41M, VOMIV V4, V5, VZ V41M, V1, VOMV V5,V6,VZ V1, V12M, VOMVI V6, V1, VZ V12M, V23M, VOM

1004

(13)

TABLE 4VECTOR DURATIONS IN THE PROPOSED SVPWM METHOD

Sector I Sector II

t 23 MT sin(z / 3 - a); t = t3 -MT sin(;z / 3 - a'

ty = t f= f3MT sin(a); t= t34 -MT sin(a);

T2-23 13; t = t0f T2-t3, -t34a;11~~~~~~~~~~~1

t,m = t m=T 12t - tt23f 23f t3412 2 t3m 2 ;4m 2

10f 10o1 tot3z = tXl = z = = t ft 2tf2 2 t3, _ ti =

2 2

tvl =tl tvl =tl

tV2 t2m tV4 t4m

tV3 t3f + t3m + t3z tV3 t3f + t3m + t3z

Sector III Sector IV

t334 MfT sin(/3 -a); t1141 MTsin(r /3 -a);

-v3 V3ty =t41 = JTs sin(a); ty = tAf= JMTs sin(a);

tz = to = T' 1 2- t3 -4 tz = to =T'Is 1 2-t -tlfm 121; 2 +23441; 1 Of=4 1f;

I(t 3 = 2 Xtl =

134

t 34+ '41

t441

t '.41+3. 2' 4 2 2' 2' 2'

'i. 2' t3 2 ti 2

tz= 2 ti 2

tV4 t4m tV4 t4m

tV3 t3m + t3z tV3 t3Sector V Sector VI

tx 1tf = J Mfl sin(z/3-a); tx =tl2f =r MfT sin( 3 -a);

3 V3ty= t12f = MT sin(a); ty = t23f =.iTs sin(a);

tz = to = T 12- tl -t2; tz = tof = 7s /2 t2 -2;Ilf ilf 12f;2 - t12f +t23f.t12f t12f t12f t12f t23ft ;t ~~~~~t1;t=_ +

'. 2 2=

2 '. 2 2. 2 2

tof tof t23ft3z 2 ;t1Z = 2 3 2

tf tft3z 2 tz = 2

tV = tif + tlm + t1Z tVI tlm + tlz

tV2 t2m tV2 t2mtV3 t3 t3 t3m + t3

effective -zero vectors toM are formed from the two basevectors, so the duration of the base vectors is just half ofthe one for the mentioned vectors.When M= 0.907, values t,, ty, tz are defined as (12). In

case of 0.907<M<0.952 the linear approximation is usedto calculate tx, ty, t,.

tV1 tV2: MW

Ts/2 Ts/2

a) For sectors I, V, VI

b) For sectors II, III, IV

Fig. 6. Pulse patterns for switching in the proposed method.

C. Overmodulation mode 2 (0.952 <M<1)Similarly as for B6, in this overmodulation mode 2,

the required Vref increases up to six step mode.When M=1, the modulation is done in two cases:T

tx=T ;tY =0;tZ =O;forO<a<f/6; (15)

tx =O;ty =T ;tZ =O;forhz/6<a<f132

From the above formulas we can induce that theduration of the respective base vectors to form theeffective and effective-zero vectors is similar to the twoabove mentioned modulation cases.When M = 0.952, values tx, ty, tz are defined as (14).

For 0.952<M<1 the linear approximation is used tocalculate tx, ty, tz.

IV. SIMULATION OF THE PROPOSED SVPWM FOR B4Matlab/ Simulink is used for the simulation of the

proposed SVPWM for the undermodulation,overmodulation mode 1 and 2. DC voltage Vdc = 600V.Output voltage fundamental harmonic f 50Hz.Switching frequency fw = 4.8 kHz.

1. Case study 1: For the undermodulation with M0.7.The phase voltage, line voltage waveforms andtrajectory of flux space vector are shown in Fig.7-9 respectively.

2. Case study 2: For the overmodulation mode 1and 2.The phase voltage, line voltage waveforms,trajectory of flux space vector are shown in Fig.10-12 for the value of modulation index M =

0.94 and in Fig. 13-15 for the value ofmodulation index M= 1.The simulation resultsdemonstrate the excellent performance of theproposed SVPWM for B4, while the goodresponses of the output voltages and flux vectorare obtained (fig.7-15, Table 5).

1005

Phase Voltage Waveform300

>- 1o

0va

,

21001

-300'0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Time, [s]

Fig. 7. Phase voltage waveform (M=0.7).

Line Voltage Waveform600

400

200

0.

-2 00

-400 --I

-600'0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Time, [s]

Fig. 8. Line voltage waveform (M=0.7).

Flux Vector Polygon

0.4

0.3

-T*wT

Line Voltage Waveform600

20 t- -I r

'o,! 0400

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02Time, [s]

Fig. 11. Line voltage waveform for in case of overmodulationmode 1(M=0.94).

Flux Vector Polygon

0.5 -P- --

0.4

0.3

0.2

-0.1 - - t -- - - -t------t-----t--

-0.2 - - T T- -- -- TI- -- ---I--' -

-0.3 X I I I /

-0.4 - - +--> I /

-0.5 -

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Fig. 12. Trajectory of flux space vector in case ofovermodulation mode I(M=0.94).

Phase Voltage Waveform

200

0.2-

0.1-

0.1

-0.2 - T - kf-I- - 7 - -I --i- - F - I-'

-0.31- 4 - 4 - -1- -I- - 4- - - -i - t-

O0_5L04-0_3_0I 2_ 0_1 0 01 020_ 3 0I4 0_5

Fig. 9. Trajectory of flux space vector (M=0.7)

Phase Voltage Waveform300

0-

. 100

100

-200-

-300' L

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02Time, [s]

Fig. 10. Phase voltage waveform in case of overmodulationmode 1 (M=0.94).

-100

-200

2300'

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02Time, [s]

Fig. 13. Phase voltage waveform in case of overmodulationmode 2 (M= 1).

Line Voltage Waveform600_400 - NI-

~~~~~~~~~~~~~~II ^ t̂ d57200 t- Ul Mu11 10 0400

6200-

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02Time, [s]

Fig. 14. Line voltage waveform in case of overmodulation mode2 (M=1).

1006

0-

Flux Vector Polygon06 -- -- -

0.4---- 1-- - - - - - ---

04

-0.2--I-t----------

-0.6 _ -_ __ _ _ I_ f _

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Fig. 15. Trajectory of flux space vector in case ofovermodulation mode 2 (M=1).

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Fig. 17. Line voltage waveform and harmonic spectrum of Vab.

M20.0ms A Chil 21.0 VI

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TABLE OF SIMULATION RESULTS FOR SVPWM CONTROLLERModulation index M 0.7 0.94 1 (six-

step)Reference voltage Vlref, [V] 94.5 126.9 135Simulated fundamental output 94.5 127.1 135phase voltage V1, [V]Distortion factor THD, [0](for first 35 harmonics)for Van 0.0155 0.5349 4.6359for Vbn 0.0146 0.5359 4.6359for Vcn 0.0067 0.5248 4.6353

V. EXPERIMENTS ON THE PROPOSED SVPWM FOR B4

To verify the proposed SVPWM an experiment hasbeen set up. The SVPWM is programmed in the controlboard TMS eZDSP2812 to generate the command pulsesfor B4 (IGBT SKM 75GB 123D, Driver SKHI 22A).

The output from FSTPI was connected to a three phaseinduction motor, which has the follows parameters: f= 50Hz, 400V,Y, 2HP, 3.4A, cos(p =0.81, 1420 rpm.

The switching frequency of IGBT is 5kHz. The DClink voltage was adjusted at 1 OOV-200V, and the splitcapacitors are rated at 3300jF.

1. Case study 1: The fundamental harmonic ofoutput voltages is 25Hz. Fig. 16-18 show thecommand pulse patterns for SI, S3; line voltageswaveforms of Vab , the phase current waveformOf ia.

2. Case study 2: The fundamental harmonic ofoutput voltages is 50Hz. Fig. 19-21 show linevoltages waveforms of Vab, Vbc, the phasecurrent waveform of ia.

~~~~~~~. . . .l

l~~~~~~~~~~~~A V

Fig. 16. Command pulse pattern for 51, S3.

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Fig. 18. Current waveform and harmonic spectrum Of iA.

TIkPreVu a

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Fig. 19. Line voltage waveform and harmonic spectrum of Vab.

Tek PreVu I bF-- ig

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Fig. 20. Line voltage waveform and harmonic spectrum of Vbc

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Ch l M1 Al ChA 1h f 4.00 V

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'

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Fig. 21. Current waveform and harmonic spectrum of iA.

i0 W~~~~~~~~~~~~~~editMaCeth

t- - - - |i S 0 ,1; 01 ggW;0Eg Set FFT

t~~~~~~~~~~~~~~~~~e FFI i -. --- 1 -',i~~ertScae t

~~~~~~....

Dual Wfm|Math|FT

Fig. 22. Line voltage waveform and harmonic spectrum of Vab(M=0.7).

M0. m11Oms A[ Chl fr -100 V

10 May 2007F--680.00Ojusj 1.6:29:40

Fig. 23. Line voltage waveform Vab and spectrum analysis(M= 1).

implementation of the proposed SVPWM is done bysimulation and in experiment to serve the practicalproduction of the cost effective inverters in the future.

REFERENCES[1] H. W. van der Broeck and J. D. van Wyk, "A comparative

investigation of a three-phase induction machine drive witha component minimized voltage-fed inverter underdifferent control options," IEEE Trans. Ind. Appl., vol. IA-20, no. 2, pp. 309-320, Mar./Apr. 1984.

[2] Frede Blaabjerg,, Sigurdur Freysson, Hans-Henrik Hansen,and S. Hansen "A New Optimized Space-VectorModulation Strategy for a Component-Minimized VoltageSource Inverter " IEEE Trans. on Power Electronics, Vol.12, No. 4, July 1997,pp 704-7 10.

[3] C. B. Jacobina, E. R. C. Da Silva, A. M. N. Lima, and R.L. A Ribeiro. "Vector and scalar control of a four switchthree phase inverter". In Conf Rec. IAS, pages 2422-2429,1995.

[4] F. Blaabjerg, S. Freysson, H. H. Hansen, and S. Hariseri."Comparison of a space-vector modulation strategy for athree phase standard and a component minimized voltagesource inverter". In Conf Rec. EPE, pages 1806-1813,Sevilha - Spain, September 1995.

[5] G. A. Covic, G. L. Peters, and J. T. Boys, "An improvedsingle phase to three phase converter for low cost ac motordrives," in Proc. PEDS '95, Singapore, vol. 1, pp. 549-554.

[6] G. T. Kim and T. A. Lipo, "VSI-PWM inverter/rectifiersystem with a reduced switch count," in Proc. IAS '95, pp.2327-2332.

[7] M. B. R. Correa, C. B. Jacobina, E. R. C. Da Silva, and A.M. N. Lima. "A General PWM Strategy for Four-SwitchThree-Phase Inverters" IEEE Trans. on Power Electronics,Vol. 21, No. 6, Nov. 2006, pp 1618-1627.

[8] G.I. Peters, G.A.Covic and J.T.Boys," Eliminating outputdistortion in four-switch inverters with three-phase loads."IEE Proc.Electr.Power Appl. .vol.IA-34, pp.326-332,1998.

[9] J. 0. P. Pinto, B. K. Bose, L. E. B. da Silva, and M. P.Kazmierkowski, "A neural network based space vectorPWM controller for voltage-fed inverter induction motordrive," IEEE Trans. Ind. Applicat., vol. 36, pp. 1628-1636,Nov./Dec. 2000.

[10] D. T. W. Liang and J. Li, "Flux vector modulation strategyfor a fours witch three-phase inverter for motor driveapplications," in Proc. IEEE PESC, Jun. 1997, pp. 612-617.

3. Case study 3: The fundamental harmonic ofoutput voltages is 50Hz. Fig. 22 shows the linevoltage waveform Vab and spectrum analysis forM=0.7 (undermodulation). Fig. 23 shows theline voltage waveform Vab and spectrum analysisfor M=1 (six-step mode).

VI. CONCLUSION

The proposed SVPWM in this paper is based on theone for six switch three phase inverters (B6, SSTP) usingprinciple of similarity where the ocx plan is divided into 6sectors and the formation of the required referencevoltage space vector is done in the same way as for B6 byusing the additional effective vectors. This facilitates theSVPWM calculation for B4 and some studies on B6 canbe applied for B4 as well through this proposed approach,e.g. SVPWM for the overmodulation. The

1008

.-~~~~I.e I* -----