Dynamic Adaptive Space Vector PWM for Four Switch Three Phase Inverter Fed Induction Motor with Compensation of DC – Link Voltage Ripple

Hong Hee Lee NARC, Ulsan

University, Korea hhlee@mail.ulsan.ac.kr

Phan Quoc Dzung Faculty of Electrical & Electronic Engineering HCMC University of

Technology Ho Chi Minh City, Vietnam

pqdung@hcmut.edu.vn

Le Dinh Khoa Faculty of Electrical & Electronic Engineering HCMC University of

Technology Ho Chi Minh City, Vietnam khoaledinh@hcmut.edu.vn

Le Minh Phuong Faculty of Electrical & Electronic Engineering HCMC University of

Technology Ho Chi Minh City, Vietnam lmphuong@hcmut.edu.vn

Abstract- This paper presents and analyses a new dynamic adaptive space vector PWM algorithm for four- switch three-phase inverters (FSTPI) fed induction motor under DC-link voltage ripple. By using reasonable mathematical transform, Space Vector PWM technique for FSTPI under DC-link voltage imbalance or ripples has been proposed, which is based on the establishment of basic space vectors and modulation technique in similarity with six-switch three-phase inverters. This approach has a very important sense to solve hard problems for FSTPI under DC-link voltage imbalance, for example ensuring the required voltage for under modulation mode and over modulation mode 1 and 2, extended to six-step mode. The compensated technique also allows reduce the size of DC-link capacitors and the cost of the inverter. Matlab/Simulink is used for the simulation of the proposed SVPWM algorithm under DC-link voltage ripple. This SVPWM approach is also validated experimentally using DSP TMS320LF2407a in FSTPI-IM system. The effectiveness of this adaptive SVPWM method and the output quality of the inverter are verified.

Keywords: Space vector Pulse-Width-Modulation, undermodulation, overmodulation, Four Switch Three Phase Inverter, Six Switch Three Phase Inverter, DC-link ripple.

I. INTRODUCTION Nowadays, a few research efforts have been directed to

develop power converters with reduced losses and cost for driving induction motors. Hence, a reduced number of inverter switches is a promising solution. Among them the four switch three phase inverter (FSTPI) (Fig.1) was introduced with four IGBT switches instead of standard six switches in a typical three-phase inverter (SSTPI) [1-3,8]. Due to the circuit configuration, the maximum obtained peak value of the line to line voltage equal Vdc/2 so the voltage Vdc is about 600V. In order to get a high dc-link voltage, in this paper authors use the single-phase diode rectifier and high dc-link voltage Fig.1 [7].The main drawback of FSTPI is the voltage ripple of DC-link capacitors. To ensure the quality of the output voltages of VSI, we must solve the mentioned above problem by using real-time compensation SVPWM technique when generating switching control signal in consideration of unbalanced DC-link voltages by direct calculation of switching times based on four basic space vectors in FSTPI.

In our work [9], the link between SVPWM for FSTPI and SSTPI have been done by using the principle of similarity and revealing complete solution for the PWM in the whole modulation index in case two DC-link voltages balanced. In

another our work [10], the adaptive SVPWM had been used for FSTIP under DC-link voltage ripple but in that proposed method, to simulate 6 non-zero vectors in SSTPI we use the effective vectors '

6'

1 ...VV which lengths are equal the length of the

shortest vector from 1V , 3V (Fig.4, 5). The content of this paper is aimed at presenting a dynamic

adaptive SVPWM, that permit increase the maximum of fundamental of output voltage greater than one that be proposed in our work [10] and another paper [4,7], for FSTPI under DC –link voltage ripple. This issue has not been approached in the above mentioned papers.

Fig. 1. Circuit configuration of the FSTPI fed induction motors.

II. ANALYSIS OF SPACE VOLTAGE VECTORS AND STATOR FLUX IN CASE OF DC LINK VOLTAGE RIPPLE

According to the scheme in Fig.2 the switching status is represented by binary variables S1 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 (one switch on, another switch off), therefore:

S1+S4 = 1 S3+S2 = 1 (1)

Phase to common point voltage depends on the turning off signal for the switch:

( ) ( ) ;1;1;0 13230211100 VSVSVVSVSVV cba ⋅−+=⋅−+== (2)

dcdc

dcdc VVVVVV .

2;.

2 21 εε +=−= (3)

Where

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V1, V2 voltage across the dc-link capacitors; V1+V2=Vdc

dcVV1

21 −=ε the imbalance factor ;

61

61 ≤≤− ε

Combinations of switching S1-S4 result in 4 general space vectors 41 VV → (Table 1).

Voltage imbalance in the DC link causes the space vector origin to shift along the

1V /3V axis (Fig.3), with

1V and 3V no

longer being equal in magnitude, as described in Table 1. In order to form the required voltage space vector refV , we

can use 3 or 4 vectors in one sampling interval Ts. For three phase induction motors the stator flux linkage vector

can be represented as follows [2, 4, 6, 9] : ( )dttV∫=Ψ (4)

In case the motor is fed from a FSTPI inverter the flux linkage vector is:

0Ψ+⋅=Ψ nn Vt (5) where n = 1..4 ; tn : duration of Vn. If the switching algorithms can ensure the best approximation by minimizing the discrepancy between vector loci Ψ and *Ψ , the stator voltage performance will be optimized. This approach is used successfully for FSTPI in case of the balance in DC link voltage [9].

TABLE 1. COMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS

S1 S3 αV βV V

0 0 3

2 2V 0 1V

1 0 3

12 VV − 3

21 VV + 2V

1 1 3

2 1V− 0 3V

0 1 3

12 VV − 3

21 VV +− 4V

Fig. 2. Voltage space vectors in the plan αβ

If PWM output voltages are synthesized without considering the non-ideal DC link conditions then unbalanced stator voltages will result, which causes large current variations and the deviation of real flux-linkage vector [4, 7].

III. NEW DYNAMIC ADAPTIVE SVPWM APPROACH FOR FSTPI WITH COMPENSATION DC-LINK VOLTAGE RIPPLE CONDITION SVPWM method proposed in this paper is based on the

principle of similarity of the one for SSTPI inverters, where plan αβ is divided into 6 sectors (sector I…VI) and the formation of Vref is done similarly as for SSTPI in conditions of DC-link voltage ripples. This facilitates the calculation of switching states for FSTPI and some developed modulation methods for SSTPI can be easily applied to FSTPI modulation method thanks to this proposed approach.

To simulate 6 non-zero vectors in SSTPI, in this proposed method, we use the effective vectors '

6'

1 ...VV , when the length of

the basic generated vector is equal )2

( 31 VV + (Fig.4, 5).

Furthermore, when V1=V2, the same equations as in the case of balanced DC-link voltages are achieved [9]. These modified vectors are formed as follows:

141'

6431'

53'

4

321'

3321'

21'

1

21;

21;

21;

21;

VVmVlVVVhVgVVfV

VeVVdVVcVVbVVaV

++=++==

++=++== (6)

where the coefficients a,b,c,d,e are defined as follows: Case 1: DC-link voltage V1 < V2 ( 1V >

3V ) (Fig.3)

( )

1221;

122

;0;12

12;21;

2221

VVVf

VVhe

gdV

VVmclbV

VVa

+===

==−====+= (7)

3/2 2V

3/)( 21 VV +−

3/2 1V−

3/)( 12 VV −

O 'O

2V

'3V

'4V

'2V

'1V

1V

'6V

3V

'5V

4V

Fig. 3. SVPWM proposed method for FSTPI in case of V1 < V2

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α

β

Vref

3/2 2V

3/)( 21 VV +−

3/2 1V−3/)( 12 VV −

O'O

3/)( 21 VV +2V

3V

4V

1V

'2V

'1V

'3V

'4V

'5V '

6V

Fig. 4. SVPWM proposed method for FSTPI in case of V1 > V2

Case 2: DC-link voltage V1 > V2 ( 1V < 3V ) (Fig.4)

( )

1221;

21

;22

21;0;22

1;22

21

VVVfhe

VVVgdmc

VVlb

VVVa

+===

−======+= (8)

To simulate zero vectors of SSTPI, we use the effective '0V :

3311'

0 tVtVtV z ⋅+⋅=⋅ (9) Where t1 and t3 are calculated by equations:

⎩⎨⎧

=+=−

ztttatft

31

;031 (10)

The basic vectors in each sector used to form the required space vector Vref is presented in Table 2.

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

hexagon. The space vector modulation in this zone is based on the formation of three voltage vectors in sequence in one sampling interval Ts so that the average output voltage meets the requirement. The calculations of the switching states in SSTPI and FSTPI are as follows for ½ Ts: [5]

( )

( )

ytxtsTzt

sMTyt

sMTxt

−−=

=

−=

2/

;sin3

;3/sin3

απ

αππ

(11)

where: tx - duration for vector Vx; ty - duration for vector Vy tz - duration for vector Vz; M – modulation index M = V*/V1sw (V* - amplitude of the required voltage vector, V1sw – peak value of six step voltage for balanced DC-link voltages ). The calculation results for the six sectors are shown in Table 2. The pulse patterns for switching are presented in Fig.6.

The proposed method ensures that these switching times are dynamically adjusted for each period Ts to compensate for the DC-link ripple. The maximum obtainable output phase voltage Vm_max is defined as follows:

)21(3

1max_ VVmV +⋅= (12)

TABLE 2. VECTOR DURATIONS IN THE PROPOSED SVPWM METHOD

Sector I

ytxtsTzt

sTMvtyt

sTMvtxt

−−=

==

−==

2/

)sin(2

32

);3/sin(2

32

'2

'1

απ

αππ

( ) ( )[ ]

13

;5.0111

taft

ztcbytaxtfaat

=

+−−−+−+

=

3

;5.0

;1

3

2

1

tyctvtytvt

tybtxatvt

+=

=

++=

Sector II ( ) ( )[ ]

13

;5.015.011

taft

ztdeytcbxtfaat

=

+−−−+−−−+

=

3

);(5.0

;1

3

2

1

tyetxctvtytxtvt

tydtxbtvt

++=

+=

++=

Sector III ( ) ( )[ ]

13

;15.011

taft

ztfytdextfaat

=

+−+−−−+

=

3

;5.0

;1

3

2

1

tyftxetvtxtvt

txdtvt

++=

=

+=

Sector IV

( ) ( )[ ]

13

;5.0111

taft

zthgytfxtfaat

=

+−−−+−+

=

ytvt

tyhtxftvt

tygtvt

5.0

;3

;1

4

3

1

=

++=

+=

Sector V

( ) ( )[ ]

13

;5.015.011

taft

ztmlythgxtfaa

t

=

+−−−+−−−+

=

)(5.0

;3

;1

4

3

1

ytxtvt

tymtxhtvt

tyltxgtvt

+=

++=

++=

Sector VI

( ) ( )[ ]

13

;15.011

taft

ztaytmlxtfaat

=

+−+−−−+

=

xtvt

txmtvt

tyatxltvt

5.0

;3

;1

4

3

1

=

+=

++=

For sector I, II, III For sector IV, V, VI

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Fig. 5. Pulse patterns for switching in the proposed method

B. Overmodulation in mode 1 (Mmax_under ≤ M ≤ Mmax_over1) Similarly as for SSTPI, this mode starts when the required

Vref goes beyond the circle inscribing the hexagon and reached its sides. When sliding on the hexagon side (M=Mmax-over1) tz = 0:

0

;2

;2sincos3

sincos3

=

−=

⋅+−=

z

xs

y

sx

t

tTt

Ttαααα

(13)

As for the undermodulation effective vectors tX,Y and effective-zero vectors tz are formed from the two basic vectors. When M = Mmax-under, values tx, ty, tz are defined as (11). In case of Mmax-under<M<Mmax-over1 the linear approximation is used to calculate tx, ty, tz. For example, In the Undermodulation zone, when m= Mmax-under:

( );3/sin31 απ

π−= sTMxt

When m=Mmax_over1:

;2sincos3

sincos32

sx

Tt ⋅+−=

αααα

Using the linear approximation to calculate the tx in this zone:

);( max_max_1max_

121 under

underover

xxxx Mm

MMtttt −⋅

−−+=

Similar to calculate ty,tz in this zone.

C. Overmodulation mode 2 (Mmax_over1≤ M ≤Mmax_over2) Similarly as for SSTPI, in this overmodulation mode 2, the

required Vref increases up to six step mode 2/3*Vdc. When M=Mmax-over2 , the modulation is done in two cases:

3//6for ;0;2

;0

;6/0for ;0;0;2

παπ

πα

≤≤===

≤≤===

zs

yx

zys

x

tTtt

ttTt (14)

When M = Mmax-over1 , values tx, ty, tz are defined as (13). For Mmax-over1 <M<Mmax-over2 the linear approximation is used to calculate tx, ty, tz. For example, In the Overmodulation zone when m= Mmax-over1

;2sincos3

sincos31

sx

Tt ⋅+−=

αααα

When m= Mmax-over2

3//6for ;0

;6/0for ;2

2

2

παπ

πα

≤≤=

≤≤=

x

sx

t

Tt

Using the linear approximation to calculate the tx in this zone:

);( 1max_1max_2max_

121 over

overover

xxxx Mm

MMtttt −⋅

−−+=

Similar to calculate ty,tz in this zone.

IV. SIMULATION OF THE PROPOSED SVPWM UNDER DC-LINK VOLTAGE IMBALANCE OR RIPPLE

Matlab/Simulink is used for the simulation of the proposed SVPWM. In this simulation we use the method that proposed in another work of our (old method)[10] in comparison with the method that we propose in this paper (proposed method).

The first simulations have been done for the undermodulation, overmodulation mode 1 and 2 under DC-link voltage imbalance with parameters as follows: DC-link voltage Vdc: 400V, Output voltage fundamental harmonic: 50Hz, Switching frequency fsw: 4.8 kHz, Sampled time: 1e-6s. 1. Case study 1: For the undermodulation with ε=0.01;M=Mmax_undermodulation. Load R=20Ω, L=40mH.

Fig. 6. Spectrum analysis for line voltage VAB (old method) M=0.889. Fundamental(50Hz)=196, THD=104.02%

Fig. 7. Spectrum analysis for line voltage VAB (proposed method) M=0.907. Fundamental(50Hz)=199.2, THD=100.73%

Fig. 8. waveforms of Phase

current for the old method. M=0.889, Fundamental

(50Hz)=4.791, THD=1.58%

Fig. 9. waveforms of Phase

current for the proposed method. M=0.907, Fundamental

(50Hz)=4.876, THD=1.53%

2. Case study 2: For the overmodulation mode 1, with ε=0.05. M= Mmax_over1. Load R=20Ω, L=40mH.

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Fig. 10. waveforms of Phase

current for the old method. Mmax_over1=0.8568 Fundamental

(50Hz)=4.612, THD=2.15%

Fig. 11. waveforms of Phase

current for the proposed method. Mmax_over1=0.952 Fundamental (50Hz)=5.002, THD=4.31%

3. Case study 3: For the overmodulation mode 2, with ε=0.05. M= Mmax over1 . Load R=20Ω, L=40mH.

Fig. 12. waveforms of Phase

current for the old method. Mmax_over2=0.9 Fundamental (50Hz)=4.849, THD=8.48%

Fig. 13. waveforms of Phase

current for the proposed method. Mmax_over2=1 Fundamental

(50Hz)=5.277, THD=9.71%

Fig. 6, 8, 10, 12 show the simulation results for the case when the old method is used, and Fig. 7, 9, 11, 13 present the results for the case when the proposed algorithm is used. the harmonic components of line voltage are also improved when the proposed method is used. The modulation index in the proposed method is greater than old method in the same zones (undermodulation and over modulation zones). So, we can increase the value of vector refV .

The second simulations are performed for SVPWM-FSTPI- IM system with parameters as follows: AC source voltage: single phase 220V, 50Hz, Capacitor: C1=C2=680uF, Reactance: L=10mH, Induction Motor model: 2HP, 380V, 50Hz, Y connection, Rs=1.723, Rr’=2.011, Lm=0.159232(H), Lls=0.017387(H), Llr’=0.019732(H), J=0.001(kg.m2), P=2, Tload = 4 N.m. Modulation index: M = 0.9, switching frequency fsw= 5 kHz,

Fig. 14. Flux linkage vector locus

at t = 0.6s. with old method

Fig. 15. Flux linkage vector locus at t = t=0.6s. with proposed method

Fig. 14, 16 show the simulation results for the case when the old algorithm is used, and Fig. 15, 17 present the results for the case when the proposed algorithm is used.

Fig. 16. Output voltage spectrum for fout=50Hz, t=0.98-1s, m=0.9 old

method. Fundamental(50Hz)=259.5, THD=111.99%

Fig. 17. Output voltage spectrum for fout=50Hz, t=0.98-1s, m=0.9 for the proposed method. Fundamental(50Hz)=258.9, THD=112.44%

Fig. 18. Three phase current waveforms with old method

Fig. 19. Three phase current waveforms with proposed method

The obtained simulation results demonstrate the good performance of the proposed SVPWM for FSTPI with dynamic compensation for DC-link voltage ripple. When M=0.9, the old method must use the overmodulation zone to generate the Vref while the proposed method the reference vector voltage Vref is generated in the undermodulation zone, so the THD of stator currents when we use the proposed method is smaller than ones that using the old method.

V. EXPERIMENTAL RESULTS FOR THE PROPOSED SVPWM The feasibility of the proposed SVPWM is verified by

experimental implementation (Fig.20). The new adaptive SVPWM is programmed in the control

board TMS DSP TMS320LF2407a to generate the command pulses for FSTPI (4 IGBT FGPF120N40TU 1200V, 40A, Driver HCPL-3120).

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The outputs from FSTPI were connected to a 3-phase induction motor, which has the follows parameters: f = 40 Hz, 380V, Y, ½ HP, cosϕ =0.81, 1420 rpm. The switching frequency of IGBT is 2 kHz. The DC link voltage was adjusted at 210V, the DC-link capacitance: C1=470uF, 450V, C2=470uF, 450V.

Fig. 20. Implementation of the adaptive SVM in the developed processor

system with an induction motor.

Fig. 21. Waveforms of DC-Link

voltage V1 and V2, Fig. 22. Phase current waveforms

ia,b,c with proposed method

Fig. 23. ouput voltage Vbc with proposed method

Fig. 24. Measured ouput voltage spectrum Vbc with proposed method

Fig.21 show the DC-link voltage ripples. Fig. 22, 23, 24

present the results for the case when the proposed algorithm is used. It can be seen from these results that implementing the proposed method the fundamentals of the output voltages are ensured and the phase currents become symmetrical. Hence, the output quality of the inverter has been enhanced.

VI. CONCLUSION The new adaptive space vector PWM method for FSTPI

under DC-link voltage ripple has been proposed, which is based on the establishment of basic space vectors and modulation technique in the principle of similarity with standard six-switch three-phase inverters. This facilitates the SVPWM calculation

for FSTPI under DC-link voltage ripple and all issues on SSTPI can be applied for FSTPI as well through this proposed approach, e.g. SVPWM for the overmodulation. The compensated technique also allows reduce the size of DC-link capacitors and the cost of the inverter.

To implement this proposed method, the DC-link voltages V1 and V2 are measured and the modified effective basic space- vectors are used with proposed mathematical converts and equations. Theory, simulation and experiment implementation of the proposed SVPWM are presented. The effectiveness of this dynamic adaptive SVPWM method and the output quality of the inverter are verified.

VII. REFERENCES [1] H. W. van der Broeck and J. D. vanWyk, “A comparative

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[2] Frede Blaabjerg,, Sigurdur Freysson, Hans-Henrik Hansen, and S. Hansen “A New Optimized Space-Vector Modulation Strategy for a Component-Minimized Voltage Source Inverter ” IEEE Trans. on Power Electronics, Vol. 12, No. 4, July 1997,pp 704-710

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

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

[5] J. O. P. Pinto, B. K. Bose, L. E. B. da Silva, and M. P. Kazmierkowski, “A neural network based space vector PWM controller for voltage-fed inverter induction motor drive,” IEEE Trans. Ind. Applicat., vol. 36, pp.1628–1636, Nov./Dec. 2000.

[6] D. T. W. Liang and J. Li, “Flux vector modulation strategy for a four switch three-phase inverter for motor drive applications,” in Proc. IEEE PESC, Jun. 1997, pp. 612---617.

[7] F. Blaabjerg, Dorin O. Neacsu, John K. Pedersen “Adaptive SVM to Compensate DC-Link Voltage Ripple for Four-Switch Three- Phase VSI” IEEE Trans. on Power Electronics, Vol. 14, No. 4, Jul. 1999, pp 743-752.

[8] Dong-Choon Lee, Young-Sin Kim, “Control of Single-Phase-to-Three-Phase AC/DC/AC PWM Converter for Induction Motor Drives” IEEE Trans. on Ind. Electronics, Vol. 54, No. 2, April 2007, pp 797-804.

[9] P.Q. Dzung, L.M. Phuong, P.Q. Vinh, N.M. Hoang,T.C. Binh, “New Space Vector Control Approach for Four Switch Three Phase Inverter (FSTPI), International Conference on Power Electronics and Drive Systems- PEDS 2007, Bangkok, Thailand, 2007

[10] Hong-Hee Lee, P.Q. Dzung, L.D. Khoa, L.M. Phuong, H.T. Thanh “The Adaptive Space Vector PWM for Four Switch Three Phase Inverter Fed Induction Motor with DC– Link Voltage Imbalance”, IEEE International Conference on Innovative Technologies for Societal Transformation- TENCON2008, Hyderabad, India, Nov. 18th -21st 2008.

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