Dynamic adaptive space vector PWM for four switch three phase inverter fed induction motor with compensation of DC link voltage ripple

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 hhle

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 V

VG G

which lengths are equal the length of the shortest vector fromVG1

,VG3

(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:

;

dc dc dc

V

2

;

1= −ε = +ε (3)

Where

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

dc

V

V1

2

1

−

=

ε the imbalance factor ; −61≤ ε ≤61

Combinations of switching S1-S4 result in 4 general space

vectors VG1 VG4

→ (Table 1)

Voltage imbalance in the DC link causes the space vector

origin to shift along the VG1

/VG3 axis (Fig.3), with

1

VG and VG3no longer being equal in magnitude, as described in Table 1

In order to form the required voltage space vector VGref

, 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] :

( )t dt

V

∫

=

ΨG G

(4)

In case the motor is fed from a FSTPI inverter the flux

linkage vector is:

0

Ψ

+

⋅

=

n

t (5)

where n = 1 4 ; tn : duration of Vn

If the switching algorithms can ensure the best approximation by

minimizing the discrepancy between vector lociΨG

andΨG*

, the stator voltage performance will be optimized This approach is

used successfully for FSTPI in case of the balance in DC link

voltage [9]

T ABLE 1 C OMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS

0 0

3

1 0

3

1

2 V

3

2

1 V

2

VG

1 1

3

2V1

0 1

3

1

2 V

3

2

1 V

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

V ref 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 V

VG G , when the length of

the basic generated vector is equal )

2 (V1 V3

G G + (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:

1 4 1 ' 6 4 3 1 ' 5 3 ' 4

3 2 1 ' 3 3 2 1 ' 2 1 ' 1

2

1

; 2

1

;

2

1

; 2

1

;

V V m V l V V V h V g V V f V

V e V V d V V c V V b V V a V

G G G G G G G G G G

G G G G G G G G G G

+ +

= +

+

=

=

+ +

= +

+

=

where the coefficients a,b,c,d,e are defined as follows:

Case 1: DC-link voltage V1 < V2 (

1

VG

>

3

VG

) (Fig.3)

1 2 2 1

; 1 2 2

; 0

; 1 2 1 2

; 2

1

; 2 2 2 1

V V V f V

V h e

g d V V V m c l b V V V a

+

=

=

=

=

=

−

=

=

=

= +

=

(7)

3 /

2V2

3 / ) (V1+V2

−

3 /

2V1

−

3 / ) (V2−V1

2

V G

' 3

V G

' 4

V G

' 2

V G

' 1

V G

1

V G

' 6

V G

3

V G

' 5

V G

4

V G

Fig 3 SVPWM proposed method for FSTPI in case of V 1 < V 2

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β

Vref

3 /

2V2

3 / ) (V1+V2

−

3

/

2V1

−

3 / (V2 −V1

O

'

O

3 / (V1+V2

2

V G

3

V G

4

V G

1

V G

' 2

V G

' 1

V G

' 3

V G

'

4

V G

' 5

6

V G

Fig 4 SVPWM proposed method for FSTPI in case of V 1 > V 2

Case 2: DC-link voltage V1 > V2 ( VG1

< VG3

) (Fig.4)

( ) 1

2 2 1

;

2

1

; 2 2 2 1

; 0

; 2 2 1

;

2

2

2

1

V V V

f

h

e

V V V g d m c V

V l b

V

V

V

a

+

=

=

=

−

=

=

=

=

=

=

+

=

(8)

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

0

VG :

3 3 1

1

'

0 t V t V t

VG ⋅ z = G ⋅ + G ⋅

(9) Where t1 and t3 are calculated by equations:

⎩

⎨

⎧

=

+

=

−

z

t

t

t

at

ft

3

1

;

0

3

1 (10)

The basic vectors in each sector used to form the required

space vector V ref is presented in Table 2

A Under modulation (0 < M < M max_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]

( )

( )

y

t

x

t

s

T

z

t

s

MT

y

t

s

MT

x

t

−

−

=

=

−

=

2

/

; sin

3

; 3 / sin

3

α

π

α π

π

(11)

where:

tx - duration for vector V x;ty - duration for vector V y

tz - duration for vector V z; 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

) 2 1 ( 3

1 max

m

T ABLE 2 V ECTOR DURATIONS IN THE PROPOSED SVPWM METHOD

Sector I

y t x t s T z t

s T M v t y t

s T M v t x t

−

−

=

=

=

−

=

=

2 /

) sin(

2 3 2

);

3 / sin(

2 3 2

' 2

' 1

α π

α π π

1 3

; 5 0 1 1 1

t a f t

z t c b y t a x t a a t

=

+

−

−

− +

− +

=

3

; 5 0

; 1

3 2 1

t y ct v t y t v t

t y bt x at v t

+

=

=

+ +

=

Sector II

1 3

; 5 0 1 5 0 1 1

t a

f t

z t d e y t c b x t a a t

=

+

−

−

− +

−

−

− +

=

3

);

( 5 0

; 1

3 2 1

t y et x ct v t

y t x t v t

t y dt x bt v t

+ +

=

+

=

+ +

=

Sector III

1 3

; 1 5 0 1 1

t a f t

z t f y t d e x t a a t

=

+

− +

−

−

− +

=

3

; 5 0

; 1

3 2 1

t y ft x et v t x t v t

t x dt v t

+ +

=

= +

=

Sector IV

1 3

; 5 0 1 1 1

t a

f t

z t h g y t f x t a a t

=

+

−

−

− +

− +

=

y t v t

t y ht x ft v t t y gt v t

5 0

; 3

; 1

4 3 1

= + +

= +

=

Sector V

1 3

; 5 0 1 5 0 1 1

t a f t

z t m l y t h g x t a

a t

=

+

−

−

− +

−

−

− +

=

) ( 5 0

; 3

; 1

4 3 1

y t x t v t

t y mt x ht v t

t y lt x gt v t

+

=

+ +

= + +

=

Sector VI

1 3

; 1 5 0 1 1

t a

f t

z t a y t m l x t f a

a t

=

+

− +

−

−

− +

=

x t v t

t x mt v t

t y at x lt v t

5 0

; 3

; 1

4 3 1

= +

= + +

=

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Fig 5 Pulse patterns for switching in the proposed method

B Overmodulation in mode 1 (M max_under ≤ M ≤ M max_over1 )

Similarly as for SSTPI, this mode starts when the required

V ref goes beyond the circle inscribing the hexagon and reached

its sides When sliding on the hexagon side (M=Mmax-over1) tz =

0:

0

;

2

; 2 sin

cos

3

sin

cos

3

=

−

=

⋅ +

−

=

z

x

s

y

s x

t

t

T

t

T t

α α

α α

(13)

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 ); sin

3

= M T s

x

t

When m=Mmax_over1:

; 2 sin cos

3

sin cos

3

2

s x

T

+

−

=

α α

α α

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

);

max_

1 max_

1 2

under over

x x x

M M

t t

t

−

− +

=

Similar to calculate ty,tz in this zone

C Overmodulation mode 2 (M max_over1 ≤ M ≤M max_over2 )

Similarly as for SSTPI, in this overmodulation mode 2, the

required V refincreases up to six step mode 2/3*Vdc

When M=Mmax-over2 , the modulation is done in two cases:

3 / /6

for

; 0

;

2

;

0

; 6 / 0

for

; 0

;

0

;

2

π α π

π α

≤

≤

=

=

=

≤

≤

=

=

=

z

s

y

x

z

y

s

x

t

T

t

t

t

t

T

t

(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

; 2 sin

cos

3

sin

cos

3

1

s x

T

+

−

=

α α

α α

When m= Mmax-over2

3 / /6

for

;

0

; 6 / 0

for

;

2

2

2

π α

π

π α

≤

≤

=

≤

≤

=

x

s

x

t

T

t

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

);

1 max_

2 max_

1 2

over over

x x x

M M

t t t

−

− +

=

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 V AB (old method) M=0.889

Fundamental(50Hz)=196, THD=104.02%

Fig 7 Spectrum analysis for line voltage V AB (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

M max_over1 =0.8568 Fundamental

(50Hz)=4.612, THD=2.15%

Fig 11 waveforms of Phase current for the proposed method

M max_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

M max_over2 =0.9 Fundamental

(50Hz)=4.849, THD=8.48%

Fig 13 waveforms of Phase current for the proposed method

M max_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 VGref

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 f out =50Hz, t=0.98-1s, m=0.9 old method Fundamental(50Hz)=259.5, THD=111.99%

Fig 17 Output voltage spectrum for f out =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

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,

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 V bc 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

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 investigation of a three-phase induction machine drive with a component minimized voltage-fed inverter under different 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-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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