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

PEDS2009

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

Hong Hee Lee

Phan Quoc Dzung

Le Dinh Khoa

Le Minh Phuong

NARC, Ulsan
University, Korea


Faculty of Electrical &
Electronic Engineering
HCMC University of
Technology
Ho Chi Minh City, Vietnam


Faculty of Electrical &
Electronic Engineering
HCMC University of
Technology
Ho Chi Minh City, Vietnam

Faculty of Electrical &
Electronic Engineering
HCMC University of
Technology
Ho Chi Minh City, Vietnam


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 sixswitch 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.

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
G G

effective vectors V1' ...V 6' which lengths are equal the length of the
G G
shortest vector from V1 , V3 (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.

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 DClink capacitors. To ensure the quality of the output voltages of

VSI, we must solve the mentioned above problem by using realtime 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

399

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
(1)
S3+S2 = 1
Phase to common point voltage depends on the turning off
signal for the switch:
Va 0 = 0; Vb 0 = S1V1 + (S1 − 1) ⋅ V2 ; Vc 0 = S3V2 + (S3 − 1) ⋅ V1; (2)
V

V
(3)
V1 = dc − ε .Vdc ; V2 = dc + ε .Vdc
2
2
Where


V1, V2 voltage across the dc-link capacitors; V1+V2=Vdc
1
1
1 V
ε = − 1 the imbalance factor ; − ≤ ε ≤
6
6
2 Vdc
Combinations of switching S1-S4 result in 4 general space
G
G
vectors V1 → V4 (Table 1).
Voltage imbalance in the DC link causes the space vector
G
G G
G
origin to shift along the V1 / V3 axis (Fig.3), with V1 and V3 no
longer being equal in magnitude, as described in Table 1.
G
In order to form the required voltage space vector Vref , 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] :
G
G
(4)
Ψ = V (t )dt

∫

In case the motor is fed from a FSTPI inverter the flux
linkage vector is:
G
G G
(5)
Ψ = t n ⋅ Vn + Ψ0
where n = 1..4 ; tn : duration of Vn.
If the switching algorithms can ensure the best approximation by
G
G
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].

S3
0

1

0

1

1

0

1

Vβ

2V2
3
V2 − V1
3
2V1
−
3
V2 − V1
3

0

G
V1

V1 + V2

G
V2

3

−

0

G
V3

V1 + V2

G
V4

G
G G
G
G
G
G
G
1 G
1 G
V1' = a V1 ; V 2' = b V1 + V 2 + c V 3 ; V 3' = d V1 + V 2 + e V 3
2
2
G
G G
G
G

G
G
G
1 G
1 G
V 4' = f V 3 ; V 5' = g V1 + h V 3 + V 4 ; V 6' = l V1 + m V 4 + V1
2
2

G
V2

G
V3'

3

G
V4'
− 2V1G/ 3
V3

G
V2'
G
V1'

(V2 − V1 ) / 3

O

G
V5'

O

2V2 / 3

G
V1

'

G
V6'
G − (V1 + V2 ) /
V4

Fig. 2.

Voltage space vectors in the plan αβ

Fig. 3.

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].

400

(6)

where the coefficients a,b,c,d,e are defined as follows:
G
G
Case 1: DC-link voltage V1 < V2 ( V1 > V3 ) (Fig.3)
a =

G
V

Vα

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
G G
method, we use the effective vectors V1' ...V6' , when the length of
G
G
V1 + V3
the basic generated vector is equal (
) (Fig.4, 5).

2
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:

V1 + V 2
V − V1
1
;b = l =
;c = m = 2
; d = g = 0;
2V 2
2
(2 V 1 )
V2
V + V2
e = h =
; f = 1
2V1
2V1

TABLE 1. COMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS

S1
0

PEDS2009
III. NEW DYNAMIC ADAPTIVE SVPWM APPROACH FOR FSTPI
WITH COMPENSATION DC-LINK VOLTAGE RIPPLE CONDITION

3

SVPWM proposed method for FSTPI in case of V1 < V2

(7)


PEDS2009

G
V2

β

Vm _ max =

(V1 + V2 ) / 3

3

(12)

⋅ (V1 + V2 )

TABLE 2. VECTOR DURATIONS IN THE PROPOSED SVPWM METHOD

G
V3'
G
V4'

− 2V1 / 3
G
V3

1

G
V2'
Vref

(V2 − V1 ) / 3

O'

G
V5'

O

Sector I
T
t x = tv ' =
M s sin( π / 3 − α );
1
π
2
Ts
2 3
t y = tv ' =
M

sin( α )
2
π
2
t z = Ts / 2 − t x − t y
2 3

G
V1'
2GV2 / 3
V1

α

G
V6'
G
V4

[

]

a
t x (1 − a ) + t y (1 − b − c − 0.5) + t z ;
a+ f
f
t3 = t1
a
t1 =

tv1 = at x + bt y + t1;
tv2 = 0.5t y ;
tv3 = ct y + t3

− (V1 + V2 ) / 3

Sector II

[

SVPWM proposed method for FSTPI in case of V1 > V2

Fig. 4.

G
G
Case 2: DC-link voltage V1 > V2 ( V1 < V3 ) (Fig.4)

tv = bt x + dt y + t1;
1

V + V2
V
V − V2
a = 1
;
; b = l = 1 ; c = m = 0; d = g = 1
(2V 2 )
2V 2

2V 2
1
V + V2
e= h= ; f = 1
2
2V1

tv = 0.5(t x + t y );
2
tv = ct x + et y + t3
3

(8)

Sector III

G
To simulate zero vectors of SSTPI, we use the effective V0' :
G
G
G
(9)
V0' ⋅ t z = V1 ⋅ t1 + V3 ⋅ t3
Where t1 and t3 are calculated by equations:
⎧ ft1 − at3 = 0;
⎨
⎩t1 + t3 = t z

(10)

ty =

3
3

π

tv1 = dt x + t1;

3

MTs sin (π / 3 − α );
MTs sin (α );

]

tv = et x + ft y + t3

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]
π

[

a

t1 =
t x (1 − e − d − 0.5) + t y (1 − f ) + t z ;
a+ f
f
t3 = t1
a

tv2 = 0.5t x ;

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

tx =

]

a
t1 =
t x (1 − b − c − 0.5) + t y (1 − e − d − 0.5) + t z ;
a+ f
f
t3 = t1
a

Sector IV

[

]

a
t x (1 − f ) + t y (1 − g − h − 0.5) + t z ;
a+ f
f
t3 = t1
a

t1 =

tv1 = gt y + t1;
tv = ft x + ht y + t3;
3
tv = 0.5t y
4

Sector V

[

]

a
t1 =
t x (1 − g − h − 0.5) + t y (1 − l − m − 0.5) + t z ;
a+ f
f
t3 = t1
a

tv1 = gt x + lt y + t1;

(11)

tv = ht x + mt y + t3;
3

tv4 = 0.5(t x + t y )

t z = Ts / 2 − t x − t y

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:
401

Sector VI

[

]

a

t x (1 − l − m − 0.5) + t y (1 − a ) + t z ;
a+ f
f
t3 = t1
a
t1 =

tv = lt x + at y + t1;
1
tv = mt x + t3;
3
tv4 = 0.5t x

For sector I, II, III

For sector IV, V, VI


PEDS2009
t x 2 − t x1
t x = t x1 +
⋅ ( m − M max_ over1 );
M max_ over 2 − M max_ over1

Similar to calculate ty,tz in this zone.
IV. SIMULATION OF THE PROPOSED SVPWM UNDER DC-LINK
VOLTAGE IMBALANCE OR RIPPLE
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:
3 cos α − sin α Ts
tx =
⋅ ;
3 cos α + sin α 2
(13)
T
t y = s − tx ;
2
tz = 0
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-undercalculate tx, ty, tz.
For example, In the Undermodulation zone, when m= Mmax-under:
t x1 =

3

π

M Ts sin (π / 3 − α );

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.

When m=Mmax_over1:
3 cos α − sin α Ts
tx2 =
⋅ ;
3 cos α + sin α 2
Using the linear approximation to calculate the tx in this zone:
t x 2 − t x1
t x = t x1 +
⋅ ( m − M max_ under );
M max_ over 1 − M max_ under
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:
T
t x = s ; t y = 0; t z = 0; for 0 ≤ α ≤ π / 6;

(14)
2
Ts
t x = 0; t y = ; t z = 0; for π/6 ≤ α ≤ π / 3
2
When M = Mmax-over1 , values tx, ty, tz are defined as (13). For
Mmax-over1 calculate tx, ty, tz.
For example, In the Overmodulation zone when m= Mmax-over1
3 cos α − sin α Ts
t x1 =
⋅ ;
3 cos α + sin α 2
When m= Mmax-over2
T
t x 2 = s ; for 0 ≤ α ≤ π / 6;
2
t x 2 = 0; for π/6 ≤ α ≤ π / 3
Using the linear approximation to calculate the tx in this zone:

402

Fig. 7.

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

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.


PEDS2009

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%
Fig. 16. Output voltage spectrum for fout=50Hz, t=0.98-1s, m=0.9 old
method. Fundamental(50Hz)=259.5, THD=111.99%

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. 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. 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
G
increase the value of vector Vref .

Fig. 18. Three phase current waveforms with old method

The second simulations are performed for SVPWM-FSTPIIM 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. 19. Three phase current waveforms with proposed method

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

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

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.

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).
403


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.

PEDS2009
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 spacevectors 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

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
404

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