Comparison of Control Strategies of DSTATACOM for Non-linear Load Compensation

Proc. of Int. Conf. onComputational Intelligence and Information Technology

Comparison of Control Strategies of DSTATACOM
for Non-linear Load Compensation
Gokulananda Sahu1, Kamalakanta Mahapatra2
1

2

Dept. of Electronics and Communication Engg. NIT, Rourkela, India
Email: gokulanandasahu@gmail.com
Dept. of Electronics and Communication Engg. NIT, Rourkela, India
Email: kmaha2@gmail.com

Abstract— For load compensation a number of control strategies have been developed by
researchers but choice of control strategy is important to cope with the operating condition
of system. In this paper five control strategies viz. instantaneous p-q theory, synchronous
reference frame Method(SRF), Modified SRF Method(MSRF), instantaneous symmetrical
component theory(ISCT) and Average unit power factor theory(AUPFT) are compared for
different two conditions. The performance of the system simulated in Matlab Platform and
evaluated considering the source current total harmonic distortion. The result shows
Modified SRF(id-iq) Method has improved system performance as compared to others.
Index Terms— Modified SRF, SRF, p-q , ISCT, AUPFT.

I. INTRODUCTION
During the last decade, there has been sudden increase in the nonlinear load(Computers, Laser
printers,SMPS, Rectifier etc.), which degrades the power quality causing a number of disturbances e.g.
heating of home appliances , noise etc in power systems[1], [2] due to harmonics.
To compensate the harmonics due to nonlinear load, a Distribution STATicCOMpensator (DSTATCOM) [3]
is used. The performance of DSTATCOM largely depends on the control strategies used for reference current
current extraction. The control strategy used conventionally, were based on active and reactive power are
found unsuitable for unbalance and harmonic conditions. Significant contribution for development of control
algorithm was made by Budeanu and Fryze. They provide power definition in frequency and time domain
and set the pathways for development universal set power definitions which led to the development of p-q
theory by Akagi [4].
In this paper performance of five control strategies such as instantaneous p-q theory, instantaneous
symmetrical component theory, SRF Method, Modified SRF Method and AUPF theory are investigated in
three phase three wire system for balanced source and nonlinear balanced and unbalanced Load.The
measures of the performance is the source current total harmonic distortion The results obtained show that
under normal operating condition all control strategies are suitable for compensation. But as the operating
condition deteriorates the performance of some control strategies degrades.
Rest of the paper is organized as follows. In section II system configuration and in section III brief
discussion on different control theories/methods are presented. In section IV the performance indices used
for evaluation are discussed. Simulation results are described in section V. Finally in section VI , conclusion
are drawn.
DOI: 03.LSCS.2013.6.116
© Association of Computer Electronics and Electrical Engineers, 2013

II. SYSTEM CONFIGURATION
Fig.1 shows the basic circuit diagram of a DSTATCOM system with non-linear and linear load connected to
three phase three wire distribution system. A nonlinear load is realized by using a three phase full bridge
diode rectifier whereas linear load is actualized by using resistive- inductive load to make the system
balanced or unbalanced. A three phase voltage source converter (VSC) working as a DSTATCOM is realized
using six insulated gate bipolar transistor (IGBTs) with anti-parallel diodes. At ac side, the interfacing
inductors are used to filter high frequency components of compensating currents.
The first harmonic load currents of positive sequence are transformed to DC quantities. The first harmonic
load currents of negative sequence and all the harmonics are transformed to non-DC quantities and undergo a
frequency shift in the spectrum.
The voltage regulator in the converter DC side is performed by a proportional–integral(P-I) controller. Its
input is the capacitor voltage error (vdcref-vdc) and it regulates the first harmonic active current of positive
sequence. It is possible to control the active power flow in the VSI and thus the capacitor voltage Vdc
remains constant.
The dynamics of each VSC are modeled by solving differential equations governing 2-level inverter. The
switching of the inverter is done by monitoring the reference and actual currents and comparison of error
with the hysteresis band of hysteresis controller (HCC).

Fig.1 system configuration of DSTATCOM

III. CONTROL STRATEGIES
A. Instantaneous p-q Theory
Instantaneous P-Q Theory was initially proposed by Akagi[4]. This theory is based on the transformation of
three phase quantities to two phase quantities in α-β frame and the Instantaneous active and reactive power
is calculated in this frame [4],[5]. Sensed inputs vsa ,vsband vsc&iLa ,iLb and iLc are fed to the controller and
these quantities are processed to generate reference commands( ∗ , ∗ , ∗ ) which are fed to a hysteresis
based PWM current controller to generate switching pulses(g1,g2and g3) for DSTATCOM.
The system terminal voltages are given as

28

v sa  V

m

v sb  V

m

v sc  V

m

s in ( w t )



s in ( w t  2 / 3 ) 
s in ( w t  2  / 3 ) 


(1)

and the respective load current are given as

iLa  I Lan sin{n ( wt )   an }



iLb  I Lbn sin{n( wt  2 / 3)  bn }
iLc  I Lcn sin{n( wt  2 / 3)   cn } 


(2)

In a, b and c coordinates a,b and c axes are fixed on the same plane apart from each other by 2π/3. These
phasors can be transformed into α-β coordinates using Clarke’s transformation as follows.

2
3

1

0

i 
i  


2
3

 v 
v  
 

v 
1/ 2   sa 
 vsb
3 / 2  3 / 2  
 vsc 
 

1/ 2

1

0

(3)

i 
1/ 2   La 
 iLb (4 )
3 / 2  3 / 2  
iLc 
 

1/ 2

Where α and β axes are the orthogonal coordinates . Conventional instantaneous power for three phase
circuit can be defined as

p  v i  v i

(5)

Where p is equal to conventional equation

p  vsa isa  vsb isb  vsc isc

(6)

Similarly, the instantaneous reactive power is defined as

q  v i  v i

(7)

Therefore in matrix form, instantaneous real and reactive power are given as

 p   v
 q   v
   

v  i 
v  i 
 

(8)

The α-β currents can be obtained as

i  1  v
i   v
  
Where

v   p 
v   q 
 

(9)

2
2
  v  v

Instantaneous active and reactive powers p and q can be decomposed into an average (dc) and oscillatory
component


p  p  p


q q q 

(10)
29

Where ̅ and are the average dc part and and are the oscillatory (ac) part of these real and reactive
instantaneous power. Reference currents are calculated to compensate the instantaneous oscillatory
component of the instantaneous active and reactive power. Therefore the reference compensating currents
∗
and ∗ in α-β coordinate can be expressed as

i*  1  v
f
*  
i f     v
 


v    p 

 
v   q 

(11)

The oscillatory part of real power p and reactive power q is obtained by using 4th order low pass Butterworth
filter of cut-off frequency 25 Hz.
These currents can be transformed in abc quantities to find reference currents in a-b-c coordinates using
reverse Clarke’s transformation.

0 
 1
i* 
fa
*
 i f  
2
*
3/2  * 
i fb   3  1/ 2
 
 1/ 2  3 / 2  i f  
i* 
 fc 



(12)

B. Synchronous Reference frame Method (SRF)
In this method Load current signal are transformed into conventional rotating frame d-q where θ is the
transformation angle. In SRF θ is time varying angle that represents the angular position of the reference
frame which is rotating at constant speed in synchronism with three phase ac voltage. There is no need
supply voltage information for SRF based controller. However the phase position angle must be determined
using voltage information.
This theory is based on the transformation of currents in synchronously rotating d-q frame [6],[7],[8].
Voltage signals are processed by the PLL[9] to generate the unit vectors. Current signals are transformed into
d-q frame and then filtered .Then compensating current transformed back to a-b-c frame and fed to hysteresis
current controller [10] for switching pulse generation.
The current components are transformed into α-β coordinates and using θ as a transformation angle again
transformed from α-β to d-q frame with help of park’s transformation.

id   cos 
i   
 q    sin 

sin   i 
 
cos   i 


(13)

SRF controller extracts the oscillating part of id and iq by use of a low pass Butterworth filter. The extracted
compensating currents ∗ and ∗ are transformed back in to α-β frame using reverse park’s transformation.

i*   cos 
f
 * 
i f    sin 
 


 sin   i* 
fd
 i* 
cos    fq 
 

(14)

Then these reference currents are transformed back to a-b-c coordinates.

0 
 1
i* 
fa
*
 i f 
2
*
i fb  
1/ 2
3 / 2   * 


3
 
 i f  
i* 
 fc 
 1/ 2  3 / 2 

(15)

C. Modified Synchronous Reference frame Method(MSRF)(id-iq)
In this method the compensating currents are obtained from instantaneous active and reactive currents id and
iq of the non-linear load [11]. However the dq load currents are derived from a synchronous reference frame
based on the transformation where θ represent the voltage vector angle.
30

id   cos 
i   
 q    sin 

sin   i 
 
cos   i 


(16)

The transformation angle is sensitive to voltage harmonics and unbalanced voltage sources, therefore dθ/dt
may not be constant.
Due to geometric relation

id 
1  v
i  

  v
 q
Where

v  i 
v  i 
 

(17)

2
2
  v  v

One of the advantages of this method is that the θ angle is calculated directly from the main voltages and thus
enables to be frequency independent. Avoiding the use of PLL it can be achieved a large frequency operating
range limited by the cut- off frequency of VSI. Furthermore the synchronization problems with unbalanced
non-sinusoidal mains voltages are also avoided. Performing the elimination of the average current
components by high pass filter the compensating reference current ∗ and ∗ are obtained.
Then the compensating reference current is obtained in α-β coordinates.

i*  
1 v
f
* 

  v
i f  
 

 v   i * 
fd
 
v   i* 
  fq 

(18)

Then these reference currents are transformed back to a-b-c coordinates.

0 
 1
i* 
fa
*
 i f 
2
*
i fb  
1/ 2
3 / 2   * 


3
i f  
 
i* 
1/ 2  3 / 2 
 fc 



(19)

D. Instantaneous Symmetrical Components Theory
The objective of this theory[12] to make source current balanced and harmonic free.
So isa  isb  isc  0
(20)
The positive sequence voltage to a phase is

V 
Where a  e

j 2 / 3

1
3

(vsa  avsb  a 2vsc )

(21)

.The angle of vector of +ve sequence









 vsa  avsb  a2vsc   isa  aisb  a2isc  

(22)

 3

3
vsb 
vsc 



1 
2
Where   (V )  tan  2
(23)
1
1 
 vsa  vsb  vsc 
2
2 




 vsb vsc 3vsa  isa  vsc vsa 3vsb  isb  vsa vsb 3vsc  isc 0
Where



tan 
3

The source deliver power must equal to the average of active power i.e.
31

(24)

vsaisa  vsb isb  vsc isc  plav

(25)

From the above relation
1

 v  v 3v
sa 
 sb sc

vsa


1
vsc  vsa 3vsb 

vsb

1
isa   0 
vsa  vsb 3vsc isb    0 

   
isc   plav 
vsc
   

(26)

The source reference currents are obtained by solving the above equation (25),

vsa   vsb  vsc  

*
isa 

2
2
2
vsa  vsb  vsc
vsb   vsc  vsa  

*
isb 

2
2
2
vsa  vsb  vsc
vsc   vsa  vsb  

*
isc 

2
2
2
vsa  vsb  vsc

plav

(27)

plav

(28)

plav

(29)

In the above relation β represents the power factor co-efficient proportionate to reactive power.
Finally under balanced and unit power factor

vsa
 plav  ploss 
s
v
*
i*  iLb  isb  iLb  sb  plav  ploss 
fb
s
v
*
i*  iLc  isc  iLc  sc  plav  ploss 
fc
s
2
2
2
Where s  vsa  vsb  vsc
*
i*  iLa  isa  iLa 
fa

Where

is the average load power and

(30)
(31)
(32)

is the losses in VSI which are computed as follows

1
 vsa iLa  vsbiLb  vsciLc dt
T
 k p  vdcref  vdc   ki   vdcref  vdc dt

plav 
ploss
Where

and

(33)
(34)

are the reference and actual capacitor voltage.

E. Average unit power factor theory(AUPF)[13]
The source must supply the sinusoidal currents in phase with the voltages.

isa 
i   plav
 sb  V 2
 isc 
 

(35)

1
 vsa iLa  vsbiLb  vsciLc dt
T

(36)

1
 vsa vsa  vsb vsb  vsc vsc dt
T

(37)

plav 
V2 

 vsa 
v 
 sb 
 vsc 
 

32

The compensator current are derived as

=

i*  iLa 
fa
 *    plav
i fb   iLb   V 2
i*  iLc 
 fc   

−
vsa 
v 
 sb 
 vsc 
 

(38)

The compensator reference currents can be compared with actual compensator currents pass through the
hysteresis band controller which generates gate pulses for voltage source converter of DSTATCOM.
IV. PERFORMANCE INDICES
Total harmonic distortion:
The total harmonic distortion (THD) [14]is used to define the effect of harmonics on the power system
voltage. It is used in low-voltage, medium-voltage, and high-voltage systems. It is expressed as a percent of
the fundamental and is defined as

50
2
h

V
THD (voltage) 

h 2

(39)

V1

50

I
THD (current ) 

2
h

h 2

(40)

I1

According to IEEE-519 the permissible limit for distortion in the signal is 5%.
V. RESULTS AND DISCUSSION
To investigate the performance of the DSTATCOM for five control strategies, simulations are performed
on matlab platform . A three phase three wire distribution system with parameters given below is considered
for simulation.
System Parameters:
Supply voltage : 50Vrms(L-N),50Hz, three phase balanced
Sourceimpedance:Rs=0.1Ω,Ls=.5mH
Nonlinear load: Three phase full bridge diode rectifier .
DCstorage Capacitor Cdc=2000µF
Interface inductor Lf=5mH ,Rf=0.1Ω
DC Link voltage Vdc=100V
Hysteresis band=0.25A
Unbalanced Load:Za=67+j31.42Ω,
Zb=37+j18.85Ω
Zc=28.5+j12.56Ω
The performance of the control algorithm is evaluated based on two different cases.
Case1- Balanced Source and balanced Non-Linear load
Case2- Balanced Source and Unbalanced Non-linear load.
33

The simulation results for case 2(fig.2a- fig.2e) of best performance achieved algorithm (MSRF Method)
are demonstrated here.

Source voltage vsa,vsb,vsc

Phase A extracted source current
100
vsa
vsb
vsc

0

iL a , iL b , iL c (A m p s )

-100

is a (A m ps )

100

0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

0
-100

0.2

0

0.02

0.04

Load current iLa,iLb,iLc
10

0.08

0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

-50

0.2

0

v dk (V olts )

iL a (A m p s )

0.16

0.18

0.2

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

200

0

0

0.02 0.04 0.06 0.08

0.1 0.12 0.14 0.16 0.18
Time(sec)

-200

0.2

X: 0.09105
Y: 103.5

0

0

Unit Power Factor

0.02

0.04

0.06

0.08

0.1 0.12
Time(sec)

Fig. 2b Phase A extracted Source current,
Compensating current and DC link Capacitor
Voltage

Fig.2a Source Voltage phase a ,b,c, Load
Currentt phase a,b,c and Load current phase a

Harmonics of Extracted Source current

Harmonics of Load current

80
vsa
isa

40

7

6

6

5

5

20

A m lit u d e (A m p s )

4

A m lit u d e ( A m p s )

A m lit u d e

0.14

Capacitor Voltage

10

60

0.12

0

Load current iLa

-10

0.1

50
iLa
iLb
iLc

0

-10

0.06

Phase A Compensating current
ifa (A m ps )

v s a , v s b , v s c (V o lt s )

Case 2
MSRF Method(id-iq)

0

3

-20

4

3

2

2

-40
1

-60
-80

0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time(sec)

Fig. 2c Unit power factor of
compensated Load

0

1

0

5

10

15

20 25 30
(Harmonic number)

35

40

Fig. 2d Harmonics of Load
current current phase a

45

50

0

0

5

10

15

20
25 30
(Harmonic number)

35

40

45

50

Fig. 2e Harmonics of extracted
Source current phase a

In case 1 the source is assumed to be sinusoidal and balanced whereas the load is considered as nonsinusoidal and balanced with load as six pulse diode full bridge rectifier. Before compensation the THD of
load current is found to be 22.2914%. After compensation the THD for different control strategies are listed
in the Table1.
In case 2 the source is balanced and sinusoidal but the load is unbalanced non sinusoidal .The THD of the
load current for phase a after compensation is summarized in Table 1.Fig. 3 demonstrates the comparison
chart of different control strategies for case1 and case 2.
The results demonstrated here are considered for phase a only.
34

TABLE-1. C OMPARISON
Control
strategy

THD(%)

p-q

CASE-1
3.0748

CASE-2
4.4580

SRF

3.4017

4.6838

MSRF(idiq)
ISCT

3.1867

3.7313

3.6914

4.2566

AUPFT

3.6482

4.5317

Fig. 3 Comparison chart of different control strategies

VI.CONCLUSION
In all cases it is observed that all the control strategies working fine and able to compensate the nonlinear
unbalanced load successfully. The THD obtained here are within the limit of 5% prescribed by IEEE 519.
From the above comparison chart it has been found that MSRF control strategyhas better performance for
harmonic cancellation for balanced source and non-linear unbalanced load condition.
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Comparison of Control Strategies of DSTATACOM for Non-linear Load Compensation

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