International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
Current Control Strategies for Unbalanced Three
Phase Three Wire System Using Shunt Active Power
Filters
P.V.Vijaykumar ,V.Pratyusha ,T.Vinoodh ,P.Shiva
Student’s
LENDI Institute of Engineering and Technology
Department of Electrical and Electronics
JONNADA
VIZIANAGARAM-535002
ANDHRAPRADESH , INDIA.
Abstract-- The main objective of the power
system is generation of electrical energy to
transmit and distribute to the end user. If a fault
exists in any one of the network it should affect
the entire power system. Transients, sagging,
variations in voltage, harmonics are some of
disturbances affecting power system. Harmonics
can cause problems that are easy to recognize
but tough to diagnose. Harmonics can be present
in current, voltage, or both. It is estimated that
as many as 60% of all electrical devices operate
with non-linear current draw.
Three phase unbalanced loads generate
current harmonics. An active power filter is
implemented when order of harmonic currents
are varying. Its structure may be either of the
series or shunt type. Shunt active power filters
(SAPF) are widely used for mitigating current
harmonics. SAPF has better harmonic
compensation than the other approaches used
for solving harmonic related problems.
ISSN: 2231-5381
The performance of SAPF depends upon
different harmonic control techniques. PI
(proportional integral) control technique is not
effective in compensating the high harmonics
generated by the 2nd harmonics at the DC link
of SAPF. To overcome this problem PR
(proportional resonant) control method is used.
In PR control there is possibility of
implementing
the
selective
harmonic
compensation without requiring excessive
computational resources compared to the other
control techniques. PR controller used in widerange of applications.
[1] INTRODUCTION
Day by day our needs are increased in terms of
power. Requirement will make burden on power
quality. Now a day most of the loads are nonlinear
due to usage of power electronic devices like
semiconductor devices used in rectifiers and
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
inverters, switching power supply and other power
electronic converters. To overcome above problems
shunt APF is recognized as cost effective solution
for compensating harmonics in low and medium
power applications.
In general PI controllers are playing major role
for controlling shunt APF. For three phase Systems
synchronous frame PI controllers can be used but it
requires computational burden in case of multiple
frame transformations. To overcome above we are
preferred to use Proportional resonant controller,
which is having similar frequency response
characteristics. PR controllers are used for reference
tracking in the stationary reference frame. The basic
functionality of a PR controller is to introduce
infinite gain at a selected resonant frequency for
eliminating steady state error at that frequency.
Conceptually, an integrator whose DC gain forces
the DC steady state error to zero in the same way
resonant portion of the PR controller whose AC
gain (GI) forces the AC steady error to zero. Due to
above advantages go for PR control method.
Under an unbalanced load the fundamental
positive and negative-sequence components will
present in to the system. The interaction of positive
and negative sequence component of switching
functions and AC currents of the APF produces 2 nd
harmonic ripple on the DC link of the APF, which
will inject 3rd harmonic component in the AC
currents of the APF and line currents. In addition
nonlinear load will inject high harmonic
components in to the load current. The interaction
of
positive and negative sequence switching
functions and high harmonic AC currents of the
APF produces high order even harmonics on the DC
link voltage of the APF, which create high order
odd harmonics in to the APF AC currents. It
will lead to deterioration of performance of the
system. It will provide more stress on the dc link
capacitor, which will reduce life cycle of the dc link
capacitor [1-3].
Some methods are proposed in the papers [1], [5]
and [6] to improve performance of the system.
Methods, which are proposed in the above papers,
are used to eliminate only the 3rd harmonic of APF
AC current, thus to reduce the distortion of the line
current but high harmonics cannot be reduced,
ISSN: 2231-5381
Moreover the even harmonics on the DC link side
still exist
By using conventional positive sequence control
method we cannot eliminate 2nd harmonic voltage
completely from the DC link voltage. Proposed
method in the paper [2] can eliminate 2nd harmonic
voltage completely from the DC link. But the
controller is complex.
To overcome above disadvantages of the control
method and series harmonics at both DC side and
AC side of the APF, PR Control method is
proposed in this paper. This method is implemented
with simple controller. PR filters can also be used
for generating the harmonic command reference
precisely in an active power filter, especially for
single-phase systems, where d–q transformation
theory is not directly applicable. Another advantage
associated with the PR controllers and filters is the
possibility of implementing selective harmonic
compensation
without
requiring
excessive
computational resources.
The remainder of the paper is organized as
follows section 2 describes mathematical modeling
of active power filter, section 3 presents control
strategy. Finally, the simulation results and
conclusion are given in section 4.
[2] MATHEMATICAL MODEL
Fig.1 Basic current harmonic scheme of an
unbalanced load
using a shunt APF.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
Fig.2 The conventional PI control Diagram.
Average current flowing through DC link of the
APF under an unbalanced load is [2]
 1  1*  1  1*
 1  1*
 1  1*
3
I dc  [Re{ddq .idq  ddq .idq }  Re{e jt .(d dq .idq )} Re{e jt .(d dq .idq )}
2
(1)
DC link voltage of APF [2]
Vdc 
Where Ai = A2Ɛ2 , Ɛ2is the error of the voltage
control loop and subscript “*” means reference
value.
From equation (4) it can be seen that 2nd harmonic
component still exist in reference current, which we
are getting from output of the PI controller. The
output of the APF current compensator is obtained
as
A j(2 t )  j(2 t )

vdq  Av sin(2et  v )  v (e e v  e e v )
2
(5)
Transforming equation (5) into the form in αβ
stationary frame, equation (5) is written as
I
3
[ I dc  2 sin( 2e t   2 )]
4C
2e
(2)
Where I2 is magnitude of second harmonic
component of DC link current of the APF. We can
represent equation (2) in the form of

 j t A j (3 t   )
 j ( t   )
v  vdq e e  v (e e v  e e v )
2
(6)
In equation (6) the 3rd harmonic component
appears in the APF current such harmonic results in
a 4th harmonic on the DC link voltage and DC link
udc  U dc  Au sin( 2e t   u )
current of the APF, which causes high order
dc
dc
harmonic in the APF AC currents. These harmonic
(3)
flows into the line and deteriorates the performance
of the system.
Where idq+1*, idq-1* are conjunction vector positive
In addition under the nonlinear load, load current
and negative sequence components of APF currents
contains not only the fundamental negative
in the rotating synchronous frame, respectively
sequence component, but also high order harmonics
+1
-1
ddq , ddq are vector of switching function positive
6k ± 1, where k = 0, 1, 2…… interaction of these
and negative sequence in the rotating synchronous
high order harmonics and fundamental negative and
frame, respectively. From (2), we can tell that the
positive sequence components leads to a series of
2nd harmonic ripple appears on the DC link terminal
high harmonics 2k, k = 0,1,2….. at DC link, e.g.,
due to the interaction of positive and negative
2nd ,4th ,6th …..
sequence components of input currents with switch
Three phase proportional resonant (PR) transfer
functions.
functions
are used for the separation of positive and
Because DC link voltage contains the 2nd
negative sequence components. In general
harmonic in (2), the output of the PI controller of
proportional integral transfer functions are used for
DC link voltage, i.e., the reference current for APF
the separation of positive and negative sequence
current loop, can be given as (DC item is
components but it requires transformation from
neglected).
stationary reference frame (αβ) to synchronous
reference frame (dq), which will increase the
Ai j (2 t )  j (2 t )
*
computational effort. Therefore we
id  A2 2 sin(2et  i )  (e e i  e e i )
2
use PR transfer functions in terms of stationary
(4)
reference frame. Here we have to do reverse
transformation from dq to αβ.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
The inverse transformation can be performed by
using the following 2×2matrix:
 Gdq1  Gdq 2
Gαβ(s) = 1 
2   jGdq1  jGdq 2
(7)
jGdq1  jGdq 2
Gdq1  Gdq 2 
2Kic s
2Ki



Kp  2
2
2
2 
s  2c s 
s  2c s  
1
1
G  
2Ki
2Kic s 
2
Kp  2
 2

2
s  2cs 2 
 s  2c s 
(11)
Comparing equations (8) and (9) with (10) and (11).
It is noted that the diagonal terms of Gαβ+(s) and
Where Gdq1 =Gdq(s+jω)
Gαβ-(s) are identical, but there non-diagonal terms
are opposite in polarity. This is inversion of polarity
Gdq2 =Gdq(s+jω)
can be viewed as equivalent to the reversal of
Given that Gdq(s) = Kp + Ki/s and Gdq(s) = Kp + rotating direction between the positive – and
Ki/(1 +(s/ωc)), the equivalent controllers in the negative- sequence synchronous frames.
Combining both the equations, the resulting
stationary frame for compensating for positivecontrollers
for compensating for both positive- and
sequence feedback error are therefore expressed as:
negative- sequence feedback errors are as expressed
2 Kis
2 Ki  as:

K
p

2 Kis


1
s2   2
s2   2 
Kp  2
0
2


Gαβ+(s) = 

1
s 
2 Kis 
2  2 Ki
Gαβ(s) = 

Kp  2
2 Kis 
2
2 
 s 2   2
s  
0
Kp  2
s   2 

(8)
(12)
2Kic s
2Ki


Kp  2

2
2
2
s  2c s 
s  2c s  
1
1
G 
2Ki
2Kic s 
2
  2
K


2
p
s2  2c s 2 
 s  2c s 
(9)
Similarly, for compensating for negative sequence
feedback error, the required transfer functions are
expressed as:
2 Kis

Kp  2

1
s 2
Gαβ-(s) = 
2
0

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2Kic s


0
Kp  2

s  2c s 2
1
1

G  
2Kic s 
2


0
Kp  2
s  2c s 2 

(13)
Equations (7- 13) are getting from [3]
In this paper I have used equations (9) and (11) for
separation of positive- and negative-sequences in
the PR control method.


[3] CONTROL STRATEGY

2 Kis 
Our control strategy is to eliminate 2 nd harmonic
Kp  2
2
s    at the DC link voltage of the APF under an
(10) unbalanced load condition.
As from above analysis, the fundamental negative
sequence component is the reason for production of
high harmonics in the line current as well as DC
side of the APF. Therefore, we have to be
diminished the fundamental negative sequence
component of APF, thereby, cancel the harmonics
in the system. In order to realize this object, we
0
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
have to maintain quadrature component of
fundamental positive sequence reference current,
which is the output of PI controller of voltage
control loop, and both the direct and quadrature
component of fundamental negative sequence
reference current must be zero.
fundamental current controller and PR controller is
used in high harmonic current controller.
In case of PR control method PR controller is
used in both the fundamental sequence current
controller and high harmonic current controller.
This control method will reduce the complexity of
id+1* = 0 and idq-1* = 0 the circuit. The PR control method is compared
(7) with the conventional control method and DC link
voltage control method. The DC link voltage
This is the basis for a PR control method of the control method block diagram is given in Fig.4
APF. The new control method block diagram for combining [1] with [2].
the APF system is shown in Fig.3. It is having two
control loops in the overall system. Outer loop is the
voltage control loop, which regulates the DC link
voltage of the APF to the reference value. The inner
loop includes the fundamental current controller and
high harmonic controller. In case of conventional
positive sequence control method and DC link
voltage control method PI controller is used in
vdc _ ref
PI
DC-link
voltage
controller
id _ ref
iq _ ref 1  0
idq _ ref
1
1
1  0
v
v
PR positive
Negative
current
controller
abc / 
vabc
PWM
+
APF
system
n
vdc
PR high
harmonic
current
controller
v
iL
abc / 
i f 
abc / 
iLabc
i fabc
Fig.3 Model of Proposed PR control method.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
vdc _ref

vdc
PI
DC-link
voltage
controller

i
*
d

id
Sinusoidal
signal
integrator
 i
q
*
q
v1
PI
current
controller
vabc
v
dq / 
 / abc
PWM
+

//dq
dq


PR high
harmonic
curernt
controller
APF
system
vn
i 0
iL
iLabc
abc / 
i f 
i fabc
abc / 
Fig.4 Model of DC link voltage control method.
[4] SIMULATION RESULTS AND
COMPARISION
Simulation results of PR control method are
compared with the conventional positive sequence
control method and DC link voltage control method.
Here we are comparing THD (total harmonic
Distortion), 3rd harmonics and 2nd, 4th, 6th harmonic
components at the DC link. Almost we are getting
same results for both DC link Voltage control
method and PR control method.
The simulation results of the APF are shown in
Table I.
1. Conventional positive sequence control method:
In the conventional positive sequence control
method positive sequence is controlled. Negative
sequence is not regulated. From the Fig.5, Fig.6 and
Fig.7, we can see line current, DC link voltage and
compensating current. Fig.8 (a) and (b) will show
THD of line current and Harmonic content of DC
link voltage.
TABLE I
PARAMETERS OF THE APF
Paramet
ers
lsa
Cdc
la
Value
0.2856
mH
0.35mF
10 mH
Paramet
ers
rsa
Value
Udc_ref
ra
700V
1mΩ
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91mΩ
Fig. 5 line current.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
Fig. 6 DC link voltage.
Fig. 9 line current.
Fig. 7 Compensating current.
Fig. 10 DC link voltage.
Fig. 8 (a) THD of line current
Fig. 11 Compensating current.
Fig. 8 (b) Harmonic content of the DC link voltage
2. DC link voltage control method:
We can control positive and negative sequences
are controlled. PI controllers are used for
controlling of both positive and negative sequences.
From the Fig.9, Fig.10 and Fig.11, we can see line
current, DC link voltage and Compensating current
of APF. Fig.12 (a) and (b) will show THD of line
current and Harmonic content of DC link voltage.
Fig. 12 (a) THD of line current
Fig. 12 (b) Harmonic content of DC link voltage
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3. Proportional Resonant (PR) control method:
PR controllers are used for the controlling of both
positive and negative sequences. From the Fig.13,
Fig.14 and Fig.15, we can see line current DC link
voltage and compensating current. Fig.16 (a) and
(b) will show THD of line current and harmonic
content of DC link voltage.
The AC current THD and ripple of DC link
voltage of the three controllers are shown in Table
II
Fig. 13 Line current.
Fig. 14 DC link voltage.
Fig. 15 Compensating current.
Fig. 16 (a) THD of line current
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Fig. 16 (b) Harmonic content of DC link voltage.
TABLE II
Comparison between three control methods
Conventional DC
PR
positive
link
control
sequence
voltage
control
control
AC
2.64%
2.66% 2.64%
current
THD
3rd
0.1368A
0.2591 0.1335A
harmoni
A
c
current
Ripple
1) 2nd
1)
1) 0.3098V
of DC
harmonic(0.38
0.2476V
voltage 65V)
2)0.5727V
(V)
2) 4th
2)
harmonic(0.63 3) 4.016V 0.6393V
72V)
3) 6th
3) 3.3V
harmonic(4.03
2V)
[5] CONCLUSION
In this paper, comparison between conventional
positive-sequence, DC link voltage control and PR
control methods are discussed based on THD and
3rd harmonic component of line current and ripple
of DC link voltage. The simulation results reveal
that distortions caused by the 3rd order harmonics on
the line current and by 2nd ripple on the DC link are
nullified, combining with the conventional positivesequence control method.
Although DC voltage control strategy cannot
mitigate the 3rd order harmonic on the line current
and 2nd ripple at the DC link, the PR control method
is implemented more simply and costa few. This
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
method should not use for power factor correction
because it is satisfied equation (7).
[6] REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
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R. Teodorescu, F. Blaabjerg, M. Liserre and
P.C. Loh, “Proportional-resonant controllers and
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2006.
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Member, IEEE, and Ambrish Chandra,
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