c0 sc0 ls12">
(2)
where 0
is the notch frequency. Notch filter extracts
fundamental sinusoid from distorted current waveform
without harmfully phase shifting of the high-order har-
monics. The ideal notch filter has zero bandwidth. How-
ever, zero bandwidth cannot be realized in practice.
The most simple type of adaptive n otch digital filter is
adaptive line enhancer (ALE) proposed by B. Widrow
[6]. The structure of ALE is shown in Figure 2.
The adaptation of the finite impulse response (FIR)
filter is realized by using the least mean square (LMS)
algorithm. Disadvantages of this ALE are a relatively
low convergence speed and potential instability.
An infinite impulse response (IIR) filter provides a
sharper magnitude response than the FIR adaptive line
enhancer. Also it requires much smaller filter length,
than the ALE based on FIR filter.
The transfer function of the second order notch IIR
filter is defined as:

21
2
1
1zaz
Hz zaz
2


(3)
where
is the pole zero contracting factor. In general,
should be close to unity to well approximate Equa-
tion (2).
As shown in [7] the transfer function of a single fre-
quency notch filter can be expressed in the form:
 
11
2
H
zA
z
(4)
where
A
z represents a transfer function of the all-
pass IIR filter.
The structure of notch filter based on all-pass IIR filter
is presented in Figure 3.
A lattice-form realization of all-pass transfer function
is shown in Figure 4.
Figure 2. Structure of ALE.
Figure 3. Structure of the notch filter.
Copyright © 2013 SciRes. EPE
S. A. TEMERBAEV ET AL.
Copyright © 2013 SciRes. EPE
1117
of its low complexity and high-speed convergence. Up-
date of the coefficients 1 and , using gradient algo-
rithm, is given as follows:
k2
k
   

11
2
11
iiii ii
i
knknenr nenrn
Dn

 
is an adaptation step. Parameter
i
Dn
where
is
defined: as
Figure 4. All-pass lattice IIR filter.

22
11
1
iiii
nDn en rn

D

In Figure 4 x(n) and y(n) are input and output signals,
respectively. Transfer function of the lattice IIR filter is
the following:
is a forgetting factor: 01
. where
5. MATHLAB-Based Simulation
b/Simulink to
APF is analyzed by consider-
in
 



21
12
21
212
1
11
Yzzkk zk
Az Xz kzkk z

 
 2

(5) The system was simulated using MathLa
verify the proposed algorithm. Schematic diagram of the
proposed controlled shunt APF is shown in Figure 6.
The linear load is defined as resistance Rlin = 100 Ohms,
non-linear load includes two rectifiers with RL load on
the dc side. Simulation process is divided into steps:
connection of the first rectifier, connection of APF and
connection of the second rectifier. All simulation process
is presented in Figure 7.
The performance of the
The polynomials of nominator and denominator of
Equation (5) have mirror symmetry. Accordingly, lattice
IIR-filter realizes all-pass transfer function with module
equal 1 in the all frequency range.
Transfer function of notch filter, shown in Figure 3 is
presented as:




21
1
2
212
211
1
211
zkz k
Hz kzkk z


 
2
1
(6) g of the following cases.
where 1 is the adaptive coefficient, which should con-
verge to 0
kcos
to reject a sinusoid with frequency
0
. Frequency suppression of notch filter can be modi-
fied by and stopband widt h by.
1 2
Adaptive IIR filter in Figure 3 is adapted using adap-
tive algorithms related to the lattice FIR filters. The
structure of the lattice second-o rder FIR filter is shown in
Figure 5. In this article gradient lattice algorithm [8] is
used for adaptation purposes. It has been chosen because
k k
Figure 5. FIR lattice filter.
Figure 6. MATHLAB scheme of shunt APF system.
S. A. TEMERBAEV ET AL.
1118
Figure 7. Simulation results.
.1. Case 1
Figure 6 in t = 0.1 sec the first rectifier is
5.2. Case 2
load is increased in t = 0.5 sec. Proposed
6. Conclusions
el adaptive method for grid current
Table 1. THD before and after 0.3 sec.
5
As shown in
connected to the grid. In the 0.3 sec the shunt APF is
connected to the grid and starts compensating harmonics
component of the non-linear load current. Changing of
THD is demonstrated in the Table 1. Grid, linear load
and non-linear load currents are presented in Figure 7.
The nonlinear
technique of calculation compensation signal operates
properly without severe transients at the instants of step
load chang e. THD is presented in Table 2.
In this paper, a nov
harmonic compensation is proposed. The load harmonic
compensation was performed by using the lattice-form
adaptive notch IIR filter. It was shown that adaptive
THD %
Signal nameBefore After
I g 11.29 1.35
I lin 5.44 0.64
I nonl 34.79 40.32
Table 2. THD before and after 0.5 sec.
THD %
Signal nameBefore After
I g 1.35 1.98
I lin 0.64 1.14
I nonl 40.32 40.28
Copyright © 2013 SciRes. EPE
S. A. TEMERBAEV ET AL. 1119
notch filtetive har-
monic filter for the sake of hic mitigation
prooach does not neey training o
notch filter. Performathe proposed l system
is verified by computer simulation. MATLAB/SIM
LINK power system tis used to sime the pro-
posed system. The ults presented
showing the effectiveness of the proposed method.
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