Active Power Filter Control Using Adaptive Signal Processing Techniques

doi:10.4236/epe.2013.54B213

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Energy and Power Engineering, 2013, 5, 1115-1119

doi:10.4236/epe.2013.54B213 Published Online July 2013 (http://www.scirp.org/journal/epe)

Active Power Filter Control Using Adaptive Signal

Pr ocessing Techniques

S. A. Temerbaev, V. P. Dovgun, N. P. Bojarskaja, A. F. Sinyagovski

Siberian Federal University, Institute of Space and Information Technologies, Chair of Systems for Automatics,

Computer-Aided Control and Design, Krasnoyarsk, Russia

Email: [email protected]

Received February, 2013

ABSTRACT

In this paper a new Active Power Filter (APF) control method is proposed . Computation of the load harmonic compen-

sation current is performed by the adaptive notch infinite impulse response (IIR) filter. Performance of the proposed

scheme has been verified by computer simulation. MATLAB/SIMULINK power system toolbox is used to simulate the

proposed system. The simulation results are presented and confirmed the effectiveness of the proposed method.

Keywords: Active Power Filter; Nonlinear Load; Harmonics

1. Introduction

The widespread use of nonlinear devices within the in-

dustrial, commercial and residential sectors has resulted

in substantial reduction of power quality in electric power

systems. Harmonic distortion produced by nonlinear

loads causes several problems, such as increased power

losses in customer equipment, power transformers and

power lines, flicker, shorter life of organic insulation [1].

In recent decades, passive and active harmonic filters

have been recognized as the most effective solutions for

harmonic mitigation.

The passive harmonic filters (PHF), consisting from

capacitors, inductors and resistors have been trad itionally

used for this task [1, 3]. The main advantages of PHF are

design simplicity and low cost. Th ey don’t require a reg-

ular service and can correct the power factor. But PHF

have many disadvantages, such as fixed compensation

characteristics, large size and resonance problems.

In recent years, active power filters (APF) have been

widely investigated for the compensation of harmonic

currents. APF allow to compensating the harmonics and

unbalance, together with power factor correction. Mod-

ern active harmonic filters have superior filtering char-

acteristics, smaller in physical size, more flexible in ap-

plication compared to their passive counterparts. They

are widely used in industrial, commercial, utility net-

works and in electric traction systems [1, 2].

Calculation of compensating signals is the important

part of APF control and affects their transient as well as

steady-state performance. Different control methods have

been proposed, ranging from the use of fast Fourier

transform (FFT) to the instantaneous P-Q theory, artifi-

cial neural networks and adaptive notch filters.

In this paper, an efficient method to obtain compen-

sating signals for the active harmonic filter is considered.

The load harmonic compensation is performed by using

the lattice-form adaptive notch IIR filter. Simulation re-

sults confirm the effectiveness of the proposed method.

2. Shunt Active Power Filter

The active power filters are basically classified into two

types: the shunt type and the series type. One of the most

popular active power filters is the shun t APF. It’s advan-

tages are good current con trol capability, easy p rotection,

and high reliability over series filters. The single-phase

operation scheme of a shunt active filter is shown in

Figure 1.

For each harmonic of order h the nonlinear load is

presented by the equivalent Norton circuit, which con-

sists of the current source

with in-parallel imped-

ance

. The grid is presented by the Thevenin equiv-

alent, which consists of the voltage source with

series impedance G

The shunt active power filter compensates current

harmonics by injecting equal but opposite harmonic

compensating current, so that the compensated current is

Figure 1. Operation scheme of shunt active filter.

S. A. TEMERBAEV ET AL.

1116

approximately a pure sinusoid. In this paper, we do not

consider the actual realization of the active filter. It is

assumed to be an ideal controlled current source, propor-

tional to the harmonic components of the load current

0FhL h

GhLh Fh

IKI





where

is the harmonic of distorted load current, and

is the harmonic of the grid current. The compensat-

ing current is proportional to the distorted load current

with subtracted fundamental component.

For h harmonic the coupling point voltage CPh as a

function of the l oad cu rrent U

can be deduced as:



Lh Gh

CPhL h

Lh Gh

KZZ

ZZ K



 (1)

Equation (1) shows the coupling point voltage CPh

if the parameter U

0

approaches one. In the ideal

case

should equal zero for the fundamental har-

monic and one for all other harmonics.

3. Calculation of Compensating Signal

The control strategies to generate compensating signals

are based on the frequency-domain or time-domain tech-

niques [1, 2, 4, 5].

Control strategy in the frequency domain is based on

the Fourier analysis of the distorted current or voltage.

The high-order harmonic components are separated from

distorted signals and combined to form compensating

commands. But the discrete Fourier transform (DFT)

loses accuracy in non-stationary situations.

The first group includes calculation methods in fre-

quency domain. Strategy of such control methods is based

on the Fourier series: discrete Fourier transform (DFT),

fast Fourier transform (FFT).

Commonly used calculation methods in the time do-

main are the instantaneou s active and reactive (P-Q) the-

ory approach, neural network theory, notch filter ap-

proach, adaptive signal processing. Most of these algo-

rithms have a much better dynamic response than the

DFT.

4. Adaptive IIR Notch Filter

Notch filters have a variety of applications in the field of

signal processing for removing single frequency or nar-

row-band sinusoidal interference.

The magnitude characteristic of the ideal notch filter is

defined as:











 (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:



1zaz

Hz zaz







(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:

 

zA









(4)

where





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.

S. A. TEMERBAEV ET AL.

1117

of its low complexity and high-speed convergence. Up-

date of the coefficients 1 and , using gradient algo-

rithm, is given as follows:

   



iiii ii

knknenr nenrn





 

is an adaptation step. Parameter





where



defined: as

Figure 4. All-pass lattice IIR filter.









iiii

nDn en rn











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-

 



212

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:



212

211

zkz k

Hz kzkk z







 

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



. 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.

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

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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