Selective Harmonic Current Mitigation with a Shunt
Active Power Filter
L. A. Cleary-Balderas Student, Member, IEEE A. Medina-Rios, Senior Member, IEEE
Facultad de Ingeniería Eléctrica, División de Estudios de Posgrado
Universidad Michoacana de San Nicolás de Hidalgo
Morelia, Michoacán, México
Email: luis_arthur_c@hotmail.com, amedinr@gmail.com
Abstract— This paper proposes a Shunt Active Power Filter
(SAPF) for harmonic mitigation based a selective harmonic
current mitigation (SHCM) method. The proposed SHCM
method improves the filtering efficiency and solves many issues
existing in highly contaminated loads. The Fast Fourier
Transform (FFT) is applied to a specific harmonic current
detection of a three-phase circuit. A simulation study of a threephase
compensated
system
is
carried
out
using
Matlab/Simulink
 to validate the proposed method.
I. INTRODUCTION
Harmonics generated from non-linear loads, such as switch
mode power converters and adjustable speed drives, as well
as other unbalanced loads in distribution networks deteriorate
power quality in power transmission and distribution systems
[1]-[2]. Nonlinear loads increase losses and produce
harmonic distortion in the grid. As a consequence, poor
power quality causes various problems in both the power grid
and connected equipment. This harmonic distortion can be
mitigated using passive filters [3]-[4]. However, the use of
traditional compensation with capacitor banks and passive
filters produces harmonic propagation and harmonic voltage
amplification, due to possible resonance between line
inductances and shunt capacitors [4]-[5]. Thus, passive filters
cannot always provide a complete compensation solution. As
an alternative, different active filter solutions have been
continuously analyzed in recent years. A conventional (APF)
is typically composed of three single phase inverters and
pulse width modulation (PWM) and can be connected to the
load either in parallel or in series [6].
The purpose of the SAPF system is to supply the harmonics
absorbed by the nonlinear load, in order to reduce harmonic
distortion in the grid. However, the harmonic compensation
using APF solutions for high-power applications is usually
limited by the available semiconductor technology.
Semiconductor limitations, due to maximum current and
voltage ratings, losses, and switching frequency in the range
of 1 kHz – 5 kHz, result in reduced harmonic mitigation
performance of higher order harmonic currents [7].
978-1-4673-2308-6/12/$31.00 ©2012 IEEE
An alternative solution is the use of selective harmonic
control, where the APF bandwidth is tuned so that the
harmonic currents are individually controlled. This allows the
APF to mitigate the dominant harmonic currents, with the
advantage of using a moderate switching frequency.
Therefore, the APF can be tuned to selectively compensate
only the characteristic harmonic currents, which are normally
applied by a typical three-phase rectifier [7]-[8].
To solve these issues of design the APF currents
compensation is based on the requirement that the source
currents after compensation must be sinusoidal and balanced
or meet harmonic current distortion limits set by IEEE-519
standard and permissible levels of the source current
imbalance [9]. Current harmonic limits based on the size of
the user with respect to the size of the power system to which
the user is connected are given in [10].
This paper proposes a SAPF to mitigate harmonic distortion
based on SHCM, offering a novel solution to suppressing
harmonic currents in high or medium voltage power systems.
The following sections are organized as follows: Section II
outlines the fundamental principles of a harmonic detection,
Section III details the proposed system configuration and
provides simulation results to verify the operation
performance of the proposed SAPF, and Section IV offers the
main conclusions drawn from the reported investigation.
II. FUNDAMENTAL PRINCIPLES
A. The principle of a harmonic detection method
Different methods of selective harmonic detection have been
developed, see Table I. In general, harmonic simulation
techniques can be identified as frequency domain, time
domain and hybrid time and frequency domain methods [11][12]. In the time domain, the method based on the
instantaneous reactive power theory has been widely adopted
for harmonic compensation and Kalman filters allow real
time calculation of harmonic parameters [13].
TABLE I
CLASSIFICATION OF THE MOST USED HARMONIC DETECTION
METHODS IN APF’S
Algorithm
Frequency-domain
Time-domain
Other
Harmonic Detection Method
Discrete Fourier Transform (DFT)
Fast Fourier Transform (FFT)
Recursive Discrete Fourier Transform
Synchronous harmonic dq-frame
Band pass filters
Instantaneous power “pq theory”
Generalized integrators
Prediction algorithms, Prony analysis
Kalman filters
Nueral networks and adaptive control
Wavelets Transform
B. Harmonic Analysis in the Frequency-Domain
The frequency-domain methods are mainly identified with
Fourier analysis, rearranged to provide the result as fast as
possible with a reduced number of calculations, allowing for
real-time implementation in DSPs [14].
The Fourier analysis is used to convert time-domain
waveforms into their component frequencies and vice-versa.
In practice, data are often available in the form a sample time
function, represented by a time series of variable amplitude,
separated by fixed time intervals of limited duration. Discrete
Fourier Transform (DFT) or its variant the Fast Fourier
Transform (FFT), are usually used for this purpose.
The frequency components provided by the DFT or FFT are
time independent. In fact, for stationary signals these
components remain the same over the time. However, this is
very different if the current waveforms are non-stationary.
Here the use of a Fourier transform alone becomes
inadequate [4]. A suitable way to extract such information is
to apply related time-frequency signal decomposition. The
FFT is used for the time-frequency decomposition, such as
the extraction of the harmonic components and phase of the
load currents. The DFT and FFT algorithms have been
applied to many useful applications in power system phasor
measurements and harmonic analysis [15].
The FFT algorithm uses an operation called decimation (in
the time or frequency domain) that relies on the recursive
decomposition of an N point DFT into two DFT transforms
of N/2 points this process can be applied to any N-sampled
signal if N is a regular power of two, so the decomposition
can be repeatedly applied until the trivial “1-point” transform
is reached and calculated. Thus, the total number of
calculations is reduced from N2 to N· log2(N).
Once the harmonic spectrum is determined, the harmonic
reference current is the summation of all sinusoidal functions
with the known amplitude, frequency, and phase [16].
The short time Fourier transform (STFT) is an extension of
the Fourier transform for the analysis of nonstationary
signals. In SFFT, a signal is divided into small time windows,
and each is analyzed using the Fourier transform as follows:
, (1)
Where is the signal, h is the window function, for example
a rectangular function and t, ω are the time and frequency
parameters, respectively. This formulation provides
localization in time while simultaneously capturing frequency
information. The time–frequency tiling for the STFT is
uniform across time and frequency. In the implementation of
the STFT, a design tradeoff must be made between time and
frequency resolution. A short-duration window provides
good time resolution at the expense of poor frequency
resolution, whereas a long-duration window provides good
frequency resolution at the expense of reduced time
resolution [17]-[18].
C. Shunt Active Power Filter
The shunt active power filter with selective harmonic current
mitigation proposed in this paper consists of cascaded
inverters. This scheme is shown in Fig. 1; the first inverter
compensates the unbalanced source currents and the other,
more significant harmonics, are compensated with each
individual inverter. This topology offers better advantages in
comparison with a single APF inverter unit. The total
compensation of the inverter unit is obtained and handles
more power to the electrical system, so also can make a more
efficient filtering of higher order harmonics and reduce
possible resonance in the power system
Fig. 1. Scheme of a selective filter in cascade array.
D. Derivation of Compensation current reference
The derivation of the reference compensation current for the
three-phase SAPF is based on the harmonic phase
coordinates frame APF-abc [19]-[20]. The reference currents
are defined as,
! ", #, $.
(2)
where are the line distorted currents, &' is the sum of the
average real power delivered to the load in each phase, ( are
peak phase voltages and (' is their sum, ) are the source
voltages, and k=a,b,c.
The proposed APF-abc configuration is shown in Fig. 2; it
consists of a reference current calculator (2) that uses the
filtering currents to feed-back and compensate the lost signal
of the line currents once the APF-abc is in operation [20].
where "9 y #9 are the Fourier coefficients and can be written
as,
'
2
"9 >A )1
$?@A '
'
2
@@A .
#9 >A )1
'
Fig. 2. APF-abc reference current filter configuration.
E. Selective harmonic current compensation proposed.
The proposed method of mitigating selective harmonic
current is implemented according with (2). If asymmetry is
present in the obtained source voltages at fundamental
frequency and the shunt APF is placed to compensate
harmonic current in a three phase four-wire electric system, it
will result in the presence of a relatively high neutral current.
To avoid this problem, once the fundamental frequency
source voltage information is obtained, it is proposed a 120°
positive sequence phase shift to be applied over the reference
signal voltages. This is done by detecting the phase angle of
the phase selected as the reference, e.g. phase ", and adding
or subtracting 120° to the other two phases. At the end of the
two-step procedure described above, the signal reference
voltages to be used for the calculation of the desired source
currents are now given as,
* +* 4 +4 7 +7 2 sin / 0*1
sin sin /
5
6
5
6
(3)
2
/ 0*1
(4)
2
/ 0*1
.
(5)
Where is reference filtering current of the phase !,
+ is the line current, where the subscript ! represents the
phases ", # or $, respectively. &' is the total active power
delivered to the load; (' is the sum of the peak value of load
voltages, 0*1 is the phase angle of the fundamental
component of the load voltage at phase ", and is the
angular speed at fundamental frequency 8 of 60Hz. The
harmonics currents 9: and phase 09:
are calculated with
(6) and (7). Equation (6) determines the amplitude of the
individual harmonic current and (7) determines their
harmonic phase shifts.
:
;"9 / #9
0:
<
1
4=
*=
(6)
(7)
(8)
(9)
Equations (8) and (9) are used to determine the compensation
currents which need to be injected by the active filter. Where
2
)1
is the reference currents defined in (3)-(5). The
calculation of each of these reference components can be
performed in digital form using the FFT algorithm based on
the time decimation. The proposed harmonic detection
control is shown in Fig. 3. It consists of two stages. The first
stage is to calculate the reference currents; this method is
based on the calculation of the sinusoidal line current shown
in Fig. 2. In the second stage, current filtering using FFT
to determine the necessary currents to be selectively injected
to achieve the harmonic current mitigation is proposed.
Fig. 3. Block diagram of selective harmonic current compensation proposed.
III. PROPOSED SYSTEM CONFIGURATION AND
SIMULATION RESULTS
A. System configuration
The proposed selective harmonic current mitigation method
is composed of three APFs in parallel, as shown in Fig. 4.
Each unit consists on three-phase voltage source inverter,
three equal series inductances B with resistances C and a
DC capacitor. For this case study, the shunt active power
filter is connected in parallel to the nonlinear load, which is a
three phase rectifier feeding a CD load. The assumed selected
harmonic current components are the fundamental current
component (60 Hz), the 5th harmonic component (300 Hz)
and the 7th harmonic component (420Hz). By injecting the
fundamental component it is possible to balance the three
phases of the current and mitigate losses. The main
parameters of the power system used in the simulations are
given in Table II.
Fig. 7 illustrates the current to be injected by the active filter.
It may be noted that has a high harmonic content, can be
impractical in some systems e.g. for the PWM inverter, these
limitations reduce efficiency in the operation of the switching
semiconductor devices such as MOSFET, IGBT, and GTO.
Fig. 4. Proposed shunt active filter based on a selective harmonic current
mitigation.
)E
BE
CE
B
C
CD
C*
C4
C7
G1 , G
TABLE II SYSTEM PARAMETERS
Supply phase voltage
Source inductance
Source resistance
Energy link inductance
Energy link resistance
Rectifier load resistance
Load resistance at phase a
Load resistance at phase b
Load resistance at phase c
DC capacitors
250(FF
0.1mH
0.003Ω
2mH
0.1Ω
30Ω
50Ω
100Ω
150Ω
500µF
B. Simulation
Fig. 5 shows the distorted and unbalanced source phase
currents. The unbalance and harmonic distortion is caused by
the unbalanced load connected to the system, i.e. C* 50Ω,
C4 100Ω, C7 150Ω, and the nonlinear load that creates
the harmonic currents consisting on a three-phase six-pulse
diode rectifier with resistive load. Fig. 6 shows the harmonic
content of the source currents without selective harmonics
compensations.
Fig. 7. APF injection currents If*abc obtained by model coordinates in
phase.
Fig. 8 shows the fundamental component of . This
component is extracted using the SFFT in the time-frequency
decomposition of the SHCM. The fundamental component
is the reactive component supplied by the APF. After this
reactive power injection, the source current is placed in phase
and balanced with the fundamental component of the source
voltage, as shown in Fig. 9.
Fig. 8. Extraction of the in the fundamental component for the APF.
Fig. 9. Results of the contribution of injection of the fundamental component
current in the three-phase system.
Fig. 5. Currents generated by the nonlinear load and unbalanced linear load.
Fig. 10 illustrates the extraction of the fifth component 5th by
. This component is extracted using the STFT in the time
frequency decomposition of the SHCM.
Fig. 10. Extraction of the fifth harmonic for the APF.
Fig. 6 Harmonic content of the source currents without compensated.
After the injection of fifth component supplied by the APF,
the system starts compensating at 0.03s, as shown in Fig. 11.
The spectral analysis of source current after filtering the 5th
harmonic is shown in Fig. 12. Please observe that the 5th
harmonic for the phase A is reduced from 11.59% to 0.68%.
References
[1]
[2]
[3]
[4]
Fig. 11. Results of the contribution of fundamental current, 5 th.
[5]
[6]
[7]
[8]
[9]
Fig. 12. Spectral analysis of source current after filtering the 5th harmonic.
.
Fig. 13 shows the results obtained of the distorted current
sources without compensation and after of the selective
compensation of the 5th and 7th harmonics.
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Fig. 13. Harmonic spectrum of source currents based on selective harmonic
compensation.
IV. CONCLUSIONS
In this paper a selective harmonic current mitigation (SHCM)
method has been proposed. The conducted simulation studies
on a three-phase circuit with linear and nonlinear unbalanced
loads, using the proposed SAPF resulted on a reduction of the
original THD from 16.25% to 3.39% or nearly five times.
The effectiveness of the proposed SHCM system makes it a
practical solution for a variety of industrial applications in
need of harmonic current mitigation.
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