A Combined Series-Parallel Active Filter System Implementation Using Generalized Non-Active Power Theory

Abstract

In this paper, a generalized non-active power theory based control strategy is implemented in a 3-phase 4-wire combined series-parallel active filter (CSPAF) system for periodic and non-periodic waveforms compensation. The CSPAF system consists of a series active filter (SAF) and a parallel active filter (PAF) combination connected a common dc-link. The generalized non-active power theory is valid for single-phase and multi-phase systems, as well as periodic and non-periodic waveforms. The theory was applied in previous studies for current control in the PAF. In this study the theory is used for current and voltage control in the CSPAF system. The CSPAF system is simulated in Matlab/Simulink and an experimental setup is also built, so that different cases can be studied in simulations or experiments. The simulation and experimental results verify that the generalized non-active power theory is suitable for periodic and non-periodic current and voltage waveforms compensation in the CSPAF system.

Full text

A Combined Series-Parallel Active Filter System
Implementation Using Generalized
Non-Active Power Theory
Mehmet Ucar, Sule Ozdemir and Engin Ozdemir
Kocaeli University, Faculty of Technology, 41380, Umuttepe, Kocaeli, Turkey
e-mails: {mucar, sozaslan, eozdemir}@kocaeli.edu.tr
Abstract—In this paper, a generalized non-active power theory
based control strategy is implemented in a 3-phase 4-wire
combined series-parallel active filter (CSPAF) system for
periodic and non-periodic waveforms compensation. The
CSPAF system consists of a series active filter (SAF) and a
parallel active filter (PAF) combination connected a common dc-
link. The generalized non-active power theory is valid for single-
phase and multi-phase systems, as well as periodic and non-
periodic waveforms. The theory was applied in previous studies
for current control in the PAF. In this study the theory is used
for current and voltage control in the CSPAF system. The
CSPAF system is simulated in Matlab/Simulink and an
experimental setup is also built, so that different cases can be
studied in simulations or experiments. The simulation and
experimental results verify that the generalized non-active
power theory is suitable for periodic and non-periodic current
and voltage waveforms compensation in the CSPAF system.
I. INTRODUCTION
The widespread use of non-linear loads and power
electronic converters has increased the generation of non-
sinusoidal and non-periodic currents and voltages in electric
power systems. Generally, power electronic converters
generate harmonic components which frequencies that are
integer multiplies of the line frequency. However, in some
cases, such as controlled 3-phase rectifiers, arc furnaces and
welding machines are typical loads, the line currents may
contain both frequency lower than the line frequency and
frequency higher than the line frequency but not the integer
multiple of line frequency [1]-[4]. These currents interact
with the impedance of the power distribution system and
disturb voltage waveforms at point of common coupling
(PCC) that can affect other loads. These waveforms are
considered as non-periodic for the period of the currents is
not equal to the period of the line voltage [1], [2].
The effects of non-periodic components of voltages and
currents are similar to that caused by harmonics. They may
contribute power loss, disturbances, measurement errors and
control malfunctions, thus degradation of the supply quality
in distribution systems [2]. Additionally, voltage sags are one
of most important power quality problems in the distribution
system and usually caused by fault conditions or by the
starting of large electric motors [5].
Various non-active power theories in the time domain
have been discussed [6]. The generalized non-active power
theory was applied compensation of the non-sinusoidal and
non-periodic load current for parallel active filter (PAF) [7],
[8] and static synchronous compensator (STATCOM) [9].
This paper presents the application of the generalized non-
active power theory for the compensation of periodic (but
non-sinusoidal) and non-periodic currents and voltages with
the combined series-parallel active filter (CSPAF) system.
The simulation and experimental results showed that the
theory proposed in this paper is applicable to the non-active
power compensation of periodic load currents and source
voltages with harmonics and non-periodic load currents and
source voltages in 3-phase 4-wire systems.
The CSPAF system consists of back-to-back connection of
the series active filter (SAF) and the PAF with a common dc-
link. The CSPAF system function is to compensate for all
current related problems such as reactive power compensation,
power factor improvement, current harmonic compensation,
and load unbalance compensation. It regulates the dc-link
voltage using the PAF. Besides, it can compensate all voltage
related problems, such as voltage harmonics, voltage sag,
flicker and regulate the load voltage using the SAF [10], [11].
Fig. 1 shows the general power circuit configuration of the
CSPAF system.
3
∼
Source
Sensitive
loads
i
L
i
S
i
PF
+
v
S
v
SF
v
L
–
SAF PAF
CSPAF system
C
DC
L
S
L
SF
L
PF
L
L
L
L
N
on-linear loads
V
DC
C
SF
R
SF
C
PF
R
PF
N
1
/N
2
PCC
Fig. 1. General power circuit configuration of the CSPAF system.
This work is supported by TUBITAK Research Fund., (No. 108E083)
978-1-4244-4783-1/10/$25.00 ©2010 IEEE 367

II. GENERALIZED NON-ACTIVE POWER THEORY
The generalized non-active power theory [7] is based on
Fryze’s definition of non-active power [12] and is an
extension of the theory proposed in [13]. Voltage vector v(t)
and current vector i(t) in a 3-phase system,
,)](),(),([)( 321
T
tvtvtvtv = (1)
.)](),(),([)( 321
T
titititi = (2)
The instantaneous power p(t) and the average power P(t)
is defined as the average value of the instantaneous power
p(t) over the averaging interval [t-Tc, t], that is
,)()()()()(
3
1
∑
=
==
p
pp
Ttitvtitvtp (3)
.)(
1
)( ∫
−
=
t
Tt
c
c
dp
T
tP
ττ
(4)
The instantaneous active current ia(t) and instantaneous
non-active current in(t) are given in (5) and (6).
)(
)(
)(
)( 2tv
tV
tP
ti p
p
a= (5)
)()()( tititi an −= (6)
In (5), voltage vp(t) is the reference voltage, which is
chosen on the basis of the characteristics of the system and the
desired compensation results. Vp(t) is the corresponding rms
value of the reference voltage vp(t), that is
.)()(
1
)( ∫
−
=
t
Tt
p
T
p
c
p
c
dvv
T
tV
τττ
(7)
The instantaneous non-active power pn(t) and average non-
active power Pn(t) are defined by averaging the instantaneous
powers over time interval [t-Tc, t],
,)()()()()(
1
∑
=
==
m
p
nppn
T
ntitvtitvtp (8)
.)(
1
)( ∫
−
=
t
Tt
n
c
n
c
dp
T
tP
ττ
(9)
In the generalized non-active power theory, the standard
definitions for an ideal 3-phase, sinusoidal power system use
the fundamental period T to define the rms values and average
active power and non-active power. If there are only
harmonics in the load current, Tc does not change the
compensation results as long as it is an integral multiple of
T/2, where T is the fundamental period of the system.
However, in other cases, such as a 3-phase load with sub-
harmonics, or a non-periodic load, Tc has significant influence
on the compensation results, and the power and energy storage
rating of the compensator’s components [7].
III. CONTROL OF THE CSPAF SYSTEM
The 3-phase 4-wire CSPAF system is realized two 3-leg
voltage source inverter (VSI) with split dc-link capacitor and
used the generalized non-active power theory based current
and voltage control techniques.
A. SAF Control Technique
Control block diagram of the SAF is shown in Fig. 2. In
the method the positive sequence detector generates auxiliary
control signals (ia1+, ib1+, ic1+) used as a reference current ip(t)
for the generalized no-active power theory. The source
voltages are input of the positive-sequence detector that
includes a phase locked loop (PLL) function [14]. The output
signals of the positive-sequence detector are ia1+, ib1+ and ic1+,
which have unity amplitude and are in phase with the
fundamental positive-sequence component of the source
voltages (vSa1+, vSb1+, vSc1+). Effective value of the reference
current Ip(t) is given in (10).
∫
−
=
t
Tt
p
T
p
c
p
c
dii
T
tI
τττ
)()(
1
)( (10)
vS
Positive
sequence
detector
Referance
voltage
calculation
(11)
-
i1+
a
v
Improved
SPWM
voltage
controller
1
Vam
(12)
X
X
÷
vSF
*
SF
v
*
Lm
V
abc
Q
∑
+
vS1+
Fig. 2. Control block diagram of the SAF.
The average power calculated given (4) by using the
reference currents and the source voltages. The sinusoidal
load voltage (va(t)) is derived by using (11) [15]. As clearly
shown in Fig. 2, the va(t) is divided by their amplitude (Vam)
calculated by (12) and multiplied the desired load voltage
magnitude (VLm) for converting the v
a(t) to the desired load
voltage (vS1+). Then, the compensation reference voltages of
the SAF are derived by (13) and compared SAF voltages.
Thus SAF switching signals are obtained by using the
improved sinusoidal pulse width modulation (SPWM) [11].
)(
)(
)(
)( 2ti
tI
tP
tv p
p
a= (11)
222
3
2
acabaaam vvvV ++= (12)
)()()( 1
*tvtvtv SSSF +
−= (13)
368

B. PAF Control Technique
The average power calculated given (4) by using load
currents and fundamental positive sequence source voltages
(vSa1+, vSb1+, vSc1+) over the averaging interval [t-Tc, t]. Desired
sinusoidal load currents (iLa1+, iLb1+, iLc1+) is derived by using
(5) and instantaneous non-active current in(t) is calculated as
in (6). Also, the additional active current ica(t) required to meet
the losses in (14) is drawn from the source by regulating the
dc-link voltage vDC to the reference VDC. A PI controller is
used to regulate the dc-link voltage vDC. The error between the
actual dc voltage and its reference value is treated in the PI
controller and the output is multiplied by a sinusoidal
fundamental template of unity amplitude for each phase of the
three phases. In addition, as shown in Fig. 3, the difference
between Vdc1 and Vdc2 is applied to the PI controller. Thus,
equal voltage sharing between the capacitors is accomplished.
The compensation reference currents of the PAF are obtained
by (15). The reference currents are compared the PAF currents
and applied to hysteresis current controller. Thus, the PAF
switching signals are obtained. Control block diagram of the
PAF is shown in Fig. 3.
()()
()()
)(
])[()(
0
212212
0
111
dtvvKvvK
dtvVKvVKvti
t
DCDCIDCDCP
t
DCDCIDCDCPSca
∫
∫
−+−+
−+−= +
(14)
)()()(
*tititi canPF −= (15)
v
S1+
Referance
current
calculation
(5)-(6)
Hysteresis
current
controller
i
L
i
PF
n
i*
PF
i
−
X
v
DC1
+
PI
2
v
DC2
PI
1
1
∑ ∑
∑
+
+
+
−
∑
∑
+ −
+ +
m
V1/
DC
V
ca
i
abc
Q
dc voltage
control
dc voltage unbalance control
Fig. 3. Control block diagram of the PAF.
IV. SIMULATION AND EXPERIMENTAL RESULTS
The CSPAF system prototype is designed and developed
in laboratory to validate the generalized non-active power
theory proposed in the paper. The power circuit and control
block diagram of the CSPAF system implementation is given
in Fig. 4. The non-linear load-1 (which contains a 3-phase
half controlled thyristor rectifier with firing angle 30˚ and a
single-phase diode rectifier are used as nonlinear loads) is the
load that requires ideal source voltages. The non-linear load-2
(which contains a 3-phase diode rectifier) is connected to the
PCC to create source voltage distortion and imitates the effect
of other loads on a radial network. The 3-phase source
voltages with distortion are synthesized by increasing system
impedance from 59 µH to 2.2 mH and connecting the non-
linear load-2 to PCC as shown in Fig. 4.
v
Sabc
3-phase
Source
C
SF
R
SF
L
SF
R
PF
C
PF
Series AF Parallel AF
i
PFa
i
PFb
i
PFc
i
PFn
i
Sa
i
Sb
i
Sc
i
Sn
Reset
v
Sb
v
Sa
v
Sc
v
SFb
v
SFa
v
SFc
CS: Hall-Effect Cu rrent-Sensor
VS: Hall-Effect V oltage Sensor
IA: Isolation Ampl ifier
CS
CS
VS
VS
Pre-charge
Resistors
Single-Phase
Transformers
L
PF
Q
AL
Q
AH
Q
BH
Q
BL
Q
CL
Q
CH
i
L
n
i
La
i
Lb
i
Lc
Voltage
Measurement Board
Voltage
Measurement Board
Current
Measurement Board
DC Voltage
Measurement Board
V
DC1
V
DC2
IA
Reset
Q
AL
Q
AH
Q
BH
Q
CH
Q
BL
Q
CL
IGBT Driver Board
(gate driver-isolation-short
circuit-high current protection)
v
SFbc
i
PFabc
v
DC2
Q
BH
Q
AL
Q
AH
Q
CH
Q
BL
Q
CL
IGBT Driver Board
(gate driver-isolation-short
circuit-high current protection)
High
Current-Voltage
Protection Board
v
DC1
Non-linear
Load-2
(Three-
Phase
Diode Rectifier)
i
La
i
Lc
i
Lb
R
L
L
L
L
i
PFb
i
PFa
i
PFc
Q
AL
Q
AH
Q
BH
Q
BL
Q
CL
Q
CH
Non-linear Load-1
(
Three-Phase
Thyristor Rectifier
and
Single-
Phase Diode
Rectifier)
Current
Measurement Board
PC
dSPACE DS1103 PPC
Controller Board
Fiber-Optic
Connection
Voltage-Current
Signal Conditioning
Interface Boards
i
PFabc
v
SFabc
v
Sabc
i
Labc
v
DC2
v
DC1
Δ-Y
Step-down
Transformer
and
Single-Phase
Sag Generator
Fig. 4. Power circuit and control block diagram of the CSPAF system implementation.
369

Additionally, the voltage-sag generator was employed to
simulate the single-phase source voltage sag for phase-a in
the laboratory. The 3-phase step-down transformer is used for
supply voltage to the CSPAF system and testing the
experimental voltage sag problem. The power circuit
configuration of the CSPAF system combines 3-phase 4-wire
SAF and PAF. Two voltage source 3-leg IGBT converters
sharing a common dc-link are used. The dc-link includes two
capacitor with the midpoint connected to the neutral wire of
the supply system. The dc-link voltage is adjusted at 400 V.
The ac side of the SAF is connected through single-phase
injection transformers in series with the input supply lines.
The PAF is connected in parallel with the output of the
system through an inductor. The CSPAF system parameters
are given in Table I.
Both AF are digitally controlled using a dSPACE DS1103
controller board, includes a real-time processor and the
necessary I/O interfaces that allow carry-out the control
operation. Owing to the switching of the parallel and the
series VSI’s, the compensating currents and voltages have
unwanted high-order harmonics that can be removed by small
high-pass passive filters represented by RPF, CPF and RSF, CSF.
The generalized non-active power theory based
compensation system is simulated and an experimental setup
is also built, so that different cases can be studied in
simulations or experiments. The first three cases for periodic
current and voltage compensation (subsections A–C) are
tested in the experimental setup and the last two cases for
(subsections D and E) are simulated in Matlab/Simulink
software since they are difficult to be carried out in an
experimental setup. The compensation of periodic currents
and voltages with fundamental period T, using a
compensation period Tc that is a multiple of T/2 is enough for
complete compensation [7].
Tektronix DPO3054
oscilloscope
Fluke 434
Power
q
ualit
y
analyser
dSPACE DS1103
controller board
SAF injection
transformers
Non-linear loads
PAF and SAF
Power stages
Control boards
PAF and SAF
passive filters
Split
dc-link capacitors
IGBT driver board
CLP1103
connector
led panel
Fig. 5. The experimental test setup photograph.
TABLE I
THE CSPAF SYSTEM PARAMETERS
Components Symbol Parameters
Power
source
Voltage, frequency VSabc, f
s
, 110V, 50Hz,
Impedance L
s
59µH
DC-link Capacitors C1, C2 4700µF, 4700µF
Reference voltage V
DC
400V
PAF Filter L
PF
, R
PF
, C
PF
3mH, 5Ω, 30µF
Swithching frequency fSWp 8kHz
SAF
Filter LS
F
, RS
F
, CS
F
2.5mH, 2Ω, 150µF
Swithching frequency fSWs 10kHz
Injection transformer N1/N2, S 2, 5.4kVA
Non-linear
loads
(rectifiers)
3-phase thyristor L
L
, L
D
C, R
DC
3mH, 5.7mH, 12Ω
1-phase diode L
L
2, C
D
C, R
DC
2mH, 330µF, 45Ω
3-phase diode C
D
C, R
DC
8800µF, 15Ω
A. Unbalanced Non-linear Load Current Compensation
The experimental results of unbalanced non-linear load
current compensation under ideal source voltages are shown
in Fig. 6.
35A/div 35A/div 35A/div 20A/div
i
Sa
i
Sb
i
Sc
i
Sn
10ms/div
(a) Source currents before compensation.
35A/div 35A/div 35A/div 20A/div
i
Sa
i
Sb
i
Sc
i
Sn
10ms/div
(b) Source currents after compensation.
10ms/div
40A/div 100V/div 40A/div 100V/div
i
Lb
v
Sb
i
Sb
v
Sb
(c) Reactive power compensation.
Fig. 6. Experimental results: Unbalanced non-linear load current
compensation under ideal source voltages.
370

Fig. 6(a) shows the unbalanced non-linear source currents
before compensation. After compensation choosing the
period as Tc=T/2 source currents are almost sinusoidal,
balanced and have very low total harmonic distortion (THD)
as shown in Fig. 6(b). Moreover, the neutral line current is
obviously diminished. Fig. 6(c) shows the experimental
waveforms of the phase difference between source voltages
and source currents for the reactive power compensation;
source voltage and load current (upper waveform) and source
voltage and current (lower waveform). The PAF compensates
the load reactive power, thus source currents are in phase
with its phase voltage and making the unity power factor
source current. The compensation results are summarized in
Table II.
TABLE II
SUMMARY OF EXPERIMENTAL RESULTS FOR
THE LOAD CURRENT COMPENSATION
Source currents (iS) Before After
RMS
(A)
phase-a 14.2 14.2
phase-b 17.6 14.2
phase-c 14.3 14.1
neutral 4.9 1.2
THD
(%)
phase-a 33.8 4.4
phase-b 29.8 4.1
phase-c 33.6 4.5
PF 0.89 0.99
B. Source Voltage Harmonic Compensation
Fig. 7 shows the experimental results of the distorted
source voltages compensation, while the load currents are
non-linear and unbalanced.
v
La
v
Lb
v
Lc
10ms/div
200V/div
200V/div 200V/div
(a) Load voltages before compensation.
200V/div
200V/div 200V/div
v
La
v
Lb
v
Lc
10ms/div
(b) Load voltages after compensation.
Fig. 7. Experimental results: Distorted source voltage compensation.
Non-linear loads draw highly distorted currents from the
utility as well as causing distortion of the voltages. The 3-
phase distorted load voltages before compensation are
demonstrated in Fig. 7(a). After compensation choosing the
period as Tc=T/2, the source voltages with distortion is
compensated to the sinusoidal waveforms are shown in Fig.
7(b). The THD of the load voltages, which was
approximately 9.3% before compensation, is approximately
4.4% after compensation. The compensation results are
summarized in Table III.
TABLE III
SUMMARY OF EXPERIMENTAL RESULTS FOR THE
DISTORTED SOURCE VOLTAGE COMPENSATION
Load voltages (v
L
) Before After
RMS
(V)
phase-a 104.1 110.5
phase-b 103.4 110.1
phase-c 104.2 109.2
THD
(%)
phase-a 9.2 4.3
phase-b 9.1 4.6
phase-c 9.6 4.4
C. Source Voltage Sag Compensation
Voltage sags are one of the most important power quality
problems because of its impact on malfunctioning electrical
equipment. Voltage sags are typically caused by remote faults
such as a single line to ground fault on the power system or
due to starting of large induction motors. Fig. 8 shows the
experimental waveforms under single-phase voltage sag with
a depth of 50% choosing the period as Tc=T/2. In the Fig. 8,
from top to bottom, phase-a source voltage, compensated
load voltage, compensated source current and load current are
showed. The load terminal voltage is regulated and almost
constant nominal value during voltage sag of phase-a using
the CSPAF system. The required power for the compensation
of the load voltage is supplied from the source. Thus, the
source currents increased. The compensation results are
summarized in Table IV.
200V/div 200V/div 30A/div 30A/div
v
Sa
v
La
i
Sa
i
La
10ms/div
Fig. 8. Experimental results: Source voltage sag compensation: source
voltage, load voltage, source current and load current waveforms.
TABLE IV
SUMMARY OF EXPERIMENTAL RESULTS FOR THE
SINGLE-PHASE VOLTAGE SAG COMPENSATION
Load voltages (v
L
) Before After
RMS
(V)
phase-a 52.1 108.3
phase-b 105.8 108.8
phase-c 106.8 109.6
371

D. Sub-Harmonic Current and Voltage Compensation
The sub-harmonic currents (frequency lower than
fundamental frequency) are typically generated by power
electronic converters [7]. The main feature of these non-
periodic currents is that the currents may have a repetitive
period. When the fundamental frequency of the source
voltage is an odd multiple of the sub-harmonic frequency, the
minimum Tc for complete compensation is 1/2 of the common
period of both fs and fsub. When fs are an even multiple of fsub,
the minimum Tc for complete compensation is the common
period of both fs and fsub [8]. In this study, source voltage and
load current contains sub-harmonics of 10 Hz frequency and
20% amplitude are given in Table V. The sub-harmonic
current and voltage compensation simulation results are
shown in Fig. 9 and Fig. 10, respectively.
TABLE V
THREE-PHASE SOURCE VOLTAGE AND
LOAD CURRENT VALUES
Parameters Fundamental Sub-harmonic
Freq. (Hz) 50 10
Currents 15 A % 20
Voltages 110 V % 20
0.15
0.2
0.25
0.3
0.35
0.4
0.45 0.5
-200
-100
0
100
200
t
(s)
v
Sabc
(V)
(a) 3-phase sub-harmonic source voltage waveforms.
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-200
-100
0
100
200
t (s)
v
Labc
(V)
(b) 3-phase load voltages after compensation.
Fig. 9. Simulation results: Sub-harmonic voltage compensation.
0.15
0.2
0.25
0.3
0.35
0.4
0.45 0.5
-25
0
25
t
(s)
i
Labc
(A)
(a) 3-phase sub-harmonic load current waveforms.
0.15
0.2
0.25
0.3
0.35
0.4
0.45 0.5
-25
0
25
t
(s)
i
Sabc
(A)
(b) 3-phase source currents after compensation.
Fig. 10. Simulation results: Sub-harmonic current compensation.
The sub-harmonic component can be completely
compensated by choosing Tc=2.5T, and the source currents
and load voltages are balanced and sinusoidal. The CSPAF
system is able to suppress all the sub-harmonic component of
the load current and the voltage at the load terminals is
constant amplitude after compensation.
E. Stochastic Non-Periodic Current and Voltage
Compensation
The arc furnace load currents may contain stochastic non-
periodic currents (frequency higher than fundamental
frequency but not an integer multiple of it). Theoretically, the
period T of a non-periodic load is infinite [7]. In a non-
periodic system, the instantaneous current varies with
different averaging interval Tc, which is different from the
periodic cases. The source current could be a pure sine wave
if Tc goes to infinity. However, this is not practical in a power
system, and Tc is chosen to have a finite value. The non-
active components in these loads cannot be completely
compensated by choosing Tc as T/2 or T, or even several
multiples of T. Choosing that period as may result in an
acceptable both source current and load voltage which are
quite close to a sine wave. If Tc is large enough, increasing Tc
further will not typically improve the compensation results
significantly [8].
In this work, 3-phase source voltage and load current
components are given in Table VI [16]. Fig. 11 and Fig. 12
shows simulation results of the stochastic non-periodic
voltage and current compensation choosing the period as
Tc=5T. After compensation, load voltages and source currents
are balanced and almost sinusoidal with low THD as shown
in Fig 11(b) and Fig 12(b). In addition, source neutral current
have been reduced considerably.
TABLE VI
THREE-PHASE SOURCE VOLTAGE AND
LOAD CURRENT COMPONENTS
Parameters Fund. Components (%)
Freq. (Hz) 50 104 117 134 147 250
Currents 15 A 30 40 20 20 50
Voltages 110 V 7.5 10 5 5 12.5
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-200
0
200
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-200
0
200
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-200
0
200
v
Sa
(V) v
Sb
(V) v
Sc
(V)
t (s)
(a) 3-phase stochastic non-periodic source voltage waveforms.
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-200
0
200
v
Labc
(V)
t (s)
(b) 3-phase load voltages after compensation.
Fig. 11. Simulation results: Stochastic non-periodic voltage compensation.
372

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-25
0
25
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-25
0
25
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-25
0
25
i
La
(A)
I
Lb
(A)
i
Lc
(A)
t
(
s
)
(a) 3-phase stochastic non-periodic load current waveforms.
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-25
0
25
i
Sabc
(A)
t
(
s
)
(b) 3-phase source currents after compensation.
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-12
0
12
i
Lnabc
(A)
t
(
s
)
(c) Load neutral current waveforms.
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-12
0
12
i
Snabc
(A)
t (s)
(d) Source neutral current after compensation.
Fig. 12. Simulation results: Stochastic non-periodic current compensation.
V. CONCLUSION
The presence of non-linear, time-variant, disturbing loads
connected to the electric power system is responsible for the
presence of periodic and non-periodic disturbances on the
line currents and voltages. In this paper, the generalized non-
active power theory, which is applicable to sinusoidal or non-
sinusoidal, periodic or non-periodic, balanced or unbalanced
electrical systems, is presented. It has been applied to the 3-
phase 4-wire CSPAF system. This theory is adapted to
different compensation objectives by changing the averaging
interval Tc. The CSPAF experimental setup system was built
and tested in the laboratory. Three cases, unbalanced
nonlinear load currents, distorted source voltages and source
voltage sag with unbalanced non-linear load currents
compensation are tested in the experiments. The sub-
harmonic and the stochastic non-periodic current and voltage
compensation are simulated in Matlab/Simulink. The
simulation and experimental results showed that the theory
proposed in the CSPAF system was applicable to non-active
power compensation of periodic and non-periodic waveforms
in 3-phase 4-wire systems.
VI. REFERENCES
[1] E. H. Watanabe and M. Aredes, “Compensation of nonperiodic currents
using the instantaneous power theory,” IEEE Power Engineering Soc.
Summer Meeting, pp. 994–999, 2000.
[2] L. S. Czarnecki, “Non-periodic currents: their properties, identification
and compensation fundamentals,” IEEE Power Engineering Soc.
Summer Meeting, pp. 971-976, 2000.
[3] H. Akagi, “Active filters and energy storage systems operated under
nonperiodic conditions,” IEEE Power Engineering Soc. Summer
Meeting, Seattle, pp. 965-970, 2000.
[4] S. A. Farghal, M. S. Kandil and Elmitwally, “Evaluation of a shunt
active power conditioner with a modified control scheme under
nonperiodic conditions,” IEE Proc. Generation, Transmission and
Distribution, vol. 149, no. 6, pp. 726-732, Nov. 2002.
[5] M. F. McGranaghan, D. R. Mueller and M. J. Samotyj, “Voltage sags
in industrial systems,” IEEE Trans. Ind. Appl., vol. 29, no. 2, pp. 397-
403, 1993.
[6] L. M. Tolbert and T. G. Habetler, “Comparison of time-based non-
active power definitions for active filtering,” IEEE Int. Power Electron.
Congress, pp. 73–79, Oct. 15-19, 2000.
[7] Y. Xu, L. M. Tolbert, F. Z. Peng, J. N. Chiasson and J. Chen,
“Compensation-based non-active power definition,” IEEE Power
Electr. Letter, vol. 1, no. 2, pp. 45-50, 2003.
[8] Y. Xu, L. M. Tolbert, J. N. Chiasson, J. B. Campbell and F. Z. Peng,
“Active filter implementation using a generalized nonactive power
theory”, IEEE Industry Applications Conference, pp. 153-160, 2006.
[9] Y. Xu, L. M. Tolbert, J. N. Chiasson, J. B. Campbell and F. Z. Peng,
“A generalised instantaneous non-active power theory for STATCOM,”
IET Electric Power Applications, pp. 853-861, 2007.
[10] H. Fujita and H. Akagi, “The unified power quality conditioner: the
integration of series and shunt active filters,” IEEE Trans. on Power
Electr., vol. 13, no. 2, 1998.
[11] M. Aredes, K. Heumann, and E. H. Walandble, “An universal active
power line conditioner,” IEEE Trans. Power Del., vol. 13, no. 2, pp.
545-551, Apr. 1998.
[12] S. Fryze, “Active, reactive, and apparent power in non-sinusoidal
systems,” Przeglad Elektrot., vol. 7, pp. 193-203 (in Polish), 1931.
[13] F. Z. Peng and L. M. Tolbert, “Compensation of non-active current in
power systems-definitions from compensation standpoint,” IEEE
Power Eng. Soc. Summer Meeting, pp. 983-987, 2000.
[14] G. W. Chang and W. C. Chen “A new reference compensation voltage
strategy for series active power filter control,” IEEE Trans. on Power
Delivery, vol. 21, no. 3, pp. 1754-1756, July 2006.
[15] M. Ucar, S. Ozdemir and E. Ozdemir, “A control strategy for combined
series-parallel active filter system under non-periodic conditions,”
International Conference on Renewable Energies and Power Quality,
ICREPQ’09, Valencia (Spain), 15-17 Apr. 2009.
[16] IEEE Interharmonic Task Force, “Interharmonic in power systems,”
Cigre 36.05/CIRED 2 CC02, Voltage Quality Working Group, 1997.
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