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 dclink. The generalized non-active power theory is valid for singlephase and multi-phase systems, as well as periodic and nonperiodic 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 nonsinusoidal 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 nonactive 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 dclink. 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.
This work is supported by TUBITAK Research Fund., (No. 108E083)
978-1-4244-4783-1/10/$25.00 ©2010 IEEE
367
LL
CSPAF system
LS
3∼
Source
vS
iS
PCC
+ vSF –
N1/N2
RSF CSF
vL
iL
iPF
LL
CPF RPF
Non-linear loads
LPF
LSF
Sensitive
loads
CDC
VDC
SAF
PAF
Fig. 1. General power circuit configuration of the CSPAF system.
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,
v(t ) = [v1 (t ), v2 (t ), v3 (t )]T ,
(1)
i (t ) = [i1 (t ), i2 (t ), i3 (t )]T .
(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
p(t ) = v T (t ) i (t ) =
∑v
p
(t ) i p (t ),
(3)
p =1
P (t ) =
1
Tc
t
∫ p(τ ) dτ .
(4)
t − Tc
The instantaneous active current ia(t) and instantaneous
non-active current in(t) are given in (5) and (6).
i a (t ) =
P(t )
V p2 (t )
v p (t )
in (t ) = i (t ) − ia (t )
However, in other cases, such as a 3-phase load with subharmonics, 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.
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).
I p (t ) =
(5)
1
Tc
t
∫i
p
T
(τ ) i p (τ ) dτ
(10)
t −Tc
(6)
vS
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
V p (t ) =
Tc
CONTROL OF THE CSPAF SYSTEM
Positive i1+
sequence
detector
*
V Lm
Referance
va
voltage
calculation
(11)
Vam
(12)
X
÷
vS1+ - + v*SF
∑
1
∫v
p
(τ ) v p (τ ) dτ .
(7)
t − Tc
The instantaneous non-active power pn(t) and average nonactive power Pn(t) are defined by averaging the instantaneous
powers over time interval [t-Tc, t],
m
pn (t ) = v T (t ) in (t ) =
∑v
p
(t ) inp (t ),
(8)
p =1
Pn (t ) =
1
Tc
t
∫ p (τ ) dτ .
n
(9)
Qabc
X
vSF
t
T
Improved
SPWM
voltage
controller
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 va(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].
t − Tc
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.
368
va (t ) =
P(t )
I p2 (t )
i p (t )
(11)
2 2
2
2
vaa + v ab
+ vac
3
(12)
v *SF (t ) = v S (t ) − v S1+ (t )
(13)
Vam =
iL
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.
1
∫ (v
+
+
−
V
+
∑
+
dc voltage
control
DC
−
∑
PI2
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 nonlinear load-2 to PCC as shown in Fig. 4.
− v DC 2 ) dt )
(15)
Single-Phase
Transformers
3-phase
Source
iLa
iSa
Δ-Y
Step-down
Transformer
and
Single-Phase
Sag Generator
CS
iSb
iSc
iSn
iLb
Non-linear Load-1
(Three-Phase
iLc
Thyristor Rectifier
and
iLn
Single-Phase Diode
LL
Rectifier)
Non-linear
Load-2
(Three-Phase
Voltage
Measurement Board
VS
iLa iLb iLc
Current
Measurement Board
Pre-charge
Resistors
Diode Rectifier)
iPFc
vSa vSb vSc
iPFb
iPFn
VS
iPFa
vSabc
ica
Qabc
dc voltage unbalance control
0
*
i PF
(t ) = in (t ) − ica (t )
+
+
PI1
∑
∑
vDC2
(14)
DC1
X
vDC1
∫
+ ( K P 2 (v DC1 − v DC 2 ) + K I 2
−
Hysteresis
current
controller
iPF
t
0
vS1+
*
iPF
∑
+
1/Vm
ica (t ) = (v S1+ [ K P1 (VDC − v DC ) + K I 1 (VDC − v DC ) dt ])
t
Referance
current in
calculation
(5)-(6)
DC Voltage
Measurement Board
vSFa
vSFb
vSFc
Series AF
QAH
Voltage
Measurement Board
QBH
Parallel AF
QCH
iPFa
iPFb
iPFc
CS
QAH
QBH
QCH
QAL
QBL
QCL
Current
Measurement Board
VDC1
IA
CS: Hall-Effect Current-Sensor
VS: Hall-Effect Voltage Sensor
IA: Isolation Amplifier
LSF
RSF
QAL
QBL
QCL
LPF
RPF
VDC2
CPF
CSF
QAH QAL QBH QBL QCH QCL
IGBT Driver Board
(gate driver-isolation-short
circuit-high current protection)
QAH QAL QBH QBL QCH QCL
Reset
IGBT Driver Board
High
Current-Voltage
Protection Board
Reset
(gate driver-isolation-short
circuit-high current protection)
vDC1 vDC2
vSabc
vSFabc
iPFabc
iLabc
Voltage-Current
Signal Conditioning
Interface Boards
dSPACE DS1103 PPC
Controller Board
Fiber-Optic
Connection
vDC1
PC
Fig. 4. Power circuit and control block diagram of the CSPAF system implementation.
369
vDC2
vSFbc
iPFabc
LL
R
dSPACE DS1103
controller board
Tektronix DPO3054
oscilloscope
TABLE I
THE CSPAF SYSTEM PARAMETERS
Components
Voltage, frequency
Impedance
Capacitors
DC-link
Reference voltage
Filter
PAF
Swithching frequency
Filter
SAF
Swithching frequency
Injection transformer
Non-linear 3-phase thyristor
loads
1-phase diode
(rectifiers) 3-phase diode
Power
source
Symbol
VSabc, fs,
Ls
C 1, C 2
VDC
LPF, RPF, CPF
fSWp
LSF, RSF, CSF
fSWs
N1/N2, S
LL, LDC, RDC
LL2, CDC, RDC
CDC, RDC
Parameters
110V, 50Hz,
59µH
4700µF, 4700µF
400V
3mH, 5Ω, 30µF
8kHz
2.5mH, 2Ω, 150µF
10kHz
2, 5.4kVA
3mH, 5.7mH, 12Ω
2mH, 330µF, 45Ω
8800µF, 15Ω
20A/div 35A/div 35A/div 35A/div
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.
iSa
iSb
iSc
iSn
10ms/div
(a) Source currents before compensation.
20A/div 35A/div 35A/div 35A/div
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].
iSa
Fluke 434
Power quality
analyser
iSb
iSc
iSn
CLP1103
connector
led panel
Split
dc-link capacitors
10ms/div
PAF and SAF
passive filters
(b) Source currents after compensation.
Control boards
IGBT driver board
PAF and SAF
Power stages
100V/div 40A/div 100V/div 40A/div
vSb
iLb
vSb
iSb
Non-linear loads
10ms/div
SAF injection
transformers
Fig. 5. The experimental test setup photograph.
(c) Reactive power compensation.
Fig. 6. Experimental results: Unbalanced
compensation under ideal source voltages.
370
non-linear load
current
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.
Non-linear loads draw highly distorted currents from the
utility as well as causing distortion of the voltages. The 3phase 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 (vL) Before
phase-a
104.1
phase-b
103.4
phase-c
104.2
phase-a
9.2
THD
phase-b
9.1
(%)
phase-c
9.6
RMS
(V)
TABLE II
SUMMARY OF EXPERIMENTAL RESULTS FOR
THE LOAD CURRENT COMPENSATION
After
14.2
14.2
14.1
1.2
4.4
4.1
4.5
0.99
200V/div
vLb
vSa
200V/div
vLa
200V/div
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.
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.
vLc
30A/div 30A/div 200V/div200V/div
Source currents (iS) Before
phase-a
14.2
phase-b
17.6
RMS
(A)
phase-c
14.3
neutral
4.9
phase-a
33.8
THD
phase-b
29.8
(%)
phase-c
33.6
PF
0.89
After
110.5
110.1
109.2
4.3
4.6
4.4
vLa
10ms/div
iSa
200V/div
vLb
iLa
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
200V/div
vLa
200V/div
(a) Load voltages before compensation.
vLc
Load voltages (vL) Before
phase-a
52.1
RMS
phase-b
105.8
(V)
phase-c
106.8
10ms/div
(b) Load voltages after compensation.
Fig. 7. Experimental results: Distorted source voltage compensation.
371
After
108.3
108.8
109.6
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 nonperiodic 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
Freq. (Hz)
Currents
Voltages
Fundamental
50
15 A
110 V
Sub-harmonic
10
% 20
% 20
vSabc(V)
200
100
0
-100
-200
t (s) 0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
(a) 3-phase sub-harmonic source voltage waveforms.
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 nonperiodic 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 nonperiodic 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 nonactive 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.
vLabc(V)
200
TABLE VI
THREE-PHASE SOURCE VOLTAGE AND
LOAD CURRENT COMPONENTS
100
0
-100
-200
t (s) 0.15
0.2
0.25
0.3
0.35
0.4
0.45
Parameters
Freq. (Hz)
Currents
Voltages
0.5
(b) 3-phase load voltages after compensation.
Fig. 9. Simulation results: Sub-harmonic voltage compensation.
vSa(V)
0
-25
t (s) 0.15
0.2
0.25
0.3
0.35
0.4
0.45
vSb(V)
iLabc(A)
104
30
7.5
Components (%)
117
134
147
40
20
20
10
5
5
250
50
12.5
200
25
0.5
vSc(V)
(a) 3-phase sub-harmonic load current waveforms.
25
-25
t (s) 0.15
0
-200
0.1
200
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0
-200
0.1
200
0
-200
t (s) 0.1
0
(a) 3-phase stochastic non-periodic source voltage waveforms.
200
0.2
0.25
0.3
0.35
0.4
0.45
0.5
vLabc(V)
iSabc(A)
Fund.
50
15 A
110 V
(b) 3-phase source currents after compensation.
Fig. 10. Simulation results: Sub-harmonic current compensation.
0
-200
t (s) 0.1
The sub-harmonic component can be completely
compensated by choosing Tc=2.5T, and the source currents
372
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
(b) 3-phase load voltages after compensation.
Fig. 11. Simulation results: Stochastic non-periodic voltage compensation.
iLa(A)
ILb(A)
iLc(A)
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.
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
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
VI.
25
[1]
0
-25
t (s) 0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
[2]
(a) 3-phase stochastic non-periodic load current waveforms.
iSabc(A)
25
[3]
0
-25
t (s) 0.1
[4]
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
(b) 3-phase source currents after compensation.
[5]
iLnabc(A)
12
0
-12
t (s) 0.1
[6]
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
[7]
(c) Load neutral current waveforms.
iSnabc(A)
12
[8]
0
-12
t (s) 0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
[9]
0.3
(d) Source neutral current after compensation.
[10]
Fig. 12. Simulation results: Stochastic non-periodic current compensation.
V.
CONCLUSION
[11]
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 nonactive power theory, which is applicable to sinusoidal or nonsinusoidal, periodic or non-periodic, balanced or unbalanced
electrical systems, is presented. It has been applied to the 3phase 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 subharmonic and the stochastic non-periodic current and voltage
[12]
[13]
[14]
[15]
[16]
373
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