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Alleviating Harmonic and Reactive Power Issues in
Smart Grid Based on the Implementation of the
Instantaneous pq Power Theory under Unbalanced
and Distorted Supply Voltages
Muhammad Shahbaz, Nadeem Jelani, Marta Molinas
Abstract Distributed Energy Resources (DER) is emerging
as the future of the electrical grid commonly known as Smart
Grid or Micro grid. The electrical infrastructure of the power
grid is under changes, in a sense that more and more independent
power producers will supply power to the network of users that
could or could not be connected to the main grid. The Micro
grids are connected to the main power system grid through
power electronic interface for flexible control so that the Micro
grid will be crucial towards a wellfunctioning network.
However, at the same time, the interface domain will be under
high stress due to nonlinear behaviour of power electronic
components. Also, the use of nonlinear loads at the consumers
end in the form of power electronic converters, UPS, electric arc
furnaces, and growing use of adjustable speed motor drives is
increasing day by day. The power electronic based interface and
loads inject harmonic current and reactive power into the supply
grid having a significant impact on voltage and power quality,
thus polluting the electric distribution network. With a network
then dominated by nonlinear components (power electronics
coupling for generators, and nonlinear loads connected to
distribution system), nonsinusoidal regimes will be a common
situation. On the other hand, there is a high degree of demand for
premium electric power because of the high number of sensitive
loads, which can malfunction if the supply has bad power quality.
The paper suggests potential solution to the harmonic current
and reactive power problems under unbalanced and distorted
regimes using shunt active power filter (SAPF) with control
based on Instantaneous active and reactive (pq) power Theory.
Keywords: Active power filters, Distributed energy resources,
Harmonics, Instantaneous pq theory, Nonlinear loads, Power
Quality, Reactive Power, Smart Grid, Total harmonics
distortion.
I. INTRODUCTION
LECTRICAL energy is a product and, like any other
product, should satisfy the proper quality requirements
called power quality limits [1].These set of limits allow
the electrical systems to function in their intended manner
without significant loss of performance or life [2]. From the
Muhammad Shahbaz, Nadeem Jelani and Marta Molinas are with the
Department of Electric Power Engineering at Norwegian University of
Science and Technology, N7491 Trondheim, Norway (emails:
muhammsh@stud.ntnu.no, nadeem.jelani@ntnu.no, marta.molinas@ntnu.no).
Paper submitted to the International Conference on Power Systems
Transients (IPST2013) in Vancouver, Canada July 1820, 2013.
last few decades, the tendency of connecting the power
electronic (PE) equipment’s based loads to the power
distribution system is increasing because of significant
improvements in the voltage and current ratings of power
electronic devices [3], [4]. PE loads are high source of
harmonics and reactive power which results in an increased
deterioration of the power system voltage and current
waveforms, because of line impedance, the voltage at the point
of common coupling (PCC) is no longer remains sinusoidal
[3], [5]. The impacts of harmonics result in deterioration of
insulation, increase in power losses, shortening life span of
electrical installations, shutdowns, misoperation of sensitive
equipment, capacitor failures, communication interference,
overheating of transformers, overloading of neutral conductor,
harmonic resonance, maloperation of electronic equipment,
distorted supply voltage, system voltage dips, protection
tripping’s, and AC/DC drives failure [2], [6], [7]. The higher
value of reactive power causes voltage stability problems, low
power factor, higher copper losses in the line conductor, and
bulky equipment’s [2].
Because of these problems, the issue of the power quality
delivered to the consumers end is of more interest than ever
before [8]. Several International standards have been set with
regards to power quality like IEEE519, IEC61000, EN
50160 and others [2], [8]. These standards demand that the
total harmonic distortion (THD) produce by electrical
equipment’s should not be higher than the defined limits of the
standards.
THD is a power quality term that is used to define the
amount of distortion in voltage or current waveform [2], [9].
THD in current waveform is given as:
2
2
21
% 100
n
n
I
THD I
=
∞
= ×
∑
(1)
where I1 is the fundamental component of current and In is
the component of current with nth order harmonics.
II. ACTIVE FILTERING
In the past, tuned passive filters were used to solve the
problems of reactive power and harmonics distortion [10].
However, these filters offered some drawbacks like they filter
only the frequencies they are tuned for, their operation cannot
E
Active
Filter
Controller
PWM
Control
L
F
C
I
L
I
L
Vs
Nonlinear Load
R
L
I
S
=+
I
C*
Ls
I
L
I
C
I
S
Compensator
I
C
L
L
Fig. 1. Basic configuration of shunt active filter.
be limited to a certain load, resonances can occur because of
the interaction between the passive filters and other loads with
severe effects [10]. To compensate these drawbacks, recent
efforts have been made on the development of an important
group of power system conditioning circuits, commonly
known as active power line conditioners (APLC) or simply
active power filters [11]. The active power filters have gained
much more attention because of excellent performance to
mitigate the harmonic and reactive power problems. However,
the performance of the active filters depends upon the control
theory that is employed to formulate the control algorithm of
the active filter controller [12].
Many control techniques have been suggested to control the
active power filters and generally have two categories. The
first category is based on time domain such as the pq theory,
the dq theory, the synchronous reference current theory,
direct power control, and conservative power theory [13]. The
second category is based on frequency domain like Fourier
Transformation, and Kalman Filter [13]. The time domain
analysis is superior over the frequency domain and of great
interest in recent years [13]. However, in this paper pq
Instantaneous power theory is used because of its excellent
performance and simplicity to develop the control algorithm
of the shunt active filter.
The voltage source inverter (VSI) based shunt active power
filter (SAPF) has used to mitigate the harmonics and reactive
power problems because of its low cost and higher efficiency
compared to current source inverter (CSI) based SAPF [14].
However, both active filters have the same functionality: to
force the converter to behave as a controlled current source
[14].
The Fig. 1 shows the basic configuration of the shunt active
filter. The supply can be sinusoidal or nonsinusoidal, and the
loads can be diode, thyristor or any other power electronic
loads. The shunt active filter draws or injects current IC in such
a way that the sum of load currents IL and converter IC is
source current IS that should be sinusoidal i.e.
S LC
III= +
(2)
In this paper, a 3level PWM natural point clamped voltage
source inverter (NPCVSI) shown in Fig. 2, has been used
because it offers low voltage stress to power semiconductors
devices, lower current or voltage harmonics, and less
electromagnetic interference [4].
Rf Ia_conv
Ib_conv
Ic_conv
Lf
Vdc2 Vdc1
S1a
S2a
S3a
S4a
S1bS1c
S2b S2c
S3b S3c
S4bS4c
Fig. 2. NPCVSI power converter for shunt active filter.
The purpose of the paper is to compensate the harmon
ics and reactive power in the source current under unbalanced
and distorted conditions of supply voltages. The THD in the
source current after the working of the Instantaneous pq
Theory based SAPF should be according to the defined
standards and it should be in phase with the distribution utility
voltage.
III. ACTIVE FILTER REFERENCE CURRENT GENERATION BY
INSTANTANEOUS PQ THEORY
The Instantaneous pq Theory is based on a set of
instantaneous powers defined in time domain that bring about
a good dynamic response with no restrictions are imposed on
voltage and current waveforms [14]. It can be applied to a 3
phase system with or without neutral wire and equally valid
for steady state and transients conditions. This theory is very
efficient and flexible in designing the controllers for APCL
based on PE devices [14]. The theory first transforms voltage
and current waveforms from abc to αβ0 coordinates by
Clarke’s transforms, then defines instantaneous powers in αβ0,
and finally computes the compensating reference currents in
abc by Inverse Clarke’s transforms. The theory always
considers the 3phase system as a unit, not a superposition or
sum of three singlephase circuits [14].
For a 3phase sinusoidal system the supply voltages and
loads currents are measured and transformed from abc to αβ0
frame using Clarke’s transform by (3) and (4):
11 1
22 2
02 11
1
3 22
33
022
a
b
c
vv
vv
vv
α
β
−−
−
=
(3)
0
11 1
22 2
2 11
1
3 22
33
022
La
Lb
Lc
ii
ii
ii
α
β
−−
−
=
(4)
where va, vb, vc are the supply voltages and iLa, iLb, iLc are the
load currents.
The instantaneous powers p and q can be written as:
vvi
pi
qvv
αβα
β
α
β
=−
(5)
From (5) we have:
22
1
vv
vv
ip
iq
vv
αβ
αβ
α
βα
β
+
−
=
(6)
where p=p
̅+p
͂ and q=q
̅+q
͂. These powers are defined as:
p=Active power for a 3phase system with or without neutral
conductor in steady state or transients. It represents the total
instantaneous energy flow per second between power source
and load.
q=Imaginary power and proportional to the quantity of energy
that is being exchanged between phases of the system. It
doesn’t contribute to energy transfer between source and load
at any time.
p
̅=Average value of the instantaneous real power and is
transfer from source and load. It is the only desired power
component to be supplied by the power source and is due to
fundamental active current.
p
͂=Oscillating component of the instantaneous real power
exchanges between source and load and doesn’t involve any
energy transfer from source to load. It is because of harmonics
and must be compunsated.
q
̅=Average value of the instantaneous imaginary power
exchenges between the system phases and doesn’t imply
energy transfer between source and load. The choice of
compensation of q
̅ depends on reactive power compenation. It
is because of fumdamental reactive current.
q
͂=Oscillating component of instantaneous imaginary power
exchanges between system phases and doesn’t transfer energy
from source to load. It is also due to harmonics and must be
compensated.
The zero sequence power p0 doesn’t exist because the
considered system is 3phase 3wire.
A. Compensation Strategy and Selection of Reference
Power for Compensation
The compensation strategy depends upon the desire
purpose to achieve. Several kinds of compensation strategies
11
1
222
333
022
a
b
c
i
ii
ii
α
β
−−
=
−
Clark Transformation
Instantaneous
power
calculation
Low pass
filter fc=50Hz
αβcurrent calculation
10
**
21 3
**
32 2
*13
22
a
b
c
ii
ii
i
α
β
= −
−−
*a
i
*b
i
*c
i
Inverse Clark
transformation
11
1
222
333
022
a
b
c
v
vv
vv
α
β
−−
=
−
1
Load
Currents
Source
Voltages
abc_
ref
compansating
currents
PI
regulator

+
‾ +

+
‾
++
DC Link voltage regulator
p vi vi
ββ
αα
= +
q vi vi
β βαα
=−
1
*22
*
Loss
c
vv c
vv
ipp
ivv q
α
β
αβ
βα
αβ
−−+
=
−
+
Fundamental
positive sequence
voltage detector
Clark Transformation
a
i
b
i
c
i
c
v
b
v
a
v
i
α
i
β
v
β
v
α
1a
v+
1b
v
+
1c
v
+
ref
v
dc
v
p
q
q−
*i
β
*
i
α
v
α
v
β
Loss
p
Fig. 3. Algorithm for the calculation of reference current of the compensator
for compensation of harmonics and reactive power.
11
1
222
333
022
a
b
c
v
vv
vv
α
β
−−
=
−
Clark Transformation
Instantaneous
power
calculation
PLL
Circuit
Lowpass
Filter f
c=
50Hz
''
1
''
22
''
''
''
ii
ii
vp
vq
ii
αβ
α
ββα
αβ
−
=
+
α βvoltage calculation
10
''
21 3
''
32 2
'13
22
a
b
c
vv
vv
v
α
β
= −
−−
'v
α
'v
β
'
a
v
'
b
v
'c
v
Inverse Clark
Transformation
v
α
v
β
'i
α
'i
β
'q
'p
'p
'q
a
v
b
v
c
v
'' '
p vi vi
αα ββ
= +
'' '
p vi vi
αβ βα
= −
Lowpass
Filter f
c=
50Hz
'i
α
'i
β
Fig. 4. Block diagram of Fundamental positive voltage detector.
are available when working with the Instantaneous pq
Theory. However, in this paper harmonics compensation (i.e
compensation of p
͂ & q
͂) and reactive power compensation (i.e
compensation of q
̅) have done.
Therefore the compensator has to select the following
powers as a reference to follow the control strategy. The
instantaneous reactive power supplied by the compensator:
c
qq= −
(7)
Instantaneous active power supplied by the compensator:
Loss
c
p pp
=−+
(8)
where p
̅Loss is the power drawn by the compensator from
the power source to make up the switching losses of the
converter and to maintain constant voltage across the dclink
capacitor at a prespecified value.
B. Reference Current Calculation for the Compensator
The compensator reference current in αβ will be:
22
*
*
1
cc
c
c
vv
ivv
p
q
vv
i
αβ
αβ
α
α
β
β
+
−
=
(9)
and in abc by Inverse Clarke’s transformation:
*10 *
21 3
**
32 2
*13
22
ca c
cb c
cc
ii
ii
i
α
β
−−
=
(10)
IV. FUNDAMENTAL POSITIVE SEQUENCE VOLTAGE DETECTOR
The designed SAF based on adopted control strategy
should perfectly determine the reference current by the
integration of the Instantaneous pq Theory to mitigate the
current harmonics and to make the source current inphase
with the utility voltage at the same time. This control works
very well in the presence of ideal supply voltages. However,
in case if the supply is unbalanced or highly distorted then the
reference current calculated by control algorithm shown in
Fig. 3 without the fundamental positive sequence voltage
detector, neither completely filter the current harmonics nor
compensate the fundamental reactive power [15]. Under
unbalanced or distorted supply voltage conditions the
Instantaneous pq Theory must have fundamental positive
sequence voltage detector for the successful operation of the
active filter.
Fig. 4 drives the fundamental positive sequence signal from
an unbalanced and distorted three phase voltage signal carried
by power lines. The phase locked loop (PLL) control circuit in
Fig. 5, described in next section, determines accurately the
fundamental frequency and phase angle of the unbalanced and
distorted measured system voltage [16]. This fundamental
frequency is used in the sine wave generator to produce the
auxiliary currents i'α and i'β which are used together with vα
and vβ in the Fig. 4 to calculate the auxiliary powers p' and q'.
However, the average values of the real (p') and imaginary
(q') powers are considered here. The average powers p
̅' and q
̅'
are composed of fundamental positive sequence component
V+1 as the auxiliary currents i'α and i'β also composed of
fundamental positive sequence component (I+1). The impact of
fundamental negative sequence component and other high
frequency harmonics appear in the oscillating components (p
͂'
and q
͂').
The instantaneous voltages v'α and v'β which correspond to
time function of fundamental positive sequence voltage
component V+1 are given by (11):
22
''
''
'1'
''
''
ii
ii
vp
vq
ii
αβ
αβ
α
βα
β
+
−
=
(11)
By applying the Inverse Clarke’s transform, the fundamen
tal positive sequence voltages (v'a, v'b, v'c) without error in
amplitude and phase angle are given in (12):
10
21 3
32 2
13
22
''
''
'
a
b
c
vv
vv
v
α
β
−−
=
(12)
A. The Design of Phase Locked Loop Circuit
The PLL circuit shown in Fig. 5, tracks continuously the
fundamental frequency of the system voltage. It works very
well under unbalanced highly distorted conditions of the
system voltage to quickly determine the system frequency and
phase angle of the measured system voltages (va, vb, vc). The
circuit uses the algorithm based on a fictitious instantaneous
power given by (13):
3
' ''' ' '
aabbcc abacbc
p vivivi vivi
ϕ
= ++ = +
(13)
sin( )
2
t
π
ω
−
1
s
∑
PIController
vab
vcb
'( )
it
a
ω
'( )
it
c
ω
'3
p
φ
ω
t
ω
t
ω
'i
α
'i
β
sin( )t
ω
cos( )
2
t
π
ω
−−
2
sin( )
3
t
π
ω
+
Fig. 5. Functional block diagram of PLL circuit.
The expression in (13) considered that i'a+ i'b+ i'c=0. The
p'3φ is called fictitious power because it is just a variable and is
not related to any instantaneous power in the power system.
The fictitious current feedback signals i'a(ωt)=sin(ωt) and
i'c(ωt)=sin(ωt+2π/3) of the PLL circuit are built by calculating
the time integral of the output ω of the PI controller. The
current i'a(ωt) lags at 120° by i'c(ωt) and both of them have
unity amplitude. The PLL circuit can reach a stable point of
operation only if the input p'3φ of the PI controller has zero
average value (p
̅'3φ=0) and has minimum low frequency
oscillating portion in p
͂'3φ, where p'3φ= p
͂'3φ+ p
̅'3φ.
The average three phase power (p'3φ=p
̅'3φ) in term of
phasors is given as:
3 3 11
' ' 3 ' cosVI
pp
ϕϕ ϕ
++
= =
(14)
The expression in (14) is valid only if the output of the PI
controller ω corresponds to the system frequency and the
feedback signal i'a(ωt) becomes orthogonal to the fundamental
positive sequence component of the measured voltage Va.
However, if the point where Va leads the signal i'a(ωt) is
reached, this is still an unstable point of operation . At this
point, an eventual disturbance that slightly increase the system
frequency (the frequency of the Vab and Vcb in Fig. 5) will
make the voltage phasor V
̇+1 rotate faster than the current
phasor built up by the feedback signals i'a(ωt) and i'c(ωt).
Hence, the displacement angle between Va and i'a(ωt), given
by cosφ in (14), becomes greater than 90°. This results to
negative average input (p
̅'3φ<0), and consequently to a
decreasing ω, making the cosφ even greater. This characterizes
an unstable point of operation. Thus, the PLL has only one
point of operation, that is i'a(ωt) leading by 90° the
fundamental positive sequence component corresponding to
Va.
Now for the same disturbance mentioned above, i'a(ωt)
leading Va by 90°, the cosφ will become less than 90° and the
average power in (14) will be positive. This will make the
current phasor to rotate faster, keeping the orthogonality
(leading currents) between the generated İ+1 [i'a(ωt)] and the
measured V
̇+1.
+


_abc
AF
I
__abc
AF
ref
I
triangular
v
−
P
IS
K
K+
PWM
Fig. 6. Block diagram of Triangular carrier PWM current control circuit.
This fundamental characteristic of the PLL circuit shown in
Fig. 5 is exploited to form auxiliary signals i'α and i'β that are
needed in the fundamental positive sequence detector of Fig.
4. Since, i'a(ωt)=sin(ωt) leads by 90° the fundamental positive
sequence component V
̇+1 of the measured system voltage.
Hence, the auxiliary current i'α(ωt)=sin(ωtπ/2) will be in
phase with V
̇+1.
V. CURRENT MODULATOR
The performance of the active filter heavily depends on the
design characteristics of the current modulator i.e method to
generate the gating signals for the VSI [4]. Mostly pulse width
modulation (PWM) strategies are employed in the active filter
controller to modulate the current modulator. In this paper,
Triangular Carrier control PWM technique is used. Fig. 6
demonstrates this method. At the input, the active filter
reference current generated by Instantaneous pq Theory and
the filter actual current are compared to produce the error. To
make the error steady, it is passed through PI controller. At the
end, steady current is compared with the triangular wave with
fixed carrier frequency to get the gate pulses for the VSI.
VI. SIMULATION RESULTS
A complete model of the shunt active filter connected to
distribution power system is simulated in Matlab/Simulink and
only the important results are presented. The parameters of the
simulated system are shown in Table I. The unbalanced and
highly distorted distribution source is supplying power to the
unbalanced diode and thyristor bridge based loads shown in
Table I. The expression for the source is shown in (15):
sin( ) sin( ) sin(3 )
sin( 120 ) 0.0909 sin( 120 ) 0.0681 sin3( 120 )
sin( 120 ) sin( 120 ) sin3( 120 )
sin(5 )
0.0455
a
bsss
c
s
tt t
tt t
tt t
t
v
vv v v
v
v
ωω ω
ωω ω
ωω ω
ω
°° °
= −+ ++ −
°° °
+− +
+
sin(7 )
sin5( 120 ) 0.0318 sin 7( 120 )
sin5( 120 ) sin7( 120 )
s
t
tt
tt
v
ω
ωω
ωω
°°
−+ −
°°
++
(15)
TABLE I
PARAMETERS OF THE SIMULATED SYSTEM
Source
parameters
v
s
=220V
RMS
(LineGround),
Rs=10µΩ, Ls=0.01mH
Filter
parameters
V
dc1
=V
dc2
=350V,C
dc1
=C
dc2
=1.8mF,
Rf=10µΩ, Lf=2mH, fs=15kz
Load
parameters
RL=10µΩ, LL=2mH
I. 3phase thyristor bridge supplying RL
load of 20Ω + 20 mH, Firing angle=15˚
II. 2phase diode bridge step change in load
connected to phaseab with Initial value
10A and final value 20 A
III. 3phase thyristor bridge supplying RL
load of 10Ω + 30 mH, Firing angle=10˚
The total simulation run time is 0.3 sec (Dell Latitude E6400
machine). Fig. 7a shows that the source voltage profile is
unbalanced and distorted. The fundamental positive sequence
Fig. 7. Source voltages, Load currents and fundamental positive sequence
voltage (a) Source voltage (b) Load current (c) Fundamental positive sequence
voltage.
voltage is extracted from the source (shown in Fig. 7c) for the
efficient working of the control. The dynamic behavior of the
active filter is checked by connecting different loads to the
system during the run time of the simulation. The loads I is
connected from the start (t=0s) of the simulation and is
triggered at firing angle of 15˚. The load II is connected
between phase ab at t= 0.1s with step change in current from
10A to 20A. The connection of load II make the load side
unbalanced. Similarly, the load III is connected at t= 0.2s and
is triggered at firing angle of 10˚. Fig. 7b shows the
connection of these loads to the system. Fig. 8b shows (i.e at
t= 0.1 s and t= 0.2 s when load II & III are connected) that the
active filter is dynamically fast and responded to the change in
load within 1 power cycle.
Fig. 7b shows that load is highly unbalanced and highly
distorted with a value of THD=20.17% shown in Fig. 9a. The
SAF closely follows the reference current generated by
Instantaneous pq Theory (shown in Fig. 8b) to supply
negative sequence current to make the source current balanced
and sinusoidal shown by Fig. 8b. The level of THD reduced
from 20.17% to 2.27% shown by Fig. 9a and 9b. However, the
THD in source current after the active filtering is not exactly
zero. It is because internal switching of the compensator itself
generates some harmonics.
Fig. 8c shows that after the operation of the active filter the
power factor of the distribution system becomes unity (source
voltage and current are in phase) and source supplies only
constant active power to the load.
Fig. 8. Active filter actual and reference current, source current after the
working of active filter, and source voltage and current for phasea (a) Active
filter actual and reference current of phasea (b) source current after the
working of active filter (c) source voltage and current for phasea.
0.1 0.15 0.2 0.25 0.3
400
200
0
200
400
Source Voltage [V]
(a)
0.1 0.15 0.2 0.25 0.3
100
50
0
50
100
Load Currents [A]
(b)
0.1 0.15 0.2 0.25 0.3
400
200
0
200
400
Time [s]
Fundamental Source
Voltage [V]
(c)
V
sa
V
sb
V
sc
I
La
I
Lb
I
Lc
V
sa+1
V
sb+1
V
sc+1
0.1 0.15 0.2 0.25 0.3
100
50
0
50
100
Active Filter Actual and
Reference Current [A]
(a)
0.1 0.15 0.2 0.25 0.3
100
50
0
50
100
Source Current after
Active Filtering [A]
(b)
0.1 0.15 0.2 0.25 0.3
400
200
0
200
400
Time [s]
Source Voltage [V],
Source Current [A]
(c)
V
sa
I
sa
I
sa
I
sb
I
sa
I
AFref
I
AFactual
0100 200 300 400 500 600 700 800 900 1000
0
5
10
Frequency (Hz)
Fundamental (50Hz) = 52.27 , THD= 20.17%
Mag (% of Fundamental)
0100 200 300 400 500 600 700 800 900 1000
0
5
10
15
Frequency (Hz)
Fundamental (50Hz) = 40.55 , THD= 2.27%
Mag (% of Fundamental)
(a)
(b)
Fig. 9. THD in source before the active filtering (THD in load current) and
after the active filtering (a) THD in source before the active filtering (THD in
load current) (b) THD in source after active the filtering.
The comparison of Fig. 9a and 9b shows that after the
operation of active filter the amplitude of the fundamental
source current reduced from 52.27 A to 40.55 A. It is because
active filter has compensated the p
͂, q
͂ and q
̅ demanded by the
load. Now, the source is supplying only active only portion of
current of 40.55 A to load.
VII. CONCLUSIONS
The solution to the harmonic and reactive power problems
for an unbalanced and distorted distribution supply system
feeding to an unbalanced nonlinear load system is provided by
shunt active power filter. The control of the shunt active
power filter is developed by Instantaneous pq Theory. The
Instantaneous pq Theory with the help of fundamental
positive sequence voltage detector computes the compensating
reference current that comprises all components that differ
from the active portion of the fundamental positive sequence
current of the load. The link between the control and
compensator is established through gating signals issued for
the semiconductor switches. The gating signals are obtained
by Carrier Control pulse width modulation technique that
works nicely to trigger the compensator based on Insulated
gate bipolar junction transistors switches. The simulations
results show that shunt active power filter has managed to
control the harmonics defined by the limits, and made the
source current balanced, sinusoidal, and inphase with the
supply voltage to ensure the supply of constant active power
from source to load.
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