INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
Published online 19 July 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.1656
Real-time application of shunt active power filter dynamic
compensation using real-time windows target
H. A. Ramos-Carranza1*,†, A. Medina1 and G. W. Chang2
1
Universidad Michoacana de San Nicolás de Hidalgo, 58030 Morelia, México
2
Nacional Chung Cheng University, 621 Chia Yi, Taiwan R.O.C.
SUMMARY
In this contribution, a control strategy in phase coordinates abc is proposed as the reference current generator to
be used by the shunt active power filter (APF) compensation device. The development of the proposed
reference current generator is described in detail. Its control design is kept simple, and transformation between
different frameworks is not needed, thus allowing the control strategy to be applicable for both three-phase and
single-phase electric systems maintaining theoretical and practical advantages. The proposed control strategy
for the reference current generator is tested using Matlab/SimulinkW with the incorporation of the Real-Time
WorkshopW for the simulation of the shunt APF compensation in real time. Based on the reported real-time
application, it is possible to obtain simulation conditions that are close to the true real-time environment under
study using only a single computer, giving accurate results with relatively low-cost hardware and providing a
more complete evaluation of the applied control strategy. The dynamic behavior and performance of the shunt
APF, using the proposed reference current calculator, have shown remarkable results. Copyright © 2012 John
Wiley & Sons, Ltd.
key words:
active power filter; reference current generator; real-time application; real-time windows target
1. INTRODUCTION
The continuous increase in the incorporation of power-electronic converters and controllers for industrial
processes and drives, and other types of nonlinear loads connected to the power system, has come together
with different associated power quality problems, such as it is the harmonic distortion of current and
voltage waveforms [1]. In particular, the shunt active power filter (APF) has demonstrated to be an
appropriated tool for the mitigation of harmonic currents and reactive power compensation [2–8].
The shunt APF has four main stages clearly identified that allow the compensation process:
(1) The reference current generator. The reference filtering currents are obtained/computed
accordingly to a chosen control strategy to achieve that purpose.
(2) The current controller. Once the reference filtering currents are calculated, these are used by a
current controller technique, usually a pulse-width modulation (PWM) controller technique,
which generates the switching control signals for operating a power-electronic converter.
(3) The power-electronic converter. Usually, a voltage-source inverter (VSI) is used to reproduce the actual
currents, as close as possible to those calculated as the reference, to be injected into the electric system.
(4) PI controller. The dc voltage of the power-electronic converter must maintain a constant dc voltage
in order to allow the correct performance of the shunt APF during compensation. Due to harmonics
and switching, the dc voltage in the dc side of the electronic converter slightly fluctuates, and a
PI controller is used to control and compensate this variation by adding a control signal.
*Correspondence to: H. A. Ramos-Carranza, Universidad Michoacana de San Nicolás de Hidalgo, 58030 Morelia,
México.
†
E-mail: aramos@faraday.fie.umich.mx
Copyright © 2012 John Wiley & Sons, Ltd.
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H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
In addition to these four stages, an inductive element is placed between the power system and the
converter, e.g. a coupling transformer. The inductive element is used as an energy link and the actual
filtering currents flow through this element to the power system performing the corrective measure and
achieving in this way the compensation of reactive power and the mitigation of harmonic distortion.
In particular, the current reference generator, described above as the first stage in the compensation
process, is of vital importance in the final performance that the shunt APF is able to provide.
Performance comparisons of different control strategies used to implement the reference current
generator can be found in [3–6].
Under the shunt APF compensation scheme, the implemented control strategy to compute the reference
filtering currents should guarantee the generation of the correct reference for the shunt APF, at all times
during the compensation process, in order to obtain the desired results. Even more, the correct reference
should be generated in spite different compensation scenarios (e.g. dynamic compensation due to load
variations) and operation system conditions (e.g. harmonic distortion/unbalance in the source voltages)
that could be present in the electric system during shunt APF compensation.
In addition, the control strategy used as the reference current generator should have other important
characteristics. First, the APF should not consume/supply active power [5]; its compensation mechanism
does not require active power. Second, feasibility of physical implementation implies the reasonably
affordable computational demand required by its internal algorithm for computing the reference currents.
All these ideas mentioned above, and previous reported work associated to the particular matter [7,9],
have motivated the authors to develop a control strategy to calculate the reference filtering currents of a
shunt APF. The proposed control strategy presented in this manuscript is developed to be able to handle
steady-state and/or dynamic compensation in either 3F-4W or 3F-3W systems. Furthermore, the reduction
of the developed control strategy from the three-phase system to a single-phase system can be implemented in a direct fashion, keeping theoretical and implementation design principles in the process as there is
no need of transformation between reference frameworks involved.
In the same workflow, one of the main targets during the control strategy design process was to find a
control strategy that can be identified as efficient, simple, and be remarked as suitable for further/possible
physical implementation of the compensation device, increasing the feasibility of its implementation. To
validate the performance of the developed control strategy for computing the reference filtering currents,
and its reasonable affordable computational demand required for the implementation of its internal
algorithm, the authors have opted for testing it with a real-time application.
With the growing importance of power quality problems to electric utilities and customers, there is
an increasing interest on the search of new techniques for accurate analysis and resolution of such
problems [10,11]. The real-time simulation techniques are used for several studies of power systems
containing nonlinear loads. Available literature details several techniques developed and implemented
to perform real-time simulations in power system analysis [10,11]. These real-time implementations
allow the evaluation of several conditions to be tryout before the hardware is built.
In this manuscript, the real-time simulation of the shunt APF compensation is developed with the
incorporation of the Real-Time Windows Target (RTWT) toolbox of Matlab/Simulink [12], which is
used as a PC solution for prototyping and testing the real-time system. Under this real-time simulation
environment, a single computer is used as a host and target [12,13]. This real-time application makes
possible the observation and evaluation of simulation conditions close to the true real-time environment
under study using a single computer, it gives accurate results with relatively low-cost hardware, and also
it provides a more complete evaluation of the applied control strategy during the calculation of the
reference filtering currents.
The complete details of the developed control strategy, the real-time implementation of the case
study, and the dynamic operation and analysis performance of the shunt APF using the proposed
control strategy are given in the sections to follow. In Section two, the derivation of formulae for
computing the reference filtering currents by the proposed control strategy is given in detail. Section
three provides the basis of the implementation procedure for the real-time simulation. The control
strategy performance presented in this manuscript is illustrated for dynamic compensation in a
three-phase four-wire system with harmonic content highly heterogeneous in phases a, b, c, as this
will be shown with a case study in Section four. The main conclusions obtained as a result of this
investigation work are given in Section five.
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
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2. CONTROL STRATEGY FOR THE DERIVATION OF THE REFERENCE FILTERING
CURRENTS
The reactive power compensation and harmonic distortion mitigation using the shunt APF compensation
device should be efficient. Once the shunt APF is in operation, the source currents should be balanced,
without harmonic distortion, and it should compensate reactive power. The proposed control strategy
for the calculation of the reference filtering currents works as a sinusoidal source current method,
calculating the desired source currents (i.e. the source currents we want to have once the shunt APF is
in operation) and subtracting them from the actual load currents in order to obtain the reference filtering
currents, e.g.
ifk ðt Þ ¼ ilk ðt Þ isk ðt Þ
k ¼ a; b; c
(1)
Where ifk ðt Þ are the instantaneous reference filtering currents, ilk(t) are the instantaneous load currents, and
isk ðt Þ are the instantaneous desired source currents. Figure 1 shows a schematic diagram of a three-phase
four-wire electric system with a shunt APF connected to the electric network. Once the source currents
and source voltages are measured, the reference filtering currents are calculated, and the APF injects
the actual filtering current of compensation.
The control strategy for computing the reference filtering currents is based in two main assumptions:
First, the amplitude of the source currents should be the same, i.e.
Im ¼ Ima ¼ Imb ¼ Imc
(2)
Second, the source currents should be in phase with the source voltages at each phase respectively, i.e.
θisk ¼ θuk
ðk ¼ a; b; cÞ
(3)
In addition, after accomplishing the above assumptions, the total average power delivered to the
load should be supplied only from the source with equally contribution by the three phases a, b, c.
Then, the total average power PT, supplied from the source to the load, can be expressed according
to Equations (4)–(5).
1
PT ¼
T
ZT
ua ðt Þisa ðt Þ þ ub ðt Þisb ðt Þ þ uc ðt Þisc ðt Þ dt
(4)
0
PT ¼
Uma Ima
Umb Imb
Umc Imc
þ
þ
2
2
2
(5)
Figure 1. Schematic diagram of the shunt APF connected to the electric network.
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
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H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
Where Umk and Imk
are the amplitudes of the instantaneous source voltages and the desired source
currents for k = a, b, c. Following the assumption in Equation (2), the total power delivered to the load
in Equation (5) now can be expressed as,
ðUma þ Umb þ Umc Þ Im
(6)
PT ¼
2
From Equation (6), it can be seen that the amplitude of the desired source currents at each phase is
given by,
Im ¼
2PT
UmT
(7)
Where UmT = Uma + Umb + Umc. Finally, a unitary signal of reference, derived from the measured
source voltage, is included to the source currents amplitude so that the desired source currents are
calculated as
2PT uk ðt Þ
k ¼ a; b; c
(8)
isk ðt Þ ¼
UmT Umk
The term within the parenthesis on the right-hand side of Equation (8) is the instantaneous unitary
signal which gives the phase to the desired source current, respectively, for each phase, so that the
assumption in Equation (3) holds.
So far, the instantaneous source voltages uk(t), used in Equation (8) to incorporate the instantaneous
unitary signal, are assumed to be free of harmonic distortion and phase balanced, i.e. purely sinusoidal
and balanced three-phase source voltages. If Equation (8) is applied as a part of the procedure for
calculating the reference filtering currents, and the source voltages uk(t) have presence of harmonic
distortion and/or phase unbalance, the resulting performance on the calculation of the desired source
currents isk ðt Þ would be really poor and erroneous [2,3]. And, as stated in Equation (1), the calculation
of the reference filtering currents will be erroneous as well. It is easy to notice that the waveform of the
desired source current, isk ðt Þ in Equation (8), will have the same shape in its instantaneous waveform as
the instantaneous unitary signal waveform, which in turn will have the shape of the waveform of the
source voltages uk(t), respectively, at each phase k.
The erroneous calculation of the reference filtering currents due to presence of nonsinusoidal source
voltages has been documented and reported in the literature [2,3], where for instance, the formulation
in Equations (8) and (1) to obtain the reference filtering currents can be regarded as the synchronous
current detection method [8], as evaluated and analyzed in [5]. Similar difficulties can be observed
in other methodologies no matter the use or not of a transformation between different frameworks [4].
For practical reasons, the control strategy should be developed assuming that the source voltages
may be harmonic distorted and/or unbalanced. Moreover, despite the harmonic content or unbalance
that might be present in the source voltages, an adequate performance in the calculation of the desired
source currents isk ðt Þ and reference filtering currents ifk ðt Þ must be achieved by the control strategy.
To tackle the aforementioned problem, in this contribution, it is proposed the use of reference signals
uk ðt Þ, instead of the actual source voltages signals uk(t), in Equation (8). These reference signals uk ðt Þ
should be obtained by post-processing the data of the actual measured source voltages. The procedure
has the following two main targets:
First, to avoid harmonic distortion that could be present in the measured source voltagesuk(t), i.e. to
obtain the reference signal voltages uk ðt Þ at each phase that will always be purely sinusoidal.
Second, to avoid phase unbalance that could be present in the measured source voltages uk(t), i.e. the
reference signal voltages uk ðt Þ will always be phase balanced.
In summary, the two-aim procedure guarantees the reference signal voltages uk ðt Þ as three-phase
pure sinusoidal and balanced signals. So that once the new instantaneous unitary signals uk ðt Þ=Uk
are formed using the reference signals uk ðt Þ, the unitary signals of reference will have the desired
characteristics that will allow the correct calculation of both the desired source currents and the
reference filtering currents.
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
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2.1. Obtaining the reference source voltages
At this stage, the goal is to extract the fundamental component information from the measured source
voltages and then process the information to form the reference source voltages to be used in Equation
(8). Diverse applications and studies require the determination of the phase and amplitude of the
voltage at fundamental frequency. These variables are needed for the determination of the reference
signal for the active filtering, the detection of peak voltages for VAR compensation and for the
extraction of power at fundamental frequency for the transient stability evaluation [14–19]. To obtain
the fundamental frequency of the source voltages, the measured data could be treated according with
the techniques described next.
2.1.1. Least-squares fitting. This curve fitting method uses least-squares error estimation to find the
amplitude and the angle of the fundamental component. Curve fitting selects the best fit of a curve
to a waveform and measures the discrete residual values between the waveform and the fitted curve.
The size of these residuals is measured by the addition of their squared values. This is then minimized
to obtain the least-square error, and the amplitude and phase of the best fitted curve are calculated.
In particular, this method has been reported as an appropriated alternative for a real-time monitoring
and analysis of harmonic variations incorporating the use of neural nets for the improvement of
computational demand and efficiency [17–19].
2.1.2. The Fourier transform. 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 of 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 time. However, this is very different if the voltage
waveforms are non-stationary, where the use of a Fourier transform alone becomes inadequate. A suitable
way to extract such information is to apply an innerly related time-frequency signal decomposition.
Therefore, for the development of the proposed reference current generator, a discrete short-time Fourier
transform [14], often referred to as the sliding-window DFT, is used for the time-frequency decomposition
of non-stationary signals, i.e. for the extraction of the fundamental component of the source voltages. It is
important to notice that any other technique for the extraction of the fundamental source voltage component,
which represents a viable option, could be incorporated for this purpose into the control strategy.
Once the fundamental component information has been extracted from the source voltages, a
phase-locked technique (PLT) is proposed to ensure symmetry in the desired source currents. At
difference of a phase-locked loop, which is generally built with a phase detector, a low-pass filter
and a voltage controller oscillator placed in a negative feedback closed-loop configuration, for the
PLT described next, it is only required to identify the phase angle of one of the phases of the source
voltage. Such information, i.e. the fundamental frequency source voltages information, has been
already obtained with any of the techniques described above, so that the application of the PLT does
not require extra processing of data.
2.1.3. Phase-locked technique. If asymmetry is present in the obtained source voltages at fundamental
frequency, and the shunt APF is placed to compensate harmonic currents and reactive power in a
three-phase four-wire electric system, it will result in the presence of a relatively high neutral current.
To avoid this problem, it is proposed to apply a 120 positive sequence phase shift over the reference
voltage signals once the fundamental frequency source voltage information is obtained. This is
achieved by detecting the phase angle of the phase selected as the reference, e.g. phase a, and adding
or subtracting 120 to the other two phases.
At the end of the two-aim procedure described above, the reference voltage signals to be used for the
calculation of the desired source currents are now of the form given in Equations (9)–(11).
ua ðt Þ ¼ Uma1 sinðot þ fa1 Þ
Copyright © 2012 John Wiley & Sons, Ltd.
(9)
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
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H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
ub ðt Þ ¼ Umb1 sinðot þ fa1 2p=3Þ
(10)
uc ðt Þ ¼ Umc1 sinðot þ fa1 þ 2p=3Þ
(11)
where uk ðt Þ are the reference voltage signals, Umk1 are the amplitudes of the source voltages at fundamental frequency, and ’a1 is the angle of the fundamental component of the source voltage at phase a.
The substitution of Equations (9)–(11) into Equation (8) gives the proposed formulation to find the
desired source currents, e.g.
isa
APF abc ðt Þ
¼
2PT Uma1 sinðot þ fa1 Þ
UT Uma1
(12)
isb
APF abc ðt Þ
¼
2PT Umb1 sinðot þ fa1 2p=3Þ
UT Uma1
(13)
isc
APF abc ðt Þ
¼
2PT Umc1 sinðot þ fa1 þ 2p=3Þ
UT Umc1
(14)
Since the power losses caused by switching and capacitor voltage variations must be supplied by the
source, a power signal Ploss is added to the power delivered to the load. Thus, taking the above into
consideration and according to Equations (6)–(7), the amplitude of the desired source currents including
power losses is redefined and given as,
Im ¼
2ðPT þ Ploss Þ
UT
(15)
where Im is the amplitude of the desired source currents including power losses. Therefore, the reference
filtering currents for phases a, b, and c are found by the arrangement of Equation (15) into Equations
(12)–(14) and then using Equation (1),
ifa ðt Þ ¼ ila ðt Þ Im sinðot fa1 Þ
(16)
ifb ðt Þ ¼ ilb ðt Þ Im sinðot þ fa1 2p=3Þ
(17)
ifc ðt Þ ¼ ilc ðt Þ Im sinðot þ fa1 þ 2p=3Þ
(18)
Under sinusoidal supply voltages the desired source currents of Equation (12)–(14) can be regarded
as a three-phase generalization of the active current definition proposed by Fryze for a single-phase
system [19]. The source currents also agree with the definition proposed by Czarnecki via orthogonal
current decomposition for the three-phase system [20], where the load current can be decomposed into
active and residual components, e.g.
ilk ðt Þ ¼ isk
APF abc ðt Þ
þ ik
residual ðt Þ
(19)
In Equation (19), isk APF abc ðt Þ is the minimum effective source current associated with the transfer of
average real power from the source to the load and the residual component is the non active component.
Thus, the residual component will be equal to the reference filtering currents allowing the not
consumption/supply of real power by the APF.
3. APF CONFIGURATION
Since Matlab/SimulinkW provides the full capabilities required for accurate simulations for testing the
case study presented in this contribution, it has been adopted as the simulation tool to be used. Figure 2
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
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Figure 2. Shunt APF configuration.
shows the digital implementation diagram in Matlab/Simulink of the shunt APF model for a real-time
simulation. The reference current calculator is implemented according to the proposed strategy to
determinate the reference filtering currents, as given by Equations (16)–(18). Once the reference
filtering currents are determined, they are input to a hysteresis-band current controller to produce the
control signals of the PWM VSI and to inject into the electric system the actual filtering currents with
the same waveform of the reference filtering currents. In the hysteresis-band current control [21], the
actual filtering current ifk(t) is left to oscillate within a window Δi placed above and below the reference
waveform ifk ðt Þ. The PWM inverter consists of six switches with anti-parallel diode across each switch
and with a split capacitor connected in parallel at the end. The split capacitor is used for energy storage
and maintains a constant dc voltage. The shunt APF only supplies/absorbs reactive power, and it does
not provide any active power to the load.
Among the various PWM techniques available, the hysteresis-band current control is widely used due
its simplicity of implementation [21]. This technique can be implemented to generate the switching pattern
in order to obtain stability, very fast response, and good accuracy, and it has proven to be most suitable for
all the applications of current controlled VSI for APFs. The switching logic is formulated as follows:
If ifk < ifk Δi =2 upper switch OFF; lower switch ON
(20)
If ifk > ifk þ Δi =2 upper switch ON; lower switch OFF
(21)
The split capacitor is used for energy storage, and even though the dc voltage slightly fluctuates due
to the harmonics, it must maintain a constant dc voltage. Since the losses produced by the switching
converter and dc voltage variations must be supplied by the source, the power signal Ploss controlled
via a PI controller, and the difference between the actual and the reference voltages of the capacitor,
Udc and U*dc, respectively, are then input to the reference current calculator.
Copyright © 2012 John Wiley & Sons, Ltd.
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DOI: 10.1002/etep
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4. REAL-TIME APPLICATION
The real-time simulation of the APF connected to the power system provides advantages in the design
process by allowing options to be tried out before the hardware is built. After creating a Simulink
model, the simulation parameters are used by Real-Time WorkshopW to generate C code and to build
the real-time application. Real-Time WorkshopW generates optimized, portable, and customizable
ANSI C or C++ code from Simulink models to create standalone implementations of models that
operate in real time in a variety of target environments, and with commercial or proprietary real-time
operating systems.
In this contribution, the real-time application of the shunt APF compensation was developed
with the incorporation of the RTWT toolbox of Matlab/Simulink. RTWT is a PC solution for
prototyping and testing real-time systems. It is an environment where a single computer is used
as a host and target. After creating a model and simulating it with Simulink in normal mode, it is
possible to generate executable code; then the application in real time is achieved with the
Simulink external mode. RTWT uses a small real-time kernel to ensure that the real-time
application runs in real time. The real-time kernel runs at CPU ring zero (privileged or kernel
mode) and uses the built-in PC clock as its primary source of time [12,13]. The kernel intercepts
the interrupt from the PC clock before the Windows operating system receives it, this blocks any
calls to the Windows operating system [12].
Communication between Simulink and the real-time application is through the Simulink external
mode interface module. This module talks directly to the real-time kernel and is used to start the
real-time application. External mode requires a communication interface to pass external parameters
to Simulink, and on the receiving end, the same communications protocol must be used to accept
new parameter values, and to insert them in the proper memory locations to be used by the real-time
application. For the case of this contribution, the host computer also serves as the target computer.
Therefore, only a virtual device driver is needed to exchange parameters between the Matlab and
Simulink memory space and the memory that is accessible by the real-time application [12]. Figure 3
shows the report of code generation for the real-time application.
Figure 3. Code generation report for APF_rtwt with Real-Time Workshop.
Copyright © 2012 John Wiley & Sons, Ltd.
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5. CASE STUDY
The potential of the developed control strategy for calculating the reference filtering currents in phase
coordinates is illustrated with the analysis of the test system of Figure 4, where the three-phase
balanced source voltages supply an assumed unbalanced nonlinear load. In this scenario, there are
three different distorting loads connected between each phase and the neutral wire, which give place
to a three-phase harmonic composition highly heterogeneous at the point of common coupling
(PCC). These loads consist on: a single-phase full-wave rectifier with a high inductance on the dc side
for phase a; a single-phase full-wave rectifier with a high capacitance on the dc side for phase b, and
multiple harmonic current injections for phase c, which represent a given single-phase nonlinear load,
as shown in Figure 4. For phases a and b, the single-phase transformer is assumed to be linear and the
multiple current injections information of the nonlinear load at phase c is given in Equation (22).
In order to simulate a load change during the shunt APF compensation, and be able to observe the
dynamic performance of the proposed control strategy in real time during the transient, a load change
after three cycles of simulation is programmed (switching ON all breakers at T = 0.6 s in Figure 4). The
load changes for phases a and b consist on adding a pure resistive load that is connected in parallel on
the dc side. For phase c, a pure resistive load is connected in parallel with the multiple harmonic
current injections that simulate the single-phase non linear load, see Figure 4.
ilc ðt Þ ¼ 3:9862 sinðot þ 172:77 Þ þ 0:28479 sinð3ot þ 2:26 Þ
(22)
þ1:5125 sinð5ot þ 4:43 Þ þ 0:4846 sinð7ot þ 6:17 Þ A
The electric circuit conditions of the test system under study are shown in Figure 5. The source
voltages are sinusoidal and balanced, as observed in Figure 5(a), and the load currents are highly
distorted/unbalanced as seen in Figure 5(b).
In particular, a meaningful and detailed analysis of the load currents is illustrated through Figures 6, 7,
and 8, for phases a, b, and c, respectively. From Figure 6(a), it is observed the load current waveform at
phase a, where both the total harmonic distortion (THD) and the current waveform are varying after three
cycles of simulation, at T = 0.06 s; Figure 6(b) and Figure 6(c) show the magnitude of the harmonic
Figure 4. Shunt APF in Matlab/SimulinkW external mode for Real-Time application.
Copyright © 2012 John Wiley & Sons, Ltd.
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DOI: 10.1002/etep
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H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
Figure 5. Electric circuit conditions of the case of study.
Figure 6. Load current at phase a.
Copyright © 2012 John Wiley & Sons, Ltd.
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Figure 7. Load current at phase b.
content in amperes and % of the fundamental, respectively. A similar condition is presented for phase b, as
it can be observed from Figure 7(a), (b), and (c). For these two phases, after the load change at T = 0.06 s,
the harmonic content in the load current is varying in both amperes and % of the fundamental.
On the other hand, the harmonic content in phase c after the load change is observed in Figure 8(a). It
can be observed that the harmonic current injections in amperes are maintaining the same magnitudes as
illustrated in Figure 8(b), and the fundamental frequency component has been increased due to the
addition of the liner load (i.e. the pure resistive element), so that as a result of this conditions, the THD
index is reduced.
Given the simulation conditions explained above, it is expected that the calculation of the reference
filtering currents, needed to generate the switching commands of the shunt APF, proceeds to adjust
their values during the load change, instantaneously as needed, in order to ensure a good performance
of the compensation device. In this way, it will be expected that the reference filtering currents for
phase a and b adjust their values after the load change condition at T = 0.06 s. For phase c, the reference
filtering current should remains constant during the complete shunt APF compensation process due to
the no change of the harmonic content in phase c, see Figure 8.
The results of the shunt APF compensation are illustrated in Figures 9 and 10. Figure 9 illustrates
the source currents at the PCC, where it can be observed the elimination of the harmonic currents in
all phases during the complete real-time simulation of the shunt APF compensation process. The neutral
current is well controlled during the complete compensation process, despite the load change conditions,
see Figure 10.
The injection currents by the APF are shown in Figure 11(a), (b), and (c), for phases a, b, and c,
respectively. As it was expected, after the load change, at T = 0.06 s, the filtering currents of phases
a and b adjust their values continuously to be able to achieve an adequate performance of the APF,
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
1300
H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
Figure 8. Load current at phase c.
meanwhile the filtering current for phase c remains constant as it was required and correctly calculated
by the proposed reference current generator.
It is important to notice that in order to be able to compensate unbalanced nonlinear currents by the
APF and maintain the neutral current controlled, it was required the use of a three-leg split capacitor as
the converter configuration of the VSI illustrated in Figure 2. The converter configuration and the
modulation technique, used for generating the switching commands, allows that the control of the
injection currents of each phase be independent to each other, working directly over the reference
Figure 9. Currents at the PCC with shunt APF compensation.
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
REAL-TIME APPLICATION OF SHUNT APF DYNAMIC COMPENSATION
1301
Figure 10. Neutral current during shunt APF compensation.
filtering current with a low computational demand required for that purpose. On the other hand, when
using simulating modulation techniques with a fixed-step solver, the integration step should be small
enough to provide accurate solutions, or the inclusion of another software package would be necessary
for obtaining a feasible solution. Giving the characteristics of the commutation technique used in this
real-time application, a maximum of 50-kHz commutation frequency was used for the appropriated
real-time operation of the shunt APF.
Figure 11. Shunt APF compensation current.
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
1302
H. A. RAMOS-CARRANZA, A. MEDINA AND G. W. CHANG
6. DISCUSSION AND CONCLUSIONS
The electric system under study and the complete dynamic model of the shunt APF has been implemented
in the real-time simulation package RTWT of Matlab/SimulinkW. This real-time implementation of
the shunt APF has included the VSI, the modulation technique, and the reference current generator.
According to the observed results obtained with the case study, it is possible to indentify the proposed
reference current generator as an efficient and accurate control strategy to calculate the reference filtering
currents needed for the shunt APF compensation process. The reference current generator has achieved
remarkable results even during the transient due to a load change condition observing a very good
dynamic response of the algorithm. Once the shunt APF is in operation, effective harmonic distortion
mitigation in the source currents has been achieved, as well as the source currents are balanced, thus
controlling the neutral current. The APF compensation ensures the mitigation of the harmonic content
in the source currents at all times in spite of the harmonic content present in dynamic load currents,
maintaining the THD on average close to 1%. This final value of THD is due to the ripple current
inherent to the APF injection currents. In addition, the reactive power compensation has been
conveniently achieved since the source currents have been placed in phase with the source voltages at
fundamental frequency.
The control strategy in phase coordinates has been developed avoiding the transformation between
different frameworks, thus it is feasible to reduce the control strategy to a single-phase application
maintaining the theoretical and practical advantages observed for the three-phase control strategy. In this
control strategy and for the work presented in this paper, the election of the sliding-window DFT for the
extraction of the fundamental component information from the source voltage relies on the good
behavior of the method, taking full advantage from the Matlab/SimulinkW and its embedded functions
supported by RTWT. RTWT avoids additional hardware requirements for a real-time application and
gives good accuracy in the solution. Since only virtual drivers are required and these are provided for
Real-Time Workshop of Matlab/Simulink, the communication links between host and target are highly
efficient. The real-time application of the shunt APF compensation has allowed us to establish the
proposed control strategy as an effective compensation strategy with affordable computational demand
required by its compensation algorithm, making it suitable for a further physical implementation of the
compensation device.
If the compensation scenario includes the electric system with unbalance in the source voltages, the use
of the positive sequence of the source voltages at fundamental frequency as the reference signals, instead
of the reference signals of Equations (9)–(11), represents a more suitable option to proceed with the
calculation of the reference filtering currents in order to obtain the desired results. Nevertheless, it is
important to notice that the use of the positive sequence at fundamental frequency signals will increase
the necessary computation demand needed by the reference current generator, and some adjustments on
the theory of the calculation of the amplitude of the desired source current should be made.
7. LIST OF SYMBOLS
ifk ðt Þ
ilk(t)
isk ðt Þ
Im, Imk
Im ; Imk
θisk
θuk
PT
uk(t)
Umk
Umk1
Ploss
Reference filtering currents
Load currents
Desired source currents after compensation
Amplitude of the source currents after compensation
Amplitude of the desired source currents after compensation
Angles of phase of the source currents
Angles of phase of the source voltages
Total average power
Instantaneous source voltages
Source voltage amplitudes
Source voltage amplitudes at fundamental component
Power losses signal
Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep
REAL-TIME APPLICATION OF SHUNT APF DYNAMIC COMPENSATION
1303
ik _ residual(t) Residual current component
Delta window for the hysteresis-band current controller
Δi
Udc
Capacitor dc voltage
Capacitor dc voltage of reference
Udc
ACKNOWLEDGEMENT
The authors gratefully acknowledge to the Univesidad Michoacana de San Nicolás de Hidalgo through the Post
grade Studies Division of the Electric Engineering Faculty for the facilities granted to carry out this investigation.
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Copyright © 2012 John Wiley & Sons, Ltd.
Int. Trans. Electr. Energ. Syst. 2013; 23:1289–1303
DOI: 10.1002/etep