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3364 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
Experimental Design of a Nonlinear Control
Technique for Three-Phase Shunt Active Power Filter
Salem Rahmani, Member, IEEE, Nassar Mendalek, Member, IEEE, and Kamal Al-Haddad, Fellow, IEEE
Abstract—This paper presents a nonlinear control technique
for a three-phase shunt active power filter (SAPF). The method
provides compensation for reactive, unbalanced, and harmonic
load current components. A proportional–integral (PI) control law
is derived through linearization of the inherently nonlinear SAPF
system model, so that the tasks of current control dynamics and
dc capacitor voltage dynamics become decoupled. This decoupling
allows us to control the SAPF output currents and the dc bus volt-
age independently of each other, thereby providing either one of
these decoupled subsystems a dynamic response that significantly
slower than that of the other. To overcome the drawbacks of the
conventional method, a computational control delay compensation
method, which delaylessly and accurately generates the SAPF
reference currents, is proposed. The first step is to extract the
SAPF reference currents from the sensed nonlinear load currents
by applying the synchronous reference frame method, where a
three-phase diode bridge rectifier with R–Lload is taken as the
nonlinear load, and then, the reference currents are modified,
so that the delay will be compensated. The converter, which is
controlled by the described control strategy, guarantees balanced
overall supply currents, unity displacement power factor, and
reduced harmonic load currents in the common coupling point.
Various simulation and experimental results demonstrate the high
performance of the nonlinear controller.
Index Terms—Active power filter, control delay compensa-
tion, modeling, nonactive load current compensation, nonlinear
control, power quality.
I. INTRODUCTION
HARMONICS are typically caused by the use of non-
linear loads, such as switch-mode power converters,
power-electronics-operated adjustable-speed drives, fluorescent
lamps, arc furnaces, welding equipment, and other nonlinear
loads used in both domestic and industrial applications. The
presence of harmonics in the system results in several effects
(including increased heating losses in transformers, motors,
and lines; low power factor; torque pulsation in motors; and
poor utilization of distribution wiring and plant). In response
to the power quality concerns of typical power distribution sys-
tems in terms of harmonic current distortion and power factor,
Manuscript received April 28, 2008; revised January 28, 2009, May 29,
2009, and September 2, 2009; acccepted December 2, 2009. Date of publication
January 8, 2010; date of current version September 10, 2010. This work
was supported by Canada Research Chair in Energy Conversion and Power
Electronics at the École de Technologie Supérieure.
S. Rahmani and K. Al-Haddad are with the École de Technologie
Supérieure, University of Québec, Montreal, QC H3C 1K3, Canada (e-mail:
Salem.Rahmani@esstt.rnu.tn; kamal@ele.etsmtl.ca).
N. Mendalek is with the Department of Electrical, Computer and Com-
munication Engineering, Notre Dame University, Louaize, Lebanon (e-mail:
nmendalek@ndu.edu.lb).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2009.2038945
IEEE 519 and IEC EN 61000-3 standards specify regulations
governing harmonic compliance. A passive filter has been a
viable approach because of low cost and high efficiency. How-
ever, the performance of the passive scheme has a limitation
since the addition of the passive filter interfaces with the
system impedance and causes resonance with other networks
[1], [2]. Numerous active solutions, which are becoming a more
effective means to meet the harmonic standards by overcoming
the drawback of the passive filter, have been proposed [3]–[10].
The SAPF operates by injecting the reactive, unbalanced, and
harmonic load current components into the utility system with
the same magnitudes as the nonactive load currents demanded
by a given nonlinear load but with opposite phases [11]–[15].
Among the subjects related to the active filter’s design and
applications, the methods for extraction of the harmonic load
currents and determination of the filter reference current play
an important and crucial role. Indeed, the accuracy and speed
of the SAPF response are related to this point [16], [17].
The methods of reference current generation are categorized
into two main fields: 1) time-domain and 2) frequency-
domain methods [11]–[17]. Time-domain methods such as
d–qtransformation (or synchronous rotating reference frame),
p–qtransformation (or instantaneous reactive power), symmet-
rical components transformation, etc., are based on the mea-
surements and transformation of three-phase quantities [12].
The main advantage of these time-domain control methods,
compared with the frequency-domain methods, based on the
fast Fourier transformation is the fast response obtained. On the
other side, frequency-domain methods provide accurate indi-
vidual and multiple harmonic load current detection. The com-
pensation method presented in this paper is the time-domain
control type of compensation, where all harmonic load current
components are targeted and compensated. An SAPF offers dif-
ferent options of compensation, such as harmonic attenuation,
load balancing, resonance elimination, and displacement power
factor improvement [1], [9]. Thus, the control strategy and the
method for extracting the nonactive load current references will
depend on the compensation objectives [11]–[17].
Although conventional linear controllers may fulfill certain
compromises between steady-state performance, and harmonic
load current compensation and dc bus voltage regulation, they
remain unable to compensate the inherent nonlinearity of such
circuits, which is generated by the switching process. This
manifests with important overshoots and long settling times,
during transients from both the ac or dc side [2], [11], [12],
[15]. On the other hand, most of the techniques mentioned in
the literature assume sinusoidal supply voltages when compen-
sating unbalanced nonlinear load currents [3], [12]. However,
0278-0046/$26.00 © 2010 IEEE
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3365
in reality, the utility voltage available at the downstream end is
nonsinusoidal due to the harmonic load currents. A thorough
investigation of the experimental results reported in [2], [8],
and [16], reveals that the total harmonic distortion (THD) in the
supply currents cannot be brought down below 5% to satisfy
the IEEE-519 standard. This is due to the presence of notches in
the supply currents, whereas feedforward control methods are
used. The drawbacks can be eliminated by using the nonlinear
control theory, ideally without exaggerating computational and
implementation complexities. In addition, Youssef et al. [18]
and Yacoubi et al. [19], [20] implemented very useful advanced
nonlinear control techniques to active rectifiers with active
filtering function. These control techniques can be applied to
active filtering technology. In [21], a nonlinear control strategy
of an SAPF based on the internal model principle is proposed.
The stabilization of the dc-link voltage dynamics is addressed,
along with the fulfillment of the harmonic load current com-
pensation objective. The two-time scale behavior of the SAF is
exploited to apply the averaging theory in the control design.
In [22], a nonlinear control strategy for an active filter is
proposed. It is based on the input–output linearization method
implemented on a dq0rotating current reference frame. The
structure balances the load currents, obtains unity displace-
ment power factor, and reduces the harmonic load currents in
arbitrary loads. In [23], the current loop dynamics in the
synchronous d–qframe are controlled using multiple-input–
multiple-output optimal control based on the predictive control
approach. The nonlinear control strategy does not require online
optimization and overcomes the aforementioned difficulties
by ensuring fast current tracking, current loop stability, and
compensation robustness under nonideal load and/or supply
conditions.
In this paper, the theoretical development of the SAPF is
based on the work done in [24]. However, no experimental vali-
dation for the proposed control was conducted. It was shown by
simulations that the nonlinear control technique enhances the
dynamic performance of the SAPF modeled in the synchronous
orthogonal “dq” frame. The exact feedback linearization theory
was applied in the design of the controller. This control strategy
allowed the decoupling of the currents, enhanced their tracking
behavior, and improved the dc voltage regulation. The reference
signals were obtained by extracting the harmonic currents from
the measured load currents. In the orthogonal frame, the funda-
mental current component can be seen as a dc component, and
as a consequence, the harmonic load currents can be extracted
with high-pass filters (HPFs). The HPFs were based on fourth-
order Butterworth low-pass filters. The main problem with
this method is the delay that occurs when the control system
is digitally implemented. Even if the HPF would perfectly
perform, not all the harmonic load currents could be filtered.
In addition, the system cannot completely compensate load
current unbalance because of the phase shift caused by the filter.
The studies on active power filters, which appeared in the
literature [1]–[17], [24], all ignore the delay time such as the
current response delay generated by the boost inductors and dc-
link voltage feedback delay due to the detection circuits.
The delay time caused by the filter control algorithm is due
to the low-pass filter used for reference current calculation and
the active filter natural response determined by boost inductors
and dc-link voltage capacitors [25]. To simplify the current
control plant to be of first-order delay type, voltage decouplers,
rotating frame transformation, and pole-zero cancellation tech-
niques were used in current regulators. In [26], the concept
of delay time was discussed. The method considered the in-
stantaneous power delay caused by the current regulators and
dc-link voltage feedback circuit and presented the load power
estimation method to improve the dynamic response of input
power regulation.
A computational control delay compensation method was
also presented in [27], where only the feedforward control
of the load current was used. The method is very effective
for decreasing the magnitudes of the lower order harmonic
load currents but cannot fully compensate the fast load current
transients. The HPF time constant is about 8 ms. It is reported
that, in the case of load current step changes, the system takes
about 19 ms to reach steady state. In addition, a multistage
adaptive filter was discussed in [28]. This method combines
a low-pass filter and an adaptive predictive filter, making it
possible to extract the sinusoidal active current component
from the distorted waveform without harmful phase shift, even
when the frequency and amplitude simultaneously altered. The
drawback of this technique is the difficulty to design the dc-link
voltage and the current regulators.
In this paper, the authors propose a detailed nonlinear control
technique, as previously introduced in [24], that uses a compu-
tational control delay compensation method to overcome the
conventional method drawbacks. The first step is to extract the
SAPF reference current. Then, the phase shift of the reference
current is modified, so that the delay will be compensated.
In addition, the nonlinear control is theoretically established
and experimentally validated using both simulations and ex-
periments. Consequently, the currents very closely track their
references. The SAPF compensates for unwanted reactive, un-
balanced, and harmonic load current components under non-
sinusoidal supply voltage conditions. The SAPF performance,
during both nominal and severe operating conditions, is then
evaluated in real time using the dSPACE DS1104 controller
board, which is supported by a Matlab/Simulink Real-Time
Workshop environment.
II. THREE-PHASE SHUNT ACTIVE FILTER TOPOLOGY
An SAPF configuration is considered in this paper in order
to avoid harmonic pollution along the power line caused by a
three-phase diode bridge rectifier load, followed by an inductor
LLin series with a resistor RL. The SAPF acts as a controlled
current source connected in parallel with the nonlinear load.
It has the structure illustrated in Fig. 1. It consists of a full-
bridge voltage source pulsewidth-modulation inverter, a dc-side
capacitor Cdc, and ac-side high-frequency inductors Lcthat are
required to shape the compensator input currents i1,i2, and i3.
A. Modeling of Shunt Active Filter
Kirchoff’s rules for voltages and currents, as applied to this
system, provide us with the three differential equations in the
3366 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
Fig. 1. Basic circuit of SAPF.
stationary abc frame
v1=v1N=Lc
di1
dt +Rci1+v1M+vMN
v2=v2N=Lc
di2
dt +Rci2+v2M+vMN
v3=v3N=Lc
di3
dt +Rci3+v3M+vMN (1)
where v1,v2, and v3denote the line-to-ground voltages of the
three-phase balanced system measured at the point of common
coupling (PCC).
Using the following assumptions:
v1+v2+v3=0,i
1+i2+i3=0
the following relation is obtained:
vMN =−1
3
3
m=1
vmM .(2)
The switching function ckof the kth leg of the converter (for
k=1,2,3) is defined as
ck=1,if Skis On and S
kis Off
0,if Skis Off and S
kis On. (3)
Thus, vkM =ckvdc. The phase-kdynamic equation of the
filter’s model is given by the following equation:
dik
dt =−Rc
Lc
ik−1
Lcck−1
3
3
m=1
cmvdc +vk
Lc
.(4)
A switching state function dnk is defined as
dnk =ck−1
3
3
m=1
cmn
.(5)
The value of dnk depends on the switching state nand the
phase k. In other words, dnk simultaneously depends on the
switching functions of the three legs of the SAPF. This shows
the interaction between the three phases.
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3367
The resulting transformed model in the synchronous orthog-
onal rotating frame is given as follows [24]:
d
dt ⎡
⎣
id
iq
vdc ⎤
⎦=⎡
⎢
⎣
−Rc
Lcω−dnd
Lc
−ω−Rc
Lc−dnq
Lc
dnd
Cdc
dnq
Cdc 0
⎤
⎥
⎦⎡
⎣
id
iq
vdc ⎤
⎦+1
Lc⎡
⎣
vd
vq
0⎤
⎦.
(6)
B. Harmonic Current Control
A PI control law was derived through linearization of the
inherently nonlinear SAPF system model, thereby decoupling
the tasks of harmonic load currents tracking and dc capacitor
voltage regulation. This decoupling allows the SAPF to com-
pensate for the ac currents and the dc-bus voltage independently
of each other but results in either one of these decoupled
subsystems having a dynamic response that is significantly
slower than that of the other. In order to obtain a fast dynamic
response of harmonic load currents compensation, the structure
of a fast inner loop (current tracking loop) and a slow outer loop
(dc voltage regulation loop) is adopted. The dynamics of the ac
currents in (6) can be rewritten as follows:
Lc
did
dt +Rcid=Lcωiq−vdcdnd +vd
Lc
diq
dt +Rciq=−Lcωid−vdcdnq +vq.(7)
Let us define the equivalent inputs as
ud=Lcωiq−vdcdnd +vd
uq=−Lcωid−vdcdnq +vq.(8)
Thus, through the input transformation (8), the coupled dynam-
ics of the currents tracking problem have been transformed
into decoupled dynamics. Hence, the currents idand iqcan
independently be controlled by acting upon inputs udand uq,
respectively. By using the error signals ˜
id=i∗
d−idand ˜
iq=
i∗
q−iq, and applying proportional integral compensation, one
can choose dnd and dnq such that
ud=kp˜
id+ki˜
iddt
uq=kp˜
iq+ki˜
iqdt. (9)
The transfer function of the PI compensator is
Gi(s)=Uq(s)
˜
Iq(s)=Ud(s)
˜
Id(s)=kp
s+ki
kp
s(10)
and the closed-loop transfer function of the current loop is
Iq(s)
I∗
q(s)=Id(s)
I∗
d(s)=kp
Lc
s+ki
kp
s2+(Rc+kp)
Lcs+ki
Lc
.(11)
For the optimal value of the damping factor ζ=√2/2,the
theoretical overshoot is 20.79%. Nevertheless, in order to elim-
Fig. 2. Inner control loop of the current iq.
Fig. 3. DC-bus voltage control loop.
inate the zero in the closed-loop transfer function, a prefilter
Gp(s)is added, as shown in Fig. 2, i.e.,
Gp(s)= 1
1+(kp/ki)s.(12)
The response of the current loops becomes that of a second-
order transfer function with no zero; hence, the following
design relations can easily be derived: kp=2ζωniLc−Rcand
ki=Lcω2
ni.
The control law is given by the following:
dnd =vd+Lcωiq−ud
vdc
(13)
dnq =vq−Lcωid−uq
vdc
.(14)
The inner control loop of the current iqis shown in Fig. 2.
C. DC Voltage Regulation
The instantaneous active and reactive powers exchanged
between the SAPF and the ac mains are given by p=vdid
and q=−vdiq(because vq=0under ideal supply conditions,
as shown here). To maintain some vdc level across the dc
capacitor of the SAPF, the losses through the active power
filter’s resistive–inductive branches can be compensated by
acting on the supply current. Ideally, it must act on the active
current component id
Cdc
dvdc
dt =dndid+dnq iq.(15)
An equivalent input udc is defined as
udc =dndid+dnq iq.(16)
To regulate the dc voltage vdc, the error ˜vdc =v∗
dc −vdc is
passed through a PI-type controller given by
udc =k1˜vdc +k2˜vdc dt. (17)
The transfer function of the PI compensator is
Gv(s)=Udc(s)
˜
Vdc(s)=k1
s+k2
k1
s.(18)
3368 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
Fig. 4. Nonlinear control scheme of the SAPF.
The resulting closed-loop transfer function is
Vdc(s)
V∗
dc(s)=2ζωnv
s+ωnv
2ζ
s2+2ζωnvs+ω2
nv
(19)
where the proportional and integral gains are
k1=2ζωnvCdc and k2=ω2
nvCdc.
Fig. 3 illustrates the outer control loop of the dc voltage.
The control effort of this outer loop is given by the follow-
ing [24]:
i∗
do =2
3
vdc
ˆ
Vudc.(20)
The reference current in (20) is added to the harmonic
reference current of idloop, as shown in Fig. 4. i∗
do is a dc
component, and it will force the SAPF to generate or to draw
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3369
Fig. 5. Delays generated by the system.
a small current at the fundamental frequency. Furthermore,
by designing the dc voltage loop to be much slower than the
current loops, there would not be any interaction between the
two loops. Fig. 4 represents the nonlinear control of the SAPF.
III. CONTROL DELAY COMPENSATION
In this paper, the analytical model and design methods are de-
scribed in continuous time. In practice, a dc-link voltage regu-
lator, current regulators, and low-pass filter are implemented by
a personal-computer-based discrete system. A computational
control delay compensation method is used. Fig. 5 illustrates
the total delay resulting from the chain of acquisition and the
real-time controller, which uses the sampling period named Ts.
The delay time Tsens caused by boost inductors and dc-link
capacitor is approximated to 100 μs, which corresponds to a
dephasing angle θsens of 2◦at 60 Hz. Moreover, the interface
communication and computing time of the algorithms fix the
minimum sampling period of the DSP. The delay Tcirc brought
by the digital circuit is thus equal to Ts. The delivered signal
by the numerical system has pace in stairs of width Ts.By
carrying out the average over each sampling period, one obtains
the signal s3. The delay Tsamp resulting from this average over
one sampling period is equal to Ts/2. The delay Tcomp due to
the discretization and the computing time is equal to 3Ts/2.The
sampling period for program execution is Ts=52μs. Thus, the
total delay Tdis approximately equal to 178 μs.
While s1is the signal without delay, s2is the signal at
the output of the sensor, and s3is the signal at the output of
the DSP.
The delay Tdinvolves a dephasing angle θd1=3.8◦at
60 Hz between the reference current and the current injected by
the SAPF. The proposed strategy consists of creating a phase
lead at 60 Hz on the reference currents to compensate for the
total delay. Therefore, from the measured voltages vs(θ)at the
PCC, the phase-locked loop rebuilds the voltages by integrating
the desired dephasings (θsens and θcomp). Consequently, the
reference currents are corrected, and the filter currents behave
as desired.
Fig. 6. Current controller performance without control delay compensation.
Fig. 7. Waveforms showing the tracking performances of the inner loop.
Where θsens is the delay caused by boost inductors and dc-
link capacitor, θcomp is the delay caused by discrete digital
implementation and the computing time.
A. Current Controller Performance
Fig. 6 shows test results of the current controller without
control delay compensation. The d-axis id,theq-axis iq, and
the phase “1” active filter current in steady-state operation su-
perposed with their respective references are shown. The results
show the appearance of a time delay between the reference
currents and the sensed currents.
Fig. 7 shows the test results of the nonlinear control with
the proposed control delay compensation method. The results
clearly show that the oscillating current harmonics injected by
the filter track their reference templates with high accuracy. It
demonstrates that the computational control delay compensa-
tion method performs very well.
3370 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
TAB L E I
SPECIFICATION PARAMETERS
IV. SIMULATION RESULTS
The nonlinear control scheme and compensation by SAPF is
simulated under MATLAB/Simulink and power system block-
set environment to estimate its performance. The nonlinear load
consists of one three-phase and one single-phase diode rectifier,
so that the effectiveness of the nonlinear control scheme to
compensate for unbalanced load can be tested. The rectifiers
are feeding R–L-type circuits. The source current waveforms
of the simulation results have been analyzed to obtain their
THD under varying load conditions. The main purpose of the
simulation is set to study three different aspects: 1) reactive and
harmonic load currents compensation; 2) dynamic response of
the SAPF to load variations; and 3) compensation of nonactive
load currents.
The system parameters used in these simulations are given in
Table I.
One can read, for the case of a balanced load, the following
main power magnitudes (active power, reactive power, dis-
tortion power, and apparent power) and power factor: PL=
818.6W; QL= 162 VA R ; DL= 207.4VAR ; SL= 859.9VA ;
and PF =95.2%.
The SAPF power magnitudes (active power, reactive power,
distortion power, and apparent power) are given as follows:
Pc=6.6W, Qc= 159 VAR , Dc= 226.6VAR, and Sc=
276.9VA.
The source power magnitudes (active power, reactive power,
and apparent power) and power factor are given as follows:
Ps= 825.2W, Qs=3 VAR , Ss= 826.2VA, and PF =
99.88%.
One can deduce that the SAPF power rating to compensate
reactive and harmonic load current components is 32.2% (Sc=
32.2%SL)of the load nominal power.
For the case of unbalanced nonlinear loads, the fundamental
positive-sequence active power, reactive power, and appar-
ent power are given as follows: PL1+ = 503.8W, QL1+ =
65.55 VAR, and SL= 532.1VA .
The SAPF fundamental positive-sequence active power,
positive-sequence reactive power, and apparent power are given
as follows: Pc1+ =8.22 W, Qc1+ =60.8VAR, and Sc=
197 VA.
The source fundamental positive-sequence active power,
positive-sequence reactive power, and apparent power are given
as follows: Ps1+ = 512 W, Qs1+ =4.75 VAR, and Ss=
513 VA.
Fig. 8. Steady-state response of the SAPF.
Therefore, the maximum rating of the SAPF to achieve
nonactive load current compensation represents 37% of the load
nominal power.
A. Reactive and Harmonic Currents Compensation of a
Nonlinear Load
The simulation results of the SAPF system are presented
in Fig. 8. The supply voltage vs1, load currents iL123, supply
currents is123, SAPF currents (ic123 ), and dc voltage vdc are
depicted there. The THD of the current generated by the non-
linear load is observed to be approximately 25.8%, whereas
the compensated supply current has a THD of approximately
2.62% at steady state. A graphical representation of the load
current (top plot) and the supply current (bottom plot) after
SAPF connection appears in Fig. 9(a) and (b). The results
presented in Figs. 8 and 9 coincide with those included in
Figs. 13 and 14 of Section V-A.
B. Response of the SAPF to Nonlinear Load Variation
In practice, nonlinear loads are usually time varying in
nature. Therefore, it is necessary to study the dynamic per-
formance of the SAPF when variations in the nonlinear loads
are considered. The nonlinear load current was subjected to
100% step decrease at t= 366.7ms and 100% step increase
at t= 483.3ms. In other terms, the value of the load resistance
is changed from 16 Ωto8Ωat t= 366.7ms and then changed
from 8 Ωto 16 Ωat t= 483.3ms. The relevant waveforms are
depicted in Fig. 10. These results confirm the good dynamic
performance of the SAPF for a rapid change in the nonlinear
load current. The waveforms presented in Fig. 10 coincide with
those included in Section V-B. As shown in Fig. 15, the settling
times of dc-link voltage vdc and line current isare less than
3 ms. Nevertheless, the results show that the computational
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3371
Fig. 9. Spectrum of phase 1. (a) Load current. (b) Source current after
compensation.
Fig. 10. Dynamic response of SAPF under varying distorted nonlinear load
conditions.
control delay compensation possesses good dynamic response
for both harmonic current compensation and dc-link voltage
regulation. It is important to note that the THD of the supply
currents are largely reduced, which is well below the IEEE-519
standard requirement.
C. Compensation of Nonactive Load Currents
With the adopted control algorithm, this test aims to evaluate
the capability of the SAPF to compensate for nonactive load
currents. To carry this out, the load consists of a three-phase
diode rectifier, followed by inductor LL=10 mH in series
with a resistor RL=16Ω, and a single-phase diode rectifier,
followed by inductor LL=10 mH in series with a resistor
RL=40 Ω. The single-phase rectifier is connected between
Fig. 11. Steady-state response of SAPF with nonlinear load unbalances.
Fig. 12. Spectrum of load currents and source currents after compensation for
asymmetrical load conditions.
phases 1 and 2, as shown in Fig. 1. The supply voltage vs1,
unbalanced three-phase load currents iL123, supply currents
is123, SAPF currents ic123 , and dc bus voltage of the SAPF are
shown in Fig. 11. One notes that these supply currents after
compensation are balanced. Furthermore, spectrum analysis of
load and line currents depicted in Fig. 12 indicates that the
SAPF can largely improve the THD of the supply currents
while feeding unbalanced load. The THD of the source currents
is123 are reduced from 15.91%, 22.12%, and 25.76% before
compensation to 1%, 1.27%, and 1.27% after compensation, re-
spectively. These results confirm the capability of the algorithm
to balance the line currents while simultaneously compensating
for reactive and harmonic load current components. The wave-
forms presented in this section and showed in Figs. 11 and 12
3372 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
TAB L E I I
MAIN HARMONIC CONTENTS OF SIMULATED SOURCE CURRENTS
Fig. 13. Steady-state response of the SAPF with diode rectifier load.
coincide with those included in Figs. 16 and 17 of Section V-C.
The harmonic contents (peak) of the main load and source
currents, along with %THD, are shown in Table II.
V. E XPERIMENTAL RESULTS
The nonlinear control method is tested on a laboratory pro-
totype of an SAPF. The SAPF consists of six insulated gate
bipolar transistor (IGBT) modules GA100TS60U of infrared.
The peak load power is 3.5 kW. The maximum rating of the
SAPF is 1 kVA. The real-time performance of the SAPF system
with developed algorithm was tested in the laboratory for
several different operating conditions, such as steady-state and
transient conditions, and under unbalanced nonlinear load. The
experimental results are presented in Figs. 13–17 and discussed
in the succeeding sections.
A. Steady-State Performance of the Nonlinear Control Scheme
With SAPF Harmonic Load Current Compensation
Experimental results aimed to validate the simulation results
of the nonlinear control have been obtained for steady-state
Fig. 14. Spectrum of the supply current in phase 1. (a) Before compensation.
(b) After compensation.
Fig. 15. Dynamic response of the SAPF under varying distorted nonlinear
load conditions.
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3373
Fig. 16. Steady-state response of the SAPF for asymmetrical load conditions.
Fig. 17. Harmonic spectra of load currents and supply currents.
operation mode, as shown in Fig. 13. These results show the
effectiveness of the SAPF to compensate harmonic currents
created by a three-phase diode rectifier type of load. In this
figure, the supply voltage vs1in phase 1, the load currents
iL123, the supply currents is123 , and the compensating currents
of the SAPF ic123 are presented. The harmonic spectrums
of load and source currents have been given in Fig. 14(a)
and (b), respectively. The compensated source current profile
shows that the SAPF was effectively working, thus reducing
the source current THD from 26% to 3.1%. This significant
reduction occurred when the utility voltage measured THD is
8.8%; consequently, the SAPF system is able to reduce the
source current THD (3.1%) well below the IEEE-519 standard
requirement.
B. Dynamic Performance of the Active Power Filter
Fig. 15 shows the transient response of the SAPF during
sudden variations in nonlinear load. It also shows the SAPF dc-
bus voltage, phase-1 supply, load, and filter currents. The load
current is abruptly decreased from 7.85 A (rms) to 3.8 A (rms)
and then increased from 3.8 A (rms) to 7.85 A (rms). As viewed
from the experimental results, the changeover from one operat-
ing condition to the other is quite smooth, therefore maintain-
ing excellent compensation. The increase in load current will
immediately be supplied from the SAPF, resulting in decreased
energy storage of the dc bus capacitor. This reduction in the dc
bus voltage of the SAPF will activate the dc voltage controller
to increase the supply current. This increased source current
tries to restore the stored energy of the capacitor in addition
to increased load active power. Within one cycle, the supply
current settles to steady-state value. Similarly, the reverse action
takes place as the load current decreases from 7.85 A (rms) to
3.8 A (rms), causing the dc link to slightly increase, as shown
in Fig. 15. This will momentarily decrease the supply current
to reduce the capacitor voltage at a set reference value. Within
one cycle of ac source, the supply current settles to steady-state
value. Since the corrective action of the voltage controller is
taken within a half cycle of the ac mains, it results in fast re-
sponse of the scheme. It was observed that this dip in the dc-link
voltage was about 7 V for 200-V dc link (3.5%). Nevertheless,
the conditions previously discussed prove that the APF system
compensates the reactive and harmonic load current compo-
nents during steady state, as well as under transient operating
conditions.
C. Compensation of Reactive, Unbalanced, and Harmonic
Load Current Components
The SAPF consists of six IGBTs (S1,S
2S3,S
1,S
2,S
3).The
load consists of three-phase and single-phase diode rectifiers,
followed by inductor LLin series with a resistor RL.The
single-phase rectifier is connected between phases 1 and 2
by closing the switch SW, as shown in Fig. 1. The global
load currents containing asymmetrical components are shown
in Fig. 16. This figure illustrates the supply voltages vs1of
phase 1, the unbalanced three phase load currents iL123,the
supply currents is123, and the SAPF currents ic123 . One can
note that supply currents after compensation are balanced.
The spectral analysis of load and line currents is performed,
using Fluke Model 41B Power Harmonics Analyzer. The results
depicted in Fig. 17 shows the ability of the SAPF to improve
the THD of the supply currents with unbalanced load. The
rms source currents before compensation was Is1=4.31 A,
Is2=4.64 A, and Is3=3.23 A; therefore, after compensation,
these currents become equal to Is1=Is2=Is3=4.56 A. The
THD of the source currents is123 are reduced, respectively, from
13.6%, 14%, and 21% before compensation to 2.9%, 3%, and
2.3% after compensation. The SAPF system works as expected.
The compensated source currents, as viewed from Fig. 16, are
sinusoidal and close to balanced. The filter currents suggest
that the SAPF system inject different currents to compensate
nonactive load current demands in each phase. This proves that
the control approach with the SAPF system can quite effec-
tively handle the most critical situation in a power distribution
system.
3374 IEEE TRANSACTI ONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010
VI. CONCLUSION
The nonlinear control algorithm of an SAPF has been imple-
mented to enhance its response for compensation of nonactive
load currents. The nonlinear control technique of the SAPF has
been designed, which is based on two inner current loops and
an outer dc bus voltage regulator loop. It has been observed
that there is no interaction between inner and outer loops in
addition to good performance in both steady-state and transient
operations. Simulation and experimental results have validated
the nonlinear control approach of the SAPF. It has been shown
that the system has 1.5 cycles for the outer voltage loop and
0.5 cycles for the inner current loop and is able to keep the THD
of the supply current below the limits specified by the IEEE-
519 standard. The obtained results have demonstrated the high
performance of the SAPF.
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Salem Rahmani (M’06) was born in Tunisia. He
received the B.Sc.A. and M.Sc.A. (electrical) de-
grees and the Specialized Scientific Studies Certifi-
cate (CESS) from the High School of Sciences and
Technologies of Tunis (ESSTT), Tunis, Tunisia, in
1992, 1995, and 2001, respectively, and the Ph.D.
degree from the National Engineering School of
Tunis (ENIT), Tunis, in 2004.
In September 2002, he was an Assistant Professor
with the Department of Electrical Engineering, High
Institute of Medical Technologies of Tunis (ISTMT),
Tunis. Since the elaboration of his Ph.D. degree, he has been a Member of the
Research Group in Power Electronics and Industrial Control (GREPCI), École
de Technologie Supérieure, University of Québec, Montreal, QC, Canada. His
research interests are power quality, active filters, and resonant converters,
including power converter topology, modeling, and control aspects.
RAHMANI et al.: EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF 3375
Nassar Mendalek (M’00) was born in Lebanon. He
received the B.E. degree in electrical engineering
from St-Joseph University, Beirut, Lebanon, in 1983
and the M.S. and Ph.D. degrees from the Ecole de
Technologie Supérieure, Montreal, QC, Canada, in
1997 and 2003, respectively.
From 1983 to 1990, he was with the Lebanese
Telecommunication Ministry as a Design and Sup-
port Engineer. From 1995 to 2004, he was with
the Research Group in Power Electronics and In-
dustrial Control (GREPCI), Ecole de Technologie
Supérieure, where he was involved in teaching and research activities related
to power electronics. Since 2004, he has been an Assistant Professor with the
Department of Electrical, Computer and Communication Engineering, Notre
Dame University, Louaize, Lebanon. He teaches courses in power electronics,
energy conversion, and analog and digital electronics. His research interests
include power quality, renewable energy, and the modeling and control aspects
of power converter topologies.
Kamal Al-Haddad (S’82–M’88–SM’92–F’07) was
born in Beirut, Lebanon, in 1954. He received
the B.Sc.A. and M.Sc.A. degrees from the Uni-
versity of Québec à Trois-Rivières, Trois-Rivières,
QC, Canada, in 1982 and 1984, respectively,
and the Ph.D. degree from the Institut National
Polythechnique, Toulouse, France, in 1988.
From June 1987 to June 1990, he was a Pro-
fessor with the Engineering Department, Université
du Québec à Trois Rivières. Since June 1990, he
has been a Professor with the Electrical Engineering
Department, École de Technologie Supérieure (ETS), Montreal, QC, where
he has been the holder of the Canada Research Chair in Electric Energy
Conversion and Power Electronics since 2002. He has supervised more than
60 Ph.D. and M.Sc.A. students working in the field of power electronics.
From 1992 to 2003, he was the Director of the graduate study programs
at the ETS. He is a Consultant and has established a very solid link with
many Canadian industries working in the field of power electronics, electric
transportation, aeronautics, and telecommunications. He is the Chief of the
ETS–Bombardier Transportation North America division, which is a joint
industrial research laboratory on electric traction system and power electronics.
He is also a coauthor of the Power System Blockset software of Matlab. He
has coauthored more than 250 transactions and conference proceeding papers.
His research interests are highly efficient static power converters; harmonics
and reactive power control using hybrid filters; and switch-mode and resonant
converters, including the modeling, control, and development of prototypes
for various industrial applications in electric traction, power supply for drives,
telecommunication, etc.
Dr. Al-Haddad is a Fellow Member of the Canadian Academy of Engineering
and a Life Member of the Circle of Excellence of the University of Quebec.
He is active in the IEEE Industrial Electronics Society, where he is the Vice
President for Publication, an AdCom member, and serves as an Associate Editor
for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. He was the
recipient of the Outstanding Researcher Award from ETS in 2000.
