IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 1, JANUARY 2008
97
Model Reference Adaptive Control Design
for a Shunt Active-Power-Filter System
Kuo-Kai Shyu, Member, IEEE, Ming-Ji Yang, Yen-Mo Chen, and Yi-Fei Lin
Abstract—In this paper, model reference adaptive control
(MRAC) is proposed for a single-phase shunt active power filter
(APF) to improve line power factor and to reduce line current
harmonics. The proposed APF controller forces the supply current to be sinusoidal, with low current harmonics, and to be
in phase with the line voltage. The advantages of using MRAC
over conventional proportional-integral control are its flexibility,
adaptability, and robustness; moreover, MRAC can self-tune the
controller gains to assure system stability. Since the APF is a
bilinear system, it is hard to design the controller. This paper
will solve the stability problem when a linearization method is
used to solve the nonlinearity of the system. Moreover, by using
Lyapunov’s stability theory and Barbalat’s lemma, an adaptive
law is designed to guarantee an asymptotic output tracking of
the system. To verify the proposed APF system, a digital signal
controller (dsPIC30F4012) is adopted to implement the algorithm
of MRAC, and a 1-kVA laboratory prototype is built to test feasibility. Experimental results are provided to verify the performance
of the proposed APF system.
Index Terms—Active power filter (APF), harmonics, model reference adaptive control (MRAC), power factor (PF).
I. I NTRODUCTION
W
ITH THE increase of nonlinear loads in utility line,
harmonic problem has been a primary concern. Those
nonlinear loads on industrial, commercial, and residential
equipment, such as diode rectifiers, thyristor converters, and
some electronic circuits, which are drawing nonsinusoidal currents, pollute the utility line due to the current harmonics that
they generate. They have brought about many problems in utility power, such as low power factor (PF), low energy efficiency,
electromagnetic interference, distortion of the line voltage, etc.
[1]. Therefore, standard regulations and recommendations,
such as IEC 61000-3-2 [2] and IEEE 519 [3], enforce a limit
on the aforementioned problems. For problems of harmonic
pollution, passive and active power filters (APFs) are typical
approaches that are used to improve the PF and to eliminate
harmonics. In the past, passive LC filters are generally used to
reduce these problems, but they have many demerits such as
its being bulky and heavy, and its resonance, tuning problem,
fixed compensation, noise, increased losses, etc. [4]. On the
contrary, the APF can solve the aforementioned problems and
Manuscript received September 7, 2006; revised July 23, 2007. This work
was supported by the National Science Council of Taiwan, R.O.C., under
Contract NSC 95-2221-E-008-081. This paper was presented at the IEEE
Industrial Conference, Paris, France, November 7–10, 2006.
The authors are with the Department of Electrical Engineering, National Central University, Chung-Li, Taoyuan 320, Taiwan, R.O.C. (e-mail:
kkshyu@ee.ncu.edu.tw; s9521089@cc.ncu.edu.tw; maki.118@yahoo.com.tw;
93521103@cc.ncu.edu.tw).
Digital Object Identifier 10.1109/TIE.2007.906131
is often used to compensate current harmonics and low PF
that is caused by a nonlinear load. In an APF connection, it
was roughly classified as in series (series APF) and in parallel
(shunt APF). A typical series APF is in the cascade path of the
power, compared with a shunt APF. It processes all the supplied
power, thus requiring more high current and voltage ratings
of devices, and involves significant switching losses. Consequently, the shunt APF is considered to be the most basic
structure of an APF [5]–[12].
In the past, most APFs use proportional plus integral and
differential (PID) control in the current/voltage control loop
[9]–[15]. When using fixed-gain PID controllers, it is necessary
to retune them for different operation regions, not to mention
the change in different loading powers. Furthermore, recent
applications need faster transient response, minimum power
dissipation, and robustness, which the PID fails to satisfy.
In view of the aforementioned problems of PID-controlled
APF, this paper adopts model reference adaptive control
(MRAC) [16]. MRAC is a well-established method that has
demonstrated its capabilities in many researches (e.g., [17]–
[25]). Many well-known MRAC results are developed in detail
in a variety of textbooks [16], [26]–[29]. In MRAC systems, the
desired performance of the plant is expressed via a reference
model, which gives the desired response to a command signal.
Hence, a considerable flexibility is granted to the designer to
alter the goals by modifying the reference model. On the other
hand, one main reason in using MRAC is the elimination of
relatively large overshoots and undershoots in the beginning
of the transient, which may disturb the stable operation of the
inverter in protecting the switching devices. Thus, it is expected
that MRAC can overcome the demerits of PID control and is a
better control strategy.
This paper presents an MRAC-based APF to cancel the
harmonic/reactive components in the line current so that the
current flow into and from the grid is sinusoidal and in phase
with the grid voltage. Since the APF is a bilinear system, it is
difficult to directly apply MRAC. This paper will solve the stability problem when a linearization method is used to solve the
nonlinearity of the system. Parameter update laws that are used
to tune the control gains are derived by the Lyapunov function.
Furthermore, the stability of the MRAC is guaranteed based on
Lyapunov stability and Barbalat’s lemma. The MRAC that is
developed in theory so far is mostly based on a higher order
algorithm that requires much more complicated mathematical
processing and far exceeds the capability of real-time processing of the previous microprocessors (e.g., 89C51, PIC16F877,
eight-bit microcontroller, etc). On the other hand, analog circuits can only keep the fixed parameters under an invariant
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Fig. 2.
Fig. 1. Shunt APF in parallel with a nonlinear load.
environmental condition. In other words, they are subject to
variation of controlled parameters in the presence of environmental changes, temperature rise, change in humidity, etc.
Fortunately, the present-day development in microprocessors
and their ability to operate in conjunction with power electronic
devices have opened up an era of high power quality. Consequently, in this paper, we adopted a digital signal controller
(dsPIC30F4012) [30] to process the operation of MRAC for
APF. The main advantage of using a digital signal controller is
its flexibility when the parameters of the reference model are
modified and the enhanced performance of the APF. Moreover,
the complexity of the hardware circuit is greatly reduced by
using a digital controller.
Finally, a 1-kVA prototype was developed to demonstrate
the performance of the proposed APF with the MRAC approach. The experimental results show that this system can both
improve the PF and greatly reduce total harmonic distortion
(THD). This paper is organized as follows. Section I gives the
introduction. Section II contains a brief description and the
operation principle of the shunt APF. In Section III, the derivation of the dynamic model of the APF system is presented.
An adaptive control law for an APF, which uses Lyapunov’s
stability theory, is proposed in Section IV. The experimental
results are shown in Section V. Finally, Section VI gives the
conclusion.
II. O PERATION P RINCIPLE OF THE S HUNT APF
The power stage of a shunt power filter needs to pass bidirectional current, and it is typically composed of a full or half
bridge with an energy storage capacitor at the dc side. In this
paper, an H-bridge is adopted for the power stage structure of
the APF, as shown in Fig. 1. As shown in Fig. 1, the H-bridge
is in parallel with a nonlinear load. The H-bridge circuit is the
same as a single phase of voltage-source inverter (VSI) while
working as an APF [or as a pulsewidth modulation (PWM)
rectifier]. The APF system that is connected in parallel with the
load could cancel the harmonic/reactive components in the line
current (iS ) so that the current flow into and from the power
Bipolar switching pattern and switching states of the H-bridge.
line is sinusoidal and in phase with the power line voltage. In
other words, the compensating current (iL ) is injected into the
line to force the line current (iS ) to become sinusoidal and to
achieve a unity PF for the APF system. The currents of the APF
system can be expressed as
iS = iO + iL
(1)
where iO is the nonlinear load current.
In this paper, the H-bridge operates in a bipolar PWM mode.
Fig. 2 shows the bipolar switching states of four switches in
the H-bridge. In Fig. 2, the two switch legs are complementary
switching states. In addition, the operation of the APF can be
divided into two modes, and its four switches have a switching
frequency of fS . In mode 1, Q2 and Q3 are turned ON, while Q1
and Q4 are turned OFF when 0 < t < DTS , where TS = 1/fS
is the switching period and D = TON /TS is the duty ratio.
In this mode, the inductor current iL increases in a positive
direction, and the magnetic energy is stored in the inductor L.
At the same time, the energy that is stored in capacitor C is
transferred to the line source and the assumptive load RL . In
mode 2, the switching states of four switches in mode 1 are
reversed when DTS < t < TS . Conversely, the energy that is
stored in L is transferred to C, RL , and the line source, and C
is accordingly charged. Fig. 3 shows their equivalent circuits,
related waveforms of the inductor current, and voltage in each
switching cycle.
To simplify the analysis, the following assumptions are derived: 1) the capacitance of C is sufficiently large so that νC
is nearly constant at one switching cycle; and 2) the switching
frequency fS is much higher than both the line frequency and
the frequency of the nonlinear load current [31]. By observing
the equivalent circuits that are shown in Fig. 3, one circuit
shows the inductor voltage and current during one switching
cycle when νS > 0, which are expressed by the following:

νL (t)= νS + νC

DT
S
for 0 ≤ t ≤ DTS (2)
1
iL (t) = iL (0) + L
(νS + νC )dt
0

νL (t)= νS − νC

T
S
for DTS ≤ t ≤ TS .
iL (t) = iL (DTS ) + L1
(νS − νC )dt
DTS
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SHYU et al.: MODEL REFERENCE ADAPTIVE CONTROL DESIGN FOR A SHUNT ACTIVE-POWER-FILTER SYSTEM
99
where n = 1 − 4 is denoted as the switch number of the VSI.
For the bipolar PWM scheme, the relationship between the high
and low side switches in the two switch legs can be expressed
by the following:
S 1 + S2 = 1
S3 + S4 = 1
.
(7)
Given the definition of Sn for each switch, the relation between
νx and νC can be expressed as
νx = [S1 − S2 ] · νC .
(8)
Accordingly, the capacitor current can be related to the inductor
current by the following:
iC + iR = [S1 − S2 ] · iL .
(9)
Therefore, the state equations of the inductor current and the
capacitor voltage are written by Kirchhoff’s laws
1
[νS − SνC ]
L
1
νC
ν̇C =
SiL −
C
RL
i̇L =
Fig. 3. Equivalent circuit, inductor current, and voltage waveforms in each
switching cycle of the APF. (a) Equivalent circuit when 0 ≤ t ≤ DTS .
(b) Equivalent circuit when DTS ≤ t ≤ TS . (c) Inductor current and voltage
waveforms.
Similar results can be obtained when νS < 0. Because the
switching frequency is sufficiently high, the load current is
almost unchanged at one switching cycle. Therefore, the initial
and peak values of the inductor current are equal to those of the
next switching interval. As shown in the volt–second balance
of inductors at one switching cycle, the average of the inductor
voltage is given by the following:
(νS + νC )DTS + (νS − νC )(1 − D)TS = 0.
(4)
It implies that
νC =
νS
.
1 − 2D
1
x1 (t) =
TS
A single-phase APF has two reactive elements because its
output voltage is higher than its input voltage; otherwise, it is
not possible to return energy from the capacitor to the load.
Consequently, in a bipolar operation mode, an H-bridge APF
represents an absolute boost converter, with a possibility of
returning energy.
To design an APF system, its dynamical model must first be
given. This section develops a model for the VSI that is used as
the APF. Fig. 3(a) and (b) shows the equivalent circuits of the
VSI at one switching cycle. Define the switching function Sn
of each VSI switch as
1 when Qn is turned ON
(6)
Sn =
0 when Qn is turned OFF
(11)
where S = (S1 − S2 ). Dynamical equations (10) and (11) are
hard to directly control because the switching function is a two
state (ON–OFF) function. This drawback could be removed if
the dynamical equations are converted into an average model
during a switching cycle.
The average model can be written by time weighing and
averaging the rate of change of the inductor current and capacitor voltages during the ON and OFF states, which are expressed by substituting S = −1 and S = 1 into the above state
equations, respectively. In the following expressions, x1 (t) and
x2 (t) represent the state variables of the average values of the
inductor current and the capacitor voltage over a switching
period, respectively. This is represented as follows:
(5)
III. D YNAMIC M ODEL OF THE APF
(10)
1
x2 (t) =
TS
t+TS
iL (τ )dτ
(12)
t
t+TS
νC (τ )dτ.
(13)
t
The average state-space model of the converter can be
written as
dx1
=
dt
νS + ν C
L
dx2
=
dt
−iL
νC
−
C
RC
·u+
νS − νC
L
·u+
· (1 − u)
iL
νC
−
C
RC
· (1 − u)
(14)
(15)
where u is the duty ratio, which can take any value between
0 and 1. By rearranging (14) and (15), we can obtain [32] the
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 1, JANUARY 2008
following:
(2u − 1)x2
νS
dx1
=
+
dt
L
L
dx2
(1 − 2u)x1
x2
=
−
.
dt
C
RL C
(16)
(17)
Consequently, the dynamic behavior of the APF can be described by the following state-space model:
ẋ = F x + Gxu + Ew
(18)
−1 0
0 L2
L
where x = [iL νC ]T , F = 1
,
G
=
−1
−2
0
C
RL C
C
1
T
E = [ L 0] , and w = νS .
Now, consider the bilinear state equation (18). If x = x0 and
u = u0 suffice to f (x0 , u0 ) = F x0 + Gx0 u0 + Ew(t) = 0,
(x0 , u0 ) is called its equilibrium or operating point. As shown
in differential equations (16) and (17), the equilibrium values
of the inductor current and the capacitor voltage can be obtained as
νS
(1 − 2u0 )
x02
=
RL (1 − 2u0 )
x02 =
(19)
x01
(20)
Fig. 4.
Control block of the proposed MRAC approach.
TABLE I
EXPERIMENTAL PARAMETERS AND CONDITIONS
where x02 and x01 are the equilibrium values of νC and iL ,
respectively. The average value of the duty ratio u0 can be
obtained from (19) as [32]
u0 =
1
2
1−
νS
x02
.
(21)
To simplify a nonlinear system model, a common approach
is the linearization method. The following will show how the
bilinear APF system is linearized. To linearize the bilinear state
equation (18) about a constant equilibrium point (x0 , u0 ), let
0 = f (x0 , u0 , w, t) = F x0 + Gx0 u0 + Ew(t).
(22)
We can expand the right-hand side of (22) into a Taylor series
about (x0 , u0 ) and then neglect the high-order terms so that
ẋ ≈ f (x0 , u0 ) +
∂f
∂x
x=x0
u=u0
(x − x0 ) +
∂f
∂u
x=x0
u=u0
(u − u0 ).
(23)
Moreover, since our interest is on the trajectories near (x0 , u0 ),
we have the following:
xδ = x − x0 ,
uδ = u − u0 .
(24)
The bilinear state equation (18) is approximately described by
a linear state equation of the form
ẋδ = (F + Gu0 )xδ + (Gx0 )uδ ≡ Ap xδ + Bp uδ
(25)
where Ap = (F + Gu0 ) and Bp = Gx0 are the linear fits to the
nonlinear function f (x, u, w, t) at x0 and u0 .
IV. A DAPTIVE C ONTROLLER D ESIGN
In the following, the MRAC scheme with an adaptive control
for the APF is presented to improve the PF performance that is
subject to the change in nonlinear load. The control objective is
either to regulate the error states to zero or to drive the system
states to track the states of a reference model. The adaptive
control is used to adjust the controller parameters online, which
is based on a measured system response. Thus, we can define a
linear time-invariant reference model as
ẋr = Ar xr + Br r
(26)
where r ∈ R1 is the reference input, xr ∈ R2×1 is the state
vector of the reference model, and Ar ∈ R2×2 and Br ∈ R2×1
are the reference model system matrix. Let the tracking error be
e = xr − xδ .
(27)
The objective here is to find an adaptive law so that the tracking
error e approaches to zero. To achieve the control objective, the
output of the adaptive controller is inferred by the system model
(25) as
r
uδ = [ θf θb ] ·
xδ
≡Θ · Z
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SHYU et al.: MODEL REFERENCE ADAPTIVE CONTROL DESIGN FOR A SHUNT ACTIVE-POWER-FILTER SYSTEM
Fig. 5.
101
Overall hardware structure of the MRAC-APF.
where θf (t) and θb (t) = [ θb1 (t) θb2 (t) ] are the feedforward
and feedback gains of the closed-loop system, respectively. By
substituting (28) into (25), we have the following:
ẋδ = (Ap + Bp θb )xδ + (Bp θf )r.
(29)
If the feedforward gain θf (t) and the feedback gain θb (t)
converge, the optimal parameters θf∗ and θb∗ are adjusted by the
adaptive controller so that the plant model matches with the
reference model, satisfying
Bp θf∗ = Br
Ap + Bp θb∗ = Ar
.
(30)
By differentiating (27) with respect to time and by combining
it with (26)–(30), we have the following:
ė = Ar e +
(Bp θb∗
− Bp θb ) xδ +
Bp θf∗
≡ Ar e + Bp ΦZ

Γ1
− Bp θf r
(31)
where Φ = [φ ϕ], in which φ = θf∗ − θf (t) and ϕ = θb∗ −
θb (t) define the parameter errors.
Consider the following Lyapunov function, which is the
candidate for system (31), as
1
V = [eT P e + trΦΓ−1 ΦT ]
2
Fig. 6. Prototype of the MRAC-APF.

where Γ = 
···
..
.
..
.
..
.

0

T
1×1

>0
· · · , in which Γ1 = Γ1 ∈ R
0
Γ2
2×2
and Γ2 = ΓT
∈
R
>
0 are positive-definite symmetric ma2
trices. Because Ar is a Hurwitz stable matrix, there exists
a unique positive-definite symmetric matrix P ∈ R2×2 that
satisfies the following:
AT
r P + P Ar = −Q
(32)
where Q = QT ∈ R2×2 > 0 is positive-definite [29].
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Fig. 7. Experimental results of the PI-APF under step changes in the nonlinear load. (a) Load changes: 200 → 600 → 200 W. (b) Zoom in 200 → 600 W.
(c) Zoom in 600 → 200 W.
The derivative of V (t) along the trajectories of (31) is given
by the following:
1
V̇ = − eT Qe + Z T ΦT BpT P e + trΦ̇Γ−1 ΦT
2
(34)
or
1
V̇ = − eT Qe + trBpT P eZ T ΦT + trΦ̇Γ−1 ΦT .
2
(35)
Accordingly, let
Φ̇ = −BpT P eZ T Γ
(36)
i.e.,
φ̇ = −BpT P erT Γ1
ϕ̇ = −BpT P exT
δ Γ2
.
(37)
Substituting (36) into (37) yields the following:
1
V̇ (t) = − eT Qe ≤ 0.
2
(38)
The aforementioned equation only ensures that V̇ (t) is always
negative, and for all initial conditions, e is bounded. Since
V̇ (t) ≤ 0, V (t) is monotonically nonincreasing and bounded.
Then, the integration of V̇ (t) yields e ∈ L2 . That is
∞
V̇ (t)dt = V (∞) − V (0)
0
(39)
and from (38)
1
−
2
∞
eQeT dt ≤ V (0)
(40)
0
since e is bounded, so that V (0) ∈ L∞ . According to Barbalat’s
lemma [29], e → 0 asymptotically as t → ∞. Therefore, we
can conclude that the system is asymptotically stable.
However, adaptive laws (37) cannot be implemented in
practice because they are not directly related to the control
parameters of (28). To make practical adaptive laws, take the
derivative of φ = θf∗ − θf (t) and ϕ = θb∗ − θb (t) so that they
will result in the following:
φ̇ = −θ̇f
.
(41)
ϕ̇ = −θ̇b
By comparing (37) with (41), we can have the following
parameter adaptive laws:
θ̇f = BpT P erT Γ1
.
(42)
θb = BpT P exT
δ Γ2
Fig. 4 shows the block diagram of the proposed MRAC-based
APF system.
V. E XPERIMENTAL V ERIFICATIONS
In this section, experimental results are provided to verify
the effectiveness of the MRAC schemes. The parameters of the
experiments are shown in Table I. To actually demonstrate the
performance of the proposed APF with the MRAC approach,
a 1-kVA prototype is developed. The equilibrium value of the
capacitor voltage x02 is a desired voltage of 250 V. Hence, we
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SHYU et al.: MODEL REFERENCE ADAPTIVE CONTROL DESIGN FOR A SHUNT ACTIVE-POWER-FILTER SYSTEM
103
Fig. 8. Experimental results of the MRAC-APF under step changes in the nonlinear load. (a) Load changes: 200 → 600 → 200 W. (b) Zoom in 200 → 600 W.
(c) Zoom in 600 → 200 W.
can get u0 = 0.19 and x01 = 0.04 A by using (20), (21), and
RL that is shown in Table I. By substituting u0 , x01 , and x02
into (25), we can obtain the following system parameters:
0
−103.33
83333.33
, Bp =
.
(43)
Ap =
620
−0.1
−80
With regard to the reference model, it is designed to have
desired system responses. Here, we have the rise time tR =
0.1 s = (1.8/ωn ), the undamped natural frequency ωn = 18,
and two distinct real root poles (overdamped). Hence, we
have the damping ratio ζ = 2.0 and the settling time tS ∼
=
(4.6/ζωn ) = 0.127 s [33]. In addition, we get the poles of the
reference model as −4.8231 and −67.1769. Accordingly, the
reference model can be obtained as
−72 −18
1
, Br =
.
(44)
Ar =
18
0
0
The positive-definite matrices P and Q are the following:
2.4533 0.0833
1 0
P =
,
Q=
.
(45)
0.0833 2.4474
0 1
Weighting scalar matrices of the adaptation laws are given as
0.000183
0
Γ1 = 0.000125,
Γ2 =
. (46)
0
0.000262
The overall hardware structure of the MRAC-APF is shown
in Fig. 5. Part number 2SK2837 of MOSFET devices and
FR604 fast recovery diodes are used for the H-bridge. A
dsPIC30F4012 digital signal controller is used to implement
the control algorithm. The laboratory prototype of the APF is
shown in Fig. 6.
Fig. 9. Measured voltage and current waveforms of the PI-APF in the steady
state. (a) During a load power of 200 W. (b) During a load power of 600 W.
Ch1: Line voltage νS . Ch2: Load current iO . Ch3: APF current iL . Ch4: Line
current iS .
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Fig. 11. Comparison of the compensation effects of the PI-APF and the
MRAC-APF. Current THD and PF before APF compensation are 85% and 0.65,
respectively.
Fig. 10. Measured voltage and current waveforms of the MRAC-APF in the
steady state. (a) During a load power of 200 W. (b) During a load power of
600 W. Ch1: Line voltage νS . Ch2: Load current iO . Ch3: APF current iL .
Ch4: Line current iS .
To verify the performances of the proposed APF, we use
the proportional-integral (PI) control instead of the MARC of
the system to have a comparison with the MRAC. The gains
of the PI controller are tuned first for a 200-W nonlinear
load in accordance with the criterion of the Ziegler–Nichols
tuning method, which tunes the gain values until the system
yields a better result [33]. Finally, the gains KP and KI are
tuned about 0.15 and 0.08, respectively. Figs. 7(a) and 8(a)
show the experimental results of the PI-APF and the MRACAPF under transient tests (step change in the nonlinear load:
200 → 600 → 200 W), respectively. As shown in Figs. 7(b)
and (c) and 8(b) and (c), although the line current waveforms
of both controllers are always sinusoidal even when subjected
to a changing nonlinear load, the line current waveforms of the
MRAC are smoother than that of the PI. Moreover, the line
current of the MRAC has no overshoot or undershoot at the
transient, as shown in Fig. 8(a). On the contrary, the line current
of the PI has some overshoots or undershoots in the transient
response, as shown in Fig. 7(a). However, no overshoot or
undershoot will ensure that the power devices will avoid the
danger that is caused by an exceeding surge current.
Fig. 9(a) and (b) shows the steady-state results of the PI-APF
for two nonlinear loads of 200 and 600 W. The line current
Fig. 12. Measured harmonics of the line currents of the PI-APF and the
MRAC-APF, which are compared with the EN61000-3-2 Class D regulation.
All load powers are about 600 W.
THDs dropped from 85% (without APF) to 7.3% (200 W) and
10.8% (600 W). The PFs are improved from 0.65 (without
APF) to 0.99 (200 W) and 0.98 (600 W). However, system
performance becomes worse if load changes. On the other hand,
the same experiments were performed, except that the proposed
MRAC controller is used instead of the PI one. Fig. 10(a) and
(b) shows the corresponding results as in Fig. 9(a) and (b).
The line current THDs dropped to about 8.3% (200 W) and
7.8% (600 W). In addition, both PFs are improved from 0.65
to 0.99 (200 and 600 W). Fig. 11 shows the comparison of
the compensation effects for both the PI-APF and MRAC-APF.
Consequently, PI control gains are turned for a fixed load to get
the best response. When the load changes, the gains of the PI
controller cannot ensure that the system has the same response
due to the lack of adaptability. However, in MRAC systems,
a considerable flexibility is granted to the designer to alter the
goals by modifying the reference model, and the MRAC can
self-tune the controller gains to assure system stability. Moreover, the robustness of the MRAC-APF can be verified by the
compared experiments. Fig. 12 shows the comparison of the PI
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SHYU et al.: MODEL REFERENCE ADAPTIVE CONTROL DESIGN FOR A SHUNT ACTIVE-POWER-FILTER SYSTEM
current harmonics, the MRAC, and the EN61000-3-2 Class D
regulation.
VI. C ONCLUSION
This paper proposes a single-phase MRAC-controlled shunt
APF. The MRAC approach improves many failures of the
fixed-gain PI controller, such as undesirable overshoots and
undershoots at the transient and nonrobustness when changing
loads. The proposed MRAC adaptive law is designed using
Lyapunov’s stability theory and Barbalat’s lemma. It guarantees
asymptotic output tracking. Furthermore, a prototype system
was built to show effectiveness and to verify the performance
of the system. Experimental results have demonstrated that the
proposed approach effectively eliminates the reactive and harmonic components of the load current. Thus, PF is improved.
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Kuo-Kai Shyu (M’98) received the B.S. degree
from Tatung Institute of Technology, Taipei, Taiwan,
R.O.C., in 1979 and the M.S. and Ph.D. degrees
from the National Chung-Kung University, Tainan,
Taiwan, in 1984 and 1987, respectively, all in electrical engineering.
In 1988, he joined the National Central University,
Chung-Li, Taoyuan, Taiwan, where he is currently
a Professor and the Chairman of the Department
of Electrical Engineering. From 1988 to 1999, he
was a Visiting Scholar with the Electrical and Computer Engineering Department, Auburn University, Auburn, AL. His teaching
and research interests include variable structure control systems and signal
processing, with applications in motor control, power electronics, and medical
instruments.
Ming-Ji Yang was born in I-Lan, Taiwan, R.O.C.,
in 1974. He received the B.S. degree in electronic
engineering from the National Taiwan University of
Science and Technology, Taipei, Taiwan, in 1999.
He is currently working toward the Ph.D. degree in
electrical engineering at the Department of Electrical
Engineering, National Central University, Chung-Li,
Taoyuan, Taiwan.
He served for two years as an R&D Engineer
with the Riye Corporation, Taoyuan, from 2000 to
2002. His research interests include power quality
improvement, power electronics control, and electric vehicle design.
Mr. Yang received the Outstanding Research Graduate Students Award from
the National Central University in 2007.
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106
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 1, JANUARY 2008
Yen-Mo Chen was born in Changhua, Taiwan,
R.O.C., in 1981. He received the B.S. degree in
electrical engineering from Chung Yuan Christian
University, Taoyuan, Taiwan, in 2004 and the M.S.
degree in electrical engineering from the National
Central University, Chung-Li, Taoyuan, in 2006.
His research interests include active power filters, uninterruptible power supplies, and power
electronics.
Yi-Fei Lin was born in Taipei, Taiwan, R.O.C., in
1981. He received the B.S. degree in electrical engineering from the Technology and Science Institute
of Northern Taiwan, Taipei, in 2004 and the M.S.
degree in electrical engineering from the National
Central University, Chung-Li, Taoyuan, Taiwan,
in 2006.
His research interests include active power filters,
automatic voltage regulators, and power electronics.
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