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 LEONARDO RODRIGUES LIMONGI,
RADU BOJOI,
GIOVANNI GRIVA,
and ALBERTO TENCONI

Comparing the
Performance of
Digital Signal
Processor-Based
Current Controllers
for Three-Phase
Active Power Filters

© ARTVILLE

20 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009 Digital Object Identifier 10.1109/MIE.2009.931894 1932-4529/09/$25.00©2009IEEE
T
he wide use of nonlinear charged at a voltage higher than the For the case in which the reference
loads, such as front-end peak line-to-line voltage (to have currents are sinusoidal at the fun-
rectifiers connected to enough voltage margin to control damental frequency (as happens
the power distribution the currents that must be injected for pulse width modulation (PWM)
systems for dc supply at the PCC). Since the APF reference boost rectifiers, for example), the
or inverter-based ap- currents are not sinusoidal, obtain- PI control is usually implemented in
plications, causes sig- ing zero steady-state error is a chal- a rotating (synchronous) (d, q) ref-
nificant power quality degradation in lenging task. erence frame aligned with the PCC
power distribution networks in terms In addition, the load input induc- voltage vector. In this case, the ac-
of current/voltage harmonics, pow- tor (Figure 1) is usually designed for tual and the reference currents are
er factor, and resonance problems. a voltage drop of less than 5% of the dc signals for steady-state operation.
Passive LC filters (together with ca- mains voltage at rated current. As a For APFs, though, the fundamental
pacitor banks for reactive power com- consequence, for high-power loads, components of the reference current
pensation) are simple, low-cost, and
high-efficiency solutions. However,
their performance strongly depends
on the source impedance and can Since the performances of all the current controllers
lead to unwanted resonance phenom- are rather similar, choosing the best solution should
ena with the network [1]. In addition,
passive solutions are not effective for be strongly influenced by the ease of implementation
applications in which the nonlinear
and the execution time.
load exhibits fast transients.
During the last decade, the re-
duced cost and increased reliability the load currents have high di/dt (the active component to keep the
of power electronics and digital sig- values, requiring very high slope dc-link capacitor charged and the re-
nal processor (DSP) technology have variations of the reference currents. active component for reactive power
driven new interest in active filter- Thus, a key issue in APF control is the compensation) are dc values in the
ing. In the case there are nonlinear current-control strategy. (d, q) synchronous reference frame
current-source loads, the shunt ac- During the last two decades, dif- aligned with the PCC voltage vector,
tive power filter (APF) is considered ferent current-control solutions for but the reference components for
an effective solution for reducing the active power filters [6]–[22] have harmonic compensation are oscillat-
current harmonics for low to medium been reported in the literature. The ing components (far from dc signals)
power applications [1]–[5]. Active fil- use of proportional-integral (PI) con- [2]. Therefore, the PI control cannot
tering is advantageous where a fast trollers is a simple and well-known adequately track current references
response to dynamic load changes solution that is effective only if the and results in steady-state error
is required [5]. In addition, the shunt reference currents are dc signals. due to the finite controller gain. For
APF represents a versatile power-
conditioning tool since it is able to
compensate the load reactive power
and the load imbalances.
The basic compensation scheme i1 + ∑ i h Diode Rectifier
i1
for a plant with a current-type nonlin- h≠1

ear load using a shunt APF is shown PCC

in Figure 1. The APF is a three-phase dc
voltage-source inverter (VSI) that has Load
only a large capacitor on its dc link. Mains iAPF1
The inverter is connected to the load Nonlinear Load
at the point of common coupling (PCC)
∑ ih = idistortion
through an input inductor. h≠1
The APF operates as a controlled
current source generating the load
harmonic currents Sh21ih (Figure 1). +
As a result, the current drawn from Three-Phase C
Inverter
the mains at the PCC will be sinu-
soidal. The APF will need an active
fundamental current component
iAPF1 to keep its dc-link capacitor FIGURE 1 – Basic current harmonic compensation scheme of a nonlinear load using a shunt APF.

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 21

this reason, PI controllers are not (k 5 1, 2, . . .) of the fundamental prototype using the same switching
suitable for active power filters un- frequency [13]. If we consider the frequency and control tasks (except-
less the switching frequency is high fundamental frequency component ing current control). In the case of
enough to yield a satisfactory con- as a positive-type sequence, the cor- current-control solutions based on
troller bandwidth [2]. responding sequence representations selective harmonic compensation
High controller bandwidth is easily of the current harmonics in stationary schemes, the harmonics were compen-
achievable by using nonlinear regula- and synchronous reference frames sated up to the 25th harmonic of the
tors, such as hysteresis controllers are illustrated in Table 1. Thus, it is load current (1,250 Hz). The main crite-
[7]. The major drawback of this solu- possible to identify specific undesired ria for performance evaluation are the
tion, however, is that a variable switch- harmonic currents, which are inde- total harmonic distortion (THD) of the
ing frequency is obtained. A constant pendently compensated according to mains line current and the transient
switching frequency can be achieved a control scheme that has a modular performance for fast load variations.
with adaptive algorithms, but a digital structure depending on the preselect- In addition, the computational burden
implementation would require field- ed harmonics to be compensated [13]. and design complexity for a 16-b fixed-
programmable gate array (FPGA)- By comparing the performance of point DSP were also evaluated.
based digital systems. Here, we focus different digital, DSP-based current-
only on DSP-based solutions. control techniques for shunt APFs requir- PI-SRF Controller
The dead-beat (DB) schemes (some- ing high-performance current control This current control is implemented in a
times featuring predictive algorithms) in applications with fast transients, we (d, q) synchronous reference frame usu-
[9]–[12] operate with constant APF hoped to identify the most promising so- ally aligned with the PCC voltage vector.
switching frequency and are compu- lution for an industrial implementation. The basic scheme of the PI-SRF control-
tationally effective. Nevertheless, the The current-control schemes im- ler, shown in Figure 2(a), should include
DB schemes are quite sensitive to pa- plemented for the comparison were decoupling and feedforward terms to
rameter detuning and to the inverter the following: improve the controller performance
dead-time effects that must be properly ■ PI controller in a synchronous ref- [6] since the reference components for
compensated. erence frame (PI-SRF) [2] harmonic compensation are oscillating
On the other hand, the current- ■ DB controller implemented in a sta- components in a (d, q) synchronous
control solutions based on selective tionary reference frame [9]–[12] reference frame. Zero steady-state error
harmonic compensation schemes ■ PI controller in a synchronous ref- can be achieved only if the APF switch-
(also known as frequency-selective erence frame with multiple rotating ing frequency is high enough to yield a
schemes) [13] – [22] have proved integrators (PI-MRI) [14] satisfactory controller bandwidth [2].
to be very interesting in terms of ■ stationary frame controller with pro-
performance, with acceptable com- portional regulator and sinusoidal DB Controller
putational requirements for industrial signal integrators (P-SSI) [19] In a DB controller, the control algo-
applications using up-to-date fixed- ■ P-SSI controller with multiple SSIs rithm calculates the APF phase voltage
point DSPs [21]. These methods can in a synchronous reference frame command to cancel the current error
be applied when the harmonic spec- (P-SSI-SRF) [21] at the end of the following sampling pe-
trum of the distortion current idistortion ■ PI controller with resonant regu- riod [9]–[12]. The control algorithm,
(Figure 1) to be compensated consists lators (PI-RES) in a synchronous which ensures a DB response for the
of harmonics that have well-known reference frame [22] first-order system modeling on the APF
orders and sequences. When the load is ■ repetitive control [20]. input inductance LF, is [9]
supplied through a three-phase diode The current-control solutions were
or thyristor front-end rectifiers, these compared through simulations and n *F, ab 1 k 2 5 4nab 1 k21 2 22nab 1 k22 2
harmonics are of order h 5 6k 6 1 experimental tests for a 25-kVA APF
2 n *F, ab 1 k21 2 1
LF
Ts
3 3 3i *F, ab 1 k21 2
TABLE 1—CURRENT HARMONICS FOR THREE-PHASE RECTIFIERS.
HARMONIC IN (a, b) HARMONIC ORDER IN (d, q) 2 2i *F, ab 1 k22 2 2iF, ab 1 k21 2 4
STATIONARY REFERENCE SYNCHRONOUS REFERENCE FRAME (1)
FRAME SEQUENCE ROTATING AT FUNDAMENTAL FREQUENCY
1 (Fundamental) Positive dc
where k is the sampling instant and
5 Negative 6 Ts is the sampling period. The other
7 Positive 6 variables in this expression, repre-
.... .... .... sented in stationary (a, b) frame, are:
6 # k21 Negative 6#k the inverter output reference voltage
components (y *F,ab), the PCC voltage
6 # k11 Positive 6#k
components (yab), the filter current

22 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009

 vαβ kp
∗ ∗
iF,αβ vF,αβ
kp
e–jϑ e–jϑ ki ∑
+ e jϑ
∗ ∗
vF,αβ s
iF,αβ + –
ki
e–jϑ ∑ ∑ e jϑ ki6+
– s iF,αβ e–j6ϑ e j6ϑ
s
iF,αβ
ki6− ∗
e–jϑ x εF,dq e j6ϑ e–j6ϑ vharm,dq
–jω1Ls s
∑
(a)
kih+
e–jhϑ e jhϑ
s
kp
kih−
e jhϑ e–jhϑ
∗
εF, αβ ∗
vF,αβ s
iF,αβ
2ki1s
∑
+ s 2 + ω21 (b)
–

kp
iF,αβ 2ki5s
s 2 + ω25 ∗
iF,αβ εF, αβ ∗
vF,αβ
2ki1s
∑
+ s 2 + ω21
–
iF,αβ 2ki6s
2kih s e–jϑ ∑ e jϑ
∑ s2 + ω26
s 2 + ω2h

εF,dq 2kih s
(c)
s2 + ω2h
∗
iF,αβ1+
(d)
e–jϑ PI
iF,αβ –
∗
vF,αβ ∗
kp6s 2 + ki6s ∗
iF,αβ + εF,αβ vF,αβ
2 ∑ e jϑ + +
∗ FDFT(z) kF
iF,αβh + s 2 + ω26 PI
e–jϑ – + –

iF,αβ – z −Na
εF,dq kphs 2 + kihs iF,αβ
2
s 2 + ω2h
(e) (f)

FIGURE 2 – Current controllers: (a) PI-SRF controller scheme, (b) PI-MRI controller with h = 6k (k = 1, 2, …), (c) P-SSI controller in stationary
reference frame with h = (6k ± 1), (k = 1, 2, ...), (d) P-SSI with multiple SSIs in synchronous reference frame with h = 6k, (k = 1, 2, ..), (e) PI-RES
controller scheme with h = 6k (k = 1, 2, ..), and (f) repetitive control scheme.

reference components (i *F,ab), and the frames rotating at (6k 6 1) v 1, vector). A PI controller is used for the
filter current components (iF,ab). The (k 5 1, 2, . . .) with proper sequence, i.e., fundamental current component regu-
main drawback of this method is relat- 25v1, 17v1, 211v1, 13v1, etc. [13]. If the lation to keep the APF dc-link capaci-
ed to the inaccuracy of the system pa- current reference generation is imple- tor charged and for reactive power
rameters. In addition, the inverter non- mented in the synchronous reference compensation. In the case that there
linear operation, due to the dead-time frame (d, q) rotating at the fundamen- are unbalanced loads, a fundamental
effects, must be taken into account. tal frequency v1, it is more convenient negative sequence PI regulator [not
to use the integrators in multiple syn- present in Figure 2(b)] should be add-
PI-MRI Controller chronous reference frames rotating at ed. This frequency selective algorithm
If the current reference generation is 6hv1, (h 5 6k, k 5 1, 2, ...) [14] [Figure requires multiple rotational transfor-
implemented in a stationary reference 2(b)]. This array of integrators has as mations to individually compensate
frame, a possible solution for selective input the current error eF,dq obtained each harmonic. Due to the delay in-
harmonic compensation is to use pure in a (d, q) synchronous reference troduced by the sampling time, the
integrators operating in reference frame (aligned with the PCC voltage PI-MRI controller becomes unstable

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 23

 3 Bd 4 5
sin d
.c d , and d 5 v0Ts
for the harmonics of high order. For [19]. For the fundamental current com- 2ki
this reason, an additional compen- ponent, a P-SSI regulator tuned on the v0 cos d21
sation angle qch must be included in fundamental frequency is used. Its
the inverse rotational transformation main function is to control both the where Ts is the sampling time.
from the harmonic reference frame active current component needed to The delay caused by the sampling
back to the synchronous reference keep the dc-link capacitor charged at period causes SSI stability loss for
frame, as shown in Figure 3. Consider- a specified voltage and the reactive large values of the resonance frequen-
ing the experimental tests performed current component for reactive power cy v 0. For this reason, a delay compen-
for our comparison, best results are compensation. Unbalanced load com- sation scheme must be implemented.
obtained if the compensation angle pensation also can be implemented We have used the compensation
corresponds to two sampling periods [19] since SSI regulators are able to scheme described in [21]: According
Ts, i.e.,: deal with both positive and negative to (3)–(5), the regulator states x1 and
current sequence components. The x2 are sinusoidal in steady-state condi-
qch 5 2hv1 Ts, h 5 6k 1 k 5 1, 2, . . . 2 . block diagram used for one SSI in our tions, having the same amplitude and
(2) comparison is shown in Figure 4. The being phase-shifted by 90 electrical
state-space model that corresponds to degrees; for this reason, the compen-
Figure 4 is [21] sation of the computation delay can be
P-SSI Controller easily performed using the rotational
To eliminate the need of multiple transformation given by
rotating reference frames, a P- SSI Output of

cos 1 v0 # kTs 2
controller [Figure 2(c)] [17], [19] is εF,dq Other MRIs
∗
y 5 3C 4 # c d #c d
vharm,dq 0 x1
sin 1 v0 # kTs 2 x2
based on the SSI [19], which guaran- kih+
e–jhϑ e j(hϑ+ϑ ch ) ∑ 0
s
tees that the actual current tracks
kih− (6)
its sinusoidal reference (with zero e jhϑ e −j(hϑ+ϑ ch )
s
steady-state error) and is tuned on a
specified frequency v 0. In the contin- FIGURE 3 – Modified inverse rotational where k $ 1 is the number of sam-
uous time domain, the transfer func- transformation from harmonic frame to (d, q) pling intervals to be compensated.
synchronous reference frame for the PI-MRI
tion of a P-SSI controller is [19] Considering the experimental tests
controller.
performed for our comparison, best
results are obtained with k 5 2. Anoth-
5 HP 1 s 2 1HSSI 1 s 2
2kis u x1 y
HP2SSI 5 kp 1 2ki ∫ er discrete form for SSIs with two sam-
s 21v 20 + +
x2 pling time delay compensation can be
(3) ω0 −ω0
∫ found in [19]. The control scheme of
Figure 2(c) has the advantage of not
where kp is the proportional gain, ki FIGURE 4 – Block diagram for an SSI having requiring rotational transformations,
is the integral gain, and v 0 is the reso- v0 as resonant frequency. but many SSIs might be necessary to
nance frequency. Using SSI regulators reach the required THD performance,

3 x 4 5 3 A 4 # 3 x 41 3 B 4 # u
provides a number of advantages. d making digital implementations com-
■ There is zero steady-state error for c dt putationally heavier than with a
y 5 3C 4 # 3x 4
(4)
signals having the same frequency PI-MRI controller.
as v 0.
■ Multiple SSIs with different reso- where P-SSI-SRF Controller
nance frequencies can operate in Using the SSI property of operat-
3x 4 5 c 3A 4 5 c
v0
d, d,
parallel without interfering with x1 0 ing on both positive and negative
each other since an SSI acts as a res- x2 2v0 0 sequence signals, the P-SSI-SRF
onant filter, tuned on its resonance controller uses multiple SSI regula-
3B 4 5 c d, 3 C 4 5 3 1 0 4.
2ki
frequency v0. 0 tors, as shown in Figure 2(d). One
■ An SSI can operate with both posi- regulator, for the fundamental cur-
tive and negative sequence signals The discrete form of (4) is given as rent component, is implemented
since an SSI is equivalent to two in- follows: in the stationary reference frame.
tegrators rotating at ±v 0. The other regulators, for the cur-
Using the concept of frequency- 3 x 1 k11 2 4 5 3 Ad 4 # 3 x 1 k 2 4 1 3 Bd 4 # u 1 k 2 rent harmonics, are all implemented
b
selective compensation, a P-SSI con- y 1 k 2 5 x1 1 k 2 in a synchronous reference frame
troller for an APF [Figure 2(c)] uses (5) rotating at the fundamental fre-
multiple SSIs in a stationary reference quency [21] and are tuned at 6kv1,
3 Ad 4 5 c
cos d sin d
frame, tuned on selected current har- d, (k 5 1, 2, . . .). In fact, each SSI is
monics of order (6k 6 1), (k 5 1, 2, . . .) 2sin d cos d equivalent to two integrators rotating

24 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009

at 6hv1. This allows simultaneous
compensation of two current har-
monics with just one regulator and Ripple Filter
requires half the number of SSIs that
are needed with the P-SSI controller.
Implementations of P-SSI-SRF con- Vs
Ls PCC LL
trollers on a 16-b fixed-point DSP are dc
reported in [5] and [21]. Load

}
Mains Vabc iL,abc
PI-RES Controller 380 V Diode Rectifier
This solution [Figure 2(e)] is a deriva- 50 Hz
tion of the P-SSI-SRF controller and LF Control
Scheme
uses the same idea of the simultane-
ous compensation of two current har-
iF,abc Vdc
monics with one regulator. The PI-RES
employs resonant regulators that are
equivalent to two complex PI regula- SF,abc +
tors rotating at 6v 0 [22]. In the continu-
ous time domain, the transfer function
C
}
of these resonant regulators is
(a)
kp s 21ki s
HPI2RES 5 2 (7)
s 21v 20
Vdc Vabc (from PCC)
where kp is the proportional gain,
ki is the integral gain, and v 0 is the *
Vdc
DC Voltage abc
resonance frequency. In the PI-RES, Regulator αβ
the reference current i *F, ab has two
Vαβ iF,abc
components: i *F, ab1 for fundamental
frequency control and i *F, abh for har-
Voltage abc
monic control [22]. For fundamental *
id,1 Filter
and PLL αβ
frequency control, a PI with a decou-
pling scheme [not shown in Figure ϑ
iF,αβ
2(e)] is used. For the harmonic con-
trol, the parameters of each reso- * SF,abc
iL,abc Reference iF,αβ v*F,αβ *
vF,abc
nant controller are calculated using Current αβ
Current PWM
the pole-zero cancellation technique Generator Control abc
for each frequency of interest. Thus,
each resonant controller is equivalent (b)
to two PI controllers rotating at 6hv1
having decoupled d and q axes. This
results in an increase in the stability FIGURE 5 – APF scheme and control system: (a) APF test layout scheme and (b) block diagram
of the whole APF control system.
of the loop, avoiding delay compensa-
tion methods used for the previous
techniques [22]. function of this DFT, which allows the steps necessary to maintain the sys-
implementation of the repetitive con- tem stability [20]. Therefore, using
Repetitive Control trol with 100 taps for 10 kHz of switch- (8) makes it possible to implement all
This current-control strategy uses a ing frequency, is given by the SSI filters of Figure 2(c) using only
repetitive-based controller along with this DFT of N coefficients in which the
a simple P (or PI) controller, as shown number of compensated harmonics is
FDFT 1 z 2 5 a a a cosa N h 1 i1Na 2 b bz
2 N21 p 2i
in Figure 2(f). The repetitive control- independent of N. This DFT filter can
N i50 kPNh
ler uses a discrete Fourier transform also be seen as a finite impulse re-
(8)
(DFT), which has a frequency re- sponse (FIR) filter [20].
sponse approximately equal to the The structure of the repetitive
frequency response of the sum of SSIs where N is the number of taps, Nh is control is shown in Figure 2(f). This
used in the P-SSI control shown in Fig- the set of selected harmonic frequen- scheme was originally proposed in
ure 2(c) [20]. The discrete transfer cies, and Na is the number of leading [20] using a feedback loop detecting

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 25

 gives the reference currents for the
*
id,1 current control [20].
+
iL,d id,h + *
iF,d
HPF *
iF,αβ
Overall System Description
iL,αβ The current-control strategies were
e–jϑ e jϑ
iL,q iq,h *
iF,q included in a digital control scheme
HPF for an APF that compensates the har-
+
- + * monics generated by a diode front-end
iq,1
kPF rectifier, as shown in Figure 5(a). The
+
ϑ quantities measured from the system
were: the load currents iL, abc, the APF
FIGURE 6 – APF reference current generation scheme. currents iF, abcs, the PCC line-to-line
voltages nabc, and the APF dc-link volt-
the harmonic current at the source ed from i *F, ab and iF, ab; after that, the age ndc. The current control block
side. In our comparison, the repetitive DFT defined in (8) is used for precise receives as inputs the APF reference
control is implemented using a feed- tracking of the selected frequencies. A and measured currents in the station-
forward loop detecting the harmonic delay of Na steps is then needed in the ary (a, b) reference frame, as well as
current at the load side. The difference feedback path to recover zero phase the position of the PCC voltage vector
between the two approaches does not shift of the loop (F DFT(z) * z–Na) at the computed by means of a phase-locked
change the performance of the cur- desired frequencies. Also, the parame- loop (PLL) scheme [21]. The block
rent control. Following the scheme of ter K F determines the controller speed diagram of the APF control scheme,
Figure 2(f), the error signal is calculat- response. The output of this scheme shown in Figure 5(b), contains two

100 1
20 ms
Supply Current

50 60 A
PI-SRF

0
A:MA(FFT(1)) 1
–50 .2 KHz
2.00 A
–100
0 5 10 15 20 25 30 35 40 45 50 55
100
Supply Current

50
Dead Beat

0 23rd 25th 29th

A
–50
1st
–100
0 5 10 15 20 25 30 35 40 45 50 55
Time (ms)
(a) (b)

1 1
20 ms 5 ms
60 A 60 A

1 1
2
5 ms
60 A

A:MA(FFT(1))
.2 KHz
2.00 A
2
29th
A
1st

(c) (d)

FIGURE 7 – Simulation and experimental results for PI-SRF and DB current controllers. (a) Simulation results. Mains current at steady-state opera-
tion for the APF using the PI-SRF and DB controllers. (b) Fourier analysis of the load current. (c) Fourier analysis of the mains current of the PI-SRF
controller. (d) Mains current and load current for steady-state operation of the PI-SRF controller. Trace 1: iSa (A). Trace 2: iLa (A).

26 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009

control loops: the dc voltage control ■ P-SSI: kp 5 1.4, ki1 5 200, ki5 5 150,
loop and the APF current control loop. TABLE 2—STEADY-STATE PERFORMANCE OF ki7 5 150, ki11 5 80, ki13 5 80, ki17 5
The dc voltage control loop is an outer CURRENT CONTROLLERS. 80, ki19 5 80, ki23 5 50, ki25 5 50
loop that uses a simple PI regulator, THD OF MAINS ■ P-SSI-SRF: kp 5 1.4, ki1 5 200, ki6 5
and its output is the active current CURRENT COMPUTED 150, ki12 5 80, ki18 5 80, ki24 5 50
CURRENT UP TO THE 50TH
reference needed to keep the dc-link CONTROL HARMONIC ■ PI-RES: kp 5 0.5, ki 5 200, kp6 5 0.2,
charged at the required value. The kp12 5 0.1, kp18 5 0.1, kp24 5 0.05, ki6 5
PI-MRI 2.51%
current control loop regulates the APF 20, ki12 5 10, ki18 5 10, ki24 5 5
P-SSI 2.59%
currents iF, ab using one of the current- ■ repetitive control: kp 5 1.4, ki1 5
control schemes we’ve presented. The P-SSI-SRF 2.57% 200, N 5 100, Na 5 3, k F 5 1.
APF current reference i *F, ab is com- PI-RES 2.59% It is important to note that all pa-
puted from the load currents iL, abc and Repetitive 2.42% rameters were set to be equivalent
from the output of the dc-link regulator to guarantee a fair comparison. For
i *d, 1, as shown in Figure 5(b). The ref- of the insulated gate bipolar transis- example, all proportional gains are
erence generator scheme [21], shown tor (IGBT) inverter is set at 730 V. equal; in the case of PI-RES current
in Figure 6, is implemented in the The inverter interface inductance, L F , control, the equivalent proportional
(d, q) reference frame aligned with and the input load inductance, L L , are constant is 1 kp 1 Sh 2kph 2 . The same
the PCC voltage vector. The harmonics equal to 250 mH. The total estimated equivalence is also valid for the inte-
to be compensated are extracted by mains inductance, L S , is about 120 mH. gral gains of the multiple rotating inte-
means of high-pass filters. The funda- The whole APF control scheme [Figure grators and sinusoidal integrators.
mental reactive reference component 5(b)] is implemented on the dSPACE The source voltages for the ex-
i *q, 1 is computed from the dc value of DS1103 development board. To guar- perimental tests are balanced and dis-
the q–axis load current component by antee the same conditions for com- torted by the nonlinear load. It must
means of the gain kPF, according to the parison, this scheme was used for all be emphasized that the influence of
desired power factor compensation the current-control techniques previ- the source voltages is important for
strategy. This reference current gen- ously described. Also, all the control the detection of the PCC voltage vec-
erator is described in detail in [21]. strategies were implemented with the tor position q, with direct influence
same switching frequency, and the on the current reference computa-
Simulation and harmonics for frequency- selective tion. The PLL used for the experi-
Experimental Results techniques were compensated up to mental tests is described in detail in
We compared the current-control the 25th load current harmonic (1,250 [21]. It is able to obtain a smooth PCC
solutions we’ve presented using Hz). The parameters of all the current- voltage vector position even under
simulations and experimental tests on control schemes tested were highly distorted PCC voltages [5], so
a 25-kVA APF prototype [Figure 5(a)] ■ PI-SRF: kp 5 1.4, ki 5 4,000 the current- control schemes should
compensating a 50-kVA nonlinear ■ PI-MRI: kp 5 1.4, ki 5 200, ki61 5 150, practically not be influenced by the
load. The APF switching frequency is ki6− 51 50, ki121 5 80, ki12− 5 80, ki181 5 PCC voltage distortion, making their
10 kHz. The dc-link reference voltage 80, ki18− 5 80, ki241 5 50, ki24− 5 50 comparison easier.

1 2
20 ms 5 ms
60 A 60 A
1
A:MA(FFT(1)) 1 1
.2 KHz 5 ms
2.00 A 60 A

2
29th
A
1st

(a) (b)

FIGURE 8 – Experimental results for the PI-MRI controller: (a) Fourier analysis of the mains current and (b) Mains current and load current for
steady-state operation. Trace 1: iSa (A). Trace 2: iLa (A).

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 27

 2 2 2
10 ms 10 ms 10 ms
60 A 1 60 A 1 60 A 1
1 1 1
10 ms 10 ms 10 ms
60 A 60 A 60 A

2 2 2

(a) (b) (c)

2 2 2
10 ms 10 ms 10 ms
60 A 1 60 A 1 60 A 1
1 1 1
10 ms 10 ms 10 ms
60 A 60 A 60 A

2 2 2

(d) (e) (f)

2 2 2
10 ms 10 ms 10 ms
60 A 1 60 A 1 60 A 1
1 1 1
10 ms 10 ms 10 ms
60 A 60 A 60 A

2 2 2

(g) (h) (i)

2
10 ms
60 A
1
1
10 ms
60 A

(j)

FIGURE 9 – Transient experimental results for all current controls based on selective harmonic compensation techniques. (a) APF transient
performance for PI-MRI control during a load turn-on, Trace 1: iSa (A) and Trace 2: iLa (A). (b) APF transient performance for PI-MRI control when
the harmonic compensation is enabled, Trace 1: iSa (A) and Trace 2: iFa (A). (c) APF transient performance for P-SSI control during a load turn-on,
Trace 1: iSa (A) and Trace 2: iLa (A). (d) APF transient performance for P-SSI control when the harmonic compensation is enabled, Trace 1: iSa (A)
and Trace 2: iFa (A). (e) APF transient performance for P-SSI-SRF control during a load turn-on, Trace 1: iSa (A) and Trace 2: iLa (A). (f) APF transient
performance for P-SSI-SRF control when the harmonic compensation is enabled, Trace 1: iSa (A) and Trace 2: iFa (A). (g) APF transient performance
for PI-RES control during a load turn-on, Trace 1: iSa (A) and Trace 2: iLa (A). (h) APF transient performance for PI-RES control when the harmonic
compensation is enabled, Trace 1: iSa (A) and Trace 2: iFa (A). (i) APF transient performance for repetitive control during a load turn-on, Trace 1: iSa
(A)and Trace 2: iLa (A). (j) APF transient performance for repetitive control when the harmonic compensation is enabled, Trace 1: iSa (A) and Trace
2: iFa (A).

Steady-State THD Performance tions about both techniques. Addition- simulation result and confirms that
Some simulations have been performed ally, the experimental steady-state per- the performance of PI-SRF and DB
to show the steady-state results of PI- formance of the PI-SRF can be evaluated current controllers is inferior to the
SRF and DB current controllers [Figure in Figure 7(b)–(d). This experimental performance of current controls based
7(a)]. The results confirm our expecta- performance corresponds with the on selective harmonic compensation.

28 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009

 60 60
1 1
40 2 40 2
20 20
0 0
–20 –20
–40 –40
–60 –60
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80
60 60
40 3 40 3
20 20
0 0
–20 –20
–40 –40
–60 –60
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80
Time (ms) Time (ms)
(a) (b)

60 60
1 1
40 2 40 2
20 20
0 0
–20 –20
–40 –40
–60 –60
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80
60 60
3 3
40 40
20 20
0 0
–20 –20
–40 –40
–60 –60
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80
Time (ms) Time (ms)
(c) (d)

60
1
40 2
20
0
–20
–40
–60
0 10 20 30 40 50 60 70 80
60
3
40
20
0
–20
–40
–60
0 10 20 30 40 50 60 70 80
Time (ms)
(e)

FIGURE 10 – Additional transient waveforms when harmonic compensation is enabled. (a) MRI control for a axis when harmonic compensation
is enabled: 1) i*Fa (A), 2) iFa (A), and 3) PFa (A). (b) P-SSI control for a axis when harmonic compensation is enabled: 1) i*Fa (A), 2) iFa (A), and 3) PFa
(A). (c) P-SSI-SRF control for a axis when harmonic compensation is enabled: 1) i*Fa (A), 2) iFa (A), and 3) PFa (A). (d) PI-RES control for a axis when
harmonic compensation is enabled: 1) i*Fa (A), 2) iFa (A), and 3) PFa (A). (e) Repetitive current control for a axis when harmonic compensation is
enabled: 1) i*Fa (A), 2) iFa (A), and 3) PFa (A).

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 29

 are more attractive in terms of design
TABLE 3—EXECUTION TIME. complexity since they are implement-
ed using the well-known FIR filter
CURRENT EXECUTION TIME EXECUTION TIME
CONTROL (WHOLE CONTROL) (CURRENT CONTROL) structures and integrators, respec-
PI-MRI 85 ms 28 ms tively. In addition, the routines for
an integrator, rotational transforma-
P-SSI-SRF 67 ms 20 ms
tions, or FIR filters can be easily im-
Repetitive 96 ms 49 ms
plemented. Another important aspect
concerning the repetitive control is
The steady-state performances of all issues for industrial applications, have the smaller number of parameters to
the techniques based on selective har- also been compared. To compare the be tuned.
monic compensation are very similar, computational burden of the current
as shown by the THD results in Table 2. controllers, the PI-MRI scheme, the Conclusions
For this reason, only the steady-state P-SSI-SRF scheme, and the repetitive We have presented a performance
experimental results for the APF us- control scheme were implemented comparison of different DSP-based
ing the PI-MRI controller are shown in a 16-b fixed-point TMS320LF2407A current-control techniques for shunt
in Figure 8(a) and (b). All the current DSP, with a 40-MHz clock frequency. APFs requiring high-performance
controllers are stable and able to com- The execution times for these current- current control. The current- control
pensate up to the 25th harmonic. control schemes are shown in Table 3. solutions have been compared
A delay compensation method is Considering only the current-control through simulations and experimen-
required by the PI-MRI, P-SSI, P-SSI- execution time, the DSP takes 20 µs to tal tests on a 25-kVA APF employing
SRF, and repetitive control starting perform the P-SSI-SRF current-control the same switching frequency (10
from the 17th harmonic, while the PI- computation. Considering the PI-MRI kHz) and the same remaining control
RES controller is stable. and repetitive controls, the execution tasks. The current controllers based
time increases to 28 µs and 49 µs, re- on selective harmonic compensation
Transient Performance spectively. However, it is also impor- performed better than the PI-SRF
To evaluate the APF dynamic perfor- tant to consider the execution time and DB controllers. With the PI-MRI,
mance, two different tests have been for the whole control implementation P-SSI, P-SSI-SRF, and PI-RES, increas-
considered. In the first case, the APF is in the case of the PI-MRI control be- ing the number of compensated har-
operating, and the load is turned on and cause the computational burden is monics is possible but not justified,
off; in the second test, the load is run- highly affected by the increased com- due to the controller complexity
ning, and the APF control enables and plexity of the PLL algorithm. Consider- and computational burden. With the
disables only the current harmonic com- ing this scenario, the DSP execution repetitive control, this complexity
pensation. The APF transient response times for the P-SSI-SRF, PI-MRI, and does not change by increasing the
for all the current controls based on repetitive control are 67 ms, 85 ms, and number of compensated harmonics.
selective harmonic compensation tech- 96 ms, respectively, and the P-SSI-SRF And when compared with other fre-
niques is described in Figure 9(a) –(j). advantage increases. quency-selective techniques, the re-
As the load is initially disconnected from Regarding the execution time for petitive control has a smaller number
the PCC in the load turn-on test, the the P-SSI, it is intuitive that the com- of parameters to be tuned.
transient time of the current controllers plexity is more or less doubled when The main criteria for perform-
is affected by the reference generator compared with the P-SSI-SRF. In the ance evaluation are the THD of the
time response. In the second transient case of the PI-RES control, the com- mains line current and the transient
test, the reference generator is in steady- plexity is similar to that of the P-SSI- performance for fast load variations.
state operation, and the transient time SRF control. Considering the same Concerning THD evaluation, all the
is due only to the current-control op- number of compensated harmonics, frequency- selective techniques
eration. For all the controllers, the refer- the difference between these two cur- obtained good results with very
ence current, the actual current, and the rent controllers regards only the delay similar performance. All the current
current error for the a-axis are shown in compensation method. Considering controllers are stable and able to com-
Figure 10(a)–(e). Note that the slowest the case presented here, in which the pensate up to the 25th harmonic. A de-
response is that of the repetitive control- current controls compensate up to the lay compensation method is required
ler, while the other controllers provide 25th load current harmonic, the P-SSI- by the PI-MRI, P-SSI, P-SSI-SRF, and
similar transient performance. SRF needs two additional rotational the repetitive control starting with
transformations to perform the delay the 17th harmonic, while the PI-RES
Computational Burden compensation method for the pairs of controller does not need delay com-
and Design Complexity harmonics (17th, 19th and 23rd, 25th). pensation up to the 25th harmonic.
The ease of implementation and the For fixed-point DSPs, the repeti- The transient experimental tests
execution time, considered important tive and PI-MRI current controllers show that the repetitive controller

30 IEEE INDUSTRIAL ELECTRONICS MAGAZINE ■ MARCH 2009

has the slowest response, while the and power conditioning systems, and Conf. Rec. IEEE APEC, vol. 3, 2005, pp. 1674–
1679.
other controllers prov ide simila r he has published more than 40 papers [6] S. Buso, L. Malesani, and P. Mattavelli, “Com-
transient performance. in international journals and confer- parison of current control techniques for ac-
tive filter applications,” IEEE Trans. Ind. Elec-
Since the performances of all the ence proceedings. He is a Member of tron., vol. 45, no. 5, pp. 722–729, Oct. 1998.
current controllers are rather similar, the IEEE. [7] M. P. Kazmierkowski and L. Malesani, “Current
control techniques for three-phase voltage-
choosing the best solution should be Giovanni Griva received a mas- source PWM converters: A survey,” IEEE Trans.
strongly influenced by the ease of im- ter’s degree in electronic engineering Ind. Electron., vol. 45, no. 5, pp. 691–703, Oct.
1998.
plementation and the execution time. from the Politecnico di Torino in Italy [8] L. Malesani and P. Tomasin, “PWM current
In terms of fixed-point DSPs, the repet- in 1990, and he earned a doctorate in control techniques of voltage source convert-
ers—A survey,” in Conf. Rec. IEEE IECON, vol. 2,
itive and PI-MRI current controllers 1994. From 1995 through 2001, he was 1993, pp. 670–675.
appear to be more attractive since, as an assistant professor in the depart- [9] D. G. Holmes and D. A. Martin, “Implementa-
tion of direct digital predictive current con-
stated earlier, they are implemented ment of electrical engineering at the troller for single and three-phase voltage
using the well-known FIR filter struc- Politecnico di Torino. Since 2002, he source inverters,” in Conf. Rec. IEEE IAS, vol. 2,
1996, pp. 906–913.
tures and integrators, respectively. has been an associate professor at [10] L. Malesani, P. Mattavelli, and S. Buso, “Robust
Additionally, the routines for an inte- Politecnico di Torino. His research ac- dead-beat current control for PWM rectifiers
and active filters,” IEEE Trans. Ind. Applicat.,
grator, rotational transformations, or tivity has focused on the design and vol. 35, no. 3, pp. 613–620, May 1999.
FIR filters can be easily obtained. In development of advanced systems in [11] S. Buso, S. Fasolo, L. Malesani, and P. Mattavel-
li, “A dead-beat adaptive hysteresis current
terms of code generation and execu- the fields of power electronics, high- control,” IEEE Trans. Ind. Applicat., vol. 36, no.
tion time, however, the P-SSI-SRF and performance electric drives, digital 4, pp. 1360–1367, July 2000.
[12] S. Buso, L. Malesani, P. Mattavelli, and R. Ve-
PI-RES require less code, and they are control for industry applications, and ronese, “Design and fully digital control of
faster than the PI-MRI since they do power conditioning systems. He has parallel active filters for thyristor rectifiers,”
in Conf. Rec. IEEE IAS, vol. 2, Oct. 1997, pp.
not require multiple rotational trans- published more than 70 papers in in- 1360–1367.
formations [21]. The execution time ternational conference proceedings [13] M. Sonnenschein and M. Weinhold, “Compari-
son of time-domain and frequency-domain
of the repetitive controller is strongly and technical journals. He is a Mem- control schemes for shunt active filters,” in
influenced by the number of coeffi- ber of the IEEE. Conf Rec. ETEP, vol. 9, no. 1, pp. 5–16, Jan.
1999.
cients N used by the FIR filter [20]; the Alberto Tenconi received a mas- [14] M. Bojyup, P. Karlsson, M. Alakula, and L. Gert-
repetitive controller implemented in ter’s degree and doctorate in electri- mar, “A multiple rotating integrator controller
for active filters,” in Conf. Rec. EPE [CD-ROM],
our comparison has N 5 100, resulting cal engineering from the Politecnico 1999.
in an execution time higher than the di Torino in Italy in 1986 and 1990, re- [15] P. Mattavelli and P. Tenti, “High perfor-
mance active filters using selective har-
other controllers. spectively. From 1988 to 1993, he was monic control,” in Conf. Rec. IEEE Power
with the Electronic System Division Eng. Society Summer Meeting, vol. 2, July
2000, pp. 977–982.
Biographies of the FIAT Research Center. He then [16] P. Mattavelli, “A closed-loop selective har-
Leonardo Rodrigues Limongi re- joined the Department of Electrical monic compensation for active filters,” IEEE
Trans. Ind. Applicat., vol. 37, no. 1, pp. 81–89,
ceived bachelor’s and master’s degrees Engineering at the Politecnico di To- Feb. 2001.
in electrical engineering from Univer- rino, where he is currently an associ- [17] D. N. Zmood, D. G. Holmes, and G. Bode, “Fre-
quency domain analysis of three phase linear
sidade Federal de Pernambuco in ate professor. His fields of interest are current regulators,” IEEE Trans. Ind. Applicat.,
Brazil in 2004 and 2006, respectively. high-performance drive design and vol. 37, no. 2, pp. 601–610, Mar. 2001.
[18] D. N. Zmood and D. G. Holmes, “Stationary
He then joined the Department of new power electronic device applica- frame current regulation of PWM inverters
Electrical Engineering at the Politecnico tions, and he has published more than with zero steady-state error,” IEEE Trans.
Power Electron., vol. 18, no. 3, pp. 814–822, May
di Torino in Italy, where he is currently 80 papers in international journals 2003.
pursuing a doctorate. His scientific in- and international conference proceed- [19] X. Yuan, W. Merk, H. Stemmler, and J. Allmel-
ing, “Stationary-frame generalized integra-
terests include power electronics and ings. He is a Member of the IEEE. tors for current control of active power fil-
power conditioning systems. ters with zero steady-state error for current
harmonics of concern under unbalanced and
Radu Bojoi received a master’s de- References distorted operating conditions,” IEEE Trans.
gree in electrical engineering from the [1] S. Battacharya, D. M. Divan, and B. Bannerjee, Ind. Applicat., vol. 38, no. 2, pp. 523–532, Mar.
“Active filter solutions for utility interface,” in 2002.
Technical University “Gh. Asachi” of Conf. Rec. IEEE ISIE, vol. 1, 1995, pp. 53–63. [20] P. Mattavelli and F. P. Marafao, “Repetitive-
Iasi in Romania in 1993, and in 2003, he [2] S. Bhattacharya, T. M. Frank, D. M. Divan, and based control for selective harmonic com-
B. Banerjee, “Parallel active filter implementa- pensation in active power filters,” IEEE Trans.
earned a doctorate from the Politecnico tion and design issues for utility interface of Ind. Electron., vol. 51, no. 5, pp. 1018–1024, Oct.
di Torino in Italy. From 1994 to 1999, adjustable speed drive systems,” in Conf. Rec. 2004.
IEEE IAS’96, vol. 2, pp. 1032–1039. [21] R. Bojoi, G. Griva, V. Bostan, M. Guerriero,
he was an assistant professor in the [3] H. Akagi, “New trends in active filters for pow- F. Farina, and F. Profumo, “Current con-
Department of Electrical Drives and er conditioning,” IEEE Trans. Ind. Applicat., vol. trol strategy for power conditioners using
32, no. 6, pp. 1312–1322, Nov. 1996. sinusoidal signal integrators in synchro-
Industrial Automation at the Technical [4] M. Sonnenschein, M. Weinhold, and R. Zurows- nous reference frame,” IEEE Trans. Power
University of Iasi. In 2004, he joined the ki, “Shunt-connected power conditioner for Electron., vol. 20, no. 6, pp. 1402–1412,
improvement of power quality in distribution Nov. 2005.
Department of Electrical Engineering of networks,” in Conf. Rec. Harmonics and Quality [22] C. Lascu, L. Asiminoaei, I. Boldea, and F. Blaab-
the Politecnico di Torino as an assistant of Power (ICHQP VII), 1996, pp. 27–32. jerg, “High performance current controller for
[5] R. Bojoi, G. Griva, F. Profumo, M. Cesano, and selective harmonic compensation in active
professor. His expertise is in advanced L. Natale, “Shunt active power filter implemen- power filters,” IEEE Trans. Power Electron., vol.
control solutions for electrical drives tation for induction heating applications,” in 22, no. 5, pp. 1826–1835, 2007.

MARCH 2009 ■ IEEE INDUSTRIAL ELECTRONICS MAGAZINE 31