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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
A Three-Phase UPS That Complies
With the Standard IEC 62040-3
Fernando Botterón and Humberto Pinheiro
Abstract—This paper proposes a down-sampled discrete-time
internal-model-based controller in the synchronous reference
frame with a reduced number of poles. This controller is suitable for three-phase pulsewidth modulation inverters with output
transformer for double-conversion uninterruptible power supply
applications. It is demonstrated that the use of a down-sampled
rate and fewer poles in the internal model results in a number
of benefits, among which are the following: 1) improvement of
the transient response; 2) increase of the stability margin of
the closed-loop system; 3) a straightforward implementation in
fixed-point digital signal processor (DSP) and microcontroller
implementation as well as a reduction of the required memory space; and 4) a simple solution for the saturation of the
output transformer. As a result, it is possible to obtain output
voltages with reduced total harmonic distortion while ensuring
good transient performance for both linear and nonlinear loads.
To confirm the advantages claimed for the proposed synchronous reference dq frame internal-model-based controller and to
demonstrate the steady-state and transient performance under the
test conditions of the International Electrotechnical Commission
Standard 62040-3, the experimental results from a 10-kVA
space-vector-modulated three-phase inverter, which is fully controlled by a DSP TMS320F241, are presented.
Index Terms—Digital control, discrete-time control, internal
model principle, power transformers, uninterruptible power
systems (UPSs).
I. I NTRODUCTION
T
HE USE of uncontrolled rectifiers within critical loads,
e.g., in computers and medical equipment, requires uninterruptible power supplies (UPSs) that are capable of maintaining low total harmonic distortion (THD) at the output voltages
even under highly distorted load currents [1]. These types of
loads distort the UPS output voltages as a result of unbalanced
nonlinear currents drawn by them, thus causing voltage drops
across the output inductance–capacitance (LC) filter, which is
used to attenuate the pulsewidth-modulation (PWM) inverter
high-frequency harmonics. This becomes a concern in mediumand high-power UPS, where the switching frequency is low
to limit the switching losses. Other factors also contribute to
UPS output voltage distortion. Among them are the inherent
Manuscript received November 7, 2005; revised February 28, 2006. This
work was supported in part by CAPES and in part by CNPq.
F. Botterón is with the Departamento de Electrónica, Facultad de Ingeniería,
Universidad Nacional de Misiones, Obera 3360, Argentina (e-mail: botteron@
gmail.com).
H. Pinheiro is with the Power Electronics and Control Research Group,
Federal University of Santa Maria, Santa Maria 97105-900, Brazil (e-mail:
humberto@ctlab.ufsm.br).
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.2007.894782
nonlinearities of the PWM inverter, fluctuations of the dc
bus voltage, and power semiconductor voltage drops. Moreover, transformerless UPSs are susceptible to interference from
spikes and transients caused by assorted devices connected to
the utility grid. These interferences, transferred through the
UPS to the load, reduce the UPS output voltage quality. Thus,
UPSs with output transformer provide a safer and more robust
solution than transformerless UPSs since the transformer offers
a galvanic isolation to the load from undesirable disturbances
of the main supply [2].
In digitally controlled systems, quantization of the analogto-digital converters, digital PWMs, and roundoff resulting
from fixed-point arithmetic can generate errors that result in
a dc component at the inverter output voltage. These errors,
added to the inevitable nonideal features of real live circuit
implementation and amplified by an inappropriate selection
of the controller, can lead the output transformer to saturate,
degrading the overall performance of the system [13]–[15]. It is
important to point out that a standard such as the International
Electrotechnical Commission (IEC) 62040-3 recommends that
the output voltage dc component shall be less than 0.1% of
its root mean square (rms) rated value and specifies that the
distortion factor “D” of sinusoidal UPS output voltages must
to be less than 8%. To deal with these issues, many discretetime control structures for single-phase and three-phase UPSs
are reported in the literature.
With the well-known Repetitive Controller [4]–[6], which
is established on the internal model principle [3], several
high-performance approaches have been proposed to achieve
high-quality output voltages in three-phase and single-phase
PWM inverters [7]–[23]. Reference [7] proposes a discretetime control strategy using a repetitive controller extended
to a proportional–integral (PI) compensator structure in stationary αβ frame to compensate voltage distortions due to
nonlinear and unbalanced loads. The steady-state performance
is improved by using a 30th-order low-pass finite-impulse
response (FIR) filter after implementing the measures to attenuate the high-frequency components so that the voltage
error contains only lower frequencies. However, the proposal
referenced above presents a cancellation issue: the zero at
z = 1 (in the discrete-time domain) of the plant introduced
by the transformer cancels with the pole at z = 1 of the
repetitive controller, which violates the internal model principle
[3], as demonstrated in [15]. This problem may eventually
lead the transformer to saturation. In [9], the modified plugin repetitive controller combined with the conventional Onesampling-ahead preview compensator in stationary αβ frame
has been reported to improve the output voltage distortion when
0278-0046/$25.00 © 2007 IEEE
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
Fig. 1.
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Three-phase PWM inverter, ∆Y transformer, filter, and load.
three-phase rectifier loads are connected at the UPS output.
However, in this case, the output transformer is not considered.
Therefore, connecting an insulating transformer at the inverter
output, a pole–zero cancellation occurs with the plug-in repetitive controller in closed loop. In [10], the author proposes
a two-layer voltage controller scheme in synchronous frame
with a PI regulator to ensure zero steady-state error at the
fundamental frequency and a repetitive-based controller with a
high-pass filter to compensate for the harmonics at the inverter
output voltages. However, inadequate choices of the high-pass
filter cutoff frequency may result in dc components that can
saturate the transformer at the inverter output. Moreover, the
repetitive controller with a high-pass filter produces pole–zero
cancellation, which may lead to output transformer saturation.
Other solutions that are also based on the internal model
principle were presented in [11] and [12]. In [11], a threelayer control scheme is proposed. It consists of a proportional
compensator in stationary αβ frame, an integral controller in
synchronous frame to compensate the fundamental component,
and a selective harmonic compensator in stationary frame based
on a passband FIR filter with unit gain and zero phase at
the selected harmonics. Reference [12] proposes a robust controller based on the passivity theory framework for three-phase
UPS. This controller guarantees asymptotic stability with good
steady-state performance for nonlinear and unbalanced loads.
Although the controllers proposed in [11] and [12] may be adequate solutions for reducing distortion in output voltages and
for operating with an insulating transformer, the computational
requirements to implement them increase significantly with
the number of compensating harmonics. In addition, since the
controller coefficients are not integer numbers, this controller
is sensitive to quantization and roundoff errors, and as a result,
the tracking at selected harmonics is compromised. References
[18] and [19] propose a down-sampled repetitive controller in
synchronous frame with reduced number of poles, which only
compensate odd harmonics in stationary frame. This controller
gives reduced THD output voltages of a three-phase UPS. It
also makes it possible to solve the output transformer saturation; still more due to the slower sampling rate, it is not
necessary to include a zero-phase-shift low-pass FIR filter [6] to
improve the robustness of the closed-loop system. On the other
hand, [20] proposes an odd-harmonic digital repetitive plugin controller to reject these kinds of disturbances in stationary
frame. This odd-harmonic repetitive controller does not have
a pole at z = 1, so it is suitable for operating with an output
transformer. However, a low-pass FIR filter must be included
in the periodic signal generator loop to reduce the repetitive
frequency gains, and this consequently increases the closedloop system robustness. As a result, this filter compromises
tracking and disturbance rejection.
On the other hand, it is important to emphasize that few
papers explore the UPS transient behaviors. Moreover, few
papers explore the controller transient behaviors using the
discrete-time internal model principle. Hence, to obtain output
voltages with reduced THD and an improved load transient,
this paper proposes a down-sampled internal-model-based controller in synchronous reference frame with a reduced number
of poles. This internal-model-based controller acts together
with a proportional–derivative (PD) predictive compensator,
which has the function to stabilize the closed-loop system. This
compensator results in a simple form for digital implementation
and only requires the measure of the UPS output voltage [15],
[23]. The main feature of the proposed internal-model-based
controller is that it is a straightforward solution for output
transformer saturation. In addition, the reduced number of poles
of the proposed internal model in synchronous frame improves
the transient performance for linear and nonlinear loads as well
as enhancing the stability margin of the closed-loop system.
Thus, it is demonstrated that the transient performance with
the proposed controller can be improved by satisfying the
rigorous output dynamic performance classification 1 of the
standard IEC 62040-3, which classifies UPS by performance.
To demonstrate the advantages claimed, the proposed discretetime controller structure is digitally implemented in a 16-bit
fixed-point digital signal processor (DSP), and experimental
results in steady state and transient conditions from a 10-kVA
prototype are given.
II. S YSTEM D ESCRIPTION
A typical double-conversion UPS power circuit is shown in
Fig. 1. Among the three-phase inverter configurations, the one
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
shown is a strong candidate since: 1) it provides galvanic isolation to the load; 2) it allows the output voltage to be selected
according to customer needs; and 3) it provides a neutral by
the delta-star (∆Y) connection. The dc-bus voltage is almost
constant and supplied by a six-pulse three-phase uncontrolled
diode rectifier, which provides energy to the inverter in normal
operation mode. The dc-to-ac conversion is accomplished by
a space-vector-modulated three-phase three-leg inverter with
insulated-gate bipolar transistor. The high-frequency harmonics
introduced by the modulation are attenuated by the LC filter. It
is important to point out that the filter inductors are located at
the transformer primary side so as not to introduce distortions
in the output voltages that result from zero-sequence voltages
produced by unbalanced load currents, which will be shorted
on the delta connection at the transformer primary side [15].
Since this inverter is not capable of controlling zero-sequence
voltages, it is important to minimize the zero-sequence impedance to reduce the distortions in the output voltages. Hence,
the topology in Fig. 1 offers a degree of freedom to minimize
the zero sequence impedance.
III. T HREE -P HASE PWM I NVERTER , ∆Y T RANSFORMER ,
F ILTER , AND L OAD M ODEL
A. Stationary Frame Model
From the circuit in Fig. 1, the dynamic equations of the
inverter, transformer, filter, and load can be obtained by applying Kirchhoff’s laws. To simplify the system modeling, it
is considered that the leakage inductances of the primary and
secondary sides of the transformer are lumped at the secondary
side. The coil resistances are also neglected. The following
equations are then obtained:


M L
−L
−L

 2L+ M+Ld


d
u12

 d iab
ML
 
u23 =
2L+ M +Ld
−L
ibc 
 −L

d

dt
u31
ica
ML
−L
−L
2L+ M +Ld
d
 
van
M


+
(1)
vbn
M + Ld
vcn
 


 
ias
iab
vas
d 
M
1
d 



−
(2)
ibs =
i
vbs
bc
dt M + Ld dt
M + Ld
ics
ica
vcs
 
 
 
v̇an
i
i
1  as
1  oa


 v̇bn
= ibs − iob  .
(3)
C
C
v̇cn
ics
ioc
In these equations, M is the mutual inductance, L is the filter
inductance, Ld is the equivalent leakage inductance, and C is
the filter capacitance. In addition, u12 , u23 , and u31 are the line
, vbn
, and
to-line PWM voltages produced by the inverter; van
vcn , and ioa , iob , and ioc are the phase-to-neutral voltages and
load currents referred to the transformer primary side; and iab ,
ibc , and ica are the phase current in the delta connection.
B. Synchronous Reference Frame State-Space Model
Transforming (1)–(3) to αβ and then to synchronous frame
as in [25], using the linear transformations given in the
Appendix, the state-space model is given by ẋdq (t) =
Adq xdq (t) + Bdq udq + Fdq wdq , where the matrices Adq ,
Bdq , and Fdq are given as


0 −ω 0
0
−M/D
0
ω 0
0
0
0
−M/D 



0 0
0
−ω −(3L+M )/D
0


Adq = 

0 0
ω
0
0
−(3L+M )/D 



 0 0 1/C 0
0
−ω
0 0
0 1/C
ω


(M + Ld )/D
0

0
(M +Ld )/D 




M/D
0


Bdq = 



0
M/D




0
0
0
0


0
0
 0
0 


 0
0 


Fdq = 
.
 0
0 


 −1/C
0 
0
−1/C
0
(4)
The state vector has been selected as xdq (t) =
[idp iqp ids iqs vd vq ]T , and the input and disturbance
vectors as udq (t) = [ud uq ]T and wdq (t) = [iod ioq ]T ,
respectively. In these matrices, D is defined as D = 3LM +
3LLd + M Ld .
From (1), it is seen that the voltages applied at the transformer input are the line-to-line voltages produced by the
inverter. To avoid an additional transformation from line-toline to phase voltages that must be performed in the DSP, the
space vector modulation is accomplished using the line-to-line
voltages referred above.
C. Synchronous Reference Frame Discrete-Time Model
To obtain a discrete-time model for the discrete-time controller design, the synchronous frame state equation in the
continuous time domain obtained above is solved throughout a
sampling period T . For this purpose, it is considered that the
control action udq (t) remains constant in a sampling period
T . Thus, the discrete-time state-space equation of the plant
that takes into account the delay of a digital implementation is
given by
G H0
xdq (kT )
H1
xdq (k+1)T
=
+
udq (kT ).
udq_d (k+1)T
udq_d (kT )
0 0
I
(5)
In (5), the additional state variable udq_d represents the
delayed control action that models the real-time digital
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
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Fig. 2. Timing chart of DSP controller. Tpwm : switching period. T : sampling period and PD compensator computing period. Td : time delay. Tim : internalmodel-based controller computing period. Tim = 2T , and Td = T .
implementation delay, and the matrices G, H0 , and H1 are
given as
G = eAdq T
Adq Td
H0 = eAdq (T −Td ) A−1
− I)Bdq
dq (e
Adq (T −Td )
H1 = A−1
− I Bdq
dq e
(6)
where Td is the time delay mentioned above, which is related
to a given DSP implementation.
It is important to note that to obtain (5), the sampling of
the variables of interest and the updating of the control law
are performed as shown in the timing chart of Fig. 2. With
this sampling scheme, it is possible to use a low switching
frequency to limit the switching losses while preserving an
acceptable sampling frequency. Also, since sampling is carried
out at zero vectors, the resulting low-frequency harmonics over
the sampled data are reduced when compared with one sample
per sampling period [24].
Since the discrete-time controller proposed here is modeled
using an input–output approach, it is useful to obtain the
input–output description of the plant, which can be found from
(5), by applying the Z transform. Strictly speaking, since the
plant represented by (5) is multiple-input–multiple-output, it is
obtained a sampled transfer function matrix of the system, i.e.,
Gp (z) = Cdq (zI − Gdq )−1 Hdq + Ddq
where
(7)
Gdq
Hdq
Cdq
G H0
=
0
0
H1
=
I
= [ 02×4 I2×2
Ddq = [02×2 ] .
02×2 ]
(8)
In this case, the resulting sampled transfer function matrix
can be written as
g1 (z) g2 (z)
(9)
Gp (z) =
−g2 (z) g1 (z)
where the sampled transfer functions g1 (z) and g2 (z) are given
by the proper rational functions
g1 (z) =
b0 z 4 + b1 z 3 + b2 z 2 + b3 z + b 4
z 5 − a1 z 4 + a2 z 3 − a3 z 2 + a4 z
g2 (z) =
−c0 z 4 − c1 z 3 − c2 z 2 + c3 z + c4
.
z 5 − a1 z 4 + a2 z 3 − a3 z 2 + a4 z
(10)
Note that (9) shows that the system presents a cross coupling
given by the transfer functions g2 (z) and −g2 (z). In order
to simplify the controller design, is useful to work with a
single-input–single-output (SISO) system. It is shown that the
influence of the cross transfer functions is negligible, or in
another words, the system is weakly coupled. It is possible to
see in Fig. 3 that for a large variation in frequency, the transfer
function g2 (z) significantly attenuates the output vq when an
input signal in ud is applied or vice versa. Hence, the system can
be treated as a SISO control problem with a transfer function
given by g1 (z) without significantly affecting the closed-loop
performance.
In order to define a proper discrete-time voltage controller for
the plant described by g1 (z), upon the internal model principle
foundation, it is important to show the impact that the zeros of
the plant have in the selection of the controller structure. Fig. 4
shows the zeros of g1 (z).
Fig. 4 shows that this plant presents a pair of zeros at the fundamental frequency in synchronous frame, which is associated
with the insulating transformer. These zeros indicate that the
transformer does not transfer the dc component to its output.
This means that an inadequate selection of the discrete-time
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Fig. 3. Frequency responses of g1 (z) and g2 (z). T = 198.41 µs.
Fig. 5.
Fig. 4. Zero map of the input–output-sampled transfer function of the
plant g1 (z).
controller may produce a pole–zero cancellation, which causes
any residual dc component from the digital implementation
to be amplified, which in turn may lead the transformer to
saturate, as demonstrated in [15]. To avoid this problem, a new
discrete-time voltage controller in synchronous frame based on
the internal model principle, and adequate for the system in
Fig. 1, will be described in the next section.
IV. P ROPOSED D ISCRETE -T IME I NTERNAL -M ODEL -B ASED
C ONTROLLER IN S YNCHRONOUS R EFERENCE F RAME
This section develops the proposed discrete-time voltage
controller based on the internal model principle in synchronous
reference frame. Let us consider the design problem of a SISO
Discrete-time feedback SISO LTI system.
linear time-invariant (LTI) system in the discrete-time domain
shown in Fig. 5, where the strictly proper transfer function of
the plant is given by g1 (z). The problem is to design a controller
with a proper transfer function gc (z) so that the feedback
system is asymptotically stable and meets the specifications of
zero error tracking in steady state even with disturbance signals
present in the plant.
The design procedure, which was developed from the internal model principle theory presented in [15] for discrete-time
systems, can be summarized in two steps: 1) introduction of
1/φ(z), a model of the reference and disturbance signals inside
the loop, where φ(z) is the least common denominator of the
unstable poles of r(z) and w(z) and 2) stabilization of the
feedback system using a conventional compensator. It must be
emphasized that neither root of the internal model φ(z) must be
a zero of the transfer function of the plant so as to ensure the
exact cancellations of the unstable modes of the reference and
disturbance signals.
A. Proposed Internal Model
With the aim of defining an adequate internal model for the
plant g1 (z), five candidate internal models are presented below.
Fig. 6 shows the pole map of a discrete-time internal model
that is often used in conventional repetitive controllers [5].
When this internal model is implemented in stationary frame,
the pole at z = 1 is cancelled with the zero of the plant at
the same location. On the other hand, if this internal model
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
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Fig. 6. Pole map. Internal model of the conventional repetitive controller [5].
T = 198.41 µs, and 1/φ(z) = 1/(z N − 1).
Fig. 8. Pole map. Internal model with poles at even multiples of 60 Hz.
T = 198.41 µs, and 1/φdq (z) = 1/(z N/2 − 1).
Fig. 7. Pole map. Internal model with poles at odd multiples of 60 Hz.
T = 198.41 µs, and 1/φ(z) = 1/(z N/2 + 1).
Fig. 9. Pole map. Internal model with reduced number of poles.
T = 198.41 µs.
is implemented in synchronous frame, the same pole–zero
cancellation occurs at 60 Hz. So this particular internal model
is inappropriate for this application as demonstrated in the
experimental result of Fig. 20. It can be seen that the output
phase voltages have the desired levels with a low THD, but
the currents at the transformer primary side appear with a
significant offset, which increases continuously, shutting down
the PWM inverter as a result of overcurrents.
Fig. 7 shows a discrete internal model with poles at frequencies that are odd multiples of 60 Hz, while Fig. 8 presents an
internal model with poles at frequencies that are even multiples
of 60 Hz. These internal models have been employed in threephase UPS controllers [18], [19] as well as in an odd-harmonic
repetitive controller [20] for single-phase applications [21],
[22]. When the internal model in Fig. 8 is implemented in
synchronous frame, there is no pole–zero cancellation with the
plant. Similarly, the pole–zero cancellation is not a concern
for the internal model of Fig. 7 in stationary frame. On the
other hand, when operating with low switching frequencies, it
is desirable to keep the sampling frequency as high as possible
to improve the closed-loop performance. Usually, Tpwm = 2T .
In this case, the high gains of the poles close to the Nyquist
frequency may lead to system instability. In order to overcome
this limitation, a zero-phase-shift low-pass FIR filter can be
included [6] to improve the robustness at high frequencies.
However, this filter will increase the tracking error and compromise disturbance rejection.
Fig. 9, on the other hand, presents an internal model with a
reduced number of poles. In this case, the internal model has
been chosen to compensate the fundamental and the harmonics
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
Fig. 10. Internal model with reduced number of poles and roundoff error in
coefficients. T = 198.41 µs.
root of φdq (zim ) is a zero of the plant. Also, this proposed
internal model is computed with a reduced sampling rate. As
a result, the Nyquist frequency of the internal-model-based
controller is smaller than the first set of harmonics generated
by the switching operation of the PWM inverter, i.e., there are
no internal model poles in the model uncertainty region of the
plant. Note that this internal model results in a reduced computational effort controller without the roundoff error of the fixedpoint implementation since the coefficients of its polynomial
are integer numbers. Therefore, we propose here a discrete-time
control structure with a faster loop at a sampling period T to
keep a satisfactory sampling rate and a down-sampled internalmodel-based controller. This results in a multirate closed-loop
system, as presented in Fig. 12.
From the two-step design procedure presented at the beginning of this section, the proposed internal-model-based controller, which operate at a sampling period Tim = 2T , can be
included in the closed loop. To complete the internal-modelbased controller design, the numerator Nim (z) of the transfer
function Gim (z) shown in Fig. 12 must be selected. To avoid
compromising the simplicity of this controller being considd
. As
ered, this numerator can be selected as Nim (zim ) = kim zim
a result, the sampled transfer function of this controller can be
written as
Gim (zim ) =
Nim (zim )
,
φdq (zim )
N/2
where φdq (zim ) = zim −1.
(11)
In this transfer function, the controller gain kim determines
the convergence time of the voltage error to zero, and the parameter d is the time advance step size used to compensate the
closed-loop phase at high frequencies [23]. These parameters
must be chosen to ensure the asymptotic stability of the closed
loop and to meet a desired performance.
The next step is to design the conventional compensator
Gc (z) to stabilize the closed loop with the plant Gp (z) = g1 (z).
In this case, a predictive PD compensator has been selected
whose proper transfer function Gc (z) is given as
Gc (z) = k1 z −1 + k2 z −2 .
Fig. 11. Pole map of the proposed internal model in synchronous frame.
N = T1 /2 T , T1 = 1/60, T = 198.41 µs, Tim = 2T , and 1/φdq (zim ) =
N/2
1/(zim − 1).
from 2nd to 7th. Note that it is possible to include more poles
if desired. This internal model is adequate for the system in
Fig. 1 since it does not cancel the zeros of g1 (z). However, the
poles of this internal model are sensitive to roundoff errors in
the polynomial coefficients, which are a concern in fixed-point
arithmetic implementation. As a result, the pole location of
the internal model can be significantly modified, as illustrated
in Fig. 10.
Based on the internal models presented above, and having
considered them inadequate for the system in Fig. 1, we now
propose a suitable discrete-time internal model for the plant
g1 (z). The pole map of the proposed internal model in synchronous frame is shown in Fig. 11. This internal model has
half the poles of the internal model shown in Fig. 8, and no
(12)
This compensator has been selected mainly for its simple
structure, which only requires the measurement of the phase
to neutral output voltages. In addition, it provides a significant
phase and gain margin to the closed-loop system. The predictive
PD controller gains k1 and k2 are determined by placement
of the dominant poles of the closed-loop system [23]. It is
important to point out that the tandem connection of Gc (z)
with Gp (z) is completely characterized by the proper transfer
function Gc (z)Gp (z) since there is no pole–zero cancellation
between Gc (z) and Gp (z), as established in [15].
B. Stability Analysis
Since the closed-loop system operates with two different
sampling rates, the stability analysis can be performed in
two steps.
Step 1: The closed-loop stability of the tandem connection of
the plant with the PD compensator must be ensured. This faster
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
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Fig. 12. Control structure of the proposed closed-loop multirate SISO discrete-time voltage controller in synchronous frame for axis “d.” z = eT s , and
zim = eTim s .
Fig. 13. Closed-loop system. Tandem connection of the plant plus predictive PD compensator.
Fig. 15. Single-rate equivalent of the multirate closed-loop system with a
sampling period Tim .
Fig. 14. Nyquist plot of Gc (z)Gp (z). k1 = 0.12, k2 = −0.08, and T =
198.41 µs.
system in Fig. 12, we transform it to an equivalent system
sampled at slower rate Tim . As a result, the equivalent closedloop system becomes as that shown in Fig. 15.
The sampled transfer function of the equivalent slow-rate
plant GMF (zim ) can be found from the equivalent slow-rate
state-space representation of the plant and PD compensator,
which is given in the Appendix. This transfer function can be
expressed as
GMF (zim )
loop operates with a sampling period T , which results in the
control structure shown in Fig. 13.
To ensure the closed-loop asymptotic stability of the system represented in Fig. 13, the roots of the polynomial 1 +
Gc (z)Gp (z) = 0 must be inside the unit circle. To demonstrate
that this closed loop is stable, the Nyquist plot of the open-loop
transfer function Gc (z)Gp (z) can be used, as shown in Fig. 14.
It can be seen that the tandem connection of Gp (z) with Gc (z)
has a large gain margin, which in this case is about 16 dB, and
an infinite phase margin. Therefore, the closed-loop system in
Fig. 13 is asymptotically stable.
Step 2: This step is to ensure the overall stability when the
proposed internal-model-based controller (11) is introduced. To
extend the previous stability criteria to the multirate controller
=
6
5
4
3
2
− n1 zim
− n2 zim
+ n3 zim
− n4 zim
+ n5 zim
n0 zim
.
7
6
5
4
3
2
zim −d1 zim −d2 zim + d3 zim + d4 zim −d5 zim + d6 zim −d7
(13)
The closed-loop stability of the tandem connection of
Gim (zim ) with GMF (zim ) can be proved using the Nyquist
criterion plots of the open-loop transfer function, i.e.,
Gim (zim )GMF (zim ). Fig. 16 shows the Nyquist plot for
N = 42, kim = 1, and d = 1. It can be seen that the closed-loop
system with an internal-model-based controller remains stable
with a significant gain and phase margin.
To demonstrate the benefit of performing the proposed
discrete-time down-sampled internal-model-based controller,
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From Fig. 12, we can see that the control law applied to the
plant is given by
ud (kT ) = ucd (kT ) + uimd (mTim ).
Fig. 16. Nyquist plot of G(zim ) = Gim (zim )GMF (zim ). N = 42, and
Tim = 396.82 µs.
(16)
Note that (14)–(16) are written for the axis “d”; therefore,
similar equations can be written for the axis “q.” Regarding the
gain, kim must be selected to guarantee a fast convergence of
the voltage error to zero, maintaining the closed-loop system
stability. The values of kim and d are given in Table II. It
is important to emphasize here that simplicity is a significant
advantage of the proposed controller if compared with the
controller presented in [11]. It becomes clear by realizing that
the proposed internal-model-based controller implementation
is just (15). In fixed-point arithmetic, the quantization and
rounding errors may result in roots of the polynomial internal
model to be quite different from the desired one (see Fig. 10).
However, since the proposed internal-model-based controller
polynomial coefficients are 1s or 0s, the internal model roots
have low sensitivity to these errors. This is another advantage if
compared with the controllers of [11, eq. (9)] and [12, eq. (27)].
V. S TEADY -S TATE AND D YNAMIC O UTPUT V OLTAGE
C HARACTERISTICS OF THE UPS
The UPS output specifications according to IEC 62040-3
must have output voltage dynamic performance characteristics
not exceeding the limits in [1, Figs. 1, 2, or 3] for the application
of increasing/decreasing load steps under linear and reference
nonlinear load for the test conditions in Section 6.3 of this
standard. The objective of classifying UPS by performance is
to provide a common base on which all UPS manufacturer and
supplier data are to be compared. This enables purchasers of
equipment with similar UPS power ratings to compare products
from different manufacturers under the same measurement
conditions.
Fig. 17. Nyquist plot of the single-rate system operating at lower sampling
frequency. G(z) = Gim (z)Gp (z)/(1 + Gp (z)Gc (z)), N = 42, kim = 1,
d = 1, and T = 396.82 µs.
the Nyquist plot of the closed-loop system in Fig. 12, which operates with a single rate at lower sampling frequency, is shown
in Fig. 17. It can be seen that the gain margin stays almost
the same if compared with the gain margin in Fig. 16, but the
phase margin decreases significantly when the system operates
at a single rate. Therefore, the stability margin of the proposed
multirate system in Fig. 12 is significantly bigger than the
single-rate system at lower sampling frequency, which therefore
represents the benefit of the proposed multirate controller.
Concerning digital implementation, by applying the inverse
Z-transform to (12) and (11), we can obtain the respective recursive difference equations of the predictive PD controller and
the proposed down-sampled internal-model-based controller as
ucd (kT ) = k1 ed (k − 1) + k2 ed (k − 2)
(14)
uimd (mTim ) = kim ed [mTim − (N/2) + d]
+ uimd [mTim − (N/2)] .
(15)
A. Reference Nonlinear Load Steps in Normal Mode
Step nonlinear loading is defined as the application of the
test circuit, which is shown in Fig. 18, for dissipating the
required steady-state output active power for the percentage
load step relative to the rated steady-state output active power
of the UPS. The load circuit is then first deenergized before
application so that its capacitor voltage starts from zero voltage
when applied to the UPS output. To determine the UPS output
dynamic performance, the deviation from the under/overvoltage
limits defined [1] must be obtained. Then, using the test circuit
in Fig. 18, the required step loads (33% of the rated output
apparent power) must be applied or reduced in accordance
with those in [1, Section 6.3.8.5] monitoring the load capacitor
voltage. The capacitor voltage changes should remain within
the stated tolerances in [1, Figs. 1 or 2, Section 5.3.1]. In
Fig. 18, Uc is the rectified voltage, R1 is the load resistor set
to dissipate an active power equal to 66% of the total apparent
power, and Rs is a series line resistor set to dissipate an active
power equal to 4% of the total apparent power. The procedure
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
2129
TABLE I
SETUP PARAMETERS
Fig. 18. Reference nonlinear load test [1].
TABLE II
CONTROLLER PARAMETERS
Fig. 19. Resistive load test [1].
for calculating the passive elements of this reference nonlinear
load is described in [1, Annex E].
B. Linear Load Steps
With the UPS operating in normal mode, a resistive load
equal to 100% of the output active power must be applied in
two steps using the circuit in Fig. 19: one equal to 20% and one
equal to 80%. The step must be performed at the peak value of
the output waveform. Similarly, unloading must be measured
by reducing the load to 20% of the rated output active power by
switching off the 80% load. In both cases, the output waveform
must be observed and stored so as to permit calculation of any
dynamic performance deviation. This deviation is referred as
the rms value above or below the rated value, which is obtained
on a successive half-cycle by half-cycle. The computed values
of this dynamic deviation must remain within the stated limits
in [1, Figs. 1, 2, or 3, Section 5.3.1].
VI. E XPERIMENTAL R ESULTS
The circuit in Fig. 1 has been tested experimentally to
verify the proposed discrete-time-voltage internal-model-based
controller using a DSP TMS320F241 to control a 10-kVA
UPS. The steady-state load tests have been performed using
resistive linear loads and nonlinear single-phase and threephase uncontrolled diode rectifiers. The reference nonlinear
load, as described in Fig. 18 and designed according to the
standard IEC 62040-3, has an input series resistor Rs = 0.5 Ω,
Fig. 20. Experimental result. Line current ia at the transformer primary side
with dc component. With the internal model of the conventional repetitive
controller. Output phase-to-neutral voltages. Voltage scale: 50 V/div. Current
scale: 10 A/div. N = 84, and T = 198.41 µs. φ(z) is in Fig. 6.
a load resistor R1 = 30 Ω, and a filter capacitor Cc = 4700 µF,
and allow to obtain a crest factor of 3. The setup parameters
are given in Table I, and the controller parameters are given
in Table II.
A. Steady-State Performance
Fig. 20 shows the output phase voltages and the input current
at the transformer primary side with a significant dc component
when the system in Fig. 1 operates with an internal model
based on the conventional repetitive controller. This fact can
be proven through the harmonic spectrum presented in Fig. 21,
which denote a dc component around 140%. On the other
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Fig. 21. Transformer primary side line current harmonics spectrum with dc
component. With the internal model of the conventional repetitive controller.
Fig. 24. Experimental result. Unbalanced linear load. With the proposed controller. Output phase-to-neutral voltages van , vbn , and vcn , and
load current ia . THD = 0.7%. Unbalance factor = 0.6%. Voltage scale:
50 V/div. Current scale: 20 A/div.
Fig. 22. Experimental result. Line current ia at the transformer primary
side without dc component. With the proposed internal-model-based controller. Output phase-to-neutral voltages. Voltage scale: 50 V/div. Current scale:
10 A/div. N = 42. φ(z) is in Fig. 11.
Fig. 25. Experimental result. Open-loop operation. Three-phase uncontrolled
rectifier at 10 kVA. Output phase-to-neutral voltages van , vbn , and vcn , and
load current ia . THD = 7%. Voltage scale: 50 V/div. Current scale: 20 A/div.
Fig. 23. Transformer primary-side line current harmonics spectrum without
dc component. With the proposed internal-model-based controller.
side, Fig. 22 shows the same waveforms as Fig. 20 with the
system in Fig. 1 operating with the proposed internal-modelbased controller. It can be seen that this current appears without
offset, as demonstrated in the harmonic spectrum of this current
given in Fig. 23, where the dc component is less than 1%,
which can be attributed to sensor error. These tests validate that
the proposed internal-model-based controller does not produce
pole–zero cancellation and consequently does not saturate the
output transformer.
The performance of the proposed controller with linear load
has been tested using an unbalanced resistive rated load connected between a phase and a neutral wire; the experimental
result is shown in Fig. 24. It can be seen that the UPS output
voltages have a low THD as well as a reduced unbalance
factor. On the other hand, Figs. 25 and 26 show the threephase line-to-neutral voltages and the nonlinear load current
in phase a, which is drawn by three-phase and single-phase
uncontrolled rectifiers, when operating without the proposed
controller. It can be seen that the THD of the output voltages
is very high, around 7% and 10%, respectively. Figs. 27 and 28
show the operation of the proposed controller with the same
nonlinear loads. It is seen that with the proposed controller,
high-quality output voltages are obtained. Also, in Fig. 28, the
single-phase uncontrolled rectifier is connected between one
phase and neutral.
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
2131
This represents the worst case with the phase-rated unbalanced nonlinear load. It can be seen from these experimental
results that the THD of the output voltages is very low, which is
around 1%, even with this severe operational condition. Also,
with the proposed controller, the unbalance factor has been
reduced below 1%. The THDs of the UPS output voltages
presented in Figs. 24, 27, and 28 are well below the limits
of IEC 62040-3. In addition, the individual odd and even
harmonics does not exceed the limits of this standard, as shown
in Fig. 29 and Table III.
B. Transient Performance
Fig. 26. Experimental result. Open-loop operation. Single-phase uncontrolled
rectifier at 10 kVA. Output phase-to-neutral voltages van , vbn , and vcn ,
and load current ia . THD = 9.8%. Voltage scale: 50 V/div. Current scale:
50 A/div.
Fig. 27. Experimental result. With the proposed controller. Three-phase uncontrolled rectifier at 10 kVA. Output phase-to-neutral voltages van , vbn , and
vcn , and load current ia . THD = 0.8%. Voltage scale: 50 V/div. Current scale:
20 A/div.
Fig. 28. Experimental result. With the proposed controller. Unbalanced load.
Single-phase uncontrolled rectifier at 3.3 kVA. Output phase-to-neutral voltages van , vbn , and vcn , and load current ia . THD = 1.2%. Unbalance
factor = 0.92%. Voltage scale: 50 V/div. Current scale: 50 A/div.
To verify the transient performance of the UPS output, the
standardized tests described in Section 6.3.7 of the standard
IEC 62040-3 were performed, and the deviations from the
undervoltage and overvoltage limits defined in [1, Figs. 1, 2, or
3] were obtained, as described in Section VI, for nonlinear and
linear loads. Fig. 30 shows the dynamic deviation of the load
capacitor voltage of each phase of the reference nonlinear loads
(Fig. 18) at loading steps. On the other hand, Fig. 31 presents
the deviation of the load capacitor voltage due to the removal
of reference nonlinear loads. Figs. 30 and 31 demonstrate
that the proposed controller satisfies the voltage limits under
dynamic conditions not exceeding the undervoltage and overvoltage transient limits of classification 1. Figs. 32 and 33 show
the dynamic deviation of the output voltage rms value when
performing the linear load steps as described in Section VI.
These experimental results again demonstrate that the proposed
controller ensures that the dynamic deviation values do not
exceed the undervoltage and overvoltage transient limits of
classification 1 both in the load application and when it is
removed. Thus, this UPS is suitable for feeding most types
of critical loads with high-quality output voltages. The experimental results for loading and removal of the reference
nonlinear load are presented in the time domain in Figs. 34
and 35. Fig. 34 shows the reference nonlinear load step from
33% to 66%, while Fig. 35 shows the reference nonlinear
removal from 66% to 33%. It can be seen that the undershoot
and overshoot require no more than one fundamental period
before returning to the rated value. It is important to note that
the output voltage transient during the nonlinear load step is
a consequence of the fact that the large reference nonlinear
load capacitor Cc is uncharged when it is connected to the
UPS output. Even in this case, the minimum load rectifier
average output voltage value does not exceed the transient
limits imposed by classification 1 in [1]. This transient can be
reduced by increasing the inverter output current capability.
The experimental waveforms for the dynamic test with linear
load are presented in Figs. 36 and 37 to complement the
information given by Figs. 32 and 33. Fig. 36 shows the linear
load step from 20% to 80% of the rated output active power,
and Fig. 37 presents the unloading step from 80% to 20%.
VII. S UMMARY
This paper has proposed a new discrete-time down-sampled
internal-model-based controller in the synchronous reference
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Fig. 29. Levels for individual harmonics UPS output voltages with the proposed controller and IEC 62040-3.
TABLE III
LEVELS FOR INDIVIDUAL HARMONICS UPS OUTPUT VOLTAGES WITH THE PROPOSED CONTROLLER
Fig. 30. Output dynamic performance characteristics of the three-phase UPS. Step reference nonlinear loading from 33% to 66% and from 66% to full load.
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
Fig. 31. Output dynamic performance characteristics of the three-phase UPS. Step reference nonlinear removal from 100% to 66% and from 66% to 33%.
Fig. 32. Output dynamic performance characteristics of the three-phase UPS. Step linear loading from 20% to 80% rated active power load.
Fig. 33. Output dynamic performance characteristics of the three-phase UPS. Step linear removal from 80% to 20% rated active power load.
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
Fig. 34. Experimental result. Output phase-to-neutral voltage van . Reference
nonlinear load step from 33% to 66%. Voltage scale: 50 V/div. Current scale:
50 A/div.
Fig. 35. Experimental result. Output phase-to-neutral voltage van . Reference
nonlinear load removal from 66% to 33%. Voltage scale: 50 V/div. Current
scale: 50 A/div.
Fig. 37. Experimental result. Output phase-to-neutral voltage van . Linear
load step from 80% to 20%. Voltage scale: 50 V/div. Current scale:
50 A/div.
in a multirate system with the plant plus a PD compensator
to stabilize the closed loop in one sampling rate and the
internal-model-based controller with half of the former sampling frequency. This paper demonstrates that, by modifying the
order of the polynomial of the internal model in synchronous
frame, it is possible to ensure that the residual dc components
(in stationary abc frame) are not amplified, thus avoiding transformer saturation. In addition, it is not necessary to include a
zero-phase-shift low-pass FIR filter in the loop of the internalmodel-based controller. With regard to digital implementation,
the proposed discrete-time controller is an attractive solution
for fixed-point DSPs because it is easy to implement and has
low sensitivity to roundoff error. In addition, for DSP and
microcontrollers with reduced random access memory, this proposed internal model saves the memory space that is required
to store the voltage error in a circular buffer. Furthermore, the
predictive PD compensator that stabilizes the closed loop has
a straightforward design and only requires the measure of the
UPS output voltages. The experimental results presented in this
paper demonstrate that the steady-state output voltages have
high quality under both linear and nonlinear loads with a low
THD and a reduced imbalance factor for unbalanced loads.
In addition, the output voltage dynamic performance of the
three-phase UPS is found to be very good, meeting the severe
classification 1 of IEC 62040-3, for both linear and nonlinear
loads.
A PPENDIX
Fig. 36. Experimental result. Output phase-to-neutral voltage van . Linear
load step from 20% to 80%. Voltage scale: 50 V/div. Current scale: 50 A/div.
frame, which is adequate for three-phase three-leg PWM inverters that operate with an insulating transformer, for UPS
applications. The proposed discrete-time control system results
The linear transformation that converts the state variables
from the stationary abc to the stationary αβ0 frame, and from
αβ to dq synchronous frame, is given by


1
−1/2 −1/2
√
√
2

3/2 − 3/2 
Tabc_αβ0 =
 0
√
√
√
3
1/ 2 1/ 2 1/ 2
Tαβ _dq =
cos(ωt) sin(ωt)
.
− sin(ωt) cos(ωt)
(17)
BOTTERÓN AND PINHEIRO: THREE-PHASE UPS THAT COMPLIES WITH THE STANDARD IEC 62040-3
The real coefficients of the transfer functions in (10) are
given as
b0 = 0.2276
b1 = 0.7325
b3 = 0.2166
b4 = 0.03064
c0 = 0.01096
c1 = 0.111
c3 = 0.03678
c4 = 0.001553
a1 = 0.2007
b2 = 0.08777
xc (k + 1)T = Gc xc (kT ) + Hc ed (kT )
0 0
1
, Hc =
, and ed (kT ) is the sampled
where Gc =
1 0
0
voltage error of axis “d” given by
ed (kT ) = rd (kT ) − yd (kT ).
a4 = 0.09056.
n1 = 0.274
n2 = 0.0366
n5 = 2.99 × 10−5
n4 = 0.0010
d1 = 0.12
d2 = 0.103
d4 = 0.0037
d5 = 0.00079
d6 = 5.23 × 10−5
xp (k + 1)T = Gdq xp (kT ) +
(i,1)
Hdq ud (kT )
(18)
(i,1)
where Gdq is given in (8), and Hdq is the first column of the
Hdq matrix in (8), where i = 1, 2, . . . 8. The output of the plant
is given by
(1,j)
yd (kT ) = Cdq xp (kT )
xp (k + 2)T
=
(i,1)
ud (kT ) = Cc xc (kT ) + Dc ed (kT ) + uim (mTim )
(19)
(1,j)
G2dq − Hdq Cc Hc Cdq
(i,1)
(22)
where Cc = [k1 k2 ], Dc = 0, uim (mTim ) is the internalmodel-based control action at sampling rate Tim , and xc (kT ) =
[ed (k − 1) ed (k − 2)]T . In order to obtain an equivalent
slow-rate state-space representation of the plant plus a PD
compensator at 2T , we can write (18) and (20) as
xp (k + 2)T
xc (k + 2)T
Space-state representation of the single-rate equivalent
closed-loop system in Fig. 15.
Here, we describe the state-space representation of the
single-rate closed-loop system operating at sampling rate Tim ,
which has been used to obtain the sampled transfer function
GMF (zim ) in (13).
Consider the state-space equations of the plant and the PD
compensator, i.e.,
(21)
The control action can be written as
d3 = 0.012
d7 = 1.36 × 10−6 .
(20)
c2 = 0.008563
These coefficients have been obtained with a sampling rate of
T = 198.41 µs.
The real coefficients of the closed-loop transfer function GMF (zim ) in (13) obtained at 2T = 396.83 µs are the
following:
n3 = 0.013
(1,j)
where Cdq is the first row of the Cdq matrix in (8), and
j = 1, 2, . . . 8. The state variable representation of the PD is
given as
a2 = 0.5854
a3 = 0.06041
n0 = 1.01
2135
=
(i,1)
G2dq
Hdq Cc Gc
xp (kT )
(1,j)
xc (kT )
−Hc Cdq Gdq
G2c
(i,1)
(i,1)
Hdq Cc Hc
Gdq Hdq
+
(1,j) (i,1)
Gc Hc
−Hc Cdq Hdq
(i,1) ed (kT )
Hdq
rd (k + 1)
+
+
ud (kT )
Hc
(i,1)
Hdq
uim (mTim ).
+
(23)
0
Substituting (21) and (22) in (23), we find the equivalent
single-rate state-space representation of the system in Fig. 15,
i.e., (24) shown at the bottom of the page.
Finally, the sampled transfer function GMF (zim ) in (13) can
be obtained by applying the Z transform to (24), which leads to
GMF (zim ) = Csr (zim I − Gsr )−1 Hsr
where the matrix Csr = [01×4
(i,1)
Hdq Cc Gc + Gdq Hdq Cc
(25)
1 01×5 ].
xp (kT )
(1,j)
(1,j)
(1,j) (i,1)
xc (kT )
−Hc Cdq Gdq − Gc Hc Cdq
G2c − Hc Cdq Hdq Cc
(i,1)
(i,1) (i,1)
(i,1) (i,1) Hdq Cc Hc + Gdq Hdq
Hdq + Gdq Hdq
Hdq
+
rd (k) +
rd (k + 1) +
uim (mTim )
(1,j) (i,1)
(1,j) (i,1)
Hc
Gc Hc − Hc Cdq Hdq
−Hc Cdq Hdq
xp (k + 2)T
xp (kT )
(24)
= Gsr
+ Hr rd (k) + Hrr rd (k + 1) + Hsr uim (mTim )
xc (k + 2)T
xc (kT )
xc (k + 2)T
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
R EFERENCES
[1] Uninterruptible Power Systems (UPS)—Part 3: Method of Specifying the
Performance and Test Requirements, First Edition 1999–03, International
Standard IEC 62040-3.
[2] R. Koffler, “Transformer or transformerless UPS?” Power Eng. J., vol. 17,
no. 3, pp. 34–36, Jun./Jul. 2003.
[3] B. Francis, O. Sebakhy, and W. Wonham, “Synthesis of multivariable
regulators: The internal model principle,” Appl. Math. Optim., vol. 1,
no. 1, pp. 64–86, 1974.
[4] M. Tomizuka, “Zero phase error tracking algorithm for digital control,”
Trans. ASME, J. Dyn. Syst. Meas. Control, vol. 109, no. 1, pp. 65–68,
Mar. 1987.
[5] M. Tomizuka, T. Tsao, and K. Chew, “Analysis and synthesis of discretetime repetitive controllers,” Trans. ASME, J. Dyn. Syst. Meas. Control,
vol. 111, no. 3, pp. 353–358, Sep. 1989.
[6] K. Chew and M. Tomizuka, “Steady-state and stochastic performance of
a modified discrete-time prototype repetitive controller,” Trans. ASME,
J. Dyn. Syst. Meas. Control, vol. 112, no. 1, pp. 35–41, Mar. 1990.
[7] U. Borup, P. N. Enjeti, and F. Blaabjerg, “A new space-vector-based
control method for UPS systems powering nonlinear and unbalanced
loads,” IEEE Trans. Power Electron., vol. 37, no. 6, pp. 1864–1870,
Nov. 2001.
[8] A. Von Jouanne, P. N. Enjeti, and D. J. Lucas, “DSP control of highpower UPS systems feeding nonlinear loads,” IEEE Trans. Ind. Electron.,
vol. 43, no. 1, pp. 121–125, Feb. 1996.
[9] K. Zhou and D. Wang, “Digital repetitive learning controller for threephase CVCF PWM inverter,” IEEE Trans. Ind. Electron., vol. 48, no. 4,
pp. 820–830, Aug. 2001.
[10] H. Oshima and K. Kawakami, “Large capacity 3-phase UPS with IGBT
PWM inverter,” in Proc. IEEE PESC, 1991, pp. 117–122.
[11] P. Mattavelli, “Synchronous-frame harmonic control for highperformance AC power supplies,” IEEE Trans. Ind. Appl., vol. 37,
no. 3, pp. 864–872, May/Jun. 2001.
[12] P. Mattavelli, G. Escobar, and A. M. Stankovic, “Dissipativity-based adaptive and robust control of UPS,” IEEE Trans. Ind. Electron., vol. 48, no. 2,
pp. 334–343, Apr. 2001.
[13] M. Li and Y. Xing, “Digital voltage regulation with flux balance
control for sine wave inverters,” in Proc. IEEE APEC, Feb. 2004, vol. 3,
pp. 1311–1314.
[14] H. Pinheiro, F. Botterón, J. R. Pinheiro, H. L. Hey, and H. A. Gründling,
“A digital controller for single-phase UPS inverters to reduce the output DC component,” in Proc. IEEE PESC, 2004, vol. 1, pp. 1311–1314.
[15] F. Botterón and H. Pinheiro, “A new discrete-time voltage controller
based on the internal model principle for three-phase voltage source PWM
inverters with ∆Y output transformer,” in Proc. IEEE PESC, 2004, vol. 1,
pp. 2508–2514.
[16] P. Mattavelli, “An improved deadbeat control for UPS using disturbance
observers,” IEEE Trans. Ind. Electron., vol. 52, no. 1, pp. 206–212,
Feb. 2005.
[17] J.-H. Choi, J.-M. Kwon, J.-H. Jung, and B.-H. Kwon, “High-performance
online UPS using three-leg-type converter,” IEEE Trans. Ind. Electron.,
vol. 52, no. 3, pp. 889–897, Jun. 2005.
[18] F. Botterón, “Controladores Discretos de Tensão Baseados no Princípio
do Modelo Interno Aplicados a Inversores Trifásicos PWM,” Ph.D. dissertation, Universidade Federal de Santa Maria—GEPOC, Santa Maria,
Brazil, Dec. 9, 2005.
[19] F. Botterón and H. Pinheiro, “Synchronous frame half-period repetitive
controller for three-phase UPS,” in Proc. 8th Brazilian Power Electron.
Conf.—COBEP, 2004, pp. 444–450.
[20] R. Griñó and R. Costa-Castelló, “Digital repetitive plug-in controller for
odd-harmonic periodic references and disturbances,” Automatica, vol. 41,
no. 1, pp. 153–157, Jan. 2005.
[21] R. Costa-Castelló, R. Griñó, and E. Fossas, “Odd-harmonic digital repetitive control of a single-phase current active filter,” IEEE Trans. Power
Electron., vol. 19, no. 4, pp. 1060–1068, Jul. 2004.
[22] K. Zhou, K.-S. Low, S.-H. Tan, D. Wang, and Y.-Q. Ye, “Odd-harmonic
repetitive controlled CVCF PWM inverter with phase lead compensation,” in Conf. Rec. IEEE IAS Annu. Meeting, 2004, vol. 1, pp. 177–182.
[23] C. Rech, H. Pinheiro, H. A. Gründling, H. L. Hey, and J. R. Pinheiro,
“Comparison of digital control techniques with repetitive integral action
for low cost PWM inverters,” IEEE Trans. Power Electron., vol. 18, no. 1,
pp. 401–410, Jan. 2003.
[24] F. Botterón, H. Pinheiro, H. A. Gründling, J. R. Pinheiro, and
H. L. Hey, “An improved discrete model for three-phase voltage-fed space
vector modulated converters,” in Proc. 7th Brazilian Power Electron.
Conf.—COBEP, 2003, pp. 911–922.
[25] F. Botterón, H. Pinheiro, H. A. Gründling, J. R. Pinheiro, and
H. L. Hey, “Digital voltage and current controllers for three-phase
PWM inverter for UPS applications,” in Conf. Rec. IEEE IAS Annu.
Meeting, Oct. 2001, vol. 4, pp. 2667–2674.
Fernando Botterón was born in Rosário, Argentina,
in 1967. He received the B.S. degree in electrical engineering from the Universidad Nacional de
Misiones, Misiones, Argentina, in 1995, and the
M.S. and Ph.D. degrees in electrical engineering
from the Federal University of Santa Maria, Santa
Maria, Brazil, in 2001 and 2005, respectively.
Since 1996, he has been a Professor in the
Departamento de Electrónica, Universidad Nacional
de Misiones. His research interest includes discretetime control and digital modulation techniques applied to static converters for medium- and high-power uninterruptible power
supplies (UPS).
Dr. Botterón is a member of the Brazilian Power Electronics Society
(SOBRAEP) and the Brazilian Society of Automatic (SBA).
Humberto Pinheiro was born in Santa Maria,
Brazil, in 1960. He received the B.S. degree from the
Federal University of Santa Maria, Santa Maria, in
1983, the M.Eng. degree from the Federal University
of Santa Catarina, Florianópolis, Brazil, in 1987,
and the Ph.D. degree from Concordia University,
Montreal, QC, Canada, in 1999.
From 1987 to 1990, he was a Research Engineer
of a Brazilian UPS company and joined the Pontíficia
Universidade Católica do Rio Grande do Sul, Brazil,
where he lectured on power electronics. Since 1991,
he has been with Federal University of Santa Maria, as an Adjunct Professor.
His research interests are uninterruptible power supplies, wind power systems,
and control applied to power electronics.