Vitor Fernão PIRES1,2, Manuel GUERREIRO1, João F. MARTINS3,5, Jose Fernando SILVA2,4
ESTSetubal- Inst. Politécnico Setúbal (1), CIEEE(2), FCT- Univ. Nova de Lisboa (3), IST-T U Lisbon (4) UNINOVA-CTS (5)
Three-Phase PWM Rectifier Employing Two Single-Phase
Buck-Boost PFC Modules and a Scott Transformer
Abstract. In this paper it is proposed a unity power factor isolated three-phase rectifier with buck-boost characteristics. This rectifier is based on the
Scott transformer and only uses two single-phase buck-boost rectifiers. In this way only two switches are used. To achieve sinusoidal input current
and high power factor, a fast and robust pulse width sliding mode modulation of the input current is proposed. An output voltage compensator is also
used to establish the amplitude of the reference currents. Several results are presented in order to show the effectiveness of the proposed rectifier.
Streszczenie. W artykule przedstawiono izolowany prostownik trójfazowy o jednostkowym współczynniku mocy i charakterystyce typu Buck-boost.
Prostownik ten powstał na bazie układu transformatora Scotta z zastosowaniem tylko dwóch jednofazowych prostowników Buck-boost. Tym
sposobem ograniczono ilość użytych kluczy do dwóch. W celu osiągnięcia sinusoidalnego prądu wejściowego i wysokiej wartości współczynnika
mocy, zaproponowano szybką i stabilną modulację szerokościową ze sterowaniem ślizgowym prądu wejściowego. Kompensator napięcia
wyjściowego jest użyty w celu ustalenia amplitudy prądów referencyjnych. Wybrane rezultaty zaprezentowano w celu zobrazowania efektywności
proponowanego prostownika (Trójfazowy prostownik PWM z zastosowaniem dwóch jednofazowych modułów PFC typu Buck-Boost i
transformatora Scotta).
Keywords: Buck.Boost, Three-Phase Rectifier, Scott Transformer.
Słowa kluczowe: Przemiennik Buck-Boost, prostownik trójfazowy, transformator Scotta
Introduction
Current harmonics produced by nonlinear loads
increase power cable losses having a negative impact on
the electric utility distribution systems and components. The
most common sources of harmonics are power electronic
loads such as adjustable speed drives and switching power
supplies. These loads use diodes, power transistors, and
other electronic switching devices to either chop waveforms
to control power, or to convert 50/60Hz AC to DC. They
offer
tremendous
advantages
in
efficiency
and
controllability. However, they draw non-sinusoidal currents
from AC power systems, and these currents produce
voltage harmonics due to line and system impedances and,
in some cases, resonance issues appear. International
standards have been introduced to enforce the limits of the
line current harmonic content of equipment connected to
the ac mains.
To satisfy the requirements of these standards,
concerning the quality of the supply current waveform of the
ac-dc converters, several circuit topologies using
controllable switches have been developed. The most used
design is the Boost type [1, 2, 3]. The line-input current of
this rectifier is shaped almost like a sinusoidal waveform to
show a near-unity power factor. Another advantage of this
rectifier types, is that, they can pre-regulate the dc output
voltage. Several single and three-phase topologies with
different switch count have been developed. Many of these
rectifiers present galvanic isolation. However, for many
medium and high power applications low frequency
isolation is used. In this way, three-phase high power factor
rectifiers based on Scott Transformer have been proposed
[4, 5, 6]. An analysis and practical aspects of rectifiers have
been presented in [7, 8].
Although the Boost converter is the dominant design, it
shows limited capability to bound inrush and dc short-circuit
currents, and its output voltage must be always higher than
the peak of the AC input voltage. These drawbacks limit the
use of this rectifier in situations where it is desirable to
obtain an output voltage smaller than the AC input voltage
peak value and/or effectively bound the inrush and DC
short-circuit current.
Unlike the high power factor boost type rectifier, the
buck-boost type presents the capability to limit inrush and
dc short-circuit currents which is very important for several
applications [9, 10, 11].
In this paper a unity power factor isolated three-phase
buck-boost type is proposed. This rectifier is based on the
Scott Transformer and only uses two switches. To control
the input line currents a pulse width modulator fast sliding
mode controller is proposed. This controller actively shapes
the input line currents achieving a near unity power factor
operation and line input current with nearly sinusoidal
shape, even when the dc inductor current has high ripple.
For the regulation of the output voltage, a proportional plus
integral controller, using only the error between the actual
dc output voltage and the reference voltage, generates the
reference value for the line current amplitude.
Converter Topology
The unity power factor isolated three-phase buck-boost
rectifier based on Scott transformer is shown in Fig. 1. This
topology uses a 3 to 2 phases transformer generating at the
secondary two 90º out of phase AC-voltages. Two singlephase Buck-Boost unity power factor converters are
connected at the output of the low frequency transformer.
Each output of the two unity power factor converters is then
shunt-connected to the DC output stage.
Fig.1. Three-phase Buck-Boost rectifier based on the Scott
Transformer
In order to have 3 to 2 phases transformer a special
connection is needed. Such connection must maintain the
fundamental characteristics of the primary side regarding
the three-phase line currents. There are two different
transformer solutions: Scott and Le-Blanc connections. In
this work it will be used the Scott transformer (Fig. 2).
PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 85 NR 10/2009
213
To control the input line current of each Buck-Boost
module, a PWM sliding mode control technique will be
used.
Considering the is current as the controlled output, the
input-output linearization of the state-space model (1) gives
the state-space equations in the controllability canonical
form (4):
⎤
⎡ θ
⎥
⎢
⎥
⎢
⎥
ω
1
d ⎡i s ⎤ ⎢ R f
⎢ ⎥ = ⎢ − L θ − L C i s + L Vs max cos(ωt ) −⎥
dt ⎣θ ⎦ ⎢
⎥
f
f f
f
⎥
⎢
α
α
1
2
⎥
⎢
i Lo1 −
i Lo 2
−
⎥
⎢
L f Cf
L f Cf
⎦
⎣
Fig.2. Connection and phasor diagram of the Scott Transformer
The output voltages of the Scott transformer are 90º
shifted and equal in magnitude. For the theoretical study of
this isolated rectifier only the secondary circuitry will be
taken into account. In this way, the input voltages of the
rectifier are two ideal AC voltages.
Rectifier Model
Considering one set of input filter, bridge rectifier plus
buck-boost converter and applying Kirchhoff laws, the
dynamic behaviour of each rectifier can be described by the
following state equations:
⎧
⎪
⎪
⎪
⎪
⎪⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪⎩
(1)
Rf
dis
= −
dt
Lf
dvC f
1
=
dt
Cf
di Lo
dt
=
dVC o
=
dt
α
Lo
is −
1
1
vC f +
vs
Lf
Lf
is −
vC f −
1− α
Co
α
Cf
i Lo
γ (1 − α )
iLo −
Lo
VC o
1
Vo
Ro Co
where:
(2)
(3)
α
⎧⎪ 1 , switch ON and vC f ≥ v Lo
= ⎨
⎪⎩ 0 , switch OFF or vC f < v Lo
γ
⎧⎪ 1 , iLo > 0
= ⎨
⎪⎩ 0 , iLo ≤ 0
This model will be used to define the system controllers.
Control Strategy
The system dynamics of each Buck-Boost module can
be divided into fast motion (input line current) and slow
motion (output voltage). In this way, owing to the separate
dynamics of the input line current and of the output voltage,
a cascade control structure is used. The reference for the
inner current loop is a sinusoidal waveform whose
amplitude is modulated by the external voltage controller as
can be seen in Fig. 3.
(4)
where:
θ=
(5)
vs − R f is − vC f
Lf
Analysing the obtained state space equations (4) and
(5), it is possible to verify that the input line current has a
strong relative degree of two [12]. In this way, a suitable
sliding surface to ensure the robustness of the closed loop
system [13] can be obtained. Equation (6) shows the
correspondent defined sliding surface.
(
S ei s , eθ
(6)
) = ( isref
− is
) + k ( θ ref
−θ
)
k is a parameter related to the time constant of the
desired first order response of input source current iS (k>0).
From (4) and (6), the sliding surface (7) is rewritten as:
(
S ei s , eθ
) = ( isref
)
− is + k
(7)
(v
k
Lf
−
s
disref
dt
−
− R f is − vC f
)
The control strategy must guarantee that the system
trajectory moves towards and stays on the sliding surface
S ei s , eθ = 0 from any initial condition. In order to
(
)
ensure this, the following stability condition must be
obtained.
(
(8)
S ei s , eθ
) S ( ei , eθ ) <
•
s
0
The stability condition (8) is ensured by the following simple
energy flow considerations:
• If S ei , eθ < 0 then isref > is , hence is must
s
(
)
increase. In this way choose α = 1
(
Fig.3. Control strategy block diagram
214
)
• If S ei s , eθ
> 0 then isref < is , hence is must
increase. In this way choose α = 0
The fixed frequency current controller is obtained using
an S-R flip-flop as presented in Figure 4.
Since the current loop presents a much faster dynamics
than the voltage loop, then its closed-loop transfer function
can be simplified and represented as a current controlled
delayed current source. In this way, the following transfer
function of the current loop is obtained:
PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 85 NR 10/2009
with the proposed control system provides almost
sinusoidal input currents and near unity power factor. Fig.
11 shows an experimental result of the rectifier output
voltage for a three-phase voltage swell. From this figure it is
possible to confirm that the experimental transient response
of the controller achieves a fast enough voltage regulation.
Fig.4. Constant frequency operation of the current controller
I
=
I ref
(9)
KI
(1 + sTd )
Where K I represents the gain and Td the time delay
of the source response.
Considering that the rectifier is conservative (input
power equals the output power) the K I gain can be
obtained from:
KI ≈
(10)
Fig.5. Simulation result of the input voltage and line current
Vs max
2 Vo
The parameters of the voltage control block can now be
obtained. From Fig. 3 it is possible to verify that the rectifier
output voltage is controlled by changing the amplitude of
the input current. In this way, from the closed loop transfer
function, equations (11) and (12) give the parameters of the
PI controller, using
2
2
for the required damping factor of
the resulting 2ª order system.
(11)
KI ≈
(12)
KI ≈
Vs max
2 Vo
Fig.6. Simulation result of the rectifier phase line currents
Vs max
2 Vo
Results
Several results are presented in order to verify the study
of this system. The simulation results have been obtained
using the program Matlab-Simulink/Power System Blockset.
For the AC side of the rectifiers a filter with 1 mH inductor
and 5 μF capacitor was used. For the output of the buckboost an inductor of 50 μΗ and a 470 μF capacitor were
used.
Fig. 5 presents a simulation result of the input voltage
and line current. From this result it is possible to verify that
the rectifier provides almost sinusoidal input current and
high power factor. Fig. 6 shows the simulation result of the
rectifier phase line currents. As can be seen these currents
are nearly sinusoidal and 90º out of phase. Fig. 7 shows the
simulation result of the transformer input line currents and
voltage in phase R. From this result it is possible to observe
the three-phase currents. They are balanced and enable
high power factor.
Fig. 8 and 9 show simulation results of the input line
currents and rectifier output voltage for a three-phase
voltage sag. As can be seen by this result, the PI controller
achieves a sufficiently fast voltage regulation.
Some experimental results are also presented. Fig. 10
shows an experimental result of the input voltage and line
current in one of the rectifiers. The total harmonic distortion
(THD) of the input line currents is 3.3%. So, from this
experimental result it is possible to confirm that this rectifier
Fig.7. Simulation result of the transformer input line currents and
voltage in phase R
Fig.8. Simulation result of the input line currents
PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 85 NR 10/2009
215
REFERENCES
[1]
[2]
[3]
[4]
Fig.9. Simulation result of the rectifier output voltage
[5]
[6]
[7]
[8]
[9]
Fig.10. Experimental result of the input voltage and line current
[10]
[11]
[12]
[13]
Fig.11. Experimental result of the rectifier output voltage
Conclusions
In this paper a unity power factor isolated three-phase
rectifier with buck-boost characteristics has been proposed.
It is based on the Scott transformer and only uses two
active switches. The rectifier is able to generate
symmetrical currents in the line. To control the rectifier
currents a fast and robust pulse with modulation sliding
mode approach was used. A PI compensator was used to
regulate the output voltage. This compensator determines
the amplitude of the reference currents. Several results
were presented to show the performances of each singlephase rectifier and the performances of the three-phase
PWM rectifier.
216
M o h a n N . , U n d e l a n d T . M . , F e r r a r o R . J., Sinusoidal
line current rectification with a 100kHz B-SIT step up
converter, IEEE Power Electronics Specialists Conference,
(1984), 92-98
B o y s J . T . , G r e e n A . W . , Current-forced single-phase
reversible rectifier, IEE Proceedings-B, 136 (1989), No. 5,
237-242
S a l m o n J . C ., Techniques for Minimizing the Input Current
Distortion of Current-Controlled Single-Phase Boost Rectifiers,
IEEE Transactions on Power Electronics, 8 (1993), No. 4, 509520
R u f f e r A . , A n d r i a n i r i n a C h . - B ., A symmetrical 3 phase
2-switch PFC-power supply for variable output voltage,
EPE'95: European Conference on Power Electronics and
Aplications, (1995)
B a d i n A . A . , B a r b i I ., Simplified Control Technique for
Three-Phase Rectifier PFC Based on the Scott Transformer,
IEEE ISIE 2006, (2006), 931-936
B a d i n A . A . , B a r b i I . , Unity Power Factor Isolated ThreePhase Rectifier With Split DC-Bus Based on the Scott
Transformer, IEEE Transactions on Power Electronics, 23
(2008), No. 3, 1278-1287
M i l l e r S . K . T . , B a r b i I . , Practical aspects of the unity
power factor isolated three-phase rectifier based on the Scott
transformer, Applied Power Electronics Conference-APEC,
(2005), 621-627
M i l l e r S . K . T . , B a r b i I . , Unity power factor isolated
three-phase rectifier," 6th INDUSCON – Internacional
Conference on Industrial Applications, (2004)
F u n a b i k i S . , T o i t a N . , M e c h i A ., A Single-Phase PWM
ac to dc Converter with a Step-up/down voltage and
Sinusoidal Source Current, IEEE IAS Annual Meeting Record,
(1991), 1017-1022
P i r e s V . F . , S i l v a J . F . , Half Bridge Single Phase BuckBoost Type ac-dc Converter with Sliding Mode Control of the
Input Source Current, IEE Proceedings – Electric Power
Applications, (2000), 61-67
Singh B., Singh B.N., Chandra A., Al-Haddad K.,
P a n d e y A . , K o t h a r i D . P . , A review of single-phase
improved power quality AC-DC converters, IEEE Transactions
on Industrial Electronics, 50 (2003), No. 5, 962 981.
G a o W . , H u n g J . , Variable structure control of nonlinear
systems: a new approach, IEEE Transactions on Industrial
Electronics, 40 (1993), No. 1, 45-44
S i l v a J . F ., Sliding Mode Control Design of Drive and
Regulation Electronics for Power Converters, Special Issue on
Power Electronics of Journal on Circuits, Systems and
Computers, 5 (1995), No 3, 355-371.
Authors: Prof. Dr Vitor Fernão Pires, ESTSetubal- Instituto
Politécnico Setúbal, Campus do IPS, 2910-761 Setúbal, Portugal,
E-mail: vpires@est.ips.pt; Prof. Dr Manuel Guerreiro, ESTSetubalInstituto Politécnico Setúbal, Campus do IPS, 2910-761 Setúbal,
Portugal, E-mail: mgaspar@est.ips.pt; Prof. Dr João Martins,
Faculdade Ciências e Tecnologia, Univ. Nova de Lisboa, 2829-516
Caparica, Portugal, E-mail: jf.martins@fct.unl.pt; Prof. Dr José
Fernando Silva, Instituto Superior Técnico, Av. Rovisco Pais, 1,
1049-001 Lisboa, Portugal, E-mail: fernandos@alfa.ist.utl.pt.
PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 85 NR 10/2009