1. Control of a Single-Stage Three-Phase Buck-Boost
Power Factor Correction Rectifier
Bryan P. Faulkner
The Bradley Department
of Electrical & Computer Engineering
Virginia Tech
Blacksburg, Virginia 24060
Email: bryanf81@vt.edu
Abstract—Advances in Power Electronics are enabling More
Electric Aircraft (MEA) to replace pneumatic systems with elec-
trical systems. Active Power Factor Correction (PFC) rectifiers
are used for AC/DC conversion, to maintain unity input power
factor. Traditional three-phase variable voltage and variable
frequency AC/DC rectification methodologies used with airplane
generators implement passive diode bridges and large DC link
capacitors. While useful, these rectifiers have several drawbacks
such as higher harmonics in the input current, poor input power
factor operation, input voltage source disturbances, and lack
output voltage regulation. To alleviate these problems, high-speed
power semiconductor devices have facilitated the development
of active switched-mode AC/DC converters that are controlled
by pulse width modulation (PWM) techniques. A single-stage
PWM-based AC/DC converter topology, which has received
limited attention and is the focus of this summer research
effort, is the three-phase buck-boost-type PFC converter. As
preliminary work, literature reviews relevant to the MEA thrust,
of aircraft electrical systems and power electronic principles,
were conducted. Once the necessary background information was
grasped, simulation and modeling of buck-boost control strategies
began. Ideally, the novel results produced during this summer
2015 REU, at the University of Maryland, will lead to a greater
acceptance of the buck-boost converter in future More Electric
Aircraft.
I. INTRODUCTION
Traditional three-phase variable voltage and variable fre-
quency AC/DC rectification methodologies in airplane genera-
tors utilize passive diode bridges and large DC link capacitors.
Passive diode-bridge based rectifiers result in higher harmonics
in the input current, poor input power factor operation, input
voltage source disturbances, and lack output voltage regu-
lation [1]. To alleviate these problems, recent progresses in
high-speed, power semiconductor devices have facilitated the
development of active switched-mode AC/DC converters that
are controlled by pulse width modulation (PWM) techniques.
The dominant topologies for active, single-stage PWM-based
AC/DC conversion are boost-type [1-2] and buck-type [3-4]
rectifiers. Three-phase, buck-boost-type, power factor correc-
tion (PFC) converters have received limited attention.
The three-phase buck-boost-type AC-DC converter topology
proposed in [5] has drawbacks such as discontinuous current
conduction mode operation, an excessive amount of power
semiconductor devices, and low conversion efficiency. The
buck-boost control strategies proposed in [6-7] need 2200µF
output capacitors (a capacitance value that is over four times
greater than the required output capacitor, used in this paper
- 500µF). To improve upon existing strategies, and to offer
a novel solution without any of the previously mentioned
drawbacks, this paper proposes a new control strategy utilizing
the input currents and output voltage of the converter using
only a single Proportional-Integral (PI) controller. The PI
compensator was designed and implemented to stabilize the
voltage loop of the system. The main objective of the control
strategy is to make the input current controller as fast and as
robust as possible, to ultimately produce high quality input
currents (low THD percentage and unity power factor). This
control structure excels in two separate areas: (1) obtaining
a fast and robust input current response (with high power
factor quality); and (2) achieving a steady state response in
a significantly less amount of settling time, under a step
change in load or reference output voltage, as compared to
conventional PI current compensators. Simply put, the control
strategy put forth in this research thrust is simple, fast, and
reliable and is perfectly suited for implementation in the active
three-phase buck-boost rectifiers of the future.
II. MORE ELECTRIC AIRCRAFT
A. Electrical Power Generation in the Boeing 777
The Boeing 777 electrical system is comprised of two
independent electrical systems: the main and the backup.
The main system involves two engine-driven integrated drive
generators, a generator driven by the auxiliary power unit
(APU), three generator control units, and a bus power control
unit [8].
In order to provide for redundant contingencies, in case
of failure, a backup electrical system is included with every
aircraft. Included in the backup design are two-engine driven
generators and one inverter/control unit. When all of the
systems/redundancy plans are considered, as a whole, they
are equivalent to a three-engine plane (the 777 only has two
physical engines); essentially, the 777 has one backup engine.
The specifications of the power generation of the 777 are noted
in Table I [8].

2. Fig. 1. Comparison of Single-Phase and Three-Phase Signals
B. Electrical Power Generation in the Boeing 787
The Boeing 787 electrical system is of a hybrid voltage
design. The system is comprised of six generators: two per
engine, and two per APU, operating at 235 VAC. Additionally,
ground power receptacles are included in the system design for
airplane servicing on the ground without the use of the APU.
All of the systems generators are directly connected to the
engine gearboxes and can be operated at a variable frequency
(360 to 800 hertz), that is proportional to the engine speed.
Characteristics of the Boeing 787 hybrid voltage system are
noted in Table I [9].
TABLE I
ELECTRICAL SYSTEM COMPARISON BETWEEN THE BOEING 777 AND THE
787
Characteristic Boeing 777 Boeing 787
AC Voltage* 115 VAC 115 VAC & 235 VAC
DC Voltage 28 VDC 28 VDC & ± 270 VDC
Operating Frequency 400 Hz 360-800 Hz
*Phase-to-Neutral RMS
C. No-Bleed Architecture
The new 235 VAC and the ± 270 VDC voltage types stem
from the new no-bleed electrical architecture, on the Boeing
787. The new architecture method results in an expanded
electrical system that is capable of generating twice as much
electricity as previous Boeing airplane models [9]. In previous
aircraft, bleed-air systems, were pneumatic air intake and
compressor systems that would provide electric power to
various airplane components; i.e. air-conditioning packs and
wing anti-ice systems, among many others [9]. With the
new 787 no-bleed architecture, which moves away from the
previous pneumatic school of thought, to the electrical, Boeing
is hoping to achieve the following [9]: (1) Fuel savings of
about 3% (2) extract as much as 35% less power from the
engines; (3) increased performance of the Auxiliary Power
Unit (APU), due to a simpler, all electric APU design; (4)
more efficient engine cycles; and (5) more efficient secondary
power extraction, power transfer, and energy usage.
III. LITERATURE REVIEW
A. Single-Phase and Three-Phase Power
Illustrated in Fig. 1, is a comparison between a single-phase
voltage, versus a three-phase voltage. A single phase signal
only has one sinusoidal value (i.e. one AC voltage, or one AC
current. For example,
V = A · cos(ωt) (1)
where A is the maximum amplitude of the single-phase
sinusoid and ω is the angular frequency.
A three-phase signal, on the other hand, the bottom graph
of Fig. 1, is composed of three separate signals, with the same
maximum amplitude and angular frequency each 120° apart.
For example, please see Eqs. (2)-(4).
Va = A · cos(ωt) (2)
Vb = A · cos(ωt − 120°) (3)
Vc = A · cos(ωt + 120°) (4)
In similar fashion to the single-phase signal, A is the same
maximum amplitude and is the same angular frequency, across
all of the sinusoids.
Another significant difference between single-phase, and
three-phase signals, is power. A single-phase signal allows
power to fall three times every cycle. A three-phase signal
delivers a constant power supply to a load.
B. Converter Topologies
1) Step-Down (Buck) Topology: The basic topology of an
AC/DC buck-type three-phase rectifier is shown in Fig. 2.
The three-phase buck-type topology forces the output voltage
to be smaller (buck) than the input voltage; contingent upon
appropriate circuit element values and duty ratio, D.
The converter includes a three-phase input voltage source
followed by three series inductors, a capacitor bank, six
switches {S1 − S6} with voltage blocking capabilities (that
can be implemented using either MOSFETs or IGBTs), six
diodes {D1 − D6}, an output inductor (LDC), and an output
filter capacitor (Co). The output inductor helps to minimize
the output current ripple, and acts as a constant current-source
(iDC). The output filter capacitor helps to minimize the output
voltage ripple, and acts as a constant voltage source (VDC) [2].
2) Step-Up (Boost) Topology: The basic topology of an
AC/DC boost-type three-phase rectifier is shown in Fig. 3.
The three-phase boost-type topology forces the output voltage
to be greater (boost) than the input voltage; contingent upon
appropriate circuit element values and duty ratio, D.
The converter includes a three-phase input voltage source
followed by three series inductors, six switches {S1 − S6}
with voltage blocking capabilities (that can be implemented
using either MOSFETs or IGBTs), and an output filter
capacitor (Co). The three series inductors following the input
three-phase source aid in boosting the input voltage and
filter the input current, thus reducing the current harmonic

3. levels. The output filter capacitor helps to minimize the output
voltage ripple, and acts as a constant voltage source (VDC)[2].
3) Step-Down, Step-Up (Buck-Boost) Topology: The basic
topology of an AC/DC buck-boost type three-phase rectifier is
shown in Fig. 4. This topology resembles a buck-type rectifier
at the input voltage, see Fig. 2, and is similar to a DC/DC buck-
boost converter towards the output. The three-phase buck-
boost-type topology allows for the output voltage to either
be greater (boost) or smaller (buck) than the input voltage,
depending upon various circuit element values and duty ratio,
D.
The converter includes a three-phase input voltage source
followed by three series inductors, a capacitor bank, six
switches {S1 − S6} with voltage blocking capabilities (that
can be implemented using either MOSFETs or IGBTs), seven
diodes {D1 − D7}, an output inductor (LDC), and an output
filter capacitor (Co). The output inductor helps to minimize
the output current ripple, and acts as a constant current-source
(I). The output filter capacitor helps to minimize the output
voltage ripple, and acts as a constant voltage source (VDC)
[2].
i1,avg(t) =
D2
Ts
2L
· v1(t) (5)
As is shown in Eq. (5), there is a perfect linear relationship
between i1,avg(t) and v1(t), demonstratiing that the Buck-
Boost topology, theoretically, has excellent, intrinsic PFC
properties [10].
Fig. 2. Step-Down (Buck) Rectifier Topology
Fig. 3. Step-Up (Boost) Rectifier Topology
Fig. 4. Step-Down, Step-Up (Buck-Boost) Rectifier Topology
C. Total Harmonic Distortion
Total Harmonic Distortion is based upon the Fourier ex-
pansion of nonsinusoidal waveforms. The THD of a distorted
current waveform, is defined by the following equation [11]:
THD =
h=hmax
h=2
Ih
I1
2 1/2
(6)
where Ik is the amplitude of the h-th order current harmonic,
I1 is the fundamental frequency of the waveform (50 or 60 Hz
component), and hmax is the maximum number of harmonics
to be included ( 40-50 on average). THD can also be a
performance indicator for distorted voltages. It is common
to multiply the THD by 100% to obtain a percentage of
distortion. Using Ik, Irms can be defined [11]:
Irms =
h=hmax
h=1
I2
h
1/2
(7)
Additionally, the relationship between current THD and rms
current can be derived [11]:
Irms = I1 1 + (THD)2 (8)
Using this relationship the power-factor definition can take
harmonic currents into account, only knowing the THD of the
current [11]:
λ =
P
S
=
I1 · cos(φ)
Irms
=
cos(φ)
1 + (THD)2
(9)
.
D. Pulse-Width Modulation
Pulse-Width Modulation (PWM) is a method used to control
output voltage, at a constant switching frequency (hence, a
constant switching time period (Ts = ton+toff), while adjusting
the on-duration of a switch. In this method the ratio of the on
duration to the switching time period, known as the switch
duty ratio (D), is varied [12].

4. Fig. 5. Space vector representation of three-phase converter
E. Space Vector Pulse-Width Modulation
Space Vector PWM (SVPWM), like PWM, also controls
average voltage output; however, SVPWM does so without a
constant switching frequency.
As shown Fig. 5, the objective of the SVPWM technique
is to approximate the reference voltage vector (V ∗
) instanta-
neously by combining the switching states corresponding to
the basic space vectors {V0, V1, V2, V3, V4, V5, V6, V7} [11].
The two following equations are used to implement
SVPWM [11]:
d1 · V1 + d2 · V2 = V ∗
(10)
including the zero vector, d0
d0 + d1 + d2 = 1. (11)
SVPWM, when applied to a three-phase
converter, allows for 8 possible switching states
{pnn, ppn, npn, npp, nnp, pnp, ppp, nnn}. Examples of
the npp and the nnp switching states, applied to a Buck-
Boost Converter are illustrated in Fig. 6 and Fig. 7 respectively
[11].
The SVPWM technique also allows for a smaller percentage
of Total Harmonic Distortion (THD), mentioned in section
III.C, for our system [11].
F. State-Space Averaging
State-space averaging techniques ease computational efforts
on digital signal processors, and linearize systems around
certain operating points. State-space averaging methods were
implemented in this research project as a means to control
the rectification process, due to the fact that the voltage and
current transients reach steady state with less oscillation than
other methods; zero-order approximations, as an example, are
more oscillatory [13]
Fig. 7. Buck-Boost Topology in the npp (V4) switching state
Fig. 8. Buck-Boost Topology in the nnp (V5) switching state
IV. CONTROL STRATEGY
In the following analyses, the following nomenclature is
used:
D duty ratio
I current across inductor LDC
Co output capacitor voltage
VMN voltage across inductor LDC
VDC output voltage
R resistance
From state-space averaging techniques, discussed in Section
II.F, the transfer function obtained for the three-phase buck-
boost-type rectifier in Fig. 4 is as follows [2]:
Gvd(s) =
Vo(s)
d(s)
=
−(I · LDC · R)s + [VDC(1 − D) + VMN (D − 1)]R
(R · LDC · Co)s2 + L · s + (D2 + 1 − 2D)R
.
(12)
The transfer function in Eg. (12) has a zero shown in Eq. (13):
s =
VDC(1 − D) + VMN (D − 1)
I · LDC
. (13)
As the zero indicates, in Eq. (13), the DC/DC converter is a
non-minimum phase system [1]. A zero is located in the right
half plane when VDC > VMN . Conversely, a zero is located
in the left half plane when VDC < VMN . If a right half zero
occurs in a system, the dynamic response in output voltage
and input current is significantly slower, in comparison to a
system with a left half zero and similar gain response. Due

5. Fig. 6. Control Structure of the Single-Stage, Three-Phase Buck-Boost AC/DC Converter
to the nature of the zero, the control circuit of the rectifier is
difficult to tune and is best suited for operation only in a given
region. However, since LC low pass filters must be designed
to allow for faster input current dynamics, rather than output
voltage dynamics, it is necessary to separate the dynamics of
the input current from the output voltage.
Additionally, the control strategy presented in Fig. 8 is
implemented using Space Vector Pulse-Width Modulation
(SVPWM) techniques, as discussed in section III.E to
generate switching pulses for the converter. Complementary
pulses were generated with a dead-band. Park Transforms
(ABC/dq0) and Clark Transforms (ABC/αβ) are also uti-
lized. The equations for Park and Clarke Transforms are shown
in Eq. (14) and Eq. (15), respectively.


ud
uq
u0

 =
2
3





cos(ωt) cos(ωt − 2π
3 ) cos(ωt + 2π
3 )
− sin(ωt) − sin(ωt − 2π
3 ) − sin(ωt − 2π
3 )
1
2
1
2
1
2










ua
ub
uc





.
(14)


uα
uβ
u0

 =





2
3 −1
3 −1
3
0 1√
3
− 1√
3
1
3
1
3
1
3










ua
ub
uc





.
(15)
V. SIMULATION RESULTS
The converter in this work has been simulated with an
input voltage of 230V (phase-neutral RMS) at 400 Hz; these
specifications were chosen, as they are typically used for
the Regulated Transformer Rectifier Unit (RTRU) in next-
generation More-Electric-Aircraft (MEA).
The simulation of this work was performed in MATLAB-
Simulink. Fig. 9 provides the simulation results of the con-
verter in both buck and boost mode, and also validates the
PFC operation with voltage regulation of the converter (as the
voltage and current sinusoids are in-phase).
During the simulation, at 50 ms, the output voltage refer-
ence, V ∗
DC, is decreased from 700V (boost-mode) to 400V
(buck-mode). The 2% settling time of the output DC voltage
is 7 ms with our proposed control. The settling time of the
control system proposed in this work is faster as compared
to a system with multiple PI controllers that takes 20ms to
reach 2% settling band. As Fig. 9 demonstrates, the proposed
control is able to achieve a unity PFC operation, and 2.3%
input current THD.
VI. CONCLUSION
The Transportation Electrification Research Experience for
Undergraduates offered an excellent opportunity to become
introduced to the field of power electronics and the ad-
vancements of the More Electric Aircraft (MEA). As pre-
liminary work, literature reviews relevant to the MEA thrust,
of aircraft electrical systems and power electronic principles,
were conducted. Once the necessary background information
was grasped, simulation and modeling of buck-boost control
strategies began.
Fig. 9. (a) DC output reference voltage; (b) DC link voltage (V) with our
proposed control and PI compensator; (c) Phase A current (A) with our
proposed control and PI compensator (d) Phase A input voltage.

6. The proposed controller presented in this work is capable
of stabilizing the single-stage three-phase buck-boost AC/DC
Rectifier with PFC operation at a rated power condition, while
undergoing a step change in either output voltage or load
power.
This body of research is under review for possible publica-
tion for the fall of 2015. Ideally, the novel results produced
during this summer research effort will lead to a greater
acceptance of the buck-boost converter in future More Electric
Aircraft.
ACKNOWLEDGMENT
I would like to thank my Research Advisor, Dr. Alireza
Khaligh for the opportunity to conduct research related to
Transportation Electrification, this summer. I would also like
to thank Dr. Khaligh, my Graduate Research Mentor, Ayan
Mallik, and all members of the Power Electronics, Energy
Harvesting and Renewable Energies Laboratory at the Univer-
sity of Maryland-College Park for their ever-present support,
encouragement, and guidance.
This work has been supported through the National Science
Foundation grant number EEC 1263063, REU Site: Summer
Engineering Research Experiences in Transportation Electrifi-
cation, which is gratefully acknowledged.
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