A New Digital Controller for Boost PFC Converter with
the Reduced Harmonic Distortion at the DCM Mode
Zhihao Wang
1
, Jun Yan
1
, Yu Yao
2
and Daying Sun
2a)
1
College of Telecommunications& Information Engineering,
Nanjing University of Posts and Telecommunication,
66 mofan road, Nanjing, China
2
School of Electronic and Optical Engineering,
Nanjing University of Science and Technology,
200 Xiaoling Wei, Nanjing, China
a)
Keywords: Power factor correction, discontinuous conduction mode, digital controller, reduced harmonic distortion.
Abstract: In this paper, motivated by improving the characters of the power factor correction (PFC) converter at the
discontinuous-conduction mode (DCM), a new digital controller for the digital PFC converter is proposed.
The digital controller mainly consists of the modulation control loop and the self-adjusting voltage control
loop. The simulation results demonstrate that the converter with the proposed digital controller can aim high
output stability and reduced harmonic distortion.
1 INTRODUCTION
With the development of electronic technology, the
power factor correction （ PFC ） converters have
been widely used to reduce the input current
harmonic distortion and satisfy the required
harmonic standards, so as to improve energy
utilization efficiency and system stability of the
electric power system (
K. Billings., 1999;
R.W.Erickson, 2004). The voltage control loop and the
current control loop are often used to regulate the
output voltage and the input current, respectively.
The output voltage is preferred to be stable near the
reference voltage and the input current is preferred
to follow the input voltage perfectly.
Meanwhile, due to the advantage such as the
improved flexibility and increased functionality, the
digital controller has been widely used in the PFC
converter system (Angel de Castro, 2003). However,
owing to the two digital control loops, the
performance improvement of the digital PFC
converter is inevitably limited by the relatively
complex digital calculation. So when the practical
application under the low power level, the signal
digital control loop for the digital PFC converter is
often preferred, and the digital PFC converters often
work at the discontinuous conduction mode (DCM).
When the digital PFC converter operating at the
DCM mode, many control methods have been
proposed to improve the final power factor and
reduce the distorted input current, while the total
control circuit complexity and the calculation burden
are increased (Barry A. Mather, 2011; Jong-Won
Shin, 2012; S.F.Lim, 2011).
A new digital controller is proposed in our paper
to improve the characters of the digital
PFC converter operating at the discontinuous
conduction mode. The whole digital PFC converter
structure with the proposed digital controller is
illustrated in section 2, the detailed control method
of the digital controller is described in section 3, and
the simulation results and the conclusion are
presented in section 4 and section 5, respectively.
2 THE WHOLE BOOST
CONVERTER STRUCTURE WITH
THE PROPOSED DIGITAL
CONTROLLE
The whole boost PFC converter structure with the
proposed digital controller is shown in Figure. 1.
The input and output voltages of the digital PFC
converter are sampled by the analog-to-digital
converter (ADC), respectively. The proposed digital
518
Wang, Z., Yan, J., Yao, Y. and Sun, D.
A New Digital Controller for Boost PFC Converter with the Reduced Harmonic Distortion at the DCM Mode.
In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 518-521
ISBN: 978-989-758-312-4
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

controller mainly consists of the modulation control
loop and the self-adjusting voltage control loop. The
final duty cycle signal for the switching tube is
converted via the digital pulse width modulator
(DPWM).
Figure 1: The whole boost PFC converter structure with
the proposed digital controller
3 THE DESIGN OF THE DIGITAL
CONTROLLER
3.1 The modulation control loop
When the digital PFC converter working at the
DCM mode, the typical inductor current of the boost
PFC converter during each switching cycle can be
shown in Figure. 2
Figure 2: The typical inductor current during each
switching cycle at DCM
From the above figure, the peak inductor current
of the PFC converter i
L(pk)
can be calculated as
 
() 1
sin sin 
 
mm
in
L
pk on on s
vtvt
v
iT T dT
L
LL
(1)
Where v
in
is the input voltage value of the PFC
converter, v
m
is the magnitude value of the input
voltage, L is the inductance of the boost inductor, T
on
is the on-time during each switching cycle, ω is the
line frequency, d
1
is the duty cycle value and T
s
is
the switching period.
According to the volt-second balance principle of
inductor current, the average inductor current i
L(av)
of
the PFC converter during each switching cycle can
be derived as
() ( ) 1 2 ( )
11
() (1 )
22


in
L
av L pk L pk m
oin
v
iiddi d
vv
(2)
Where d
2
is the falling time ratio of inductor
current and v
o
is the output voltage value of the PFC
converter. Based on the formula (1) and (2), the
input current i
in
can be rewritten as
2
()
sin
()
2sin




om
ms
in L av
om
vv t
dT
ii
Lvv t
(3)
When the digital PFC converter is regulated to
the steady mode, the output of the voltage control
loop d
m
can be defined as a constant under the
constant switching frequency. Based on the formula
(3), the actual input current i
in
of the PFC converter
is not sinusoidal, so the input current cannot follow
the input voltage perfectly, which resulting in the
improved harmonic distortion and the low power
factor.
To reduce the harmonic distortion and improve
the power factor, the modulation control loop in the
digital controller is adopted to regulate the final duty
cycle value, and the output of the modulation control
loop ξ is concluded as
1  
in
o
v
v
(4)
Based on the formula (3) and (4), the actual input
current i
in
of the digital PFC converter can be
regulated, and can be concluded as
22
sin
()
()
2sin2





om
ms ms
in in
om
vv t
dT dT
iv
Lvv t L
(5)
According to the formula (5), the input current of
the digital PFC converter is sinusoidal, and the input
current can follow the input voltage perfectly, the
harmonic distortion can be reduced and the final
power factor can be improved effectively under the
DCM mode.
3.2 The self-adjusting voltage control
loop
Meanwhile, the digital controller of the PFC
converter is preferred to regulate the output voltage
v
o
to the reference voltage v
ref
, which is aimed by the
self-adjusting voltage control loop in Figure 1. In the
conventional control loop, the PI compensator is
often used, which can be typically expressed as
A New Digital Controller for Boost PFC Converter with the Reduced Harmonic Distortion at the DCM Mode
519

()
i
vp
K
Gs K
s

(6)
Furthermore, based on the above control
principle, the digital compensator for the digital
controller of the PFC converter should be redesigned
by the pole-zero mapping technique and the discrete
time control law of the digital compensator can be
redesigned as
[] [ 1] [] [ 1]  
mm pv iv
dk dk Kek Kek
(7)
Where e
v
[k] and e
v
[k-1] are the errors between
the output voltage and the reference voltage, and
d
m
[k] and d
m
[k-1] are the output values of the self-
adjusting voltage control loop during the k
th
and (k-
1)
th
switching cycle, respectively. Bases on the
formula (7), the digital control characteristic of the
self-adjusting voltage control loop can be effectively
adjusted by changing the gain and the parameters,
which determine the frequency of the compensator
zero. If the amplitude of the voltage error signal is
smaller than the threshold value, the digital voltage
loop enters into the low-bandwidth mode, which can
eliminate the second harmonic pollution and reduce
the harmonic distortion. If the amplitude of the
voltage error signal is higher than the threshold
value, the digital PFC converter is preferred to
regulate the output voltage to the reference voltage
quickly, and the digital controller is preferred to
regulate into the middle-bandwidth mode or high-
bandwidth mode. The change of control loop mode
is implemented via the change of the compensator
coefficient value K
p
and K
i
, and the change principle
of the coefficient are based on the low-frequency
model of the digital PFC converter, which is
obtained by the averaging value over half line cycle.
4 SIMULATION RESULTS
The digital boost PFC converter at the DCM mode
with the proposed digital controller has been
simulated via the Matlab/Simulink environment. The
converter parameters are as follows: input voltage
v
in
=90-264V, output voltage v
o
=460V, output power
P
o
=120W, line frequency f
line
=50Hz, the switching
frequency f
s
=100kHz. Furthermore the power device
components of the prototype are as follows: boost
inductor L=200uH, output filter capacitor C=200uF.
v
o
i
in
v
in
i
L

(a)
v
o
i
in
v
in
i
L

(b)
Figure 3: The waveforms of the output voltage, input
current, input voltage and the inductor current of the
digital PFC converter
The output voltage, input current, input voltage
and the inductor current waveforms of the digital
PFC converter under the input voltage 220VAC with
20% load and the input voltage 264VAC with 100%
load are shown in Figure 3, respectively. From the
figure, it can be observed that the input current of
the digital PFC converter can follow the input
voltage perfectly whenever at the high or low input
voltage, or under the light or heavy load. The digital
PFC converter based on the proposed digital
controller can aim high system stability and low
harmonic distortion.
5 CONCLUSIONS
This paper proposes a new digital controller for the
digital boost PFC converter at the DCM mode. The
digital controller mainly consists of the modulation
control loop and the self-adjusting voltage control
loop. Finally the simulation results confirm the
satisfactory performance in harmonic distortion for
the digital boost PFC converter.
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
520

ACKNOWLEDGEMENTS
The authors should like to thank the National Nature
Science Foundation of China (61604075 and
61504065), and the Fundamental Research Funds for
the Central Universities (30917012202).
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A New Digital Controller for Boost PFC Converter with the Reduced Harmonic Distortion at the DCM Mode
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