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AN IMPROVED INTEGRATION-RESET CONTROLLED
SINGLE PHASE UNITY-POWER-FACTOR BOOST
RECTIFIER WITH LOWER DISTORTION
Chongming Qiao and Keyue M. Smedley
Department of Electrical and Computer
Engineering
University of California, Irvine, CA 92697
Tel: (949) 824-6710
Fax: (949)824-3203
E-mail: Smedley@uci.edu
Abstract: This paper proposes an improved
integration method to realize single phase power
factor correction in continuous conduction mode by
adding a ripple compensation network comprised
of two resistors to the basic integration control
circuitry. This method effectively reduces the total
harmonic distortion (THD) in the input current.
The proposed method is easy to implement.
Theoretical analysis is given in detail.
Experimental results demonstrate the validity of the
approach. This method is very suitable for IC
fabrication.
1
Introduction
In accordance with the operation mode of the
power stage, power factor corrected rectifiers
(PFC) may be divided into three categories:
Continuous Conduction Mode (CCM), Critical
Conduction Mode (CrCM) and Discontinuous
Conduction Mode (CCM). For high power
applications (above one kilowatts), CCM operated
rectifiers are preferred due to their low conducted
noise, low conduction losses in the semiconductor
switches and inductors, and low inductor core
losses. Average mode control and peak current
control are often used to control CCM operated
rectifiers. The average current control method has
demonstrated lower input current harmonic than
the peak current control. Unfortunately, both of
these control methods are complex because both of
them require a stabilization ramp for their current
control loops. Furthermore, a sensor of the rectified
AC voltage is used to provide a current reference
and a multiplier is used to scale the reference so
that it reflects the output current and voltage
requirements. In order to simplify the control
scheme, several control methods have been
proposed [1-4]. The nonlinear-carrier-control [3] in
the first time eliminated the need of a multiplier.
The integration control [1,5] generalized constant
frequency power factor correctors with a unified
integrator-based PWM controller for any boostrelated converters. This control method employs
Zheren Lai and Mehmet Nabant
Linfinity Microelectronics Inc.
11861 Western Ave.
Garden Grove, CA 92841
Tel: (714) 898-8121
Fax: (714) 893-2579
Email: Zheren@linfinity.com
integrators with reset to control the CCM
operated rectifiers and eliminates the need of the
multiplier.
Similar to the peak current control method, the
integration peak current controlled rectifiers also
exhibit input current distortions. For integration
controlled Boost rectifiers (in this paper the
trailing-edge modulation peak inductor current
controlled boost rectifier [1] is used for
investigation), several sources of input current
distortion are listed as follows:
(1). Input inductor current ripple that causes the
average current to deviate from the ideal
sinusoidal waveform.
(2). Partially discontinuous operation of the input
inductor current.
(3). The 120Hz ripple at the output is fed into the
output of the voltage error amplifier.
In this paper, an improved control method is
proposed to reduce the input current distortion by
adding a simple ripple compensation network to
the integration control method. With this method,
the distortion source (1) is eliminated and source
(2) is significantly decreased by reducing the
subinterval where the converter operates in
DCM. In the following discussion, this proposed
control method is called improved integration
control while the integration control without
compensation is referred as the basic integration
control.
In Section 2, the scheme of the basic
integration controlled boost rectifier is reviewed.
In Section 3, the proposed compensation method
and its function in the converter is detailed.
Experimental results are provided to demonstrate
the validity of the theory in Section 4. Finally, a
conclusion is given in Section 5.
Notation conventions are as follows: Capital
letters are used for quantities associated with
steady-state unless indicated explicitly; lower
letters represent time-variant variables; a
quantities in a pair of angular-brackets is the
local-average of the quantity, i.e. the average in
each switching cycle.
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2
Review of the basic integration
controlled boost PFC
A typical single phase PFC is comprised of a diode
bridge in series with a DC-DC converter. Fig. 1
shows the schematic of the integration controlled
boost PFC rectifier with an additional
compensation network comprised of R1 and R2.
Without this compensation network, the control
method realized through an integrator with reset is
the basic integration control.
For PFC applications, the control goal of the DCDC converter is
ig =
Vg
--------------------(1)
Re
where Re is the emulated resistance. Vg and ig
are the input voltage and current of the DC-DC
converter respectively( see Fig. 1).
ig
L
Vo
C
Rs
R
O Int I
w/reset
Vm
AV(s)
Vref
CLK
Fig. 1. The schematic of the improved integration
controlled boost PFC rectifier
During the quasi-steady state, a DC-DC converter
satisfies the following equation
Vo
= M (D) ---------------(2)
Vg
where M(D) is the conversion ratio of the DC-DC
converter. Combination of equation (1) and (2)
leads to the general PFC control function
Vm
--------(3)
M (D)
R ⋅V
where Vm = s o and Rs is the equivalent
Re
Rs ⋅ i g =
current sensing resistance.
For boost converter, the conversion ratio is
M ( D) =
1
. The general PFC control
1− D
function becomes
Rs ⋅ i g = Vm ⋅ (1 − D) -------(4)
current is sensed for the control. The equation (4)
can be reorganized as
Rs ⋅ i Lpk = Vm − Vm ⋅ D --------(5)
In Fig.1, excluding the compensation network R1
and R2, the above equation is achieved as
follows:
Vm − Rs ⋅ i Lpk =
Vm
⋅ D ⋅ T -----------(6)
τ
where τ is the integration time constant; Vm is
the output of the voltage loop error amplifier and
T is the switching period. By setting τ = T , the
equation (6) will be the same as the equation (5).
With this peak current control, input peak current
is proportional to the input voltage that is given
by
Vm
⋅ Vg --------(7)
Rs ⋅Vo
The following conclusion: is drawn from the
above analysis:
First, when the current ripple is small enough
comparing with average current, the peak current
approximately equals the average current, the
control goal of PFC (see equation (1)) is
achieved. However, when the input current is
smaller, the current ripple will cause larger
distortion. The average inductor current (which is
R2
Q Q
S R
average input current i g . Therefore, the peak
iLpk =
R1 Compensation
Network
Vg
Assuming current ripple is small, the peak input
inductor current i Lpk approximately equals the
also the average input current
ig
for boost
converter) equals the peak inductor current minus
the current ripple. Therefore, the average input
current is given by
ig =
Vg
Vm
1T
⋅ Vg −
⋅ V g ⋅ (1 − ) -(8)
2L
Vo
R s ⋅ Vo
Second, the equation (8) is generated based on
the assumption that the converter operates in
CCM. In reality, when the input current is near
zero or the load is light, the converter will operate
in discontinuous mode during certain region.
During DCM interval, the conversion ratio
Vo
Vg
is not a unique function of duty cycle; it is also a
function of switching period T, inductance L,
load resistance, input and output voltage ratio
Mg,, i.e.
Vo
= f (T , L, R, M g , D ) . The
Vg
average input current during the DCM interval
will also related to these parameters such as T, L,
R, Mg., D and is no longer proportional to the
input voltage. A typical average inductor current
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waveform during the half line cycle is shown in
Fig.2.
compensation network reduces θ as shown in
Fig. 3
I
B
In Fig. 3 (a) and (b), Vm and Vm are the output
of voltage error amplifier for the basic and
improved integration controlled rectifiers
I
Fig. 2. Typical average inductor current during half
line cycle for integration controlled boost PFC
rectifiers
Fig. 2 shows the average inductor current in a half
line cycle. The converter operates in CCM when
θ ≤ wt ≤ π − θ and DCM for the rest of the half
cycle. The larger the DCM conduction angle θ is,
the greater the distortion is. The proposed control
method will eliminate or reduce these distortions.
3
Vm − Rs ⋅ i Lpk =
Vm − k ⋅ V g
T
Following the same procedure, we can get the
average
inductor
current
as
follows:
Vm ⋅ V g
+(
k
T
) ⋅ V g ⋅ D --(10)
−
Rs 2 ⋅ L
Rs ⋅ Vo
R ⋅T
Let k = s
, the average inductor current will
2⋅ L
ig =
T
<
VmB
(as shown in Fig.3 (b)). .
T
Vm ⋅ V g
R s ⋅ Vo
VmB −
-------(11)
From equation (11), the average input current will
be exactly proportional to the input voltage. Thus,
the distortion due to inductor current ripple
(distortion source (1)) is eliminated.
3.2
Reduction of DCM region
Another advantage of the compensation is to
reduce the subinterval in each half line cycle where
the converter operates in DCM, i.e. the proposed
Rs ⋅ iLB
B
m
V
⋅t
T
t0
t
T
(a)
⋅ D ⋅ T ----(9)
R2
where k =
R1 + R 2
be
VmI − k ⋅ V g
The improved integration
controlled boost PFC rectifiers
3.1
Ripple compensation
In Fig.1, the improved integration controlled PFC
boost rectifier is presented with the addition of the
compensation network comprised of resistors R1,
R2 and a summer. With this compensation network,
the control equation (6) is modified as
ig =
B
respectively. Likewise, i L and i L are the
inductor currents of converters respectively,
where the superscript “ I “ refers to the improved
integration control while “ B “ refers to the basic
integration control.
Suppose the two converters operate in the same
conditions (i.e. same input voltage and load).
When t < t 0 , we assume that both the converter
operate in DCM. In most case, the slope of the
compensation loop for the improved integration
controlled converter is smaller than that of the
basic integration controlled converter, i.e.
VmI −
VmB −
VmI − k ⋅ Vg
T
⋅t
Rs ⋅ iLI
VmB
⋅t
T
t0
T
t
(b)
Fig. 3. The control scheme comparison between
the basic and improved integration control
(a). The basic integration control. (b) The
improved integration control
Fig. 3 shows that the inductor current will go
from DCM into CCM earlier for improved
integration control comparing with the basic
integration control. In other words, the proposed
method leads to smaller θ , thus converter
operates in smaller DCM region. Therefore, the
proposed method reduced the distortion caused
by the partial discontinuous conduction mode.
This is verified by comparing the DCM
conduction angle θ for the basic and improved
integration controlled boost PFC.
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The DCM conduction angle θ can be found as
follows (the derivation is shown in Appendix):
Fig. 4 The DCM conduction angle θ
 1
θ I = a sin 
 Mg

(b) M g = 0.8, (if Vo = 385V , Vgrms = 220V ) .
 1
θ B = a sin
 Mg

1

L Po, n
4
⋅ − 2⋅ ⋅
+
⋅ M g  ---(13)
2
2

T R ⋅ Mg 3 ⋅ π


B
Vgm
, where Vo is the output voltage).
Vo
Po ,n =
normalized
output
power,
i.e.
Vo ⋅ I o
; I o is the output current; Pmax is
Pmax
the nominal output power and R is nominal load
resistance.
Fig.4 shows the DCM conduction angle θ , θ
vs. the normalized load for the improved and the
basic integration controlled PFC boost rectifiers
respectively. It is clear that in most case, the DCM
conduction angle θ for improved integration
control is smaller than that of the basic integration
control. Therefore, the distortion of the input
current should be lower.
I
B
π
2
Mg = 0.44
Inductance
L = 1mH ;
; the rated resistance R=593Ω
( Pmax = 250W when Vo = 385V ) .
Fig. 2 shows that the converter operates in
completely CCM if θ = 0 . Likewise, the
converter operates in completely DCM when
θ = π . By setting DCM conduction angle
2
θ = 0 and θ = π
for equation (12) and (13), the
2
boundary condition equations (14) and (15) for
the improved and the basic integration control
are obtained respectively.
θ I = 0 CCM / CCM & DCM boundary

P I = R ⋅ T ⋅ M 2
g
 o ,n1 4 ⋅ L

 I π
CCM & DCM / DCM boundary
θ =
2

R ⋅T
 I
2
 Po ,n 2 = 4 ⋅ L ⋅ M g ⋅ (1 − M g )
-------(14)
θ B = 0 CCM / CCM & DCM boundary

1
4
1 2 + 3⋅π ⋅ M g
 B
⋅ T ⋅ R ⋅ M g2
 Po,n1 = 2 ⋅
L

----(15)
 B π
CCM & DCM / DCM boundary
θ =
2

1
4
 B
1 2 + 3⋅π ⋅ M g − M g
⋅ T ⋅ R ⋅ M g2
 Po,n 2 = ⋅
L
2

Fig. 5 shows the CCM and CCM&DCM
boundary for both control methods. The CCM is
obviously enlarged for improved integration
control.
1
Improved
integration
control
I
0.628
θB
Test
1.257
0.942
θ
load.
T = 10uS ( f = 100kHz )
the peak input voltage and output voltage, i.e.
Po ,n is
normalized
conditions:
where θ and θ are DCM conduction angle for
the improved and the basic integration controlled
PFC respectively. M g is the voltage ratio between
Mg =
and
(a) M g = 0.44 (if Vo = 385V ,Vgrms = 120V ) .

4 ⋅ Po, n L  
 ---(12)
⋅ 1 − 2
⋅

M g ⋅ R T  


I
θ vs.
B
I
0.314
0
PoI,n1
PoB, n1
0.8
CCM&DCM
or DCM
CCM
0.6
0.1
0.28
0.46
Po,n
0.64
0.82
Basic
integration
control
1
0.4
CCM&DCM
or DCM
CCM
0.2
(a)
0
0.2
0.36
0.52
0.68
0.84
Mg
Mg = 0.8
1.257
Fig. 5. The CCM and CCM&DCM boundary for
improved/basic integration control
0.942
θ
I
θB
0.628
4
0.314
0
0.1
0.325
(b)
0.55
0.775
1
Experiment Verification
A 250W prototype boost PFC is built in order to
verify the theoretical analysis. The experimental
conditions are as follows:
1
5 of 6
Input voltage ranges from 85V to 270V (RMS);
the output voltage is Vo = 385V , f = 100kHz ;
the input inductance is L = 1mH .
Fig. 6 shows the experiment result for THD
comparison of the two methods vs. the normalized
load. The THD is very close for both converters
when the power approaches the full load. However,
at the light and medium load, the THD is
significantly reduced using improved integration
control. This is further verified by the measured
input current waveforms. Fig. 7 shows the
waveforms of the input current when input voltage
is 220Vrms and the output power is 100w(40% of
full load). The experiments demonstrated that the
proposed method not only reduces the distortion
when inductor operates on CCM mode, but also
enlarges the CCM region.
(a)
THD comparison for Vg=120V
20
THD
15
.
10
5
0
0
0.2
0.4
0.6
0.8
1
Po,n
THD1 Basic integration controlled PFC
THD2 Improved integration controlled PFC
of full load). Top curve: input AC voltage,
100V/div, 5ms/div. Bottom curve: input AC
current, 1A/div., 5ms/div
(a).
THD comparison for Vg=220V
5
60
50
40
THD(%)
(b)
Fig. 7 Line voltage and input current waveforms
for an experimental 250W power factor corrected
rectifier using basic/improved integration control
respectively
(a) Basic integration control. (b) Improved
integration
control
Experimental
conditions: V g = 220Vrms , Pout=100W (40%
30
20
10
0
0
0.2
0.4
0.6
0.8
1
Po,n
THD3 Basic integration controlled PFC
THD4 Improved integration controlled PFC
(b)
Fig. 6 The THD comparison between the
improved/basic integration controlled boost PFC
rectifier for input voltage Vg (rms) = 120V (a) and
Vg (rms) = 220V
(b)
Conclusion
Integration control method enables simple, low
cost, stable power factor control of continuous
conduction
mode
rectifiers.
A
simple
compensation network is proposed in the paper to
improve the performance of the integration
controlled PFC. The proposed method has
following advantages
• Eliminate the input current distortion caused
by current ripple;
• Has lower THD for light and medium load by
significant reducing the DCM conduction angle
θ;
• Easy to implement, only two resistors needed
to add into the circuitry;
• Easy to integrated in a single integration chip;
The disadvantage is the need to sense the input
voltage. However, in practice, the input voltage is
required to compensate the input RMS variation
anyway. The theoretical analysis is verified by
the experimental results.
6 of 6
REFERENCES
[1]. Lai, Z.; Smedley, K.M. “A family of powerfactor-correction controllers”. APEC'97. New
York, NY, USA: IEEE, 1997. p.66-73 vol.1
[2]. J.P. Gegner, C.Q.Lee. "Linear Peak Current
Mode Control: A Simple Active Power Factor
Correction Control Technique For Continuous
Mode". PESC 96 Record. New York, NY, USA:
IEEE, 1996. p.196-202 vol.1. 2 vol. xxiv+2000 pp.
[3]. D. Maksimovic, "Nonlinear-Carrier Control
For High Power Factor Boost Rectifiers", IEEE
Transactions on Power Electronics, vol.11, (no.4),
IEEE, July 1996. p.578-84.
[4]. Maksimovic, D. Design of the clamped-current
high-power-factor
boost
rectifier.
IEEE
Transactions on Industry Applications, vol.31,
(no.5), Sept.-Oct. 1995. p.986-92.
[5]. Lai, Z, Smedley,K.M. “A General Constant
Frequency Pulse-Width Modulator and Its
Applications”. IEEE Transactions on Circuits and
Systems I: Fundamental Theory and Applications,
vol 45.(no.4), IEEE, April, 1998.P.386-96.
Appendix
The derivation of the DCM conduction angle
(1) Improved integration control
From section 2, if we set k =
θ
Rs ⋅ T
, the equation
2⋅L
(9) can be rewritten as
Vm − Rs ⋅ i Lpk
R ⋅T
= (Vm − S
⋅ V g ) ⋅ D -(16)
2⋅ L
If the converter operates in DCM, the inductor peak
current is given by
iLpk
V
= g ⋅ D ⋅ T --------(17)
L
Substituting equation (17) into (16), yields
DDCM =
1
-------(18)
1 + ⋅ Vg , n
Ln
Vm
 1
θ = a sin 
 M g
Assuming the average input power equals output
power during each line cycle and power factor
equals unity, we can get
V gm
2
power; Pmax =
ig
rms
Vo
= 1−
Vo
------(21)
At the CCM and DCM boundary, ( wt = θ ),
DCCM should equal to DDCM , which gives us
normalized
output
Vo2
. Pmax is the rated power; R
R
=
1 Vm ⋅ V gm
1 Vm
⋅
=
⋅
⋅ M g -2 RS ⋅ Vo
2 RS
Vm =
2 ⋅ RS ⋅ Vo Po , n
⋅ 2 -------------(25)
R
Mg
Substituting (25) into (22), we get
 1
θ I = a sin 
 M g

4⋅ P
L 
⋅ 1 − 2 o , n ⋅  -(26)
 M ⋅ R T 
g


(2) Basic integration control
Assuming the input power equals the output
power during one line cycle, yields
2π
1
⋅ ∫ Vg ⋅ i g ⋅ dwt = Po ,n ⋅ Pmax --(27)
2 ⋅π 0
where i g is determined by equation (8).
Rs Vo T 2 Rs Vo Po , n
4 V gm TRs
+ 2
−
⋅
2⋅L
3⋅π
L
Mg R
--------(28)
Following the similar procedure, we can get the
DCM conduction angle θ
follows
If the boost converter operates in CCM, the duty
ratio is given by
DCCM = 1 −
the
(24)
Combination of equation (24) and (23) yields
Vm =
V gm ⋅ sin wt
= Pout = Po , n ⋅ Pmax -
is rated load.
For the first order approximation, the input
average input current can be expressed by
equation (11) no matter what kind of mode the
converter operates. From equation (11), we have
operates in the DCM subinterval; Ln is normalized
Vg
rms
Po ,n is
We have
R ⋅ T ⋅ V0
Ln = S
----(19)
2⋅ L
Vg Vgm ⋅ sin wt
---(20)
Vg , n =
=
Vo
V0
⋅ ig
(23)
where
Where D DCM is the duty cycle when converter
inductance; Vg ,n is the normalized input voltage.
 V 
⋅ 1 − m   ----(22)
Ln  

 1
θ B = a sin 
 M g
-------(29)
B
that is shown as
1

L P
4
⋅  − 2 ⋅ ⋅ o,n 2 +
⋅ M g 
2

T R ⋅ M g 3 ⋅π

