 A Novel Three-Phase PFC Rectifier
Using a Harmonic Current Injection Method
I. Ashida*, J. Itoh** Nagaoka University of Technology, Niigata, Japan

Abstract-- This paper proposes a novel circuit topology
for a three-phase power factor correction (PFC) rectifier
using a harmonics current injection method.
In
consideration of lower cost, the harmonics injection method
is more suitable than a conventional six-arm pulse widthmodulation (PWM) rectifier. The harmonics injection
current is simply generated by only one switching leg. As aresult, the proposed circuit has the advantage of only two
switches. An optimal injection current is achieved in orderto obtain an input current of sinusoidal waveforms. This
paper discusses the basic operation and optimal design
method for the proposed circuit. In addition, the validity ofthe proposed circuit is confirmed by simulation andexperimental results. An input current of almost sinusoidal
waveform was obtained and an input current total
harmonic distortion (THD) of 8.5% was obtained at a loadof approximately 1 kW.

proposed circuit consists of two switching devices; twoLC filters and a harmonic injection network. Thus, theproposed rectifier can realize lower cost than theconventional injection type PFC rectifiers. In addition,high efficiency is achieved, because the main current
passes through only two diodes in addition to the dioderectifier. The injection current is controlled by the
optimum method given in [3], in order to suppress the
input current distortion. This paper describes the featuresof the proposed rectifier, and gives details of theoperation and the optimum design method. Simulationand experimental results show the validity of the
proposed circuit and design method.

Index Terms-- Harmonic current injection, Three-phase
diode rectifier, High power factor, Input current harmonic.

A. Harmonic current injection method
Figure 1 shows the basic circuit configuration of thecurrent injection method. The principle of this method isthat the input current is composed of an input current of
the diode rectifier and an injection current as shown in
Fig. 1(b). When the injection current ih, is defined by Eq.
(1), the harmonic component in the input current ia can be
expressed by Eq. (2).
ih  kid sin(3Zt )(1)

I. INTRODUCTION

II. CIRCUIT TOPOLOGY

Recently, the harmonics current in a power grid cancause various problems, such as line voltage distortion,
heating of power factor correction capacitors and so on.
Power factor correction (PFC) rectifiers, which suppress
the harmonics current, are still a very important
technology. One of the most popular PFC methods forthree-phase input is a full-bridge type pulse withmodulation (PWM) rectifier, which consists of six arms
and a boost-up reactor. The conventional PWM rectifier
can obtain a sinusoidal input current without harmonics
distortion. However, in regard to cost, the conventional
PWM rectifier is not the best solution for the PFC. On
the other hand, many three-phase PFC rectifiers that use
current injection methods have been proposed [1-10].  These types of rectifiers can realize a low cost system,
because they do not require many switching devices incomparison with a conventional PWM rectifier. One
famous rectifier that uses the current injection method iscalled the Minnesota rectifier [1]. This circuit uses twoboost-up choppers in part of the DC-stage. The
Minnesota rectifier contains many switching devices in
the main current path. Therefore, it is difficult to obtainhigh efficiency due to the increase in conduction losses
from the switching devices in the main path.
This paper proposes a new simple three-phase PFC
rectifier using a harmonic current injection method. The

1-4244-0844-X/07/$20.00 ©2007 IEEE.

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iA

ia

iP

iB

ib

Harmonic current
generation circuit

iC

ic

Injection
NetworkidiQih(a) Circuit configuration.

[A] 10ia

0-10[A] 10

iA

0
-10
0

20
10
15
Time[msec](b) Current waveform.
Fig. 1. Circuit for the harmonic current injection method.
5

ia

3

S

k·
2
§
id ¨ 2  ¸ sin Zt  ki d sin 3Zt
3
4
©
¹

(2)

3i d § 2 5 ·3i d § 2 7 ·¨  k ¸ sin 7Zt¨  k ¸ sin 5Zt S ©5 8 ¹S ©7 8 ¹

where id is the dc link current, Z is the angularfrequency of the input voltage, and k is the injection
current gain.
Although the 1/5 and 1/7 of the 5th and 7th harmoniccomponents are contained in the diode rectifier current ia,
those components are decreased by the injection current
gain, k. The optimum injection gain k is set to 3/4 inorder to obtain minimum values of the 5th and 7th
harmonics components.
Figure 2 shows examples of the harmonic current
injection network. The harmonics current is equally
injected through these circuits to AC side. The power
capacity of the injection network is not so large, sinceeach phase current becomes about 1/4 of the DC linkcurrent. It should be noted that if a system has an
isolation transformer in the input side, the neutral point of
the isolation transformer can be used instead of theinjection network.
B. Conventional circuit
Figure 3 shows one of the conventional three-phase
PFC rectifiers using the harmonic current injection
method, which is called a Minnesota rectifier. This
rectifier consists of a three-phase diode bridge rectifier,two series-connection boost converters, and the harmonic
current injection network. In this circuit, the injection
current ih is generated by controlling iP and iQ. The
injection current is obtained using Eq. (3).
i h i p  iQ
             (3)The features of this circuit are as follows: theefficiency decreases because the main current pathcontains two diodes in addition to the diode bridge part;the output voltage vd is constrained in Eq. (4), because theboost converter is used based on the neutral point voltageof the power supply.
vd t 2Vm(4)
where, Vm represents the peak value of the input voltage.
C. Proposed circuit
Figure 4 shows the main circuit of the proposed threephase PFC rectifier, which uses a single leg for the
harmonic current injection circuit. This rectifier requiresa three-phase diode bridge, a switching leg that consistsof S1 and S2, a filter reactor Lf, filter capacitor Cf, a DC
reactor Ld, and the harmonic current injection network.
The harmonic component of the switching frequency in
the DC current is reduced by the LC-filter.
In this circuit, the injection current ih is directly
controlled by S1 and S2. The injection current flows
depending on the voltage difference between points P or
N and point M. That is, when S1 is turned on, theinjection current can be obtained by Eq. (5), if the currentof the capacitor Cf is neglected.

(a) Tuned(b) Star/delta(c) Zigzag
LC filter.
 transformer.
transformer.
Fig.2. Harmonic current injection network.

Fig. 3. Main circuit of a Minnesota rectifier.

Fig.4. Main circuit of the proposed three-phase harmonic current
injection method PFC rectifier.

dih
dt

1
(VP  VM ) ! 0
L f  Linj

(5)

Similarly, when S2 is turned on, the injection current
becomes that given by Eq. (6).
dih
dt

1
(VN  VM )  0
L f  Linj

(6)

where Linj is the leakage inductance of the current
injection network.
Hence, it is possible to control the injection current,
since the increase and decrease of the current can becontrolled by S1 and S2, as shown in Eqs. (5) and (6). It
is noted that the output voltage vd of the proposed circuit
becomes the same as a normal three-phase diode bridge.
The proposed rectifier has following advantages overthe conventional rectifier (Minnesota rectifier):(a) High efficiency is obtained because the maincurrent passes through only two diodes, which areused as a diode bridge.
(b) The filter reactor realizes a reduction in size, due tothe following AC current. In the conventional
circuit, LP, LQ requires a DC reactor. The volume of
the AC reactor is smaller than the DC reactor.
III. CONTROL STRATEGY
Figure 5 shows the relation between the input current
command and the optimum injection current command ih.
As discussed in chapter II, the injection current can
improve the input current waveform to a sinusoidal
current. In this chapter, we apply an optimum harmonic1303

current to the proposed circuit. While the ia is blocked by
the diode rectifier, the injection current ih only appears in
the input current. Hence, the waveform of ih has to fit toa part of the sinusoidal waveform if we want to achieve asinusoidal input current. As a result, the optimum
harmonic current is obtained by the middle signal in thethree-phase current command, as show in Ref. [4].
Therefore, the optimum harmonic current command ih is
obtained by Eq. (7).
ih 3>i A , iB , iC @max  3>i A , iB , iC @min(7)
Fig.5. Input current reference and ih*.

where >i A , iB , iC @max represents the maximum input
current

command,and>iA , iB , iC @minrepresenttheminimum input current commands. The input current
commands >iA , iB , iC @ are unity sinusoidal waveforms,
which are synchronized with the power supply voltage.
Figure 6 shows the control block diagram of the
proposed circuit. A hysteresis current controller isapplied in order to suppress the switching ripple of theinjection current. In this case, the ripple current can becontrolled by the bandwidth of the hysteresis current
controller. The input voltages vA, vB, vC and DC
inductance current iLd are detected in order to calculate
the input current commands iA*, iB*, iC*. It should be
noted that an inexpensive detection circuit, such as ashunt resistor, can be used since the DC link current
detection does not require quick response or highaccuracy. The optimum harmonic current command ih*
is calculated from iA*, iB*, iC* and Eq. (7).
IV. CIRCUIT DESIGN
A. Design of the DC link reactor
In the proposed circuit, iP and iQ, shown in Fig. 4,
depend on the difference between the DC link reactor
current iLd and ih, although ih is directly controlled by thehysteresis current regulator. Therefore, to suppress the
distortion of the input current, the DC link reactor current
iLd must be maintained as constant. However, the iLdripple is caused by the diode bridge output voltage vPM,
and vPM is obtained using Eq. (8).
vPM

3 3

S

Vm 

6 3
6 3
Vm cos 6Zt 
Vm cos12Zt  
143S
35S

(8)

where, Vm is the peak of the input voltage.
From Eq. (8), the AC component of the DC link
reactor current iLdAC is obtained by Eq. (9)
iLdAC



6 3 Vm
6 3 Vmsin 12Zt 
sin 6Zt 
143S 12ZLd
35S 6ZLd(9)

It should be mentioned that in Eq. (8) the 6th harmonic
current is dominant in iLdAC. Therefore, only the 6th
harmonic current is considered in the following
discussions. The ripple rate of the DC current caused by
the 6th harmonic current is equal to the ripple rate of theoutput power under constant DC voltage. That is, thetotal harmonics distortion (THD) of the DC side THDDC
can be calculated by Eq. (10).
THDDC

I m6
u 100
Id

3VI 6
u 100
3VI

I5  I7
u 100
I

(10)

Fig. 6. Control block diagram for the proposed circuit.

Fig.7. Simulation circuit for the ripple analysis.

where, Im6 is the peak value of the 6th harmonic current, I
is the fundamental frequency component of the input
current, I5,I6 and I7 are the 5th, 6th and 7th harmoniccomponents for the input current, Id is the value of theDC current, and V is the input voltage.
The 5th and 7th harmonic components in the input
current appear when the DC current contains the 6th
harmonic component. Then, the input current THD(THDAC) is calculated by Eq. (11).
THDAC

I 52  I 72
I

u 100

(11)

Therefore Eq. (12), which expresses the relationshipbetween THDAC and THDDC is derived from Eqs. (10) and
(11).
THDAC

I 52  I 72
I5  I7

THDDC

(12)

Figure 7 shows the simulation circuit used to confirm
the propriety of Eq. (12). Ideal current sources are usedinstead of the switching leg and the DC reactor. The
current source idAC assumes the ripple of the 6th harmonicin the dc current. The relationship of THDDC and THDAC
is investigated by changing the magnitude of the current
source idAC.
Figure 8 shows the comparison of the simulation
results and calculated results from Eq. (12). The
simulated results agree well with the calculated results
using Eq. (12). In this case, the relation of Eq. (13) isobtained, because the magnitude of I5 is almost the sameas the magnitude of I7.

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THDDC(13)

The propriety of equation (13) was identified assimulation result by agreement of equation (13).
Figure 9 shows relation between the value of the DC
link reactor and the THD of the input current, and isderived from Eqs. (9) and (13). The value of the dc
reactor is expressed by the percentage unit based on the
power supply voltage, frequency and converter power
capacity. It is suggested from Fig. 9, that the DC reactorof 10% is required in order to obtain an input current
THD of less than 10%.
B. Design of the LC-filter
The proposed circuit reduces the harmonic componentof the switching frequency using a LC-filter. The filter
reactor Lf and capacitor Cf are connected in parallel withthe output side of the diode bridge. There are two factorsthat influence the input current in the LC-filter design.
1) Phase shift of harmonic current
Figure 10 illustrates the influence of the LC filter
using a simulation waveform of the input current when
the phase between the injection current ih and the DC
current iP or iQ is delayed by the LC filter. The phaseshift from the LC filter causes the distortion of the input
current, because the current ia can not pass through thediode rectifier, except for only 60 degreesin the half
period of the power supply. Figure 10(b) shows therelationship between the input current THD and the phaseshift by the simulation. As a result, the input current
THD increases in proportion to the phase shift.
The input current THD can be reduced by increasing
the impedance of the LC-filter, because the phase shift iscaused by the LC filter current. The impedance of the
LC-filter(Zf) is expressed by Eq. (14)Zf

2 j ZL f 1
j ZC f2

j1  2Z L f C f

ZC f

(14)

Figure 11 shows the relation between the impedance
ratio of Zf to the rated impedance Z0, which is based on
the rated voltage, frequency and power capacity, and the
input current THD. It is noted that the decrease of the
input current THD depends on the increase in Zf
2) Harmonic component of the switching frequency
If the cutoff frequency (fc) of the LC-filter is close to
the switching frequency (fs), the harmonic component of
the fs remains. Therefore, the fc has to be designed at a
sufficiently low frequency for the fs. However, too low a
fc causes a phase shift, as discussed previously.
On the other hand, the switching frequency fs depends
on the hysteresis width Ihis, the impedance of the current
injection network Linj, and the filter reactor Lf, as shownin Eq. (15), because the PWM pattern is used by thehysteresis current regulator.
fs

1 >v A , vB , vC @max
L f  Linj
2 I his(15)>v A , vB , vC @max

means the maximum input

wherevoltage. Linj and Ihis are designed from equation (15).

1305

Fig. 8. Distortion in the input current depending on the ripple rateof iLd.
Input current THD [%]2

Fig.9. Relation between the DC link reactor and the input current
THD.

(a) Simulation waveform for input current.

Input current THD [%]

THDAC

㪏
㪍
㪋
㪉
㪇

㪉
㪋
㪍
㪏
㪧㪿㪸㫊㪼㩷㫊㪿㫀㪽㫋㩷㪲㪻㪼㪾㫉㪼㪼㪴㪈㪇(b) Input current THD dependence on the phase shift.
Fig.10. The influence of the phase shift of the harmonic current
on the input current THD.

Fig.11. Relation between Zf/Z0 and the input current THD.

Figure 12 shows the relationships amongst the input
current THD, the LC-filter impedance and the cutoff
frequency when the DC reactor current is maintained as
constant. In the fc /fs region from 20% to 90%, theincrease in the input current THD depends on the increaseof the cutoff frequency, because the harmonic componentof the switching frequency dominates the distortion of the
input current. However, in the fc /fs region around 10%,the input current THD is increased from the influence ofthe phase shift. Similarly, in case of the Zf/Z0 region
under 50, the LC-filter current causes distortion of the
input current.

9080

10 2  8 2

6[%]

70

21
17

䂥㪘

THD [%]

60

23

50

15
40
30

27-29
25-27
23-25
21-23
19-21
17-19
15-17
13-15
11-13
9-11
7-9

20

10

THD 2  THD f 2

19

13

20

30

40

50

60

70

80

10
90

fc/fs [%]

C. Example of the circuit design
The circuit parameters can be designed from Fig. 9 and
12 in order to realize the desired input current THD. For
example, an input current THD of less than 10% can be
designed for the proposed circuit. Firstly, the cutoff
frequency is selected as 20% of the switching frequency,
using Fig. 12. Then the impedance of Lf is obtained at
2.4%, and the admittance of Cf is simultaneously
determined as 5.5%. As a result, the design point in Fig.
12 is selected at an input current THD of approximately
8%. The 6th harmonic current is dominant in the THD
that is caused by the DC link reactor (THDDCL), and theresonant frequency of the LC filter dominates the
harmonics components of the input current THD.
Therefore, the allowance for the DC reactor current
THDDCL is obtained by Eq. (16), using THDf. which
dominates the resonant frequency. In this example, theDC reactor current THD has to suppress less than 6%.
Lastly, the value of the DC reactor is determined as 14%
from Fig. 9.
THDDCL

11

Zf/Z0

9

Fig.12. Relation between the filter and the input current THD.
TABLE 1 SIMULATION CONDITIONS.
Item
Value
Item
Rated line
200 V
Rated output
voltage
power
fC/ fS
20 %Cf(admitance)
50 Hz
Lf
Input frequency
DC capacitor
2200 uF
Ld

Value
1 kW
5.50 %
2.40 %
14 %Fig.13. Simulation results for the proposed circuit.

(16)

V. SIMULATION AND EXPERIMENTAL RESULTS
Table 1 shows the experimental and simulation
conditions that were derived in chapter III-C. The
simulation is used in order to check the fundamental
operation and the validity of the circuit parameters. The
switching frequency depends on the hysteresis bandwidth
and the reactor as already explained. The switchingfrequency is designed to be approximately 10 kHz. It isnoted that the DC reactor seems to have a large value.
However, the DC reactor can be small for use with anelectric inductor [11] or a current type load.
Figure 13 shows the simulation results of the proposed
circuit using the parameters of Table 1. A THD of 7.2%
and a unity power factor are obtained. In addition, aconstant output voltage on the DC side is also obtained.
It is noted that the one of the causes of this is the DC linkcurrent ripple, which occurs with the current distortion
around the peak of the input current.
Figure 14 shows the experimental results of the
proposed circuit with a resistive load under the same
condition as shown in Fig. 13. We can confirm that thesinusoidal input current and unity power factor are

Fig.14. Experimental results for the proposed circuit.

obtained are the same as the simulated results.
Furthermore, it is confirmed that the output voltage isalso maintained constant. A THD of 8.5 %, which isalmost the same as the simulated results, was obtained.
We consider that the causes of the difference between thesimulated and experimental results are the accuracy of thecircuit parameters and the imbalance in the impedance ofthe power supply.
Figure 15 shows the THD characteristics of the input
current against the output power. The input current THDof the proposed circuit increases according to thedecrease in the output power, since the harmonics current
is constant, although the fundamental current becomes1306

small in the light load region.
Figure 16 shows the efficiency and input power factor
for the proposed converter. A maximum efficiency of
96.2 % is obtained. In addition, an input power factor ofover 99% is obtained for a load over 50%. In the lightload region, the power factor decreases, because the THDof the input current increases as shown in Fig. 15.
Figure 17 shows a comparison of the converter loss
between the proposed circuit and a conventional circuit
based on the experimental results. The conventional
circuit was made under the conditions given in Table 2.
A maximum efficiency of 95.4% was obtained for theconventional circuit at the rated load. Therefore, theproposed circuit improves the efficiency by 0.8%
compared to the conventional circuit. The converter loss
can be reduced by approximately 20% at the rated loadusing the proposed circuit. It is noted that the differencein the loss between the proposed and conventional circuit
increases according to a heavy load. The reason for thisis that the condition loss of the boost up diode in theconventional circuit dominates the total loss.

Fig.15. Characteristics of the input current THD.
TABLE 2 EXPERIMENTAL CONDITIONS FOR CONVENTIONALCIRCUIT.
Item
Value
Item
Value
Rated Line
Rated output
200 V
1 kW
voltage
power
Input frequency
50 Hz
L
2.40 %
DC capacitor
2200 uF
100

Input power factor

98
96
Efficiency
94
92
90

0

0.5
1.0
Output power [kW]1.5

Loss [W]Fig.16. Efficiency and input power factor for the proposed circuit.

VI. CONCLUSIONSThis paper proposed a novel three-phase current injection
method PFC rectifier. In addition, the basic operation andoptimum design were discussed. The proposed circuit has thefollowing features;-the additional circuit components to the normal dioderectifier are one leg, a LC filter and injection circuit;- the input current THD is 8.5% at the rated load (1 kW);-the proposed circuit can reduce the converter loss by 20%
that for the conventional Minnesota rectifier.

The validity of the proposed circuit and the optimum
design method are confirmed with simulated andexperimental results. In future study, the volume of the
DC reactor will be reduced by optimum control,
depending on the DC current ripple.
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Fig.17. Comparison of the converter loss.

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