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7264 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 31, NO. 10, OCTOBER 2016

Performance Comparison of Three-Step and Six-Step

PWM in Average-Current-Controlled Three-Phase

Six-Switch Boost PFC Rectiﬁer

Laszlo Huber, Senior Member, IEEE, Misha Kumar, and Milan M. Jovanovi

c, Fellow, IEEE

Abstract—In this paper, a three-step PWM method for the

average-current-controlled three-phase six-switch boost PFC rec-

tiﬁer is proposed. It is shown that the three-step PWM compared

to the conventional six-step PWM exhibits a lower total harmonic

distortion of the input currents and higher power factor. However,

the three-step PWM, unlikethesix-stepPWM,isadversely affected

by the duty-cycle limitations and has unbalanced conduction losses

of the upper and lower switches of the three-phase rectiﬁer bridge.

The average-current control of the three-step and six-step PWM

is illustrated with MATLAB/Simulink simulation waveforms and

experimentally veriﬁed on a 3 kW prototype.

Index Terms—Average-current control, discontinuous space-

vector modulation (SVM), duty-cycle limitation, low-pass ﬁltering

and sampling, power factor(PF),segment detection, six-step PWM,

three-phase six-switch boost PFC rectiﬁer, three-step PWM, total

harmonic distortion (THD), zero-sequence signal (ZSS) injection.

I. INTRODUCTION

ODAY, the active three-phase power factor correction

(PFC) rectiﬁers need to meet very challenging perfor-

mance requirements. In the majority of applications, the in-

put current of the active three-phase PFC rectiﬁers is required to

have a total harmonic distortion (THD) less than 5% and a power

factor (PF) greater than 0.99 [1]. One of the most cost-effective

topologies that can meet these requirements is the three-phase

six-switch boost PFC rectiﬁer [2], which is usually implemented

without a neutral-point connection.

A number of control methods that can achieve a high quality

of input currents in the three-phase six-switch boost PFC rec-

tiﬁer are available [3], [4]. Generally, approaches using direct

control of input current versus, for example, direct power con-

trol, result in a better quality of the input currents [5]. Today, the

control circuit is usually implemented with digital technology.

One direct current control method, well suited for the digital

implementation, is the average current control [6], [7].

In a three-wire three-phase applications because the sum of

the phase currents is zero, the control can be implemented by

having only two out of the three current controllers actively

shaping the current at a given time. The desired current in the

inactive-controller phase is obtained by the sum of currents of

Manuscript received August 10, 2015; accepted October 29, 2015. Date of

publication December 8, 2015; date of current version May 20, 2016. Recom-

mended for publication by Associate Editor T. Shimizu.

The authors are with the PowerElectronics Laboratory, Delta Products Corpo-

ration, Research Triangle Park, NC 27709 USA (e-mail: lhuber@deltartp.com;

misha.kumar@delta-corp.com; milan@deltartp.com).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TPEL.2015.2506554

the actively controlled phases. One implementation of this con-

trol method is based on dividing the line cycle of the input phase

voltages into six 60° segments [six-step pulse width modulation

(PWM)] as shown in Fig. 1(a) [8], [9]. In each 60° segment, the

controller in the phase with the highest absolute value voltage is

disabled, i.e., switches in the corresponding leg are turned

OFF,

which results in reduced switching losses.

In this paper, another implementation of this control method

is proposed. It is based on dividing the line cycle of the input

phase voltages into three 120° segments (three-step PWM) as

shown in Fig. 2. In each 120° segment, the controller in the phase

with the most positive (or most negative) phase voltage is dis-

abled, i.e., the switches in the corresponding leg are turned

OFF.

The three-step PWM is equivalent to the discontinuous space-

vector modulation with unbalanced conduction losses between

the upper and lower switches [10].

A detailed performance comparison of the three-step and six-

step PWM in the average-current controlled three-phase six-

switch boost PFC rectiﬁer is also provided in this paper. It is

shown that the three-step PWM compared to the six-step PWM

exhibits lower THD of input currents and higher PF. The oper-

ation of the three-step and six-step PWM is illustrated with the

MATLAB/Simulink simulation waveforms and experimentally

veriﬁed on a 3-kW prototype.

II. A

VERAGE CURRENT CONTROL WITH THREE-STEP AND

SIX-STEP PWM

In the six-step PWM, a line cycle of input phase voltages

is divided into six 60° segments such that within a 60° seg-

ment none of the three-phase voltages changes sign, as shown

in Fig. 1(a). In each 60° segment, the controller in the phase with

the highest absolute value voltage is disabled, i.e., switches in

the corresponding leg are turned

OFF. For example, in segment

I, the controller in phase “a” is disabled, i.e., switches S

and

are turned OFF, as shown in Fig. 1(b). The simpliﬁed circuit

diagram of the three-phase six-switch boost PFC rectiﬁer with

six-step PWM in segment I is shown in Fig. 1(c). Since in seg-

ment I, the leg in phase “a” is disabled and the phase current i

is positive, rectiﬁer input aR is connected to the positive output

rail (through diode D

). By sinusoidal modulation of switches

in legs “b” and “c,” desired sinusoidal average phase-to-phase

voltages v

aRbR

and v

aRcR

can be generated between the rectiﬁer

inputs, respectively. As the sum of the phase–phase voltages at

the rectiﬁer inputs must be zero, a desired voltage v

bRcR

is au-

tomatically generated. To generate sinusoidal average phase-to-

phase voltages between rectiﬁer inputs, the current controllers

See http://www.ieee.org/publications

standards/publications/rights/index.html for more information.

HUBER et al.: PERFORMANCE COMPARISON OF THREE-STEP AND SIX-STEP PWM 7265

Fig. 1. Six-step PWM: (a) 60º segments, (b) circuit diagram in segment I, (c) simpliﬁed circuit diagram in segment I.

Fig. 2. Three-step PWM with 120º segments referenced to: (a) positive enve-

lope, (b) negative envelope of input phase voltages.

are designed to control phase–phase currents. The output of

the phase–phase-current controllers determines the phase–phase

duty cycles d

, d

, and d

so that in steady-state operation

aRbR

= d

, v

bRcR

= d

, and v

cRaR

= d

. Switch

duty cycles d

, d

and d

are obtained from phase–phase

duty cycles so that d

= d

− d

, d

= d

− d

, and

= d

− d

. For example, in segment I, d

=1and, there-

fore, d

=1− d

and d

=1+d

. It should be noted that

=1means that the rectiﬁer input aR is connected to the

positive output rail due to the conduction of diode D

.The

steady-state duty cycle of all switches is summarized in Table I,

whereas, the variation of duty cycle d

during the whole line cy-

cle is shownin Fig. 3 as an example. As can be seen in Fig. 3, duty

cycle d

exhibits abrupt changes at 60°-segment transitions,

TABLE I

TEADY-STATE DUTY-CYCLE OF SWITCHES FOR SIX-STEP PWM

60° Segment d

I101 − d

1+d

−d

II −d

1+d

1 − d

III 1+d

−d

101 − d

IV 0 1 −d

1+d

1 − d

V 1 − d

1+d

−d

VI d

1 − d

01−d

1+d

Fig. 3. Duty cycle of upper switch in phase “a” for six-step PWM at 120 V

rms

input voltage.

which induces input-current transients at the segment transi-

tions. These transients, which can be seenas notchesand glitches

in the input current waveforms and can be regarded as segment-

transition noise, may cause false segment detection in the

six-step PWM.

In the proposed three-step PWM, a line cycle of input phase

voltages is divided into three 120° segments such that within

a 120° segment one-phase voltage is always greater or smaller

than the other two phase voltages, as shown in Figs. 2(a) and

(b), respectively. Accordingly, the three-step PWM is either

referenced to the positive or to the negative envelope of the

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