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Current Interactions Mitigation in 3-Phase PFC Modular Rectifier through Differential-Mode Choke Filter Boost Converter

February 2021
Applied Sciences 11(4):1-19

DOI:10.3390/app11041684

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CC BY 4.0

Authors:

José Gonçalves

Universidade NOVA de Lisboa

Stanimir Valtchev

New University of Lisbon; TU Sofia and BFU Bulgaria

Rui Melicio

IDMEC, Instituto Superior Técnico, University of Lisbon, Portugal

In this paper, a new way to mitigate the current interactions is proposed. The problem of current interactions arises when a modular three-phase (3-phase) rectifier (three single-phase modules) with boost converter for power factor correction (PFC) is used. A new differential-mode choke filter is implemented in the developed boost converter. The choke here is a specially made differential inductor in the input of the boost converter that eliminates the known current interactions. To prove the new concept, a study of the level of mitigation of the current interactions is presented. The control is operated in continuous driving mode (CCM), and the popular UC3854B circuit was used for this. The rectifier proposal is validated through a set of simulations performed on the PSIM 12.0 platform, as well as the construction of a prototype. With the results obtained, it is confirmed that the differential-mode choke filter eliminates the current interactions. It is observed that at the input of the rectifier, a sinusoidal alternating current with a low level of harmonic distortion is consumed from the grid. The sinusoidal shape of the phase current proves that a better power factor capable of meeting the international standards is obtained, and that the circuit in its initial version is operational. This proven result promises a good PFC operation, to guarantee the better quality of the electrical energy, being able to be applied in systems that require a high PFC, e.g., in battery charging, wind systems, or in aeronautics and spacecrafts.

Three-phase hybrid rectifiers types [7,8].

…

Proposal of three-phase modular rectifier.

…

First interaction of current traveled in phase a.

…

Second interaction of current traveled in phase a.

…

+16

Interaction analysis interval.

…

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applied

sciences

Article

Current Interactions Mitigation in 3-Phase PFC Modular Rectifier

through Differential-Mode Choke Filter Boost Converter

JoséTeixeira Gonçalves 1,* , Stanimir Valtchev 1,* and Rui Melicio 2,3





Citation: Gonçalves, J.T.; Valtchev, S.;

Melicio, R. Current Interactions

Mitigation in 3-Phase PFC Modular

Rectiﬁer through Differential-Mode

Choke Filter Boost Converter. Appl.

Sci. 2021,11, 1684. https://doi.org/

10.3390/app11041684

Academic Editors: Radu Godina,

Edris Pouresmaeil and Eduardo M.

G. Rodrigues

Received: 30 December 2020

Accepted: 9 February 2021

Published: 13 February 2021

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Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

1Departamento de Engenharia Eletrotécnica e Computador, CTS/UNINOVA, FCT,

Universidade NOVA de Lisboa, 2829-516 Monte Caparica, Portugal

2IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal;

ruimelicio@gmail.com

ICT, Escola de Ciências e Tecnologia, Universidade de Évora, Rua Romão Ramalho 59, 7002-554 Évora, Portugal

*Correspondence: jt.goncalves@campus.fct.unl.pt (J.T.G.); ssv@fct.unl.pt (S.V.)

Abstract:

In this paper, a new way to mitigate the current interactions is proposed. The problem

of current interactions arises when a modular three-phase (3-phase) rectiﬁer (three single-phase

modules) with boost converter for power factor correction (PFC) is used. A new differential-mode

choke ﬁlter is implemented in the developed boost converter. The choke here is a specially made

differential inductor in the input of the boost converter that eliminates the known current interactions.

To prove the new concept, a study of the level of mitigation of the current interactions is presented.

The control is operated in continuous driving mode (CCM), and the popular UC3854B circuit was

used for this. The rectiﬁer proposal is validated through a set of simulations performed on the PSIM

12.0 platform, as well as the construction of a prototype. With the results obtained, it is conﬁrmed that

the differential-mode choke ﬁlter eliminates the current interactions. It is observed that at the input

of the rectiﬁer, a sinusoidal alternating current with a low level of harmonic distortion is consumed

from the grid. The sinusoidal shape of the phase current proves that a better power factor capable of

meeting the international standards is obtained, and that the circuit in its initial version is operational.

This proven result promises a good PFC operation, to guarantee the better quality of the electrical

energy, being able to be applied in systems that require a high PFC, e.g., in battery charging, wind

systems, or in aeronautics and spacecrafts.

Keywords:

three-phase rectiﬁer; boost converter; interactions; differential-mode choke ﬁlter; wind

energy; aeronautics and spacecrafts

1. Introduction

Most electrical loads use direct current (DC) electrical energy, which implies the use

of a rectiﬁer that converts alternating current (AC) electrical energy to DC, which is also

known as a static rectiﬁer. The rectiﬁer was widely developed thanks to the emergence

of semiconductor devices as diodes (1900s) and transistors (1950s) a story told already

in [

]. There are several types of AC–DC converters (rectiﬁers) prepared for various loads.

The character of the load depends on the respective need and the cost associated with the

rectiﬁer. Brieﬂy, rectiﬁers are classiﬁed into two groups, bidirectional and unidirectional.

The bidirectional rectiﬁers are usually formed by a Graetz bridge (single-phase or

three-phase) with transistors (MOSFETs, IGBTs, etc.), thus requiring a control circuit to

drive the transistors. They are often used as a ﬁrst stage for an AC–DC–AC converter, when

after the rectiﬁer the goal is to inject energy to the grid. As an example, some wind turbines

apply this double conversion for producing the ﬁnal AC power [

–

] or in aeronautical

applications [5].

The unidirectional rectiﬁers use diodes as a switching device in most of the cases.

There are other unidirectional rectiﬁers, implemented as switching converters, but they

own the possibility to be reformatted into bidirectional ones. The diodes and thyristors are

Appl. Sci. 2021,11, 1684. https://doi.org/10.3390/app11041684 https://www.mdpi.com/journal/applsci

Appl. Sci. 2021,11, 1684 2 of 19

naturally commutated by the periodic changes of the polarity of the AC supply voltage.

These rectiﬁers are also commonly constructed as Graetz bridges of diodes, single-phase or

three-phase ones. The diodes Graetz bridges are more attractive, as they are simple, robust,

reliable, and low-cost rectiﬁers when compared to the to the bidirectional rectiﬁers or any

sophisticated AC–DC switching converters. Single-phase rectiﬁers are used for loads that

demand lower power, and some of them are coupled to a converter in order to reduce

the disturbances that the rectiﬁer can inject into the electrical network. The three-phase

rectiﬁers, on the other hand, cause great disturbance in the electrical network, due to the

large amount of power demanded by the load and its nature (usually inductive, sometimes

capacitive and nonlinear loads), compromising the quality of the energy in the electrical

network [

]. Therefore, in order to dimension the three-phase rectiﬁers, some important

parameters must be analyzed, being the rectiﬁer and the interface between the grid and the

load [6]. Brieﬂy, the following criteria are most important:

Criteria for connecting correctly the rectiﬁer to the grid:

•Voltage level and its variation;

•Nominal frequency and its variation;

•Minimum power factor (PF) value allowed by the energy supplier;

•Harmonic distortion level that the energy supplier allows.

Criteria for connecting the rectiﬁer to the load:

•Nominal voltage and respective operating current variation;

•Maximum allowed ripple of voltage and current;

•Accurate and reliable regulation of the current and voltage, as the load requires.

Additional criteria:

•Efﬁciency;

•Guarantee of reliability;

•Acceptable physical and mechanical parameters (weight, volume, temperature).

The drawback of the unidirectional diode or thyristor rectiﬁers is the high total

harmonic distortion (THD) that it injects into the electric grid and the low total power

factor (PF) value. With this, the rectiﬁer compromises the quality of energy in the electrical

network. As a way of safeguarding and control of the quality of energy in the electric

grid, some standards are emerging. Examples of international standards used on energy

quality are IEC61000-3-2 and IEC61000-3-4, and for the THD of the current injected into the

electrical network, IEEE Std 519-2014 is used.

As a way to use the more sophisticated unidirectional rectiﬁers in the electric networks,

some versions of them are aimed to improve the total harmonic distortion (THD). It can

be seen in Figure 1that some rectiﬁers are power factor correctors (PFC), keeping the

THD as low as possible, complying with the established standards [

]. In most cases,

another converter is associated with the rectiﬁer, to control the current. There is also the

possibility to associate an active power ﬁlter to the rectiﬁer’s input terminals, in order to

compensate the currents generated by the rectiﬁer, thus obtaining a good quality sinusoidal

current [

] at the rectiﬁer input. Some studies are focused on improving the efﬁciency of

the active power ﬁlter and simplifying the control system, as in [

]. Other studies focus

on implementing the hysteresis, called also Bang-Bang control [11].

In this case study, the modular three-phase rectiﬁers associated with a boost converter

will be analyzed, as this combination improves the power factor (PF). This effect is achieved

by shaping the input currents sinusoidally, thus guaranteeing a minimum THD at the input.

Appl. Sci. 2021,11, 1684 3 of 19

Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 20

Figure 1. Three-phase hybrid rectifiers types [7,8].

In this case study, the modular three-phase rectifiers associated with a boost con-

verter will be analyzed, as this combination improves the power factor (PF). This effect is

achieved by shaping the input currents sinusoidally, thus guaranteeing a minimum THD

at the input.

1.1. Three-Phase Modular Rectifiers with Boost Converter

The three-phase modular rectifiers with additional converter are usually composed

of three single-phase modules, where each module controls its phase individually. In the

numerous configurations that can be created, the single-phase rectifiers interact with each

other, which eliminates the possibility of control by the involved boost converter [12–14].

This becomes a problem, since the purpose of the individual rectifiers is to control the

current independently and to obtain a sinusoidal current with low THD and high PF in

each phase. There are some three-phase modular rectifiers that were created with the abil-

ity to eliminate those current interactions. Here, some more relevant rectifiers are sug-

gested by this paper.

A simple way to solve the current interaction problem in a modular three-phase rec-

tifier is analyzed in [15,16]. In this work, the author was concerned with the avoiding the

interaction between the phase input currents of the rectifier. For this, a transformer is im-

plemented at the input of each single-phase rectifier. This isolation by transformers makes

the interaction current stay in the secondary circuit of each rectifier and is not seen as

effect in the primary circuit. The primary currents and the sensors to control them do not

see any disturbance then. In this case, the PFC is working correctly but at the expense of

transformers application. The problem with this solution is that the transformers are grid

frequency type, and this, depending on the power of the rectifier, obliges them to be

heavy, bulky, and expensive.

In [17–19], to eliminate the current interaction, the author implemented yet another

diode at the output of the negative pole of each boost converter. This diode is polarized

inversely to the direction of the interaction current. An inductor at the negative terminal

of the input of each boost converter do the rest of the job. The inductor of a classic boost

converter in this case is split in two, one in the positive pole and one in the negative pole.

The mitigation of the interaction occurs because the impedance of the inductor is high

(due to the switching frequency) and therefore blocks the interaction current. Another

method similar to this one but with a slight difference is presented in [20,21]. In this

method, the two inductors of the boost converter are replaced by a coil winding inductor

coupled to increase the inductance effect by a factor 4, as it is calculated there. By this

special double-windings inductor, the filtering effect better eliminates the possible inter-

actions. The problem of this last solution [20,21] is the increased danger of the possible

saturation of the inductor, since it is a coupled inductor with concordant windings.

Figure 1. Three-phase hybrid rectiﬁers types [7,8].

1.1. Three-Phase Modular Rectiﬁers with Boost Converter

The three-phase modular rectifiers with additional converter are usually composed

of three single-phase modules, where each module controls its phase individually. In the

numerous configurations that can be created, the single-phase rectifiers interact with each

other, which eliminates the possibility of control by the involved boost converter [

–

This becomes a problem, since the purpose of the individual rectifiers is to control the current

independently and to obtain a sinusoidal current with low THD and high PF in each phase.

There are some three-phase modular rectifiers that were created with the ability to eliminate

those current interactions. Here, some more relevant rectifiers are suggested by this paper.

A simple way to solve the current interaction problem in a modular three-phase

rectiﬁer is analyzed in [

]. In this work, the author was concerned with the avoiding

the interaction between the phase input currents of the rectiﬁer. For this, a transformer

is implemented at the input of each single-phase rectiﬁer. This isolation by transformers

makes the interaction current stay in the secondary circuit of each rectiﬁer and is not seen

as effect in the primary circuit. The primary currents and the sensors to control them do

not see any disturbance then. In this case, the PFC is working correctly but at the expense

of transformers application. The problem with this solution is that the transformers are

grid frequency type, and this, depending on the power of the rectiﬁer, obliges them to be

heavy, bulky, and expensive.

In [

–

], to eliminate the current interaction, the author implemented yet another

diode at the output of the negative pole of each boost converter. This diode is polarized

inversely to the direction of the interaction current. An inductor at the negative terminal

of the input of each boost converter do the rest of the job. The inductor of a classic boost

converter in this case is split in two, one in the positive pole and one in the negative pole.

The mitigation of the interaction occurs because the impedance of the inductor is high (due

to the switching frequency) and therefore blocks the interaction current. Another method

similar to this one but with a slight difference is presented in [

]. In this method, the

two inductors of the boost converter are replaced by a coil winding inductor coupled

to increase the inductance effect by a factor 4, as it is calculated there. By this special

double-windings inductor, the ﬁltering effect better eliminates the possible interactions.

The problem of this last solution [

] is the increased danger of the possible saturation

of the inductor, since it is a coupled inductor with concordant windings.

Another possibility is also presented in [

], where the author replaces the inductor

of the boost converter with a coupled inductor of discordant windings in each converter

and implements a diode at the output of the negative pole of each converter. The coupled

inductor implemented in addition to the boost inductor introduces impedance differences.

The impedance in the direction of the interaction current is much higher than the impedance

in the direction of the normal current; thus, the circuit functions as an additional ﬁlter for

the interaction current. This solution [

] shows good results. One technology problem is

the winding of the inductor core, since the coupled inductor must block the passage of the

Appl. Sci. 2021,11, 1684 4 of 19

interaction current and let the normal current pass. These inductors are not easy to ﬁnd

ready to be supplied and require a special attention.

1.2. Problem and Objectives

As already seen, there are some techniques to mitigate current interactions in modular

three-phase rectiﬁers with boost converter and PFC, some of which stand out better than

others. The problem is that these techniques to mitigate current interactions have some

characteristics that may be undesirable, such as the increase in volume, weight, saturation,

and constructive complexity.

To solve these problems (volume, weight, saturation, and constructive complexity),

it is proposed to introduce DMCF in each boost converter (between the inductor and the

switching transistor) of the modular three-phase rectiﬁer, to ﬁlter the current interactions.

In the same way, isolate the supply circuit with the control circuit as much as possible using

the interface circuit, but without losing simultaneous operation.

The general objective of this work is to propose a modular three-phase rectiﬁer (three

modules) with boost converters and power factor correction capable of mitigating current

interactions through the DMCF. To achieve the general objective, it is essential to outline

the speciﬁc objectives. Thus, the speciﬁc objectives to be achieved are as follows:

•

Demonstrate that the DMCF is capable of mitigating the current interaction that

appears in three-phase modular rectiﬁers (three modules) with boost converters and

power factor correction;

•

Show that the interface circuit is able to isolate the power circuit with the control

circuit in order to avoid current interactions;

•

Enable other researchers to replicate the proposed circuit by simulation and prove its

functionality or develop improvements.

2. Design Proposal of the Three-Phase Modular Rectiﬁer

2.1. Proposal of Three-Phase Modular Rectiﬁer

The proposed three-phase modular rectiﬁer is illustrated in Figure 2. It is composed

of three single-phase rectiﬁer modules, each of which is connected to a boost converter

with control in the CCM. The connection of the rectiﬁer to the grid can be made in star (Y)

or delta (

∆

) conﬁguration. Here, in this particular case, it will be dealt with the star (Y)

connection. This proposed rectiﬁer has the purpose of rectifying a three-phase alternating

current, producing a direct current with stable output voltage. A high PF and low THD is

expected, thanks to the implementation of the differential-mode choke ﬁlter (DMCF) as

a part of the boost converter. This DMCF can be implemented before or after the boost

converter inductor.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 20

Figure 2. Proposal of three-phase modular rectifier.

2.2. Operating Principle of the Proposed Rectifier

This rectifier is developed precisely to work with voltage and three-phase current of

sinusoidal signal, expressed by:







(1)

Here  is the voltage in phase a, b, and c;  is the peak voltage.

The operating principle is based on Figure 2. In Figure 2, it is seen that the power

supplied by the source is distributed over three paths, since the modular three-phase rec-

tifier is composed of three rectifiers. The analysis can also be done through the input cur-

rents, , which will be distributed to the three rectifiers consecutively and

can be calculated by:



























(2)

Here  is the input current in phases a, b, and c, and  is the output

power.

Each current will thus be rectified by its corresponding rectifier composed of a bridge

of four diodes, after which a DMCF has been implemented to the respective boost con-

verter. The DMCF and the boost stage are there in order to eliminate the current interac-

tions (as is explained later in Section 2.3), and to serve the purpose of producing at the

input of the rectifier a sinusoidal waveform of the phase current. The current is produced

in phase with the voltage, thus guaranteeing a high PF and a low THD. Each rectifier

connected to its boost converter thus produces an output current  and  respec-

tively, which will then be added together, thus obtaining the output current  for charg-

ing the output capacitor, which acts as a filter and supplies the total current to the load.

The current that charges the filter capacitor varies its amplitude, but the output voltage

remains stable. As the converter is a boost converter, the output voltage will be higher

than the input voltage.

The total input power can be given by:

Figure 2. Proposal of three-phase modular rectiﬁer.

Appl. Sci. 2021,11, 1684 5 of 19

2.2. Operating Principle of the Proposed Rectiﬁer

This rectiﬁer is developed precisely to work with voltage and three-phase current of

sinusoidal signal, expressed by:











Vina (t)=VpSin(wt)

Vinb (t)=VpSin(wt −120)

Vinc (t)=VpSin(wt +120)

(1)

Here Vina,Vinb ,Vinc is the voltage in phase a, b, and c; Vpis the peak voltage.

The operating principle is based on Figure 2. In Figure 2, it is seen that the power

supplied by the source is distributed over three paths, since the modular three-phase

rectiﬁer is composed of three rectiﬁers. The analysis can also be done through the input

currents,

iina

iinb

and iinc

, which will be distributed to the three rectiﬁers consecutively

and can be calculated by:











iina (t)=2

VpSin (wt)

iinb (t)=2

VpSin (wt −120)

iinc (t)=2

VpSin (wt +120)

(2)

Here

iina

iinb

iinc

is the input current in phases a, b, and c, and

is the output power.

Each current will thus be rectiﬁed by its corresponding rectiﬁer composed of a bridge

of four diodes, after which a DMCF has been implemented to the respective boost converter.

The DMCF and the boost stage are there in order to eliminate the current interactions (as is

explained later in Section 2.3), and to serve the purpose of producing at the input of the

rectiﬁer a sinusoidal waveform of the phase current. The current is produced in phase

with the voltage, thus guaranteeing a high PF and a low THD. Each rectiﬁer connected to

its boost converter thus produces an output current

Io1

Io2

, and

Io3

, respectively, which

will then be added together, thus obtaining the output current

for charging the output

capacitor, which acts as a ﬁlter and supplies the total current to the load. The current that

charges the ﬁlter capacitor varies its amplitude, but the output voltage remains stable. As

the converter is a boost converter, the output voltage will be higher than the input voltage.

The total input power can be given by:

Pin =3VpIp

2=VoIo(3)

Ip=2VoIo

3Vo(4)

Here,

is the input power,

is the peak current value,

is the peak voltage,

the converter output voltage, and Iois the output current.

2.3. Mitigation of Current Interaction

If a converter with three rectiﬁers and a boost converter for each rectiﬁer is built,

all connected in parallel, as in Figures 3and 4, the interactions will appear, thus making

difﬁcult the possibility of control. For a better understanding, it will be considered an

analysis in a determined angular interval of the period from 30

◦

to 90

◦

. Only the two most

positive phases, presented in Figure 5, will be considered. It is considered that the switch

of the boost converter will be in the ON or OFF condition of its switching. During the

considered interval, the analysis is made by two switching states, ON and OFF.

Appl. Sci. 2021,11, 1684 6 of 19

Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 20

𝑃𝑖𝑛 = 3 𝑉𝑝 𝐼𝑝

2=𝑉𝑜 𝐼𝑜

(3)

𝐼𝑝=2 𝑉𝑜 𝐼𝑜

3 𝑉𝑜

(4)

Here, 𝑃𝑖𝑛 is the input power, 𝐼𝑝 is the peak current value, 𝑉𝑝 is the peak voltage, 𝑉𝑜

is the converter output voltage, and 𝐼𝑜 is the output current.

2.3. Mitigation of Current Interaction

If a converter with three rectifiers and a boost converter for each rectifier is built, all

connected in parallel, as in Figures 3 and 4, the interactions will appear, thus making dif-

ficult the possibility of control. For a better understanding, it will be considered an analy-

sis in a determined angular interval of the period from 30° to 90°. Only the two most pos-

itive phases, presented in Figure 5, will be considered. It is considered that the switch of

the boost converter will be in the ON or OFF condition of its switching. During the con-

sidered interval, the analysis is made by two switching states, ON and OFF.

Figure 3. First interaction of current traveled in phase a.

Figure 4. Second interaction of current traveled in phase a.

Figure 5. Interaction analysis interval.

Figure 3. First interaction of current traveled in phase a.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 20

𝑃𝑖𝑛 = 3 𝑉𝑝 𝐼𝑝

2=𝑉𝑜 𝐼𝑜

(3)

𝐼𝑝=2 𝑉𝑜 𝐼𝑜

3 𝑉𝑜

(4)

Here, 𝑃𝑖𝑛 is the input power, 𝐼𝑝 is the peak current value, 𝑉𝑝 is the peak voltage, 𝑉𝑜

is the converter output voltage, and 𝐼𝑜 is the output current.

2.3. Mitigation of Current Interaction

If a converter with three rectifiers and a boost converter for each rectifier is built, all

connected in parallel, as in Figures 3 and 4, the interactions will appear, thus making dif-

ficult the possibility of control. For a better understanding, it will be considered an analy-

sis in a determined angular interval of the period from 30° to 90°. Only the two most pos-

itive phases, presented in Figure 5, will be considered. It is considered that the switch of

the boost converter will be in the ON or OFF condition of its switching. During the con-

sidered interval, the analysis is made by two switching states, ON and OFF.

Figure 3. First interaction of current traveled in phase a.

Figure 4. Second interaction of current traveled in phase a.

Figure 5. Interaction analysis interval.

Figure 4. Second interaction of current traveled in phase a.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 20

𝑃𝑖𝑛 = 3 𝑉𝑝 𝐼𝑝

2=𝑉𝑜 𝐼𝑜

(3)

𝐼𝑝=2 𝑉𝑜 𝐼𝑜

3 𝑉𝑜

(4)

Here, 𝑃𝑖𝑛 is the input power, 𝐼𝑝 is the peak current value, 𝑉𝑝 is the peak voltage, 𝑉𝑜

is the converter output voltage, and 𝐼𝑜 is the output current.

2.3. Mitigation of Current Interaction

If a converter with three rectifiers and a boost converter for each rectifier is built, all

connected in parallel, as in Figures 3 and 4, the interactions will appear, thus making dif-

ficult the possibility of control. For a better understanding, it will be considered an analy-

sis in a determined angular interval of the period from 30° to 90°. Only the two most pos-

itive phases, presented in Figure 5, will be considered. It is considered that the switch of

the boost converter will be in the ON or OFF condition of its switching. During the con-

sidered interval, the analysis is made by two switching states, ON and OFF.

Figure 3. First interaction of current traveled in phase a.

Figure 4. Second interaction of current traveled in phase a.

Figure 5. Interaction analysis interval.

In the ON switching state, it can be noticed that the ﬁrst interaction takes place, where

the interaction current will pass from diode D1 of the ﬁrst rectiﬁer and diode D7 of the

second rectiﬁer, since these diodes are directly polarized and also present a greater potential

difference, that is, Vina >0 and Vinb <0 as shown in Figure 3[18,20,21].

In order to eliminate the ON switching interaction, a change is made in the boost

converter, placing one more diode at the output of the negative terminal of each boost

converter, polarized inversely to the direction of the interaction current. With this, the ON

switching interaction is thus eliminated [18,20,21].

When the switching goes to the OFF state, the second interaction appears. In this

second interaction, the current coming out of diode D1 will pass through the output

capacitor, connecting to diode D7 of the second rectiﬁer, since

Vina >

and Vinb <

0, as

shown in Figure 4[18,20,21].

In order to eliminate the off switching interaction, this paper proposes the implementa-

tion of a differential-mode choke ﬁlter (DMCF) between the boost inductor and the switch,

as shown in the rectiﬁer proposed in Figure 2.

The DMCF will cause the same current that travels in the positive direction (in the

primary inductor) to return in the negative direction (in the secondary inductor) of the

Appl. Sci. 2021,11, 1684 7 of 19

same phase. It is important to note that there will be no saturation in the DMCF inductors,

since the core of the DMCF will cancel the magnetizing generated by the positive and

negative currents, as they ﬂow in opposite directions to the core.

The mitigation of the current interaction can be explained as follows:

As previously mentioned, and illustrated in Figure 4, the second interaction occurs

because the value of the impedance where the interaction current travels (D1 to D7) is

practically the same as the impedance for the normal current path (D1 to D4). Therefore,

the secret is to make the impedance value for the normal current path (D1 to D4) as low as

possible, in relation to the impedance value of the interaction current path (D1 to D7). This

is possible when a DMCF is implemented. This change must be made in each of the three

boost converters, in a way that the current of the respective boost converter travels freely

along its own desired path and the path for the interaction current is made difﬁcult.

Considering the analyzed interval of interaction (Figure 5), the circuit shown in

Figure 4can be simpliﬁed, but now including the DMCF, for a better understanding of the

mitigation of the interaction. This is made in a mathematical analysis of the mitigation of

the interaction current. The simpliﬁed wiring diagram is illustrated in Figure 6, where two

rectiﬁers with their respective boost converters and the DMCF, with the normal current

path (

Io1and Io2

) and the current interaction path (

), can be seen. Following this same

ﬁgure, a mathematical analysis of the mitigation of the current interaction is made.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 20

In the ON switching state, it can be noticed that the first interaction takes place, where

the interaction current will pass from diode D1 of the first rectifier and diode D7 of the

second rectifier, since these diodes are directly polarized and also present a greater poten-

tial difference, that is,    as shown in Figure 3 [18,20,21].

In order to eliminate the ON switching interaction, a change is made in the boost

converter, placing one more diode at the output of the negative terminal of each boost

converter, polarized inversely to the direction of the interaction current. With this, the ON

switching interaction is thus eliminated [18,20,21].

When the switching goes to the OFF state, the second interaction appears. In this

second interaction, the current coming out of diode D1 will pass through the output ca-

pacitor, connecting to diode D7 of the second rectifier, since   , as

shown in Figure 4 [18,20,21].

In order to eliminate the off switching interaction, this paper proposes the implemen-

tation of a differential-mode choke filter (DMCF) between the boost inductor and the

switch, as shown in the rectifier proposed in Figure 2.

The DMCF will cause the same current that travels in the positive direction (in the

primary inductor) to return in the negative direction (in the secondary inductor) of the

same phase. It is important to note that there will be no saturation in the DMCF inductors,

since the core of the DMCF will cancel the magnetizing generated by the positive and

negative currents, as they flow in opposite directions to the core.

The mitigation of the current interaction can be explained as follows:

As previously mentioned, and illustrated in Figure 4, the second interaction occurs

because the value of the impedance where the interaction current travels (D1 to D7) is

practically the same as the impedance for the normal current path (D1 to D4). Therefore,

the secret is to make the impedance value for the normal current path (D1 to D4) as low

as possible, in relation to the impedance value of the interaction current path (D1 to D7).

This is possible when a DMCF is implemented. This change must be made in each of the

three boost converters, in a way that the current of the respective boost converter travels

freely along its own desired path and the path for the interaction current is made difficult.

Considering the analyzed interval of interaction (Figure 5), the circuit shown in Fig-

ure 4 can be simplified, but now including the DMCF, for a better understanding of the

mitigation of the interaction. This is made in a mathematical analysis of the mitigation of

the interaction current. The simplified wiring diagram is illustrated in Figure 6, where two

rectifiers with their respective boost converters and the DMCF, with the normal current

path () and the current interaction path (), can be seen. Following this same

figure, a mathematical analysis of the mitigation of the current interaction is made.

Figure 6. Representation of the analysis of current interaction mitigation in the proposed rectifier.

Here,  and  represent the phase a and b terminals,  is the phase a imped-

ance with neutral,  is the impedance in the combination of the phase a with phase b,

 is the boost inductor,  is the resistance, and  is the inductor.

Figure 6. Representation of the analysis of current interaction mitigation in the proposed rectiﬁer.

Here,

and

represent the phase a and b terminals,

ZFaN

is the phase a impedance

with neutral,

ZFab

is the impedance in the combination of the phase a with phase b,

the boost inductor, Ris the resistance, and Lis the inductor.

Mathematical Analysis of Current Interaction Mitigation

Analyzing Figure 6, it is noted that the secret to a better elimination of the interaction

is to make the impedance value

ZFaN

where the normal current ﬂows

are as low as

possible and the value of impedance

ZFab

where the current interaction

travels is as high

as possible. For this analysis, the impedances of the diodes, the output capacitor, and the

load can be disregarded, since these impedances will be the same for the two analyzed

paths. To do this, ﬁrst the analysis of the ZFaN impedance is done.

In the boost 1 converter, the currents

I11

I12

are the currents that ﬂow through each

coil of the DMCF,

R11

and

R12

are the two DC resistances respectively, so their impedances

(Z) are given similarly in [22]:

Z1=R11 +jwL11 +jwM I12

I11

(5)

Z2=R12 +jwL12 +jwM I11

I12

(6)

If L11 =L12 =Land K=1, then M will be given by:

M=KpL11L12 (7)

Appl. Sci. 2021,11, 1684 8 of 19

Here Mis the mutual inductance; Kis the magnetic coupling coefﬁcient.

Knowing that a DMCF is applied, its current travels in opposite directions in the

coupled inductors (I11 =−I12), and if assuming that M=L, then it is obtained:

Z1=R11 +jw(L11 −M)(8)

Z2=R12 +jw(L12 −M)(9)

With this, it can be calculated the impedance

ZFaN

, taking into account the impedances

of the coupled inductor (Z12) and the boost inductors (Zb1), given by:

Z12 =Z1+Z2(10)

Zb1=Rb1+jwLb1(11)

Thus, the ZFa N impedance will be given by:

ZFaN =Z12 +Zb1(12)

To calculate the impedance

ZFab

, the path of the current

must ﬁrst be analyzed.

It is noted that it travels in three inductors connected in series (

Lb1

L11

L22

), with

Lb1

and

L11

being inductors in the ﬁrst boost converter and

L22

being an inductor in the

second boost converter. For better understanding, the impedances will be separated in two

impedances, corresponding to

Zab1

for the ﬁrst boost converter and to

Zab2

for the second,

as given below:

Zab1=Rb1+jwLb1+(R11 +jwL11 )(13)

Zab2=R22 +jwL22 (14)

The ZFab impedance is given by:

ZFab =Zab1+Zab2(15)

The mitigation of the current interaction occurs when the impedance

ZFaN

is much

lower than the impedance

ZFab

, according to (16), which proves the appearance of current

Iaand not current It.

ZFaN << ZFab (16)

3. Implementation of the Proposed Three-Phase Modular Rectiﬁer

To validate the proposed three-phase rectiﬁer, a simulation study was carried out,

using the PSIM software version 12. The construction of an experimental prototype is

under development. The most important parameters used in the simulation are shown in

Table 1. It is important to note that the proposed rectiﬁer was dimensioned and analyzed

for a power of 20 kW, and therefore the load has a value of 29

Ω

. However, to analyze the

behavior of the PF and the THD of the rectiﬁer in changes in load resistance, it will also be

evaluated for 1%, 20%, 40%, 60%, and 80% of the 20 kW power. This corresponds to loads

of 289 (1%), 144 (20%), 72 (40%), 48 (60%), 36 (80%), and 29 Ω(100%).

The proposed circuit is divided (assembled) in the PSIM by three circuits, the power

circuit, the interface circuit, and the control circuit, as can be analyzed in Appendix A.

Appl. Sci. 2021,11, 1684 9 of 19

Table 1. Parameters used in the simulation.

Components Description Values

Vlin−rms RMS line voltage 380 V

F Network frequency 50 Hz

VoOutput voltage 760 V

PoOutput power 20 kW

LbInductance of boost inductor 1 mH

L1,L2Self inductance of DMCF 1 mH

M Mutual inductance of DMCF 0.99 mH

CoOutput capacitor 3300 uF

RoLoad 29 Ω

fsSwitching frequency 100 kHz

Power circuit: this is where the energy is processed between the source and the load.

Among the various elements constituted, the boost converter inductor, the DMCF, and the

output capacitor are most important. The boost inductor

was calculated according to

(17), whereas the output capacitor

is calculated by (18), similarly to the proposed in [

Lb=3·V2

p·2Vo−3Vp

fs·∆IL%·4·Po·Vo(17)

Co=2·Po·thold

o−(0.9·V0)2(18)

where

is the switching frequency,

∆IL%

is the current variation in the boost inductor in

percentage, and

thold

is the hold-up time (the time that the system keeps the energy in the

output capacitor).

The value of the inductances in DMCF, illustrated in Table 1, is chosen for a best

possible operation of the circuit.

Control circuit: The control strategy for the proposed three-phase rectiﬁer is based

on [

]. The control technique is performed using mean values in continuous driving

mode. To this end, the IC UC3854B was used, since it internally incorporates all the circuits

necessary for the implementation of the control and was designed for boost converters

with single-phase PFC. For better understanding, a basic diagram of the UC3854B control

process is illustrated in Figure 7, in just one rectiﬁer module. Basically, control starts at the

multiplier/divider, with the reference current as the output and parameters A, B, and C

as input.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 20

Figure 7. Basic diagram of UC3854B control.

Parameter A is the synchronism signal, that is, a rectified sinusoid signal from the

input voltage, and defines the shape, frequency, and phase of that reference signal trans-

formed into a current signal.

Parameter B is the voltage regulator error signal, which provides control of the out-

put voltage by varying the error signal that adjusts the amplitude of the reference current

according to the load variation. It corresponds to the necessary amplitudes of the sinusoi-

dal phase current that the rectifier should take from the input.

The parameter C is the feed-forward control signal that corresponds to the rms value

of the input voltage. That signal is obtained by approximated value obtained by filtering.

By this action, the reaction of the boost converter is faster, taking care for the rms variation

of the input phase voltage.

In this way, the reference current depends directly on parameters A, B, and C, and is

thus compared (regulated) with the current signal of the input (obtained by means of a

current sensor). Then, the regulated reference current is injected into the PWM block (com-

posed of a comparator, a sawtooth wave generator, and a control circuit) to generate the

necessary control pulses for the IGBT, explained in [23].

Interface circuit: The interface circuit is responsible for making the connection be-

tween the power circuit and the control circuit in an isolated way to avoid possible inter-

actions. In short, the isolation is done in the phase current, phase voltage, Vo signal, and

the IGBT control signal.

Phase current: To obtain the current signal, a Hall effect current sensor is used, to-

gether with a precision rectifier, to rectify the sensor signal in its negative polarity half-

wave, and then it is injected into the UC3854B.

Phase voltage: To obtain the voltage signal in isolation, transformers were used in

each phase, with a 230 V/6 V ratio. Then, these voltages were rectified by a precision rec-

tifier in positive polarity and sent to UC3854B. It is important to note that the signals ob-

tained from the precision rectifier were also used by an adder to obtain the rms signal of

the phase voltage.

Vo signal: The isolation on this DC bus signal is more to prevent any signal or noise

from the load from interfering directly in the voltage control loop. For this purpose, a Hall-

type voltage sensor was used.

IGBT control signal: This is also a crucial point and must be isolated to avoid interac-

tions. For this purpose, drivers with galvanic isolation were used in each driver canal.

Prototype Implementation

The prototype is under construction (being improved and tested). The power circuit,

the interface circuit, and the control circuit have already been built, as shown in Figure 8.

Figure 7. Basic diagram of UC3854B control.

Appl. Sci. 2021,11, 1684 10 of 19

Parameter A is the synchronism signal, that is, a rectiﬁed sinusoid signal from the input

voltage, and deﬁnes the shape, frequency, and phase of that reference signal transformed

into a current signal.

Parameter B is the voltage regulator error signal, which provides control of the output

voltage by varying the error signal that adjusts the amplitude of the reference current

according to the load variation. It corresponds to the necessary amplitudes of the sinusoidal

phase current that the rectiﬁer should take from the input.

The parameter C is the feed-forward control signal that corresponds to the rms value

of the input voltage. That signal is obtained by approximated value obtained by ﬁltering.

By this action, the reaction of the boost converter is faster, taking care for the rms variation

of the input phase voltage.

In this way, the reference current depends directly on parameters A, B, and C, and

is thus compared (regulated) with the current signal of the input (obtained by means of

a current sensor). Then, the regulated reference current is injected into the PWM block

(composed of a comparator, a sawtooth wave generator, and a control circuit) to generate

the necessary control pulses for the IGBT, explained in [23].

Interface circuit: The interface circuit is responsible for making the connection between

the power circuit and the control circuit in an isolated way to avoid possible interactions.

In short, the isolation is done in the phase current, phase voltage, Vosignal, and the IGBT

control signal.

Phase current: To obtain the current signal, a Hall effect current sensor is used, together

with a precision rectiﬁer, to rectify the sensor signal in its negative polarity half-wave, and

then it is injected into the UC3854B.

Phase voltage: To obtain the voltage signal in isolation, transformers were used in

each phase, with a 230 V/6 V ratio. Then, these voltages were rectiﬁed by a precision

rectiﬁer in positive polarity and sent to UC3854B. It is important to note that the signals

obtained from the precision rectiﬁer were also used by an adder to obtain the rms signal of

the phase voltage.

signal: The isolation on this DC bus signal is more to prevent any signal or noise

from the load from interfering directly in the voltage control loop. For this purpose, a

Hall-type voltage sensor was used.

IGBT control signal: This is also a crucial point and must be isolated to avoid interac-

tions. For this purpose, drivers with galvanic isolation were used in each driver canal.

Prototype Implementation

The prototype is under construction (being improved and tested). The power circuit,

the interface circuit, and the control circuit have already been built, as shown in Figure 8. It

was built for a power of 20 kW, but the ﬁrst tests are being carried out with a load of 74

Ω

which corresponds to a power of 6 kW. The values of the boost inductor, the DMCF, the

output capacitor, and other technical parameters (input voltage, mains frequency, switching

frequency) were constructed with values according to Table 1.

In Figure 8, (A) is the digital multimeter model IDM91E with voltage divider (1/2),

with the recorded voltage value of 666 V; (B) is the digital oscilloscope model TDS3014

B of 100 MHz, and 1.25 GS/s; (C) is the boost 1 inductor, with the inductance value of

0.5 mH + 0.5 mH;

(D) is the differential-mode choke ﬁlter (DMCF); (E) is control circuit 1;

(F) is the circuit interface; (G) is an AC Electric Energy Tester, Model AT3010, that records

the voltage value 230.8 V, the current value 9.237 A, the active power value 2.108 kW, the

power factor value 0.98, the frequency value 50 Hz, and the ambient temperature value

15 ◦C; and (H) is the power circuit.

Appl. Sci. 2021,11, 1684 11 of 19

Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 20

It was built for a power of 20 kW, but the first tests are being carried out with a load of 74

Ω, which corresponds to a power of 6 kW. The values of the boost inductor, the DMCF,

the output capacitor, and other technical parameters (input voltage, mains frequency,

switching frequency) were constructed with values according to Table 1.

Figure 8. Prototype in development.

In Figure 8, (A) is the digital multimeter model IDM91E with voltage divider (1/2),

with the recorded voltage value of 666 V; (B) is the digital oscilloscope model TDS3014 B

of 100 MHz, and 1.25 GS/s; (C) is the boost 1 inductor, with the inductance value of 0.5

mH + 0.5 mH; (D) is the differential-mode choke filter (DMCF); (E) is control circuit 1; (F)

is the circuit interface; (G) is an AC Electric Energy Tester, Model AT3010, that records the

voltage value 230.8 V, the current value 9.237 A, the active power value 2.108 kW, the

power factor value 0.98, the frequency value 50 Hz, and the ambient temperature value

15 °C; and (H) is the power circuit.

The prototype interface and control circuits are shown in Figure 9.

Figure 9. Prototype interface and control circuits.

A B C

Figure 8. Prototype in development.

The prototype interface and control circuits are shown in Figure 9.

Figure 9illustrates some components of the interface circuit and control circuit that

are being tested due to the interconnection between them and their efﬁciencies. The

components are: (A) is drives (CGD15SG00D2) for the correct functioning of the IGBTs

(IXYN50N170CV1); (B) is the voltage hall sensor (LV 25-P); (C) is the precision rectiﬁer;

(D) is the switch control; (E) are the current hall sensors (LAH 50-P); and (F) is the control

circuit 1 (UC3854B).

Some measured results from the reduced prototype tests are presented in Section 4,

together with the results by simulation.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 20

It was built for a power of 20 kW, but the first tests are being carried out with a load of 74

Ω, which corresponds to a power of 6 kW. The values of the boost inductor, the DMCF,

the output capacitor, and other technical parameters (input voltage, mains frequency,

switching frequency) were constructed with values according to Table 1.

Figure 8. Prototype in development.

In Figure 8, (A) is the digital multimeter model IDM91E with voltage divider (1/2),

with the recorded voltage value of 666 V; (B) is the digital oscilloscope model TDS3014 B

of 100 MHz, and 1.25 GS/s; (C) is the boost 1 inductor, with the inductance value of 0.5

mH + 0.5 mH; (D) is the differential-mode choke filter (DMCF); (E) is control circuit 1; (F)

is the circuit interface; (G) is an AC Electric Energy Tester, Model AT3010, that records the

voltage value 230.8 V, the current value 9.237 A, the active power value 2.108 kW, the

power factor value 0.98, the frequency value 50 Hz, and the ambient temperature value

15 °C; and (H) is the power circuit.

The prototype interface and control circuits are shown in Figure 9.

Figure 9. Prototype interface and control circuits.

A B C

Figure 9. Prototype interface and control circuits.

Figure 10 illustrates the instruments used to measure current and voltage in phase a.

For current measurement, a current probe on the 10 mV/A scale shown in Figure 10a was

used. In the case of measuring the network voltage signal, a voltage transformer was used

Appl. Sci. 2021,11, 1684 12 of 19

for galvanically isolated measurement with a 230 V/18 V model CTFCS150-18 pro-Power

ratio, illustrated in Figure 10b.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 20

Figure 9 illustrates some components of the interface circuit and control circuit that

are being tested due to the interconnection between them and their efficiencies. The com-

ponents are: (A) is drives (CGD15SG00D2) for the correct functioning of the IGBTs

(IXYN50N170CV1); (B) is the voltage hall sensor (LV 25-P); (C) is the precision rectifier;

(D) is the switch control; (E) are the current hall sensors (LAH 50-P); and (F) is the control

circuit 1 (UC3854B).

Some measured results from the reduced prototype tests are presented in Section 4,

together with the results by simulation.

Figure 10 illustrates the instruments used to measure current and voltage in phase a.

For current measurement, a current probe on the 10 mV/A scale shown in Figure 10a was

used. In the case of measuring the network voltage signal, a voltage transformer was used

for galvanically isolated measurement with a 230 V/18 V model CTFCS150-18 pro-Power

ratio, illustrated in Figure 10b.

(a)

(b)

Figure 10. Instruments used for measurement in phase a: (a) current probe used in current meas-

urement; (b) voltage transformer for galvanically isolated measurement.

4. Results and Discussion

For the results obtained, the rectifier input and output parameters are analyzed. The

input parameters are thus analyzed considering the values of currents, voltages, fast Fou-

rier transform (fft) results, power factor (pf) and total harmonic distortion (thd). for the

output parameters; the values of the currents and voltage are considered too. The availa-

ble results of the prototype are also presented and studied.

From the input currents, the sinusoidal shape and displacement of 120 degrees be-

tween the phases is taken to prove the results. With the results, it can be concluded that

the currents are being rectified by each module of the rectifier independently, and corre-

spond to the three-phase system, as shown in Figure 11.

Figure 11. Rectifier input currents (full power, Table 1).

Figure 10.

Instruments used for measurement in phase a: (

) current probe used in current measure-

ment; (b) voltage transformer for galvanically isolated measurement.

4. Results and Discussion

For the results obtained, the rectiﬁer input and output parameters are analyzed. The

input parameters are thus analyzed considering the values of currents, voltages, fast Fourier

transform (fft) results, power factor (pf) and total harmonic distortion (thd). for the output

parameters; the values of the currents and voltage are considered too. The available results

of the prototype are also presented and studied.

From the input currents, the sinusoidal shape and displacement of 120 degrees be-

tween the phases is taken to prove the results. With the results, it can be concluded that the

currents are being rectiﬁed by each module of the rectiﬁer independently, and correspond

to the three-phase system, as shown in Figure 11.