Neutral current compensation in three phase, four wire systems a review

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Electric

Power

Systems

Research

86 (2012) 170–

180
Contents

lists

available

at

SciVerse

ScienceDirect
Electric

Power

Systems

Research
j

ourna

l

ho

me

p

a

ge:

www.elsevier.com/locate/epsr
Review
Neutral

current

compensation

in

three-phase,

four-wire

systems:

A

review
D.

Sreenivasarao
∗
, Pramod

Agarwal,

Biswarup

Das
Electrical

Engineering

Department,

Indian

Institute

of

Technology

Roorkee,

Roorkee,

India
a

r

t

i

c

l

e

i

n

f

o
Article

history:
Received

7

July

2011
Received

in

revised

form
20

December

2011
Accepted

23

December

2011
Available online 26 January 2012
Keywords:
Active

power

ﬁlters

(APF)
Harmonic

elimination
Neutral

current

compensation
Power

quality
Three-phase

four-wire

distribution

system
Transformers
a

b

s

t

r

a

c

t
In

many

residential

and

ofﬁce

buildings,

power

is

distributed

through

a

three-phase,

four-wire

(3P4W)
systems.

The

non-linear

and

unbalanced

loads

in

these

systems

may

result

in

excessive

neutral

currents,
which

may

potentially

damage

the

neutral

conductor

and

distribution

transformer

while

affecting

the
safety

of

the

consumers.

Several

techniques

have

been

reported

in

literature

to

overcome

this

problem.
This

paper

presents

a

comprehensive

review

of

neutral

current

compensation

methods,

their

topologies,
and

their

technical

and

economical

limitations.

Simulations

are

also

carried

out

in

MATLAB/SIMULINK
environment

for

comparing

the

existing

methods.
© 2011 Elsevier B.V. All rights reserved.
Contents
1.

Introduction

.

.

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.

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. 171
2.

Problems

of

high

neutral

currents

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

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.

.

. 171
3.

Recommended

practices

for

handling

excess

neutral

currents

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

. 171
4.

Passive

harmonic

ﬁlters

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

.

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.

. 171
5.

Synchronous

machine

as

a

ﬁlter

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

. 172
6.

Transformer

based

topologies

.

.

.

.

.

.

.

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.

.

.

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.

.

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.

.

.

.

.

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.

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.

.

. 172
6.1.

Zigzag

transformer

.

.

.

.

.

.

.

.

.

.

.

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.

.

.

.

.

.

.

.

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.

.

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.

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.

.

. 172
6.1.1.

Operation

of

zigzag

transformer

with

unbalanced/distorted

supply

voltages

.

.

.

.

.

.

.

.

.

.

.

.

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.

.

. 172
6.2.

Star-delta

transformer.

.

.

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.

.

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.

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.

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.

. 173
6.3.

T-connected

transformer

.

.

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. 173
6.4.

Star-hexagon

transformer

.

.

.

.

.

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.

.

. 173
6.4.1.

Zigzag

transformer

with

single-phase

shunt

APF

.

.

.

.

.

.

.

.

.

.

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.

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.

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.

.

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.

.

. 174
6.4.2.

Zigzag

transformer

with

single-phase

series

APF

.

.

.

.

.

.

.

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.

. 175
6.4.3.

Star-delta

transformer

with

single-phase

half-bridge

PWM

APF

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

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.

. 175
7.

Three-phase,

four-wire

active

power

ﬁlters

.

.

.

.

.

.

.

.

.

.

.

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.

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.

.

.

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.

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. 176
7.1.

Three

H-bridge

shunt

APF

topology

.

.

.

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.

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.

. 176
7.2.

Three-phase,

four-wire

capacitor

midpoint

APF

topology.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

. 176
7.3.

Three-phase,

four-wire

four-leg

APF

topology.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

.

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. 177
8.

Conclusion.

.

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. 178
References

.

.

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.

. 178
∗
Corresponding

author.
E-mail

address:

(D.

Sreenivasarao).
0378-7796/$

–

see

front

matter ©

2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2011.12.014
D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180 171
1.

Introduction
The

three-phase,

four-wire

(3P4W)

electrical

distribution

sys-
tems

have

been

widely

employed

to

deliver

electric

power

to
single-phase

and/or

three-phase

loads

in

manufacturing

plants,
commercial

and

residential

buildings.

In

these

systems

single-
phase

supply

to

small

loads

is

provided

by

one

of

the

phase
conductors

and

neutral

wires.

To

balance

the

load

on

each

of
the

phases,

the

single-phase

loads

are

evenly

distributed

to

the
various

ﬂoors.

In

practice,

these

single-phase

loads

are

not

com-
pletely

balanced,

thus

resulting

in

a

net

current

ﬂowing

through
the

neutral

conductor.

These

are

not

the

only

sources

for

neutral
current

but

there

are

other

sources

such

as

non-linear

loads,

where
even

perfectly

balanced

single-phase

non-linear

loads

on

3P4W
system

can

result

in

signiﬁcant

neutral

current.

Nonlinear

loads,
such

as

power

electronic

based

equipment,

have

phase

currents
which

are

non-sinusoidal

and

the

vector

sum

of

balanced,

nonsinu-
soidal,

three-phase

currents

does

not

necessarily

equal

to

zero

and
result

current

in

the

neutral

conductor

[1–4].

With

sinusoidal

load
currents,

the

neutral

current

depends

only

on

the

system

unbal-
ance.

But,

in

a

balanced

system

with

harmonic

distorted

current
waveforms,

only

the

triplen

harmonics

(i.e.

with

harmonic

order
multiple

of

3)

contribute

to

the

neutral

current.

When

both

har-
monic

distortion

and

load

current

unbalance

are

simultaneously
present,

the

neutral

current

may

contain

all

harmonics

[1–14].
The

paper

discusses

the

problems

of

high

neutral

currents,

rec-
ommended

practices

for

handling

the

excess

neutral

currents

and
presents

comprehensive

review

of

technical

and

economical

limits
for

compensating

these

neutral

currents.
2.

Problems

of

high

neutral

currents
Unbalanced

and

non-linear

loads

on

3P4W

system

causes

exces-
sive

neutral

current

and

the

problems

related

to

the

excessive
current

in

the

neutral

conductor

are:

[3,4]
•
Overloading

of

distribution

feeders

and

transformers:

With

four
current

carrying

conductors,

the

distribution

system

feeders

and
transformers

may

overload

and

cause

additional

heat

loss.
•
Common

mode

noise:

The

voltage

difference

between

neutral
and

ground

causes

common

mode

noise

in

3P4W

power

sys-
tems.

This

common

mode

voltage

can

result

in

the

malfunction
of

sensitive

electronic

equipments.
•
Flat-topping

of

voltage

waveform:

The

power

supplies

use

the
peak

voltage

of

the

sine

wave

to

keep

the

capacitors

at

full

charge,
reductions

in

the

peak

voltage

appear

as

low

voltage

to

the

power
supply,

even

though

the

rms

value

of

the

voltage

may

be

normal.
•
Wiring

failure:

In

old

buildings,

load

growth

with

passage

of

time
makes

size

of

neutral

conductor

insufﬁcient

and

cause

wiring
failure

and

poses

a

ﬁre

hazard.
3.

Recommended

practices

for

handling

excess

neutral
currents
The

high

neutral

currents

in

3P4W

system

have

detrimental
effect

on

both

distribution

system

and

end

users.

The

rec-
ommended

practices

and

temporary

measures

recommend

by
different

agencies

to

reduce/eliminate

the

neutral

current

are

given
below

[15–19].

•
Over

sizing

of

neutral

conductor:

Over

sizing

of

neutral

conductor
is

an

expensive

solution,

while

the

overloading

of

distribution
transformer

and

feeder

remains

unaddressed

[4,16].
•
Derating

of

distribution

transformer:

With

non-linear

loads,

the
maximum

loading

of

transformer

should

be

reduced

to

below

its
Fig.

1.

A

four

branch

star

connected

passive

ﬁlter.
rated

capacity

to

avoid

overheating

the

distribution

transformer
and

excessive

distortion

in

output

voltage.

Derating

of

transform-
ers

for

three-phase

three

wire

supplies

and

3P4W

power

supplies
are

similar,

yet

they

have

signiﬁcantly

different

crest

factors

and
neutral

current

[4,18].
•
Separate

neutral

conductors:

Use

of

separate

neutral

conductors
for

non-linear

loads

to

avoid

shared

neutral

conductors

is

also

practiced.

However,

this

is

almost

impossible

where

loads

are
widely

scattered.
The

above

recommended

practices

are

effective

temporary

mea-
sures

and

have

serious

drawbacks.

The

only

solution

for

handling
these

excess

neutral

current

is

to

incorporate

the

neutral

current
compensation

devices.

There

are

various

approaches

reported

in
the

literature

for

compensating

neutral

currents.

Passive

solutions
such

as

zero

sequence

harmonic

ﬁlters,

synchronous

machine,

spe-

cially

designed

transformers

and

active

solutions

such

as

3P4W
active

power

ﬁlters

(APF).

Details

of

these

methods

and

their

com-
parisons

are

given

below.
4.

Passive

harmonic

ﬁlters
The

ﬁltering

of

excess

neutral

current

in

3P4W

systems

was
achieved

through

the

use

of

single-phase

passive

ﬁlters

connected
between

each

phase

conductor

and

the

neutral

wire.

These

passive
harmonic

ﬁlters

comprise

of

passive

elements

such

as

inductors,
capacitor,

and

resistors

and

tuned

to

a

particular

harmonic

fre-
quency(s)

[20–25].

A

solution

for

ﬁltering

current

harmonics

in
3P4W

networks

based

on

the

usage

of

a

four-branch

star

connected
ﬁlter

topology

is

depicted

in

Fig.

1

and

presented

in

[23].

This

topol-
ogy

has

four

individual

star-connected

passive

branches

(three
phase-branches

and

one

neutral

branch).

The

impedance

of

the
phase

branches

of

the

ﬁlter

are

identical

and

different

from

neutral
branch.

The

phase

branches

are

tuned

to

the

positive/negative-
sequence

harmonics

such

as

5th,

7th

and/or

11th,

13th

and

the
neutral

branch

is

tuned

to

3rd

and/or

9th.
Passive

solutions,

albeit

simple,

are

bulky

and

expensive.

Also,
the

sensitivity

of

the

components

to

temperature

and

aging

can
result

in

ineffective

ﬁltering

as

the

critical

frequencies

and

the

qual-
ity

factor

drifts.

Another

bigger

problem

is

the

possibility

of

exciting

a

resonance

condition

with

the

ac

system

impedance,

which

can
worsen

the

situation

[24,25].
172 D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180
Fig.

2.

Schematic

diagram

for

neutral

current

compensation

with

synchronous
machine.
5.

Synchronous

machine

as

a

ﬁlter
Simultaneous

absorption

all

the

zero-sequence

harmonic

cur-
rents

of

the

neutral

wire

using

a

synchronous

machine

has

been
proposed

in

[26].

If

the

zero-sequence

impedance

of

the

syn-
chronous

machine

is

sufﬁciently

smaller

than

that

of

the

power

source,

then

the

synchronous

machine

would

allow

the

absorp-
tion

of

the

zero-sequence

harmonic

currents.

This

can

be

done

by
selecting

the

coil

pitch

of

the

armature

winding

as

2/3.

As

a

result,
the

zero-sequence

reactance

of

the

synchronous

machine

reaches
minimum

value.

The

only

limiting

factor

of

the

zero-sequence

har-
monics

is

armature

resistance

of

the

synchronous

machine.

Hence,
it

is

possible

to

absorb

all

the

zero-sequence

harmonic

currents

by
the

synchronous

machine.

Fig.

2

shows

the

basic

system

in

which
the

synchronous

machine

is

used

for

absorbing

the

zero-sequence
harmonic

currents.

In

this

method

the

synchronous

machine

is
connected

in

shunt

between

the

utility

and

nonlinear

load.

The
neutral

point

of

the

armature

winding

of

synchronous

machine

is
connected

to

the

neutral

line

through

a

switch.

A

buffer

reactor

is
installed

on

the

utility

side

of

the

neutral

line

so

that

the

harmonic
compensation

characteristics

do

not

depend

on

the

impedance
of

the

utility

side.

This

method

does

not

require

any

additional
controller

and

the

synchronous

machine

can

be

operated

as

a

syn-
chronous

condenser

to

control

the

reactive

power

in

distribution
systems

and/or

operate

as

a

motor

or

generator

set.

However,

its
compensation

characteristics

depend

on

zero-sequence

impedance
of

the

synchronous

machine

and

buffer

reactor.
The

high

initial

and

maintenance

cost

of

the

synchronous
machine

limits

its

application.

The

passive

neutral

current

com-
pensation

technique

using

different

transformer

topologies

can
reduce/eliminates

the

neutral

current

to

a

great

extent.
6.

Transformer

based

topologies
The

neutral

current

compensation

for

a

3P4W

distribution

sys-
tem

using

different

transformer

topologies

have

been

analysed

by
different

researchers.

Some

of

the

important

transformer

topolo-
gies

are

discussed

below:
6.1.

Zigzag

transformer
In

past

the

zigzag

transformer

was

used

for

creating

a

neutral,
thereby

converting

a

three-phase,

three-wire

(3P3W)

distribution
system

to

a

3P4W

system

[27].

But,

the

use

of

zigzag

transformer

is
articulated

to

reduce

the

neutral

current

in

3P4W

system

[27–37].
The

schematic

diagram

of

the

basic

topology

is

illustrated

in

Fig.

3.
In

this

method

the

zigzag

transformer

is

connected

in

parallel

to

the
load,

and

it

is

connected

as

close

as

possible

to

the

load.

A

zigzag
transformer

consists

of

three

single-phase

transformers

with

the
turn

ratio

of

1:1.

Therefore,

the

input

currents

ﬂowing

into

the
Fig.

3.

A

zigzag

transformer

for

reducing

the

neutral

current

in

3P4W

systems.
primary

windings

is

equal

to

the

output

currents

ﬂowing

out

from
secondary

windings.

Then,

the

three-phase

currents

ﬂowing

into
three

transformers

must

be

equal.

Hence,

ideally

the

zigzag

trans-
former

can

be

regarded

as

open-circuit

for

the

positive-sequence
and

the

negative-sequence

currents

[31].

Then,

the

current

ﬂowing
through

the

zigzag

transformer

is

only

the

zero-sequence

compo-
nent.

But

in

practice

the

impedance

offered

for

the

zero-sequence
currents

is

a

function

of

the

zero-sequence

impedances

of

the

utility
system,

zigzag

transformer

and

the

neutral

conductor

[31].

How-

ever,

the

impedance

of

the

utility

system,

the

zigzag

transformer
and

the

neutral

conductor

are

very

small

in

most

practical

cases
[31].

So

a

large

value

of

the

zero-sequence

currents

will

circulate
between

zigzag

transformer

and

load.
The

rating

of

the

zigzag

transformer

depends

on

the

amount

of
load

imbalance

and

harmonic

content.

To

reduce

the

neutral

cur-
rent

of

utility

side

furthermore

it

is

advised

to

insert

an

inductor
(Z
n
)

in

the

neutral

conductor

of

the

utility

side

in

order

to

split

the
current

into

two

paths,

one

to

the

distribution

transformer

and

the
other

to

the

zigzag

transformer

[27,31].
6.1.1.

Operation

of

zigzag

transformer

with

unbalanced/distorted
supply

voltages

In

case

of

an

unbalanced

and/or

distorted

system

voltage,

then
a

zero-sequence

voltage

also

exists.

This

zero-sequence

voltage
generates

a

fundamental

zero-sequence

current

ﬂowing

through
the

three-phase

utility

conductors,

zigzag

transformer

and

utility
neutral

conductor.

However,

the

impedance

of

the

utility

system,
the

zigzag

transformer

and

the

neutral

conductor

are

very

small
in

most

of

the

3P4W

distribution

power

systems.

Hence,

there
is

a

signiﬁcant

neutral

current

ﬂow

into

the

zigzag

transformer
and

this

neutral

current

adversely

affect

the

performance

of

the
zigzag

transformer.

This

excess

neutral

current

may

result

in

the
burn-down

of

the

zigzag

transformer,

the

neutral

conductor

and
the

distribution

power

transformer

[31].

To

alleviate

this

problem,
the

zigzag

transformer

is

not

recommended

in

unbalanced

and/or
distorted

voltage

of

3P4W

distribution

power

system

except

an
inductor

(Z
n
)

is

inserted

in

the

neutral

conductor

of

the

utility

side
[31].

The

inserted

inductor

serves

three

purposes:
1.

Increases

the

attenuation

rate

by

spiriting

more

neutral

current
towards

zigzag

transformer

[27,31].
2.

Reduce

the

undesired

increase

of

the

neutral

current

if

the

sys-
tem

voltage

is

unbalanced

and/or

distorted

[31].
3.

Reduces

the

fault

current

in

case

of

a

line-to-neutral

fault

[27].
The

attenuation

of

this

neutral

current

is

a

function

of

the
inserted

inductor.

If

a

large

inductor

is

inserted

a

better

com-
pensation

is

achieved

[27].

The

effect

of

buffer

reactor

(Z
n
)

on
the

performance

of

zigzag

transformer

topology,

simulations

are
carried

out

in

MATLAB/SIMULINK

environment.

The

summary

of
D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180 173
Table

1
The

performance

of

the

zigzag

transformer

based

compensator

with

different

values

of

inserted

inductors.
Source

neutral

current

without

compensator

(rms,

A)

19.3
Source

neutral

current

after

compensation
with

inserted

inductor

(Zn)

(rms,

A)
No

inductor 1

mH

2

mH

3

mH

5

mH

10

mH
10.3 6.2

5.0

3.6

1.8

1.1
the

simulated

results

are

tabulated

in

Table

1.

From

the

table

it
is

observed

that

the

source

neutral

current

decreases

with

the
increase

in

the

buffer

reactor

and

improves

the

performance

of
zigzag

transformer.
However,

insertion

of

additional

inductor

may

result

in

the

neu-
tral

voltage

variation

[31].

Many

electrical

facilities

use

the

neutral
line

as

the

referred

ground,

the

neutral

voltage

variation

or

raising
the

neutral

voltage

of

the

load

side

may

cause

shut

down

or

abnor-
mal

operation

of

the

electric

facilities

in

the

load

side.

Therefore,
this

method

can

reduce

the

neutral

current

to

a

large

extent

but

it
will

not

completely

compensate

the

same.
6.2.

Star-delta

transformer
In

this

method

a

star-delta

transformer

used

for

the

reduction
of

neutral

current

in

3P4W

system

[38,39]

is

shown

in

Fig.

4.

Nor-
mally

a

limb

core

construction

is

used

in

the

star

winding

of

the
transformer,

because

the

zero

sequence

ﬂux

in

the

three

legs

does
not

add

to

zero

as

in

the

positive

sequence

case.

Instead,

the

sum

of
these

ﬂuxes

must

seek

a

path

through

the

air

or

through

the

trans-
former

tank,

either

of

which

presents

a

large

reluctance.

The

result
is

a

low

zero

sequence

excitation

impedance.

Hence,

the

star

con-
nected

primary

winding

of

the

transformer

offers

a

low

impedance
path

for

the

zero

sequence

currents.

The

delta

connected

secondary
winding

provides

a

path

for

the

induced

zero

sequence

currents

to
circulate

[39].
The

main

disadvantage

of

this

topology

is

that

its

compensation
characteristics

are

depends

on

the

impedance

of

the

transformer,
location

and

source

voltage

[31].

However,

this

method

can

reduce
only

the

neural

current

to

a

large

extent

but

it

will

not

completely
compensate

the

same.
6.3.

T-connected

transformer
In

this

method

a

T-connected

transformer

is

used

for

the

reduc-
tion

of

neutral

current

in

3P4W

systems

[40].

Here

the

T-connected
transformer

is

connected

in

parallel

and

as

close

as

possible

to
the

load.

Fig.

5

shows

the

schematic

diagram

of

the

T-connected
transformer

for

neutral

current

compensation

in

3P4W

system.
The

T-connected

transformer

consists

of

two

single-phase

trans-
formers

(one

two-winding

and

one

three-winding)

arranged

in

a
T-connection

[40].

This

arrangement

has

the

advantage

of

using
standard

two

single-phase

transformers;

consequently,

the

cores
Fig.

4.

A

star-delta

transformer

for

reducing

the

neutral

current

in

3P4W

systems.
Fig.

5.

A

T-connected

transformer

for

reducing

the

neutral

current

in

3P4W

systems.
are

economical

to

build

and

easy

to

assemble.

Accordingly,

the
transformer

is

small

in

ﬂoor

space,

low

in

height,

and

with

a
lower

weight

than

any

of

the

other

types

of

transformers

available
[41–43].
With

proper

selection

of

winding

arrangements,

the

T-
connected

transformer

can

be

regarded

as

open-circuit

for

the
positive

and

negative

sequence

currents.

Hence,

the

current

ﬂow-
ing

through

the

T-connected

transformer

is

only

the

zero-sequence
component

[40].

But

in

practice

the

impedance

offered

for

the

zero-
sequence

current

is

a

function

of

the

zero-sequence

impedances

of
the

utility

system,

T-connected

transformer

and

the

neutral

con-
ductor.

The

rating

of

the

T-connected

transformer

depends

on

the
amount

of

load

imbalance

and

harmonic

content

[40].
Similar

to

the

zigzag

transformer,

its

compensation

character-
istics

are

depends

on

the

impedance

of

the

transformer,

location
and

source

voltage

[31].

However,

this

method

can

reduce

only

the
neural

current

to

a

large

extent

but

not

completely

compensate

the
same.
6.4.

Star-hexagon

transformer
A

star-hexagon

transformer

can

also

be

used

for

the

reduc-
tion

of

neutral

current

in

3P4W

systems

[44,45].

Fig.

6

shows

the
schematic

diagram

of

star-hexagon

transformer

conﬁguration

for
neutral

current

compensation

in

3P4W

system.

A

star-hexagon
transformer

is

constructed

from

three

single-phase

three-winding
Fig.

6.

A

star-hexagon

transformer

for

reducing

the

neutral

current

in

3P4W

sys-
tems.
174 D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180
transformers.

In

this

method

the

star

connected

primary

provides
a

low

impedance

path

for

the

zero-sequence

harmonic

currents.

The

hexagon

connected

secondary

winding

provides

a

path

for

the
induced

zero

sequence

currents

to

circulate

[44–46].

Similar

to

the
zigzag

transformer,

its

compensation

characteristics

depend

on

the
impedance

of

the

transformer,

location

and

source

voltage

[31].
However,

this

method

can

reduce

only

the

zero-sequence

harmonic
current

to

a

large

extent

but

it

will

not

completely

compensate

the
same.
The

compensation

characteristics

of

transformer

based

meth-
ods

depend

on

source

voltage

conditions.

Effects

of

source

voltage
on

the

performance

of

transformer

based

topologies

have

been
investigated

in

MATLAB/SIMULINK

environment.

The

summary

of
the

simulated

results

are

given

in

Table

2,

and

observations

are

as
under:
•
Under

ideal

source

voltage

conditions,

transformer

attenuates
the

neutral

current

to

a

large

extent

but

it

will

not

completely
eliminate

the

same.
•

When

source

voltage

having

unbalance

and/or

distortions,

it
causes

signiﬁcant

rise

in

the

neutral

and

line

currents.

When

both
harmonic

distortion

and

unbalance

are

simultaneously

present
in

the

source

voltage,

then

the

raise

in

the

neutral

current

is
stringent.
The

comparison

of

the

neutral

current

compensation

methods

in

3P4W

systems

with

different

transformer

conﬁgurations

are

given
in

Table

3.

The

kVA

rating

of

the

transformer

is

primarily

decided
by

the

amount

of

the

neutral

current.

The

kVA

rating

of

the

trans-
former

is

calculated

by

considering

the

product

of

the

rms

values
of

the

voltage

and

current

associated

with

each

of

its

windings.

It

is
observed

from

Table

3

that,

zigzag

transformer

approach

requires
least

kVA

rating

but

it

may

require

three

single-phase

transformers
with

turn’s

ratio

of

1:1.

The

T-connected

transformer

requires

only
two

single-phase

transformers

and

also

its

rating

is

nearly

equal

to
the

zigzag

transformer

and

far

less

than

star/delta

transformer.
However,

the

transformer

based

methods

can

reduce

the

neural
current

to

a

large

extent

but

it

will

not

completely

compensate

the
same.

Complete

compensation

of

neutral

current

is

achieved

by
using

a

hybrid

ﬁlter.

The

main

advantages

of

these

hybrid

ﬁlters
are:

[28,29]
1.

The

compensator

effectiveness

is

independent

of

the

zero-

sequence

impedance

of

the

transformer

and

its

installation
location.
2.

It

greatly

reduces

the

size

of

the

active

power

ﬁlter

(APF).
Several

hybrid

approaches

are

reported

in

literature

and

are
given

below

[28,29,32,33,39].
6.4.1.

Zigzag

transformer

with

single-phase

shunt

APF
Fig.

7

shows

a

ﬁlter

scheme

for

compensation

of

neutral

current
in

3P4W

system

[28,29].

In

this

hybrid

ﬁlter

topology

a

single

phase
APF

is

connected

in

between

the

neutral

conductor

of

the

utility

and
the

neutral

point

of

the

zigzag

transformer.

The

single

phase

APF
is

controlled

in

such

a

way

that,

it

produces

the

desired

compen-
sating

current.

These

compensating

currents

are

injected

through
the

neutral

of

the

zigzag

transformer.

DC

voltage

is

maintained
across

the

capacitor

of

the

single-phase

APF

by

using

a

separate

single-phase

transformer

with

a

diode

rectiﬁer

bridge

of

a

very

low
kilo-Volt

Ampere

(kVA)

rating

[28].

Rating

of

the

single-phase

APF
is

very

small;

this

is

due

a

low

voltage

between

the

transformer
neutral

and

the

utility

neutral.

The

low

kVA

rating

of

the

invert-
ers

also

reduces

cost

as

well

as

power

losses

and

the

generated
Electromagnetic

Interference

(EMI).

However,

this

will

not

be

the
Table

2
The

performance

of

the

transformer

based

compensators

under

different

voltage

conditions.

Utility

voltage
conditions
Source

currents

before
compensation

(rms,

A)
Source

currents

after

compensation

(rms,

A)
Isa

Isb

Isc

Isn

With

only

zigzag

(Fig.

3)

With

star-delta

connected
transformer

(Fig.

4)
With

T-connected

transformer
(Fig.

5)
With

star-hexagon

transformer
(Fig.

6)
Isa

Isb

Isc

Isn

Isa

Isb

Isc

Isn

Isa

Isb

Isc

Isn

Isa

Isb

Isc

Isn
Ideal

53.42

52.92

35.36

19.42

49.44

52.92

39.98

9.30

45.21

50.02

42.10

11.13

49.44

50.19

44.11

8.98

48.12

53.13

45.99

12.01
Amplitude

unbalance
(50%

sag

in

Phase

A)
32.21

50.63

33.03

17.71

19.79

50.67

52.13

56.92

26.79

53.67

51.18

60.92

23.43

45.34

51.67

54.76

27.46

48.56

50.80

56.79
Phase

unbalance

(20
◦
,
−120
◦
&

−240
◦
)
52.07

55.79

32.45

13.53

57.59

44.73

44.68

30.44

52.32

48.31

40.60

28.21

46.99

34.22

46.79

34.76

50.13

41.17

49.88

37.89
Amplitude

&

phase
unbalance
31.35

51.25

31.71

14.59

28.09

46.10

54.72

60.70

30.11

42.34

53.90

55.62

22.70

50.61

45.67

55.92

25.22

53.61

48.22

60.11
Distorted

(15%

3th

&
10%

5th

order
harmonics)
53.56

53.39

35.08

21.91

51.21

54.75

40.97

39.07

50.23

48.68

45.09

36.43

45.42

58.21

35.70

46.21

43.67

55.87

37.55

46.39
Distorted

&

unbalanced
(amplitude

&

phase)
30.31

53.52

32.19

16.98

27.21

49.08

56.42

70.10

34.21

45.21

55.00

73.21

20.19

55.44

52.78

68.39

26.80

53.46

55.73

73.28
D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180 175
Table

3
Comparison

of

neutral

current

compensation

methods

in

three-phase,

four-wire

system

with

different

transformer

conﬁgurations

[37,40,46].
Transformer

type

Zigzag

(Fig.

3)

Star-delta

(Fig.

4)

T-connected
(Fig.

5)
Star-hexagon
(Fig.

6)
Number

of

transformers
required

to

build
3

(single-phase
two-winding)
1

(three-phase
two-winding)
2

(single-phase
three-winding

and
single-phase
two-winding)
3

(single-phase
three-winding)
Winding

voltages
(V
l
=

line-to-line

voltage)
V
l

3
:
V
l
3
V
l
√
3
:
V
l
√
3
V
l
√
3
:
V
l
2
√
3
:
V
l
2
√
3

and
V
l
2
:
V
l
2
V
l
√
3
:
V
l
√
3
:
V
l
√
3
Primary

winding

current
(I
n
=

neutral

current)
I
n
3
I
n
3
I
n
3
I
n
3
Transformer

rating
V
l
I
n
3
=

0.333V
l
I
n

V
l
I
n
√
3
=

0.577V
l
I
n

1
3
√
3
+
1
6

V
l
I
n
=
0.359V
l
I
n

V
l
I
n
√
3
=

0.577V
l
I
n
Is

it

a

standard

transformer? No Yes

No

No
Space

requirement Low

High

Lowest

Highest
Induce

circulating

currents

in
the

secondary

winding
No

Yes

No

Yes
Effectiveness

of

neutral

current

compensation

(based

on
simulation

study

under

ideal
utility

voltage

from

Table

2)
Better

than
star-delta

and
star-hexagon
Good

Better

than
star-delta

and
star-hexagon
Good
Cost

of

the

compensator

Low

High

Lowest

Highest
case

under

transient

as

well

as

abnormal

unbalanced

utility

volt-
age

conditions.

Under

these

conditions,

an

appropriate

Metal

Oxide
Varistors

(MOV)

must

be

used

to

protect

the

single-phase

inverter
and

zigzag

transformer

[29].
6.4.2.

Zigzag

transformer

with

single-phase

series

APF
Fig.

8

shows

a

ﬁlter

scheme

for

compensation

of

neutral

cur-
rent

in

3P4W

system

[32,33].

In

this

type

of

hybrid

ﬁlter

topology,
a

zigzag

transformer

is

connected

in

parallel

with

the

load

and

a
single-phase

pulse-width-modulation

(PWM)

APF

is

connected

in
series

with

the

neutral

conductor.

Proper

operation

of

PWM

APF
increases

the

effectiveness

of

circulation

of

the

neutral

current

of
the

load

via

the

zigzag

transformer.

The

DC

capacitor

of

the

PWM
APF

is

recovered

by

drawing

real

power

from

the

utility

or

from
an

external

supply

[32].

This

series

connection

of

the

PWM

APF
results

in

signiﬁcant

reduction

in

kVA

rating

of

the

inverter

[32].
This

is

because,

only

the

currents

other

than

zero-sequence

(the
zero-sequence

will

ﬂow

through

the

zigzag

transformer)

could

only
ﬂow

through

the

inverter

[32].

A

bypass

switch

(S)

is

placed

in

par-
allel

with

the

active

power

ﬁlter

and

will

be

operated

in

case

of

inverter

failure

or

under

abnormal

utility

conditions

[28].
Fig.

7.

A

hybrid

approach

for

compensation

of

neutral

current:

a

zigzag

transformer
with

single-phase

shunt

APF.
Fig.

8.

A

hybrid

approach

for

compensation

of

neutral

current:

a

zigzag

transformer
with

single-phase

series

APF.
6.4.3.

Star-delta

transformer

with

single-phase

half-bridge

PWM
APF
Fig.

9

shows

a

hybrid

topology

with

star-delta

transformer

[39].
In

this

method

a

single-phase

half-bridge

PWM

APF

is

connected
to

the

neutral

of

the

transformer

primary

and

neutral

conductor.

A
Fig.

9.

A

hybrid

approach

for

compensation

of

neutral

current:

a

star-delta

trans-
former

with

single-phase

APF.
176 D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180
three-phase

diode

bridge

rectiﬁer

is

connected

to

the

delta

wind-
ing

to

provide

the

necessary

real

power

to

maintain

the

dc

voltage
across

the

capacitors

of

the

single-phase

half-bridge

PWM

APF.
Proper

switching

signals

are

used

to

control

the

PWM

APF

in

such

a
way

that

it

produces

the

desired

current

to

compensate

the

neutral
current.

This

harmonic

current

is

injected

through

the

neutral

of
the

transformer.
The

above

mentioned

methods

are

used

only

for

neural

cur-
rent

compensation.

Compensation

of

neutral

current

along

with
elimination

of

phase

harmonic

currents

can

be

done

by

incorpo-
rating

a

three-phase,

three-wire

APF

to

the

zigzag

transformer
[28,29,34–36].

These

approaches

greatly

reduce

the

rating

of

the
active

ﬁlter.

The

main

reason

for

the

reduction

in

the

APF

rating
is

due

to

the

separation

of

the

zero-sequence

currents

from

the
positive

and

negative-sequence

currents

to

be

compensated

[28].
7.

Three-phase,

four-wire

active

power

ﬁlters
Now-a-days,

power-electronics-based

compensators

such

as
Distribution

STATic

COMpensator

(D-STATCOM),

Dynamic

Voltage
Restorer

(DVR),

Solid

State

Fault

Current

Limiter

(SSFCL),

Active
Power

Filter

(APF),

and

Solid

State

Transfer

Switch

(SSTC)

have
been

used

to

overcome

the

power

quality

problems

[47].

These
power

electronic

based

compensators

will

solve

the

power

quality
problems

by

injecting

voltage

or

current

referring

to

the

amount

of
reference

voltage

or

current

of

the

distribution

system

[3,47].
Among

these

solutions,

APF

are

specially

designed

to

3P4W
systems

for

compensating

neutral

current

along

with

necessary
compensation

features

of

the

three-phase,

three-wire

APFs

[48,49].
These

compensators

can

compensate

not

only

the

neutral

cur-
rent,

but

also

compensate

harmonics

from

the

positive-

and
negative-sequence

components

of

the

load

current.

Three

differ-
ent

topologies

are

available

for

3P4W

systems

and

are

given

below
[48–55,103].
1.

Three

H-bridge

shunt

APF

topology.
2. 3P4W

capacitor

midpoint

(or

split-capacitor)

APF

topology.
3.

3P4W

four-leg

APF

topology.
The

ﬁrst

one

uses

three

H-bridge

voltage

source

inverters

and
these

H-bridge

are

connected

through

isolation

transformers.

The
capacitor

midpoint

topology

and

four-leg

topologies

are

looking
similar.

The

fundamental

difference

between

these

two

topologies
is

the

number

of

power

semiconductor

devices

and

the

connection
of

the

neutral

wire.

The

other

possible

3P4W

topologies

such

as
combination

of

capacitor

midpoint

and

four-leg

topology

[53]

and
the

method

proposed

in

[54].

In

the

later

method

the

neutral

con-
ductor

of

the

utility

is

directly

connected

to

the

positive

or

negative
terminal

of

the

DC

bus.
The

performance

of

the

3P4W

APFs

depend

on

the

control
algorithm

i.e.

the

extraction

of

the

current

components

for

com-
pensation.

Control

schemes

for

the

three-phase,

three-wire

active
power

ﬁlers

[56–62]

are

not

directly

applicable

here

and

require
additional

considerations

in

the

control

circuitry

for

the

compen-
sation

of

the

neutral

current.

To

achieve

this

there

are

various
control

schemes

are

reported

in

the

literature

and

some

of

these
are

instantaneous

reactive

power

(IRP)

theory,

instantaneous

com-
pensation,

instantaneous

symmetrical

components,

synchronous
reference

frame

(SRF)

theory,

computation

based

on

per

phase
basis,

Adaline

based

control

algorithm

and

scheme

based

on

neu-
ral

network

etc.

[63–80].

The

rest

of

the

details

of

the

previously
mentioned

topologies

are

given

below:
Fig.

10.

The

three

H-bridge

shunt

APF

topology.
7.1.

Three

H-bridge

shunt

APF

topology
Fig.

10

shows

the

three

H-bridge

shunt

APF

topology.

It

consists
of

three

single-phase

full

bridge

(H-bridge)

voltage

source

inverters
with

a

common

self

supporting

DC

bus

[50].

Here

all

12

switching
devices

are

used

to

realise

the

3P4W

shunt

APF

system.

These

H-
bridge

inverters

are

connected

to

the

3P4W

system

by

using

three
single-phase

isolation

transformers.
Considering

the

structural

advantage

of

this

topology,

the

con-
trol

can

be

done

either

as

a

three-phase

unit

or

three

separate
single-phase

units.

An

independent

phase

control

approach

based
on

single-phase

instantaneous

reactive

power

theory

is

presented
in

[80,81].
In

this

topology

the

maximum

voltage

that

appears

across

each
H-bridge

is

the

single-phase

voltage

and

not

the

three-phase

volt-
age,

as

in

the

case

of

split

capacitor

or

four-leg

topology

[51,52].
This

result

into

a

reduction

of

DC

bus

voltage

by

a

factor

of
√
3

Thus
the

reference

DC

bus

voltage

needed

for

proper

operation

of

shunt
APF

also

reduces

by

a

maximum

factor

of
√
3,

this

reduces

the

rat-
ing

of

inverter.

But,

the

main

disadvantage

of

this

topology

is

the
increased

number

of

switching

devices.
7.2.

Three-phase,

four-wire

capacitor

midpoint

APF

topology
The

capacitor

midpoint

APF

topology

utilizes

the

standard
three-phase

conventional

inverter

where

the

dc

capacitor

is

split
and

the

neutral

wire

is

directly

connected

to

the

electrical

midpoint
of

the

capacitors

through

an

optional

inductance

[51,52].

The

split
capacitors

allow

load

neutral

current

to

ﬂow

through

one

of

the

dc
capacitors

C
dc1
,

C
dc2
and

return

to

the

ac

neural

wire.

Fig.

11

shows
the

capacitor

midpoint

APF

topology

used

in

3P4W

systems.
Fig.

11.

The

3P4W

capacitor

midpoint

topology.
D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180 177
Fig.

12.

The

3P4W

four-leg

topology.
One

of

the

serious

problems

with

this

topology

is

voltage

unbal-
ance

between

the

capacitors

[49].

This

is

due

to

the

direct

ﬂow

of
the

neutral

current

through

one

of

the

capacitors,

causing

voltage
variations

among

them.

There

are

two

possible

ways

to

balance

the
capacitors:

1.

By

adjusting

the

switching

of

the

inverter

(such

as

dynamic

hys-
teresis

controller)

[49,82–89].

This

approach

requires

additional
control

circuitry.
2. By

using

additional

power

electronic

switching

circuitry

(such

as
choppers)

[90].

This

approach

increases

the

cost

when

compared
with

the

former

one.
7.3.

Three-phase,

four-wire

four-leg

APF

topology
Fig.

12

shows

the

four-leg

APF

topology

used

in

3P4W

systems
[51,52].

In

this

topology

three

of

the

switch

legs

are

connected

to
the

three

phase

conductors

through

a

series

inductance

while

the
fourth

switch

leg

is

connected

to

the

neutral

conductor

with

an
optional

inductor.

This

topology

is

most

suitable

for

compensa-
tion

of

high

neutral

currents

[48].

Despite

having

higher

number
of

switching

devices

this

topology

outweighed

the

split

capacitor
topology

by

number

of

factors

[48,49,51,52].
Better

controllability:

In

this

topology

only

one

dc-bus

voltage
needs

to

be

regulated,

as

opposed

to

two

in

the

capacitor

mid-
point

topology.

This

signiﬁcantly

simpliﬁes

the

control

circuitry
with

better

controllability

[48].
Lower

dc

voltage

and

current

requirement:

This

topology
requires

a

lower

dc-bus

voltage

and

capacitor

current

with

it
[51,52].
High

order

harmonics

in

dc

side

current:

The

dc

side

current
in

three

H-bridge

and

capacitor

midpoint

topology

must

handle
the

low

order

harmonics.

These

low

order

harmonics

contribute

to
signiﬁcant

ripple

on

the

dc-bus

voltage.

But

in

four

leg

topology,
the

dc

side

current

has

only

higher

order

harmonics

and

will

not
contribute

to

signiﬁcant

ripple

on

the

dc-bus

voltage

[51,52].
The

main

disadvantage

of

this

topology

is

the

difﬁculty

in

control
of

the

four-leg

inverter.

The

conventional

voltage

or

current

con-
trolled

methods

[91]

are

not

directly

applicable

here

and

require
special

consideration.

Several

modulation

methods

for

the

four-leg
converter

have

been

suggested

in

[92–101].

Among

these

meth-
ods,

the

carrier-based

pulse

width

modulation

(PWM)

methods

are
heuristic

and

can

be

easily

applied

to

four-leg

converters

[92,93].
Nevertheless,

the

space

vector

PWM

(SVPWM)

is

very

interest-
ing

because

it

offers

signiﬁcant

ﬂexibility

to

optimize

switching
waveforms

and

it

is

well

suited

for

digital

implementation

[94–98].
Mathematical

modelling

of

the

four-leg

inverter

is

given

in

[102].
3P4W

APFs

may

use

simple

2-level

inverter

structures

with
high

switching

frequency

or

multilevel

inverter

topologies

with
relatively

low

switching

frequency

[104,105].

However,

currently
there

is

tough

competition

for

high-power

medium-voltage

appli-
cations

between

the

use

of

classic

power

converter

topologies

using
high-voltage

semiconductors

and

new

converter

topologies

using
medium-voltage

devices.

Multilevel

inverters

built

using

mature
medium-voltage

semiconductors

are

competing

in

development
race

with

classic

power

converters

using

high-voltage

semicon-
ductors.

Nowadays,

multilevel

inverters

are

a

good

solution

for

high
power

applications

due

to

the

fact

that

they

can

achieve

high

power
using

mature

medium-power

semiconductor

technology

[105].
The

comparison

of

3P4W

APFs

are

given

in

Table

4.

The

signiﬁ-
cant

factor

that

may

decide

the

selection

of

these

topologies

is

the
overall

cost

involved

to

realise

the

3P4W

APF.

Owing

to

the

topolog-
ical

advantage

of

three

H-bridge

topology,

the

required

reference
DC

bus

voltage

for

APF

is

reduced

maximum

by

a

factor

of
√
3.

The
high

cost

of

three

H-bridge

topology

owing

to

an

increased

number
of

semiconductor

devices

can

be

counterbalanced

by

reduction

in
voltage

rating

of

the

devices,

and

thus

making

this

topology

suitable
for

high-voltage

and

high

power

application.

For

low-to-medium-
power

applications,

the

low

cost

of

capacitor

midpoint

topology

can
Table

4
Comparison

of

three-phase,

four-wire

system

active

power

ﬁlters

[51,52]

[103].
Active

ﬁlter

topology

Three

H-bridge

(Fig.

10)

Capacitor

midpoint

(Fig.

11)

Four-leg

APF

(Fig.

12)
Number

of

switching

devices

(2-level

inverter)

12

6

8
Number

of

capacitors

1

2

1
Additional

sensor

requirement

None

One

extra

DC

bus

voltage
sensor

(total

two)
One

extra

current

sensor
DC-Side

Voltage

(V
l
=line-to-line

voltage)

≥

2/3V
l
≥
√
2
0.87
V

l
≥
√
2V
l
DC-side

current

harmonics

Lower

order

harmonics

Lower

order

harmonics

Higher

order

harmonics

only

Need

of

coupling

transformer

Necessary

Not

necessary

Not

necessary
Control

over

neutral

current

Indirect

Indirect

Direct

(using

4th

leg)
Effectiveness

of

neutral

current

compensation

Better

performance

than
capacitor

midpoint
May

degrade

with

high

neutral
currents
Better

performance

than
capacitor

midpoint

and

three
H-bridge
Overall

cost

High

Low

Moderate
Main

advantage

Reduced

dc

voltage
requirement
Least

number

of

switching
devices
Better

controllability
Main

disadvantage

More

number

of

switching
devices
Capacitor

unbalance

problem
due

to

voltage

difference
across

two

capacitors
More

number

of

switching
devices
Application

and

topology

selection

Suitable

for

high

voltage,
medium

to

high

power
applications.

Suitable

for
compensating

high

neutral
currents.
Suitable

for

low

to

medium
power

applications.
Suitable

for

low

to

medium
power

applications.

Suitable
for

compensating

high

neutral

currents.
178 D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180
Table

5
Comparison

of

neutral

current

compensation

techniques

in

three-phase,

four-wire

systems.
Features

Type

of

solution
Transformer

based

solutions

Three-phase,

four-wire

active

power

ﬁlters
Basic

principle
Provides

low

impedance

path

for

zero-sequence

harmonics
currents.
Compensate

by

injecting

equal-but-opposite

compensating

current.
Depending

upon

the

selection

of

transformer,

these

currents
may

circulate

in

the

secondary

winding

of

the

transformer

or
may

circulate

between

load

and

transformer.
Effectiveness

of

neutral

current
compensation
Compensates

only

zero-sequence

harmonics

(complete
compensation

is

possible

with

addition

of

1-␸

APF)
Completely

compensates

neutral

current
Operation

under

unbalanced

and/or
distorted

utility

voltage

conditions
Degrades

and

causes

uneven

raise

of

neutral

and

line

currents

(but

with

addition

of

1-␸ APF

this

problem

can

be

alleviated

to
some

extent)
Degrades

(with

proper

design

of

controller

this
problem

can

be

alleviated

to

some

extent)
Phase

harmonic

compensation,
reactive

power

compensation

and
ﬂicker

mitigation
Not

possible

(possible

only

with

addition

of

three-phase,
three-wire

compensator)
Possible

(this

is

the

native

feature

of

3P4W
APFs)
Rating

of

the

compensator

Very

less

(low

kVA

rating

of

the

compensator

reduces

cost,
power

losses

and

the

generated

electromagnetic

interference)
Very

high
Robustness

of

compensator

High

because

of

passive

compensation

Less
Effect

of

location

on

compensating
characteristics
Dependent

Independent
Effect

of

source

impedance

on
compensating

characteristics
Dependent Independent

(dependent

only

when

load
impedance

is

less

than

source

impedance)
Effect

of

buffer

reactor

(Zn)

on
compensating

characteristics
Dependent

(but

no

buffer

reactor

is

required

with

addition

of
1-␸

APF)

No

buffer

reactor

is

required
Design

of

compensator

Less

complex

Complex
Cost

of

the

compensator Less High
Application

and

topology

selection
Suitable

for

high

voltage,

medium

to

high

power

applications
Suitable

for

low

to

medium

power

applications
Not

suitable

with

unbalanced

and/or

distorted

utilities

voltages
be

selected.

For

better

performance

at

moderate

cost,

the

four-leg
topology

could

be

a

best

option

for

low-to-medium-power

appli-
cations.
The

merits

and

demerits

of

transformer

based

topologies

and
3P4W

APFs

are

given

in

Table

5.

The

application

of

transformers

for
reduction

of

neutral

current

is

advantageous

due

to

reduced

rating,
passive

compensation,

rugged,

low

cost,

easy

installation

and

less
complex

over

active

compensation

techniques.

But,

its

compensa-
tion

characteristics

are

strongly

dependent

on

system

impedance
and

utility

voltage

conditions.

The

3P4W

APF

helps

to

achieve
other

controllable

objectives

such

as

reactive

power

compensation,
ﬂicker

mitigation,

voltage

sag/swell

reduction

and

also

their

com-
pensation

characteristics

are

independent

of

system

impedance.
However,

for

3P4W

APFs

requires

large

rating

inverter.
8.

Conclusion
In

this

paper,

causes,

problems,

recommendations

and

mitiga-
tion

techniques

of

excess

neutral

current

have

been

investigated

for
3P4W

distribution

systems.

Neutral

current

in

these

systems

has
serious

drawbacks

and

the

only

solution

for

handling

these

cur-
rents

is

to

incorporate

the

neutral

current

compensation

devices
within

the

distribution

system.
Passive

harmonic

ﬁlters

for

neutral

current

compensation

are
bulky

and

may

cause

resonance

with

system

impedance.

The

trans-
former

based

methods

can

reduce

the

neutral

current

to

a

large
extent

but,

it

will

not

completely

compensate

the

same

and

also
its

compensation

characteristics

are

depends

on

zero-sequence
impedance

of

the

transformer

and

the

utility

voltage

conditions.
For

complete

compensation,

a

hybrid

approach

is

must.

However,
the

application

of

transformers

for

reduction

of

neutral

current

has

an

advantage

due

to

passive

compensation,

ruggedness,

and

less
complexity

over

the

active

compensation

techniques.

Among

all
transformer

based

methods,

zigzag

transformer

approach

has

least
kVA

rating.
The

3P4W

APFs

are

specially

designed

for

neutral

current
compensation

and

harmonic

elimination

in

line-currents.

The

com-
mercial

success

of

these

ﬁlters

is

due

to

their

acceptable

cost,
coupled

with

desirable

technical

features

such

as

extremely

fast

response

time,

ﬂexibility

of

control,

continuous

operation

with
virtually

no

maintenance

and

simultaneously

other

controllable
objectives

can

be

achievable.

However,

the

large

rating

of

the
inverter

is

main

drawback

of

these

topologies.

The

rating

of

these
3P4W

APF

can

be

greatly

reduced

by

replacing

with

a

hybrid

ﬁlter
topology

which

consists

of

a

3P3W

APF,

a

special

transformer

(such
as

zigzag)

and

a

single-phase

APF.
References
[1]

J.

Arrillaga,

N.R.

Watson,

Power

System

Harmonics,

2nd

edition,

John

Wiley
&

Sons

Ltd.,

2003.
[2]

R.C.

Dugan,

M.F.

McGranaghan,

H.W.

Beaty,

Electric

Power

Systems

Quality,
2nd

edition,

McGraw-Hill,

New

York,

2006.
[3]

A.

Moreno-Munoz,

Power

Quality:

Mitigation

Technologies

in

a

Distributed
Environment,

Springer-Verlag

limited,

London,

2007.
[4]

T.M.

Gruzs,

A

survey

of

neutral

currents

in

three-phase

computer

power

sys-
tems,

IEEE

Trans.

Ind.

Appl.

26

(4)

(1990)

719–725.
[5]

A C.

Liew,

Excessive

neutral

currents

in

three-phase

ﬂuorescent

lighting

cir-
cuits,

IEEE

Trans.

Ind.

Appl.

25

(4)

(1989)

776–782.
[6]

H.O.

Aintablian,

H.W.

Hill

Jr.,

Harmonic

currents

generated

by

personal

com-
puters

and

their

effects

on

the

distribution

system

neutral

current,

in:

Conf.
IEEE

Ind.

Appl.,

vol.

2,

October,

1993,

pp.

1483–1495.
[7]

D.O.

Koval,

C.

Carter,

Power

quality

characteristics

of

computer

loads,

IEEE
Trans.

Ind.

Appl.

33

(3)

(1997)

613–621.
[8]

J.C.

Balda,

A.R.

Oliva,

D.W.

McNabb,

R.D.

Richardson,

Measurements

of

neutral
currents

and

voltages

on

a

distribution

feeder,

IEEE

Trans.

Power

Deliv.

12

(4)
(1997)

1799–1804.
[9]

A.

Capasso,

R.

Lamedica,

A.

Prudenzi,

Experimental

characterization

of
personal

computers

harmonic

impact

on

power

quality,

Comput.

Stand.

Inter-
faces

21

(1999)

321–333.
[10]

D.P.

Manjure,

E.B.

Makram,

Impact

of

unbalance

on

power

system

harmonics,
in:

Proc.

10th

Int.

Conf.

Harmonics

and

Quality

of

Power,

vol.

1,

October

6–9,
2002,

pp.

328–333.
[11]

D.

Maheswaran,

A.

Kalyanasundaram,

S.

Kameshwaran,

Power

quality

issues
in

a

distribution

network

impact

of

neutral

current

due

to

nonlinear

loads,

in:
Proc.

of

India

Int.

Conf.

on

Power

Electronics,

December,

2006,

pp.

150–155.
[12]

J.A.

Pomilio,

S.M.

Deckmann,

Characterization

and

compensation

of

harmon-

ics

and

reactive

power

of

residential

and

commercial

loads,

IEEE

Trans.

Power
Deliv.

22

(2)

(2007)

1049–1055.
[13]

Nonlinear

loads

mean

trouble,

EC&M,

pp.

83–90,

March

1988.
[14]

S.

Mohamadian,

A.

Shoulaie,

Comprehensive

deﬁnitions

for

evaluating
harmonic

distortion

and

unbalanced

conditions

in

three

and

four-wire

three-
phase

systems

based

on

IEEE

standard

1459,

IEEE

Trans.

Power

Deliv.

26

(3)
(2011)

174–1782.
D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180 179
[15]

IEEE

Recommended

Practices

and

Requirements

for

Harmonics

Control

in
Electric

Power

Systems,

IEEE

Standard,

vol.

519,

1992.
[16]

A.

Hiranandani,

Calculation

of

cable

ampacities

including

the

effects

of

har-
monics,

IEEE

Ind.

Appl.

Mag.

4

(2)

(1998)

42–51.

[17]

CBEMA

Information

Letter,

CBEMA,

ESC-3

Committee,

CBEMA,

311

First

St.,
N.W.,

Suite

500,

Washington,

DC

20001.
[18]

Recommended

Practice

For

Establishing

Transformer

Capability

When

Sup-
plying

Nonsinusoidal

Load

Currents,

ANSI/IEEE

C57.110-1986,

IEEE,

Inc.,

New
York,

NY,

1986,

10017.
[19] J.P.

Nelson,

The

grounding

of

power

systems

above

600

volts:

a

practical

view
point,

in:

Proc.

IEEE/IAS,

2003,

pp.

13–22.
[20] F.Z.

Peng,

Harmonic

sources

and

ﬁltering

approaches,

IEEE

Trans.

Ind.

Appl.

7
(2001)

18–25.
[21] F.Z.

Peng,

G.J.

Su,

A

series

LC

ﬁlter

for

harmonic

compensation

of

ac

drives,

in:
Proc.

IEEE

Power

Electron.

Specialist

Conf.,

1999,

pp.

213–218.
[22] S.

Senini,

P.J.

Wolfs,

Hybrid

active

ﬁlter

for

harmonically

unbalanced

three
phase

three

wire

railway

traction

loads,

IEEE

Trans.

Power

Electron.

15

(4)
(2000)

702–710.
[23]

P.

Rodriguez,

J.

Ignacio

Candela,

A.

Luna,

L.

Asiminoaei,

R.

Teodorescu,

F.

Blaab-
jerg,

Current

harmonics

cancellation

in

three-phase,

four-wire

systems

by
using

a

four-branch

star

ﬁltering

topology,

IEEE

Trans.

Power

Electron.

24

(8)
(2009)

1939–1950.

[24]

J.C.

Das,

Passive

ﬁlters

–

potentialities

and

limitations,

IEEE

Trans.

Ind.

Appl.
40

(2004)

232–241.

[25]

C.J.

Wu,

J.C.

Chiang,

S.S.

Yen,

C.J.

Liao,

J.S.

Yang,

T.Y.

Guo,

Investigation

and
mitigation

of

harmonic

ampliﬁcation

problems

caused

by

single-tuned

ﬁlters,
IEEE

Trans.

Power

Deliv.

13

(3)

(1998)

800–806.
[26]

T.

Fukami,

T.

Onchi,

N.

Naoe,

R.

Hanaoka,

Compensation

for

neutral

current
harmonics

in

a

three-phase,

four-wire

system

by

a

synchronous

machine,
IEEE

Trans.

Ind.

Appl.

38

(2002)

1232–1236.
[27]

P.P.

Khera,

Application

of

zig-zag

transformers

for

reducing

harmonics

in

the
neutral

conductor

of

low

voltage

distribution

system,

in:

Proc.

IEEE/IAS,

vol.
2,

1990,

pp.

1092–1096.
[28]

G.

Kamath,

N.

Mohan,

A

novel,

reduced

rating

active

ﬁlter

for

3-phase,

4-wire
loads,

in:

Proc.

IEEE

APEC’94,

vol.

2,

1994,

pp.

936–940.
[29] G.

Kamath,

N.

Mohan,

V.D.

Albertson,

Hardware

implementation

of

a

novel,
reduced

rating

active

ﬁlter

for

3-phase,

4-wire

loads,

in:

Proc.

IEEE

APEC’95,
vol.

2,

1995,

pp.

984–989.
[30]

R.

Apolonio,

J.C.

de

Oliveira,

A.B.

de

Vasconcellos,

Three-phase

electromag-
netic

ﬁlter

for

zero

sequence

harmonics,

in:

Proc.

IEEE

Int.

Conf.

Harmonic
and

Quality

of

Power,

2004,

pp.

613–618.
[31]

H L.

Jou,

J C.

Wu,

K D.

Wu,

W J.

Chiang,

Y H.

Chen,

Analysis

of

zig-zag

trans-
former

applying

in

the

three-phase,

four-wire

distribution

power

system,
IEEE

Trans.

Power

Deliv.

20

(2)

(2005)

1168–1173.
[32] S.

Choi,

M.

Jang,

A

reduced-rating

hybrid

ﬁlter

to

suppress

neutral

current
harmonics

in

three-phase,

four-wire

systems,

IEEE

Trans.

Ind.

Electron.

Lett.
51

(2004)

927–930.
[33] S.

Choi,

M.

Jang,

Analysis

and

control

of

a

single-phase-inverter

– zigzag-
transformer

hybrid

neutral-current

suppressor

in

three-phase

four-wire
systems,

IEEE

Trans.

Ind.

Electron.

54

(2007)

2201–2208.
[34]

H L.

Jou,

K D.

Wu,

J C.

Wu,

W J.

Chiang,

A

three-phase,

four-wire

power
ﬁlter

comprising

a

three-phase

three-wire

active

ﬁlter

and

a

zig-zag

trans-
former,

IEEE

Trans.

Power

Electron.

23

(1)

(2008)

252–259.
[35]

B.

Singh,

P.

Jayaprakash,

T.R.

Somayajulu,

D.P.

Kothari,

Reduced

rating
VSC

with

a

zig-zag

transformer

for

current

compensation

in

a

three-
phase,

four-wire

distribution

system,

IEEE

Trans.

Power

Deliv.

24

(1)

(2009)
249–259.
[36]

B.

Singh,

P.

Jayaprakash,

S.

Kumar,

D.P.

Kothari,

Implementation

of

neural-
network-controlled

three-leg

VSC

and

a

transformer

as

three-phase

four-wire
DSTATCOM,

IEEE

Trans.

Ind.

Appl.

47

(4)

(2011)

1892–1901.
[37]

B.

Singh,

P.

Jayaprakash,

D.P.

Kothari,

Magnetics

for

neutral

current

compen-
sation

in

three-phase

four-wire

distribution

system,

in:

Conf.

PEDES,

2010,
pp.

1–7.
[38] I.J.

Pitel,

P.

Enjeti,

Active

harmonic

power

ﬁlter

apparatus

and

method,

US
Patent

US

5,568,371,

22nd

October,

1996.
[39]

P.N.

Enjeti,

W.

Shireen,

P.

Packebush,

I.J.

Pitel,

Analysis

and

design

of

a

new
active

power

ﬁlter

to

cancel

neutral

current

harmonics

in

three-phase,

four-
wire

electric

distribution

systems,

IEEE

Trans.

Ind.

Appl.

30

(1994)

1565–1572.
[40]

B.

Singh,

P.

Jayaprakash,

D.P.

Kothari,

A

T-connected

transformer

and

three-
leg

VSC

based

DSTATCOM

for

power

quality

improvement,

IEEE

Trans.

Power
Electron.

23

(6)

(2008)

2710–2718.
[41]

E.W.

Manning,

The

T-connected

3-phase

transformer,

Trans.

AIEE

Power

Appl.
Syst.

77

(1958)

1021–1023.
[42]

B.A.

Cogbill,

J.A.

Hetrick,

Analysis

of

T–T

connections

of

two

single

phase
transformers,

IEEE

Trans.

Power

App.

Syst.

PAS

87

(2)

(1968)

388–394.
[43]

G.

Olivier,

R.

Cojocaru,

A.

Lefèvre,

Analytical

model

of

a

T-connected

three-
phase

transformer,

Math.

Comput.

Simul.

63

(2003)

407–419.
[44]

P.

Jayaprakash,

B.

Singh,

D.P.

Kothari,

Three-phase

4-wire

DSTATCOM

based
on

H-bridge

VSC

with

a

star/hexagon

transformer

for

power

quality

improve-
ment,

in:

IEEE

Region

10

Colloquium

and

the

Third

Int.

Conf.

on

Ind.

and

Inf.
Systems,

2008,

pp.

1–6.
[45]

B.

Singh,

P.

Jayaprakash,

D.P.

Kothari,

Three

leg

VSC

with

a

star-hexagon

trans-
former

based

DSTATCOM

for

power

quality

improvement

in

three-phase,
four-wire

distribution

system,

Int.

J.

Emerg.

Electr.

Power

Syst.

9

(8)

(2008)

1.
[46] B.

Singh,

S.

Gairola,

A.

Chandra,

K.

Al-Haddad,

Power

quality

improve-
ments

in

isolated

twelve

pulse

AC–DC

converters

using

delta/double

polygon

transformer,

in:

IEEE

Power

Electron.

Spec.

Conf.

(PESC’07),

June,

2007,

pp.
2848–2853.
[47]

N.G.

Hingorani,

Introducing

custom

power,

in:

IEEE

Spectrum,

June,

1995,

pp.
41–48.
[48]

B.

Singh,

K.

Al-Haddad,

A.

Chandra,

A

review

of

active

power

ﬁlters

for

power
quality

improvement,

IEEE

Trans.

Ind.

Electron.

45

(5)

(1999)

960–971.
[49]

H.

Akagi,

E.H.

Watanabe,

M.

Aredes,

Instantaneous

Power

Theory

and

Appli-
cations

to

Power

Conditioning,

Wiley,

Hoboken,

NJ,

2007.
[50]

F.Z.

Peng,

H.

Akagi,

A.

Nabae,

A

novel

harmonic

power

ﬁlter,

in:

PESC’88,

April,
1988,

pp.

1151–1158.
[51]

C.A.

Quinn,

N.

Mohan,

Active

ﬁltering

of

harmonic

currents

in

three-phase,
four-wire

systems

with

three-phase

and

single-phase

nonlinear

loads,

in:
Proc.

IEEE

APEC’92,

1992,

pp.

829–835.
[52] C.A.

Quinn,

N.

Mohan,

H.

Mehta,

A

four-wire,

current-controlled

converter
provides

harmonic

neutralization

in

three-phase,

four-wire

systems,

in:

Proc.
IEEE

APEC,

1993,

pp.

841–846.
[53]

P.

Salmeron,

J.C.

Montano,

J.R.

Vazquiez,

A.

Perez,

Compensation

in

nonsi-
nusoidal,

unbalanced

three-phase,

four-wire

systems

with

active

power-line

conditioner,

IEEE

Trans.

Power

Electron.

19

(4)

(2004)

1968–1974.
[54] H.L.

Jou,

K.D.

Wu,

J.C.

Wu,

C.H.

Li,

M.S.

Huang,

Novel

power

converter

topology
for

three-phase,

four-wire

hybrid

power

ﬁlter,

IET

Power

Electron.

1

(1)

(2008)
164–173.
[55]

F.R.

Quintela,

J.M.G.

Arévalo,

R.C.

Redondo,

N.R.

Melchor,

Four-wire

three-
phase

load

balancing

with

static

VAr

compensators,

Electr.

Power

Energ.

Syst.
33

(2011)

562–568.
[56]

B.

Singh,

J.

Solanki,

A

comparison

of

control

algorithms

for

DSTATCOM,

IEEE
Trans.

Ind.

Electron.

56

(7)

(2009)

2738–2745.
[57]

H.

Akagi,

Y.

Kanazawa,

A.

Nabae,

Instantaneous

reactive

power

comprising
switching

devices

without

energy

storage

components,

IEEE

Trans.

Ind.

Appl.
20

(3)

(1984)

625–630.
[58]

M.

Kale,

E.

Ozdemir,

Harmonic

and

reactive

power

compensation

with

shunt
active

power

ﬁlter

under

non-ideal

mains

voltage,

Electr.

Power

Syst.

Res.

77
(2005)

363–370.
[59]

S.J.

Huang,

et

al.,

A

study

of

three-phase

active

power

ﬁlters

under

non-ideal
mains

voltages,

Electr.

Power

Syst.

Res.

49

(1999)

125–137.
[60] S.

Saad,

L.

Zellouma,

Fuzzy

logic

controller

for

three-level

shunt

active

ﬁl-
ter

compensating

harmonics

and

reactive

power,

Electr.

Power

Syst.

Res.

79
(2009)

1337–1341.
[61]

A.

Bhattacharya,

C.

Chakraborty,

A

shunt

active

power

ﬁlter

with

enhanced
performance

using

ANN-based

predictive

and

adaptive

controllers,

IEEE
Trans.

Ind.

Electron.

58

(2)

(2011)

421–428.
[62]

R.R.

Pereira,

C.H.

da

Silva,

L.E.B.

da

Silva,

G.

Lambert-Torres,

J.O.P.

Pinto,

New
strategies

for

application

of

adaptive

ﬁlters

in

active

power

ﬁlters,

IEEE

Trans.
Ind.

Electron.

47

(3)

(2011)

1136–1141.
[63] M.

Aredes,

J.

Hafner,

K.

Heumann,

Three-phase,

four-wire

shunt

active

ﬁlter
control

strategies,

IEEE

Trans.

Power

Electron.

12

(2)

(1997)

311–318.
[64]

M.I.M.

Montero,

E.R.

Cadaval,

F.B.

González,

Comparison

of

control

strategies
for

shunt

active

power

ﬁlters

in

three-phase,

four-wire

systems,

IEEE

Trans.
Power

Electron.

22

(1)

(2007)

229–236.
[65]

A.

Chandra,

B.

Singh,

B.N.

Singh,

K.

Al-Haddad,

An

improved

control

algo-

rithm

of

shunt

active

ﬁlter

for

voltage

regulation,

harmonic

elimination,
power-factor

correction,

and

balancing

of

nonlinear

loads,

IEEE

Trans.

Power
Electron.

15

(3)

(2000)

495–507.
[66]

R.

Gri
˜
nó,

R.

Cardoner,

R.

Costa-Castelló,

E.

Fossas,

Digital

repetitive

control

of
a

three-phase,

four-wire

shunt

active

ﬁlter,

IEEE

Trans.

Ind.

Electron.

54

(3)
(2007)

1495–1503.
[67]

V.

Khadkikar,

A.

Chandra,

A

novel

structure

for

three-phase,

four-wire

distri-
bution

system

utilizing

uniﬁed

power

quality

conditioner

(UPQC),

IEEE

Trans.
Ind.

Appl.

45

(5)

(2009)

1897–1902.
[68]

H.

Akagi,

S.

Ogasawara,

H.

Kim,

The

theory

of

instantaneous

power

in

three-

phase,

four-wire

systems:

a

comprehensive

approach,

in:

Proc.

IEEE

IAS

Annu.
Meeting,

1999,

pp.

431–439.
[69]

M.

Aredes,

E.H.

Watanabe,

New

control

algorithms

for

series

and

shunt

three-
phase,

four-wire

active

power

ﬁlters,

IEEE

Trans.

Power

Deliv.

11

(3)

(1995)
1649–1656.
[70]

B.N.

Singh,

P.

Rastgoufard,

B.

Singh,

A.

Chandra,

K.A.

Haddad,

Design,

simula-
tion

and

implementation

of

three

pole/four

pole

topologies

for

active

ﬁlters,
Inst.

Electr.

Eng.

Proc.

Electr.

Power

Appl.

151

(4)

(2004)

467–476.
[71]

M.

Ucar,

E.

Ozdemir,

Control

of

a

3-phase

4-leg

active

power

ﬁlter

under

non-
ideal

mains

voltage

condition,

Electr.

Power

Syst.

Res.

78

(2008)

58–73.
[72]

P.

Salmerón,

R.S.

Herrera,

Instantaneous

reactive

power

theory

–

a

gen-
eral

approach

to

poly-phase

systems,

Electr.

Power

Syst.

Res.

79

(2009)
1263–1270.
[73]

J.C.

Monta
˜
no,

Reviewing

concepts

of

instantaneous

and

average

compensa-
tions

in

polyphase

systems,

IEEE

Trans.

Ind.

Electron.

58

(1)

(2011)

213–220.
[74]

C.

Madtharad,

S.

Premrudeepreechacharn,

Active

power

ﬁlter

for

three-phase
four-wire

electric

systems

using

neural

networks,

Electr.

Power

Syst.

Res.

60
(2002)

179–192.
[75]

B.

Singh,

P.

Jayaprakash,

D.P.

Kothari,

New

control

approach

for

capacitor
supported

DSTATCOM

in

three-phase

four

wire

distribution

system

under
non-ideal

supply

voltage

conditions

based

on

synchronous

reference

frame
theory,

Electr.

Power

Energ.

Syst.

33

(2011)

1109–1117.
[76]

B.

Singh,

K.

Al-Haddad,

A.

Chandra,

Harmonic

elimination,

reactive

power
compensation

and

load

balancing

in

three-phase,

four-wire

electric

distribu-
tion

systems

supplying

non-linear

loads,

Electr.

Power

Syst.

Res.

44

(1998)
93–100.
180 D.

Sreenivasarao

et

al.

/

Electric

Power

Systems

Research

86 (2012) 170–

180
[77]

M.C.

Benhabib,

S.

Saadate,

New

control

approach

for

four-wire

active

power
ﬁlter

based

on

the

use

of

synchronous

reference

frame,

Electr.

Power

Syst.
Res.

73

(2005)

353–362.
[78]

S.

Orts-Grau,

F.J.

Gimeno-Sales,

A.

Abellán-García,

S.

Seguí-Chilet,

J.C.

Alfonso-
Gil,

Improved

shunt

active

power

compensator

for

IEEE

standard

1459
compliance,

IEEE

Trans.

Power

Deliv.

25

(4)

(2010)

2692–2701.
[79]

P.

Salmeron,

S.P.

Litran,

A

control

strategy

for

hybrid

power

ﬁlter

to

com-
pensate

four-wires

three-phase

systems,

IEEE

Trans.

Power

Electron.

25

(7)
(2010)

1923–1931.
[80] V.

Khadkikar,

A.

Chandra,

An

independent

control

approach

for

three-phase,
four-wire

shunt

active

ﬁlter

based

on

three

H-bridge

topology

under

unbal-
anced

load

conditions,

in:

Power

Electron.

Spec.

Conf.,

August,

2008,

pp.
4643–4649.
[81] M.T.

Haque,

Single-phase

PQ

theory,

in:

Proc.

Annu.

Conf.

IEEE

Power

Electron.
Spc.

(PESC’02),

vol.

4,

June,

2002,

pp.

1815–1820.
[82] C.S.

Ma,

T.J.

Kim,

D.W.

Kang,

D.S.

Hyun,

A

simple

control

strategy

for

balanc-
ing

the

DC-link

voltage

of

neutral-point-clamped

inverter

at

low

modulation
index,

in:

Proc.

IECON,

November

2–6,

2003,

pp.

2167–2172.
[83]

A.

Shukla,

A.

Ghosh,

A.

Joshi,

Control

schemes

for

DC

capacitor
voltages

equalization

in

diode-clamped

multilevel

inverter-
based

DSTATCOM,

IEEE

Trans.

Power

Deliv.

23

(2)

(2008)
1139–1149.
[84]

A.

Shukla,

A.

Ghosh,

A.

Joshi,

Improved

multilevel

hysteresis

current

regula-
tion

and

capacitor

voltage

balancing

schemes

for

ﬂying

capacitor

multilevel
inverter,

IEEE

Trans.

Power

Electron.

23

(2)

(2008)

518–529.
[85]

D.W.

Kang,

B.K.

Lee,

J.H.

Jeon,

T.J.

Kim,

D.S.

Hyun,

A

symmetric

carrier

tech-
nique

of

CRPWM

for

voltage

balance

method

of

ﬂying-capacitor

multilevel

inverter,

IEEE

Trans.

Ind.

Electron.

52

(3)

(2005)

879–888.
[86]

M.P.

Kazmierkowski,

L.

Malesani,

Current

control

techniques

for

three-phase
voltage-source

PWM

converters:

a

survey,

IEEE

Trans.

Ind.

Electron.

45

(5)
(1998)

691–703.

[87] M.K.

Mishra,

A.

Joshi,

A.

Ghosh,

Control

for

equalization

of

capacitor

voltages
in

neutral

clamped

shunt

compensator,

IEEE

Trans.

Power

Deliv.

18

(2)

(2003)
538–544.
[88]

J.A.

Barrena,

L.

Marroyo,

M.A.R.

Vidal,

J.R.T.

Apraiz,

Individual

voltage

bal-
ancing

strategy

for

PWM

cascaded

H-bridge

converter

based

STATCOM,

IEEE
Trans.

Ind.

Electron.

55

(1)

(2008)

21–29.
[89]

N Y.

Dai,

M C.

Wong,

F.

Ng,

Y D.

Han,

A

FPGA-based

generalized

pulse

width
modulator

for

three-leg

center-split

and

four-leg

voltage

source

inverters,
IEEE

Trans.

Power

Electron.

23

(3)

(2008)

1472–1484.
[90]

S.

Srikanthan,

M.K.

Mishra,

DC

capacitor

voltage

equalization

in

neutral
clamped

inverters

for

DSTATCOM

application,

IEEE

Trans.

Ind.

Electron.

57
(8)

(2010)

2768–2775.
[91]

D.G.

Holmes,

T.A.

Lipo,

Pulse

Width

Modulation

for

Power

Converters,

Wiley,
Hoboken,

NJ,

2003.
[92]

J H.

Kim,

S K.

Sul,

A

carrier-based

PWM

method

for

three

phase

four-leg
voltage

source

converters,

IEEE

Trans.

Power

Electron.

19

(1)

(2004)

66–75.
[93]

J.

Kim,

S.

Sul,

N.

Enjeti,

A

carrier-based

PWM

method

with

optimal

switching
sequence

for

a

multilevel

four-leg

voltage-source

inverter,

IEEE

Trans.

Ind.
Appl.

44

(4)

(2008)

1239–1248.
[94] F.

Wang,

Sine-triangle

versus

space-vector

modulation

for

three-level

PWM
voltage-source

inverters,

IEEE

Trans.

Ind.

Appl.

38

(2)

(2002)

500–506.
[95] R.

Zhang,

V.H.

Prasad,

D.

Boroyevich,

Three-dimensional

space

vector

modu-

lation

for

four-leg

voltage

source

converters,

IEEE

Trans.

Power

Electron.

17
(3)

(2002)

314–326.
[96]

M.A.

Perales,

M.M.

Prats,

R.

Portillo,

J.L.

Mora,

J.I.

Leon,

L.G.

Franquelo,

Three-
dimensional

space

vector

modulation

in

ABC

coordinates

for

four-leg

voltage
source

converters,

IEEE

Power

Electron.

Lett.

1

(4)

(2003)

104–109.
[97] C.

Liu,

J.

Lai,

F.C.

Lee,

D.

Chen,

R.

Zhang,

Common-mode

components

compari-
son

for

different

SVM

schemes

in

three-phase

four-legged

converter,

in:

Proc.
3rd

Int.

Conf.

Power

Electron.

Motion

Control,

vol.

2,

August

15–18,

2000,

pp.
633–638.
[98] O.

Lopez,

J.

Alvarez,

J.

Doval-Gandoy,

F.

Freijedo,

A.

Lago,

C.M.

Penalver,

Four-
dimensional

space

vector

PWM

algorithm

for

multilevel

four-leg

converters,
in:

Conf.

IECON’08,

November,

2008,

pp.

3252–3259.
[99]

P.

Lohia,

M.K.

Mishra,

K.

Karthikeyan,

K.

Vasudevan,

A

minimally

switched
control

algorithm

for

three-phase

four-leg

VSI

topology

to

compensate
unbalanced

and

nonlinear

load,

IEEE

Trans.

Power

Electron.

23

(4)

(2008)
1935–1944.
[100]

G.

Dong,

O.

Ojo,

Current

regulation

in

four-leg

voltage-source

converters,

IEEE
Trans.

Ind.

Electron.

54

(4)

(2007)

2095–2105.
[101]

Vincent

George,

M.K.

Mishra,

Design

and

analysis

of

user-deﬁned

constant
switching

frequency

current-control-based

four-leg

DSTATCOM,

IEEE

Trans.
Power

Electron.

24

(9)

(2009)

2148–2158.
[102] S.

Srikanthan,

M.K.

Mishra,

Modeling

of

a

four-leg

inverter

based

DSTATCOM
for

load

compensation,

in:

Int.

Conf.

on

Power

System

Technology,

2010,

pp.
1–6.
[103]

V.

Khadkikar,

A.

Chandra,

B.

Singh,

Digital

signal

processor

implementation
and

performance

evaluation

of

split

capacitor,

four-leg

and

three

H-bridge-
based

three-phase

four-wire

shunt

active

ﬁlters,

IET

Power

Electron.

4

(4)
(2011)

463–470.
[104]

J.

Rodriguez,

J.

Lai,

F.Z.

Peng,

Multilevel

inverters:

a

survey

of

topologies,
controls,

and

applications,

IEEE

Trans.

Ind.

Electron.

49

(4)

(2002)

724–738.
[105]

S.

Kouro,

M.

Malinowski,

K.

Gopa

Kumar,

J.

Pou,

L.G.

Franquelo,

B.

Wu,

J.
Rodriguez,

M.A.

Perez,

J.I.

Leon,

Recent

advances

and

industrial

applications
of

multilevel

converters,

IEEE

Trans.

Ind.

Electron.

57

(8)

(2010)

2553–2578.

Neutral current compensation in three phase, four wire systems a review

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