Low voltage ride-through of DFIG and brushless DFIG: Similarities and differences

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Electric
Power
Systems
Research
110
(2014)
64–72
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cate/epsr
Low
voltage
ride-through
of
DFIG
and
brushless
DFIG:
Similarities
and
differences
S.
Tohidia,∗,
P.
Tavnerb,
R.
McMahonc,
H.
Oraeea,
M.R.
Zolghadria,
S.
Shaoc,
E.
Abdic
aDepartment
of
Electrical
Engineering,
Sharif
University
of
Technology,
Tehran,
Iran
bSchool
of
Engineering
and
Computing
Sciences,
Durham
University,
Durham,
UK
cEngineering
Department,
University
of
Cambridge,
Cambridge,
UK
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
25
August
2013
Received
in
revised
form
24
November
2013
Accepted
31
December
2013
Available
online
14
February
2014
Keywords:
Wind
turbine
Doubly
fed
induction
generator
(DFIG),
Brushless
doubly
fed
induction
generator
(BDFIG),
Low
voltage
ride-through
(LVRT),
Voltage
dip
a
b
s
t
r
a
c
t
The
brushless
doubly
fed
induction
generator
(BDFIG)
has
been
proposed
as
a
viable
alternative
in
wind
turbines
to
the
commonly
used
doubly
fed
induction
generator
(DFIG).
The
BDFIG
retains
the
benefits
of
the
DFIG,
i.e.
variable
speed
operation
with
a
partially
rated
converter,
but
without
the
use
of
brush
gear
and
slip
rings,
thereby
conferring
enhanced
reliability.
As
low
voltage
ride-through
(LVRT)
performance
of
the
DFIG-based
wind
turbine
is
well
understood,
this
paper
aims
to
analyze
LVRT
behavior
of
the
BDFIG-based
wind
turbine
in
a
similar
way.
In
order
to
achieve
this
goal,
the
equivalence
between
their
two-axis
model
parameters
is
investigated.
The
variation
of
flux
linkages,
back-EMFs
and
currents
of
both
types
of
generator
are
elaborated
during
three
phase
voltage
dips.
Moreover,
the
structural
differences
between
the
two
generators,
which
lead
to
different
equivalent
parameters
and
hence
different
LVRT
capabilities,
are
investigated.
The
analytical
results
are
verified
via
time-domain
simulations
for
medium
size
wind
turbine
genera-
tors
as
well
as
experimental
results
of
a
voltage
dip
on
a
prototype
250
kVA
BDFIG.
©
2014
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
With
increasing
penetration
of
wind
energy
into
electrical
power
systems,
many
countries
have
introduced
connection
Grid
Codes
to
regulate
the
effect
of
wind
farms
on
the
grid.
One
of
the
most
important
and
demanding
requirements
of
these
codes
deals
with
the
low
voltage
ride-through
(LVRT)
capability
of
wind
turbines
(WTs).
LVRT
arises
as
Grid
Codes
require
WTs
to
remain
connected
during
grid
voltage
dips
according
to
a
pre-determined
curve.
For
example,
LVRT
characteristics
of
the
German
Transpower
Grid
Code
are
shown
in
Fig.
1
[1].
According
to
this
Grid
Code,
WTs
must
tolerate
voltage
dips
from
the
highest
value
of
the
three
line
voltages
with
a
profile
above
the
bold
line
of
Fig.
1,
i.e.
in
the
gray
region,
without
disconnecting.
The
most
widely
installed
modern
variable
speed
WTs
employs
the
doubly
fed
induction
generator
(DFIG).
Using
the
DFIG
in
WTs
provides
a
degree
of
variable
speed
operation,
when
using
partially
rated
bi-directional
converter
and
associated
filters.
The
disadvan-
tage
of
the
DFIG
is
its
unavoidable
use
of
brush-gear
and
slip-rings,
which
reduce
reliability
[2].
∗Corresponding
author
at:
Department
of
Electrical
Engineering,
Sharif
University
of
Technology,
Azadi
Street,
Tehran,
Iran.
Tel.:
+98
9141586094.
E-mail
address:
stohidi@yahoo.com
(S.
Tohidi).
The
brushless
DIFG
(BDFIG)
has
been
proposed
as
an
alterna-
tive
to
the
DFIG
in
variable
speed
WTs.
The
BDFIG
retains
the
main
benefits
of
DFIG
without
brush-gear
or
slip-rings,
leading
to
higher
reliability
and
less
maintenance.
Extensive
analytical
investigations
have
been
made
into
the
LVRT
capability
of
DFIG
including
methods
to
improve
its
perfor-
mance.
FACTS
devices
[3],
supercapacitor
energy
storage
[4],
series
grid-side
converter
[5],
crowbar
and
static
transfer
switches
[6],
energy
capacitor
systems
[7],
series
dynamic
resistors
[8],
dynamic
voltage
restorers
[9,10]
and
controller
modifications
[11–16]
have
all
been
suggested
to
improve
DFIG
LVRT
capability.
On
the
other
hand,
many
aspects
of
the
BDFIG
or
more
generally
the
Brushless
Doubly
Fed
Machine
(BDFM),
such
as
steady-state
modeling
[17]
and
analysis
[18],
dynamic
modeling
[19,20]
and
control
[21–23]
have
been
studied
in
the
literature
and
BDFIG
LVRT
performance
has
been
studied
using
crowbar
and
series
dynamic
resistors
[24].
The
DFIG
has
been
used
in
WTs
since
late
1980s
and
many
WT
manufacturers
have
wide
experience
of
its
operation
and
control.
It
appears
that
if
BDFIG
is
analyzed
and
controlled
in
a
similar
way,
it
would
facilitate
the
understanding
of
its
LVRT
behavior.
Addition-
ally,
the
control
systems
proposed
for
enhancing
LVRT
capability
of
DFIG
can
also
be
used
for
BDFIG,
albeit
with
some
modifications.
At
the
current
stage
of
BDFIG
design,
due
to
the
relatively
lower
torque
densities
predicted
for
BDFIGs
compared
to
conventional
0378-7796/$
–
see
front
matter
©
2014
Elsevier
B.V.
All
rights
reserved.
http://dx.doi.org/10.1016/j.epsr.2013.12.018

S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
65
Nomenclature
p
pole
number
Nrnumber
of
BDFIG
rotor
circuits
v
voltage
i
current

flux
linkage
e
back
electro-motive
force
R
winding
resistance
L
self
inductance
Llleakage
inductance
M
mutual
inductance
T
torque
ω
angular
speed
Q
reactive
power
J
inertia
Ksshaft
stiffness
D
shaft
damping
coefficient

shaft
twist
angle
ı
winding
damping
factor
Subscripts
and
superscripts
s
DFIG
stator
r
rotor
p
BDFIG
power
winding
c
BDFIG
control
winding
e
electrical
m
mechanical
transient
0
steady-state
(pre-fault)
b
base
induction
machines
[18],
a
BDFIG
could
be
larger
than
a
DFIG
of
the
same
rating
and
speed.
However,
experiments
on
an
actual
medium
scale
BDFIG
show
satisfactory
steady
state
and
dynamic
performance
[25],
which
could
be
improved
further
with
advances
in
design.
As
the
BDFIG
has
a
complex
air
gap
flux,
this
paper
aims
to
facilitate
BDFIG
LVRT
analysis
similar
to
a
DFIG
by
presenting
the
equivalences
between
the
BDFIG
and
DFIG.
Moreover,
their
LVRT
capability
will
be
compared,
reflecting
the
effect
of
inherent
fea-
tures
in
such
generators
on
their
equivalent
parameters.
The
structure
of
the
paper
is
as
follows:
Section
2
explains
the
modeling
and
control
of
both
generators;
Section
3
elaborates
their
LVRT
performance,
using
a
dq
model,
in
which
variations
of
flux
linkages
and
EMFs
are
analyzed;
and
also
compares
their
LVRT
capabilities
taking
into
account
the
differences
between
their
parameters;
in
Section
4,
simulation
results
are
presented
to
Fig.
1.
German
Transpower
Grid
Code
LVRT
curve
[1].
Fig.
2.
WT
with
DFIG.
verify
the
analysis;
and
finally
in
Section
5,
experimental
results
of
a
severe
voltage
dip
at
terminals
of
a
250
kVA
BDFIG
is
presented
to
verify
analysis
and
simulations.
2.
Principles
of
DFIG
and
BDFIG
A
WT
with
DFIG
is
illustrated
in
Fig.
2.
The
generator
is
a
wound
rotor
induction
machine,
in
which
the
rotor
winding
(RW)
is
con-
nected,
via
brush
gear
and
slip
rings,
to
a
bi-directional,
partially
rated
converter
and
its
stator
winding
(SW)
and
the
converter
are
connected
to
the
grid
in
parallel.
The
converter
consists
of
two
inverters
connected
back-to-back
via
a
DC
link
capacitor.
The
rotor
side
inverter
(RSI)
controls
the
rotor
speed
and
stator
reac-
tive
power,
while
the
grid
side
inverter
(GSI)
controls
the
DC
link
voltage
to
remain
essentially
constant.
The
BDFIG,
on
the
other
hand,
has
two
stator
windings
while
its
RW
is
shorted,
not
requiring
brush-gear
or
slip-rings.
As
can
be
observed
in
Fig.
3,
one
of
the
stator
windings,
the
power
winding
(PW),
is
connected
directly
to
the
grid
while
the
other,
the
control
winding
(CW),
is
connected
to
the
grid
via
a
partially
rated
con-
verter.
The
converter
is
identical
to
that
used
in
the
DFIG,
except
the
inverters
need
to
be
named
machine
side
inverter
(MSI)
and
grid
side
inverter
(GSI).
The
PW
and
CW
have
different
pole
pair
numbers
to
avoid
direct
electromagnetic
coupling
between
them.
This
difference
is
selected
to
be
greater
than
1
to
prevent
unbalanced
magnetic
pull
on
the
rotor
[26].
The
RW
should
be
designed
such
that
in
addition
to
direct
coupling
with
each
stator
winding,
it
establishes
cross
cou-
pling
between
the
PW
and
CW.
In
fact,
the
rotor
acts
as
an
interface
between
the
two
stator
windings
and
associates
their
different
pole
number
fields
together.
To
satisfy
this
requirement,
the
number
of
rotor
circuits
or
pole
pairs,
Nr,
should
be
related
to
the
stator
winding
pole
numbers
as:
Nr=
pp+
pc(1)
The
most
popular
rotor
structure
proposed
so
far
for
the
BDFIG
is
the
nested-loop
rotor,
in
which
each
nest
represents
one
cir-
cuit
[26].
The
RW
produces
a
magneto-motive
force
(MMF)
in
response
to
each
of
the
PW
or
CW
MMFs,
which
has
space
har-
monic
content
orders
of
ppand
pcas
well
as
other
undesired
higher
orders.
In
this
way,
the
pppole
pair
MMFs
from
the
PW
and
RW
Fig.
3.
WT
with
BDFIG.

66
S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
and
the
pcpole
pair
MMFs
from
the
CW
and
RW
interact
to
pro-
duce
the
rotor
electromagnetic
torque.
The
unusual
structure
of
the
nested
loop
rotor
leads
to
unwanted
space
harmonics
to
a
cer-
tain
degree
and
hence
the
rotor
design
is
currently
under
extensive
investigation.
2.1.
Two
axis
models
of
DFIG
and
BDFIG
The
two
axis
model
for
DFIG
in
the
synchronously
rotating
ref-
erence
frame
is
stated
[27]
as
(2)–(6).
vs=
Rsis+
jωss+ds
dt (2)
vr=
Rrir+
j(ωs−
psωr)r+dr
dt (3)
s=
Lsis+
Msr ir(4)
r=
Msr is+
Lrir(5)
Te=
−3
2psIm [∗
sis](6)
If
the
stator
flux
linkage
under
normal
conditions
is
selected
as
the
d-axis
of
the
reference
frame,
the
SW
reactive
power
and
rotor
speed
can
be
controlled
via
the
d
and
q-axes
of
the
RW
current,
respectively
[28].
The
BDFIG
model
in
the
pppole
pair
synchronously
rotating
ref-
erence
frame
is
obtained
and
experimentally
validated
as
(7)–(13)
in
[19].
vp=
Rpip+
jωpp+dp
dt (7)
vc=
Rcic+
j(ωp−
Nrωr)c+dc
dt (8)
vr=
Rrir+
j(ωp−
ppωr)r+dr
dt =
0
(9)
p=
Lpip+
Mpr ir(10)
c=
Lcic+
Mcr ir(11)
r=
Mpr ip+
Mcr ic+
Lrir(12)
Te=
−3
2ppIm ∗
pip−3
2pcIm [ci∗
c](13)
Similarly,
if
the
d-axis
reference
frame
is
aligned
to
the
PW
flux
linkage,
the
PW
reactive
power
and
rotor
speed
can
be
con-
trolled
by
d
and
q-axes
of
the
CW
current,
respectively
[21].
Hence,
the
reactive
power
and
rotor
speed
controllers
for
DFIG
and
BDFIG
can
be
considered
as
shown
in
Fig.
4,
where
the
parameters
for
the
BDFIG
are
shown
in
parentheses.
As
the
dynam-
ics
of
the
internal
current
control
loop
are
fast,
they
are
not
considered.
In
addition,
the
two-mass
drive
train
model
of
the
turbine
and
generator
can
be
stated
as
(14)–(16).
Tm=
Jtdωt
dt +
Ks
+
D(ωt−
ωg)
(14)
Te=
−Jgdωr
dt +
Ks
+
D(ωt−
ωg)
(15)
d
dt =
ωt−
ωg(16)
Combining
(9)–(12)
results
in
(17)
for
BDFIG
rotor
current.
ir=−(j(ωp−
ppωr)
+
s)Mpr
Lpp+Mcr
Lcc
Rr+
(j(ωp−
ppωr)
+
s)Lr−M2
pr
Lp−M2
cr
Lc(17)
Fig.
4.
Controllers
of
DFIG
(BDFIG):
(a)
rotor
speed
controller;
and
(b)
reactive
power
controller.
Current
BDFIG
rotors
with
nested-loop
cages
typically
exhibit
an
RW
resistance
lower
in
magnitude
than
other
term
of
the
denom-
inator
of
the
right-hand
side
of
(17)
and
hence
can
be
neglected.
However,
by
substituting
(10)
and
(11)
into
(17)
and
omitting
Rr,
the
rotor
current
is
obtained
as:
ir=
−Mpr
Lr
ip−Mcr
Lr
ic(18)
Substituting
(18)
into
(10)
and
(11)
leads
to:
p=
Lpeip+
Meic(19)
c=
Meip+
Lceic(20)
where
Lpe,
Lce and
Mpc are
termed
as
“PW
effective
self-inductance”,
“CW
effective
self-inductance”
and
“PW
and
CW
cross-mutual
inductance”,
respectively.
These
parameters
are
calculated
as
fol-
lows:
Lpe =
Lp−
M2
pr
Lr
(21)
Lce =
Lc−M2
cr
Lr
(22)
Mpc =
−Mpr Mcr
Lr
(23)
Thus,
Eqs.
(7),
(8),
(19)
and
(20)
express
the
BDFIG
dynamic
model.
Comparing
these
equations
with
the
corresponding
rela-
tions
for
DFIG
(2)–(5)
show
the
similarities
between
the
dynamic
models
of
the
two
configurations.
3.
LVRT
analysis
3.1.
LVRT
of
DFIG
Although
the
majority
of
faults
in
electric
power
systems
are
asymmetrical,
a
symmetrical
fault
is
a
particular
case
whose
anal-
ysis
can
pave
the
way
to
studying
asymmetrical
faults.
This
paper
therefore
focuses
on
three
phase
voltage
dips
and
asymmetrical
faults
will
be
the
subject
of
future
publications.
When
a
three-phase
voltage
dip
occurs
at
the
machine
terminals
at
t
=
0,
the
synchronously
rotating
stator
flux
linkage
decreases
in
proportion
to
the
terminal
voltage.
On
the
other
hand,
accord-
ing
to
the
principle
of
constant
flux
linkage,
the
value
of
stator
flux
linkage
cannot
vary
instantaneously.
Therefore,
sis
divided
into
two
portions.
The
first
part
rotates
at
the
synchronous
speed

S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
67
with
amplitude
proportional
to
the
remaining
voltage
and
the
sec-
ond
part,
with
amplitude
proportional
to
the
voltage
dip,
ceases
to
rotate
and
is
described
as
frozen.
Neglecting
Rsin
(2),
an
approx-
imate
relationship
for
sduring
the
transient
can
be
obtained,
as
follows:
s=
vs
jωs+
vs−0−
vs
jωs
e−jωste−ıst(24)
Here,
ısis
strictly
dependant
on
Rs.
Now,
if
(24)
is
referred
to
the
DFIG’s
rotor
reference
frame,
(25)
will
be
obtained.
r
s=
vs
jωs
e−j(psωr−ωs)t+
vs−0−
vs
jωs
e−jpsωrte−ıst(25)
This
equation
means
that
the
rotating
and
frozen
fluxes
rotate
with
respect
to
the
rotor
at
ωs−
psωrand
−psωr,
respectively.
In
addition,
combining
(2)–(5)
results
in
(26)
which
expresses
the
DFIG
dynamics
from
the
rotor
point
of
view.
vr=
R
rir+
j(ωs−
psωr)L
rir+
L
r
dir
dt +
er
R
r=
Rr+
RsMsr
Ls2
L
r=
Lr−M2
sr
Ls
er=Msr
Lsvs−Rs
Ls+
jpsωrs
(26)
If
(26)
is
transferred
to
the
rotor
reference
frame,
(27)
will
be
obtained.
vr
r=
R
rir
r+
L
r
dir
r
dt +
er
r
er
r=Msr
Lsvse−j(Pωr−ωs)t−Rs
Ls+
jpsωrr
s(27)
Substituting
(25)
into
(27)
gives
the
EMF
induced
in
the
DFIG
rotor
during
transients.
As
expected,
the
EMF
induced
in
the
RW
has
frequencies
of
ωs−
psωrand
−psωr.
er
r=Msr
jωsLs−Rs
Ls+
j(ωs−
psωr)vse−j(psωr−ωs)t
−Rs
Ls+
jpsωr(vs−0−
vs)e−jpsωrte−ıst(28)
Table
1
Equivalent
parameters
of
DFIG
and
BDFIG.
DFIG
SW
RW
RsLsRrLrMsr R
rL
r
BDFIG
PW
CW
RpLpe RcLce Mpc R
cL
c
3.2.
LVRT
of
BDFIG
As
for
BDFIG,
the
three-phase
voltage
dip
at
the
generator
termi-
nals
at
t
=
0
leads
to
variation
of
PW
flux
linkage
in
the
same
way
as
DFIG
stator
flux
linkage.
Therefore,
considering
(7)
PW
flux
linkage
can
be
obtained
as
(29).
p=
vp
jωp+
vp−0−
vp
jωp
e−jωpte−ıpt(29)
The
amplitudes
of
the
rotating
and
frozen
fluxes
are
similar
to
those
of
DFIG.
The
speed
of
rotating
and
frozen
parts
relative
to
the
rotor
is
now
ωp−
ppωrand
−ppωr,
respectively.
The
rotor
reacts
to
this
transient
flux
and
its
MMF
leads
to
production
of
pppole
pair
fields
with
similar
rotational
speed.
As
mentioned
before,
the
special
design
of
BDFIG
rotor
leads
to
the
production
of
other
space
harmonic
fields,
particularly
pcpole
pair.
The
latter
field
has
two
parts
that
rotate
with
respect
to
the
rotor
with
the
same
speed
as
corresponding
pppole
pair
parts,
but
in
opposite
directions.
In
other
words,
the
components
of
pcpole
pair
field
rotate
at
ppωr−
ωp
and
ppωrwith
respect
to
the
rotor
or
at
Nrωr−
ωpand
Nrωrwith
respect
to
the
CW.
Meanwhile,
transferring
(29)
to
the
BDFIG’s
CW
stationary
reference
frame
results
in
(30),
which
show
the
resulting
frequencies.
Transformations
for
moving
between
different
BDFIG
reference
frames
can
be
found
in
[19].
c
p=
vp
jωp
ej(Nrωr−ωp)t+
vp−0−
vp
jωp
ejNrωrte−ıpt(30)
Using
a
similar
procedure
to
that
described
for
DFIG,
the
BDFIG’s
dynamics
from
the
CW
point
of
view
and
in
the
CW
stationary
ref-
erence
frame
are
obtained
as
(31),
clearly
showing
the
similarities
between
the
two
generators.
vc
c=
R
cic
c+
L
c
dic
c
dt +
ec
c
R
c=
Rc+
RpMpc
Lpe 2
,
L
c=
Lce −
M2
pc
Lpe
ec
c=Mpc
jωpLpe −Rp
Lpe +
jωp−
Nrωrvpej(Nrωr−ωp)t−Rp
Lpe +
jNrωr(vp−0−
vp)ejNrωrte−ıpt
(31)
3.3.
Similarities
between
LVRT
of
DFIG
and
BDFIG
According
to
the
analysis
presented
above,
equivalent
parame-
ters
between
the
DFIG
and
BDFIG
are
summarized
in
Table
1.
In
addition,
the
amplitudes
and
frequencies
of
the
undamped
and
damped
EMFs,
due
to
the
previously
mentioned
rotating
and
frozen
fluxes,
during
DFIG
and
BDFIG
steady
state
and
transient
conditions
are
compared
in
Table
2.
It
should
be
noted
that
in
order
to
sim-
plify
the
comparison,
resistances
of
DFIG
SW
and
BDFIG
PW
are
neglected
in
the
calculation
of
EMFs
shown
in
the
table.
Table
2
Equivalence
between
DFIG
RW
and
BDFIG
CW
induced-EMFs.
Undamped
EMF
due
to
the
rotating
flux
Damped
EMF
due
to
the
frozen
flux
Frequency Amplitude Frequency Amplitude
Normal
conditions
Transient
conditions
DFIG
ωs−
psωr
ωs−
psωr
ωs
Msr
Ls
vs−0
ωs−
psωr
ωs
Msr
Ls
vs−psωr
ps␻r
␻s
Msr
Ls
(vs−0−
vs)
BDFIG
Nrωr−
ωp
ωp−
Nrωr
ωp
Mpc
Lpe
vp−0
ωp−
Nrωr
ωp
Mpc
Lpe
vpNrωr
Nrωr
ωp
Mpc
Lpe
(vp−0−
vp)

68
S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
Table
3
Comparison
of
250
kVA
DFIG
and
BDFIG
per-unit
equivalent
parameters.
DFIG RsLsRrLrMsr R
rL
r
0.007
2.559
0.005
2.547
2.417
0.011
0.264
BDFIG RpLpe RcLce Mpc R
cL
c
0.017
2.503
0.020
2.471
2.225
0.033
0.492
It
is
noteworthy
that
if
psωrin
a
DFIG
and
Nrωrin
a
BDFIG
have
the
same
values,
the
control,
dynamics
and
ride
through
analysis
of
the
BDFIG
can
be
treated
in
a
similar
way
to
DFIG.
This
similarity
is
an
advantage,
as
almost
all
DFIG
ride-through
enhancement
strate-
gies
can
also
be
applied
to
the
BDFIG
with
minor
modifications.
Nevertheless,
there
are
some
differences
between
their
parameters,
which
lead
to
different
LVRT
performances,
which
will
be
discussed.
3.4.
Comparison
between
DFIG
and
BDFIG
parameters
It
is
recognized
that
the
main
problem
of
DFIG
ride
through
is
the
high
current
induced
in
the
rotor
due
to
the
transient
EMF
described
in
Section
4.
Hence,
to
protect
the
converter
power
elec-
tronic
switches
and
DC
link
capacitor,
either
the
DFIG
needs
to
be
disconnected
from
the
grid
or
additional
hardware,
such
a
crowbar,
will
have
to
come
into
operation
in
the
rotor
circuit
during
severe
voltage
dips.
Table
2
shows
that
the
EMFs
induced
in
the
DFIG
RW
and
BDFIG
CW
will
have
similar
amplitudes
and
frequencies.
Thus,
to
compare
BDFIG
CW
and
DFIG
RW
transient
currents,
their
transient
resis-
tances
and
inductances
must
be
compared.
These
parameters
are
dependent
upon
machine
design,
and
it
may
therefore
be
difficult
to
generalize.
But
there
are
distinct
structural
differences
between
DFIG
and
BDFIG,
which
lead
to
natural
differences
in
their
param-
eters.
The
physical
reasons
for
these
differences
are
as
follows:
•There
are
three
coupled
windings
in
BDFIG
(PW,
CW
and
rotor)
as
opposed
to
two
coupled
windings
in
DFIG
(SW
and
RW).
Hence,
higher
total
leakage
inductance
and
resistance
referred
to
BDFIG
PW
or
CW
must
be
expected
compared
to
the
same
quantities
referred
to
DFIG
SW
or
RW,
respectively.
•The
BDFIG
rotor
has
a
special
structure.
The
most
commonly
used
form
–
known
as
nested
loop
rotor
–
produces
more
space
harmonics
than
a
standard
winding,
reflected
in
an
increased
differential
leakage
flux.
Hence,
the
per-unit
rotor
leakage
induct-
ance
of
BDFIG
will
be
higher
than
that
of
DFIG.
3.4.1.
Numerical
comparison
Taking
into
account
the
differences,
it
is
expected
that
the
equivalent
transient
inductance
of
BDFIG
will
be
higher
than
a
conventional
DFIG
of
the
same
rating.
In
Table
3,
the
equivalent
parameters
of
a
250
kVA
DFIG
and
BDFIG
are
compared.
The
BDFIG
parameters
have
been
obtained
through
measurements
on
a
250
kVA
4/8-pole
prototype
machine
recently
manufactured.
With
regard
to
DFIG,
the
authors
were
unable
to
find
compa-
rable
250
kVA
parameters
but
used
per-unit
parameters
from
a
representative
6-pole,
1.67
MVA
DFIG
taken
from
the
literature
[29].
Moreover,
the
per-unit
parameters
of
BDFIG
and
the
five
representative
wind
turbine
DFIGs
taken
from
the
literature
are
presented
in
Table
A.1
in
Appendix.
This
table
shows
close
agreement
between
the
per-unit
values
of
resistances
and
leakage
inductances
for
a
range
of
DFIGs.
Comparison
between
the
parameters
shown
in
Table
3
shows
that
the
PW
and
CW
effective
leakage
inductances
(0.278
and
0.246
pu)
are
higher
than
those
for
DFIG
SW
and
RW
(0.142
and
0.130
pu),
respectively.
In
particular,
the
transient
inductance
of
BDFIG
CW
is
higher
than
that
of
DFIG
RW
leading
to
a
lower
tran-
sient
current
in
BDFIG
CW
during
a
voltage
dip.
The
larger
equivalent
resistances
of
BDFIG
arise
partly
from
dif-
ferences
in
construction
and
design
choices,
as
BDFIG
resistances
depend
on
slot
area
and
winding
turn
number
[30].
More
signifi-
cant
is
that
the
counterpart
to
a
4/8-pole
BDFIG
is
a
12-pole
DFIG;
the
resistances
of
such
a
machine
are
likely
to
be
higher
than
those
for
lower
pole
number
machines.
Care
must
therefore
be
taken
in
making
comparisons,
especially
as
few
large
BDFIGs
have
yet
been
constructed
and
limited
data
is
available.
Hence,
BDFIG
and
its
associated
converter
should
tolerate
more
severe
voltage
dips
than
DFIG,
without
disconnection
from
grid
or
the
use
of
additional
hardware.
Furthermore,
to
satisfy
an
LVRT
grid
code,
if
required,
a
BDFIG
would
need
lower
rated
protective
hard-
ware
than
a
DFIG.
In
order
to
confirm
these
predictions,
simulations
have
been
performed
using
the
available
data.
The
LVRT
performance
is
significantly
affected
by
the
converter
controllers,
hence
extensive
attention
has
been
paid
to
devising
control
schemes
to
give
improved
DFIG
LVRT
capability
[11–16].
A
good
control
strategy
enables
a
DFIG
to
ride-through
small
voltage
dips,
but
simulations,
confirmed
by
experimental
results,
show
that
satisfactory
DFIG
LVRT
under
severe
voltage
dip
conditions
could
not
be
achieved
without
resorting
to
additional
hardware,
such
as
a
crowbar.
4.
Electro-mechanical
simulation
To
investigate
the
above
discussion
in
greater
detail,
LVRT
electro-mechanical
simulations
are
performed
for
both
generators
in
Table
3
using
their
complete
dq
models
(stated
in
(2)–(16)
and
Fig.
4)
in
MATLAB/Simulink.
A
150
ms,
100%
terminal
voltage
dip
is
applied
to
both
generators
at
t
=
0,
as
shown
in
Fig.
5.
The
results
are
shown
in
Fig.
6.
In
these
simulations
both
generators
were
assumed
to
be
working
at
rated
torque
and
speed
at
unity
power
factor
prior
to
voltage
dip.
The
drive
train
parameters
and
base
values
are
included
in
Tables
A.2
and
A.3
in
Appendix,
respectively.
In
Fig.
6(a)
the
rotor
speed
deviations
are
compared.
As
expected,
the
generators
experience
similar
rotor
speed
increases.
From
Fig.
6(b),
it
can
be
concluded
that
the
peak
of
BDFIG
PW
current
is
lower
than
that
of
DFIG
SW
current.
More
importantly,
Fig.
6(c)
shows
that
the
peak
of
BDFIG
CW
current
is
significantly
less
than
that
of
DFIG
rotor
current.
Therefore,
the
MSI
can
remain
connected
to
the
BDFIG
during
voltage
dips
simply
by
overrating
the
converter
switches.
Alternatively,
this
may
be
achieved
by
optimizing
the
MSI
controller
to
inject
appropriate
voltage
to
control
the
CW
current
and
ensure
that
it
remains
below
the
maximum
permissible
value.
The
DFIG
rotor
current
peak
is
more
than
7
pu
and
the
genera-
tor
must
be
disconnected
from
the
grid
to
protect
the
converter.
To
Fig.
5.
The
applied
terminal
voltage
dip.

S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
69
Fig.
6.
Responses
of
BDFIG
and
DFIG
to
a
100%
voltage
dip
for
150
ms:
(a)
rotor
speed;
(b)
DFIG
SW
and
BDFIG
PW
currents;
(c)
DFIG
RW
and
BDFIG
CW
currents;
(d)
DFIG
SW
and
BDFIG
PW
flux
linkages;
(e)
DFIG
RW
and
BDFIG
CW
flux
linkages;
(f)
electromagnetic
torque;
(g)
active
power;
and
(h)
reactive
power.
prevent
disconnection,
external
hardware
such
as
a
crowbar
must
be
introduced
into
the
rotor
circuit,
as
widely
proposed
in
the
liter-
ature
[31,32].
Using
the
crowbar
protects
the
converter,
but
causes
other
problems
such
as
reactive
power
consumption,
loss
of
con-
trol
and
additional
cost.
Even
if
a
crowbar
is
required
in
a
BDFIG
for
LVRT
improvement,
its
rating
can
be
significantly
lower
than
that
applied
to
a
DFIG.
Fig.
6(d)
and
(e)
illustrates
the
flux
linkage
variations.
The
fluc-
tuations
of
BDFIG
PW
and
CW
flux
linkages
are
lower
than
DFIG
stator
and
rotor
flux
linkages,
respectively.
As
the
flux
amplitudes
are
shown
in
dq
reference
frame
in
these
figures,
the
undamped
rotating
and
damped
frozen
fluxes
appear
as
DC
and
AC
variables,
respectively.
Fig.
6
(f–h)
also
shows
that
the
active
power,
reactive
power
and
electromagnetic
torque
deviations
are
lower
for
the
BDFIG
than
the
DFIG.
4.1.
Influence
of
BDFIG
rotor
resistance
In
the
analysis
of
Section
3.1,
the
BDFIG
rotor
resistance
was
neglected.
In
order
to
investigate
the
accuracy
of
this
simplifica-
tion
more
thoroughly,
simulations
for
the
above
voltage
dip
were
compared,
with
and
without
rotor
resistance.
Fig.
7
illustrates
the
PW
and
CW
current
variations,
which
shows
negligible
effect
of
rotor
resistance,
validating
the
proposed
analytical
derivation.
5.
Experimental
validation
LVRT
tests
have
also
been
carried
out
on
the
manufactured
BDFIG,
which
have
also
been
simulated.
The
test
set-up
is
shown
in
Fig.
8.
The
prototype
D400
250
kVA
BDFIG
is
coupled
to
an
induc-
tion
motor.
The
motor
is
controlled
by
a
commercial
AC
drive
(ABB
ACS800).
The
shaft
speed,
voltages
and
currents
of
each
stator
phase

70
S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
Fig.
7.
Influence
of
the
BDFIG
rotor
resistance
on
(a)
PW
current
and
(b)
CW
current.
are
measured
by
an
incremental
encoder
with
10,000
pulses
per
revolution,
LEM
LV25-p
transducer
and
LEM
LTA
100-p
transducer,
respectively.
The
PW
is
connected
to
the
grid
via
an
autotransformer
and
6
PLC
controlled
contactors
are
switched
to
apply
a
sudden
voltage
dip
at
the
PW
terminals.
As
shown
in
Fig.
9(a),
an
88%
three
phase
voltage
dip
is
applied
at
t
=
0.
Considering
Fig.
9(b),
the
CW
current
peak
is
3.15
pu,
show-
ing
clear
agreement
between
experimental
and
simulated
results.
Fig.
8.
LVRT
test
rig.
Fig.
9.
Experimental
results
of
D400
BDFIG
subjected
to
a
three-phase
voltage
dip:
(a)
PW
voltage
and
(b)
CW
current.
The
observed
differences
between
experimental
and
simulated
results
are
in
part,
due
to
neglecting
the
higher
order
space
harmonics
in
the
rotor
MMF
as
well
as
higher
order
time
har-
monics
of
the
converter
voltage
in
the
simulations.
However,
the
main
criterion
for
comparing
LVRT
performance
is
converter
switch
peak
current,
which
is
almost
identical
in
simulation
and
test.
6.
Conclusions
The
structure,
control
and
dynamics
of
DFIG
and
BDFIG
as
WT
generators
have
been
described
in
general
and
their
differences
compared.
Their
LVRT
performance
during
three
phase
voltage
dips
is
then
compared
theoretically
and
confirmed
by
electro-
mechanical
simulation.
The
results
show
that
the
EMFs
induced
in
BDFIG
CW
or
DFIG
RW,
both
connected
to
partially
rated
converters,
are
similar
in
form
but
the
peak
transient
current
in
the
BDFIG
CW
will
be
lower
than
that
in
the
DFIG
SW
primarily
due
to
the
higher
transient
inductance
of
BDFIG
CW
compared
to
a
similar
DFIG
RW.
In
addition,
relatively
higher
transient
CW
resistance
would
further
limit
the
CW
current
variations.
Therefore,
the
BDFIG
can
tolerate
more
severe
voltage
dips
during
ride-through
compared
to
a
similar
DFIG
of
the
same
rating.
An
LVRT
test
on
a
prototype
250
kVA
BDFIG
also
validated
the
results
of
analysis
and
simulations.
In
conclusion,
the
structure
of
BDFIG
naturally
affords
a
better
LVRT
performance
than
an
equiv-
alent
DFIG.
Finally,
to
satisfy
an
LVRT
Grid
Code,
BDFIG
will
need
protective
hardware
of
significantly
lower
rating
than
the
DFIG.

S.
Tohidi
et
al.
/
Electric
Power
Systems
Research
110
(2014)
64–72
71
Appendix.
Table
A.1
Parameters
of
the
BDFIG
Compared
to
Several
DFIGs.
Generator
Rating
(MVA)
Pole
pair
numbers
Stator
parameters
(pu)
Mutual
Inductances
(pu)
Rotor
parameters
(pu)
Source
BDFIG
pppcNr
2RpRcLlp Llc Mpr Mcr RrLlr
0.25a2
4
3
0.017
0.020
0.045
0.125
6.764
3.496
0.019
0.366
Prototype
D400
BDFIG
DFIG
psRsLls Msr RrLlr
1.67b3
0.007
0.142
2.417
0.005
0.130
[29]
2.00
2
0.003
0.110
2.500
0.003
0.070
[33]
2.00
2
0.005
0.139
3.953
0.005
0.149
[15]
2.00
2
0.005
0.105
3.953
0.006
0.100
[8]
10.00
2
0.007
0.171
2.900
0.019
0.040
[6]
aBDFIG
considered
for
comparison
in
this
paper.
bDFIG
considered
for
comparison
in
this
paper.
Table
A.2
Drive
train
per-unit
parameters.
JtJgKsD
8
0.184
0.5
0.1
Table
A.3
Base
parameters.
Sb(kVA)
Vb(V)
(Phase
peak
value)
Ib(kA)
(Phase
peak
value)
wb(rad/s)
DFIG
BDFIG
250
6902/3250
√3
×
690
√2
1000
×2
60 500
×2
60
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