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PIDR Sliding Mode Current Control with Online Inductance Estimator for VSC MVDC System Converter Stations under Unbalanced Grid Voltage Conditions.pdf


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Energies
Energies 2018,
2018, 11,
11,xx FOR
FOR PEER
PEER REVIEW
REVIEW

44 of
of 20
20

Energies 2018, 11, 2599

4 of 20

EEg1g1

IIg1g1
PPg1g1++jQ
jQg1g1

20
20kV
kV

++

PCC2
PCC2

YYgg

--

CS1
CS1

IIg2g2
PPg2g2++jQ
jQg2g2

CS2
CS2

EEg2g2

DGs
DGs

Loads
Loads

TT11

--

RRg2g2==84
84mΩ

LLg2g2==12
12mH
mH

15
15MVA
MVA
110/10
110/10kV
kV
RRTT=0.003
=0.003
XXTT=0.08
=0.08

TT22

Filter
Filter
200kVA
kVA
200

++

=1mF
CC11=1mF

RRg1g1==84
84mΩ

LLg1g1==12
12mH
mH

YYgg

Filter
Filter
200kVA
kVA
200

AC
AC
B
System
System11 B11

10
10km
km
RRdd=0.12
=0.12Ω/km
Ω/km
LLdd=0.1
=0.1mH/km
mH/km

=1mF
CC22=1mF

~~

15
15MVA
MVA
110/10
110/10kV
kV
RRTT=0.003
=0.003
XXTT=0.08
=0.08

110
110kV
kV
50
50Hz
Hz
1500
MVA
1500 MVA

~~

110
110kV
kV
50
50Hz
Hz
1500
MVA
1500 MVA

PCC1
PCC1

2.
2. Mathematic
Mathematic Model
Model of
of the
the Studied
Studied VSC-MVDC
VSC-MVDC System
System
2. Mathematic Model of the Studied VSC-MVDC System
2.1.
2.1. Schematic
Schematic of
of the
the VSC-MVDC
VSC-MVDC System
System Studied
Studied
2.1. Schematic of the VSC-MVDC System Studied
The
The single-line
single-line diagram
diagram of
of the
the two-terminal
two-terminal VSC-MVDC
VSC-MVDC system
system studied
studied is
is shown
shown in
in Figure
Figure 1.
1.
The
mainly
stations
(CS1
CS2),
AC
inductor
and
The single-line
diagramof
theconverter
two-terminal
VSC-MVDC
studied
is shown
in Figure
1.
The system
system
mainly consists
consists
ofoftwo
two
converter
stations
(CS1 and
andsystem
CS2), the
the
AC filtering
filtering
inductor
and
DC
capacitor
each
and
the
To
lines,
there
The
system
mainlyfor
consists
of two
stations (CS1 lines.
and CS2),
theDC
AC transmission
filtering
inductor
and
DC
DC bus
bus
capacitor
for
each CS,
CS,
andconverter
the DC
DC transmission
transmission
lines.
To the
the
DC
transmission
lines,
there
may
be
loads
and
DGs.
figure,
are
listed.
Those
with
bus capacitor
for each
CS,
and
the In
DC
transmission
lines.
To the DCparameters
transmission
there
may
be
may
be connected
connected
loads
and
DGs.
In the
the
figure, the
the main
main technical
technical
parameters
arelines,
listed.
Those
with
aaconnected
unit
the
physical
values
and
without
aa unit
denote
per-unit
loads denote
and
DGs.
the figure,
the main
technical
parameters
listed.
Thosethe
with
a unit
unit provided
provided
denote
theInactual
actual
physical
values
and those
those
withoutare
unit
denote
the
per-unit
values.
provided
denote
the
actual
physical
values
and
those
without
a
unit
denote
the
per-unit
values.
values.

AC
AC
BB22 System
System22

Figure
Figure 1.
1. Single-line
Single-line diagram
diagram of
of the
the two-terminal
two-terminal voltage
voltage source
source converter
converter medium
medium voltage
voltage direct
direct
Single-line
diagram
current
(VSC-MVDC) system
system studied.
studied.
current (VSC-MVDC)

Theschematic
schematicof
ofthree-phase
three-phaseVSC
VSCfor
foreach
each
CS
shown
Figure
2.
In
figure,
egcgc
,and
egc ,
The
CS
is
shown
in
Figure
2.
figure,
eegaga,,eega
gb
,, and
gb
The
schematic
of
three-phase
VSC
for
each
CS
isis
shown
inin
Figure
2. In
In the
thethe
figure,
gb,,, ee
i
,
i
,
i
denote
the
grid
voltage
and
current,
respectively;
u
,
u
,
u
denote
the
converter
pole
iiand
ga
,
i
gb
,
i
gc
denote
the
grid
voltage
and
current,
respectively;
u
ca
,
u
cb
,
u
cc
denote
the
converter
pole
ga
gc
ca
cc
gb
cb
ga, igb, igc denote the grid voltage and current, respectively; uca, ucb, ucc denote the converter pole
voltage,
R
andLLLgggdenote
denotethe
theresistance
resistanceand
andinductance
inductance of
of
the
AC
filtering
denote
voltage,
dc
voltage, R
Rggg and
and
denote
the
resistance
and
inductance
of the
the AC
AC filtering
filtering inductor;
inductor; CC and
and uudc
dc denote
denote
the DC
DC bus
bus capacitor
capacitor
and
voltage
respectively.
the
the
DC
bus
capacitor and
and voltage
voltage respectively.
respectively.
T1
T1
eegaga
eegbgb
eegcgc

~~
~~
~~

RRgg

LLgg i
igaga

RRgg

LLgg i
igbgb

RRgg

LLgg i
igcgc

T3
T3

T5
T5

uucaca

++
CC
uudcdc

uucbcb
uucccc
T2
T2

T4
T4

--

T6
T6

Figure
Figure 2.
2. Schematic
Schematic of
of three-phase
three-phase VSC
VSC for
for each
each converter
converter station.
station.

The
CSare
areidentical,
identical,so
controllers are
The structures
structures of
of the
the current
current control
control loops
loops for
for each
each CS
CS
are
identical,
so that
that their
their controllers
are
designed
designed under
under aa unified
unified framework.
framework. In
Inaddition,
addition,assume
assumethe
the grid
grid voltage
voltage on
on each
each side
side contains
contains the
the
fundamental
components only
only and
and that
that the
the grid
grid frequency
fundamental components
frequency is
is 50
50 Hz
Hz ifif not
not otherwise
otherwise specified.
specified.
2.2. Mathematical
MathematicalModel
Model of
of the
the CS
CS
2.2.
2.2.
Mathematical
Model
of
the
CS
Underunbalanced
unbalancedgrid
gridvoltage
voltageconditions,
conditions,
the
space
vectors
of
grid
voltage,
current
Under
the
space
vectors
of
grid
voltage,
current
and
the
Under
unbalanced
grid
voltage
conditions,
the
space
vectors
of the
thethe
grid
voltage,
current
andand
the
the
converter
pole
voltage
can
be
decomposed
into
the
PS
and
negative
sequence
(NS)
components.
converter
pole
voltage
can
be
decomposed
into
the
PS
and
negative
sequence
(NS)
components.
converter pole voltage can be decomposed into the PS and negative sequence (NS) components. In
In
In Figure
3, the
space
vector
of
grid
voltage
in
and
SRF
is shown
as
example.
Figure
3,
space
vector
of
grid
voltage
in
PS
and
NS
SRF
is
as
example.
Figure
3, the
the
space
vector
of the
thethe
grid
voltage
in the
thethe
PSPS
and
NSNS
SRF
is shown
shown
as an
anan
example.