optimal power flow in multi-terminal hvdc networks for dc-system operator: constant current...
TRANSCRIPT
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 1/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
Dr Francisco M. Gonzalez-Longatt
@fglongatt
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 2/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• The power injections (Pi)in a DC grid are controlledby the converters.
• On a MTDC grid asSupergrid, the power flowinto, or out of, eachconverter can bedynamically changedwithout anyreconfiguration of theHVDC grid.
• The purpose of this paperis to present an optimalpower flow methodconsidering DC-ISOoperation objectives.
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 3/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• The introduction of HVDCgrids brings with it majorchallenges, andopportunities.
• In this paper, DC-ISO isdefined as a private orpublic entity, and it tocoordinates, controls andmonitors the operation ofthe DC transmission systeminvolving one or severalpower park modules andone or several TSOs. DC-ISO is expected to performthe same functions as ISOs,but cover only the MTDCsystem.
DC-connected Power
Parks
Pdc,k
MTDC System
Meshed
DC
Network
Bulk generationBulk Transmission
TSO1
TSOk
TSOn
......
......
Power
Park 1
Power
Park m
......
Synchronous
Areas
Customers
DC
Independent
System
Operator
Single
Market
Service
Providers
.........
...
Grid Side
Converters
Transmission
System Operators
DC-Wide-Area
Supervision and Control Power Park
Converter
......
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 4/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• DC-ISO will uses the OPF in order to dispatch the MTDCaccording to signals provided by the pool market.
• The steady-state behaviour of a MTDC system can be described bya set of nonlinear set of the algebraic equations:
• G is the set of algebraic equations define the power balance at network
• X is state vector
• Y is the vector of independent variable.
• The state vector contains the state variables describing the state ofthe MTDC system, it contain dependent variables.
, G X Y 0
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 5/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• OPF is formulated mathematically as a general constrainedoptimization problem where set of constraints are taking inaccount.
• The most basic and general OPF formulation is based on a problemof minimization without inequality constraints as:
• Subject to:
• where f(X,Y) is the function to be optimized.
min ,f X Y
, G X Y 0
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 6/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• In this paper, system loses are located on the DC transmissionsystem and it is assumed to be the Joule heating or ohmic heating inthe cables.
• Under the previous assumption, the total losses in a MTDC systemcan be written as:
• where Pdc,i are the elements in Pdc calculated in terms of the nodalvoltages using:
• where the DC current Udc =[Udc,1, Udc,2, ...,Udc,ndc]T is the DC
voltage vector and YDC is the DC nodal admittance matrix.
,
1
dcn
losses dc i
i
f P P
X,Y
convK dc dc dc dcP = U Y U
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 7/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• Bound constraints: Lower (Xmin) and upper (Xmax) bounds limitthe components of the solution X. Bound constraints are written inthe form of:
• DC-voltage at station converters (Udc,i) are written as boundconstraints based on operational limits:
• Nonlinear equality constraints: Nonlinear inequality constraintshave the form G(X,Y) = 0, where G is a vector of constraints, onecomponent for each constraint.
• The mathematical formulation of the OPF includes a set ofnonlinear equality constraints as:
min maxX < X < X
min , maxdc iU U U
, G X Y 0
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 8/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• Linear inequality constraints: have a form as:
AieqX < Bieq
• where Aieq is an n-by-m matrix, which represents m constraints foran n-dimensional vector X. Bieq is m-dimensional.
• Linear equality constraints: have a form as:
AeqX = Beq
• where Aeq is an n-by-m matrix, which represents m’ constraints foran n-dimensional vector X. Beq is m-dimensional.
max
conv convI < I max
conv dc dc convI = Y U I
MTDC
network
1
i
ndc
Udc,1
Udc,k
j
k
Udc,ndc
Udc,i Udc,j
Ii,j
, , ,
esp
ij i i dc i dc j ijI Y U U I =
The current flowing through the cable connected between node i
and node j, Iij, is written using nodal analysis as:
where Yi,j is the correspondent element of the YDC is the DC nodal
admittance matrix, and Iijesp represents the operational current
defined by the DC-ISO for that specific branch.
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 9/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• Test systems:
GSC1
GSC2 WFC1
PWF1 = 0.95p.u
R13 = 0.045
WF1
AC1
AC2R23 =
0.052
R12 =
0.0
.07
3
①
②
③ I12 = 0.50 p.u
P-mode
V-mode
V-mode
①
②
③
④
⑤
GSC1
GSC2 WFC1
PWF1 = 0.75p.u
R14 = 0.052
WF1
AC1
AC2R24 = 0.052
GSC3AC3R 34 =
0.073
WFC2
R35 = 0.073
PWF2 = 0.85p.u
WF2
I14 = 0.3 p.u
GSC1
WFC3
AC1
R46 = 0.0500
PWF2 = 0.30p.u
R45 = 0.0250 R57 = 0.0325
PWF3 = 0.50p.u
GSC2 AC2
WFC1
PWF1 = 0.40 p.u
R14 =
0.0
10
0R
24 =
0.0
12
5 R35 =
0.0
07
5
①
② ③
WFC2
⑦ ④ ⑤ ⑥
WF1
WF3
I15 = 0.10 p.u
Test system I: 3Node+1WF+2ACTest system II: 5-Node+2WF+3AC Test System
Test system III:
7-Node+3WF+2AC Test
System
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 10/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• The proposed OPF methodology is tested considering power lossesas objective function.
• Bound constraints are considered in all simulations in order toensure a secure system operation (0.90 < Udc < 1.10 p.u).
• (i) Case I: No Linear equality constraints Case I, no currentconstraints in any under-sea cable scenario.
• (ii) Case II: Linear equality constraints is considered to ensureconstant current operation in one cable.
GSC1
GSC2 WFC1
PWF1 = 0.95p.u
R13 = 0.045
WF1
AC1
AC2R23 =
0.052
R1
2 =
0.0
.073
①
②
③ I12 = 0.50 p.u
P-mode
V-mode
V-mode
①
②
③
④
⑤
GSC1
GSC2 WFC1
PWF1 = 0.75p.u
R14 = 0.052
WF1
AC1
AC2R24 = 0.052
GSC3AC3R 34 =
0.073
WFC2
R35 = 0.073
PWF2 = 0.85p.u
WF2
I14 = 0.3 p.u
GSC1
WFC3
AC1
R46 = 0.0500
PWF2 = 0.30p.u
R45 = 0.0250 R57 = 0.0325
PWF3 = 0.50p.u
GSC2 AC2
WFC1
PWF1 = 0.40 p.u
R14 =
0.0
10
0R
24 =
0.0
12
5 R35 =
0.0
07
5
①
② ③
WFC2
⑦ ④ ⑤ ⑥
WF1
WF3
I15 = 0.10 p.u
Test system I: 3Node+1WF+2AC Test system II: 5-Node+2WF+3AC Test System Test system III: 7-Node+3WF+2AC Test System
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 11/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
SIMULATION RESULTS OF OPF: TEST SYSTEM I
SIMULATION RESULTS OF OPF: TEST SYSTEM II
SIMULATION RESULTS OF OPF: TEST SYSTEM III
Node
Case I Case II
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
① 1.0896 -0.2315 -0.5045 1.1000 0.6434 1.4155
② 1.0896 -0.2003 -0.4365 1.0635 -1.0778 -2.2925
③ 1.1000 0.4318 0.9500 1.0935 0.4344 0.9500
Node
Case I Case II
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
① 1.1000 0.3000 0.6600 1.0720 -0.1274 -0.2731
② 1.0645 -0.3829 -0.8152 1.0720 -0.1274 -0.2731
③ 1.0652 -0.6516 -1.3881 1.0718 -0.4792 -1.0273
④ 1.0844 0.3458 0.7500 1.0786 0.3477 0.7500
⑤ 1.0936 0.3886 0.8500 1.1000 0.3864 0.8500
Node
Case I Case II
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
Udc
(pu)
Idc
(p.u)
Pdc
(p.u)
① 1.1000 0.1818 0.4000 1.1000 0.1818 0.4000
② 1.0999 0.1364 0.3000 1.0999 0.1364 0.3000
③ 1.0979 0.2277 0.5000 1.0974 0.2278 0.5000
④ 1.0982 0.0000 0.0000 1.0982 0.0000 0.0000
⑤ 1.0962 0.0000 0.0000 1.0957 0.0000 0.0000
⑥ 1.0862 -0.2396 -0.5205 1.0873 -0.2182 -0.4745
⑦ 1.0863 -0.3063 -0.6654 1.0850 -0.3278 -0.7114
Optimal solution are
found on all simulation
scenarios if no branch
constraints are
considered (Case I).
The participation of
grid side converters
(GSC) on DC-voltage
regulation allows the
optimal operation of
the MVSCDC
fulfilling all the
considered constraints
(Case II).
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 12/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• As expected, Case I exhibit lower power losses compared with Case II.
• The additional linear equality constraint added by constant current operation produces apredefined power flow in one branch inside the MVSCDC increasing the losses
• The constant current operation, linear equality constraint, adds stress on searching the
OPF solution which increases the total simulation time
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 13/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
• This paper roughly introduces the new concept of DCIndependent System Operator, DC-ISO.
• A methodology for an optimal steady-state operation of aMTDC system based on DC-ISO objectives has been presented inthis paper.
• DC-ISO might use a path inside the MTDC as interconnectors forinternational electricity trade allowing inter TSO operation; underthis condition the current magnitude and direction in one or severalundersea cable inside the MTDC must be loaded at very specificvalue under variables conditions.
• This paper proposes the use of a type linear equality constraintsbased on nodal analysis to include this specific operational modeto the OPF.
www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 14/1550th
Inte
rnat
iona
l Uni
vers
ities
Pow
er E
ngin
eerin
g C
onfe
renc
e (U
PE
C20
15)S
epte
mbe
r
1st -
4th,
201
5 | S
taffo
rdsh
ire U
nive
rsity
, UK
All
right
s re
serv
ed. N
o pa
rt o
f thi
s pu
blic
atio
n m
ay b
e re
prod
uced
or
dist
ribut
ed in
any
form
with
out
perm
issi
on o
f the
aut
hor.
Cop
yrig
ht ©
200
8-20
15. h
ttp:w
ww
.fglo
ngat
t.org
@fglongatt
Dr Francisco M. Gonzalez-Longatt
@fglongatt