Mehr als dieVergangenheit unddieGegenwart
interessiert mich dieZukunft,
denn inihr gedenke ich zu leben.
(AlbertEinstein)
Technicaland economic designof asimplified
highly renewable
European
electricity system
Letthe
weather
decide!
1
2000– 2007:1h,45x45km²
1980– 2010:1h,30x30km²
AARHUS
UNIVERSITY
AU
Renewable
Energy
Atlas
DEPARTMENT OF ENGINEERING
Modelingof ahighly renewable
Europeanelectricity system
R
n
G (t) − Ln (t) =
= Bn (t) + Pn (t) + Sn (t)
actio =reactio
GnR (t) = GnW (t) + GnS (t)
R
n
G
𝐶" 𝑡 = 𝑚𝑎𝑥 𝐵" 𝑡 , 0
= γ n Ln
W
n
G
𝐺"# 𝑡 = −𝑚𝑖𝑛 𝐵" 𝑡 , 0
R
n
= αn G
GnS = (1− α n ) GnR
𝐹1 𝑡 = 2 𝑃𝑇𝐷𝐹1" 𝑃" 𝑡
"
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
R
n
G (t) − Ln (t) = Bn (t) + Pn (t)
γn = 1
α n = 0.7
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
How much ...
...windenergy?
...solarPVenergy?
...backup energy +power?
...transmission?
...storage?
What are important
temporaland spatial scales?
I. Timescales:storage
II. Spatialscales:backup+transmission
III. Costs
IV. Outlook
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
I.Timescales:how much storage?
5
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
Europeanaggregation:
Wind+Solar powergeneration+Load
3TIMESCALES:
diurnal (1h-1d)
synoptic (2-10d)
seasonal
(1y)
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
Howmuchstorage?@100%penetrationinEU
S(t) − S(t −1) =
#% η Δ(t) (Δ > 0)
in
= $ -1
%& ηout Δ(t) (Δ < 0)
storage
energy
capacity
CE = max S(t) − min S(t)
t
t
ηin = ηout = 1
α
Seasonaloptimalmix
=60%windpower
AARHUS
UNIVERSITY
AU
+40%solarpower
DEPARTMENT OF ENGINEERING
Howmuchstorage?@100%penetrationinEU
CS = 10% L
annual
storage
energy
capacity
= 340 TWh
NOTPOSSIBLE:
Pumped Hydro,
Compressed Air
POSSIBLE:
H2storage
25TWh =0.008av.y.l.
6h“battery”storage
2.2TWh =0.0007
av.y.l
α
annualconsumption(2009)=3360TWh
70%windpowergeneration=875GWinstalledcapacity
=175.000x5MWturbines=4350x200MWwindfarms
≈115000km²
30%solarPVpowergeneration=550GWinstalledcapacity≈3500- 7500km²
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
StorageSingularity
renewablepenetration
GnR = γ n Ln
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
StorageSingularity
CE (random) << CE (original)
CE (random) ∝
1
γ −1
δ
CE (1h) ≈ CE (1d)
δ =1
temporalcorrelations
p ( Δ(t +1d) | Δ(t))
Δ(t + τ ) Δ(t)
Δ2
synoptictimescale
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
II.Spatialscales:
howmuchbackup
+transmission?
11
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
Couplingschemesbetweentransmissionandbackup
Δ n (t) = GnRES (t) − Ln (t) = Bn (t) + Pn (t)
Pn (t) = 0
min
(∑
min
Zeroflow
n
)
GnB (t)
(∑ F (t))
2
l
l
Localizedflow
Bn (t) = β (t) Ln
Δ (t)
∑
β (t) =
∑ L
n
n
n
n
Flowwith
AARHUS
UNIVERSITY
AU
synchronizedbalancing
DEPARTMENT OF ENGINEERING
Balancingdistribution(Germany)
RES
n
Bn (t) = G
(t) − Ln (t) − Pn (t)
GnRES = Ln
α n = 0.7
Zeroflow
Localizedflow
Synchronizedflow
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
backup
energy
backup
capacity
𝐺"#
𝑚𝑎𝑥6 𝐺"#
Zeroflow
Localizedflow
Synchronizedflow
transmission
capacity
∑ max
l
q
Fl
Localizedflow
Synchronizedflow
Zeroflow
Localizedflow
Synchronizedflow
RES
AARHUS
AU
n UNIVERSITY
G
= Ln
DEPARTMENT OF ENGINEERING
Principal
flow patterns
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
backup
energy
backup
capacity
𝐺"#
𝑚𝑎𝑥6 𝐺"#
Zeroflow
Localizedflow
Synchronizedflow
transmission
capacity
∑ max
l
q
Fl
Localizedflow
Synchronizedflow
Zeroflow
Localizedflow
Synchronizedflow
Zeroflow
GnB ≈ 0.24
α n ≈ 0.70
Flowwith
synch.bal.
B
GEU
≈ 0.15
α EU ≈ 0.80
RES
AARHUS
AU
n UNIVERSITY
G
= Ln
DEPARTMENT OF ENGINEERING
beyond EU:world-wide grid
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
III.Costs
18
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
backup
energy
backup
capacity
𝐺"#
𝑚𝑎𝑥6 𝐺"#
transmission
capacity
∑ max
l
AU
q
Fl
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
n the denominator is, for different sources, often
enerated energy. In the case of VRES, when some of
comes at a time when it is not needed, one would
he denominator as the actual usage of generated
ase, since we look at both conventional backup and
This section first focuses on the dependence of the four technical objectives (12), (13), (14) and (18) on the penetration parameters gn ¼ g, the mixing parameters an ¼ a, and the three
transmission paradigms. The penetration and mixing parameters
are chosen to be the same for each country. In the second subsection, the g and a dependence of the economic objective (21) is
discussed, again for all three transmission paradigms.
Levelized CostofSYSTEMEnergy
MWh) for energy delivered by the system as a function of the wind mix (an ¼ a) for different penetrations of renewables (gn ¼ g): g ¼ 0.5 (top row), g ¼ 1.0
¼ 1.5 (bottom row). Contributions from transmission costs are shown in green, wind power in blue, solar power in yellow, backup capacity in red and backup
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
Heterogeneous
renewableelectricitynetworks
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
unity.
Whopaysfortheheterogeneity?
flow
tracing
T
T
Figure 5. Relative link capacity ln
l in the export picture for the nodes DE = Germany (left) and AT = Au
colour-coded links. Also shown is the average export transfer function (13), shown as colour-coded nodes.
Challenge:cooperative2020à2050investments+markets
UNIVERSITY
AU AARHUS
DEPARTMENT OF ENGINEERING
much of the positive injection (Pn)+ at node n is exported to a sink node(m.
1) The latter
een outlined
in the introduction.
‘load-proportional’
is based
on the average load of
much
of the negative
injection (PnThe
)− atfirst
node
n is imported fromusage
a sourcennode
m. The
ountry
n,
also illustrated
in figure 5. Whereas the German exports spread over the whole
r Austria mainly serves first neighbours and bigger second
L n neighbours with its exports.
(1)
T,
ons are not shown. They are similar to the export
n = transfer functions.
Lm
åpropositions
flow tracing based usage measure with two simplified
which already have
m
(1)
uction.
The
first
‘load-proportional’
usage
(n2) is based on the average load of T
whereas the second ‘link-based’ assignment
associates the capacity usage
of a link l = (m
n) to
Flowtracing
n
ncident nodes n and m only,
w J. Phys. 17 (2015) 105002
(1)
n
=
Ln
åm
Lm
T,
l
(2)
n
=
å
l (n)
T
l
2
B Tranb
.
(15)
(1)
(2)
(2) l incident to node n. Both assignments
T
Here
denotes all links
add
up to ån (ni) = T
n (and
n ) to
ased’l(n)
assignment
associates
the
capacity
usage
of
a
link
its
l
=
m
n
n
l
The
new
flow
tracing
based
nodal
usage
of
the
network
can be expressed as the sum of nodal link capaci
ly,
12) over all links,
T
(2)
l
(3)
T
(16)
.
n = å
= å ln
.
n
l (n) 2
l
(1)
(i )
T.
(3) (2) add
T . For
incident
to node
n. Bothalso
assignments
up to
=European
Note
that this
assignment
adds up to å
the
simplified
transmission netwo
å
n andn =
n
n
n
n
(3) nodal usage of the network can be expressed as the sum of nodal link capacities
(1)
(2)
ased
n is illustrated in figure 6, and compared to the two other propositions
n and
n from (15) and (16
For the three biggest countries Germany, France and Great Britain the new assignment (17) turns out to
(3)
Tassignment (15). For the next two countries Italy and Spain it is the oppo
maller than the load-proportional
(17)
n = å ln .
(3)
(2)
his excess usage of the network
l becomes clearer when comparing
n directly to
n . Since France is
(3)
T . to
entral,
it has
large
four countries,
explains network,
the rather big green bar in figu
also
adds
up to
Forthe
theother
simplified
Europeanwhich
transmission
ånlink capacities
n =
AARHUS
Great Britain, Spain and also Italy are peripheral. They
the direct links
to France,
but also the lin
(1) not only(2use
)
UNIVERSITY
AU
6, and compared to the two other propositions
and
from
(15)
and
(16).
n
n
eyond. This explains the reduction from (n2) to (n3) for France at the expense of an increase for Great
DEPARTMENT OF ENGINEERING
. Phys. 17 (2015) 105002
Flowtracing
B Tranberg et al
gure 2. Illustration of a simple five-node network with (a) an injection and a resulting flow pattern, (b) the flow tracing of exports,
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
much of the positive injection (Pn)+ at node n is exported
L nto a sink node(m.
1) The latter
een outlined
in the introduction.
‘load-proportional’
is based
on the average load of
(1)
much
of the negative
injection (PnThe
)− atfirst
node
imported fromusage
a Tsource
m. The
, nnode
nn is=
ountry
n,
L m over the whole
also illustrated
in figure 5. Whereas the German exports
åm spread
r Austria mainly serves first neighbours and bigger second
L n neighbours with its exports.
(
2
)
T
(1)
T ,capacity usage
as the
‘link-based’
assignment
associates
the
of a link l = (m
=
ons
aresecond
not shown.
They are similar
to the export
transfer
functions.
n
l
n
Lm
åpropositions
nt nodes
and m
only,
flow
tracingnbased
usage
measure with two simplified
which already have
m
(1)
uction.
The
first
‘load-proportional’
usage
thecapacity
averageusage
load of T of a link l = (m
(n2) is based on T
whereas the second ‘link-based’ assignment
associates the
n) to
Flowtracing
n (2)
ncident nodes n and m only,
w J. Phys. 17 (2015) 105002
n
=
å
l
l (n) T2
.
l
B Tranb
(2)
l
(1)
T,
1) f (t ) =(2)(∣15
(ifl
)
=
. power(flow
)t )∣up
3.
Colour component
cn.
asna function
of the
(a)
based
on
the
F
(
:
n =
l
ln(t)
(n) denotes allFigure
links
l incident
to node
Both
assignments
and
add
to
l
n
n
n
2 (CH, IT) between
l (n)l =
m
based on the flowLtracing
of imports. The link
Switzerland and Italy, andnthe nod
Ln
å
å
å
m
he new flow tracing
based
nodal
usageone
ofhour
the network
can
expressed(2)as the Energy
sum ofAtlas
nodal
linkT
(1) long Renewable
(i ) from
chosen.
dot
represents
contained
in
thebe
8 years
data
(2)Each
T
Here
l(n)
denotes
all
links
l
incident
to
node
n.
Both
assignments
and
add
up
to
ån inn 1=− q =
n (m
n
ased’
a linkflow
l=
n associates
ver
allassignment
links, conditional
l of
average áthe
latter, the
extreme
events f n>) toTits
, which happen
cln ∣ fcapacity
ñ. For theusage
l the lsum of nodal link capaci
l
The
new
flow
tracing
based
nodal
usage
of
the
network
can
be
expressed
as
T
ly,
mapped onto fl = l .
(3)
T
12) over all links,
=
.
å
n
ln
T
(2)
l
(3)
T
(16)
.
n = å
= ål ln
.
n
l (n) 2
(3)
T
hat this assignment also adds up to ån n = l T. For the simplifiedT European transmission
(1)
(i )
lT
(3) (2) add
dsimplified
T . lFor
incident
to node
n. Bothalso
assignments
and
up
to
T
=European
(1. )
(2)
Note
that
this
assignment
adds
up
to
the
transmission
netwo
=
å
n
n
n
åto
n
n
=
f
c
s illustrated in figure 6, and compared
the
two
other
propositions
and
n
l
ln
ln
n
n ffrom
l
l dfl (15) a
ò
ò
C
(3) nodal usage of the network can be expressed as the0sum1of(1)
(2)
ased
nodall (link) capacities
is
illustrated
in
figure
6,
and
compared
to
the
two
other
propositions
and
(16
n
n
n from (15)
or the three biggest countries Germany, France and Great Britain the new assignment
(17)and
turns
For the three biggest countries Germany, France and Great Britain the new assignment (17) turns out to
er than
the load-proportional
assignment
(15). For the next two countries Italy and Spain it is th
(3)
Tassignment (15). For the next two countries Italy and Spain it is the oppo
maller than the
load-proportional
(17
) to (check
(3)
2)
for
thenetwork
fraction
of
link
used
bycomparing
node n. It is(straightforward
thatFran
thi
n = å
ln . capacity
.
xcess
usage
of
the
becomes
clearer
when
directly
to
Since
3
)
(
2
)
n
n
T
T
his excess usage of the network
l becomes clearer when comparing
n directly to
n . Since France is
=
.
å
ln
l
n capacities
l, it hasit large
link
the
other
four
countries,which
which
explains
rather
big green
(3)
Tto
entral,
large
link capacities
to
the
other
four countries,
explains
the the
rather
big green
bar in bar
figu
also
adds has
up to
For
the
simplified
European
transmission
network,
=
.
å
n
Based
on
the
eight
years
long
hourly
Renewable
Energy
Atlas
data
from
[2],
the
r
n also Italy are peripheral. They not only use the direct links toAARHUS
Britain,
Spain
and
France,
but
also
Great
Britain,
Spain
and alsoT ItalyTare peripheral. They
the direct links
to
France,
but
also
the
lin
(1) not only(2use
)
UNIVERSITY
AU
6, and compared
to the two
other
propositions
(15)
and
(16).
capacities
are
summarized
Each
row
in
this
figure
represents
li
n (in
n 4.from
((2))
3(and
)3)figure
ln
l
d. ThisThis
explains
thethe
reduction
to nn for
forFrance
France
at the
expense
an increase
fora G
eyond.
explains
reductionfrom
from n to
at the
expense
of anofincrease
for Great
()
DEPARTMENT OF ENGINEERING
Flowtracing
New J. Phys. 17 (2015) 105002
B Tranberg et al
AU
Figure 4. L × N matrix of the relative nodal link capacities
T
ln
T
l
resulting from a 50%/50% combination of the export / import
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
IV.Morechallenges
wind + solar + hydro + bio +
+ transmission + storage
coupling of electricity + heating + transportation.
backup flexibility classes
big networks:
renormalization scaling of power flows,
small-world AC/DC networks,
self-organizing power flows.
climate change + mesoscale turbulence
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
FunRes
Res
FundamentalResearchon
Renewable Energy Systems
atthe interface between engineering +physics +mathematics
MartinGreiner,AarhusUniversity
greiner@eng.au.dk
(1) Highly Renewable Energy Systems
(2) Complex Networks
(3) Wind-farmModeling+Optimization
(4) Turbulence
MTherkildsen (Master)
PNybroe
(Master)
JOtten
(Master)
JBjerre
(Master)
JHerp
(Master)
UPoulsen (AssistProf)
CPoulsen
(Master)
MRaunbak
(Master)
MKofoed
(Master)
LSchwenk_Nebbe (Master)
NSkou-Nielsen
(Master)
EEriksen
(Master)
BTranberg
(Master)
SKozarcanin
(Master)
MDahl
(Master)
AThomsen
(Master)
BSairanen
(Master)
TJensen
(Master)
TZeyer
(Master)
RRodriguez
(PhD)
MRasmussen
(PostDoc)
GAndresen(Assit Prof)
MHansen
(Master)
KHolm
(Master)
ASøndergaard
(Master)
DSchlachtberger (FIASPhD)
JHörsch
(FIASPhD)
SHempel
(FIASMaster)
TBrown
(FIASPostDoc)
MSchäfer
(FIAS)
SSchramm(FIAS)
SBecker
(FIASPhD)
DHeide
(FIASPhD)
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
DHeide et.al.:Seasonableoptimalmixofwindandsolarpowerinafuture,highlyrenewableEurope,
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SBeckeret.al.:Transmission gridextensionsduringthebuild-up ofafullyrenewablepan-Europeanelectricity
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TVJensenet.al.:Emergenceofaphasetransitionfortherequiredamountofstorageinhighly renewableelectricity
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transmission gridextensions,Energy72(2014) 443-458.
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Energy76(2014)49-58.
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Energy81(2015)437-445.
RARodriguezet.al.:Cost-optimaldesignofasimplified, highly renewablepan-Europeanelectricitysystem,
Energy83(2015)658-668.
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network,Energy,Sustainability&Society5(2015)21.
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systemanalysis, Energy93(2015) 1074-1088.
BTranberg et.al.:Powerflowtracinginasimplified highlyrenewableEuropeanelectricitynetwork,
NewJ.Physics17(2015)105002.
DPSchlachtberger et.al.:Backupflexibilityclasses inrenewableelectricitysystems,
EnergyConversionandManagement (2015)submitted.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING