Wind power forecast errors

Transcription

Future volumes and costs
Elforsk rapport 11:01
Fredrik Carlsson
May 2011
Future volumes and costs
Elforsk rapport 11:01
Fredrik Carlsson
May 2011
ELFORSK
Preface
The purpose of this project was to investigate the imbalance volume due to
wind power forecast errors for the system as well as for different actors and
the costs associated to the imbalances. The reduction of imbalance costs by
trading at the adjustment market Elbas for different actors is also
investigated.
The work was carried out by Fredrik Carlsson, Vattenfall Research and
Development, as a project within the Swedish wind energy research
programme “Vindforsk – III”. The report is the final report for project V-317.
Vindforsk – III is funded by ABB, Arise windpower, AQSystem, E.ON Elnät,
E.ON Vind Sverige, EBL-kompetanse, Falkenberg Energi, Fortum, Fred. Olsen
Renwables, Gothia wind, Göteborg Energi, HS Kraft, Jämtkraft, Karlstads
Energi, Luleå Energi, Mälarenergi, o2 Vindkompaniet, Rabbalshede Kraft,
Skellefteå Kraft, Statkraft, Stena Renewable, Svenska Kraftnät, Tekniska
Verken i Linköping, Triventus, Wallenstam, Varberg Energi, Vattenfall
Vindkraft, Vestas Northern Europe, Öresundskraft and the Swedish Energy
Agency.
Comments on the work and the final report have been given by a reference
group with the following members: Elisabet Norgren, SvK, Elin Broström, SvK,
Rebecka Nilsson, SvK, Sture Larsson, SvK, Bo Wrang, Vattenfall, Kjell
Gustafsson, Statkraft, Peter Blomqvist, Arise, Susanne Franzén, Fortum,
Mohammad Hesamzadeh, KTH, Lennart Söder, KTH, and Anders Björck,
Elforsk.
Stockholm May 2011
Anders Björck
Elforsk, Electricity and Power Production
Vindforsk-III Programme manager
ELFORSK
ELFORSK
Sammanfattning
Vindkraften är en av de snabbast växande förnybara energikällor i elsystemet,
vilket är helt i linje med både Sveriges och EU:s mål. För elmarknaden finns
det framförallt två utmaningar vid en större andel vindkraft i elsystemet produktionens variation och förutsägbarhet. Produktionsvariationen är inte
behandlad i denna utredning, men både variationen och förutsägbarheten är
kopplade till behovet av reglerkraft, det vill säga att reglera produktionen till
den nivå som konsumenterna använder. Förutsägbarheten är viktig eftersom
försäljningen sker klockan 12.00 för nästkommande dygn på elmarknaden,
det vill säga 12 - 36 timmar före produktionstimmen. En prognos behöver
alltså göras för försäljningsvolymen, vilket är mycket svårt så långt i förväg
för en intermittent källa som vindkraft. Det prognosfel som då uppstår måste
om det är stort nog regleras med sekundärreglering som Svenska Kraftnät
avropar och köper. Kostnaden för regleringen får de balansansvariga som
orsakade prognosfelet betala. Mindre prognosfel på systemnivå regleras
däremot enbart med hjälp av primärreglering och då debiteras ingen för det,
men kostnaden som SvK har för att hantera detta får alla balansansvariga
dela på genom avgifterna till SvK.
För att studera kostnaden för framtida prognosfel har ett antal scenarier med
10 - 55 TWh ny vindkraft i det svenska systemet utvecklats och undersökts.
Fokus är på 10 TWh, som kallas för 5 GW fallet, vilket består av 1,5 GW redan
installerad effekt och 3,5 GW ny vindkraft. Storleken på prognosfelen för de
framtida scenarierna har antagits kunna utvecklas till en standardavvikelse på
13% av installerad effekt, vilket är mycket bra då den ligger på cirka 20% i
Sverige idag, men i andra länder som Tyskland runt 15%. Scenarierna bygger
på existerande planer på nya vindkraftsparker för att göra scenarierna så
troliga som möjligt. För att få olika perspektiv har åtta balansansvariga
aktörer skapats med olika ägande. Aktörerna äger all ny vindkraft (dvs inte
existerande) i scenarierna och aktörerna skiljer sig från varandra genom att
äga vindkraft med olika geografisk placering och spridning. Det ger
vindkraftsinvesterare en möjlighet att hitta någon aktör att jämföra sig med
som liknar deras investeringsplaner. Rapporten har främst fokuserat på
•
att uppskatta volymen felprognoser för enskilda aktörer och för
systemet,
•
att uppskatta kostnaderna för prognosfelen för de olika aktörerna vid
olika scenarier,
•
att undersöka hur elområden påverkar ovanstående,
•
att undersöka olika alternativ till att minska kostnaderna för
prognosfel, vilket kan göras genom att t ex minska storleken på
prognosfelen genom att handla på intradagmarknaden Elbas eller
genom att förbättra prognoskvaliteten eller genom att ändra
marknadskonstruktionen.
Eftersom de framtida scenarierna är osäkra, har några parametrar varierats, t
ex prognoskvaliteten, utbyggnadens geografiska koncentration, samt hur ofta
flaskhalsar i nätet uppstår.
ELFORSK
35
5 GW (10 - 15 TWh) scenario
Today's prices (2009)
Future prices
30
Future prices & bidding zones
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figur A: Visar kostnaden för prognosfel idag utan elområden (blå), samt för
ett framtida scenario med framtida reglerkraftspriser utan (röd) och med
(gul) elområden i ett 10 – 15 TWh vindkraft scenario, dvs 5 GW GW.
50
Future wind power scenarios
45
40
Future prices with bidding zones:
5 GW = 10 - 15 TWh
35
12 GW = 30 TWh
kr/MWh
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figur B: Visar kostnaden för prognosfel idag utan elområden samt för
framtida scenarier med elområden och framtida reglerkraftspriser med 10 –
15 och 30 TWh ny vindkraft, dvs 5 GW och 12 GW.
ELFORSK
Slutsatsen är att kostnaderna för prognosfelen för vindkraftsägarna ökar från
dagens kostnader om cirka 5 - 10 kr/MWh upp till 30 kr/MWh (3 öre/kWh)
med 10 TWh ny vindkraft, se Figur A. I Figur B visas även ett scenario med
30 TWh ny vindkraft. Observera att resultaten utgår från en mycket hög
prognoskvalitet, i dagens verklighet är kostnaden redan ca 15 - 20 kr/MWh
med dagens prognoskvalitet, varför ökningen inte blir så dramatisk i praktiken
om prognoskvaliteten ökar i takt med att vindkraften byggs ut. Kostnaden för
olika aktörer varierar eftersom de har sin vindkraft i olika elområden och
eftersom de har olika geografisk spridning, vilket påverkar sammanlagringen
av prognosfelet.
De huvudsakliga skälen till högre kostnader för vindkraftsägarna kan
sammanfattas genom nedanstående fem punkter, där 10 TWh sceneriet är
utgångspunkten.
1. Reglerpriserna blir högre när efterfrågan på reglerkraft ökar med
ökande prognosfel. Dock skulle reglerpriserna kunnat ha bli ännu
högre om toppnoteringarna av reglerpriserna hade beaktats i
modellen. De timmar med toppnoteringar av priser är dock relativt få
och representerar situationer med brist på billig kraft, där dyra
anläggningar måste startas. Det skulle kunna höja kostnaden med
ytterligare cirka 10%.
2. Det blir fler timmar med prognosfel åt samma håll som systemet för de
enskilda vindkraftsägarna, vilket gör att vindkraftsägarna måste betala
för fler timmar, eftersom man betalar när man ökar systemets
prognosfel. Det sker eftersom vindkraften blir den som orsakar
prognosfelet i systemet i allt större utsträckning och medför att
vindkraften måste betala för 70% av reglertimmarna i stället för 50%
som det är idag.
3. Det blir färre timmar utan sekundärreglering, eftersom sannolikheten
för små prognosfel blir lägre. Det medför att antalet timmar som inte
behöver betalas för minskas från cirka 2000 h till 1 500 timmar.
4. De överföringsbegränsningar som finns i transmissionsnätet kommer
från och med den 1 november 2011 att hanteras genom införandet av
elområden. Det innebär också att aktörerna måste hålla balansen
inom varje elområde och att det inte längre blir någon ekonomisk
sammanlagringseffekt mellan elområdena för positiva och negativa
prognosfel eftersom de alltid ska avräknas separat. Dock är det så att
även utan elområden så måste prognosfelen hanteras, och kostnaden
för att hantera dem med Sverige som ett elområde hade då
marknaden fått betala via t ex tarifferna.
5. En ytterligare orsak till ökade kostnader är att prisnivån för att reglera
upp i södra Sverige kommer att gå upp eftersom sekundärreglering
uppåt ofta måste köpas lokalt. Eftersom de flesta vindkraftverk
planeras i söder får det en viss effekt, eftersom modellen antagit att
inget utrymme för sekundärreglering reserveras mellan snitten.
ELFORSK
40
35
Future Prices & Bidding zones
Future Prices & Bidding zones and
Elbas
30
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figur C: Fördelen med att handla på intradagmarknaden Elbas i ett framtida
Sverige med elområden och 10 – 15 TWh (5 GW) vindkraft.
Två av de fem förklaringarna (punkt 2 och 3) handlar om antalet timmar som
man måste betala för och lägger man ihop dessa så är det nästan tre gånger
så många timmar som aktörerna måste betala för. Det är därför det främsta
skälet till den högre kostnaden för aktörerna och tillsammans med stigande
priser - särskilt i södra Sverige – blir kostnaderna höga.
Det finns dessutom möjligheter för vindkraftsägarna att minska sina
kostnader genom att t ex handla på intradagmarknaden Elbas, eller genom
att förbättra sina prognoser, se Figur C. Det finns dock kostnader förenade
med detta, vilket gör att det inte lönar sig för små aktörer.
Att tänka på är att även om elområden ger en negativ effekt för
vindkraftsägare, speciellt i södra Sverige, kommer förmodligen det högre
spotpriset i södra Sverige sannolikt ge mycket mer intäkter än de extra
kostnaderna.
Slutligen så bör man relatera kostnaderna för prognosfel till inkomsterna från
försäljningen på Nord Pool Spot, och resultaten visar att kostnaden och
kostnadsökningen inte är särskilt stora, kostnaden hamnar på cirka 1 – 10%
av inkomsten från försäljningen på Nord Pool Spot.
ELFORSK
Summary
Wind power is one of the renewable energy sources in the electricity system
that grows most rapid, which is in line with both Swedish and EU
governmental goals. There are however two market challenges that need to
be addressed with a larger proportion of wind power – that is variability and
predictability. Predictability is important since the spot market Nord Pool Spot
requires forecasts of production 12 – 36 hours ahead. The forecast errors
must be regulated with regulating power, which is expensive for the actors
causing the forecast errors. The variability is not addressed in this report;
however, both variability and predictability are connected to the need for the
electric power system’s ability to regulate power – that is, to be able to
produce what the consumers consume.
This report has investigated a number of scenarios with 10 – 55 TWh of wind
power installed in the Swedish system. The focus has been on a base scenario
with 10 TWh new wind power consisting of 3,5 GW new wind power and 1,5
GW already installed power, which gives 5 GW. The size of the forecast errors
of future scenarios have been assumed to develop to a standard deviation at
13% of installed capacity, which is very good since it is around 20% in
Sweden today, however in other countries such as Germany, around 15%.
The scenarios are based on planned wind farms to make the scenarios as true
as possible. Eight different actors with balance responsibility have been
created that own all the new wind power (not the already installed) in the
scenarios. They have been chosen to differ from small to large and from
concentrated location to wide spread – which give present owners of wind
farms a possibility to find some of the constructed actor that is similar to their
targets. The investigation in this report has mainly focused on
•
the forecast error volumes due to wind power forecast errors for the
system as well as for different actors,
•
the costs associated to the forecast errors,
•
the effect of the introduction of four bidding zones in Sweden, and
•
options to reduce costs such as reduction of forecast errors by trading
at the intraday market, better forecasts, and changed market design.
To be able to simulate the consequence of forecast errors on the future
market, models of forecast errors and the market are developed. That means
that the forecast errors have been modelled for single farms, small areas and
the whole country. The regulating market has been modelled so that its
correlation to the spot market and the effect of increased forecast errors has
been taken into account.
Since future perspectives are uncertain, some parameter variations have been
investigated to see their influences. The main attention has been on varying
the standard deviation of forecast errors. Other parameter variations have
been on the geographic location/distribution of new wind farms, and the
amount of hours with congestions.
ELFORSK
35
Future prices
30
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figur A: The costs for forecast error Today without bidding zones (blue), and
for future scenario with future prices without (red) and with (yellow) bidding
zones in a 10 – 15 TWh wind power scenario, that is 5 GW.
50
Future wind power scenarios
45
40
5 GW = 10 - 15 TWh
35
12 GW = 30 TWh
kr/MWh
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure B: The costs for forecast error with today’s regulating prices and
without bidding zones; and for the future with future regulating prices and
with bidding zones with 10 – 15 TWh (5 GW) and 30 TWh (12 GW) new wind
power.
ELFORSK
The main conclusion that is drawn from the study is that the costs for forecast
errors for the wind power owners increase from today’s costs that is about 5 –
10 kr/MWh to future 30 kr/MWh (3 öre/kWh) with 10 TWh new wind power,
see Figure A. In Figure B a 30 TWh scenario is also shown. It should be noted
that the present and future cost is based on very high forecast quality, and as
the forecast error quality is much lower today, the cost in reality is about 15 20 kr/MWh. So, the increased costs will not be so dramatic in practice. The
cost varies between the actors since they have their wind power in different
bidding zones and also different concentrations which affect the forecast error
volume. It should be noted that these numbers represents higher forecast
quality than used today.
To sum up the main reasons to the higher cost for the wind power owners;
they can be explained by five main points below, which are focused on the 10
TWh scenario:
1. The regulating prices become higher, due to higher demand for
regulating power with increased forecast errors. However, the prices
for up regulation could possibly be even higher if peak price hours had
been taken into account. These hours usually represents cases where
there is a lack of possibility to increase the power in running plants,
where very expensive reserve plants needs to be up started. That
could increase the price further with another 10%.
2. There are more hours with forecast error in the same direction as the
system for the wind power owners, since the wind power will be the
one causing the forecast error. This changes the number of hours that
the wind power owners must pay for to 70% of the hours with forecast
errors instead of 50% as it is today.
3. There are also fewer hours with no up or down regulations, since the
chance for small forecast errors becomes lower. This changes the
number of hours that does not need to be paid for from 2000 h to 1
500 h, that is a 25% reduction.
4. The transmission system has a limited transmission capacity, which
will from November 1, 2011 be handled by introducing bidding zones.
This means that the balance needs to be maintained within each zone
for the wind power owners. For wind power owners with wind power in
several bidding zones, the possibility to aggregate positive and
negative forecast errors for several bidding zones will be financially
impossible, since they will be settled separately. It should be noted,
however, that even without bidding zones, the costs for handling
forecast errors with Sweden as one bidding zone would be present in
the system, and that cost would be distributed to the market via for
instance the tariffs.
5. One additional reason to increased costs is that the price level for
regulating power upwards in the South of Sweden will go up, since
secondary regulation often needs to be bought locally and since most
wind power is planned in the South of Sweden. Regulating prices in the
north will however go down, but as said, as most wind will be located
in the South of Sweden this has a minor effect.
ELFORSK
40
35
Elbas
30
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure C: The impact on forecast error related costs when acting on the
intraday market Elbas with 10 TWh of new wind power.
Two (number 2 and 3) of the five explanations above are about paying hours.
We see that it is almost three times as many hours that the actor has to pay
for. So, the main reason for higher cost is that the amount of hours to pay is
so much higher, and together with rising prices – especially in the South of
Sweden – the costs get very high.
As a wind power owner, one should understand that although bidding zones
give a negative effect on regulating costs, the increased spot price in the
South will most likely give much more revenues than the added costs for
regulating power.
There are possibilities for the wind power owners to reduce forecast error
related costs by either trading at the intraday market Elbas or improving
quality of forecasts, which is shown in Figure C. It has also been investigated
possible options for the TSO to change the market design to either one-price
system or shorter time-horizons for the market.
Finally, the forecast error related cost should be related to the revenues. The
results show that although the cost is increasing much, it is still a relatively
small part of the income related to the spot price, in the order of 1 – 10%,
with 10 TWh new wind power.
ELFORSK
List of contents
1
Introduction
1.1
1.2
1.3
1.4
1.5
1.6
1.7
2
Wind power scenarios
2.1
2.2
2.3
2.4
3
4
4.4
5
6
25
Forecast errors on the market ......................................................... 25
Case studies ................................................................................. 25
Model of forecast errors.................................................................. 28
4.3.1 Forecast errors for single wind farms (sites) ........................... 28
4.3.2 Forecast errors for areas and neighbouring areas .................... 28
Actors .......................................................................................... 31
Simulations of forecast errors and costs
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
15
Background .................................................................................. 15
Description ................................................................................... 15
Bidding zones ............................................................................... 17
Implications of bidding zones .......................................................... 20
One- and two price systems ............................................................ 20
Market models .............................................................................. 20
Market coefficients and verification .................................................. 22
Jiggling ........................................................................................ 24
Note about 2009 market ................................................................ 24
Forecast errors
4.1
4.2
4.3
9
Looking into the future ..................................................................... 9
Scenario with about 5 GW wind power .............................................. 10
Scenarios with more than 5 GW wind power ...................................... 11
Actors .......................................................................................... 12
Electricity market
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
1
Background .................................................................................... 1
Variability and predictability .............................................................. 2
Investigation .................................................................................. 5
Limitations of work .......................................................................... 5
Literature review ............................................................................. 6
Outline of the report ........................................................................ 7
Acknowledgements .......................................................................... 7
33
Simulation environment ................................................................. 33
Forecast error with 5 GW wind power ............................................... 33
Market costs for forecast errors ....................................................... 34
Actors share of wind power ............................................................. 34
Forecast error costs ....................................................................... 35
Update of production plan ............................................................... 36
Trading on intraday market............................................................. 37
Influence of forecast quality on imbalance costs ................................. 38
Congestions .................................................................................. 38
Geographic distribution .................................................................. 39
Changed market design to 6 h markets ............................................ 40
Changed market design to one-price system ..................................... 40
30 TWh scenario ........................................................................... 41
All projects – 55 TWh ..................................................................... 42
Maximum forecast error ................................................................. 42
Summary ..................................................................................... 43
Closure
45
ELFORSK
6.1
6.2
Conclusions .................................................................................. 45
Future work .................................................................................. 47
7
References
49
8
Appendices
51
8.1
8.2
Wind power projects ...................................................................... 51
Distances used between areas and correlation coefficient .................... 53
ELFORSK
1
Introduction
1.1
Background
Wind power is growing rapidly all over the world as it is one of the most
promising renewable energy sources1 (RES) in terms of price. The focus on
RES started due to the increased awareness that pollution from some energy
production might harm our planet. This is and has also been the trend in
Sweden, where wind power increases by 10% annually, and produces about
3,5 TWh during 2010, see Figure 1. In Sweden, the new installed RES mainly
consists of wind power and biomass, and to support the development, the
electricity certificate system has been introduced by the government. In
2009, about 17% of the electricity certificate obliged electricity was produced
by wind power (2,5 TWh). The other parts was biomass (10 TWh),
hydropower (2,5 TWh), solar power (0,2 TWh), etc. The electricity certificate
has the goal to increase the renewable electricity production by 25 TWh at
2020 relative to the 2002 level. The Swedish Energy Agency made 2009 a
forecast that the – now by the parliament decided quotas of the electricity
certificate system – will lead to around 12,5 TWh wind power electricity at
2020.
The electricity production in Sweden is about 150 TWh (40% hydro and 40%
nuclear, 20% other sources), which means that wind power presently
contributes by 2%. Increasing energy from wind power means more wind
turbines and more installed power. The installed wind power in Sweden is
about 1,5 GW which is produced by 1500 wind turbines. It is clear from these
numbers, that more wind power is to come.
Energy produced from wind power [TWh]
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Figure 1: Annual wind power production (TWh) in Sweden 1994 – 2010 [1].
1
"Energy from renewable sources" means renewable non-fossil energy sources: wind,
solar, geothermal, wave, tidal, hydropower, biomass, landfill gas, sewage treatment
plant gas and biogases [EU]
1
ELFORSK
1,4
Wind power 2010
1,2
1,0
GW
0,8
0,6
0,4
0,2
0,0
01-jan
02-mar
01-maj
30-jun
29-aug
28-okt
27-dec
Figure 2: Hourly wind power production in the whole Sweden during 2010.
1.2
Variability and predictability
Renewable energy sources such as wind power and hydropower have some
similarities and some differences. First of all, they both have a varying power
source (wind speed respectively precipitation), however, since wind energy
(kinetic energy) is more difficult to store than hydro (potential energy) the
wind power production will vary almost instantly with changed wind speed.
The variation of wind power is illustrated in Figure 2, and shows that although
the wind power is quite spread out in Sweden, it varies much – peak
production was 1386 MW and lowest was 8 MW during 2010. The variation
that is also referred to as intermittency makes wind power quite unreliable in
the short-term perspective (hours – days). In the longer perspective (annual)
the variation of wind energy is quite small (±15%) and in fact smaller
compared to hydropower (variation of precipitation). In Sweden the water
inflow to hydropower stations is about 65 ± 20 TWh.
Since there is no built-in energy storage in the wind power, the wind power
producer has to sell the power when it blows. A power producer that has
energy storage can choose when to produce electric energy, depending on the
current and expected future market energy price and the producer’s costs of
producing and storing electric energy, etc. It is not only wind power that has
to sell at once; solar power and some hydropower stations with no reservoir
(for instance Älvkarleby power station 130 MW) have to do it as well. These
producers have no control over their energy production. It is of course
possible to reduce or even stop the production; however that is only beneficial
if it costs to produce, which could happen when spot prices are negative.
2
ELFORSK
Lillgrund forecast
100
Lillgrund production
MWh/h
80
60
40
20
0
2009-02-27
2009-03-01
2009-03-03
2009-03-05
2009-03-07
2009-03-09
2009-03-11
2009-03-13
2009-03-15
2009-03-17
Figure 3: Hourly production and 12 – 36 h forecast for Lillgrund.
Electrical energy is sold at the Nord Pool Spot. To do that, it is necessary to
predict (forecast) the production, as the energy is sold 12 – 36 hours ahead.
All producers do forecasts of their production, wind power producers by using
weather forecasts of wind speeds, and by that, estimating their future
production. Such a forecast of wind power production is illustrated in Figure 3
for the Lillgrund wind farm (Figure 4). If the actual production differs from the
planned production, the producer will have to pay for the deviation. Since the
electric power system needs to be in balance, the TSO (SvK) needs to buy
power from someone (another electric power producer) when there is a
forecast error to compensate that. This is called regulation and costs money
for the compensating (regulating) actor. The actors causing the forecast
errors must pay for their forecast error volumes. The costs are settled
according to the regulating prices and distributed among the actors who
caused forecast errors. The process is called balance settlement and takes
place the day after the production day. To conclude this, as wind power
producers have difficulties to do precise forecast as compared to hydropower
or nuclear power, additional costs are added for handling the forecast errors.
One new aspect on the Nord Pool market is that Sweden will be divided into
four bidding zones (price areas) November 1, 2011 [7], when there are
congestions at bottlenecks in the grid. Today, actors that have production and
corresponding forecast errors in two or several bidding zones are able to sum
up all forecast errors in Sweden and only pay for the net contribution of
forecast errors. As this new rule is introduced, the actors need to maintain
their own balance in each bidding zone every hour (and not only at
congestions), which means that the actors will have to pay for forecast errors
in each bidding zone and not for the sum of them (net contribution). This also
implies that some actors may not be able to internally regulate to be in
balance between different price areas – this will result in more need for
regulating power on the market or more trading on the intraday market Elbas.
3
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Figure 4: Lillgrund wind farm.
If an actor knows that his plan will not be fulfilled, for instance if the actor has
updated the wind forecast that shows a deviation from earlier forecasts, there
is an option to improve the balance by buying or selling power at the intraday
market Elbas. This could be done up to one hour before the actual production
hour. The drawback of trading at the intraday market is that the trade itself
costs money and that the new forecast usually is not correct, however usually
lower.
A producer who has other controllable production sources besides its wind
production in the same bidding zone may control that production in order to
keep the production plan. That control, is not totally free of costs, due to that
•
the regulating power is often produced at lower efficiency,
•
the production must consider the forecast error from the wind power
and reserve space in the production to handle the forecast error, such
as having larger margins in the water reservoirs, etc. It may also have
the consequence that it will not be possible to produce maximum at
the hours with highest prices, and
•
sub-optimisation occurs in the market, so several producers regulate
more together than needed.
The conclusion of this is that internal reduction of forecast errors may lead to
a sub-optimisation that is not beneficial for the producers and the market.
Denmark has chosen to cancel the rule for the actors of being in balance, and
instead put higher demand on updating the production plans.
4
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2005
700
2006
2007
600
2008
2009
500
2010
2011
GWh
400
300
200
100
0
Jan
Feb
Mar
Apr
Maj
Jun
Jul
Aug
Sep
Okt
Nov
Dec
Figure 5: Monthly wind power production during 2005 – 2010 in Sweden [1].
1.3
Investigation
This investigation focuses on the future forecast errors and its associated
costs. As a starting point, a scenario with 10 TWh new wind power in Sweden
has been created. Furthermore, additional scenarios with 30 and 50 TWh has
been created as well. The report investigates
•
the size of wind power forecast errors for the system as well as for
different actors,
•
the costs associated to the forecast errors,
•
how the introduction of bidding zones impacts forecast errors and
corresponding costs,
•
what options the actors have to reduce costs, for example reduction of
forecast errors by trading at the intraday market or improved forecast
quality, and
•
the impact of different market designs.
1.4
Limitations of work
This work is modelling the electricity market. However, models do always
contain simplifications of reality, and this work is no exception to that. This
work has been simplified in the following way:
•
All actors are assumed to buy the same forecast per area (six areas),
and with the same quality. However, as the forecast quality has been
set to a very high quality, this does not have much effect.
•
The correlation between forecast errors, congestions, and wind power
production is not taken into account. However, as the new rules state
that forecast errors will be handled per bidding zone regardless of
congestions, it is only the wind power production that will have some
effect. That effect is quite small, since only up (not down and non)
5
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regulating hours have got higher prices, and more or less limited to
bidding the zone in the South of Sweden (SE4).
•
Future transmission capacity extension between the bidding zones.
•
Possible decommission of production plants (for instance nuclear), or
reduced capacity of for instance hydro due to new rules of more
spilling, etc.
However, since several scenarios are studied and simulated on the amount of
congestions, the last two items on the list above can be extracted from these
studies.
1.5
Literature review
There have been a number of investigations in adjacent areas that have been
published. Some of these publications are listed below with a brief summary
and how it relates to this report.
•
The report “A massive introduction of wind power - Changed market
conditions?” investigates the forecast errors in a scenario with 4 000
MW wind power in Sweden, where 50% of the installed capacity is in
the North and 50% in the South of the country [6]. This is one of the
differences to this study, where about 75% of the wind power is
located to the South of Sweden. Another difference is that the
imbalances in the system 2006 was 0,9 TWh/year, while in this study
which uses imbalances from 2009, the imbalance is 1,3 TWh/year.
•
The paper “Future wind power production variations in the Swedish
power system” investigates the variation of wind power in a 4 000 MW
scenario and the conclusion is that the variation from hour to hour is
about 500 MW [22].
•
The report “Effektvariationer av Vindkraft” investigates a scenario with
4000 MW wind power in Sweden. The size and location of possible
future wind power farms are suggested and possible production is
calculated [10].
•
The report “4000 MW wind power in Sweden” evaluates the increased
need for regulating power, due to increased wind power production,
based on the calculated production data [14].
•
The possibility to profit from providing regulating power is investigated
in the report “Future Trading with Regulating Power” [9].
•
In the PhD thesis “The Impact of Large Scale Wind Power Production
on the Nordic Electricity System” [8] the influence of a large amount of
wind power on the Nordic power system is investigated, proving that if
wind power is installed over a large area the influence of a sudden
change in the power supply is decreasing due to the smoothing effect.
This smoothing effect is of important concern for the wind power
producer and for this investigation as well.
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1.6
Outline of the report
This report is divided into six chapters and a brief outline of these chapters is
listed below.
Chapter 1 introduces the reader to the subject and the background of the
topic, as well as what has been done before.
Chapter 2 summarises the future plans of new wind power in Sweden. Based
on that, scenarios in Sweden with eight wind power actors with balance
responsibility are derived.
Chapter 3 explains how the electricity market works in the Nordic countries
and presents the model of the market to be used in this study.
Chapter 4 investigates forecasting of wind power, and how the forecast
errors can be modelled for a single site, larger areas with many sites and
spread-out sites and areas.
Chapter 5 shows simulation results of the forecast errors and gives results on
costs today and for the future.
Chapter 6 makes conclusions from the investigation and also gives some
suggestions on how the forecast errors could be handled. Some ideas on
future work are also suggested.
1.7
Acknowledgements
The reference group are thanked for valuable comments on the report as well
as good suggestions during the work. The author would also like to thank Mr
Emil Eriksson, formerly at Vattenfall R&D, for the work with scenarios and Dr
Viktoria Neimane, Dr Jonas Persson, and Mr Urban Axelsson, at Vattenfall
R&D, for valuable comments.
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8
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2
Wind power scenarios
2.1
Looking into the future
To construct future presumable wind power scenarios, we can base that on
facts, incentives, plans, and ideas on what the future will look like. One way
to do that is to look on investment plans made by wind power owners. Plans
have been made on building small and large wind farms by a number of
electric power producers, companies and associations, since wind power is
becoming a safe and good investment. Future plans for large (> 10 MW) wind
farms in Sweden are compiled in a map and published monthly by Svensk
Vindenergi at its homepage www.svenskvindenergi.se [12], and can be seen
in Figure 6. There are also others who have compiled lists, for instance SvK
and the daily newspaper DN. These compiled lists will serve as base scenarios
in this investigation. In general, there are plans for the near future that
consist of about 4 GW new wind power capacity giving 10 TWh that is very
realistic to be built, since most of these projects are either under construction
or have got permission to build or are seeking permission to build. Beyond
that, plans for another 40 – 50 TWh (15 – 20 GW) exists, however these are
less certain. This report focuses therefore on a 5 GW scenario (10 - 15 TWh)
consisting on today’s 1,5 GW and 3,5 GW of new wind power. This will be the
base scenario, and beyond that all other projects will serve as linear
expansion scenarios, that are further explained in the following chapters.
Figure 6: Operating and planned projects in Sweden >10 MW [9].
9
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2.2
Scenario with about 5 GW wind power
The base scenario is based on wind power projects that are under
construction, have got the permissions or are seeking permissions. These
have been listed in the appendices in Table 17, and as can be seen, these
wind farm projects sum up to about 3,5 GW (11,3 TWh). Together with wind
power already installed in Sweden (1,5 GW), the scenario represents 5 GW
installed capacity, which will generate about 15 TWh. However, there are
some indications that the full load hours in the future projects are
overestimated, in this scenario 5 GW probably represent 10 – 15 TWh. From
the table, it can be seen that the most of the wind power is located in bidding
zone four (SE 4) that is in the South of Sweden. This is illustrated in Figure 7.
In some scenarios, even the scenarios below 5 GW will be studied, then the 5
GW scenarios will be scaled down linearly as
Case xGW = 1,5 GW + c1 ⋅ 3,5 GW ,
(1)
where c1 is variable between 0 and 1. For instance, to study the effect of 1,75
GW new wind power, the variable c1 is selected to be c1 = 0,5.
Table 1 shows the full load hours that are used in this report in each bidding
zone. These are based on the wind power projects shown in Table 17.
However, these numbers are quite high compared to the full load hours from
the wind power today in Sweden, which is in the order of 3 TWh / 1,5 GW =
2000 h. The electric power production from the wind farms as well as the
energy production per year is also shown in the table.
12,00
10,00
[TWh]
8,00
6,00
4,00
2,00
0,00
4
3
2
1
Total
Area
Figure 7: New wind power in each bidding zone in a scenario with 3,5 GW
new wind power.
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Table 1: Energy and power in each bidding zone.
Area
Full load hours
[h]
Energy production
[TWh]
Rated power
[MW]
2.3
SE 1
SE 2
SE 3
SE 4
Sum
2800
2800
3000
3200
3080
685
1985
1010
7620
11300
245
709
337
2381
3671
Scenarios with more than 5 GW wind power
In this report, scenarios with more than 5 GW are also studied. These
scenarios are based on the projects that have not been seeking permission
yet, but have done initial studies that include installed power, expected
annual energy delivery, site location, number of turbines, etc. A listing of
these projects can be found in the appendices in Table 18. These additional
projects sum up to about 40 TWh of new wind power, which means that when
we add the base scenario we have about 50 TWh of new wind power projects.
Intermediate scenarios between the base scenario and maximum of 50 TWh
will be scaled as
Case xGW = 1,5 GW + 3,5 GW + c 2 ⋅ 15 GW ,
(2)
New wind power production in each bidding zone
[new TWh]
where c2 is variable between 0 and 1. For instance, to study a 30 TWh (≈ 12
GW) scenario, the variable c2 is selected to be c2 = 0,5.
20
SE 1
SE 2
SE 3
15
SE 4
10
5
0
0
5
10
15
20
25
30
Scenario [new TWh]
Figure 8: Location of new wind installations.
11
35
40
45
50
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2.4
Actors
Eight different types of wind power actors have been created to be able to
study different ownership characteristics of wind power in terms of geographic
concentration/spread out, location in different bidding zones, small scale/large
scale, etc. The actor’s location and portfolio of wind power is compiled in
Table 2. All actors are balance responsible actors. The actors have different
amount of wind power in their portfolio and the geographical spread-out is
also different for the actors. Actor number 1 owns the most of the wind power
of the actors (about 50%), which is seen in Figure 9. All the actors except
number 7 have their wind power at several sites in the areas that they are
operating, while actor number 7 owns one single site. Actor number 7 will due
to that not gain any effect of spatial smoothening, and will therefore have a
higher relative forecast error compared to the other actors, which is explained
more in detail in Chapter 4.
The eight actors created in this report represent eight different ownerships
and the ambition is that most of the wind power investors in Sweden should
be able to find one of the created actors to correspond well with their
investment plans. For example, since only the forecast errors is modeled, an
investor in the Northern part of Sweden, who just wants to invest in one site,
can look upon actor 7. The forecast error quality is not dependent on location;
it is only the full load hours (and price) that depend on location.
Table 2: The actors proportion of the amount of wind power in each bidding
zone in a 5 GW scenario with 3,5 GW new wind power.
SE 4
SE 3
SE 2
SE 1
1
100%
57%
100%
57%
100%
41%
100%
26%
2
26%
2%
27%
3
8%
8%
4
0%
5
9%
6
0%
7
8
Actor
Sum
Full
Power
Energy
load h
MW
GWh
3 106
1 902
5 907
19%
3 089
862
2 664
0%
28%
3 083
281
867
0%
22%
19%
2 800
204
570
12%
0%
0%
3 167
253
801
10%
0%
7%
2 931
52
153
0%
0%
10%
0%
2 800
74
207
0%
10%
0%
0%
3 000
34
103
2373
337
709
245
3 078
3 664
11 275
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Installed capacity [MW]
2000
1500
1000
500
0
1
2
3
4
5
6
7
Actors
Figure 9: Installed capacity per actor with 3,5 GW new wind power.
13
8
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Figure 10: The forecast error areas in the different bidding zones.
14
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3
Electricity market
3.1
Background
The Nordic countries deregulated the market for electric power trading and
created Nord Pool in 1993 as the market place for power trade. Norway was
the first country trading on this market, and Sweden started trading 1996,
Denmark and Finland joined some years later.
3.2
Description
The Transmission System Operator (TSO) in Sweden is Svenska Kraftnät
(SvK). Svenska Kraftnät is responsible for maintaining the country's spinning
power balance. This responsibility is executed through, for instance, entering
into agreements with companies who want to become balance responsible
actors. The balance responsible actor undertakes to plan, on an hourly basis,
in such a way that the production and purchasing of power correspond to the
anticipated consumption and sales of the consumers/suppliers that the
company has the balance responsibility for, and subsequently to financially
regulate balance discrepancies vis-à-vis2 Svenska Kraftnät. A balance
responsible has several possibilities of creating a balance between the supply
and consumption of power; for example, through bilateral deals with other
balance responsible actors, trading on the power exchange and planning own
production resources. A power trading company can either handle the balance
responsibility itself or engage a company, which has an agreement with
Svenska Kraftnät regarding balance responsibility. Normally there is a fee
associated with buying balance responsibility services from somebody else.
Presently there are about 30 balance responsible actors in Sweden.
Since electric power is traded for future actions, forecast of the future electric
power consumption and productions have to be made. At Nord Pool Spot, the
trades are performed mainly at the spot market, however the production
plans can be adjusted at the intraday market Elbas and the balance service is
supported by means of a regulating market. The market actors send bids to
Nord Pool of their volumes and prices no later than 12.00 the day prior to the
day of delivery (Figure 11). Bids are made for each hour of the day, so
forecasts are needed for 12 – 36 hours ahead for all 24 hours. Several bids
with different volume and price for each hour are possible to send to the spot
market. Two hours before the spot market closure, the TSO informs the
market of the existing transfer capacities at every existing bidding zone
border. This is important information because the transfer capacity limitations
have an impact on the spot price.
2
French for 'face to face'. Often used in the sense of 'in relation to'.
15
ELFORSK
Figure 11: Sequence of events on the Nordic power market Nord Pool.
The Nordic intraday market Elbas provides a possibility to adjust the
production plans after the gate is closed (Figure 11). The regulating market
provides the secondary regulation for balance service and is maintained by
the TSO. Balance providers that are willing within 10 minutes to increase or
decrease the level of production or consumption have the possibility to add
regulating bids at the regulating market. The balance settlement is then
settled the day after delivery. This forecast error for an actor is calculated by
ΔE = E p − E s ,
(3)
where Ep is the energy production during the hour and Es is the predicted
energy sold at the Nord Pool spot market and the intraday market. The TSO in
Sweden has a balance service function, and has the task to distribute the
costs of maintaining the balance between the actors on the market via
balance settlement. The actors will get paid according to rules, which state
that if an actor for instance has overproduction that helps (reduces) the
system’s imbalance (forecast error); the actor will get paid by the spot price
Ps. In the opposite case (not helping), the actor will pay the down or up
regulation price for the imbalance, Pd respectively Pu. This is illustrated in
Figure 12. In other words if the difference between the spot price and
regulating price is
ΔPup = Pup − Pspot ,
(4)
ΔPdown = Pdown − Pspot ,
(5)
then the cost for the actors increasing the system’s forecast error can be
expressed as
Cost = ΔP ⋅ ΔE .
16
(6)
ELFORSK
Balance settlement
Produced > Predicted
Produced < Predicted
Up regulation
Down regulation
Up regulation
Down regulation
Income =
Ep * Ps
Income =
Es * Ps + (Ep - Es) * Pd
Income =
Es * Ps - (Es - Ep) * Pu
Income =
Ep * Ps
Figure 12: Price calculation for actors at Nord Pool.
In the case where no regulation is needed, all actors get the spot price for
their over- or underproduction. For some few hours during the year there is
both up- and down regulation. For these hours the largest volume determines
the direction for the whole hour. The rules make it expensive to have high
forecast errors, and are therefore driving actors to minimise them. This is
good for the electric power system since it works as an economic regulator,
which makes the electric power system stable.
3.3
Bidding zones
At the Nord Pool markets, there are several bidding zones with different prices
in the different areas. As long as there are no congestions (no transfer
limitations of electric power) in the electric transmission system, the price is
the same in the different areas. However, as congestions occur, the cheapest
power is not available anymore in all bidding zones, which gives different
prices.
Presently, Sweden is kept as one bidding zone despite the congestions in the
transmission network. This is handled by Svenska Kraftnät by limitation on
export capacities at the planning stage and counter trading during the
operation stage. However this will be changed in November 1, 2011. From
this date, Sweden will have four bidding zones (see Figure 15) and when
there are congestions between bidding zones, there will be different prices.
Svenska Kraftnät has analysed the number of hours in each bidding zone that
have indicated the need for limitation in trading capacity, see Figure 13. From
the figure we can see that in most of the cases when there are congestions,
they occur in SE4. About 4000 h (45%) during 2008 had this indication. The
probabilities of congestions have been modelled according to Table 3. These
probabilities are an assumption based on today’s market, but the probabilities
for congestions have been reduced to 30% to compensate for future wind
power and future transmission capacity increase. The introduction of bidding
zones will also affect the market as well, since the marked player will adapt to
the new system, however that is not taken into account in this study. The
probability can of course be changed if transmission capacity between the
bidding zones is increased further or vice versa if production plants are
decommissioned or getting reduced capacity. Because of that, several
simulations with different probabilities are included in this study.
17
ELFORSK
Figure 13: Swedish bidding zones that indicated a need for restrictions on
trade capacity measured in number of hours per quarter [7].
Measurement SE3->SE4
5000
Trade capacity SE3->SE4
4500
4000
MWh/h
3500
3000
2500
2000
1500
1000
500
0
2009-1004
2009-1005
2009-1006
2009-1007
2009-1008
2009-1009
2009-1010
2009-1011
2009-1012
2009-1013
2009-1014
Figure 14: An example of trading capacity and what is transmitted through
section 4 – between bidding zones SE3 and SE4.
18
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Figure 15: Future bidding zones that will come into operation in Sweden,
November 1, 2011 [7].
Table 3: Modelled cases of bidding zones and its probability to occur.
Case
SE 1
SE 2
SE 3
A
B
C
D
SE 4
Probability
5%
10%
15%
70%
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3.4
Implications of bidding zones
As future bidding zones are introduced, the forecast errors in different bidding
zones for the same actor are no longer summed up, which means that if an
actor has – 50 MW in one zone and +50 MW in another zone, the actor will
have to pay for 50 MW instead of 0 MW as it is today, if the regulation is the
same in both bidding zones. In the worst case, if the regulation is in opposite
directions in different bidding zones the actor in the example above can end
up paying for 100 MW of forecast errors. The principle that forecast errors are
settled separately for each bidding zone is done both during the hours with
congestions when Sweden is divided into the bidding zones, and also during
the hours when Sweden remains as one bidding zone. Because of this, the
costs for forecast errors will be higher for actors with wind power in different
bidding zones, as these will be gross settled, instead of net.
A possible scenario is that this rule will be changed, so that forecast errors
can be summed up when Sweden is not divided into bidding zones. For this
case we assume the scenario with the number of hours with congestions
corresponding to 30% of the time. Moreover, the correlation between forecast
errors and congestion is not taken into account.
3.5
One- and two price systems
In Sweden there is a two-price system for regulating power, so the settlement
(buy/sell) depends on the actor’s direction compared to the system’s
direction, see Figure 12. This implies that
•
the forecast error for an actor that has its forecast error in the same
direction as the system is settled according to the regulating price,
and
•
the forecast error for an actor that has its forecast error in the
opposite direction to the system is settled according to the spot price.
In other word, when you increase the error in the system, your error is
settled to regulating price, while decreasing it, you are settled only to spot
price, since you have helped the system to maintain balance. However, in
some countries there is a one-price system where you are always settled to
the regulating price, which means that you can earn money when you help
(decrease the error of) the system.
3.6
Market models
A model of the electricity market is needed to be able to study the effect of
increased regulating volumes. The TSO will always buy the cheapest offer,
however, the volumes are limited, and therefore there is a correlation
between volume and price. Furthermore, there is of course a strong relation
between the different markets: spot, Elbas, and regulating, as they all trade
the same goods (electric energy). Models have previously been developed for
instance in [20], which was further developed in [9]. Such models will be
used here for Elbas and the regulating market.
20
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100
90
80
70
60
50
40
30
20
10
0
2009-01-01
2009-03-02
2009-05-01
2009-06-30
2009-08-29
2009-10-28
2009-12-27
Figure 16: Spot price in (€/MWh ≈ öre/kWh) for the Swedish bidding zone
2009.
1000
900
Regulating price [kr/MWh]
800
700
600
Up
500
Dow n
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000
Spot price [kr/MWh]
Figure 17: How the regulating price relates to the spot price.
The model is described by the equations below. The variables k1, k2, and k3,
are different for the different markets and different for up or down volumes.
Pup = k1 ⋅ Pspot + k 2 ⋅ Ee + k 3
(7)
Pdown = k1 ⋅ Pspot + k 2 ⋅ E e + k 3
(8)
The equations provide the relation between the spot price Pspot, the hourly
forecasted error volume Ee on the Swedish market and a bias term k3. To
illustrate how the regulating prices relate to the spot price and the volume,
these relations have been plotted in Figure 17 and Figure 18. There is as seen
from Figure 17, a close relation between the down and up regulation prices in
relation to the Elspot market price. However, the relation to the regulating
volume is not as clear as seen in Figure 18, but there is still a trend with
increased prices with increased volumes.
21
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Spot - Regulating price [€/MWh]
50,00
Up
40,00
Dow n
30,00
Linjär (Dow n)
20,00
10,00
0,00
-1500
-1000
-500
-10,00
0
500
1000
1500
-20,00
-30,00
-40,00
-50,00
Volum e [MWh]
10,00
Up
8,00
Spot - Regulating price [€/MWh]
Dow n
Linjär (Dow n)
6,00
Linjär (Up)
4,00
2,00
0,00
-200
-150
-100
-50
-2,00
0
50
100
150
200
-4,00
-6,00
-8,00
-10,00
Volum e [MWh]
Figure 18: How the regulating volume relates to the price increase.
3.7
Market coefficients and verification
The coefficients k1, k2 and k3 in equations (4) and (5), can be calculated from
the real statistical data by using for example the least square method, and
shown in Table 5. Since bidding zones is introduced, the model used in this
study is extended in relation to the one used in previous studies [9], by
including different coefficients for different bidding zones. It is assumed that
the TSO will not reserve power in the transmission system between the
bidding zones for secondary regulation, which means that secondary
regulation needs to be bought locally. The coefficients for down prices have
been considered to be the same as today for all bidding zones, since down
regulation of hydro will always be possible in all bidding zones. However, for
up regulation, today’s prices in Sweden have been used only to find the
coefficient for bidding zone SE1. To find the coefficients for SE4, the prices in
DK east has been used. For SE2 and SE3 intermediate values have been used.
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Table 4: Statistics of the electricity market.
Market
Spot
Down
SE
Up
SE
Up
DK
Down
volume
Up
Volume
Mean
393
311
465
717
196
182
Table 5: The coefficients in the model of the markets.
Market
Regulating
market
Elbas
Symbol
Down
Up
SE 1
Up
SE 2
Up
SE 3
Up
SE 4
None
k1
1
1
1
1
1
1
k2
0,05
0,2
0,3
0,5
1,5
0
k3
-41
50
50
50
100
0
k1
1
1
1
1
1
1
k2
0,02
0,02
0,02
0,02
0,02
0
k3
-5
5
5
5
5
0
A fast and simplified verification of the model can also be done by using Table
4, and calculating the model value for up regulating to 393 + 182·0,2 + 50 =
479 kr/MWh, which is close to the mean 465 kr/MWh.
To verify the model further, the regulating price was calculated based on the
spot price and the regulating volumes for 2009. As can be seen in Figure 19,
the model follows the real prices very well. The average difference between
the regulating price and the spot price was about 80 kr/MWh during 2009.
60
Price Up
Model
55
SE Spotprice €/MWh
€/MWh
50
45
40
35
30
2009-01-03
2009-01-03
2009-01-04
2009-01-04
2009-01-05
2009-01-05
2009-01-06
2009-01-06
Figure 19: The modelled regulating prices, and for comparison the real
regulating and spot prices.
23
2009-01-07
ELFORSK
3.8
Jiggling
The forecast errors are naturally never zero. There was a so-called “jiggle
allowance3” up to 2009 at the regulating market, to avoid billing of very small
amounts of forecast errors. On the other hand, the TSO do not call for
regulation if the forecast error on a system level is very small, and it has been
assumed that forecast errors lower than 100 MW on a system level and 50
MW on a bidding zone level do not result in regulation. That means that none
has to pay during that hour, since primary regulation takes care of balancing
the system.
3.9
Note about 2009 market
The number of hours with regulation for up is 2900 h and down is 3864 h, so
non-regulating hours are 8760 – 2900 – 3864 = 1996 h.
3
In Swedish this is referred to as ”vingelmån”.
24
ELFORSK
4
Forecast errors
4.1
Forecast errors on the market
The electricity market is as described in the previous chapter designed to
receive bids at noon for the following day. Thus power producers make
forecasts for 12 – 36 hours ahead and since wind power forecasts are
uncertain there will be forecast errors. Production forecasts are based on
weather forecasts of wind speeds, wind direction, and temperature. Weather
forecasts could be bought from forecasting institutes for instance SMHI4 or
WPPT. The wind speed is then used to calculate the production. The relation
between wind speed and production is well-known and is provided by the
manufacturer of the wind power plant. The wind speed may vary fast and can
in the most extreme situations change from very low wind speed to high
within minutes. Production may also go from full production to zero
production within minutes in case of a storm that forces the wind mills to shut
down to prevent damage.
A balance responsible actor has two choices on how to handle forecast error
volumes; either to adjust the forecast errors at the intraday market Elbas or
to leave the forecast error to balance settlement and take the corresponding
costs. Choosing the intraday market means that the volume corresponding to
the forecast error is most likely to be bought/sold at worse prices compared
to the spot price and trading itself also costs money (personnel, updated
forecasts, trading taxes). In the second choice there may be high costs
associated with high regulating prices. Both choices are costly, however
making improved forecasts is costly as well, which means that the actor has
to optimise the costs of these three items (improved forecasts, trading at
intraday market, or leaving to the regulating market).
4.2
Case studies
To make a model of the forecast errors we can analyse statistical data of
existing wind farms. Such data was made available for the wind farms
Lillgrund, Horns Rev5 and on-shore wind in Denmark – all operated by
Vattenfall. The wind power sites have the installed power 110 MW, 160 MW
respectively 215 MW. The annual mean power production for Horns Rev is
about 62 MW, which corresponds to 3370 full load hours. Figure 20 shows the
wind power production for Horns Rev during March 2009, together with the
forecasted production. Most of the time the forecasted production is near the
real production, however during some hours the difference is very high.
Compare with Figure 3.
4
SMHI = The Swedish Metrology and Hydrology Institute (Sveriges Meteorologiska och
Hydrologiska Institutet).
5
Horns Rev is an offshore wind power farm Southwest of Denmark.
25
ELFORSK
160
Hornsrev forecast
140
Hornsrev production
120
MWh/h
100
80
60
40
20
0
2009-02-27
2009-03-01
2009-03-03
2009-03-05
2009-03-07
2009-03-09
2009-03-11
2009-03-13
2009-03-15
2009-03-17
Figure 20: Hourly production and 12-36 h forecast for Hornsrev.
The time series contain hourly discrete values. The values contain the average
power during one hour in MW or MWh/h. From now on the production is
denoted Pp(t) and the forecasted production is denoted Pf(t). The difference
between them is then the forecast error and it is denoted as Pe(t) = Pp(t) –
Pf(t). The forecast error has a mean value (mathematical expectation) that is
E( Pe (t )) = 0 MW ,
(9)
which means that μ = 0 MW as the mean value for our model of the forecast
error. The standard deviation for the forecast error is
σ abs = var(Pe (t )) = 34 MW .
(10)
The relative standard deviation6 of the forecast error for Horns Rev is
calculated as
σ rel =
var( Pe (t ))
160 MW
=
34 MW
= 21% .
160 MW
(11)
Another measure is the mean absolute error (deviation) of the forecast error,
that is for Horns Rev
MAE = 26 MW ,
(12)
and compared to the mean production 62 MW, it is 40%, and normalised with
installed capacity it is NMAE = 16%.
6
With the relative standard deviation for the forecast error, the standard deviation is
related to the installed power (and not the forecast error).
26
ELFORSK
1200
Number of hours [h]
1000
800
DK land 215 MW
600
Hornsrev 160 MW
Lillgrund 110 MW
400
200
80
70
60
50
40
30
20
10
0
-1
0
-2
0
-3
0
-4
0
-5
0
-6
0
-7
0
-8
0
0
Forecast error [MWh/h]
Figure 21: The distribution of forecast error volumes during 2009.
For the other sites the same calculations are made, which are shown in Table
6. On-shore wind in Denmark has a very low standard deviation that is only
6% since the wind power is spread out which lowers the forecast error. This is
also seen in Figure 21, where the forecast errors are more concentrated
around zero volume. The distribution is similar to a normal distribution;
therefore that distribution will be used in the model. The annual forecast error
for normal distribution can be calculated by using the following equation
MAE
σ
2
=
π
= 80% .
(13)
Table 6: Data for different sites for 2009.
Symbol
Lillgrund
Horns rev
DK on-shore
Unit
Power
P
110
160
215
MW
Energy
E
320
550
300
GWh
Full load hours
T
2900
3400
1400
H
Mean absolute
forecast error
MAE
22
26
8
MWh/h
Normalised mean
forecast error
NMAE
20%
16%
4%
-
190
230
70
GWh
Annual
forecast error
Forecast error
standard dev
σ
31
34
12
MWh/h
Forecast error
standard dev rel
σrel
28%
21%
6%
-
27
ELFORSK
Lillgrund prognosfel
100,0
60,0
MW
20,0
2009-01-07
-20,0
2009-02-06
2009-03-08
2009-04-07
2009-05-07
2009-06-06
-60,0
-100,0
Figure 22: A sample period of the hourly forecast error at Lillgrund.
4.3
Model of forecast errors
4.3.1 Forecast errors for single wind farms (sites)
The distribution of forecast error for wind power will be approximated by a
normal distribution. The standard deviation for 12 – 36 h is in the base
scenario assumed to be 13% for sites, as this is assumed to be possible in the
near future of 10 TWh new wind power as German reports has shown
deviation of about 15% for 24 h forecasts, see Table 7. However, this is quite
far from the studied cases Lillgrund (28%) and Horns Rev (21%), so higher
standard deviation will be studied as well as more improved forecast below
13%.
Table 7: Standard deviation of forecast error related to the forecast time [17].
Horizon
6 hours
Time-horizon
12 hours
Time-horizon
24 hours
Time-horizon
36 hours
Time-horizon
0 km
12%
15%
15%
18%
4.3.2 Forecast errors for areas and neighbouring areas
A wind power actor that owns several wind farms at different sites will do
forecasts for each site. As the forecast errors are normal distributions, these
will add to each other. It is well known that the total forecast error for several
wind farms is reduced (relatively, absolutely it increases), in mathematical
terms that could be expressed as a reduced standard deviation for sums of
forecast errors. Two forecast errors expressed as the normal distributed
stochastic processes X(t)∈N(μx,σ) and Y(t)∈N(μy,σ) is also a normal
distribution that is expressed as
28
ELFORSK
X + Y ∈ N ( μ x + μ y , σ x2 + σ y2 + 2 cov( X , Y ) ) .
(14)
If the stochastic processes are independent then Cramér’s theorem may be
used, and the stochastic process is reduced to
X + Y ∈ N ( μ x + μ y , σ x2 + σ y2 ) ,
(15)
so if we add two independent forecast errors, the standard deviation increases
only with the square root. This is also referred to as spatial smoothing effect.
Since there is often a correlation between wind forecast errors for nearby
farms, the forecast error cannot be assumed to be uncorrelated to other
forecast errors. The distance between Lillgrund and Horns Rev is 350 km, and
the correlation between the forecast errors is
ρ LG , HR =
cov( PLG (t ), PHR (t ))
σ LGσ HR
= 0,1 ,
(16)
and the standard deviation is 48 MW / (110 + 160 MW) = 18%. This is
significantly lower than 21% respectively 28%, and represents about 75% of
the original standard deviations. Observe that this is the average over a year,
on daily basis that correlation is changed, which is seen in Figure 23, where
the correlation is measured as a floating 24-hour average. That is due to that
wind is coming from different directions and the speed of change in weather
situations.
There are studies made on the correlations between forecast errors from
several wind farms (ensembles) [14]. These have investigated the
relationships between the standard deviation for forecast errors for both large
areas with several wind farms and for long distances between wind farm
areas. For large areas, the relation between the standard deviation of a single
wind farm and the standard deviation of an ensemble of several wind farms
are shown in Table 8. Larger areas give lower standard deviation of the total
forecast error. Table 9 shows the correlation of forecast errors for different
distances between the ensembles of wind farms, and of course longer
distances give lower correlation. It was found out in equation (13) that the
correlation for Lillgrund and Horns Rev was 10%, which is well in line with
Table 9.
29
ELFORSK
1,2
1
0,8
0,6
0,4
0,2
0
2009-01-01
-0,2
2009-01-03
2009-01-05
2009-01-07
2009-01-09
2009-01-11
-0,4
-0,6
-0,8
Figure 23: The correlation between forecast errors at Lillgrund and Horns
Rev.
One interesting conclusion is that for shorter time horizons, the correlation is
lower, probably due to more accurate forecasts which are more precise in
time and location. For longer time horizons, bad forecasting of weather fronts
affects neighbouring areas more. The effect of that is for example that the
standard deviation for an actor going from 24 h forecasts (σ = 13%) to 6 h
forecast (σ = 10%) having a couple of farms in two neighbouring 350 km
areas (0,71 → 0,65) and all power equal to 1 p.u., the standard deviation is
changed from
(0,13 ⋅ 0,71) 2 + (0,13 ⋅ 0,71) 2 + 2 ⋅ 0,15 ⋅ (0,13 ⋅ 0,71) 2 = 7%
(17)
(0,10 ⋅ 0,65) 2 + (0,10 ⋅ 0,65) 2 + 2 ⋅ 0,09 ⋅ (0,10 ⋅ 0,65) 2 = 5% .
(18)
1
2
to
1
2
Table 8: The ratio between the standard deviation of an ensemble and single
forecast error time series for various region sizes and time horizons [14]
Diameter
Equation
0 km
σ ensemble
σ sin gle
140 km
350 km
30
3 - 9 hours
Time-horizon
12 - 36 hours
Time-horizon
100%
100%
78%
82%
65%
71%
ELFORSK
Table 9: The correlation of forecast errors for different distances between
ensembles [14]
3 - 9 hours
Time-horizon
12 - 36 hours
Time-horizon
0 km
100%
100%
300 km
10%
22%
Distance
Equation
350 km
cov( X (t ), Y (t ))
9%
15%
400 km
σ xσ y
7%
12%
500 km
5%
11%
>600 km
0%
0%
In this study, the correlation between congestions and forecast errors has not
been considered although there is a correlation. However, the rules imply that
forecasts errors will be treated separately for each bidding zone regardless of
congestions. That means that the effect of this correlation is very small, since
it do not affect the forecast error volumes, only the price on up regulating,
since down regulating price is always the same for the whole of Sweden.
4.4
Actors
In Chapter 2, eight actors were presented with different wind farm ownership
structure in terms of size and locations. To be able to calculate the annual
forecast errors resulted from forecast errors for the actors, six circular areas
have been created with two different diameters. Area 1 has the diameter 140
km and the other five areas have the diameter 350 km. We assume that all
actors are buying forecasts from the same weather institute in each area. This
means that actors that have wind power in the same area have the forecast
errors that are correlated by 100%. It is now possible to calculate the
standard deviation of the forecast error for each actor in each area, by using
Table 8. By using the data from Table 9, it is possible to sum up the standard
deviation for each actor by using a more general form of equation (15), that
is
n
σ all = var(∑ X i ) =
i =1
n
n
∑∑ cov( X , X
i =1 j =1
i
j
).
(19)
Table 10 shows the annual forecast error (imbalances) for the eight actors.
For the actors, with wind farms located in all areas, particularly actor 1, the
forecast error (and therefore imbalances) is very low compared to actors with
just one site (actor 7) or just one area (actor 8).
Another important observation, which can be made from the table, is that on
the system level (column named “total” in the table), the relative forecast
error are small – only σ =7,4% and 17% of production.
31
ELFORSK
Table 10: Annual forecast errors for the eight actors
5 907
Standard
deviation
MW
151,6
Standard
deviation
%
8,0%
Forecast
error
GWh
1060
Error /
Production
%
18%
2 664
68,5
7,9%
479
18%
281
867
21,3
7,6%
149
17%
4
204
570
14,9
7,3%
104
18%
5
253
801
23,6
9,3%
165
21%
6
52
153
3,5
6,7%
25
16%
7
74
207
9,6
13,0%
67
32%
8
34
103
3,1
9,1%
22
21%
Total
3 664
11 275
269,6
7,4%
1885
17%
Actor
Power
MW
1
1 902
2
862
3
Energy
GWh
32
ELFORSK
5
Simulations of forecast errors and
costs
5.1
Simulation environment
The simulations have been carried out in Microsoft Excel. The normal
distributions for the six areas have been randomly generated for all 8760 h
(365 · 24 h) during the year. From these, each actor has got six distributions
as in Figure 10, which is reduced to four distributions, corresponding to each
bidding zone. These are scaled proportionally to the actors’ amounts of
forecast error in each area. It is assumed that all actors use the same forecast
error per area (100% correlation) and has the same quality. The distributions
for each area are correlated according to Table 9, which is in order of about
10 – 20%, depending on the distance between the areas. The standard
deviation of the forecast error for a single wind farm has been chosen to 13%
for 12 – 36 hour forecasts as stated earlier.
The cost of the forecast error is calculated by taking the volume of the
forecast errors for each hour for each actor and then multiplying with the
hourly price. The price has been calculated from the forecast error volume
(today’s + new wind) on system level. This has been done for three cases:
•
Today’s prices - Balance settlement according to Today’s (2009)
regulating market prices
•
Future prices - Modelled future (higher) prices for the system with 3,5
GW new wind power, that is a 5 GW scenario corresponding to about
10 – 15 TWh.
•
Future prices & Bidding zones - The introduction of future bidding
zones together with future prices (as the previous bullet).
5.2
Forecast error with 5 GW wind power
The annual forecast error during 2009 at the regulating market was 1,3 TWh.
Related to the electric power production in Sweden, which is about 150 TWh,
the forecast error is only about 1 percent. The introduction of new wind power
in the electric power system will however generate additional forecast errors,
see Figure 24. The 5 GW scenario will give annual forecast errors for the
actors of about 2,0 TWh. However, since the forecast errors are not totally
correlated, this amount partly reduces, and therefore gives only 1,8 TWh that
needs to be regulated. When the future forecast errors are added to the
forecast errors on the current market it sums up to 2,4 TWh.
33
Annual forecast error [GWh/Year]
ELFORSK
1 000
800
600
400
200
0
1
2
3
4
5
6
7
8
Actors
Figure 24: The annual forecast errors for all actors.
5.3
Market costs for forecast errors
The forecast errors for the system are lower than or equal the absolute sum
of the actors’ forecast errors, which means that the actors will pay more than
the costs for regulating power. That is however not an increased market cost.
It just means that the TSO will have increased revenues on that, which might
lead to decreased costs on other costs for the actors, for instance tariffs. In
other words the financing of the costs for the TSO will be shared differently.
But, as this cost is put on forecast error generating actors, these actors gets
increased costs.
5.4
Actors share of wind power
A number of scenarios that have been simulated with different amount of
future wind power and the actors’ proportion of that amount are shown in
Table 11 and Table 12. These show the corresponding power respectively
energy.
Table 11: Scenarios in (TWh) and related power amount (MW) of wind power
per actor.
Energy
Actor
1
5
10
951
1902
2
431
862
3
141
281
4
102
5
126
6
7
15
20
25
30
35
40
45
50
2683
3464
4245
5026
5808
6589
7370
8151
1186
1510
1833
2157
2480
2804
3128
3451
535
789
1042
1296
1549
1803
2057
2310
204
375
546
717
888
1059
1230
1401
1573
253
348
442
537
632
726
821
916
1011
26
52
141
229
318
406
495
583
671
760
37
74
97
120
142
165
188
211
233
256
8
17
34
75
116
156
197
238
278
319
360
Total
1832
3664
5439
7215
8991
10767
12543
14319
16095
17871
34
ELFORSK
Table 12: Scenarios energy amount (TWh) of wind power per actor.
Energy
Actor
1
5
10
15
20
25
30
35
40
45
50
3,0
5,9
8,3
10,6
13,0
15,3
17,7
20,0
22,4
24,7
2
1,3
2,7
3,6
4,6
5,5
6,5
7,5
8,4
9,4
10,4
3
0,4
0,9
1,6
2,3
3,1
3,8
4,5
5,3
6,0
6,7
4
0,3
0,6
1,0
1,5
2,0
2,5
3,0
3,4
3,9
4,4
5
0,4
0,8
1,1
1,4
1,7
2,0
2,3
2,6
2,9
3,1
6
0,1
0,2
0,4
0,7
0,9
1,2
1,4
1,7
1,9
2,2
7
0,1
0,2
0,3
0,3
0,4
0,5
0,5
0,6
0,7
0,7
8
0,1
0,1
0,2
0,3
0,5
0,6
0,7
0,8
1,0
1,1
Total
5,6
11,3
16,5
21,8
27,0
32,3
37,6
42,8
48,1
53,3
5.5
Forecast error costs
The costs for the actors for their forecast errors is simulated in the base
scenario with 3,5 GW new wind power, that represent about 5 GW installed
wind in Sweden. The results are shown in Figure 25 for three different cases
in section 5.1. It is seen that the costs for actor 7 who owns a single wind
farm in SE2 increase its costs from about 10 kr/MWh to about 12,5 kr/MWh.
The actors that own wind power spread over large areas have lower prices
today (5 kr/MWh), however as these actors (e.g. actor 1) become market
drivers for the forecast errors, they have to pay for more hours which
increase their costs. The introduction of new bidding zones has an impact
mainly on actors that have a large amount of installed wind power in SE4. The
impact is quite dramatic, due to increased prices and the disability to reduce
forecast errors from different bidding zones. Another driver for higher prices is
that the number of hours with no regulation reduces.
35
Future prices
30
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
A t
Figure 25: Cost for the forecast errors on future market with and without new
bidding zones in Sweden, and comparison with Today’s prices. 5 GW scenario.
35
ELFORSK
5.6
Update of production plan
In 2009, there was a new rule introduced for presenting and updating the
production plan. If an updated production plan is handed in (at latest 45 min
before the production hour), the forecast error according to the plan will be
settled according to a one-price system instead of a two-price system, see
section 3.5. The forecast error that differs from the production plan will be
settled according to two-price system as normal. One hour before the
production hour, the standard deviation of the new forecast error is about
9%. This new forecast error is correlated to the original forecast error with
about 50%. This means that the amount that will be charged (traded) with
the one-price system is according to equation (14) about
0,13 2 - 0,09 2 - 2·0,13·0,09·50% = 6% .
(20)
So it means that 6% is traded with one-price system (1 PS) and 9% with twoprice system (2 PS). Table 13 shows some examples of the difference
between this, where green means income and red means cost. As seen, with
one-price system you can earn money when you help the system as opposed
to two-price where you do not get anything (except the spot) when you help
the system. This case was not simulated since the model was not made for it;
however it is similar to the following chapters “Trading on intraday market”
and “Changed market design to one-price system”. The general conclusion is
that it is beneficial; however as most part of the forecast error still remains
and the updated forecast error also has to be paid for the benefit is small.
Table 13: The difference of charge between updated forecast that is charged
with one-price (1) and not updated that is charged with two-price (2) system.
Actor is
Underproducing
Overproducing
Underproducing
Overproducing
Forecast
24h
Forecast
1h
Productio
n 0h
100 MW
90 MW
80 MW
80 MW
90 MW
100 MW
90 MW
80 MW
100 MW
90 MW
100 MW
80 MW
36
Down
0
10
20
20
10
10
0
10
MW
MW
MW
MW
MW
·
·
·
·
·
ΔPdown
ΔPdown
ΔPdown
ΔPdown
ΔPdown
MW · ΔPdown
Up
20
20
0
10
0
10
10
10
MW · ΔPup
MW · ΔPup
MW · ΔPup
MW · ΔPup
MW · ΔPup
MW · ΔPup
PS
2
1
2
1
2
1
2
1
ELFORSK
40
35
Future Prices and Elbas
30
Elbas
25
kr/MWh
Future Prices
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure 26: Cost of the forecast errors on the future regulating market and the
total costs if Elbas is used. Scenario 5 GW (10 – 15 TWh).
5.7
Trading on intraday market
The intraday market Elbas can be used to update the production plan, by
buying or selling forecasted under- or overproduction. This may be a good
option to reduce the costs on the regulating market. However, the new
forecast must be significantly better (much lower forecast error), as there is a
cost associated with trading on the intraday market. Updating the forecast
can be done in several ways, for instance buying additional forecasts from a
weather forecast institute. Another option is to use the persistence method,
which does not require the actor to buy a service. However, there will be
costs for trading. The persistence method for 1 h ahead gives a standard
deviation of about 9% [6], [17]. If all actors trade on Elbas, this results in 1,4
TWh forecast errors annually for the actors, which reduces by spatial
smoothing to 1,2 TWh. The contribution to the market is just 2,0 – 1,3 = 0,7
TWh/year, since the forecast errors are only partially correlated. That is a
significant (25%) reduction compared to not trading on Elbas.
The relation between the spot market and the intraday market is very close as
seen from Table 5. As it is so close we assume there is only a trading cost of
about 1 Mkr/year for personnel. The results are shown in Figure 26, and it is
clear that for actors with a lot of wind power it is profitable to act on the
intraday market since the additional personnel costs are so small. However,
for small actors with costs that are in the same level as new personnel costs it
is not beneficial.
37
ELFORSK
80
Std dev = 0,08
Std dev = 0,13
70
Std dev = 0,20
60
kr/MWh
50
40
30
20
10
0
1
2
3
4
5
6
7
8
Aktör
Figure 27: Costs due to different standard deviations (σ = 0,08, σ = 0,13, σ =
0,20) of the forecast quality. Scenario 5 GW (10 – 15 TWh) and future prices
& bidding zones.
5.8
Influence of forecast quality on imbalance costs
In this report it is assumed that the relative standard deviation of the forecast
error is 13%. However, forecast quality is improving over the years as
weather models become more reliable, and there is an increased demand on
wind speed models as wind power is expanding all over the world. Improved
forecasts result in lower forecast errors for the actors as well as on the
system level, which in its turn reduces the regulating price and cost for
regulating.
In Figure 27, the actors’ costs have been calculated for different standard
deviations, and it is very clear that the reduced forecast errors give lower
costs. The standard deviation for forecast errors for Lillgrund and Horns Rev
was calculated in earlier chapters to about 20%. This number will probably
improve (decrease) slowly by a percentage point per year.
5.9
Congestions
As new bidding zones are introduced, the cost will increase especially for
those actors who have wind farms in different bidding zones, since each
bidding zone will be charged separately at every hour (regardless of
congestions). Wind farms located in bidding zone SE 4 will of course be
affected most since price increases dramatically in SE 4, see Chapter 3. It has
been assumed that the number of hours with congestion is about 30%;
however, historically there have been indications on about 45% of the hours
during some part of the year 2009. The effect of different number of hours
that Sweden is split into bidding zones is presented in Figure 28. The number
of hours that has been used in the simulation with congestions has been
assembled in Table 14.
38
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Table 14: Modelled bidding zones and its probability to occur.
Case
SE 1
SE 2
SE 3
SE 4
A
B
C
D
10%
0%
Probability
As is=30%
5%
50%
10%
100%
100%
3%
10%
20%
0%
7%
15%
30%
0%
90%
70%
50%
0%
80
Bidding zones = Every hour
Bidding zones = 50% of hours
70
60
kr/MWh
50
40
30
20
10
0
1
2
3
4
5
6
7
8
Actor
Figure 28: Costs for the forecast errors depending on the amount of hours
where Sweden is split into bidding zones.
5.10 Geographic distribution
There might be other scenarios for wind power distribution between the North
and South of Sweden. Several simulation cases have been run with modified
wind power distribution. The same wind farms and actor ownership has been
used, but the ownership in the south and north has been scaled up and down.
The results show that if all wind power is moved to the south, the cost
increases from about 15 kr/MWh to 21 kr/MWh with new prices and adding
future bidding zones, then the cost increases from 30 kr/MWh to 43 kr/MWh.
39
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40
3 - 9 h future prices
35
12 - 36 h future prices
30
3 - 9 h future prices & biddning zones
kr/MWh
25
12 - 36 h future prices & biddings
zones
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure 29: Costs of forecast errors due to different time horizons, with and
without new bidding zones. Scenario 5 GW (10 – 15 TWh).
5.11 Changed market design to 6 h markets
One way of reducing wind power owners exposure to the costs due to forecast
errors is to change the market design. The market design could be designed
to receive bids for 3 – 9 h ahead, which is every sixth hour. In [17], it was
found that going from 24 h to 6 h forecasts, the standard deviation for wind
power forecast error decreases from 15% to 12%. As we have been using
13%, this would mean that the standard deviation decreases also by three
percentage points from 13% to about 10 %. The impact of this is illustrated in
Figure 29, where we can see that the forecast error costs reduces significant.
5.12 Changed market design to one-price system
In Sweden there is a two-price system (PS) for regulating power, which
means that the forecast errors of the actors who help the system is settled
according to the spot price while the ones creating the forecast error get the
regulating price. With a one-price system, the actors always get the
regulating price (if there has been regulation) for the forecast error volume,
more explained in section 3.5.
40
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40
2-price & No Net
2-price & Net
35
1-price
30
kr/MWh
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure 30: The effect of different market designs regarding different rules for
billing the forecast errors. Scenario 5 GW (10 – 15 TWh) with future prices &
bidding zones.
When bidding zones are introduced in Sweden, each bidding zone will be
settled separately, so the spatial smoothing effect between zones for an actor
do not have any economic effect anymore, so you pay for the gross forecast
error instead of the net forecast error. However, to illustrate the possibility of
summing the forecast errors for all bidding zones that has been kept as one
bidding zone (net), this is illustrated in Figure 30. It is clear that a one-price
market is beneficial for everyone. However, for actors that have wind power
in regions that is not a big part of the market earns most, and in regions with
a lot of wind (and forecast errors) the benefit of a one-price system is very
small.
Table 15: Comparison between settlement with a one-price (1) and a twoprice (2) system, in relation to the spot price.
Actor is
Underproducing
Overproducing
Forecast
24h
Production
0h
100 MW
80 MW
80 MW
100 MW
System is overproducing
0
20 MW · ΔPdown
20 MW · ΔPdown
20 MW · ΔPdown
System is underproducing
20 MW · ΔPup
20 MW · ΔPup
0
20 MW · ΔPup
PS
2
1
2
1
5.13 30 TWh scenario
A 30 TWh (12 GW = 10.5 GW new wind + 1.5 GW already installed)) scenario
has been simulated as well, with future bidding zones. The results of the
simulation are shown in Figure 31. It is clear that the costs for the actors
reach even higher levels – up to 45 kr/MWh. The forecast error on system
level increase to about 3,4 TWh annually.
41
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12 GW (30 TWh) scenario
50
Today's prices
Future prices
45
40
35
kr/MWh
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Actor
Figure 31: Cost for the forecast errors on future market with and without new
bidding zones in Sweden, and comparison with today’s prices. 12 GW (30
TWh) scenario.
5.14 All projects – 55 TWh
If all wind power projects for which it was applied for permission or just made
the initial study were realised it would result in 17,5 GW new wind installed
capacity producing up to 52.5 TWh wind. So that would give 19 GW (17,5 +
1,5) and 55 TWh (52,5 + 2,5). Figure 32 illustrates the result of the
simulation for this scenario. It can be seen that the costs are increasing quite
much. The forecast error on system level increase to about 5 TWh annually.
5.15 Maximum forecast error
The annual forecast errors on the market increases from 1,3 TWh/year (2009)
to about 2,5 TWh/year in the 10 TWh scenario, that is an average increase
from 150 MWh/h to 285 MWh/h. The future wind power itself generates about
1,8 TWh/year, but the contribution to the market is just 2,5 – 1,3 = 1,2
TWh/year, since the forecast errors are only partially correlated. The worst
case forecast error for an hour increases from 1,5 GW to 2 GW in the
simulation. As new bidding zones are introduced, the ability for actors to
internally balance the power will be more difficult (impossible for some) as it
is no longer possible to balance a bad forecast of wind in the South with hydro
in the North. That results in even higher forecast errors in the future, but is
not part of this study. However, that could be a cheaper solution for everyone
including the market, as sub-optimisation by each actor is decreased.
42
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19 GW (55 TWh) scenario
70
Today's prices
Future prices
60
kr/MWh
50
40
30
20
10
0
1
2
3
4
5
6
7
8
Actor
Figure 32: Cost of the forecast errors on future market with and without new
bidding zones in Sweden, and comparison with Today’s prices. 19 GW (55
TWh) scenario.
5.16 Summary
To summarise the results for the 5 GW wind power scenario, some of the
results has been assembled in Table 16. The revenues have been calculated
by assuming that the spot price is 400 kr/MWh. The different cases are as
earlier “Today’s prices”, “Future prices”, “Bidding zones with future prices”,
and “Acting on Elbas”. The difference is the cost model, except for Elbas,
where the standard deviation is lower.
There are increased annual costs for forecast errors for the wind power
actors; if we compare the cost on 2009 market and the future market, it is
almost three times, as it increases from about 5 - 10 kr/MWh to about 30
kr/MWh. However, actors do probably not pay only 5 kr/MWh today, rather 10
– 15 kr/MWh, since the standard deviation of the forecast error is much
higher today. However, it can be assumed to be improved in the future. Actor
7, who just owns one site in SE2, has only increased its cost by 30%, from 10
kr/MWh to 13 kr/MWh. The main difference between actor 1 and actor 7, is
that actor 1 is so large that its forecast errors will influence the systems
aggregated forecast error, consequently actor 1 has much more often its
forecast error in the same direction as the system.
The simulation have of course some limitations, and it should be pointed out
that it could be even more expensive to pay for the forecast error, since the
model do not reflect peek regulating price hours and the standard deviation is
assumed to be quite low (13%).
43
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Table 16: Summary of simulation results with 5 GW wind power.
Actors
Power
MW
Energy
GWh
Income
Mkr
FE
GWh
FE /
Energy
1
2
3
4
5
6
7
8
1 902
862
281
204
253
52
74
34
5 907
2 663
867
571
801
153
207
103
2 363
1 066
347
228
320
62
83
41
1 053
474
149
85
164
19
66
16
17,8%
17,8%
17,2%
14,9%
20,6%
12,9%
31,8%
15,6%
4,5
2,5
5,0
0,6
2,1
0,5
5,21
4,41
6,26
3,72
10,04
4,50
1,3%
1,1%
1,6%
0,9%
2,5%
1,1%
Cost with today’s prices
Cost
32,3
14,7
[Mkr/år]
Cost
5,47
5,51
kr/MWh
Cost /
1,4%
1,4%
Income
Cost with Future prices
Cost
[Mkr/år]
Cost
kr/MWh
Cost /
Income
88,5
39,8
12,3
3,7
13,7
1,0
2,7
0,8
14,98
14,95
14,14
6,45
17,06
6,34
13,04
7,72
3,7%
3,7%
3,5%
1,6%
4,3%
1,6%
3,3%
1,9%
Cost with Future prices & Bidding zones
Cost
[Mkr/år]
Cost
kr/MWh
Cost /
Income
181
82,6
25,4
4,5
27,3
1,2
2,7
0,76
30,69
31,00
29,29
7,88
34,10
7,85
13,25
7,38
7,7%
7,7%
7,3%
2,0%
8,5%
2,0%
3,3%
1,8%
Cost with Future prices & Bidding zones when acting on Elbas
Cost
[Mkr/år]
Cost
kr/MWh
Cost /
Income
96,2
44,3
14,2
3,2
15,7
1,6
2,6
1,4
16,28
16,61
16,33
5,67
19,58
10,17
12,55
13,98
4,1%
4,2%
4,1%
1,4%
4,9%
2,5%
3,1%
3,5%
44
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6
Closure
6.1
Conclusions
There are two market challenges that need to be addressed with a larger
proportion of wind power – that is variability and predictability. Predictability,
which is the topic of this study, is important since the spot market Nord Pool
requires production forecast of 12 – 36 hours ahead. Forecast errors must be
regulated with regulating power, which creates costs for the actors who are
causing the forecast errors. With a geographical spread-out of owners’
installed wind power, the relative forecast errors reduce, due to the spatial
smoothing effect.
With increased installed capacity of wind power, the forecast errors on system
level will increase from 1,3 TWh/year (2009) to about 2,5 TWh/year in the 10
TWh scenario. In general that gives higher forecast errors per hour, (however
during some hours there will of course be very low forecast errors and hence
regulating prices close to spot prices). Owners can also reduce their forecast
errors by acting on the intraday market Elbas which leads to reduced forecast
error on system level as well, about 2,0 TWh. However as there are costs
associated with additional trading; it is not necessary beneficial for small scale
operators. The remaining forecast errors on system level must be handled by
the TSO. As the TSO in general have to call for more regulating power, that
will lead to both more hours with regulation and more volume per hour.
Larger volumes will lead to regulating prices with a higher deviation from spot
prices.
With the introduction of 10 TWh new wind power in Sweden, there will be a
large difference in annual costs for forecast errors; if we compare the cost on
2009 market and the future market, it is almost three times. For example, the
cost could rise from about 10 kr/MWh to about 30 kr/MWh for some actors. It
should be noted that the present and future cost is based on very high
forecast quality, and as the forecast error quality is much lower today, the
cost in reality is about 15 - 20 kr/MWh. So, the increased costs will not be so
dramatic in practice. To sum up the main reasons to the higher cost; they can
be explained by five main points, which are:
1. The regulating prices become higher, due to higher demand for
regulating power with increased forecast errors. However, the prices
for up regulation could possibly be even higher if peak price hours had
been taken into account. These hours usually represents cases where
there is a lack of possibility to increase the power in running plants,
where very expensive reserve plants needs to be up started. That
could increase the price further with another 10%.
2. There are fewer hours with error in the right direction for the wind
power owners, since the wind power will be the one causing the
45
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forecast error. This give a change that the wind power must pay for
70% of the hours with forecast errors instead of 50% as it is today.
3. There are also fewer hours with no up or down regulations, since the
chance for small forecast errors becomes lower. This changes the
number of hours that does not need to be paid for from 2000 h to 1
500 h, that is a 25% reduction.
4. The transmission system has a limited transmission capacity, which
will from November 1, 2011 be handled by introducing bidding zones.
This means that the balance needs to be maintained within each zone
for the wind power owners. For wind power owners with wind power in
several bidding zones, the possibility to aggregate positive and
negative forecast errors for several bidding zones will be financially
impossible, since they will be settled separately. It should be noted,
however, that even without bidding zones, the costs for handling
forecast errors with Sweden as one bidding zone would be present in
the system, and that cost would be distributed to the market via for
instance the tariffs.
5. One additional reason to increased costs is that the price level for
regulating power upwards in the South of Sweden will go up, since
secondary regulation often needs to be bought locally and since most
wind power is planned in the South of Sweden. Regulating prices in the
north will however go down, but as said, as most wind will be located
in the South of Sweden this has a minor effect.
Two (number 2 and 3) of the five explanations above are about paying hours.
We see that it is almost three times as many hours that the actor has to pay
for. So, the main reason for higher cost is that the amount of hours to pay is
so much higher, and together with rising prices – especially in the South of
Sweden – the costs get very high.
As a wind power owner, one should understand that although the introduction
of bidding zones in Sweden give a negative effect on regulating costs in the
South of Sweden, the increased spot price in the south will most likely give
much more revenues than the added costs for regulating power.
Finally, the cost should be related to revenues. The results show that although
the cost is increasing a lot, it is still a relatively small part of the income
related to the spot price, just in the order of 1 – 10% with 10 TWh new wind
power. However, as some wind owners have income in the range of several
M€, 5% of that is a lot of money – that could be put into improving forecasts.
46
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6.2
Future work
The work has been simplified in some aspects and to move further some
models could be improved. Here are some suggestions on future work.
•
The prices do not reflect the very high price hours, and as the demand
for more regulating power is needed, there will be more of these
hours. An attempt to develop the price model to reflect these hours
could be done
•
Forecast errors have been modelled as normal distributions, which is
not entirely correct. This model could be improved. Moreover, using
forecast from several institutes could be studied as a way to reduce
the forecast error.
•
Develop a Graphical User Interface to the model and export it to a
program file, so wind power actors could use the program to put in
their specific wind plans in some future scenarios and simulate future
costs.
•
Investigate the historical effect on regulating power in countries that
have introduced a lot of wind power.
•
Investigate the impact if the rule of being in balance was removed –
how much the need for regulating power increase, and what would be
the benefits and drawbacks on spot and regulating prices.
•
Investigate the impact on Swedish regulating power as European
needs for future use of Swedish regulating power increases.
47
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48
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7
References
[1]
Statistiska Centralbyråns statistikdatabas på internet.
[2]
European Union: Proposal for a Directive Of The European Parliament
And Of The Council on the promotion of the use of energy from
renewable sources.
http://ec.europa.eu/energy/climate_actions/doc/2008_res_directive_
en.pdf. 23 jan 2008.
[3]
Regeringen: “Förnybar el med gröna certifikat”.
proposition 2005/06:154. Riksdagsbeslut 2006-06-14.
[4]
Energimyndigheten: “Nytt planeringsmål för vindkraften år 2020”. ER
2007:45, ISSN 1403-1892. 2007.
[5]
Svensk energi: “Så här når vi förnybarhetsmålet”
http://www.svenskenergi.se/sv/Aktuellt/Artiklar-till-startsidan/EfterEUs-bordefordelning/
[6]
Fredrik Carlsson, Viktoria Neimane: “A massive introduction of wind
power - Changed market conditions?” Elforsk rapport 08:41.
[7]
Anmälningsområden på den Svenska Elmarknaden, Svenska Kraftnät,
2009-10-15, nr 2009/35.
[8]
Prisområden på Elmarknaden (POMPE). EMIR 2007:2.
[9]
Magnus Brandberg and Niklas Broman: “Future
Regulating Power”, Uppsala Universitet, 2006.
[10]
Mikael Magnusson, Roland Krieg and Margitta Nord, Hans Bergström:
“Effektvariationer av vindkraft”, Elforsk rapport 04:34, 2004.
[11]
Hannele Holttinen, “The Impact of Large Scale Wind Power Production
on the Nordic Electricity System”, PhD thesis, VTT, 2004
[12]
Svensk vindenergis hemsida: http://www.svenskvindenergi.se/
[13]
Nordel Annual report 2006.
[14]
Urban Axelsson, Robin Murray, and Viktoria Neimane, “4000 MW wind
power in Sweden”, Elforsk report, 2005.
[15]
Hannele Holttinen, “Optimal electricity market for wind power”,
Energy Policy 2005. Publication H.
[16]
The Swedish Electricity Market and the Role of Svenska Kraftnät.
Path: http://www.svk.se/upload/4184/Engwebb.pdf
[17]
Ulrich Focken, Matthias Lange, Kai Mönnich, and Hans-Peter Waldl: A
Statistical Analysis of the Reduction of the Wind Power Prediction
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Error by Spatial Smoothing Effects, Department of Energy and
Semiconductor Research, Faculty of Physics, Carl von Ossietzky,
University of Oldenburg, Germany, 2001.
[18]
ISET Abschlussbericht: ”Entwicklung eines Rechenmodells zur
Windleistungsprognose für das Gebiet des deutschen Verbundnetzes”.
Forschungsvorhaben Nr. 0329915A, Laufzeit: 01.05.2002 –
31.03.2005.
[19]
Lange; Matthias, Analysis of the Uncertainty of Wind Power
Predictions, Department of Mathematics and Science, Faculty of
Physics, Carl von Ossietzky, University of Oldenburg, Germany, 2003.
[20]
Klaus Skytte: The regulating power market on the Nordic power
exchange Nord Pool: an econometric analysis, 1999, Energy
Economics 21; 295 – 308, System Analysis Department, Risö National
Laboratory, Denmark.
[21]
TradeWind: “Forecast error of aggregated wind power”. April 2007.
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Jonas Olsson, Lars Skoglund, Fredrik Carlsson, and Lina Bertling:
“Future wind power production variations in the Swedish power
system”. IEEE Innovative Smart Grids Conference, Göteborg, 2010.
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8
Appendices
8.1
Wind power projects
Table 17: Wind power projects in the near future in Sweden
Project
Sjisjka
Rautirova
Uljabuouda
Dragaliden
Bondön
Hornberget
Storliden
Jokkmokksliden
Gabrielsberget
Stor-Rotliden
Hörnefors 1
Hörnefors 2
Håcksta
Hudiksvall/Rogsta
Storrun
Havsnäs
Stentjärnåsen
Rätan-Digerberget
Bliekevare
Blaiken
GlötesvåIen
Hedboberget 1
Hedboberget 2
Högberget
Klinte Vindpark
Tavelberget
Sundbyholm
Vettåsen/Finnbergen
Bösjövarden
Mässingberget
Säliträdberget
Fjällberget/Saxberget
Kyrkberget
Korpfjället
Gässlingegrund
Brattön 1
Hud/Kil
Röbergsfjället
Silkomhöjden
Torserud
Årjäng NV
Töftedalsfjället
Brahehus
Brattön 2
Tolvmanstegen
Laholm
Lillgrund
Råbelöf
Brunsmo
Utgrunden 1
Yttre Stengrund
Sotared
Hjuleberg
Mönsterås
Hakarp
Östra Herrestad
Stora Middelgrund
Kriegers flak
Trolleboda
Utgrunden 2
Skottarevet
Kårehamn
Total
Company
Energy
O2 Vindkompaniet
O2 Vindkompaniet
Skelefte Kraftöft
Svevind
NordanVind
Jämtkraft
Skelefte Kraftöft
Skelefte Kraftöft
Svevind
O2 Vindkompaniet
Ume Energi
Ume Energi
Ume Energi
Ume Energi
Dong Energy
RES Skandinavien
Wallenstam
Wallenstam
O2 Vindkompaniet
Skelefte Kraftöft
O2 Vindkompaniet
O2 Vindkompaniet
O2 Vindkompaniet
Dala Vind
Siral
Dala Vind
Kafjärdens vindKraftöft
Eolus wind
O2 Vindkompaniet
O2 Vindkompaniet
O2 Vindkompaniet
Stena renew energy
Nordisk vindkraft
O2 Vindkompaniet
Vindpark Vänern
Rabbalshede Kraft
Rabbalshede Kraft
O2 Vindkompaniet
Eolus windus
Universal Wind
Rabbalshede Kraft
Rabbalshede Kraft
O2 Vindkompaniet
Rabbalshede Kraft
Eolus wind
An
Vattenfall
Ari
Ari
Vattenfall
Vattenfall
Triventus
Vattenfall
Ari
Eolus wind
Vattenfall
Universal Wind
Vattenfall
Vattenfall
EON
Favonius
EON
0,25TWh
0,14TWh
0,08TWh
0,07TWh
0,08TWh
0,031TWh
0,052TWh
0,07TWh
0,24TWh
0,24TWh
0,03TWh
0,03TWh
0,025TWh
0,03TWh
0,08TWh
0,25TWh
0,03TWh
0,03TWh
0,83TWh
0,8TWh
0,27TWh
0,03TWh
0,03TWh
0,025TWh
0,025TWh
0,035TWh
0,06TWh
0,04TWh
0,05TWh
0,07TWh
0,04TWh
0,11TWh
0,062TWh
0,08TWh
0,08TWh
0,04TWh
0,04TWh
0,047TWh
0,031TWh
0,14TWh
0,05TWh
0,15TWh
0,05TWh
0,024TWh
0,24TWh
0,07TWh
0,33TWh
0,03TWh
0,037TWh
0,04TWh
0,03TWh
0,03TWh
0,13TWh
0,066TWh
0,04TWh
0,06TWh
3,00TWh
2,60TWh
0,45TWh
0,27TWh
0,50TWh
0,17TWh
11,3TWh
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Table 18: Wind power projects in the not so near future in Sweden
Project
Luongastunturi
Markbygden
Klocktärnan
Ytterberg
Åmliden
Vinliden
Ögonfägnaden
Björkhöjden
Tandsjö
Stormossen
Norrhälsinge
Dyrvallsåsen
Sörby
Stamåsen
Bodhögarna
Raftsjöhöjden
Mörttjärnberget
Ope
Gevsjön
Middagsfjället
Lillhärdal
Storgrundet
Tönsen
Fallåsberget
Lingbo
Vettåsen
Finngrunden
Forsmark
Ljusterö
Selaön
Oxelösund
Söderköping
Mästermyr
Loftahammar
Västervik
Årjäng
Knappa
Sögårdsfjället
Gunnarsvattnet
Mungseröd
Skaveröd
Forshälla
Töreboda
Ryfors bruk
Hornamossen
Mönsters
Miletorp
Eriksmåla
Videbäcksmåla
Karlskrona
Södra Midsjöbanken
Hanöbukten
Taggen
Berg
Hökhult
Skeppetorp
Klaverström
Herråkra
Markaryd
Erikdal
Vråskogen
Hjortseryd
Byholma
Sällstorp
Ulvatorp
Hylte
Femsjö
Gastensbo
Sävsered
Halmstad
Orken
Uddared
Knäred
Putsered
Hönsholma
Färingtofta
Linderödsåsen
Total
Company
O2 Vindkompaniet
Svevind
Wpd Scandinavia
RES Scandinavien
RES Scandinavien
RES Scandinavien
Statkraft Sverige
Statkraft Sverige
Wpd Scandinavia
Wpd Scandinavia
RES Scandinavien
Eolus wind
Kraftö
Statkraft Sverige
Statkraft Sverige
Statkraft Sverige
Statkraft Sverige
Rabbalshede Kraft
Prosperous Wind
Fredr Olsen
Rabbalshede Kraft
Wpd Scandinavia
O2 Vindkompaniet
O2 Vindkompaniet
Eolus wind
Eolus wind
Wpd Scandinavia
Vattenfall
Kraftö
Kraftö
Kabeko
Arise Windpower
Vattenfall
Rabbalshede Kraft
Arise Windpower
Rabbalshede Kraft
Gothia Wind
Rabbalshede Kraft
Vattenfall
Eolus wind
Rabbalshede Kraft
Rabbalshede Kraft
Prosperous Wind
HS Kraft
O2 Vindkompaniet
Arise Windpower
HS Kraft
Vattenfall
Wpd Scandinavia
Arise Windpower
Eon wind
Blekinge offshore
Vattenfall
Vattenfall
Vattenfall
Vattenfall
Arise Windpower
Kraftö
Svevind
Stena Renewables
Stena Renewables
Stena Renewables
Prosperous Wind
Eolus wind
Gothia Wind
Arise Windpower
Stena Renewables
Eon wind
Stena Renewables
Arise Windpower
Eon wind
Stena Renewables
Eon wind
Stena Renewables
Kraftö
Eon wind
HS Kraft
Energy
0,42
12,00
1,90
0,13
0,12
0,11
0,20
1,35
0,08
0,08
0,50
0,08
0,19
0,25
0,37
0,05
0,21
0,17
0,07
0,50
0,54
0,80
0,27
0,06
0,10
0,05
5,50
0,14
0,10
0,06
0,60
0,15
0,26
0,20
0,27
0,23
0,08
0,07
0,08
0,04
0,08
0,10
0,08
0,10
0,14
0,27
0,06
0,11
0,07
0,10
3,00
5,00
1,00
0,16
0,12
0,16
0,30
0,18
0,24
0,16
0,40
0,24
0,12
0,08
0,08
0,11
0,16
0,08
0,08
0,24
0,05
0,08
0,08
0,15
0,05
0,10
0,20
42,10
52
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
Twh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
TWh
ELFORSK
8.2
Distances used between areas and correlation
coefficient
Table 19: Distances between areas with wind power
1
2
3
4
5
6
1
0
300
350
750
800
1200
2
300
0
400
550
700
1050
3
350
400
0
500
500
900
4
750
550
500
0
300
500
5
1050
700
500
300
0
450
6
1200
1050
900
500
450
0
Table 20: Correlation coefficient used between areas for 12 – 36 h.
1
2
3
4
5
6
1
1
0,2
0,14
0
0
0
2
0,2
1
0,12
0
0
0
3
0,14
0,12
1
0
0
0
4
0
0
0
1
0,2
0,11
5
0
0
0
0,2
1
0,12
6
0
0
0
0,11
0,12
1
53
ELFORSK
Abbreviations
AC
Alternating Current
AKF
Auto correlation function
DC
Direct Current
EU
European Union
EWEA
European Wind Energy Association
HVDC
High Voltage Direct Current
INPS
Interconnected Nordic Power System
MAE
Mean Average Error
NMAE
Normalised Mean Average Error
Nordel
Organisation for the Nordic Transmission System Operators
NPS
Nord Pool Spot
PS
Price System (one or two)
p.u.
Per unit
RES
Renewable Energy Source
SvK
Affärsverket Svenska kraftnät
TSO
Transmission System Operator
54
ELFORSK
List of Symbols
Symbols
Quantity
Unit
E
Energy
J, Wh
f
Frequency
Hz
I
Current
A
J
Inertia
kgm2
MAE
Mean Absoulute Error
MWh
NMAE
Normalised Mean Average Error
ΔP
Regulating price – spot price
kr/MWh
P
Cost / price
kr/MWh
P
Power
W
Q
Reactive Power
VA, var
r(τ)
Covariance function or AKF r(τ) = cov(X(t),X(t+τ))
t
Time
s, h
U
Voltage
V
π
Pi = 3,14159265358
ρ
Correlation coefficient ρ = cov(X,Y)/(σxσy)
ρ(τ)
Correlation coefficient ρ(τ) = r(τ)/σ2
σ
Standard deviation
σ2
Variance
μ
Expected value, mean value
τ
Time difference
s, h
ω
Angular frequency
rad/s
MW=MWh/h
List of Operators
E(X)
Expected value
cov(X,Y)
Covariance
N(m,σ)
Normal distribution
P(X>0)
Probability
var(X)
Variance
55
ELFORSK
Index
balance responsible ................. 15
balance responsible actor ......... 15
balance service ....................... 16
balance settlement .................. 16
base case ............................... 11
bidding zones................. 3, 20, 22
bottlenecks ............................... 3
congestions ................... 3, 17, 31
correlation .............................. 29
Cramér’s theorem.................... 29
down regulation ...................... 17
eight actors ............................ 12
Elba....................................... 20
Elbas ....................................... 4
electricity production.................. 1
forecast ................................. 25
forecast error .......................... 12
full load hours ......................... 10
geographic concentration .......... 12
Hornsrev ........................... 25, 26
hydro....................................... 1
hydro power ............................. 2
imbalances ............................. 31
independent ........................... 29
intraday market ...................... 16
jiggle ..................................... 24
Lillgrund .............................. 3, 28
market design ......................... 40
mathematical expectation ......... 26
mean absolute error ................ 26
model .................................... 20
NMAE .................... 26, 27, 53, 54
Nord Pool Spot ..................... 3, 15
Nordic countries ...................... 15
normal distribution .................. 27
nuclear .................................... 1
one price system ..................... 40
precipitation ............................. 2
predict ..................................... 3
price areas .......................... 3, 17
regulating power ....................... 3
regulating price ....................... 23
Renewable energy sources.......... 2
renewable sources ..................... 1
RES ......................................... 1
scenarios ................................. 9
simulations ............................. 33
solar power .............................. 2
spatial smoothing effect ........... 29
spinning power balance ............ 15
standard deviation ................... 26
statistical data ........................ 25
stochastic process ................... 29
Svensk Vindkraft ....................... 9
time horizons .......................... 30
TSO....................................... 16
two price system ..................... 40
varying power ........................... 2
weather forecasts ................. 3, 25
weather institute ..................... 31
56
ELFORSK
2
ELFORSK
3

Wind power forecast errors

Transcription

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