Clustering methods to find representative days for modelling the Portuguese electricity system
Abstract
Power system modelling affects decisions on over $450 billion worth of assets world-wide each year. While complex and computationally demanding models, when properly simplified a balance between accuracy and simulation time can be achieved. Solutions and results for this thoroughly studied problem tend to be rather case-specific, and the Portuguese system presents challenges that make existing approaches insufficient. To better understand this system and how its peculiarities can be used to reduce its modelling complexity, a model of the Portuguese electricity system using PLEXOS software was developed and used to test the impact of different clustering techniques on the model’s output results. We show that including natural hydro inflow in the clustering to find representative days for a system where hydro generation plays such a large role can improve model output accuracy. This is typically ignored in the literature. Additionally, we demonstrate that using data disregarding daylight saving time changes can have an impact on results. Finally, we indicate that intraday downsampling might have limited effect on modelling accuracy, and open the way for future work on weighting clustering input dimensions differently to improve accuracy of representative days.
Full text
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Clus e ing me hods o ind ep esen a i e days
o modelling he Po uguese elec ici y sys em
João Vasco da Sil a Palmei o
Disse a ion p esen ed as pa ial equi emen o ob aining
he Mas e ’s deg ee in In o ma ion Managemen
ii
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
CLUSTERING METHODS TO FIND REPRESENTATIVE DAYS FOR
MODELLING THE PORTUGUESE ELECTRICITY SYSTEM
by
João Vasco da Sil a Palmei o
Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in In o ma ion
Managemen , wi h a specializa ion in Knowledge Managemen and Business In elligence
Ad iso : Ian James Sco , PhD
July 2021
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ACKNOWLEDGEMENTS
E e yone ha has, a some poin , been a pa o my li e has, in one way o ano he , in luenced he way
I hink, hus been pa o he p ocess ha led o his hesis, and o ha I am glad o hank you. Teache s
and P o esso s ha e nu u ed my pu sui o knowledge since I was a li le kid, leading me o achie e
wha I ha e so a . In pa icula , I would like o hank D Ian Sco , who no only laid ou he g ounds
o his wo k, bu also guided me h ough his endea ou wi h consis en dedica ion, pa ience, and
lexibili y, igh o he end o i . I also hank D Flá io Pinhei o o helping jump s a his p ojec . I
would also like o acknowledge he con ibu ion o my o me colleagues a EU ACER, who ha e aken
my in e es in he Ene gy Ma ke s o a whole new le el, and ne e le any o my ceaseless ques ions
unanswe ed.
To my iends and colleagues, hank you o all he ime oge he , knowledge sha ed, and ad ice gi en.
You ha e made i much easie o me o ake his jou ney. I ha e o especially hank Luís Fe ei a, o
no gi ing up on me when I needed his help debugging code.
Pe haps mos impo an ly, I would like o hank my amily, and my pa ne in pa icula , Ma ia João,
o always belie ing I would see his p ojec o he end, e en when i seemed o be so a om i , and
suppo ing me he whole way h ough in a way only hey possibly could.
i
ABSTRACT
Powe sys em modelling a ec s decisions on o e $450 billion wo h o asse s wo ld-wide each yea .
While complex and compu a ionally demanding models, when p ope ly simpli ied a balance be ween
accu acy and simula ion ime can be achie ed. Solu ions and esul s o his ho oughly s udied
p oblem end o be a he case-speci ic, and he Po uguese sys em p esen s challenges ha make
exis ing app oaches insu icien . To be e unde s and his sys em and how i s peculia i ies can be used
o educe i s modelling complexi y, a model o he Po uguese elec ici y sys em using PLEXOS
so wa e was de eloped and used o es he impac o di e en clus e ing echniques on he model’s
ou pu esul s. We show ha including na u al hyd o in low in he clus e ing o ind ep esen a i e
days o a sys em whe e hyd o gene a ion plays such a la ge ole can imp o e model ou pu accu acy.
This is ypically igno ed in he li e a u e. Addi ionally, we demons a e ha using da a dis ega ding
dayligh sa ing ime changes can ha e an impac on esul s. Finally, we indica e ha in aday
downsampling migh ha e limi ed e ec on modelling accu acy, and open he way o u u e wo k on
weigh ing clus e ing inpu dimensions di e en ly o imp o e accu acy o ep esen a i e days.
KEYWORDS
Clus e ing; Ene gy Economics; Powe Sys em Modelling; Renewable Ene gy Sou ces; Rep esen a i e
days; Time Se ies
INDEX
1. In oduc ion ............................................................................................................. 1
2. Li e a u e e iew ..................................................................................................... 7
3. Resea ch Ques ions and objec i es ........................................................................ 12
4. Me hodology ......................................................................................................... 14
4.1. Da a collec ion and elec ici y ma ke model de elopmen ............................. 14
4.2. Da a explo a o y analysis ................................................................................ 18
4.3. Da a P ep ocessing ......................................................................................... 21
4.4. Clus e ing ........................................................................................................ 23
4.5. Assessmen o clus e ing app oaches .............................................................. 25
5. Resul s and discussion ........................................................................................... 27
6. Conclusions ............................................................................................................ 37
7. Limi a ions and ecommenda ions o u u e wo ks .............................................. 39
8. Bibliog aphy ........................................................................................................... 40
9. Annexes ................................................................................................................. 45
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LIST OF FIGURES
Figu e 1 – A. Diag am exempli ying a e ically in eg a ed elec ici y ma ke monopoly.
B. Diag am exempli ying a wholesale and e ail compe i ion elec ici y ma ke . .............1
Figu e 2 – Theo e ical compa ison o o al cos and unning ime o ossil uel and nuclea
gene a o s – sc eening cu e. .........................................................................................3
Figu e 3 – Example o gene a ion me i o de .........................................................................4
Figu e 4 - Hyd o gene a ion capaci y as a pe cen age o o al ins alled capaci y in Eu opean
coun ies in 2021. Sou ce: (ENTSO-E, 2021). ...................................................................6
Figu e 5 – O e iew o p ocess s eps. ...................................................................................14
Figu e 6 – Compa ison be ween yea ly a e age PLEXOS model p ice and OMIE Spo p ices o
Po ugal (OMIE, 2021). .................................................................................................17
Figu e 7 – Compa ison be ween yea ly o al gene a ion o biomass, gas, and coal om PLEXOS
model and TP’s ac ual gene a ion. ................................................................................18
Figu e 8 – Co ela ion ma ix be ween he i e-yea hou ly se ies o load, sola , wind, and he
na u al in low o hyd o un-o - i e , pumped s o age, and ese oi . ...........................18
Figu e 9 – Mon hly o al GWh o Load, Sola , Wind, and Hyd o Run-o -Ri e by yea (2016-
2020) ............................................................................................................................19
Figu e 10 – Hou ly a e age MWh daily p o ile in CET by mon h o load, sola , wind, and hyd o
un-o - i e , a e age o 2016-2020. ..............................................................................20
Figu e 11 – Hou ly a e age load MWh by weekday in CET, 2016-2020 Po ugal. ..................21
Figu e 12 – S anda dised and Non-S anda dised Load, Sola , and Wind da a clus e ed oge he
using k-means wi h 4 clus e s o 2016. ........................................................................22
Figu e 13 – Boxplo s o load, sola , wind, and hyd o un-o - i e inpu da ase s and o load ne
o sola , wind, and un-o - i e . ....................................................................................23
Figu e 14 – NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al gene a ion cos
by clus e ing wi h load, sola , and wind da a all wi h he same weigh . ........................27
Figu e 15 – Euclidean dis ance be ween o iginal inpu da a (o load, sola and wind) and he
medoids om clus e ing wi h hese dimensions all wi h he same weigh , by numbe o
clus e s. ........................................................................................................................28
Figu e 16 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 3 dimensions
(load, sola , and wind) all wi h he same weigh . ..........................................................29
Figu e 17 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 4 dimensions
(load, sola , wind, and hyd o un-o - i e ) all wi h he same weigh . ............................29
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Figu e 18 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 6 dimensions
(load, sola , wind, hyd o un-o - i e , hyd o pumped s o age, and hyd o ese oi ) all
wi h he same weigh . ..................................................................................................30
Figu e 19 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al
gene a ion cos by k numbe o clus e s (CET). De ail by dimensions used o clus e ing,
all dimensions ha ing he same weigh . ........................................................................30
Figu e 20 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al
gene a ion cos by numbe o clus e s. De ail by downsampling, wi h all hou s (CET) wi h
o iginal alues e sus all 24 hou s in each day a e aged ou . Clus e ing wi h all 6
dimensions ha ing he same weigh . ............................................................................31
Figu e 21 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al
gene a ion cos by numbe o clus e s. De ail by downsampling, wi h all hou s (CET) wi h
o iginal alues e sus all 24 hou s in each day a e aged ou . Clus e ing wi h only load,
sola and wind, he 3 dimensions ha ing he same weigh . ...........................................32
Figu e 22 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al
gene a ion cos by numbe o clus e s (CET). Compa ison o no downsampling wi h all six
dimensions wi h he same weigh e sus downsampling o one a e age alue a day, and
sola and wind wi h 50% mo e weigh each. .................................................................33
Figu e 23 – Euclidean dis ance be ween o iginal inpu da a o load and he medoids om
clus e ing wi h: h ee dimensions unweigh ed wi h no downsampling; six dimensions
unweigh ed wi h no downsampling; and six dimensions downsampling o one a e age
alue a day. ...................................................................................................................34
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LIST OF TABLES
Table 1 - Combus ion gene a ion cos s and p ope ies .........................................................17
Table 2 – De ailed model esul s o he dis ibu ion o he o al cos NRMSD by each yea o
model uns wi h no downsampling and no weigh ing wi h he six dimensions (CET) wi h
1-20, 25, 30, 40, 50 k clus e s. .......................................................................................35
Table 3 – De ailed model esul s o he dis ibu ion o he o al cos NRMSD by each yea o
model uns wi h downsampling o he minimum one a e age alue pe day and
emphasising sola and wind dimensions by 50% (CET) wi h 1-20, 25, 30, 40, 50, and 100
k clus e s. .....................................................................................................................36
Table 4 – De ailed model esul s o all model uns wi h clus e ed da a ...............................46
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LIST OF ABBREVIATIONS AND ACRONYMS
CCGT Combined Cycle Gas Tu bine
CET Cen al Eu opean Time
CGTEP Combined Gene a ion and T ansmission Expansion Planning
CO2 Ca bon Dioxide
CUC Clus e ed Uni Commi men
DGEG Di eção Ge al de Ene gia e Geologia
DST Dayligh Sa ing Time
DTW Dynamic Time Wa ping
ENTSO-E Eu opean Ne wo k o T ansmission Sys em Ope a o s o Elec ici y
ETS Emissions T ading Sys em
EU Eu opean Union
EV Elec ic Vehicle
FC Fixed Cos
GEP Gene a ion Expansion Planning
GJ Gigajoule
GWh Gigawa -hou
IAM In eg a ed Assessmen Models
IEA In e na ional Ene gy Agency
IRES In e mi en Renewable Ene gy Sou ces
MIBEL Me cado Ibé ico de Elec icidade
MW Megawa
MWh Megawa -hou
NEM Na ional Elec ici y Ma ke
NRMSD No malised Roo Mean Squa e De ia ion
OCGT Open Cycle Gas Tu bine
PV Pho o ol aic
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Figu e 4 - Hyd o gene a ion capaci y as a pe cen age o o al ins alled capaci y in Eu opean coun ies
in 2021. Sou ce: ENTSOE (2021).
Figu e 4 p esen s he hyd o gene a ion capaci y as a pe cen age o o al capaci y in majo EU powe
sys ems. I showcases a pa icula i y o he Po uguese powe sys em whe e hyd o gene a ion plays a
e y impo an ole, ep esen ing o e one hi d o o al capaci y, hus making modelling a he
dependen on hyd o a ailabili y.
The In e na ional Ene gy Agency (2019) epo s ha in 2018 o e $450 billion we e in es ed globally
in elec ici y gene a ion capaci y, o which mo e han hal was on RES. These in es men decisions
a ec no only e e yone who consumes elec ici y, bu also li e ally e e y li ing being on he plane
since i deeply impac s esou ce usage and pollu ion. As o 2016 elec ici y and hea ing p oduc ion
accoun ed o mo e han 40% o global CO2 emissions (In e na ional Ene gy Agency, 2018).
I is clea hen ha he elec ici y sec o is an impo an and changing one. To make decisions in hese
a eas we ely on he use o models. Howe e , hese models a e la ge and complex, and we need o
educe complexi y whe e possible. One way o do ha is h ough ep esen a i e days.
In he emainde o his hesis we e iew he li e a u e on powe sys em modelling and hei pu pose,
he selec ion o ep esen a i e days and he measu ing o hei accu acy. We hen desc ibe how we
buil such model o he Po uguese elec ici y sys em, educed i s complexi y, and measu ed he
accu acy o said complexi y educ ion.
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2. LITERATURE REVIEW
Since he c ea ion o he i s ene gy sys em models by he In e na ional Ene gy Agency (IEA) and he
In e na ional Ins i u e o Applied Sys ems Analysis in he 1970s (P enninge , 2017) he ene gy sys ems
ha e become much mo e complex and a iable. Powe sys em modelling has con inued o e ol e,
allowing build and policy decisions o be eliably da a d i en.
Powe sys ems a e only one ca ego y o e a mul i ude o model ypes, a ying in scope and aim, ha
ha e been used o di e en ends (Poncele , 2018; Sco , 2021):
• In eg a ed assessmen models (IAMs) s udy long- e m in e disciplina y p oblems o a global
scope. Se e al au ho s (see e.g., Cla ke e al., 2014; Moss e al., 2010) used IAMs o analyse
policies o clima e change mi iga ion.
• Ene gy-economy models a e used o s udy he in e ac ion be ween an ene gy and an
economic sys em. These a e usually modelled a a na ional o egional le el and wi h a ime
scope be ween 20 and 100 yea s. Messne & Sch a enholze (2000) linked a mac oeconomic
model wi h a de ailed ene gy supply model o in eg a e he in luence o ene gy supply cos s
in mac oeconomic p oduc ion ac o s op imisa ion.
• Ene gy-sys em planning models ha e hei scope limi ed o he ene gy sys ems in pa icula ,
usually modelling he en i e chain om ex ac ion o inal ene gy consump ion in all majo
o ms o a pa icula coun y o egion o e mul iple decades. Gö z, Blesl, Fahl, & Voß (2012)
used hese models o s udy how o se policy a ge s o educe g eenhouse gas emission ac oss
EU ETS and non-ETS sec o s.
• Powe -sys em planning models’ scope is es ic ed o only he powe sys em i sel , wi h he
upside o allowing mo e de ailed ep esen a ions o such complex models. These models can
be u he ca ego ised:
▪ Gene a ion expansion planning (GEP) is used o unde s and which gene a ion uni s
should be ins alled o decommissioned o mee expec demand o e a planning
ho izon. GEP usually igno es o g ea ly simpli ies ansmission cos s.
▪ T ansmission expansion planning (TEP) aims o minimise ansmission cos s.
▪ Combined gene a ion and ansmission expansion planning (CGTEP) akes in o
accoun bo h he need o plan ins alled capaci y and i s loca ion, conside ing he
ansmission cos s associa ed.
Ou model is amed as a powe sys em planning model, in pa icula ma ke moni o ing o uni
commi men , which needs o be aken in o accoun by GEP models. Fo he emainde o his sec ion
we will de ail how powe sys em models in pa icula ha e been used, hei complexi y educed, and
hei accu acy measu ed.
K ajačić, Duić, & Ca alho (2011) used he H2RES model o pe o m sys em planning and p esen
echnical solu ions o 100% RES elec ici y p oduc ion scena ios in Po ugal. The au ho s showed ha
a 100% RES solu ion a ou s hyd o and wind powe , wi h la ge pump s o age hyd o acili ies o a oid
unnecessa y ejec ion o a iable enewable gene a ion and smoo h ne demand cu es.
Ellis on, MacGill, & Diesendo (2013) simula ed he Aus alian powe sys em o seek he leas cos ly
solu ions o supplying he Aus alian Na ional Elec ici y Ma ke (NEM) wi h 100% RES elec ici y in
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2030. The au ho s ound ha , depending on he discoun a e and he u u e emission p ices, going
100% enewable could be a cheape solu ion o he Aus alian NEM.
Pillai & Bak-Jensen (2010) s udied how inc easing elec ic ehicle (EV) loads a ec s a ypical Danish
p ima y dis ibu ion ne wo k, bo h wi h con olled and uncon olled cha ging modes. The s udy
concluded ha only a 10% (o o al ca s) in eg a ion o uncon olled cha ging EVs is easible, wi h a
much la ge in eg a ion o be possible wi h con olled cha ging. Fo his s udy he au ho s used a
model o he powe sys em o he Danish island o Bo nholm.
The i s wo abo e-men ioned examples emphasise he e e mo e ecu ing need o s ee ocus in o
RES when modelling powe sys ems, as hey a e mo e di icul o model and p edic due o in insic
ola ili y and a he same ime a e g owing in con ibu ion o he sys ems. The hi d highligh s he
ad an ages o in oducing V2G and p osume s o powe sys em models.
Simula ing an elec ici y sys em o e many yea s and co ec ly conside ing in es men decisions,
medium- e m cons ain s, and inancial incen i es can p o e compu a ionally di icul , especially when
needed o un housands o imes using Mon e Ca lo me hods o es ima e ma ginal cos s (Boo h, 1972;
Mazumda & Ch zan, 1995). The e a e 8760 hou s in a non-leap yea o which inpu s and cons ain s
need o be conside ed, bo h sepa a ely and aking in o conside a ion he p e ious and ollowing hou s’
gene a ion p o ile. A decision o gene a e a a gi en ime is no independen ly aken due o
oppo uni y cos s, amp up and amp down cos s, minimum gene a ion le els, minimum up and down
ime, and o he cons ain s.
In o de o accoun o some o he a o emen ioned ch onological dependency, he mos common
agg ega ion o elec ici y demand da a in he li e a u e is ep esen a i e days (Yegane a , Amin-
Nase i, & Sheikh-El-Eslami, 2020). Howe e , he me hods o selec hese ypical days in a way ha
main ains he essen ial a iabili y o he models di e conside ably (Ko zu , Ma kewi z, Robinius, &
S ol en, 2018). Agg ega ing hou ly yea -long p o iles in o ep esen a i e days o weeks can
conside ably educe his massi e compu a ional equi emen and, i p ope ly achie ed, main ain high
accu acy while allowing o mo e and quicke simula ions. G een, S a ell, & Vasilakos (2014) ha e
shown ha clus e ing yea -long p o iles in o 6 o 10 ep esen a i e days can inc ease he p ocessing
speed by a ac o o o e 100.
Ha ing es ablished he alue o accu a ely modelling elec ici y sys ems, and he need o educe he
complexi y and compu a ional cos o such sys ems, he nex s ep is o conside how his complexi y
educ ion has p e iously been unde aken.
The e a e academic s udies ha look solely in o clus e ing demand da a (Hassan, Khos a i, Jaa a , &
Raza, 2014), usually ne o IRES (Sis e nes & Webs e , 2013; Yegane a e al., 2020), s udies ha clus e
demand and wind gene a ion sepa a ely (G een e al., 2014), and s udies ha conside load, wind, and
sola gene a ion as IRES become a conside able pa o ins alled capaci y (Me ick, 2016;
Nahmmache , Schmid, Hi h, & Knop , 2016; Poncele , Hoschle, Dela ue, Vi ag, & D haeselee , 2017).
S udies ha e used o he dimensions, usually o di e en ends.
Se e al au ho s (see e.g., Me ick, 2016; Nahmmache e al., 2016; Poncele e al., 2017) ha e all
clea ly s a ed ha , as IRES become an inc easingly impo an pa o ene gy sys ems, using ne demand
o ind ep esen a i e days ends o deeply unde es ima e o he a iabili y in oduced by IRES. These
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s udies emphasize he impo ance o including IRES along wi h demand on u u e wo ks o ind
ep esen a i e days o sys ems wi h signi ican IRES pene a ion. This means ha , o selec
ep esen a i e days, we should include each se ies indi idually a he han dilu ing hem by ne ing
demand. Fu he mo e, as ma ke s e ol e we should in es iga e which new dimensions can be u he
included o imp o e selec ion.
Pina, Sil a, & Fe ão (2011) de eloped new modelling me hodologies using a ypical weekday,
Sa u day, and Sunday o each season o he Po uguese island o São Miguel (Azo es). Unlike ou
s udy, he aim o hei esea ch was o examine modelling echniques a he han clus e ing
echniques, and o alida e he s udy o he peculia insula elec ici y sys em o São Miguel island.
To he bes o ou knowledge, no s udies on clus e ing o modelling only he Po uguese mainland
elec ici y sys em ha e been published.
To unde s and how accu a e dimension educ ion me hods a e we can compa e and measu e model
inpu da a and/o model ou pu (s) (K is iansen, Ko pås, & Hä el, 2017). Hä el, K is iansen, & Ko pås
(2017) ha e shown ha he mos accu a e sampling echnique when compa ing he model inpu da a
will no necessa ily yield he mos accu a e model ou pu . On he one hand, assessing accu acy in
e ms o model inpu da a can p esen a mo e gene alisable conclusion. Howe e , he mo e case-
speci ic app oach o assessing accu acy in e ms o model ou pu can show how clus e ing ac ually
does impac he end-goal o modelling.
S udies ha e used bo h me hods o compa e sampling echniques applied o powe sys em planning
models. Wi hin each me hod, he a iables used o make he compa isons also di e .
Fo measu ing accu acy in e ms o model inpu da a Ko zu e al. (2018) used sola i adia ion,
empe a u e, elec ici y load, and wind p o ile, whe eas Nahmmache e al. (2016) compa ed he daily
p o iles o onsho e wind, sola pho o ol aic (PV), and elec ici y demand.
Liu, Sioshansi, & Conejo (2018), K is iansen e al (2017), and Sco , Ca alho, Bo e ud, & Sil a (2019)
analysed esul s using bo h me hods. The i s s udy compa ed wind, sola , and demand daily du a ion
cu es (inpu da a) and in es men decisions (model ou pu ). K is iansen e al. (2017) compa ed load,
onsho e wind, o sho e wind, sola , and hyd o (inpu da a) and ope a ional cos pe o mance (model
ou pu ), showing ha he anking o sampling echniques was no he same wi h bo h compa ison
me hods. Sco e al. (2019) analysed he no malised oo mean squa e de ia ion (NRMSD) o du a ion
cu es o demand, wind, sola and amp (model inpu s), and also compa ed expansion model esul s.
Howe e , measu ing he dimension educ ion echniques’ accu acy was ound mos commonly in
e ms o powe sys em planning model ou pu s. G een e al. (2014) used elec ici y cos , ca bon
in ensi y, annual ou pu and e enue, and numbe o plan s a -ups and ou ages. Teichg aebe &
B and (2019) used p oblem speci ic objec i e unc ions (ba e y cha ge/discha ge op imiza ion and
gas u bine scheduling). P enninge (2017) compa ed deployed capaci y o key echnologies and he
le elized cos o elec ici y. Yegane a e al. (2020) used new capaci y added o he gene a ion lee
(long- e m planning modelling). Sis e nes & Webs e (2013) used gene a o s’ capaci y and
commi men . Assessing each model ou pu indi idually allows a e y comp ehensi e analysis o he
esul s, bu i also makes hem di icul o p ocess and analyse. Ins ead, Me ick (2016) used a single
compa ison me ic composed o se e al model ou pu s. This solu ion makes i much simple o
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compa e esul s bu hides how clus e ing a ia ions a ec di e en model ou pu s indi idually, and is
highly dependen on he ele ance o he combina ion o ou pu s used.
The endency seems o be pu ing mo e ocus on assessing i a clus e ing echnique can p o ide
accu a e model esul s. Ne e heless, always bea ing in mind he esul s a e mo e case speci ic. This
emphasises he impo ance o building an accu a e powe sys em model o compa e on, ha s ill is
gene al enough o allow ex apola ing esul s.
P e ious s udies no only a y in he way he model is buil and assessed, bu also in he clus e ing
echniques used.
Ins ead o using complex clus e ing me hods, one could conside simply g ouping hou s wi h (almos )
he same demand, howe e i has been shown ha such does no occu equen ly wi hin he same
yea . Acco ding o Me ick (2016), wi h less han 40 clus e s one can cap u e he as majo i y o he
a iance o a yea ’s 8760 hou s o demand. Howe e , i also including a wind and a sola p o ile,
app oxima ely 1000 hou s a e equi ed o cap u e simila ly low a iance. E en hough his is al eady a
conside able downsize om he o iginal 8760 hou s, i is no enough o a compu a ion educ ion o
some s udies. Fu he mo e, his would assume he e a e no cons ain s ha span ac oss ime, i.e., ha
hou s could be ea ed as ch onologically independen . As desc ibed in sec ion 1, he models should
conside he hou ly sequencies. Fo ha eason mos s udies ake in o accoun cons ain s ac oss ime
by using ep esen a i e days (o weeks), assuming ch onological independency be ween days (o
weeks). In his case, 20 days ou o 365 in a yea would be enough o ha e a low le el o a iance i
only g oss demand was o be modelled, ising o 300 days i conside ing wind and sola p o iles. The
esul s a e e en wo se when agg ega ing weekly, as no wo iden ical weeks we e ound in Me ick’s
s udy when conside ing load and a ailabili y o wind and sola (Me ick, 2016).
Rep esen a i e load cu es a e ypical daily cu es ep esen ing a g oup o load p o iles wi h analogous
demand pa e ns. In oduced by Balachand a & Chand u (1999), we e la e used by G een e al. (2014)
o demons a e how comple e yea -long p o iles o he B i ish elec ici y sys em can be p ocessed
abou 60 imes as e using only a se o 6 o 10 ep esen a i e hou s and s ill yield accu a e esul s o
es ima ion o a e age and ma ginal cos o elec ici y. Howe e , hei esul s when modelling a e
e en s such as plan s a s, ou ages and peak equi emen s we e shown o be much less accu a e, wi h
clus e ing esul s g ossly unde es ima ing hem. This comes o show ha app oaches ha assume
ch onological independency become less accu a e and hus less ele an wi h he inc ease o IRES.
In hese s udies he k-means algo i hm (o a a ian o i ) was used o clus e he da a se as a whole.
Howe e , he ha des pa s o accu a ely model a e in bo h ends o he demand spec um, i.e., he
high peaks and he low plunges, due o he na u e o ma ginal cos s o he gene a ion mix.
Pineda & Mo ales (2018) used a a ian o k-means by choosing a medoid only a e pe o ming all k-
means i e a ions in o de o educe smoo hing esul s.
Liu e al. (2018) and Teichg aebe & B and (2019) used dynamic ime wa ping (DTW) dis ance as a
shape-based clus e ing me hod o ind ep esen a i e days. In oduced in Sakoe & Chiba (1971, 1978)
applied o speech ecogni ion, DTW inds op imal alignmen be ween wo sequen ial se s o da a,
ha ing been demons a ed o ha e meaning ul applica ions wi h ime se ies (Pe i jean, Ke e lin, &
Gança ski, 2011).
11
P enninge (2017) used a ious combina ions o h ee di e en me hods o inc ease he
compu a ional ac abili y o high- esolu ion planning model o G ea B i ain’s elec ici y sys em wi h
25 yea s o simula ed wind and sola PV gene a ion: downsampling, clus e ing, and heu is ics. This
s udy di e s om mos o he s o including a longe han usual da ase , combining me hods ha
ackle di e en aspec s o he p oblem, and compa ing simula ions o he same model wi h di e en
scena ios o sha e o IRES in he gene a ion mix. Downsampling is he simples o he h ee me hods,
consis ing o educing he esolu ion o he whole se ies (e.g., om hou ly o 3-hou ly). Howe e
simple a me hod, downsampling ended o wo sen esul s when modelling wi h a high sha e o
enewables, as high a iabili y usually equi es high ime esolu ion o be co ec ly modelled. To
clus e , he au ho used bo h k-means and hie a chical app oaches, desc ibing ha he sum o squa ed
e o ended o la en o be ween 10 and 15 clus e s. The hi d me hod used, heu is ic selec ion,
e e s o selec ing days o weeks based on p e-de ined c i e ia such as he week con aining he
maximum and minimum daily a e age o a ime se ies. When combined wi h clus e ing, heu is ic
selec ion allows o selec ex eme days ha would o he wise be la ened ou e en hough hey can
be e y impo an o model. The au ho concluded ha app oaches including heu is ic me hods
ended o yield s able esul s and can he e o e be p e e able o models wi h a high sha e o IRES.
F om his li e a u e we conclude ha powe sys em modelling has an impo an economic impac , and
educing i s complexi y is a pe inen p oblem ha is becoming inc easingly mo e di icul as ma ke s
e ol e in o mo e ola ile scena ios (e.g., wi h mo e IRES). The mos widely used app oach o his
p oblem is o selec ep esen a i e days a he han hou s due o ch onological dependencies. To
selec hese days we should clus e all IRES indi idually and no use ne demand, and o assess hei
accu acy conside he e ec on model ou pu s a he han inpu s. Howe e , om he li e a u e i is
no clea how a hyd o domina ed sys em like Po ugal, wi h he associa ed addi ional wea he
dependan a iables, should be modelled.
12
3. RESEARCH QUESTIONS AND OBJECTIVES
Va ious s udies, namely he ones men ioned in Sec ion 2, ha e explo ed mul iple me hods o educe
he complexi y and compu a ional equi emen s o elec ici y sys em modelling, and o e alua e he
accu acy o said me hods.
This esea ch aims o be e unde s and how echniques o educe modelling complexi y can be
e icien ly applied o he Po uguese powe sys em in pa icula . We sough o adap and combine
some o he echniques men ioned in he p e ious sec ion o he speci ic cha ac e is ics o he
Po uguese sys em. We s udied he e ec s o di e en clus e ing echniques using h ee di e en
me hods o compa e he accu acy o he clus e ing, se ing ou o add ess he ollowing ques ions:
Q1: How many ep esen a i e days a e needed o e ec i ely model a yea o he Po uguese
powe sys em?
The numbe o ep esen a i e days needed o accu a ely model a powe sys em di ec ly a ec s how
much o he modelling cos s and compu a ional demand can be educed. As he numbe o
ep esen a i e days inc eases, so should he modelling accu acy. Howe e , his ends o happen a
inc easingly smalle imp o emen a es, p o iding a ade-o be ween modelling cos s and accu acy.
Q2: Is he clus e ing accu acy a ec ed by using inpu da a ha igno e dayligh sa ing ime
(DST) change ( ime seasonali y)?
This ques ion in pa icula was no ound in any o he li e a u e e iewed. Time se ies da a in UTC
(Coo dina ed Uni e sal Time) igno es dayligh sa ing ime changes and is commonly used o ime
se ies da ase s since i a oids ha ing an hou wi h missing da a and ano he wi h wo eco ds each
yea . When using a da ase ha conside s DST, such as CET (Cen al Eu opean Time), hose wo hou s
a yea need o be ixed. Howe e , people end o ha e a schedule ha akes he DST in o conside a ion,
meaning ha he in luences on elec ici y demand p o iles om people’s quo idian ac i i ies end o
be always a he same CET ime, bu no UTC. Fo example, i a ac o y s a s wo king a 9 a.m. CET, i
will p o oke an inc ease in demand a 9 a.m. CET he whole yea , bu a 9 a.m. UTC hal o he yea
and 10 a.m. UTC he o he hal . Howe e , as his does no impac he p o iles o IRES, he e ec s o
ime seasonali y on he clus e ing migh change when including IRES se ies.
Q3: Does he unusual p e alence o hyd o gene a ion capaci y o he Po uguese sys em mean
ha hyd o gene a ion da a can imp o e he clus e ing accu acy?
E en hough i is becoming inc easingly ecu en o include wind and sola da a in he clus e ing o
complexi y educ ion s udies (see sec ion 2), hyd o na u al in low ends o be le ou o he clus e ing.
Because, con a ily o mos sys ems s udied in he li e a u e e iewed, o e a hi d o he ins alled
capaci y in Po ugal is hyd o (see Figu e 4), his can be a meaning ul dimension o include when
clus e ing o he Po uguese sys em.
Q4: Should all inpu da a dimensions be gi en he same weigh when clus e ing?
In sec ion 2 we ha e desc ibed a ious app oaches o clus e ing ep esen a i e days o powe sys em
modelling, wi h s udies including di e en model inpu da a in hei clus e ing, and wi h ha ha ing
di e en esul s. Some dimensions a e mo e ola ile be ween days (see sec ion 4.2) and ha de o
13
ep esen (see sec ion 4.3), bu i hese a e no mo e impo an o he model hen including hem
could maximise ep esen a i eness o unimpo an se ies. Howe e , inco po a ing a ce ain dimension
in o he clus e ing does no need o be a ze o-sum game. We de eloped a new app oach and s udied
how weigh ing di e en ly he a ious dimensions in he clus e ing a ec s he model’s accu acy. Fo
example, we a e in oducing hyd o na u al in low. Would his be gi en he same weigh as wha we
we e al eady conside ing? Hyd o is e y impo an o gene a ion capaci y bu maybe less ola ile. Can
we unde s and how he ola ili y, co ela ion wi h demand, and capaci y o ha ype o gene a ion
a ec he weigh ing gi en o ha dimension?
Q5: Do in aday agg ega ions (downsampling) ha e a signi ican impac on he model’s
accu acy when combined wi h o he echniques?
The numbe o ep esen a i e days can only be educed up o a ce ain poin be o e accu acy s a s
d opping d as ically. Howe e , a model’s complexi y can also be educed wi h in aday agg ega ions,
such as downsampling. P enninge (2017) showed ha downsampling can wo sen esul s when
clus e ing wi h high sha es o enewables. Howe e , he majo enewables in Po ugal a e hyd o and
wind, which p esen much less in aday a iabili y han o example sola (see sec ion 4.2).
Fu he mo e, we in end o combine downsampling wi h he p e iously desc ibed weigh ing echnique.
In o de o answe hese ques ions we s a ed by collec ing, analysing, and p ep ocessing he da a. We
hen cons uc ed and benchma ked a model o he Po uguese elec ici y sys em, and de eloped bo h
a weigh ing and a downsampling app oach o subsequen ly clus e he da a (wi h and wi hou hese
wo app oaches). Finally, ecu si ely an he model wi h he clus e ed da a, ex ac ed and compa ed
he esul s.
14
4. METHODOLOGY
In his sec ion we desc ibe he o e all me hodology used o his s udy. I s a s wi h collec ing he
da a ha is hen used o c ea e a wo king model o he Po uguese elec ici y sys em (sec ion 4.1).
Then we analysed he model inpu da a o be e unde s and how i beha es in o de o e icien ly
educe i s complexi y (sec ion 4.2). A e wa ds he da a was p ep ocessed using he echniques
de eloped o his s udy (sec ion 4.3) be o e being clus e ed (sec ion 4.4). Finally, we had o de elop
me ics o e ec i ely measu e he accu acy o he p e iously applied complexi y educ ion echniques,
compa ing model esul s wi h he ones o he o iginal model (sec ion 4.5).
Figu e 5 – O e iew o p ocess s eps.
Figu e 5 p esen s an o e iew o he p ocess s eps ha had o be epea ed o each di e en
combina ion o weigh ing, downsampling, ime seasonali y (CET/UTC), and numbe o clus e s. This
was a a he ime-consuming ask, specially se ing up he model wi h he di e en clus e ed inpu
da a, and ex ac ing and compa ing he esul s.
In he emainde o his sec ion we ou line each o hese asks in de ail.
4.1. DATA COLLECTION AND ELECTRICITY MARKET MODEL DEVELOPMENT
The main objec i e o he modelling was o de elop a ep esen a ion o he Po uguese elec ici y
sys em in o de o apply al eady de eloped clus e ing echniques and also o explo e new ways o
agg ega e in a-annual empo al a iabili y o elec ici y demand da a along wi h wind, sola and hyd o
a ailabili y. Thus, s udying how di e en clus e ing algo i hms and di e en pa i ion sizes a ec he
accu acy o simula ions on he Po uguese elec ici y sys em. The in en ion is o u he unde s and
which a iables o he sys em can be accu a ely simula ed aking only a ac ion o he o iginal
simula ion ime and wha me hods can be used o imp o e his accu acy.
A simpli ied model o he Po uguese elec ici y sys em was de eloped using PLEXOS ma ke
simula ion so wa e. PLEXOS is a p oblem-sol ing engine, p o iding a single in eg a ed hub o mul iple
sys ems and allowing modelling op ions om e y simple o in ica e and complex sys ems. PLEXOS
ansla es he model uns in o a se ies o linea -p og amming p oblems ha hen need a sol e o be
op imised. The sol e package used o his s udy was he open-sou ce GNU Linea P og amming Ki
8
.
8
The model was c ea ed and an on a lap op unning wi h Windows 10 P o 64bi s wi h an In el® Co e™
i7-8550U CPU @ 1.80GHz p ocesso and 16GB RAM.
15
The ul ima e goal o his model was no o eplica e he eal sys em in he mos comple e and ac ual
way, bu a he o make i a wo king p ac ical ep esen a ion o he sys em, allowing he s udy o how
educing inpu da a a ec s he model’s ou pu s.
Po ugal was modelled as a single egion, assuming i o be as an isola ed coppe pla e wi h no
ansmission sys em cons ain s, neglec able ansmission losses and no c oss-zonal ades.
Th ee g oups o gene a ion ypes we e conside ed:
• combus ion gene a o s: ossil ha d coal, ossil gas, and biomass
9
;
• dispa chable enewables: hyd o pumped s o age, and hyd o ese oi ;
• in e mi en enewables: sola , wind, and hyd o un-o - i e .
The gene a ion capaci y pe uni ype was eplica ed om Eu opean Ne wo k o T ansmission Sys em
Ope a o s o Elec ici y (ENTSO-E) T anspa ency Pla o m (TP) da a (ENTSO-E, 2021). Howe e ,
because he aim o his s udy was no o unde s and which gene a o s a e speci ically dispa ched,
clus e ed uni commi men (CUC)
10
was used so ha all di e en gene a o s o he same ype we e
g ouped in o an a e age one, ha ing as many o hese uni s as in he eal sys em, and s icking o he
eal o al maximum gene a ion capaci y desc ibed in TP. This mean ha ansmission sys em cos s
could also be dis ega ded o he pu pose o his s udy. Since speci ic gene a ion e iciency (hea a e)
da a was no eadily and eliably a ailable and uel p ices end o be a he ola ile, we conside ed
s anda d and cons an indus y alues o hese a iables.
Fo ossil uelled gene a o s, emission cos s we e implied in uel cos s ins ead o modelling emission
cos s sepa a ely, meaning ha emission cos s we e conside ed cons an along wi h uel p ices.
The model was de eloped o 5 yea s (2016-2020), aking in hou ly da a om ENTSO-E (2021) o
Po uguese load
11
, and sola , wind and hyd o un-o - i e gene a ion.
Acco ding o ENTSO-E’s TP da a, hyd o gene a ion capaci y ep esen s o e a hi d o Po ugal’s o al
capaci y (see Figu e 4). Hyd o (wi h i s sub ypes o gene a ion) has e y pa icula cha ac e is ics, and
mis ep esen ing i in a sys em whe e i plays such a la ge ole can deeply a ec he model’s
pe o mance. In o de o mo e accu a ely simula e hyd o gene a ion, hou ly his o ical gene a ion
alues om un-o - i e uni s aken om TP we e used as a p oxy o na u al in low. Fo ese oi
gene a o s, since hei gene a ion can be con olled up o a ce ain poin , na u al in low had o be
calcula ed as hou ly gene a ion minus he hou ly a e age o he di e ence be ween he week’s inal
9
Biomass is conside ed a enewable ene gy sou ce in he Eu opean Union assuming i s uel’s o igin is
gua an eed o be sus ainable. Fo he pu pose o his s udy all biomass powe plan s we e conside ed equal in
e iciency and uel cos s, ending i ele an he uel’s sou ce o he s udy’s ou come. Fu he mo e, biomass was
g ouped in o he combus ion gene a o s’ g oup a he han dispa chable enewables’ because o modelling
simila i y when dis ega ding cos s o emissions, such as he case. See EU’s biomass de ini ion and sus ainabili y
c i e ia a : h ps://ec.eu opa.eu/ene gy/ opics/ enewable-ene gy/biomass_en
10
CUC consis s o g ouping iden ical o simila powe plan s o educe he model’s complexi y by u ning
bina y commi men a iables o all plan s wi hin a g oup in o a single in ege a iable. CUC has been shown o
in oduce e y li le e o in o powe sys em models while educing he compu a ional cos , al hough g ouping
noniden ical gene a ion uni s can inc ease he e o (Meus, Poncele , & Dela ue, 2018).
11
We used load and demand in e changeably since ansmission losses we e no modelled.
22
(i.e., poin ’s dis ance) han load o sola , e en hough i is no necessa ily mo e impo an o he
model
14
.
Figu e 12 – S anda dised and Non-S anda dised Load, Sola , and Wind da a clus e ed oge he using
k-means wi h 4 clus e s o 2016.
Figu e 12 shows an example o how no s anda dizing he da a can a ec clus e ing esul s. I p esen s
he esul s o he same k-means clus e ing in o ou clus e s o 24-hou p o iles o load, sola and wind,
wi h he same inpu da a p ep ocessed di e en ly, p o iding a clea iew on how he clus e ing e o
is exogenously alloca ed when he da a had been s anda dised by dimension ( op ow) compa ed o
when he clus e ed da a had no been s anda dised (bo om ow). In Figu e 12 line cha s o he op
ow he load p o iles we e clus e ed in o days wi h high, wo medium (one wi h a e wo king hou s
peak) and low demand, he sola p o iles in o days wi h mo e peak p oduc ion and mo e hou s o
gene a ion (summe -like p o iles) and wo days wi h less hou s o p oduc ion (win e -like p o iles, one
cloudie han he o he ), and he wind p o iles we e mos ly sepa a ed in o wo g oups (windy and non-
windy days). On he o he hand, in he bo om ow load p o iles we e clus e ed only in o high and low
demand days, sola had much less clea win e /summe sepa a ion wi h mos ly jus a cloudie day,
and wind was clus e ed in o ou isually di e en p o iles. This shows ha no s anda dizing he inpu
da a can lead o a la ge ocus on wind since i has mo e in e -day a iabili y hen he o he dimensions.
As he o iginal da a comes om a eliable sou ce and has no missing alues
15
, i is p edic ed ha no
ou lie was p oduced by poo da a quali y. The ou lie s seen in Figu e 13 a e in ac an impo an aspec
o he model inpu , especially he ones ha ep esen hou s o high ne demand ha will lead o
blackou s i he e is no enough ins alled capaci y.
14
This hypo hesis was es ed by weigh ing he di e en dimensions as desc ibed in Sec ion 4.4
15
Excep o he dayligh sa ing ime changes in he CET da ase s, whe e he wo hou s we e a e aged.
23
Since we in ended o main ain he da a’s o iginal shape and did no ea ou lie s, s anda diza ion was
a ou ed o e Max-Min No maliza ion (Bhanda i, 2020).
The esul was a da a able wi h 144 columns which we e he conca ena ion o he 24 hou s in a day
o each o he 6 dimensions, and as many ows as he e we e days o each o he yea s sepa a ely.
Figu e 13 – Boxplo s o load, sola , wind, and hyd o un-o - i e inpu da ase s and o load ne o
sola , wind, and un-o - i e .
4.4. CLUSTERING
A e he aw da a o hou ly load, sola gene a ion, wind gene a ion, hyd o un-o - i e gene a ion,
hyd o pumped s o age na u al in low, and hyd o ese oi na u al in low we e p ep ocessed, di e en
clus e ing echniques we e ied ou and es ed.
When clus e ing wi h k-means, he esul ing cen oid is an a e age alue o inpu poin s, whe eas wi h
k-medoids we ge an ac ual day as ou pu . Because o his, k-means ends o o e ly smoo h he da a
in a way ha can make i un ealis ic when examining in e empo al cons ain s in he modelled
sys em. Thus, p e en ing he clus e ing om cap u ing he ac ual a iabili y o he sys em.
Also bea ing in mind ha one o he goals was o clus e wi h mul iple combina ions o he six inpu
da a dimensions (load, sola , wind, hyd o un-o - i e , hyd o pumped s o age, and hyd o ese oi ) we
op ed o use k-medoids wi h Euclidean dis ance o clus e he da a. This way ensu ing we could use
he medoids da a o he same day o he dimensions ha we e no being used o he clus e ing. Fo
example, when clus e ing only wi h load, sola and wind da a, he da a o he h ee hyd o dimensions
would be picked om each medoid’s e e ence day. O he s such as Heube ge , S a ell, Shah, & Dowell
(2017) and Pineda & Mo ales (2018)ha e op ed o clus e using k-means and a e all i e a ions use
he closes poin s o he cen oids as medoids o a oid smoo hing e ec s.
As i was shown in sec ion 2, he mos common p ocedu e in simila s udies is o ei he only use
demand da a o o also include sola and wind gene a ion, wi h a endency o include IRES as hei
con ibu ion o he elec ici y sys ems inc eases. Since he la ges enewable ene gy sou ce in Po ugal
24
is hyd o, we ha e decided o es clus e ing wi h load, sola , and wind ( om he e onwa ds e e ed o
as clus e ing wi h 3 dimensions), o es wi h also in e mi en hyd o (adding hyd o un-o - i e o
clus e wi h 4 dimensions), and inally o include he dispa chable hyd o by adding he na u al in low
o hyd o pumped s o age and hyd o ese oi (clus e ing wi h 6 dimensions). All da a was aken in
hou ly, excep o he calcula ed na u al in low o hyd o pumped s o age and ese oi , which was
weekly. In o de o eed he model wi h hese las wo dimensions and s ill un i wi h hou ly
g anula i y, he weekly alues we e aken as an hou ly a e age o all hou s o each week.
Using he h ee hyd o na u al in low da a se s as sepa a e dimensions could mean o e ly ocusing on
hyd o da a and no add much in o ma ion o he clus e ing gi en ha he h ee se ies a e highly
co ela ed (Figu e 8). In o de o unde s and which se ies con ibu e he mos o he clus e ing wi hou
uling any o hem ou , we ha e es ed clus e ing wi h di e en weigh s o each dimension. Because
he clus e ing used he Euclidean dis ance, he weigh ing was pe o med by mul iplying he
s anda dised alues o each dimension by he squa e oo o he weigh . In p ac ical e ms, i he
weigh s o all dimensions a e he same he e is no weigh ing, i he weigh o a dimension is ze o i is
no being conside ed o he clus e ing, and i he weigh o a dimension is 2 i is he same as including
ha dimension wo imes in he Euclidean dis ance (see demons a ion in he annexes – sec ion 9).
As he numbe o ep esen a i e days can only be educed o a ce ain amoun while main aining
easonable ep esen a i eness, we ha e also a emp ed o combine i wi h educing in aday
dimensionali y, as sugges ed by P enninge (2017). This downsampling was achie ed by a e aging
consecu i e hou s, easing he 24h di e en daily hou s o 12, 8, 6, 4, 2, and 1 di e en one(s).
16
S anda diza ion and weigh ing we e pe o med as ollows:
√𝑤×𝑥−𝜇
𝜎
Whe e 𝑥 is he inpu hou ly alue (al eady downsampled i ha is he case), 𝜇 is he a e age o he se
o 𝑥’s hou and dimension, 𝜎 is he s anda d de ia ion o he se o 𝑥’s hou and dimension, and 𝑤 is
he weigh gi en o 𝑥’s dimension. When downsampling was applied, 𝑥 would be he a e age alue o
he in aday agg ega ed hou s o 𝑥’s dimension and day.
To pe o m and pipeline hese asks, a py hon sc ip was de eloped, using he sciki -lea n KMedoids
package (sciki -lea n, 2019) o clus e ing.
In an a emp o imp o e he e iciency o he clus e ing, pa allelisa ion o he p ocessing was
in oduced in o he sc ip using a mul ip ocessing py hon package. Howe e , his package p o ed
incompa ible wi h he combina ion o he en i onmen used o de elop he sc ip s (Spyde o
Windows) and modula p og amming, used o ensu e code consis ency and homogeneous
main enance o he sc ip s. This pa allelisa ion s a egy was d opped as i did no p o ide much added
alue o he s udy, since he ecu si e clus e ing was a mino pa o he consump ion o p ocessing
ime and capaci y, wi h he majo i y o i being used o ake he clus e ed da a and ans o m i in o a
o ma ha he PLEXOS model could eed om and hen ex ac and compa e he ou pu s.
16
Since he g anula i y o he na u al in low o hyd o pumped s o age and hyd o ese oi is weekly (all
daily alues wi hin a week a e he same a e age ones due o aw da a es ic ions), he e is no impac in changing
he da a g anula i y o hese wo dimensions.
25
4.5. ASSESSMENT OF CLUSTERING APPROACHES
In sec ion 2 we ha e de ailed how di e en compa ison me ics ha e been used in p e ious s udies,
and he meaning ulness o hei esul s. In his esea ch we aimed no o unde s and how accu a e ou
clus e ing was, bu a he how ep esen a i e in he model i was. This mean ha ins ead o using
me ics ha compa e he clus e ing, e.g., Euclidean dis ance be ween he o iginal da ase and he
clus e cen e, mo e complex model ou pu compa ison me ics had o be de ised.
The NRMSD o h ee compa ison me ics was used o assess and compa e he accu acy o each model
un: hou ly p ice du a ion cu e, yea ly gene a ion by uni ype, and yea ly o al gene a ion cos .
NRMSD o each o he compa ison me ics was calcula ed as ollows:
√∑(𝑥𝑖𝑐 −𝑥𝑖𝑜)2
𝑛
𝑖=1 𝑛
∑𝑥𝑖𝑜
𝑛
𝑖=1
𝑛
Whe e 𝑥𝑖𝑜 is he 𝑖 - h alue ou pu o he o iginal model un, 𝑥𝑖𝑐 is he 𝑖- h alue ou pu o he clus e ed
model un, and 𝑛 is he numbe o da a poin s o he calcula ed compa ison me ic.
The hou ly p ice du a ion cu e is he p ice p o ile o de ed descendan . I compa es how well he
model p edic ed he amoun o ime a ce ain ma ke p ice was ma ched. This me ic had 43848 da a
poin s
17
om each model un.
The yea ly gene a ion by uni ype desc ibes how much each o he 8 di e en gene a ion uni ypes
18
p oduced in each yea . This me ic compa es no only he o al amoun s gene a ed bu also how i was
dis ibu ed be ween he di e en uni s. The me ic had 40 da a poin s
19
om each model un.
The hi d and las compa ison me ic - yea ly gene a ion cos - ep esen s he o al wholesale
gene a ion cos o he en i e sys em o each o he i e yea s (meaning 5 da a poin s om each model
un). We ha e also used his me ic o unde s and how he NRMSD is dis ibu ed be ween he i e
yea s o he s udy, i.e., which yea s we e mo e o less di icul o accu a ely clus e acco ding o his
me ic.
We ha e decided o use hese me ics because hey ep esen key ou pu s o models o eplica e. The
abo e-men ioned me ics p esen an o e iew o p ice o ma ion, uni commi men , and sys em cos s,
espec i ely.
We ha e also expe imen ed clus e ing each dimension sepa a ely and hen using he combina ions o
clus e s o he a ious dimensions as he medoids, howe e his me hod p o ed o be bo h ine icien
and unscalable.
Consecu i ely unning he model wi h di e en ly clus e ed da a, ex ac ing he esul s and compa ing
hem was a a he labo ious ask. The e we e in ini e dimension-weigh ing combina ions ha could
be es ed, along wi h downsampling and ime seasonali y. This had o be pe o med a a la ge-enough
scale o ha e a decen a ie y o combina ions o compa e. The compa ison would s ill be meaning ul
17
365 days imes 5 yea s (plus wo days o he wo non-leap yea s o 2016 and 2020) imes 24h.
18
Biomass, coal, gas, hyd o pumped s o age, hyd o ese oi , hyd o un-o - i e , sola , and wind.
19
8 uni ypes imes 5 yea s.
26
e en wi h much less compa ison poin s i we used a se o k clus e s ha showed some e u n and
ended o no be e y ola ile. So, we decided o use only 6, 8, 10, 12, and 14 clus e s o pe o m his
ask ecu si ely and hen un o 1-20, 25, 30, 40, 50, and 100 clus e s o he mos p omising cases.
27
5. RESULTS AND DISCUSSION
In his sec ion we e iew he esul s o he di e en clus e ing app oaches o ep esen a i e day
selec ion. Fi s we es ed he beha iou o he h ee compa ison me ics used in his s udy. Figu e 14
p o ides a ep esen a i e example o ha , showing a endency o he h ee me ics o co ela e, wi h
mo e simila i ies be ween he NRMSD o yea ly gene a ion by uni ype and o al yea ly cos , while
hou ly p ice du a ion cu e had o e all la ge e o s. This poin s ou ha p ice is he mos di icul and
sensi i e model ou pu . Changing, o example, wind inpu , will di ec ly a ec wind and gas
20
p oduc ion, bu only indi ec ly ha e epe cussions on he p ice i i changes he highes SRMC a ha
poin in ime.
The e was some e o ola ili y, wi h cases o lowe k numbe o clus e s ha ing less e o . This was o
be expec ed when clus e ing wi h k-medoids, since i equi es eal da a poin s o medoids. As he
numbe o clus e s inc eases, a la ge pa o he whole da ase is included, bu no necessa ily adding
o he same days p e iously picked, which can a ec sensi i e ou pu s. Using he a e age o he
NRMSD o he h ee compa ison me hods helped la en his a iance.
Figu e 14 – NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al gene a ion cos by
clus e ing wi h load, sola , and wind da a all wi h he same weigh .
Figu e 15 showcases an example o using Euclidean dis ance be ween o iginal and clus e ed inpu
da ase s as accu acy me ics, opposed o he model ou pu me ics we ha e used. In his example,
esul s always ge be e as k numbe o clus e s inc eases, since mo e o he o al o iginal da ase is
used ia medoids. Wind appea s o be mo e di icul o clus e han load and sola , due i ’s he ola ili y
men ion in sec ion 4.2. E en hough he Euclidean dis ance o Sola seems o be e y low, i does no
mean i is su icien ly ep esen ed wi h only one day, emphasising he need o judge he clus e ing
based on i s e ec s on model ou pu s a he han i s inpu s.
20
Assuming ha ne load is demanding all gene a o s o p oduce a ha poin in ime since gas was he
las gene a o in he me i o de .
28
Figu e 15 – Euclidean dis ance be ween o iginal inpu da a (o load, sola and wind) and he medoids
om clus e ing wi h hese dimensions all wi h he same weigh , by numbe o clus e s.
Figu e 16 o Figu e 18 showcase how clus e ing wi h da a in CET e sus UTC can lead o di e en model
esul s, depending on he dimensions used o clus e . When clus e ing only wi h load, sola and wind
da a, ime seasonali y did appea o ha e an impac on he esul s (see Figu e 16). Howe e , when
hyd o was included in he clus e ing, his impac ended o ade, wi h he dis inc ion becoming unclea
(see Figu e 17 and Figu e 18).
Because o he da a cons ain s on na u al in low o hyd o pumped s o age and ese oi (men ioned
in sec ion 4) hese dimensions only ha e weekly a iances. Fo his eason i came wi h no su p ise
ha in oducing hese dimensions led o ading he di e ences be ween using CET and UTC da a.
Howe e , his also happened when only in oducing hyd o un-o - i e . This migh ha e o do wi h
na u al i e in low no being linked o schedules bu a he wi h na u al e en s (e.g., empe a u e
changes). This means ha using inpu da a in CET ins ead o UTC migh no impac sys ems whe e he
o e whelming p esence o IRES educes he ela i e impo ance o demand in he model.
29
Figu e 16 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 3 dimensions (load,
sola , and wind) all wi h he same weigh .
Figu e 17 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 4 dimensions (load,
sola , wind, and hyd o un-o - i e ) all wi h he same weigh .
30
Figu e 18 – A e age NRMSD compa ing clus e ing wi h CET s UTC da a, wi h 6 dimensions (load,
sola , wind, hyd o un-o - i e , hyd o pumped s o age, and hyd o ese oi ) all wi h he same weigh .
Figu e 19 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al gene a ion
cos by k numbe o clus e s (CET). De ail by dimensions used o clus e ing, all dimensions ha ing
he same weigh .
Figu e 19 shows he di e ence in a e age NRMSD o he h ee me ics using 3, 4, and 6 dimensions o
clus e ing. Clus e ing wi h only load, sola , and wind (3 dimension) was consis en ly he wo s op ion,
e en i no by a la ge ma gin. Clus e ing wi h 4 and 6 dimensions e u ned compa able esul s,
al hough clus e ing wi h he 6 dimensions showed some sepa a ion wi h mo e han 10 clus e s,
con e ging again wi h o e 20 clus e s. This happens because wi h ewe k clus e s he clus e ing
chooses e y simila days when conside ing 6 o 4 dimensions. Howe e , as k inc eases, he clus e ing
has mo e eedom o choose a la ge a ie y o ep esen a i e days, and because i has mo e de ailed
in o ma ion wi h 6 dimensions han wi h 4, i ends o choose ep esen a i e days mo e accu a ely.
This shows ha , i we can use a highe k numbe o clus e s, i is use ul o include mul iple hyd o se ies.
31
The a e age educ ion on he a e age NRMSD o he h ee compa ison me ics o k clus e s be ween
1-20 was 32% om using 3 o 4 clus e dimension, and 11% om using 4 o 6 dimensions.
F om hese igu es we can also in e ha , e en hough he e o ends o all as k g ows, he inc ease
in accu acy becomes a he low wi h k la ge han 12. In ui i ely using he elbow me hod and also by
analysing he dec easing a e-o - e u n, be ween 4 and 8 clus e s would be conside ed he cu -o
poin since a e ha he e u n becomes esidual. This numbe o days needed o e icien ly ep esen
he sys em is sligh ly lowe han in mos o simila s udies (on di e en sys ems). To accu a ely model
G ea B i ain’s elec ici y sys em G een e al. (2014) used 6 o 10 ep esen a i e days, while P enninge
(2017) ound he bes ade-o be ween 10 o 15.
Figu e 20 – A e age NRMSD o p ice du a ion cu e, gene a ion by uni ype, and o al gene a ion
cos by numbe o clus e s. De ail by downsampling, wi h all hou s (CET) wi h o iginal alues e sus
all 24 hou s in each day a e aged ou . Clus e ing wi h all 6 dimensions ha ing he same weigh .
Figu e 20 po ai s he e ec o downsampling in he a e age NRMSD o he h ee compa ison me ics.
Reducing in aday g anula i y by a e aging ou consecu i e hou s had li le o no e ec on model
esul s acco ding o all h ee o he accu acy me ics used. Figu e 21 depic s a simila compa ison, bu
his ime clus e ing wi h only 3 dimensions. While in his case downsampling in oduced e en mo e
ola ili y o he esul s, he o e all di e ences we e a a he small and no conclusi e dec ease in
accu acy. These esul s, al hough o a di e en sys em and using di e en me ics, oppose he
conclusions om P enninge (2017) s a ing ha downsampling consis en ly wo sens esul s when
conside ing high sha es o IRES by smoo hing peak demand.
38
complexi y- educ ion echnique should be u he s udied in o he models o he Po uguese sys em
whe e all inpu da a dimensions ha e ull (hou ly) g anula i y.
39
7. LIMITATIONS AND RECOMMENDATIONS FOR FUTURE WORKS
This s udy expanded he li e a u e by in es iga ing me hods o c ea e ep esen a i e days o he
Po uguese elec ici y sys em, combining di e en compa ison me ics wi h mul iple clus e ing, ime
seasonali y, downsampling and weigh ing echniques. Howe e , he esea ch needed o make
assump ions and o e come challenges ha may ha e implica ions in he esul s. In addi ion, hese
indings sugges u he a eas o explo a ion.
Hyd o gene a ion is impo an o some coun ies like Po ugal, howe e he a ailable hyd o da a was
limi ed because ENTSO-E’s TP only publishes weekly hyd o s o age da a, needed o calcula e na u al
in low o hyd o pumped s o age and hyd o ese oi . We belie e ha ha ing a hyd o pumped s o age
and hyd o ese oi da ase wi h less g anula i y (weekly) han he es o he da ase (hou ly) migh
ha e educed he ele ance o he conclusions aken when compa ing clus e ing wi h all 6 dimensions.
We hus een o ce he need o mo e comple e, cen alised, ha monised, and well-documen ed powe
sys em modelling da a sou ces as p esen ed by Wiese e al. (2018). As p osume s, V2G, and g een
ene gy demand become e e mo e equen , he impo ance o including hem in powe sys em
models also inc eases. Howe e , his will only be possible wi h he publica ion o eliable, consis en ,
and well-documen ed da a on hese dimensions.
The h ee model accu acy measu es used (NRMSD o hou ly p ice du a ion cu e, yea ly gene a ion
pe uni ype, and yea ly o al cos s) ended o be a he co ela ed be ween each o he , indica ing
ha all h ee me ics we e b oadly measu ing model pe o mance and no p o iding con adic o y
esul s. Howe e , hey also ended o ha e small NRMSD a ia ion be ween di e en k numbe o
clus e s and clus e ing echniques, limi ing he ange o compa isons ha could be made.
F om his expe ience we conclude ha mo e di e si ied compa ison me ics could be es ed o a mo e
insigh ul compa ison, e en ually using me ics ha ake in o accoun high and low peak e en s.
Ex eme e en s (a bo h ends o he spec um) a e he mos di icul o model and can ha e g ea
impac s on build decisions. Fo example, long pe iods o d ough can mean ha mo e dispa chable
powe plan s migh need o be buil in o de o coun e balance IRES’s ola ili y, as dispa chable hyd o
would no ha e enough s o ed ene gy o peak sha ing.
Some o he a o emen ioned esul s’ ola ili y could ha e been in oduced by using k-medoids, so o
u u e wo ks we sugges compa ing esul s wi h di e en clus e ing me hods, namely by choosing a
medoid only a e all k-means i e a ions ha e an, as pe o med by Pineda & Mo ales (2018). DTW
could also be implemen ed wi h he men ioned clus e ing echniques. Howe e , he da ase s would
need o be se ou di e en ly, as conca ena ing a ious dimensions he way we did i (see sec ion 4.3)
b eaks he in e empo al sequence o a imese ies.
Di e en ly weigh ing clus e ing inpu dimensions was shown o be able o imp o e modelling esul s.
Howe e , we we e no able o s udy how case-speci ic hese indings a e, and wha a e he
consequences o main aining he weigh s o each dimension as a sys em e ol es and changes i s
dynamics, namely when he pene a ion o IRES inc eases. In o de o ind op imal weigh s, a
co ela ion be ween each dimension’s cha ac e is ics and i s weigh could be es ablished and
compa ed in models wi h di e en capaci y mixes. Ideally, in es iga ing a o mula o deciding he
weigh o each dimension based on hei ela i e capaci y, ola ili y, p o ile ype, and o he a ibu es.
40
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45
9. ANNEXES
The demons a ion bellow demons a es how weigh ing dimensions in he Euclidean dis ance is
equi alen o mul iplying he alues o a dimension by he squa e oo o he weigh igh be o e
calcula ing he Euclidean dis ance. This example showcases ha including a dimension wice in he
Euclidean dis ance is equi alen o weigh ing he same dimension by 2 using he squa e oo o he
weigh .
𝑑(𝑎𝑖,𝑏𝑖)=√(𝑎𝑖,𝑥 −𝑏𝑖,𝑥)2+(𝑎𝑖,𝑦 −𝑏𝑖,𝑦)2+(𝑎𝑖,𝑦 −𝑏𝑖,𝑦)2=√(𝑎𝑖,𝑥 −𝑏𝑖,𝑥)2+2∗(𝑎𝑖,𝑦 −𝑏𝑖,𝑦)2
=√(𝑎𝑖,𝑥 −𝑏𝑖,𝑥)2+(√2(𝑎𝑖,𝑦 −𝑏𝑖,𝑦))2=√(𝑎𝑖,𝑥 −𝑏𝑖,𝑥)2+(√2∗𝑎𝑖,𝑦 −√2∗𝑏𝑖,𝑦))2
Whe e 𝑖 is he hou o he days 𝑎 and 𝑏, o he dimensions 𝑥 and 𝑦.
46
Table 4 – De ailed model esul s o all model uns wi h clus e ed da a
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
0,5
1
1
1
1
1
24
CET
6
0,121
0,078
0,092
0,097
0%
9%
18%
2%
70%
0,5
1
1
1
1
1
24
CET
8
0,100
0,075
0,054
0,076
0%
28%
59%
6%
7%
0,5
1
1
1
1
1
24
CET
10
0,067
0,050
0,041
0,053
5%
46%
47%
1%
1%
0,5
1
1
1
1
1
24
CET
12
0,081
0,051
0,049
0,061
5%
31%
54%
2%
9%
0,5
1
1
1
1
1
24
CET
14
0,067
0,036
0,028
0,044
29%
0%
1%
39%
31%
0,5
1,5
1,5
1
1
1
24
CET
6
0,119
0,091
0,101
0,103
14%
32%
34%
16%
5%
0,5
1,5
1,5
1
1
1
24
CET
8
0,124
0,081
0,085
0,097
9%
8%
71%
1%
11%
0,5
1,5
1,5
1
1
1
24
CET
10
0,123
0,085
0,090
0,099
2%
1%
61%
21%
15%
0,5
1,5
1,5
1
1
1
24
CET
12
0,114
0,068
0,074
0,085
7%
6%
51%
31%
5%
0,5
1,5
1,5
1
1
1
24
CET
14
0,112
0,063
0,066
0,080
27%
1%
41%
20%
11%
1
0,5
1
1
1
1
24
CET
6
0,137
0,087
0,055
0,093
1%
0%
3%
0%
96%
1
0,5
1
1
1
1
24
CET
8
0,140
0,070
0,047
0,086
16%
0%
17%
5%
61%
47
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
0,5
1
1
1
1
24
CET
10
0,106
0,068
0,053
0,075
26%
22%
10%
3%
38%
1
0,5
1
1
1
1
24
CET
12
0,100
0,058
0,035
0,064
36%
0%
8%
0%
55%
1
0,5
1
1
1
1
24
CET
14
0,096
0,051
0,045
0,064
25%
13%
7%
1%
54%
1
1
0,5
1
1
1
24
CET
6
0,147
0,122
0,097
0,122
8%
14%
0%
9%
68%
1
1
0,5
1
1
1
24
CET
8
0,140
0,098
0,086
0,108
7%
9%
4%
53%
27%
1
1
0,5
1
1
1
24
CET
10
0,132
0,087
0,081
0,100
1%
8%
16%
37%
38%
1
1
0,5
1
1
1
24
CET
12
0,124
0,074
0,074
0,091
5%
29%
8%
29%
29%
1
1
0,5
1
1
1
24
CET
14
0,116
0,075
0,071
0,087
6%
9%
27%
21%
38%
1
1
1
0
0
0
1
CET
1
0,445
0,483
0,458
0,462
43%
12%
3%
4%
39%
1
1
1
0
0
0
1
CET
2
0,445
0,315
0,319
0,360
49%
14%
0%
16%
21%
1
1
1
0
0
0
1
CET
3
0,445
0,321
0,307
0,358
48%
0%
0%
26%
26%
1
1
1
0
0
0
1
CET
4
0,202
0,224
0,208
0,211
15%
14%
25%
5%
41%
1
1
1
0
0
0
1
CET
5
0,234
0,213
0,137
0,195
1%
38%
38%
15%
7%
1
1
1
0
0
0
1
CET
6
0,254
0,212
0,191
0,219
39%
17%
34%
8%
1%
54
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0
0
1
CET
6
0,154
0,114
0,061
0,110
1%
7%
1%
85%
6%
1
1
1
1
0
0
1
CET
7
0,137
0,079
0,057
0,091
29%
1%
16%
50%
4%
1
1
1
1
0
0
1
CET
8
0,178
0,088
0,042
0,103
31%
2%
24%
40%
3%
1
1
1
1
0
0
1
CET
9
0,149
0,086
0,038
0,091
44%
43%
2%
10%
0%
1
1
1
1
0
0
1
CET
10
0,142
0,113
0,068
0,107
30%
13%
20%
7%
29%
1
1
1
1
0
0
1
CET
11
0,117
0,110
0,089
0,106
1%
24%
41%
4%
30%
1
1
1
1
0
0
1
CET
12
0,107
0,060
0,025
0,064
27%
1%
3%
0%
69%
1
1
1
1
0
0
1
CET
13
0,105
0,057
0,035
0,065
31%
16%
16%
6%
31%
1
1
1
1
0
0
1
CET
14
0,094
0,060
0,036
0,063
9%
8%
68%
12%
3%
1
1
1
1
0
0
1
CET
15
0,100
0,068
0,052
0,073
15%
37%
8%
35%
5%
1
1
1
1
0
0
1
CET
16
0,117
0,065
0,048
0,076
25%
28%
15%
15%
17%
1
1
1
1
0
0
1
CET
17
0,090
0,057
0,040
0,062
0%
46%
44%
4%
5%
1
1
1
1
0
0
1
CET
18
0,097
0,049
0,030
0,059
0%
12%
36%
0%
52%
1
1
1
1
0
0
1
CET
19
0,105
0,054
0,026
0,062
10%
2%
39%
17%
33%
55
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0
0
1
CET
20
0,092
0,053
0,025
0,057
2%
13%
32%
26%
27%
1
1
1
1
0
0
1
CET
25
0,069
0,042
0,031
0,048
0%
3%
46%
3%
48%
1
1
1
1
0
0
1
CET
30
0,066
0,044
0,035
0,048
7%
3%
65%
2%
23%
1
1
1
1
0
0
1
CET
40
0,057
0,041
0,028
0,042
2%
5%
35%
1%
58%
1
1
1
1
0
0
1
CET
50
0,063
0,034
0,022
0,040
28%
15%
5%
7%
44%
1
1
1
1
0
0
1
CET
100
0,033
0,035
0,027
0,032
3%
5%
1%
57%
34%
1
1
1
1
0
0
24
CET
1
0,445
0,311
0,315
0,357
24%
4%
21%
10%
41%
1
1
1
1
0
0
24
CET
2
0,254
0,173
0,153
0,194
23%
8%
7%
6%
56%
1
1
1
1
0
0
24
CET
3
0,169
0,145
0,126
0,147
34%
5%
43%
6%
12%
1
1
1
1
0
0
24
CET
4
0,064
0,121
0,107
0,097
7%
0%
51%
9%
33%
1
1
1
1
0
0
24
CET
5
0,067
0,125
0,099
0,097
2%
18%
48%
7%
26%
1
1
1
1
0
0
24
CET
6
0,058
0,097
0,075
0,076
2%
51%
5%
8%
35%
1
1
1
1
0
0
24
CET
7
0,049
0,081
0,065
0,065
6%
26%
1%
4%
63%
1
1
1
1
0
0
24
CET
8
0,118
0,094
0,085
0,099
0%
15%
59%
25%
0%
56
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0
0
24
CET
9
0,125
0,076
0,060
0,087
8%
0%
77%
6%
8%
1
1
1
1
0
0
24
CET
10
0,091
0,090
0,077
0,086
13%
2%
45%
1%
39%
1
1
1
1
0
0
24
CET
11
0,089
0,099
0,087
0,092
11%
0%
31%
3%
55%
1
1
1
1
0
0
24
CET
12
0,102
0,089
0,077
0,089
20%
13%
17%
9%
41%
1
1
1
1
0
0
24
CET
13
0,107
0,096
0,088
0,097
20%
14%
23%
11%
32%
1
1
1
1
0
0
24
CET
14
0,103
0,085
0,071
0,086
9%
22%
31%
10%
27%
1
1
1
1
0
0
24
CET
15
0,101
0,083
0,070
0,084
9%
14%
33%
7%
37%
1
1
1
1
0
0
24
CET
16
0,085
0,078
0,063
0,075
3%
3%
33%
9%
51%
1
1
1
1
0
0
24
CET
17
0,084
0,084
0,077
0,082
5%
6%
39%
10%
40%
1
1
1
1
0
0
24
CET
18
0,084
0,069
0,062
0,072
1%
4%
55%
6%
35%
1
1
1
1
0
0
24
CET
19
0,076
0,077
0,072
0,075
0%
11%
40%
6%
44%
1
1
1
1
0
0
24
CET
20
0,078
0,082
0,076
0,078
2%
14%
25%
19%
40%
1
1
1
1
0
0
24
CET
25
0,071
0,047
0,041
0,053
2%
2%
50%
1%
46%
1
1
1
1
0
0
24
CET
30
0,071
0,047
0,039
0,053
6%
1%
51%
0%
42%
57
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0
0
24
CET
40
0,066
0,050
0,045
0,054
5%
15%
7%
7%
66%
1
1
1
1
0
0
24
CET
50
0,056
0,036
0,034
0,042
14%
31%
6%
9%
40%
1
1
1
1
0
0
24
CET
100
0,056
0,019
0,020
0,032
26%
1%
5%
38%
31%
1
1
1
1
0
0
24
UTC
1
0,439
0,291
0,289
0,340
25%
3%
25%
10%
38%
1
1
1
1
0
0
24
UTC
2
0,241
0,190
0,186
0,206
19%
27%
23%
2%
29%
1
1
1
1
0
0
24
UTC
3
0,169
0,167
0,151
0,162
1%
13%
54%
5%
27%
1
1
1
1
0
0
24
UTC
4
0,098
0,145
0,093
0,112
1%
9%
39%
40%
10%
1
1
1
1
0
0
24
UTC
5
0,069
0,112
0,069
0,084
21%
0%
26%
36%
17%
1
1
1
1
0
0
24
UTC
6
0,068
0,097
0,073
0,079
8%
37%
1%
6%
48%
1
1
1
1
0
0
24
UTC
7
0,093
0,108
0,080
0,094
11%
3%
60%
12%
15%
1
1
1
1
0
0
24
UTC
8
0,129
0,110
0,075
0,104
2%
5%
48%
44%
0%
1
1
1
1
0
0
24
UTC
9
0,122
0,099
0,073
0,098
2%
12%
35%
48%
4%
1
1
1
1
0
0
24
UTC
10
0,133
0,086
0,073
0,097
26%
0%
48%
16%
10%
1
1
1
1
0
0
24
UTC
11
0,114
0,080
0,066
0,087
27%
0%
47%
3%
23%
58
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0
0
24
UTC
12
0,126
0,079
0,073
0,093
25%
0%
69%
1%
5%
1
1
1
1
0
0
24
UTC
13
0,126
0,071
0,066
0,087
44%
0%
55%
1%
0%
1
1
1
1
0
0
24
UTC
14
0,120
0,066
0,051
0,079
18%
5%
55%
20%
0%
1
1
1
1
0
0
24
UTC
15
0,112
0,066
0,055
0,078
14%
8%
56%
20%
1%
1
1
1
1
0
0
24
UTC
16
0,097
0,062
0,058
0,072
6%
0%
78%
14%
2%
1
1
1
1
0
0
24
UTC
17
0,093
0,060
0,059
0,071
2%
3%
65%
20%
10%
1
1
1
1
0
0
24
UTC
18
0,090
0,061
0,061
0,071
6%
3%
55%
31%
5%
1
1
1
1
0
0
24
UTC
19
0,083
0,044
0,039
0,055
15%
20%
50%
12%
2%
1
1
1
1
0
0
24
UTC
20
0,054
0,040
0,039
0,044
4%
15%
38%
38%
6%
1
1
1
1
0
0
24
UTC
25
0,085
0,038
0,021
0,048
15%
51%
0%
25%
9%
1
1
1
1
0
0
24
UTC
30
0,092
0,042
0,031
0,055
10%
6%
72%
6%
6%
1
1
1
1
0
0
24
UTC
40
0,065
0,041
0,033
0,046
8%
4%
44%
13%
31%
1
1
1
1
0
0
24
UTC
50
0,068
0,038
0,028
0,045
0%
15%
64%
2%
19%
1
1
1
1
0
0
24
UTC
100
0,048
0,021
0,016
0,028
18%
19%
10%
3%
50%
59
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
0,5
1
24
CET
6
0,109
0,078
0,037
0,075
7%
0%
7%
58%
29%
1
1
1
1
0,5
1
24
CET
8
0,101
0,071
0,050
0,074
3%
28%
23%
24%
22%
1
1
1
1
0,5
1
24
CET
10
0,107
0,058
0,058
0,075
1%
18%
48%
8%
25%
1
1
1
1
0,5
1
24
CET
12
0,087
0,045
0,040
0,057
9%
27%
42%
2%
20%
1
1
1
1
0,5
1
24
CET
14
0,080
0,042
0,030
0,051
22%
17%
28%
27%
6%
1
1
1
1
1
0,5
24
CET
6
0,109
0,078
0,037
0,075
7%
0%
5%
59%
29%
1
1
1
1
1
0,5
24
CET
8
0,102
0,071
0,051
0,075
3%
27%
22%
24%
24%
1
1
1
1
1
0,5
24
CET
10
0,107
0,058
0,058
0,075
1%
18%
48%
8%
25%
1
1
1
1
1
0,5
24
CET
12
0,087
0,045
0,040
0,057
9%
27%
42%
2%
20%
1
1
1
1
1
0,5
24
CET
14
0,080
0,039
0,032
0,050
19%
27%
24%
24%
5%
1
1
1
1
1
1
1
CET
1
0,445
0,331
0,332
0,369
67%
0%
19%
13%
1%
1
1
1
1
1
1
1
CET
2
0,251
0,154
0,130
0,179
1%
63%
12%
3%
22%
1
1
1
1
1
1
1
CET
3
0,203
0,105
0,066
0,125
9%
65%
19%
1%
6%
1
1
1
1
1
1
1
CET
4
0,129
0,111
0,110
0,116
2%
68%
28%
0%
1%
60
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
1
1
1
CET
5
0,117
0,085
0,059
0,087
40%
21%
4%
2%
34%
1
1
1
1
1
1
1
CET
6
0,127
0,079
0,056
0,088
3%
87%
7%
1%
3%
1
1
1
1
1
1
1
CET
7
0,130
0,059
0,033
0,074
4%
75%
11%
3%
7%
1
1
1
1
1
1
1
CET
8
0,174
0,090
0,083
0,115
1%
10%
47%
14%
27%
1
1
1
1
1
1
1
CET
9
0,158
0,082
0,066
0,102
1%
5%
43%
23%
28%
1
1
1
1
1
1
1
CET
10
0,146
0,067
0,048
0,087
3%
5%
32%
7%
53%
1
1
1
1
1
1
1
CET
11
0,143
0,061
0,042
0,082
29%
5%
15%
9%
42%
1
1
1
1
1
1
1
CET
12
0,133
0,059
0,027
0,073
68%
0%
7%
3%
22%
1
1
1
1
1
1
1
CET
13
0,130
0,067
0,030
0,076
81%
13%
0%
2%
5%
1
1
1
1
1
1
1
CET
14
0,117
0,059
0,032
0,069
59%
23%
6%
12%
0%
1
1
1
1
1
1
1
CET
15
0,108
0,062
0,038
0,069
46%
32%
2%
8%
12%
1
1
1
1
1
1
1
CET
16
0,093
0,052
0,030
0,058
38%
10%
7%
1%
44%
1
1
1
1
1
1
1
CET
17
0,089
0,052
0,029
0,056
33%
6%
20%
12%
29%
1
1
1
1
1
1
1
CET
18
0,083
0,052
0,028
0,054
19%
8%
21%
13%
40%
61
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
1
1
1
CET
19
0,084
0,046
0,018
0,049
16%
12%
35%
31%
6%
1
1
1
1
1
1
1
CET
20
0,091
0,045
0,023
0,053
5%
9%
4%
81%
1%
1
1
1
1
1
1
1
CET
25
0,080
0,041
0,020
0,047
32%
56%
4%
5%
3%
1
1
1
1
1
1
1
CET
30
0,078
0,037
0,022
0,046
45%
45%
0%
2%
8%
1
1
1
1
1
1
1
CET
40
0,072
0,030
0,013
0,039
2%
79%
1%
6%
13%
1
1
1
1
1
1
1
CET
50
0,060
0,031
0,015
0,035
6%
0%
47%
41%
7%
1
1
1
1
1
1
1
CET
100
0,059
0,022
0,010
0,030
0%
29%
17%
25%
29%
1
1
1
1
1
1
2
CET
6
0,156
0,088
0,088
0,111
8%
33%
9%
7%
42%
1
1
1
1
1
1
2
CET
8
0,155
0,066
0,061
0,094
4%
24%
8%
54%
11%
1
1
1
1
1
1
2
CET
10
0,115
0,050
0,024
0,063
38%
8%
1%
31%
21%
1
1
1
1
1
1
2
CET
12
0,114
0,053
0,035
0,067
43%
3%
13%
37%
4%
1
1
1
1
1
1
2
CET
14
0,111
0,052
0,040
0,068
24%
10%
29%
37%
0%
1
1
1
1
1
1
3
CET
6
0,112
0,081
0,066
0,086
27%
19%
6%
3%
44%
1
1
1
1
1
1
3
CET
8
0,101
0,061
0,038
0,067
19%
1%
31%
16%
33%
62
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
1
1
3
CET
10
0,120
0,067
0,064
0,084
28%
0%
40%
29%
3%
1
1
1
1
1
1
3
CET
12
0,103
0,055
0,050
0,069
43%
5%
27%
22%
3%
1
1
1
1
1
1
3
CET
14
0,108
0,056
0,057
0,074
24%
26%
23%
22%
5%
1
1
1
1
1
1
4
CET
6
0,131
0,073
0,027
0,077
19%
37%
16%
22%
6%
1
1
1
1
1
1
4
CET
8
0,123
0,102
0,083
0,103
21%
20%
4%
33%
22%
1
1
1
1
1
1
4
CET
10
0,131
0,092
0,076
0,100
50%
7%
2%
25%
16%
1
1
1
1
1
1
4
CET
12
0,100
0,055
0,045
0,066
35%
11%
21%
32%
1%
1
1
1
1
1
1
4
CET
14
0,115
0,047
0,032
0,065
21%
6%
14%
45%
13%
1
1
1
1
1
1
6
CET
6
0,137
0,110
0,086
0,111
6%
27%
2%
12%
52%
1
1
1
1
1
1
6
CET
8
0,089
0,063
0,044
0,065
4%
19%
1%
53%
22%
1
1
1
1
1
1
6
CET
10
0,116
0,054
0,040
0,070
25%
8%
0%
25%
41%
1
1
1
1
1
1
6
CET
12
0,119
0,076
0,066
0,087
18%
48%
11%
1%
23%
1
1
1
1
1
1
6
CET
14
0,104
0,056
0,037
0,066
33%
41%
3%
3%
21%
1
1
1
1
1
1
8
CET
6
0,138
0,088
0,060
0,095
17%
3%
6%
26%
47%
63
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
1
1
1
1
8
CET
8
0,109
0,062
0,043
0,071
0%
0%
7%
75%
18%
1
1
1
1
1
1
8
CET
10
0,116
0,063
0,056
0,078
1%
43%
1%
11%
43%
1
1
1
1
1
1
8
CET
12
0,096
0,056
0,045
0,066
0%
77%
6%
9%
7%
1
1
1
1
1
1
8
CET
14
0,092
0,041
0,025
0,053
0%
58%
3%
2%
37%
1
1
1
1
1
1
12
CET
6
0,122
0,074
0,050
0,082
69%
0%
18%
12%
0%
1
1
1
1
1
1
12
CET
8
0,104
0,066
0,058
0,076
2%
6%
1%
37%
53%
1
1
1
1
1
1
12
CET
10
0,115
0,071
0,062
0,083
13%
1%
3%
50%
34%
1
1
1
1
1
1
12
CET
12
0,108
0,060
0,058
0,076
15%
3%
26%
31%
26%
1
1
1
1
1
1
12
CET
14
0,115
0,067
0,061
0,081
9%
22%
31%
0%
38%
1
1
1
1
1
1
24
CET
1
0,445
0,307
0,293
0,348
27%
0%
25%
12%
36%
1
1
1
1
1
1
24
CET
2
0,164
0,137
0,111
0,137
38%
2%
17%
4%
39%
1
1
1
1
1
1
24
CET
3
0,233
0,167
0,150
0,183
17%
20%
11%
0%
51%
1
1
1
1
1
1
24
CET
4
0,149
0,091
0,068
0,102
27%
28%
40%
4%
0%
1
1
1
1
1
1
24
CET
5
0,107
0,109
0,083
0,100
21%
50%
25%
1%
3%
70
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1
2
1
1
1
24
CET
14
0,103
0,052
0,054
0,069
3%
6%
6%
62%
24%
1
1,2
1
1
1
1
24
CET
6
0,101
0,086
0,063
0,083
4%
26%
4%
49%
16%
1
1,2
1
1
1
1
24
CET
8
0,146
0,087
0,066
0,099
3%
4%
1%
36%
56%
1
1,2
1
1
1
1
24
CET
10
0,116
0,067
0,056
0,080
11%
0%
6%
2%
81%
1
1,2
1
1
1
1
24
CET
12
0,103
0,061
0,049
0,071
1%
1%
0%
32%
66%
1
1,2
1
1
1
1
24
CET
14
0,096
0,053
0,041
0,063
2%
3%
27%
16%
52%
1
1,2
1,2
1
1
1
24
CET
6
0,100
0,079
0,083
0,087
49%
1%
34%
9%
7%
1
1,2
1,2
1
1
1
24
CET
8
0,111
0,071
0,065
0,082
8%
18%
68%
4%
2%
1
1,2
1,2
1
1
1
24
CET
10
0,115
0,074
0,070
0,086
9%
6%
51%
0%
34%
1
1,2
1,2
1
1
1
24
CET
12
0,114
0,050
0,035
0,067
8%
2%
20%
5%
64%
1
1,2
1,2
1
1
1
24
CET
14
0,108
0,052
0,041
0,067
21%
13%
6%
44%
17%
1
1,3
1,3
1
1
1
24
CET
6
0,085
0,074
0,053
0,071
1%
0%
2%
82%
15%
1
1,3
1,3
1
1
1
24
CET
8
0,103
0,071
0,059
0,078
0%
22%
10%
51%
16%
1
1,3
1,3
1
1
1
24
CET
10
0,101
0,065
0,053
0,073
2%
15%
6%
29%
49%
71
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,3
1,3
1
1
1
24
CET
12
0,089
0,051
0,044
0,061
21%
11%
2%
49%
16%
1
1,3
1,3
1
1
1
24
CET
14
0,109
0,058
0,053
0,073
20%
21%
10%
35%
14%
1
1,4
1,4
1
1
1
24
CET
6
0,118
0,084
0,058
0,087
5%
34%
49%
12%
0%
1
1,4
1,4
1
1
1
24
CET
8
0,134
0,073
0,061
0,089
0%
21%
36%
36%
6%
1
1,4
1,4
1
1
1
24
CET
10
0,101
0,069
0,068
0,079
0%
8%
86%
5%
0%
1
1,4
1,4
1
1
1
24
CET
12
0,091
0,053
0,055
0,066
6%
8%
74%
4%
7%
1
1,4
1,4
1
1
1
24
CET
14
0,075
0,049
0,045
0,056
2%
18%
39%
18%
24%
1
1,5
1
1
1
1
24
CET
6
0,134
0,092
0,076
0,101
25%
2%
0%
16%
57%
1
1,5
1
1
1
1
24
CET
8
0,104
0,075
0,043
0,074
9%
25%
14%
0%
52%
1
1,5
1
1
1
1
24
CET
10
0,109
0,064
0,040
0,071
15%
6%
8%
4%
68%
1
1,5
1
1
1
1
24
CET
12
0,090
0,051
0,026
0,056
13%
12%
23%
2%
49%
1
1,5
1
1
1
1
24
CET
14
0,090
0,067
0,053
0,070
18%
28%
21%
10%
23%
1
1,5
1,5
0,5
0,5
0,5
24
CET
6
0,137
0,080
0,060
0,092
14%
24%
1%
27%
35%
1
1,5
1,5
0,5
0,5
0,5
24
CET
8
0,134
0,083
0,072
0,097
11%
0%
33%
45%
11%
72
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,5
1,5
0,5
0,5
0,5
24
CET
10
0,114
0,062
0,043
0,073
38%
48%
0%
8%
7%
1
1,5
1,5
0,5
0,5
0,5
24
CET
12
0,112
0,056
0,052
0,074
29%
1%
35%
29%
6%
1
1,5
1,5
0,5
0,5
0,5
24
CET
14
0,112
0,049
0,047
0,069
30%
3%
8%
59%
0%
1
1,5
1,5
1
1
1
1
CET
1
0,445
0,349
0,353
0,382
59%
12%
17%
11%
1%
1
1,5
1,5
1
1
1
1
CET
2
0,268
0,160
0,122
0,184
0%
6%
14%
58%
22%
1
1,5
1,5
1
1
1
1
CET
3
0,238
0,125
0,105
0,156
37%
3%
0%
49%
11%
1
1,5
1,5
1
1
1
1
CET
4
0,196
0,094
0,044
0,112
43%
6%
16%
8%
28%
1
1,5
1,5
1
1
1
1
CET
5
0,165
0,080
0,056
0,100
23%
0%
9%
5%
63%
1
1,5
1,5
1
1
1
1
CET
6
0,146
0,074
0,047
0,089
53%
12%
13%
0%
21%
1
1,5
1,5
1
1
1
1
CET
7
0,141
0,067
0,032
0,080
74%
11%
15%
1%
0%
1
1,5
1,5
1
1
1
1
CET
8
0,126
0,074
0,048
0,083
2%
56%
0%
38%
4%
1
1,5
1,5
1
1
1
1
CET
9
0,139
0,073
0,051
0,088
2%
46%
8%
35%
9%
1
1,5
1,5
1
1
1
1
CET
10
0,145
0,063
0,047
0,085
13%
47%
5%
30%
6%
1
1,5
1,5
1
1
1
1
CET
11
0,134
0,063
0,051
0,083
0%
57%
6%
24%
13%
73
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,5
1,5
1
1
1
1
CET
12
0,121
0,058
0,029
0,069
41%
4%
27%
17%
10%
1
1,5
1,5
1
1
1
1
CET
13
0,119
0,063
0,032
0,071
9%
1%
60%
26%
4%
1
1,5
1,5
1
1
1
1
CET
14
0,122
0,056
0,032
0,070
27%
12%
2%
60%
0%
1
1,5
1,5
1
1
1
1
CET
15
0,121
0,051
0,028
0,067
24%
16%
7%
53%
1%
1
1,5
1,5
1
1
1
1
CET
16
0,121
0,050
0,019
0,064
15%
44%
13%
11%
16%
1
1,5
1,5
1
1
1
1
CET
17
0,112
0,049
0,019
0,060
4%
59%
15%
0%
22%
1
1,5
1,5
1
1
1
1
CET
18
0,112
0,051
0,033
0,065
0%
48%
47%
1%
4%
1
1,5
1,5
1
1
1
1
CET
19
0,106
0,047
0,027
0,060
32%
44%
13%
9%
2%
1
1,5
1,5
1
1
1
1
CET
20
0,112
0,049
0,033
0,065
23%
16%
58%
3%
0%
1
1,5
1,5
1
1
1
1
CET
25
0,082
0,045
0,025
0,051
15%
0%
36%
45%
4%
1
1,5
1,5
1
1
1
1
CET
30
0,056
0,044
0,031
0,044
1%
3%
2%
34%
60%
1
1,5
1,5
1
1
1
1
CET
40
0,068
0,034
0,014
0,039
8%
9%
8%
34%
42%
1
1,5
1,5
1
1
1
1
CET
50
0,076
0,028
0,007
0,037
28%
19%
0%
27%
26%
1
1,5
1,5
1
1
1
1
CET
100
0,045
0,024
0,011
0,027
3%
52%
37%
0%
8%
74
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,5
1,5
1
1
1
24
CET
1
0,445
0,307
0,293
0,348
27%
0%
25%
12%
36%
1
1,5
1,5
1
1
1
24
CET
2
0,184
0,152
0,112
0,149
28%
23%
15%
3%
30%
1
1,5
1,5
1
1
1
24
CET
3
0,192
0,140
0,129
0,153
11%
43%
2%
8%
36%
1
1,5
1,5
1
1
1
24
CET
4
0,180
0,115
0,102
0,132
30%
32%
0%
1%
37%
1
1,5
1,5
1
1
1
24
CET
5
0,126
0,070
0,045
0,080
16%
4%
67%
13%
0%
1
1,5
1,5
1
1
1
24
CET
6
0,117
0,059
0,043
0,073
11%
7%
58%
25%
0%
1
1,5
1,5
1
1
1
24
CET
7
0,130
0,071
0,057
0,086
0%
0%
44%
25%
31%
1
1,5
1,5
1
1
1
24
CET
8
0,103
0,060
0,040
0,067
0%
1%
31%
51%
17%
1
1,5
1,5
1
1
1
24
CET
9
0,103
0,063
0,043
0,070
1%
0%
0%
83%
15%
1
1,5
1,5
1
1
1
24
CET
10
0,087
0,056
0,025
0,056
1%
9%
43%
46%
1%
1
1,5
1,5
1
1
1
24
CET
11
0,091
0,053
0,018
0,054
0%
3%
42%
54%
1%
1
1,5
1,5
1
1
1
24
CET
12
0,092
0,059
0,044
0,065
0%
1%
13%
9%
76%
1
1,5
1,5
1
1
1
24
CET
13
0,091
0,051
0,035
0,059
5%
0%
2%
44%
49%
1
1,5
1,5
1
1
1
24
CET
14
0,088
0,049
0,033
0,057
15%
10%
1%
39%
36%
75
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,5
1,5
1
1
1
24
CET
15
0,090
0,050
0,034
0,058
3%
16%
30%
20%
31%
1
1,5
1,5
1
1
1
24
CET
16
0,096
0,047
0,035
0,059
5%
16%
24%
16%
38%
1
1,5
1,5
1
1
1
24
CET
17
0,097
0,044
0,031
0,057
1%
17%
2%
19%
62%
1
1,5
1,5
1
1
1
24
CET
18
0,094
0,047
0,040
0,060
1%
37%
16%
2%
45%
1
1,5
1,5
1
1
1
24
CET
19
0,084
0,044
0,032
0,053
3%
83%
5%
2%
7%
1
1,5
1,5
1
1
1
24
CET
20
0,088
0,043
0,033
0,055
1%
43%
41%
3%
12%
1
1,5
1,5
1
1
1
24
CET
25
0,091
0,043
0,042
0,059
13%
39%
33%
0%
15%
1
1,5
1,5
1
1
1
24
CET
30
0,088
0,036
0,035
0,053
6%
35%
35%
5%
19%
1
1,5
1,5
1
1
1
24
CET
40
0,068
0,025
0,022
0,038
17%
12%
25%
15%
31%
1
1,5
1,5
1
1
1
24
CET
50
0,069
0,026
0,022
0,039
1%
9%
37%
16%
37%
1
1,5
1,5
1
1
1
24
CET
100
0,035
0,018
0,016
0,023
4%
35%
8%
33%
20%
1
1,6
1,6
1
1
1
24
CET
6
0,084
0,068
0,051
0,068
6%
46%
36%
11%
1%
1
1,6
1,6
1
1
1
24
CET
8
0,115
0,075
0,076
0,089
9%
38%
4%
25%
24%
1
1,6
1,6
1
1
1
24
CET
10
0,115
0,066
0,066
0,082
20%
46%
0%
22%
11%
76
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
1,6
1,6
1
1
1
24
CET
12
0,097
0,059
0,050
0,069
19%
63%
3%
2%
13%
1
1,6
1,6
1
1
1
24
CET
14
0,096
0,037
0,026
0,053
29%
37%
18%
2%
14%
1
1,7
1,7
1
1
1
24
CET
6
0,096
0,073
0,062
0,077
3%
18%
28%
48%
2%
1
1,7
1,7
1
1
1
24
CET
8
0,136
0,071
0,054
0,087
4%
28%
13%
28%
27%
1
1,7
1,7
1
1
1
24
CET
10
0,118
0,060
0,048
0,075
17%
0%
70%
3%
9%
1
1,7
1,7
1
1
1
24
CET
12
0,128
0,068
0,063
0,086
13%
0%
69%
1%
17%
1
1,7
1,7
1
1
1
24
CET
14
0,109
0,061
0,065
0,078
20%
1%
73%
6%
0%
1
1,8
1,8
1
1
1
24
CET
6
0,088
0,070
0,064
0,074
5%
4%
68%
16%
6%
1
1,8
1,8
1
1
1
24
CET
8
0,135
0,082
0,082
0,099
0%
15%
22%
3%
60%
1
1,8
1,8
1
1
1
24
CET
10
0,137
0,080
0,086
0,101
4%
4%
44%
13%
34%
1
1,8
1,8
1
1
1
24
CET
12
0,123
0,067
0,072
0,087
8%
5%
49%
12%
26%
1
1,8
1,8
1
1
1
24
CET
14
0,107
0,051
0,045
0,068
22%
14%
51%
2%
11%
1
2
1
1
1
1
24
CET
6
0,093
0,062
0,042
0,066
3%
8%
77%
11%
2%
1
2
1
1
1
1
24
CET
8
0,119
0,083
0,065
0,089
0%
35%
32%
0%
32%
77
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1
2
1
1
1
1
24
CET
10
0,122
0,084
0,076
0,094
31%
17%
32%
0%
20%
1
2
1
1
1
1
24
CET
12
0,116
0,074
0,056
0,082
28%
12%
42%
2%
15%
1
2
1
1
1
1
24
CET
14
0,112
0,068
0,058
0,079
43%
7%
6%
4%
39%
1
2
2
1
1
1
24
CET
6
0,092
0,086
0,078
0,085
0%
9%
84%
7%
0%
1
2
2
1
1
1
24
CET
8
0,093
0,068
0,048
0,070
6%
0%
49%
16%
29%
1
2
2
1
1
1
24
CET
10
0,113
0,051
0,038
0,067
26%
11%
42%
13%
8%
1
2
2
1
1
1
24
CET
12
0,113
0,070
0,079
0,087
15%
6%
74%
2%
4%
1
2
2
1
1
1
24
CET
14
0,106
0,067
0,074
0,082
6%
15%
78%
1%
0%
1,5
1
1
1
1
1
24
CET
6
0,146
0,102
0,058
0,102
6%
0%
5%
23%
66%
1,5
1
1
1
1
1
24
CET
8
0,126
0,079
0,061
0,088
8%
2%
3%
74%
12%
1,5
1
1
1
1
1
24
CET
10
0,095
0,053
0,029
0,059
23%
35%
0%
42%
0%
1,5
1
1
1
1
1
24
CET
12
0,102
0,052
0,041
0,065
31%
18%
18%
12%
21%
1,5
1
1
1
1
1
24
CET
14
0,106
0,054
0,048
0,069
48%
16%
3%
2%
30%
1,5
1,5
1,5
1,5
1
1
24
CET
6
0,111
0,092
0,038
0,080
22%
8%
11%
15%
44%
78
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
1,5
1,5
1,5
1,5
1
1
24
CET
8
0,132
0,070
0,049
0,084
49%
3%
36%
1%
12%
1,5
1,5
1,5
1,5
1
1
24
CET
10
0,131
0,073
0,060
0,088
52%
4%
8%
2%
34%
1,5
1,5
1,5
1,5
1
1
24
CET
12
0,124
0,060
0,059
0,081
25%
23%
37%
6%
10%
1,5
1,5
1,5
1,5
1
1
24
CET
14
0,117
0,052
0,049
0,072
54%
1%
26%
8%
10%
2
1
1
1
1
1
24
CET
6
0,142
0,115
0,104
0,121
20%
1%
60%
7%
12%
2
1
1
1
1
1
24
CET
8
0,130
0,091
0,068
0,096
0%
1%
47%
30%
23%
2
1
1
1
1
1
24
CET
10
0,114
0,063
0,049
0,076
26%
2%
46%
8%
17%
2
1
1
1
1
1
24
CET
12
0,092
0,059
0,050
0,067
6%
13%
46%
2%
33%
2
1
1
1
1
1
24
CET
14
0,076
0,051
0,025
0,050
3%
0%
53%
5%
39%
2
2
2
1
1
1
24
CET
6
0,118
0,089
0,064
0,090
37%
0%
33%
2%
28%
2
2
2
1
1
1
24
CET
8
0,118
0,077
0,070
0,088
3%
8%
43%
2%
44%
2
2
2
1
1
1
24
CET
10
0,092
0,066
0,053
0,070
1%
0%
77%
5%
17%
2
2
2
1
1
1
24
CET
12
0,086
0,046
0,031
0,054
3%
1%
91%
4%
2%
2
2
2
1
1
1
24
CET
14
0,085
0,048
0,034
0,056
0%
17%
75%
8%
0%
79
Weigh Load
Weigh Sola
Weigh Wind
Weigh Run-o -
i e
Weigh Pumped
s o age
Weigh
Rese oi
Downsampling
(# hou s)
Time
Clus e s
NRMSD P ice
NRMSD
Gene a ion
NRMSD Cos
A e age o 3
me ics NRMSD
% NRMSD Cos
2016
% NRMSD Cos
2017
% NRMSD Cos
2018
% NRMSD Cos
2019
% NRMSD Cos
2020
2
2
2
2
1
1
24
CET
6
0,124
0,069
0,035
0,076
47%
13%
13%
9%
18%
2
2
2
2
1
1
24
CET
8
0,122
0,070
0,049
0,081
3%
3%
92%
0%
2%
2
2
2
2
1
1
24
CET
10
0,113
0,074
0,069
0,085
1%
0%
62%
3%
33%
2
2
2
2
1
1
24
CET
12
0,117
0,077
0,084
0,093
10%
13%
59%
0%
18%
2
2
2
2
1
1
24
CET
14
0,107
0,058
0,051
0,072
12%
12%
62%
14%
1%
3
1
1
1
1
1
24
CET
6
0,124
0,121
0,093
0,113
44%
0%
36%
4%
16%
3
1
1
1
1
1
24
CET
8
0,106
0,059
0,039
0,068
12%
78%
4%
5%
1%
3
1
1
1
1
1
24
CET
10
0,122
0,094
0,068
0,094
15%
54%
2%
18%
10%
3
1
1
1
1
1
24
CET
12
0,092
0,070
0,059
0,074
18%
16%
9%
37%
19%
3
1
1
1
1
1
24
CET
14
0,093
0,060
0,048
0,067
29%
20%
1%
21%
28%