Full text
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Sho ‐Te mElec ici yDemandFo ecas ingwi h
MachineLea ning
E nes oJa ie Aguila Mad id
Panamacases udy
P ojec Wo kp esen edas hepa ial equi emen o
ob ainingaMas e 'sdeg eeinDa aScienceandAd anced
Analy ics
ii
NOVAIn o ma ionManagemen School
Ins i u oSupe io deEs a ís icaeGes ãodeIn o mação
Uni e sidadeNo adeLisboa
SHORT‐TERMELECTRICITYDEMANDFORECASTINGWITHMACHINE
LEARNING
Panamacases udy
by
E nes oJa ie Aguila Mad id
P ojec Wo kp esen edas hepa ial equi emen o ob ainingaMas e 'sdeg eeinDa aScience
andAd ancedAnaly ics,specializa ioninBusinessAnaly ics
Ad iso :NunoMigueldaConceiçãoAn ónio
Ma ch2021
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ACKNOWLEDGEMENTS
I hank all he people who ha e been in e es ed in his p ojec 's p og ess. I mainly hank my pa en s
and sis e o hei suppo ; o my ad iso , p o esso Nuno An onio, o accep ing his p ojec o his
aluable ime and guidance. Also, I wan o acknowledge my p o esso s and colleagues who helped
me de elop as a pe son and a p o essional h oughou my ca ee .
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ABSTRACT
An accu a e sho - e m load o ecas ing (STLF) is one o he mos c i ical inpu s o powe plan uni s’
planning commi men . STLF educes he o e all planning unce ain y added by he in e mi en
p oduc ion o enewable sou ces; hus, i helps o minimize he hyd o- he mal elec ici y p oduc ion
cos s in a powe g id. Al hough he e is some esea ch in he ield and e en se e al esea ch
applica ions, he e is a con inual need o imp o e o ecas s. This p ojec p oposes a se o machine
lea ning (ML) models o imp o e he accu acy o 168 hou s o ecas s. The de eloped models employ
ea u es om mul iple sou ces, such as his o ical load, wea he , and holidays. O he i e ML models
de eloped and es ed in a ious load p o ile con ex s, he Ex eme G adien Boos ing Reg esso
(XGBoos ) algo i hm showed he bes esul s, su passing p e ious his o ical weekly p edic ions based
on neu al ne wo ks. Addi ionally, because XGBoos models a e based on an ensemble o decision
ees, i acili a ed he model’s in e p e a ion, which p o ided a ele an addi ional esul , he
ea u es’ impo ance in he o ecas ing.
KEYWORDS
Sho -Te m Load Fo ecas ing; Machine Lea ning; Weekly o ecas ; Elec ici y ma ke ; Ex eme
G adien Boos ing Reg esso (XGBoos )
INDEX
1. In oduc ion ................................................................................................................ 10
1.1. Backg ound .......................................................................................................... 10
1.2. P oblem and jus i ica ion .................................................................................... 10
1.3. Objec i es ............................................................................................................ 11
2. Li e a u e e iew ........................................................................................................ 12
2.1. Sho -Te m Load Fo ecas ing .............................................................................. 12
2.2. Fo ecas ing Me hods ........................................................................................... 12
2.2.1. Classical S a is ical Time-Se ies models ....................................................... 12
2.2.2. Machine Lea ning Reg ession models .......................................................... 13
2.2.3. Deep Lea ning models .................................................................................. 16
2.2.4. Combined echniques and o he o ecas ing app oaches ........................... 16
3. Me hodology .............................................................................................................. 18
3.1. Ha dwa e and So wa e ...................................................................................... 18
3.2. Da a sou ces, ex ac ion, and ans o ma ion .................................................... 18
3.3. Da a p e-p ocessing............................................................................................. 19
3.3.1. Missing alues and ou lie s .......................................................................... 19
3.3.2. Fea u e Enginee ing ..................................................................................... 19
3.3.3. Fea u e Selec ion .......................................................................................... 19
3.3.4. Da ase spli in o ain and es da ase s ..................................................... 20
3.4. Modelling ............................................................................................................. 21
3.4.1. Machine Lea ning candida e models ........................................................... 21
3.4.2. Models aining and hype pa ame e uning............................................... 23
3.5. E alua ion me ics ............................................................................................... 25
4. Resul s and discussion ................................................................................................ 26
4.1. Fo ecas Resul s ................................................................................................... 26
4.2. Fea u e Impo ance Resul s ................................................................................ 30
4.3. Hype pa ame e Sea ch Resul s .......................................................................... 31
4.4. Benchma king ...................................................................................................... 34
5. Conclusions ................................................................................................................. 35
6. Limi a ions and ecommenda ions o u u e wo ks ................................................. 36
7. Bibliog aphy ................................................................................................................ 37
8. Appendices ................................................................................................................. 44
8.1. Appendix 1. Da a eposi o y ................................................................................ 44
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8.2. Appendix 2. Da e- ime spli s ............................................................................... 44
8.3. Appendix 3. Hou ly load illus a ion o each aining- es ing pai .................... 45
8.3.1. Tes ing week 1. Week 15, Ap il 2019. Holy week. ....................................... 45
8.3.2. Tes ing week 2. Week 21, May 2019. .......................................................... 45
8.3.3. Tes ing week 3. Week 24, June 2019. .......................................................... 46
8.3.4. Tes ing week 4. Week 29, July 2019. ........................................................... 46
8.3.5. Tes ing week 5. Week 33, Augus 2019. ...................................................... 47
8.3.6. Tes ing week 6. Week 37, Sep embe 2019. ................................................ 47
8.3.7. Tes ing week 7. Week 41, Oc obe 2019. .................................................... 48
8.3.8. Tes ing week 8. Week 44, No embe 2019. Na ional holidays. .................. 48
8.3.9. Tes ing week 9. Week 51, Decembe 2019. Ch is mas. ............................... 49
8.3.10. Tes ing week 10. Week 1, Janua y 2020. Ma y s Day. ........................ 49
8.3.11. Tes ing week 11. Week 6, Feb ua y 2020. ............................................ 50
8.3.12. Tes ing week 12. Week 10, Ma ch 2020. .............................................. 50
8.3.13. Tes ing week 13. Week 20, May 2020. Qua an ine pe iod. .................. 51
8.3.14. Tes ing week 14. Week 24, Jun 2020. Qua an ine pe iod. ................... 51
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LIST OF FIGURES
Figu e 1. Na ional elec ici y load s. Tempe a u e in Panama Ci y. ....................................... 20
Figu e 2. Hyb id model s uc u e. ............................................................................................ 22
Figu e 3. Sliding window ime-based c oss- alida ion. ............................................................ 23
Figu e 4. Box-whiske plo s o each candida e model and he p e-dispa ch load o ecas .
(a) MAPE e alua ion esul s;
(b) RMSE e alua ion esul s ............................................................................................. 26
Figu e 5. P e-dispa ch and XGB o ecas compa ison wi h he eal load.
(a) Week 51, 2019 (21s o 27 h, Dec 2019);
(b) Week 10, 2020 (7 h o 13 h, Ma 2019);
(c) Week 24, 2020 (13 h o 19 h, Jun 2019) ....................................................................... 29
Figu e 6. Weekly p e-dispa ch s. ML candida es’ models.
(a) Hou ly o ecas o Week 15, 2019 (13 h o 19 h, Ap 2019);
(b) F equency dis ibu ion o e o by o ecas , o Week 15, Ap 2019 ......................... 30
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LIST OF TABLES
Table 1. Va iables’ desc ip ion and uni s o measu e .............................................................. 18
Table 2. Hype pa ame e space by model ............................................................................... 24
Table 3. E alua ion me ics ...................................................................................................... 25
Table 4. E o s dis ibu ion by model, by me ic ..................................................................... 27
Table 5. E alua ion me ics by model, o each es ing week, and ho izon a e age .............. 28
Table 6. A e age ea u e impo ance by ML model exp essed in pe cen age ........................ 31
Table 7. Hype pa ame e op imiza ion esul s o egula days’ models, by es ing week .... 32
Table 8. Hype pa ame e op imiza ion esul s o holidays’ models, by es ing week ........... 33
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LIST OF ABBREVIATIONS AND ACRONYMS
ANN A i icial Neu al Ne wo ks
ARIMA Au o eg essi e In eg a ed Mo ing A e age
CND Cen o Nacional de Despacho; Na ional Dispa ch Cen e
DL Deep Lea ning
KNN K-Nea es Neighbo s Reg esso
L h Elec ici y Load in hou h
LMA Lags’ Mo ing A e age
LSTM Long Sho -Te m Memo y
MAPE Mean Absolu e Pe cen age E o
ML Machine Lea ning
MLR Mul iple Linea Reg ession
MWh Megawa -hou
P e-disp. His o ical weekly p e-dispa ch o ecas
RF Random Fo es Reg esso
RMSE Roo Mean Squa ed E o
RNN Recu en Neu al Ne wo ks
STLF Sho -Te m Load Fo ecas ing
SVR Suppo Vec o Reg esso
XGB Ex eme G adien Boos ing Reg esso (XGBoos )
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2.2.3. Deep Lea ning models
Long Sho -Te m Memo y (LSTM)
F om all neu al ne wo k’s app oaches, Recu en Neu al Ne wo ks (RNN) a e aking an impo an place
in he STLF ield, especially LSTM, because con a y o s anda d eed o wa d neu al ne wo ks, LSTM
has eedback connec ions. Which is bene icial o deal wi h ime-se ies o ecas ing applica ions. Many
au ho s a e ecen ly using i because o i s ema kable esul s in ime se ies lea ning asks like he
hou ly wea he o ecas , and sola i adia ion (Zou e al., 2019). (Yan e al., 2019) a emp o o ecas
he nex 24 hou s load om a sma g id. They compa ed he LSTM esul s wi h a back-p opaga ion
ANN and SVR, demons a ing ha LSTM can o e a MAPE o 1.9 % agains 3.3 % om ANN and 4.8 %
o SVR.
The wo k published by (Abbasimeh e al., 2020) add esses he STLF o a u ni u e company wi h a
me hod based on a mul ilaye LSTM and compa e i o o he models like ARIMA, exponen ial
smoo hing, k-nea es neighbo s eg esso , and ANN. Mo eo e , hei esul s showed ha LSTM
pe o med be e in bo h RMSE and MAPE, ollowed by SVM and ANN.
A no ewo hy con ibu ion is published by (A e & El awil, 2020), using Swi ze land load and
empe a u e da a. Acco ding o hese esea che s, deep lea ning me hods has a supe io pe o mance
in elec ici y STLF, howe e , “ he po en ial o using hese me hods has no ye been ully exploi ed in
e ms o he hidden laye s uc u es.” Fo his eason, hey e alua e deep-s acked LSTM wi h mul iple
laye s o bo h Unidi ec ional LSTM (Uni-LSTM), Bidi ec ional LSTM (Bi-LSTM), and SVR as a baseline
model. Thei esul s showed ha Bi-LSTM MAPE was 0.22% agains MAPE abo e 2% o Uni-LSTM and
SVR.
2.2.4. Combined echniques and o he o ecas ing app oaches
Because XGB p o ides he ea u e impo ance p ope y, he au ho s o Re e ence (Zheng e al., 2017)
p oposed a hyb id algo i hm o classi y simila days wi h K-means clus e ing ed by XGB ea u e
impo ance esul s. Once he classi ica ion is done, an empi ical mode me hod is used o decompose
simila days’ da a in o se e al in insic mode unc ions o ain sepa a ed long sho - e m memo y
(LSTM) models, and inally, a ime-se ies econs uc ion om indi idual LSTM model p edic ions. This
hyb id model using LSTM pe o med be e o STLF o e 24 and 168 hou s ho izons, a e compa ing
wi h ARIMA, SVR, and back-p opaga ion neu al ne wo k using he same simila day app oach as ini ial
inpu .
(Xue e al., 2019) p oposed a mul i-s ep-ahead o ecas ing me hodology using XGB and SVR o o ecas
hou ly hea load, whe e “di ec ” and “ ecu si e” o ecas ing s a egies a e compa ed. The di ec
me hod in ol es an independen model o p edic each pe iod on he o ecas ing ho izon, while he
“ ecu si e” me hod conside s a unique model ha i e a es one s ep a a ime o e he o ecas ing
ho izon, using he p e ious p edic ed s eps as an inpu a iable o he ollowing o ecas ing s ep.
Pe o mance is he main disad an age o he di ec s a egy because i needs o ain as many models
as desi ed pe iods o o ecas s. The ecu si e s a egy is sensi i e o p edic ion e o s, meaning ha
p edic ion e o s will p opaga e along he o ecas ing ho izon.
A s udy o o ecas he 10-day s eam low o a hyd oelec ic dam used a decomposi ion-based
me hodology o compa e XGB and SVR (Yu e al., 2020). In his s udy, he s eam low ime-se ies we e
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decomposed in o se en con iguous equency componen s using he Fou ie T ans o m. Then, each
componen was o ecas ed independen ly by he SVR o XGB. The s udy esul s showed ha SVR
ou pe o med XGB in e ms o e alua ion c i e ia h ough he Fou ie decomposi ion me hodology.
Ano he solu ion joining ANN wi h ensemble app oaches is p esen ed by (Khwaja e al., 2020), whe e
he au ho s seek o imp o e ANN gene aliza ion abili y using bagging-boos ing. When aining
ensembles o ANNs in pa allel, each ensemble uses a boo s apped sample o he aining da a and
consis s o aining he ANNs sequen ially, and his me hod educes he STLF e o bu inc eases he
compu a ional ime because o he se e al aining p ocedu es. Al e na i ely, o aining se e al ANN
sequen ially, (Singh & Dwi edi, 2018) p opose an e olu iona y no el op imiza ion p ocedu e o uning
an ANN. Fo ins ance, a oiding he issues ela ed o ANN uning like o e i ing and selec ing he bes
ANN a chi ec u e. Thei esul s achie ed a 4.86% MAPE. Based on he esul s om (F. Liu e al., 2006;
Zheng e al., 2017), ANN o STLF can ou pe o m o he o ecas ing me hods i a obus
hype pa ame e op imiza ion is pe o med o a oid he issues ela ed o ANN uning.
The hyb idiza ion o he successi e geome ic ans o ma ions model (SGTM) neu al-like s uc u e is
ano he p omising app oach o STLF, as used by (Vi ynskyi e al., 2018) o p edic Libya’s sola
adia ion. This app oach demons a ed a highe accu acy han MLR, SVR, RF, and mul ilaye
pe cep on neu al ne wo k, besides ha ing a as e aining ime due o he non-i e a i e aining
p ocedu e.
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3. METHODOLOGY
3.1. HARDWARE AND SOFTWARE
This p ojec was de eloped on a compu e wi h an i5-9300H p ocesso and 8 Gigaby es o RAM. Colab
(Google, 2020) hos ed Jupy e no ebooks se ice, which p o ides wo CPU and 12 Gigaby es o RAM
pe session, and Jupy e Lab no ebook ins ances om Google Cloud Pla o m (GCP, 2021) o mo e
ex ensi e execu ions, selec ing he 16 CPU and 64 Gigaby es o RAM con igu a ion. All he
expe imen s we e de eloped wi h Py hon (Rossum e al., 2009).
3.2. DATA SOURCES, EXTRACTION, AND TRANSFORMATION
All da a sou ces o de elop his p ojec a e publicly a ailable; he da a will conside hou ly eco ds
om Janua y 2015 un il June 2020 and a e he ollowing:
1. His o ical elec ici y load om Panama, a ailable on daily pos -dispa ch epo s (CND, 2021c), and
his o ical weekly o ecas s a ailable on weekly p e-dispa ch epo s (CND, 2021e).
2. Calenda in o ma ion ela ed o holidays, and school pe iod, p o ided by Panama’s Minis y o
Educa ion ough O icial Gaze e (Gace a, 2020) and holidays websi es (When On Ea h?, 2021).
3. Wea he a iables, such as empe a u e, ela i e humidi y, p ecipi a ion, and wind speed om
h ee main ci ies in Panama, a e ga he ed om Ea hDa a sa elli e da a (GES DISC, 2015).
The load da ase s a e a ailable in Excel iles on a daily and weekly basis, wi h hou ly g anula i y.
Holidays and school pe iods da a is spa se, along wi h websi es and PDF iles. These pe iods a e
ep esen ed wi h bina y a iables, and da e anges a e manually inpu ed in o Excel iles. Bo h Excel
da ase s a e impo ed and con e ed in o da a ames (McKinney & Team, 2020). Wea he da a is
a ailable on daily Ne CDF iles, which can be ea ed wi h ne CDF (Nadh, 2021) and xa ay (Hoye &
Hamman, 2017) o selec he desi ed a iables and subsequen ly con e hese da ase s in o da a
ames. Once all da ase s we e in he same da a ame o ma , hey we e me ged on da e- ime index.
Finally, he esul o hese s eps is: a ime-se ies wi h he his o ical o ecas along wi h i s da e- ime
imes amp as he index, and a da a ame wi h he same imes amp index and 16 columns, one o
each o he ollowing ea u es shown in Table 1. Bo h objec s ha e 48,048 eco ds. Whe e sub-index c
s ands o ci y, meaning ha wea he a iables a e a ailable o Da id, San iago, and Panama Ci y.
Va iable
Desc ip ion
Uni o measu e
Na ional load
Na ional elec ici y load, excluding expo s
MWh
Holiday
Holiday bina y indica o
-
Holiday ID
Holiday iden i ica ion numbe
-
School
School pe iod bina y indica o
-
Temp. 2mc
2 me e s ai empe a u e
ºC
Hum. 2mc
2 me e s speci ic humidi y
%
Wind 2mc
2 me e s wind speed
m/s
P ecipi a ionc
To al p ecipi able liquid wa e
l/m2
Load Fo ecas
His o ical na ional load o ecas , excluding expo s
MWh
Table 1. Va iables’ desc ip ion and uni s o measu e.
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3.3. DATA PRE-PROCESSING
3.3.1. Missing alues and ou lie s
The e a e no missing alues on he da ase s, and an ini ial ou lie ’s e ision was made by no malizing
each a iable. Only a ew low alues on he load we e de ec ed due o hou ly blackou s and damages
in he powe g id, bu all eco ds we e kep .
3.3.2. Fea u e Enginee ing
The se o a iables used o ain he ML models, also called ea u es, a e ea ed in his sec ion. New
a iables ela ed o he da e- ime index a e c ea ed o eed he ML models wi h his ex a in o ma ion
abou ime, wi h his being one o he mos c i ical s eps o STLF (X. Liu e al., 2020; Zhang e al., 2019).
The new ea u es added o he da ase s a e yea , mon h numbe , day o he mon h, week o he yea ,
day o he week, he hou o he day, he hou o he week, weekend indica o . All being in ege
a iables, excep o he bina y weekend indica o . I is essen ial o cla i y ha Sa u day is conside ed
he i s day o he week. Fo ins ance, he i s week o each yea is he i s comple e week s a ing
on Sa u day, and his is espec ed o keep he CND epo s calenda s uc u e o u he compa isons.
Load weekly lags and load weekly mo ing a e age ea u es we e new calcula ed ea u es ha help o
cap u e he mos ecen changes o load (Pin o e al., 2021), keeping he hou ly g anula i y. These
we e calcula ed om he second p eceding week un il he ou h week, adding wo mo e ea u es o
he cu en da ase .
Gi en an hou 𝒉, o o ecas he load 𝑳 a his hou 𝑳𝒉, he load’s lags can be deno ed as 𝑳𝒉−𝒊, whe e
𝒊 emains in he hou ly g anula i y. Following his no a ion, he included lag ea u es a e: 𝑳𝒉−𝟏𝟔𝟖,
𝑳𝒉−𝟑𝟑𝟔, 𝑳𝒉−𝟓𝟎𝟒 and 𝑳𝒉−𝟔𝟕𝟐 which co esponds o he p e ious week, he second las , hi d las and
ou h las week’s load. The lags’ mo ing a e ages (LMA) a e calcula ed om he weekly lags ollowing
equa ion (1). The independen a iable 𝒎 ep esen s he ea lies week o conside , and 𝒏 s ands o
he la es week o conside in he mo ing a e age. Following equa ion (1), he conside ed LMA we e
𝑳𝑴𝑨𝒉(𝟏,𝟑) and 𝑳𝑴𝑨𝒉(𝟏,𝟒).
𝑳𝑴𝑨𝒉(𝒎,𝒏)=∑𝑳𝒉−𝟏𝟔𝟖𝒎+𝑳𝒉−𝟏𝟔𝟖(𝒎+𝟏)+⋯ + 𝑳𝒉−𝟏𝟔𝟖(𝒏−𝟏)+𝑳𝒉−𝟏𝟔𝟖𝒏
𝒏
𝒎𝒏−𝒎+𝟏 ; 𝑤ℎ𝑒𝑟𝑒 𝒎≥𝟏∧ 𝒏>𝒎 (1)
3.3.3. Fea u e Selec ion
The decision o which a iables should be used o ain he ML models is c i ical o ob ain good esul s.
This p ocess, known as ea u e selec ion, also educes compu a ion ime, dec eases da a s o age
equi emen s, simpli ies models, e ades he cu se o dimensionali y, and enhances gene aliza ion,
a oiding o e i ing (Eseye e al., 2019). Fo hese easons, se e al ea u e selec ion echniques we e
pe o med along wi h he STLF s a e-o - he-a (Beci o ic & Coso ic, 2016; X. Liu e al., 2020); and he
p oblem unde s anding o selec essen ial ea u es. The explo ed Fea u e Selec ion echniques we e:
ea u e a iance, co ela ion wi h he a ge , edundancy among eg esso s (Han e al., 2011), and
ea u e impo ance acco ding o he de aul models mul iple linea eg ession, decision ee eg esso ,
andom o es eg esso , and ex eme g adien boos ing eg esso .
20
A e ha ing 28 eg esso s and a de ined a ge , he ea u e selec ion analysis showed ha 10
eg esso s would signi ican ly con ibu e o o ecas . Consequen ly, he bes eg esso s a e:
▪ 𝐿𝒉−𝟑𝟑𝟔
▪ 𝐿𝒉−𝟓𝟎𝟒
▪ 𝐿𝒉−𝟔𝟕𝟐
▪ 𝐿𝑀𝐴𝒉(𝟏,𝟒)
▪ 𝑑𝑎𝑦_𝑜𝑓_𝑡ℎ𝑒_𝑤𝑒𝑒𝑘𝒉
▪ 𝑤𝑒𝑒𝑘𝑒𝑛𝑑_𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟𝒉
▪ ℎ𝑜𝑙𝑖𝑑𝑎𝑦_𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟𝒉
▪ ℎ𝑜𝑙𝑖𝑑𝑎𝑦_𝐼𝐷𝒉
▪ ℎ𝑜𝑢𝑟_𝑜𝑓_𝑡ℎ𝑒_𝑑𝑎𝑦𝒉
▪ 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒_2𝑚_𝑖𝑛_𝑃𝑎𝑛𝑎𝑚𝑎_𝑐𝑖𝑡𝑦𝒉
The empe a u e was an essen ial wea he a iable due o i s posi i e ela ionship wi h elec ici y load
(Boya, 2019), as illus a ed in Figu e 1. This igu e shows he ypical load ange, om 800 o 1600 MWh,
and a empe a u e ange be ween 23 and 33 ºC. The dashed line iden i ies he linea equa ion (2):
𝑳𝒉= 4.8 ∙ 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒_2𝑚_𝑖𝑛_𝑃𝑎𝑛𝑎𝑚𝑎_𝑐𝑖𝑡𝑦𝒉−867.5 (2)
Which indica es ha 1 °C inc ease in empe a u e ep esen s a 74.8 MWh elec ici y load inc ease.
Figu e 1. Na ional elec ici y load s. Tempe a u e in Panama Ci y.
3.3.4. Da ase spli in o ain and es da ase s
Be o e spli ing he da a in o aining and es da ase s, he hou ly eco ds a he beginning and he
end o he ho izon a e d opped i hey do no belong o a comple e 168 hou s weekly block o
consis ency on aining, alida ion, and es ing. A e his, 283 comple e weeks a e a ailable wi h
hou ly eco ds. The da ase is spli in o ain and es , keeping he ch onological eco ds. Reco ds a e
so ed by da e- ime index, always lea ing he las week o es ing and he emaining olde da a o
aining. Based on his logic, he e a e 14 pai s o ain- es da ase s selec ed. Twel e pai s, ha ing a
es ing week o each mon h o he las yea o eco ds be o e he 2020 qua an ine s a ed due o he
COVID-19 pandemic, and wo mo e a e he qua an ine began. To no e, he o icial lockdown in
Panama s a ed on Wednesday, 25 Ma ch o 2020, which co esponds o week 12—2020 (La Es ella
de Panamá, 2021). Mo e de ails abou he 14 ain- es pai s a e a ailable in appendices 2 and 3.
0
400
800
1200
1600
2000
22 24 26 28 30 32 34 36
Elec ici y load (MWh)
Tempe a u e in Panama ci y (ºC)
21
These c i e ia es he models unde egula and i egula condi ions since he qua an ine pe iod
p esen ed a lowe demand wi h a ypical hou ly p o iles. The selec ed es ing weeks also included
ypical days and holidays o es he models on di e en condi ions h oughou he yea .
As men ioned in he backg ound sec ion, he planning p ocess is weekly done, ypically s a ing e e y
Wednesday o o ecas he week s a ing on Sa u day as he i s day o he weekly planning ho izon.
So, he a ailable eco ds o o ecas ing usually a e upda ed e e y Tuesday a midnigh , hen execu ed
on Wednesdays o he planning 168 hou s ho izon ha s a s e e y Sa u day and inishes on each
F iday. Fo his eason, he o ecas should conside a leas a gap o 72 hou s o unseen da a be o e
he i s pe iod o p edic .
3.4. MODELLING
3.4.1. Machine Lea ning candida e models
S udies ha e shown ha many decision-make s exhibi an inhe en dis us o au oma ed p edic i e
models, e en i hey a e p o en o be mo e accu a e han human o ecas e s (Die o s e al., 2015).
One way o o e come “algo i hm a e sion” is o p o ide hem wi h in e p e abili y (Be simas e al.,
2019). Fo hese easons, he cu en p ojec explo es a se o candida e ML models ha ha e been
p o en as o ecas e s wi hin he STLF s a e-o - he-a , bu also models ha can o e a ce ain le el o
in e p e abili y.
The candida e ML models conside ed in his p ojec a e Mul iple Linea Reg ession (MLR), k-nea es
neighbo s eg esso (KNN), epsilon-suppo ec o eg ession (SVR), andom o es eg esso (RF), and
ex eme g adien boos ing eg esso (XGB). All hese es ima o s we e execu ed using a pipeline wi h a
de aul Min–Max scale as he i s s ep. These ML models, he pipeline s uc u e, and he scale s we e
om sci-ki lea n (Ped egosa e al., 2011), excep o XGB (XGB De elope s, 2021).
MLR uses wo o mo e independen a iables o p edic a dependen a iable by i ing a linea
equa ion. This me hod’s assump ions a e ha : he dependen a iable and he esiduals a e no mally
dis ibu ed, he e a e linea ela ionships be ween he dependen and independen a iables, and no
collinea i y should exis be ween eg esso s. Since MLR can include many independen a iables, i can
p o ide an unde s anding o he ela ionships (Zhang e al., 2019), bu i p esen s he disad an age o
being sensi i e o ou lie s.
KNN is no ypical o STLF. Ne e heless, hei esul s can be in e p e ed, and some esea che s used
i as a baseline model (Johannesen e al., 2019). The KNN me hod sea ches o he k mos simila
ins ances; when he k mos simila samples a e ound, he a ge is ob ained by local in e pola ion o
he a ge s associa ed wi h he k ound ins ances (Abbasimeh e al., 2020). The main disad an age o
his me hod is ha i ends o o e i , and i has ew hype pa ame e s o change his si ua ion.
SVR is a eg ession e sion o he Suppo Vec o Machine (SVM) which was ini ially designed o
classi ica ion p oblems (Vine & Zhedano , 2011). In con as o o dina y leas squa es o MLR, he
objec i e unc ion o SVR is o minimize he L2-no m o he coe icien ec o , no he squa ed e o .
The e o e m is hen cons ained by a speci ied ma gin ε (epsilon). SVR is equen ly used o STLF
wi h he linea (X. Liu e al., 2020) o adial basis unc ion (RBF) ke nel (Cao e al., 2020), iden i ying
load pa e ns be e han o he linea models (Amin & Hoque, 2019).
22
RF is an ensemble lea ning me hod wi h gene aliza ion abili y. I i s many decision ees on a ious
sub-samples o he da ase and uses a e aging o imp o e he o ecas and a oid o e i ing. Fo hese
easons, i seems sui able o STLF, bu he ew esea che s ha conside his model ha e
demons a ed a weak pe o mance on hei esul s (Pin o e al., 2021).
XGB is ano he ensemble ML algo i hm based on g adien boos ing lib a y, bu enhanced and designed
o be highly e icien , lexible, and po able (XGB De elope s, 2021). P o iding a o wa d s age-wise
addi i e model ha i s eg ession ees on many s ages while he eg ession loss unc ion is
minimized. Due o i s ecen de elopmen , XGB is no a ma u ed STLF me hod, hough, esea che s
a e s a ing o use i , showing ou s anding pe o mances agains adi ional me hods (J. Cai e al., 2020;
Had i e al., 2019).
In STLF, o ecas ing holidays’ load is one o he mos challenging p oblems due o he lack o eco ds,
he low equency o hese e en s, and hei unusual consump ion pa e ns. A way o imp o e he
holidays’ o ecas s accu acy is o de elop and ain a pa icula model specialized in o ecas ing
holidays (Zhu e al., 2021), along wi h ano he model o non-holidays. This p ojec conside ed a hyb id
model ha me ges he weekly o ecas s o non-holidays and holidays, as illus a ed in Figu e 2. This
hyb id model s uc u e was applied o each candida e algo i hm. Thus, each hyb id model is composed
o wo models wi h he same eg ession algo i hm. The main eason o de elop a hyb id model was o
ain he holidays’ model only wi h holidays’ eco ds and including he la ges numbe o eco ds
possible.
Fo ecas nex week
Regula days’
Holidays’ model
Weekly o ecas
Do no il e eco ds
T ain model wi h weekly ime-
based c oss- alida ion:
las 2.8 yea s
Fo ecas whole week
Keep only holidays and d op
holidays indica o ea u e
T ain model wi h daily ime-
based c oss- alida ion:
all holidays’ eco ds included
Fo ecas holidays
Hyb id model
Join o ecas s, eplacing holidays’ model
o ecas o e egula days' model
o ecas .
Figu e 2. Hyb id model s uc u e.
23
3.4.2. Models aining and hype pa ame e uning
Once he aining and es ing weeks pai s we e de ined, models we e ained wi h he ea lies ain-
es pai , ollowing he o wa d sliding window app oach (Sugia awan & Ha a i, 2019) o ime-based
c oss- alida ion (He man-Sa a , 2021). The idea o ime-based c oss- alida ion is o i e a i ely spli
he aining se in o wo olds a each s ep, always keeping he alida ion se ahead o he aining se .
This p ocess o de ining olds, aining he model, p edic ing he alida ion old, and e alua ing he
model pe o mance while changing hype pa ame e s and mo ing he aining/ alida ion se s u he
in o he u u e is illus a ed in Figu e 3.
Figu e 3. Sliding window ime-based c oss- alida ion.
The egula days’ model’s sliding window cha ac e is ics a e 149 weeks (2.8 yea s) o
aining/ alida ion. Wi hin hose, 64 a e alida ion weeks, excluding he las 72 hou s om each
alida ion old o comply wi h he h ee-day unknown gap when o ecas ing he weekly demand on
eal condi ions; inally, he o wa d s ep on he aining/ alida ion p ocess is one week (168 hou s).
Fo he holidays’ model, only holidays eco ds a e kep , and he sliding window conside s all holidays
eco ds a ailable since he yea 2015 (as shown in Figu e 2). The o ecas ing ho izon o he holidays’
model is 24 hou s; o ins ance, he sliding window p ocess also conside s o ecas ing a holiday du ing
he aining p ocess.
The hype pa ame e uning was pe o med wi h Op una op imiza ion amewo k (Akiba e al., 2019),
keeping he sliding window a ibu es. The models’ uning p ocess consis s o maximizing he “nega i e
mean oo squa ed e o ” (-RMSE) while sampling he de ined hype pa ame e space wi h he T ee-
s uc u ed Pa zen Es ima o (TPE) algo i hm (Be gs a e al., 2011). The op imiza ion s udies we e
cons ained o 30 ials, which implies ha 30 di e en hype pa ame e combina ions a e explo ed in
he aining p ocess. On each ial, o each pa ame e , TPE i s one Gaussian Mix u e Model (GMM)
𝒍(𝒙) o he se o pa ame e alues associa ed wi h he bes objec i e alues, and ano he GMM 𝒈(𝒙)
o he emaining pa ame e alues (Op una, 2018a). Then TPE chooses he pa ame e alue 𝒙 ha
maximizes he a io 𝒍(𝒙)/𝒈(𝒙).
I is aluable o men ion ha as a i s ial o add ess his STLF ask, all candida e’s models we e ained
wi h a wo-s ep andomized and g id-sea ch c oss- alida ion app oach as sugges ed by (Die ich e al.,
2020), bu i esul ed compu a ionally oo expensi e. To educe he compu a ional wo k and execu ion
ime, bu wi hou losing quali y on esul s, Op una hype pa ame e op imiza ion was chosen; aiming
o simula e he models' upda es along he ime by aining each candida e model be o e o ecas ing
each es ing week.
24
This hype pa ame e uning was pe o med indi idually o bo h models inside he Hyb id mode: he
egula ’s days model and he holidays’ model. The hype pa ame e op imiza ion was pe o med o
each es ing week, aiming o p edic each es ing week wi h upda ed models along he ime. The
explo ed hype pa ame e space o each algo i hm is shown in Table 2. The absen pa ame e s we e
conside ed wi h hei de aul alue, and he hype pa ame e spaces a e exp essed in e ms o he ial
me hod om Op una, which desc ibes mo e p ecisely he explo ed dis ibu ions and anges o alues
o each pa ame e (Op una, 2018b).
Model
Hype pa ame e
Hype pa ame e space
KNN
n_neighbo s
sugges _in ('n_neighbo s', 3, 50, 2)
weigh s
sugges _ca ego ical('weigh s', ['uni o m', 'dis ance'])
me ic
sugges _ca ego ical('me ic', ['minkowski', 'euclidean', 'manha an'])
lea _size
sugges _in ('lea _size', 1, 50, 5)
SVR
ke nel
sugges _ca ego ical('ke nel', ['linea ', ' b '])
epsilon
sugges _loguni o m('epsilon', 0.0001, 10)
C
sugges _loguni o m('C', 0.001, 3000)
ol
ial.sugges _uni o m(' ol', 1×10−5, 1×10−2)
gamma
sugges _ca ego ical('gamma', ['scale', 'au o'])
RF
c i e ion
mse
n_es ima o s
sugges _in ('n_es ima o s', 40, 200, 20)
max_samples
sugges _disc e e_uni o m('max_samples', 0.6, 0.9, 0.05)
max_dep h
sugges _in ('max_dep h', 7, 21, 3)
ccp_alpha
sugges _loguni o m('ccp_alpha', 1×10−6, 1×10−3)
andom_s a e
123
XGB
e al_me ic
mse
n_es ima o s
sugges _in ('n_es ima o s', 300, 500, 50)
max_dep h
sugges _in ('max_dep h', 3, 7)
subsample
sugges _disc e e_uni o m('subsample', 0.6, 0.9, 0.05)
colsample_by ee
sugges _disc e e_uni o m('colsample_by ee', 0.6, 0.9, 0.05)
colsample_byle el
sugges _disc e e_uni o m('colsample_byle el', 0.6, 0.9, 0.1)
colsample_bynode
sugges _disc e e_uni o m('colsample_bynode', 0.6, 0.9, 0.1)
lea ning_ a e
sugges _loguni o m('lea ning_ a e',0.0001, 0.1)
min_child_weigh
sugges _in ('min_child_weigh ', 1, 7, 2)
gamma
sugges _loguni o m('gamma', 0.00001, 2)
lambda
sugges _loguni o m(' eg_lambda', 1, 5)
alpha
sugges _loguni o m(' eg_alpha', 0.00001, 2)
andom_s a e
123
Table 2. Hype pa ame e space by model.
25
3.5. EVALUATION METRICS
This p ojec add esses many e alua ion me ics o sys ema ically e alua e he ML models’
pe o mance, including he adi ional me ics o ML o ecas ing, as well as o he speci ic me ics o
STLF. These e alua ion me ics and hei o mula ion a e lis ed in Table 3. Whe e 𝑨 is a weekly se o
ac ual hou ly load alues, 𝑭 is a weekly se o o ecas ed hou ly alues, and subindex 𝒉 s ands o a
speci ic hou . Fo his p ojec , all es ing se s we e whole weeks wi h 168 hou s, so 𝒏 is equal o 168.
Me ic
De ini ion
Equa ion
Uni
MAPE
Mean Absolu e Pe cen age E o
𝑀𝐴𝑃𝐸= 1
𝑛∑ |𝐴ℎ−𝐹ℎ
𝐴ℎ|
𝑛
ℎ=1 ×100%
%
RMSE
Roo Mean Squa e E o
𝑅𝑀𝑆𝐸= √1
𝑛∑(𝐴ℎ−𝐹ℎ)2
𝑛
ℎ=1
MWh
Peak
Peak Load Absolu e Pe cen age E o
𝑃𝑒𝑎𝑘= |max(𝐴)−max(𝐹)
max(𝐴)|×100%
%
Valley
Valley Load Absolu e Pe cen age E o
𝑉𝑎𝑙𝑙𝑒𝑦= |min(𝐴)−min(𝐹)
min(𝐴)|×100%
%
Ene gy
Ene gy Absolu e Pe cen age E o
𝐸𝑛𝑒𝑟𝑔𝑦= |∑𝐴ℎ
𝑛
ℎ=1 −∑𝐹ℎ
𝑛
ℎ=1
∑𝐴ℎ
𝑛
ℎ=1 |×100%
%
Table 3. E alua ion me ics.
32
Model
yea
2019
2020
week no.
15
21
24
29
33
37
41
44
51
1
6
10
20
24
mon h
Ap
May
Jun
Jul
Aug
Sep
Oc
No
Dec
Jan
Feb
Ma
May
Jun
KNN
n_neighbo s
41
31
31
31
41
31
31
37
31
37
37
31
29
35
weigh s
dis .
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
me ic
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
lea _size
11
1
1
1
16
16
1
46
46
1
16
16
21
46
SVR
ke nel
b
b
b
b
b
b
b
b
b
b
b
b
b
b
epsilon
2.48927
8.25782
0.00082
0.01421
0.00033
0.00092
0.02024
0.86639
0.00013
6.93334
0.00014
0.02678
7.16092
0.02286
C
415.13
409.21
299.93
304.05
318.07
332.74
331.23
367.35
315.65
2938.91
296.54
307.96
243.53
308.42
ol
0.00694
0.00350
0.00868
0.00780
0.00853
0.00811
0.00012
0.00876
0.00024
0.00931
0.00293
0.00772
0.00072
0.00882
RF
n_es ima o s
140
140
100
80
120
200
180
180
200
180
200
200
200
180
max_samples
0.60
0.65
0.70
0.70
0.60
0.65
0.70
0.70
0.65
0.65
0.60
0.60
0.60
0.60
max_dep h
10
10
10
13
13
13
10
13
13
10
13
13
10
10
ccp_alpha
1.59×10−4
2.33×10−6
2.86×10−5
1.50×10−5
9.16×10−5
9.83×10−4
3.87×10−6
1.68×10−4
1.19×10−6
8.10×10−5
1.73×10−5
3.65×10−6
3.54×10−4
9.72×10−4
XGB
n_es ima o s
350
400
350
400
500
400
600
550
350
600
500
600
600
550
max_dep h
5
4
4
5
4
5
4
5
5
5
5
5
4
4
subsample
0.75
0.75
0.70
0.65
0.65
0.75
0.65
0.65
0.60
0.75
0.75
0.65
0.70
0.75
colsample_by ee
0.75
0.70
0.65
0.80
0.70
0.60
0.75
0.80
0.60
0.60
0.70
0.70
0.75
0.65
colsample_byle el
0.70
0.90
0.80
0.65
0.70
0.85
0.80
0.60
0.75
0.60
0.90
0.65
0.85
0.85
colsample_bynode
0.70
0.75
0.80
0.60
0.65
0.70
0.90
0.60
0.90
0.70
0.85
0.85
0.75
0.75
lea ning_ a e
0.050016
0.066828
0.057397
0.030956
0.051173
0.039766
0.036783
0.022305
0.052250
0.041089
0.042121
0.027303
0.027487
0.021568
min_child_weigh
7
3
3
7
7
1
7
3
5
3
1
7
7
3
gamma
1.7696
0.9889
0.0440
0.1366
0.0039
5.81×10−5
1.65×10−3
1.71×10−4
0.9251
7.12×10−4
0.0220
1.34×10−3
1.35×10−5
0.8903
lambda
1.1940
1.4665
3.1788
1.1477
3.6228
3.6026
2.5763
1.6005
3.2689
3.7203
2.6808
1.7332
1.0280
3.6871
alpha
1.0194
0.1336
0.0457
0.0209
2.94×10−3
0.0183
3.00×10−3
4.55×10−4
0.0338
7.46×10−5
7.47×10−4
9.20×10−5
0.0738
0.2525
Table 7. Hype pa ame e op imiza ion esul s o egula days’ models, by es ing week.
33
Model
yea
2019
2020
week no.
15
21
24
29
33
37
41
44
51
1
6
10
20
24
mon h
Ap
May
Jun
Jul
Aug
Sep
Oc
No
Dec
Jan
Feb
Ma
May
Jun
KNN
n_neighbo s
25
25
33
21
15
27
21
15
39
39
21
29
21
29
weigh s
dis .
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
dis
me ic
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
manh .
lea _size
1
11
1
26
46
26
21
1
26
6
46
16
11
26
SVR
ke nel
b
b
b
b
b
b
b
b
b
b
b
b
b
b
epsilon
0.00264
0.00045
0.00017
9.45318
6.31538
1.09855
5.73192
0.00023
0.20928
0.90036
2.22753
8.30718
0.00029
0.62205
C
2802.99
626.41
460.37
807.35
303.19
257.51
609.51
248.33
149.49
151.74
142.09
111.01
2774.43
234.76
ol
0.00794
0.00852
0.00967
0.00998
0.00185
0.00361
0.00556
0.00671
0.00540
0.00417
0.00991
0.00606
0.00321
0.00592
RF
n_es ima o s
100
100
140
200
100
200
100
200
80
100
140
140
100
100
max_samples
0.80
0.80
0.80
0.60
0.80
0.80
0.80
0.80
0.60
0.80
0.80
0.80
0.80
0.80
max_dep h
19
13
19
16
16
16
16
19
19
13
19
19
16
19
ccp_alpha
2.24×10−5
5.31×10−5
1.51×10−6
4.70×10−5
6.03×10−5
8.83×10−4
2.24×10−5
4.45×10−5
2.09×10−5
2.84×10−4
7.46×10−6
4.46×10−5
8.40×10−6
1.06×10−4
XGB
n_es ima o s
300
500
500
300
500
300
500
500
300
450
350
450
500
300
max_dep h
4
6
4
5
7
4
7
4
6
7
4
6
4
7
subsample
0.80
0.90
0.60
0.80
0.75
0.80
0.70
0.75
0.90
0.70
0.80
0.70
0.60
0.85
colsample_by ee
0.70
0.90
0.90
0.65
0.75
0.60
0.60
0.80
0.90
0.65
0.80
0.65
0.70
0.90
colsample_byle el
0.80
0.90
0.90
0.80
0.90
0.80
0.90
0.90
0.70
0.90
0.80
0.90
0.80
0.80
colsample_bynode
0.90
0.80
0.90
0.90
0.90
0.90
0.80
0.70
0.90
0.80
0.80
0.90
0.90
0.60
lea ning_ a e
0.059702
0.022990
0.099259
0.096232
0.058822
0.046665
0.026215
0.046144
0.096558
0.031292
0.072094
0.090842
0.065184
0.090743
min_child_weigh
5
3
7
3
3
5
5
5
7
7
7
3
3
3
gamma
2.86×10−3
1.47×10−3
0.0464
6.64×10−4
2.29×10−3
0.5343
3.46×10−5
2.52×10−3
1.20×10−5
3.40×10−5
1.8331
0.4352
1.93×10−5
0.0833
lambda
3.6348
1.2237
1.1215
1.0615
1.6029
1.4756
3.2333
4.3853
1.6743
1.0481
1.2192
2.0430
1.6593
1.7202
alpha
4.44×10−5
2.85×10−3
1.11×10−3
3.07×10−4
6.56×10−4
1.99×10−5
8.60×10−5
1.61×10−3
9.33×10−5
1.06×10−4
1.62×10−4
4.51×10−3
9.24×10−4
6.46×10−4
Table 8. Hype pa ame e op imiza ion esul s o holidays’ models, by es ing week.
34
4.4. BENCHMARKING
The esul s ob ained in his p ojec can be in e p e ed om he pe spec i e o any ime-se ies
o ecas ing esea ch using ML echniques since he s anda d ML me hodologies o STLF we e applied
o ain and e alua e esul s, as exposed in he li e a u e e iew. Fo example, he selec ed ea u es
ac oss he STLF ield o s udy ma ch his p ojec ’s bes ea u es: he load’s lags, he hou o he day,
and empe a u e. Holidays and weekends’ bina y indica o s also con ibu e since hey help de e mine
a high o low load ange.
In con as wi h mos o he s udies whe e esea che s o ecas 24 o 48 hou s, his p ojec add essed
a 168-hou ho izon, conside ing a 72-hou gap be o e he i s o ecas ing pe iod. A second
di e en ia ion is he implemen a ion o a hyb id model o enhance he holidays’ o ecas ; wi hin he
weekly o ecas ing ho izon. Besides he ypical MAPE and RMSE e alua ion me ics, his p ojec
p oposed load peak, load alley, and ene gy e alua ion as seconda y, p ac ical me ics ha analys s
can easily moni o . Ano he dis inc ion o his p ojec is he di e si y o es ing pe iods, p esen ing
STLF o egula wo king days, holidays, and i egula pe iods du ing he 2020 qua an ine. This p ojec ’s
mos impo an dis inc ion is compa ing he o icial weekly p e-dispa ch o ecas as a baseline and
alida ing he esul s.
As exposed in he in oduc ion sec ion, his p ojec ’s di ec implica ion is o ecas ing Panama’s
na ional load. Howe e , hese models can be ained and applied o coun ies o egions wi h simila
condi ions.
35
5. CONCLUSIONS
This p ojec ’s main objec i es we e o e alua e cu en Panama’s o icial load o ecas and de elop a
se o Machine Lea ning models o imp o e his o icial load o ecas . Fo ins ance, he models we e
de eloped and benchma ked wi h da a and p e ious o ecas s om Panama’s powe sys em. This
p ojec p esen ed a no el hyb id me hodology o imp o e he weekly STLF o ecas o he Panama
case s udy o add ess he o ecas ing ask, keeping a 72-hou gap. A se o i e p o en algo i hms
ac oss he esea ch ield we e chosen o de elop he hyb id models and subsequen ly compa e hei
esul s agains he o icial o ecas ing ool eco ds on di e se es ing weeks. Resul s along 14 es ing
weeks con i med he sui abili y o he XGB algo i hm o he hyb id me hodology. Fi s , o ime
e iciency on aining and p edic ing; second, o lexibili y due o he pa ame e space; and hi d, o
he ease o p o iding ce ain in e p e abili y h ough i s ea u e impo ance p ope y.
Fo he abo e-exposed easons, his p ojec makes se e al signi ican con ibu ions o he ield o
s udy. Fi s , i shows ha models buil wi h XGB ha e supe io pe o mance o models buil wi h o he
algo i hms. Second, i con i ms ha empe a u e plays an impo an ole in STLF. Thi d, i
demons a es he excellen pe o mance o ML models by o ecas ing o a longe ho izon han ypical
esea ch; and e en wi h a h ee-day gap o da a be o e he o ecas . Las ly, his p ojec iden i ies public
da a ha o he esea che s can use o imp o e a amed o ecas ing ask. De ails abou his p ojec
da ase eposi o y a e a ailable in Appendix 1.
This p ojec also has se e al p ac ical implica ions. The i s and main implica ion is o eplace he
cu en o ecas ing ool o he Panama case s udy, hus allowing Panama o educe cos s and imp o e
STLF pe o mance. Second, his model could be ained and applied in o he coun ies o egions wi h
simila condi ions. Fu he mo e, he posi i e impac s o p o iding a mo e accu a e STLF will educe
he planning unce ain y added by he in e mi en enewable p oduc ion and subsequen ly be close
o he op imal hyd o- he mal cos s scheduled in he weekly uni commi men . This hi d p ac ical
implica ion leads o a ou h: o he speci ic case o he Panama ene gy spo ma ke , because i is a
ma ginalis ma ke , accu a e STLF can also educe he hou ly ene gy p ice unce ain y in he wholesale
elec ici y ma ke .
36
6. LIMITATIONS AND RECOMMENDATIONS FOR FUTURE WORKS
Fu u e wo k wi hin his speci ic esea ch can include mo e his o ical load eco ds o ain models in
pa icula si ua ions, like holidays. Ano he app oach o enhance o ecas s is o classi y load p o iles
using clus e ing echniques p io aining (Zheng e al., 2017), and use s acking echniques o enhance
he o ecas accu acy, e en hough i inc eases he aining and p edic ing ime (Massaoudi e al.,
2021).
In he pa icula case s udy o Panama’s na ional load, he e a e special consume s named au o-
gene a o s: he Panama Canal and Mine a Panama (CND, 2021a). These consume s ha e a signi ican
load, bu as hei agen ’s name sugges s, hey supply hei own demand wi h hei own powe plan s
mos o he ime, excep o scheduled main enance pe iods on hei powe plan s o un o eseen
una ailabili y on hei powe plan s (CND, 2021d). Those agen s will consume ene gy om he na ional
powe sys em du ing hose e en s, causing an ex a inc ease in he na ional load. I his addi ional load
can be scheduled, i is be e o ack he elec ici y load by consume and o ecas only he esiden ial,
comme cial, and indus ial load, hen add au o-gene a o s i needed. This load seg ega ion a oids
dis o ions on he load o ecas , as s a ed in au o-gene a o s me hodology (CND, 2021b). In his
con ex , ano he esea ch a enue o de elop STLF by consume s eme ges, bu i equi es da a wi h
his seg ega ion.
Since DL models a e ou o his p ojec scope, and DL models equi e mo e eco ds han ML models,
unidi ec ional and bidi ec ional LSTM we e no compa ed in he esea ch. Howe e , u u e s udies
should e alua e hese algo i hms’ pe o mance ha ha e p o en good o STLF (A e & El awil, 2020).
Simila ly, non-i e a i e ANN-based algo i hms can be explo ed due o hei good pe o mance and low
aining ime, like (Vi ynskyi e al., 2018) compa ed wi h a se o ML models.
Al hough he e a e cu en ly se e al wea he o ecas s a ailable wi h hou ly g anula i y (Visual
C ossing, 2021), because he empe a u e is c ucial o STLF, i is ad isable o coun wi h an accu a e
empe a u e o ecas o eed his STLF model. Hence, a empe a u e o ecas model can complemen
his p ojec .
I is ad ised o do a weekly load pa e ns e ision since consump ion pa e ns can change in he u u e.
An example o ab up changes on he hou ly load p o ile was exposed in his p ojec du ing he 2020
qua an ine pe iod. Howe e , o he ending consump ion pa e ns (Ande sen e al., 2019), like
echa ging mo e elec ic ehicles and ha ing mo e sola p oduc ion behind- he-me e , will p oduce
esiden ial and comme cial hou ly consump ion changes. This e ision implies ha o ecas ing models
should be upda ed mo e o en, and e en ha hey need o be mo e obus .
A possible solu ion o o e come hese issues is o au oma ically enable he models o lea n wi h new
da a e e y week by deploying he “Champion-Challenge ” app oach (Abbo , 2014). A weekly
hype pa ame e uning is execu ed o upda e he models and make hem compe e o ensu e he bes
pe o mance along ime.
The inal goal o STLF is o educe he unce ain y on eal- ime dispa ch o hyd o- he mal powe plan s
because he wind and sola a ms a e non-dispa chable powe plan s. Consequen ly, ano he way o
educe he planning unce ain y and complemen he STLF is by p o iding an accu a e o ecas o
wind and sola p oduc ion and o he non-dispa chable powe plan s, i any.
37
7. BIBLIOGRAPHY
Abbasimeh , H., Shabani, M., & Youse i, M. (2020). An op imized model using LSTM ne wo k o
demand o ecas ing. Compu e s and Indus ial Enginee ing, 143(July 2019), 106435.
h ps://doi.o g/10.1016/j.cie.2020.106435
Abbo , D. (2014). Applied P edic i e Analy ics. P inciples and echniques o he p o essional da a
analys . (p. 372). Indianapolis, IN, USA: John Wiley & Sons, Inc.
Adeoye, O., & Spa a u, C. (2019). Modelling and o ecas ing hou ly elec ici y demand in Wes
A ican coun ies. Applied Ene gy, 242(Ma ch), 311–333.
h ps://doi.o g/10.1016/j.apene gy.2019.03.057
Aguila Mad id, E., & Valdés Bosquez, L. (2017). Impac o wind and pho o ol aic gene a ion inpu in
Panama ; Impac o de la en ada de la gene ación eólica y o o ol aica en Panamá. I+D
Tecnológico, 13(1), 71-82. Re ie ed om h ps:// e is as.u p.ac.pa/index.php/id-
ecnologico/a icle/ iew/1440
Akiba, T., Sano, S., Yanase, T., Oh a, T., & Koyama, M. (2019). Op una: A nex -gene a ion
hype pa ame e op imiza ion amewo k. A Xi , 2623–2631.
h ps://doi.o g/10.1145/3292500.3330701
Al-Musaylh, M. S., Deo, R. C., Adamowski, J. F., & Li, Y. (2018). Sho - e m elec ici y demand
o ecas ing wi h MARS, SVR and ARIMA models using agg ega ed demand da a in Queensland,
Aus alia. Ad anced Enginee ing In o ma ics, 35(No embe 2017), 1–16.
h ps://doi.o g/10.1016/j.aei.2017.11.002
Alex J., S., & Schölkop , B. (2004). A u o ial on suppo ec o eg ession. S a is ics and Compu ing,
14, 199–222. h p://dx.doi.o g/10.1088/1751-8113/44/8/085201
Amin, M. A. Al, & Hoque, M. A. (2019). Compa ison o ARIMA and SVM o sho - e m load
o ecas ing. IEMECON 2019 - 9 h Annual In o ma ion Technology, Elec omechanical
Enginee ing and Mic oelec onics Con e ence, 205–210.
h ps://doi.o g/10.1109/IEMECONX.2019.8877077
Amjady, N. (2001). Sho - e m hou ly load o ecas ing using ime-se ies modeling wi h peak load
es ima ion capabili y. IEEE T ansac ions on Powe Sys ems, 16(4), 798–805.
h ps://doi.o g/10.1109/59.962429
Ande sen, F. M., Henningsen, G., Mølle , N. F., & La sen, H. V. (2019). Long- e m p ojec ions o he
hou ly elec ici y consump ion in Danish municipali ies. Ene gy, 186, 115890.
h ps://doi.o g/10.1016/j.ene gy.2019.115890
A e , S., & El awil, A. B. (2020). Assessmen o s acked unidi ec ional and bidi ec ional long sho -
e m memo y ne wo ks o elec ici y load o ecas ing. Elec ic Powe Sys ems Resea ch,
187(Ap il), 106489. h ps://doi.o g/10.1016/j.eps .2020.106489
Ba aka , E. H., & Al-Qasem, J. M. (1998). Me hodology o weekly load o ecas ing. IEEE T ansac ions
on Powe Sys ems, 13(4), 1548–1555. h ps://doi.o g/10.1109/59.736304
38
Beci o ic, E., & Coso ic, M. (2016). Machine lea ning echniques o sho -Te m load o ecas ing. 4 h
In e na ional Symposium on En i onmen F iendly Ene gies and Applica ions, EFEA 2016.
h ps://doi.o g/10.1109/EFEA.2016.7748789
Be gs a, J., Ba dene , R., Bengio, Y., & Kégl, B. (2011). Algo i hms o hype -pa ame e op imiza ion.
Ad ances in Neu al In o ma ion P ocessing Sys ems 24: 25 h Annual Con e ence on Neu al
In o ma ion P ocessing Sys ems 2011, NIPS 2011, 1–9. Re ie ed om
h ps://pape s.nips.cc/pape /2011/ ile/86e8 7ab32c d12577bc2619bc635690-Pape .pd
Be simas, D., Dela ue, A., Jaille , P., & Ma in, S. (2019). The P ice o In e p e abili y.
h ps://a xi .o g/abs/1907.03419
Boya, C. (2019). Analyzing he ela ionship be ween empe a u e and load demand in he egions
wi h he highes elec ici y consump ion in he epublic o Panama. P oceedings - 2019 7 h
In e na ional Enginee ing, Sciences and Technology Con e ence, IESTEC 2019, 132–137.
h ps://doi.o g/10.1109/IESTEC46403.2019.00-88
Cai, J., Cai, H., Cai, Y., Wu, L., & Shen, Y. (2020). Sho - e m Fo ecas ing o Use Powe Load in China
Based on XGBoos . 3, 1–5. h ps://doi.o g/10.1109/appeec48164.2020.9220335
Cai, Y., Xie, Q., Wang, C., & Lu, F. (2011). Sho - e m load o ecas ing o ci y holidays based on
gene ic suppo ec o machines. 2011 In e na ional Con e ence on Elec ical and Con ol
Enginee ing, ICECE 2011 - P oceedings, 1, 3144–3147.
h ps://doi.o g/10.1109/ICECENG.2011.6057627
Cao, L., Li, Y., Zhang, J., Jiang, Y., Han, Y., & Wei, J. (2020). Elec ical load p edic ion o heal hca e
buildings h ough single and ensemble lea ning. Ene gy Repo s, 6, 2751–2767.
h ps://doi.o g/10.1016/j.egy .2020.10.005
Chapagain, K., & Ki ipiyakul, S. (2018). Sho -Te m Elec ici y Demand Fo ecas ing wi h Seasonal and
In e ac ions o Va iables o Thailand. IEECON 2018 - 6 h In e na ional Elec ical Enginee ing
Cong ess, Ma ch 2009, 2018–2021. h ps://doi.o g/10.1109/IEECON.2018.8712189
CND-si . (2021, Ma ch 2). Sis ema de In o mación en Tiempo Real. Re ei ed om
h p://si .cnd.com.pa/m/pub/sin.h ml
CND. (2021a, Ma ch 2). In o me de Planeamien o Ope a i o - Semes e I 2020. Re ei ed om
h ps://si iop i ado.cnd.com.pa/In o me/Download/36121?key=VXd9e23Z9JRA5aIUR21R-
P8gocoGOMqd So79FduN
CND. (2021b, Ma ch 2). Me odologías de De allle (ene o 2021). Me odologías de De alle. Re ei ed
om h ps://www.cnd.com.pa/index.php/ace ca/documen os/no mas
CND. (2021c, Ma ch 2). Pos -dispa ch – Ope a ions Repo s. Re ie ed om
h ps://www.cnd.com.pa/index.php/in o mes/ca ego ia/in o mes-de-ope aciones? ipo=60
CND. (2021d, Ma ch 2). Reglas Come ciales. Reglas Come ciales Pa a El Me cado Mayo is a de
Elec icidad. Re ei ed om h ps://www.cnd.com.pa/index.php/ace ca/documen os/no mas
39
CND. (2021e, Ma ch 2). Weekly p e-dispa ch – Ope a ions Repo s. Re ei ed om
h ps://www.cnd.com.pa/index.php/in o mes/ca ego ia/in o mes-de-
ope aciones? ipo=68&anio=2019&semana=0
Die ich, B., Wal he , J., Weigold, M., & Abele, E. (2020). Machine lea ning based e y sho e m
load o ecas ing o machine ools. Applied Ene gy, 276(Feb ua y), 115440.
h ps://doi.o g/10.1016/j.apene gy.2020.115440
Die o s , B. J., Simmons, J. P., & Massey, C. (2015). Algo i hm a e sion: People e oneously a oid
algo i hms a e seeing hem e . Jou nal o Expe imen al Psychology: Gene al, 144(1), 114–126.
h ps://doi.o g/10.1037/xge0000033
Do, L. P. C., Lin, K. H., & Molná , P. (2016). Elec ici y consump ion modelling: A case o Ge many.
Economic Modelling, 55, 92–101. h ps://doi.o g/10.1016/j.econmod.2016.02.010
Du a, S., Li, Y., Venka a aman, A., Cos a, L. M., Jiang, T., Plana, R., To djman, P., Choo, F. H., Foo, C.
F., & Pu gen, H. B. (2017). Load and Renewable Ene gy Fo ecas ing o a Mic og id using
Pe sis ence Technique. Ene gy P ocedia, 143, 617–622.
h ps://doi.o g/10.1016/j.egyp o.2017.12.736
Eseye, A. T., Leh onen, M., Tukia, T., Uimonen, S., & Milla , R. J. (2019). Machine Lea ning Based
In eg a ed Fea u e Selec ion App oach o Imp o ed Elec ici y Demand Fo ecas ing in
Decen alized Ene gy Sys ems. IEEE Access, 7, 91463–91475.
h ps://doi.o g/10.1109/ACCESS.2019.2924685
Fe nandes, R. S. S., Bichpu iya, Y. K., Rao, M. S. S., & Soman, S. A. (2011). Day ahead load o ecas ing
models o holidays in Indian con ex . 2011 In e na ional Con e ence on Powe and Ene gy
Sys ems, ICPS 2011, 1–5. h ps://doi.o g/10.1109/ICPES.2011.6156652
Fe ei a, P. M., Cuambe, I. D., Ruano, A. E., & Pes ana, R. (2013). Fo ecas ing he Po uguese
elec ici y consump ion using leas -squa es suppo ec o machines. IFAC P oceedings Volumes
(IFAC-Pape sOnline), 3(PART 1), 411–416. h ps://doi.o g/10.3182/20130902-3-CN-3020.00138
Fe ei a, P. M., Ruano, A. E., & Pes ana, R. (2010). Imp o ing he iden i ica ion o RBF p edic i e
models o o ecas he Po uguese elec ici y consump ion ? IFAC P oceedings Volumes (IFAC-
Pape sOnline), 1(PART 1), 208–213. h ps://doi.o g/10.3182/20100329-3-p -3006.00039
Gace a. (2020). Busqueda A anzada Gace a. Gace a O icial. Re ei ed om
h ps://www.gace ao icial.gob.pa/Busqueda-A anzada
GCP. (2021). AI Pla o m No ebooks | Google Cloud Pla o m. Re ie ed om
h ps://cloud.google.com/ai-pla o m-no ebooks
GES DISC. (2015). Global Modeling and Assimila ion O ice (GMAO) (2015), MERRA-2
a g1_2d_sl _Nx: 2d,1-Hou ly,Time-A e aged,Single-Le el,Assimila ion,Single-Le el Diagnos ics
V5.12.4, G eenbel , MD, USA. Changes; Global Modeling and Assimila ion O ice (GMAO).
h ps://doi.o g/10.5067/VJAFPLI1CSIV
40
Google. (2020). Colabo a o y – Google. Colabo a o y F equen ly Asked Ques ions. Re ie ed om
h ps:// esea ch.google.com/colabo a o y/ aq.h ml
Had i, S., Nai malek, Y., Najib, M., Bakhouya, M., Fakh i, Y., & Ela oussi, M. (2019). A compa a i e
s udy o p edic i e app oaches o load o ecas ing in sma buildings. P ocedia Compu e
Science, 160, 173–180. h ps://doi.o g/10.1016/j.p ocs.2019.09.458
Han, J., Kambe , M., & Pei, J. (2011). Da a Mining. Concep s and Techniques, 3 d Edi ion, pp. 99-110
(The Mo gan Kau mann Se ies in Da a Managemen Sys ems).
He man-Sa a , O. (2021, Ma ch 2). Time Based C oss Valida ion. Time Based C oss Valida ion.
Re ie ed om h ps:// owa dsda ascience.com/ ime-based-c oss- alida ion-d259b13d42b8
HITACHI-ABB. (2021, Ma ch 2). Nos adamus. Sho - e m enewable, demand and p ice o ecas ing.
Re ie ed om h ps://www.hi achiabb-powe g ids.com/cn/en/o e ing/p oduc -and-
sys em/ene gy-po olio-managemen / ading-and- isk-managemen /nos adamus
Hossein, S., & Mohammad, S. S. (2011). Elec ic Powe Sys em Planning. (p. 10). Be lin, Heidelbe g,
Ge many: Sp inge .
Hoye , S., & Hamman, J. J. (2017). xa ay: N-D labeled A ays and Da ase s in Py hon. Jou nal o Open
Resea ch So wa e, 5. h ps://doi.o g/10.5334/jo s.148
Johannesen, N. J., Kolhe, M., & Goodwin, M. (2019). Rela i e e alua ion o eg ession ools o u ban
a ea elec ical ene gy demand o ecas ing. Jou nal o Cleane P oduc ion, 218, 555–564.
h ps://doi.o g/10.1016/j.jclep o.2019.01.108
Khwaja, A. S., Anpalagan, A., Naeem, M., & Venka esh, B. (2020). Join bagged-boos ed a i icial
neu al ne wo ks: Using ensemble machine lea ning o imp o e sho - e m elec ici y load
o ecas ing. Elec ic Powe Sys ems Resea ch, 179(June 2019), 106080.
h ps://doi.o g/10.1016/j.eps .2019.106080
La Es ella de Panamá. (2021, Ma ch 2). Cua en ena en Panamá. Calles Desie as En El P ime Día de
Cua en ena To al En Panamá Po COVID-19. Re ei ed om
h ps://www.laes ella.com.pa/nacional/200325/calles-desie as-p ime -dia-cua en ena- o al-
panama-co id-19
Lebo sa, M. E., Sigauke, C., Be e, A., Fildes, R., & Boylan, J. E. (2018). Sho e m elec ici y demand
o ecas ing using pa ially linea addi i e quan ile eg ession wi h an applica ion o he uni
commi men p oblem. Applied Ene gy, 222(Decembe 2017), 104–118.
h ps://doi.o g/10.1016/j.apene gy.2018.03.155
Li, C. (2020). Designing a sho - e m load o ecas ing model in he u ban sma g id sys em. Applied
Ene gy, 266(Janua y), 114850. h ps://doi.o g/10.1016/j.apene gy.2020.114850
Liao, X., Cao, N., Li, M., & Kang, X. (2019). Resea ch on Sho -Te m Load Fo ecas ing Using XGBoos
Based on Simila Days. P oceedings - 2019 In e na ional Con e ence on In elligen
T anspo a ion, Big Da a and Sma Ci y, ICITBS 2019, 675–678.
h ps://doi.o g/10.1109/ICITBS.2019.00167
41
Liu, F., Findlay, R. D., & Song, Q. (2006). A neu al ne wo k based sho e m elec ic load o ecas ing
in On a io Canada. CIMCA 2006: In e na ional Con e ence on Compu a ional In elligence o
Modelling, Con ol and Au oma ion, Join ly wi h IAWTIC 2006: In e na ional Con e ence on
In elligen Agen s Web Technologies ..., 0–6. h ps://doi.o g/10.1109/CIMCA.2006.17
Liu, X., Zhang, Z., & Song, Z. (2020). A compa a i e s udy o he da a-d i en day-ahead hou ly
p o incial load o ecas ing me hods: F om classical da a mining o deep lea ning. Renewable
and Sus ainable Ene gy Re iews, 119(No embe 2019), 109632.
h ps://doi.o g/10.1016/j. se .2019.109632
Liu, Y., Luo, H., Zhao, B., Zhao, X., & Han, Z. (2019). Sho -Te m Powe Load Fo ecas ing Based on
Clus e ing and XGBoos Me hod. P oceedings o he IEEE In e na ional Con e ence on So wa e
Enginee ing and Se ice Sciences, ICSESS, 2018-No em, 536–539.
h ps://doi.o g/10.1109/ICSESS.2018.8663907
Massaoudi, M., Re aa , S. S., Chihi, I., T abelsi, M., Ouesla i, F. S., & Abu-Rub, H. (2021). A no el
s acked gene aliza ion ensemble-based hyb id LGBM-XGB-MLP model o Sho -Te m Load
Fo ecas ing. Ene gy, 214, 118874. h ps://doi.o g/10.1016/j.ene gy.2020.118874
McKinney, W., & Team, P. D. (2020). pandas: powe ul Py hon da a analysis oolki Release 1.1.4.
h ps://doi.o g/10.5281/zenodo.3509134
Mo ales-España, G., La o e, J. M., & Ramos, A. (2013). Tigh and compac MILP o mula ion o s a -
up and shu -down amping in uni commi men . IEEE T ansac ions on Powe Sys ems, 28(2),
1288–1296. h ps://doi.o g/10.1109/TPWRS.2012.2222938
Nadh, K. (2021, Ma ch 2). ne CDF4 API documen a ion. Ne CDF4 API Documen a ion. Re ie ed om
h ps://unida a.gi hub.io/ne cd 4-py hon/
Omidi, A., Ba aka i, S. M., & Ta akoli, S. (2015). Applica ion o nusuppo ec o eg ession in sho -
e m load o ecas ing. 20 h Elec ical Powe Dis ibu ion Con e ence, EPDC 2015, Ap il, 32–36.
h ps://doi.o g/10.1109/EPDC.2015.7330469
Op una. (2021a, Ma ch 2). TPE Sample — Op una 2.5.0 documen a ion. Re ei ed om
h ps://op una. ead hedocs.io/en/s able/ e e ence/gene a ed/op una.sample s.TPESample .h
ml
Op una. (2021b, Ma ch 2). T ial — Op una 2.5.0 documen a ion. Re ei ed om
h ps://op una. ead hedocs.io/en/s able/ e e ence/gene a ed/op una. ial.T ial.h ml
Pa e akis, N. G., Mocanu, E., Gibescu, M., S appe s, B., & Van Als , W. (2017). Deep lea ning e sus
adi ional machine lea ning me hods o agg ega ed ene gy demand p edic ion. 2017 IEEE PES
Inno a i e Sma G id Technologies Con e ence Eu ope, ISGT-Eu ope 2017 - P oceedings, 2018-
Janua, 1–6. h ps://doi.o g/10.1109/ISGTEu ope.2017.8260289
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8.3.7. Tes ing week 7. Week 41, Oc obe 2019.
8.3.8. Tes ing week 8. Week 44, No embe 2019. Na ional holidays.
49
8.3.9. Tes ing week 9. Week 51, Decembe 2019. Ch is mas.
8.3.10. Tes ing week 10. Week 1, Janua y 2020. Ma y s Day.
50
8.3.11. Tes ing week 11. Week 6, Feb ua y 2020.
8.3.12. Tes ing week 12. Week 10, Ma ch 2020.
51
8.3.13. Tes ing week 13. Week 20, May 2020. Qua an ine pe iod.
8.3.14. Tes ing week 14. Week 24, Jun 2020. Qua an ine pe iod.
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