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Ni Ding

To cite this version:

Ni Ding. Load models for operarion and planning of electricity distribution networks with metering

data. Engineering Sciences [physics]. Université de Grenoble, 2012. English. �tel-00862879�

Spéialité: Génie Életrique

Arrêtéministériel: 7 Aut 2006

Présentée par

Ni DING

Thèse dirigée par Yvon BÉSANGERet

odirigée par Frédéri WURTZ

préparée ausein du

Laboratoire G2ELAB

dans l'Éole Dotorale: EEATS

Load models for operation and planning of

eletriity distribution networks with smart

metering data

Thèse soutenue publiquementle 30 Novembre 2012,

devant lejury omposé de:

Pr. Nouredine Hadjsaid

GrenobleINP, Président

Pr. Carlo Alberto Nui

UniversitédeBologne,Rapporteur

Pr. Corinne Alonso

UniversitédeToulouse,Rapporteur

Pr. Didier Mayer

MinedeParis,Membre

Pr. Yvon Bésanger

GrenobleINP,Membre

Dr. Frédéri Wurtz

CNRSGrenoble,Membre

Invités:

M. Olivier Devaux

EDFR&D

M. Alain Glatigny

ShneiderEletri

Aknowledgments xiii

Notations xix

1 General introdution: the new problemati of load models

in the smart grid ontext 1

1.1 Bakground: smartgrid and smart meters for load modeling . . 2

1.2 Motivation and objetives . . . 3

1.2.a Fornetwork operationneed. . . 4

1.2.b Fornetwork planningneed . . . 5

1.3 Contributions of the thesis . . . 6

1.4 Sope and organization of the dissertation . . . 7

A Short-term load foreasting models for monitoring and state es- timator 11 2 Load foreastingtehniques andshort-term modelframework 13 2.1 Literature review . . . 14

2.1.a Foreastingleadtimesandinuene fators. . . 14

2.1.b Foreastingmethods . . . 16

2.1.b-i Classialapproah . . . 18

2.1.b-ii Artiialintelligentapproah . . . 25

2.1.b-iii Hybridmodels . . . 35

2.1. Literaturereviewonlusionsandperspetives . . . 37

2.2 Data desription . . . 40

2.2.a MV/LVsubstation . . . 40

2.2.a-i Temperatureinuene . . . 41

2.2.a-ii Daytypeinuene . . . 42

2.2.a-iii Timeinuene . . . 42

2.2.b MVfeeder . . . 45

2.3 Choies of Time series and NN methods . . . 45

2.4 Performane riteriaand referene ase . . . 46

2.4.a Performaneriteria: MAPEandMAE . . . 46

2.4.b Referenease: thenaivemodel . . . 47

2.5 Conlusion . . . 47

3 Time series model 49

3.1 Additive time series model and proedure overview . . . 50

3.2 Statistial tools . . . 51

3.2.a DummyVariableRegression . . . 51

3.2.b TrendComponentEstimation . . . 52

3.2. CyliComponentEstimation . . . 52

3.2.d TestsofStationarity . . . 53

3.2.e SmoothedPeriodogram . . . 53

3.2.f RegressionModelwithFourierComponents . . . 54

3.2.g ANOVA NullityTest . . . 54

3.2.h CompleteForeastingModel . . . 55

3.3 Appliation example results . . . 55

3.3.a Trainingset . . . 55

3.3.b Testset . . . 57

3.3. ResidualAnalysis . . . 60

3.3.-i Normality. . . 60

3.3.-ii Independene . . . 61

3.4 Weather unertainty . . . 62

3.5 Conlusion . . . 64

4 Neural network model 67 4.1 Mahine learning tehnique . . . 68

4.2 Multi Layer Pereptrons and trainingproess . . . 69

4.3 Model design. . . 71

4.3.a Variableseletion . . . 71

4.3.b Modelseletion . . . 73

4.3.b-i Modelseletionmethodology . . . 73

4.3.b-ii Assessmentofthegeneralizationabilityofthemodels . . . 74

4.4 Numerial illustration . . . 76

4.4.a Framework . . . 76

4.4.b Modeldesign: anillustrativeexample . . . 77

4.4.b-i Variableseletionexample. . . 77

4.4.b-ii Seletingthebest modelforagivenomplexity . . . 81

4.4.b-iii Complexityseletionexample. . . 81

4.4. Results . . . 83

4.5 Overall omparison with the time series model . . . 85

4.6 Conlusion and perspetive . . . 86

B Load estimation models for distribution network planning 89 5 Loadresearhprojetsindistributionnetworks: stateofthe art 91 5.1 Deision making in distribution network planning . . . 92

5.1.a Coinidentload . . . 93

5.1.b TypialLoadProle(TLP) . . . 95

5.2 Load researh projets in different ountries . . . 96

5.2.a FinlandDSOmodel . . . 97

5.2.b DenmarkDongEnergy . . . 98

5.2. NorwaySINTEFEnergyResearh . . . 99

5.2.d Taipowersystem. . . 99

5.3 Frenh load researh projet . . . .100

5.3.a Datadesription. . . .102

5.3.b EDFBAGHEERA model. . . .103

5.3.b-i TMB temperatureandbasimodel. . . .104

5.3.b-ii Commonoeientestimation . . . .105

5.3.b-iii Spei parameterestimation . . . .105

5.3.b-iv Illustrativeexampleandmodel's output . . . .107

5.4 Conlusion . . . .111

6 Nonparametri model 113 6.1 Nonparametri model. . . .115

6.1.a Statistialtests . . . .116

6.1.b Kerneldensityestimation. . . .117

6.1. CUSUMalgorithm . . . .117

6.1.d Kernelregression . . . .118

6.1.e Smoothingparameterseletion: ross-validationtehnique. . . .119

6.2 Computational example . . . .120

6.2.a Illustrativeexampleresults . . . .121

6.2.b ComparisonwiththeBAGHEERAmodel. . . .124

6.3 Validation study . . . .127

6.4 Disussion . . . .129

6.4.a Citationsoftheupper-bounddenitionsin EDFreports. . . .130

6.4.b Upperboundin thenonparametrimodels . . . .131

6.4. Validationtrialontheupper-bound estimation . . . .132

6.5 Conlusion and perspetive . . . .137

7 General onlusion and perspetive 139 7.1 Conlusion . . . .139

7.2 Perspetive . . . .140

Bibliographie 154

Appendies 155

A Time series model's result summary 155

B Binary hypothesis test 157

C Example of ANOVA nullity test 159

D Comparisonresultsof naivemodel, timeseriesmodelandneu-

ralnetwork model 161

E Résumé français 169

E.1 Introdution générale: la nouvelle problématique du modèle

de harge dans le ontexte du réseau intelligent . . . .169

E.1.a Réseauintelligentetompteurs intelligentspourlesmodèlesdeharge . . .169

E.1.b Objetifset plandurésuméfrançais . . . .170

E.1. Contributiondethèse . . . .172

E.2 Modèle de harge préditif ourt terme pour la onduite et l'estimateur d'état. . . .173

E.2.a Méthodesdelaprévisiondehargedanslalittérature . . . .174

E.2.b Desriptiondedonnées . . . .178

E.2. Choixdesméthodes: sériehronologiqueetréseaudeneurones . . . .180

E.2.d Critèresdeperformaneet modèlederéférene. . . .181

E.2.e Modèlesériehronologique . . . .182

E.2.f Modèleréseaudeneurones . . . .187

E.2.f-i Coneptiondumodèle . . . .188

E.2.f-ii Comparaisonglobaleavelemodèledesériehronologique. . . .191

E.3 Modèled'estimation de hargepour laplanifiation du réseau de distribution . . . .193

E.3.a ModèleBAGHEERA . . . .195

E.3.b Modèlenonparamétrique. . . .198

E.4 Conlusions et perspetives générales . . . .199

1.1 Availablemeasurements intheFrenh distribution networks . . . 3

1.2 Relationshipamongforeasting models,SE, andADA funtions. . . 5

2.1 Summaryof loadforeasting methods intwo dimensions . . . 17

2.2 Singlepereptronstruture . . . 27

2.3 One-hidden-layer network struture . . . 27

2.4 Supervised learningproedure . . . 28

2.5 Reurrent neural network struture . . . 29

2.6 FuzzyLogi proess . . . 34

2.7 Fuzzylogi: inputvariables membership funtion . . . 35

2.8 Fuzzylogi: outputvariablesmembership funtion. . . 35

2.9 Daily average load and temperature data through

414

^{days (from Sept. 9,} 2009 to Ot. 27,2010)ofsubstation CE_MOU (mainly residential) . . . 40

2.10 Dailyaverage loadthrough

414

^{days (from Sept. 9,2009 to Ot. 27,2010)} ofsubstation VI_LOG (mixedserviesetor andindustrial) . . . 41

2.11 Dailyaverage loadthrough

414

^{days (from Sept. 9,2009 to Ot. 27,2010)} ofsubstation CE_FRO (anindustrial lient) . . . 41

2.12 Normal week ompared to the week with a national holiday of Substation CE_FRO (an industriallient) . . . 43

2.13 Similarity index alulatedbased onall days of substationCE_MOU . . . . 44

2.14 SimilarityindexwithoutweekendsandpubliholidaysofsubstationCE_MOU 44 2.15 MVfeeders and position ofonneted MV/LVsubstations . . . 45

3.1 Stepsof the designed timeseriesforeasting method . . . 51

3.2 Trainingset andtest setperiodsof theavailable data. . . 55

3.3 A weekly onsumption pattern (Otober 5,2009 to Otober11, 2009) of a mixedindustrialand serviesetorsubstation VI_LOG. . . 56

3.4 SubstationVI_LOG,MAEriteriaalulatedonthetrainingset(117days) fordierent slidingwindow sizes(weeks). . . 56

3.5 PeriodogramofthedetrendedtrainingdatasetsmoothedbytheDaniellkernel 57 3.6 Substation VI_LOG, omparison of the foreasting results with the real measurementson the test setperiod(297 days). . . 58

3.7 Substation VI_LOG,two-day-ahead load foreastingresults on weekdays . . 58

3.8 Substation VI_LOG,two-day-ahead load foreastingresults on weekends . . 59

3.9 Substation VI_LOG,densityfuntion plotandumulative densityfuntion plotof theresidual. . . 61

3.10 Substation VI_LOG,evolutionof autoorrelationfuntionsof eah step . . . 62

3.11 Histogram of the Gaussian distributed temperature unertainty adding to

theatual temperature . . . 63

3.12 Three-day foreasting temperatures ompared to theatual temperatures . . 64

4.1 Orthogonal forward rankingproess. . . 73

4.2 Neural network seletion proedure . . . 74

4.3 Separation of the loadurve into the daily averagepower and theintraday power variation . . . 77

4.4 Generation of seondary variables and probe variables. . . 78

4.5 Cumulative probability for a probe variable to have a better rank than a andidate variable. . . 80

4.6 Modelseletion for the intradaypowervariationmodel . . . 82

4.7 Neural networkomplexityseletion strategieswithVLOOsoreand lever- age distribution . . . 82

5.1 Network deision makingproedure . . . 93

5.2 Example ofoinidene fator alulation . . . 94

5.3 Distribution Load Estimation (DLE)proess . . . 97

5.4 Voltage-drop andtap hanger adjustment. . . .101

5.5 Two-year(July 01, 2004

∼

^{June 30, 2006) daily average loads of o-peak/} on-peak optionlient no.5 . . . .103

5.6 Two-year(July01,2004

∼

^{June30,2006)dailyaverageloadsofbasioption} lient no.18 . . . .103

5.7 O-peak/on-peak option lientno.5: urve tting on o-peak dailyenergy use . . . .108

5.8 O-peak/on-peak option lientno.5: urve tting on on-peakdaily energy use . . . .108

5.9 Basioption lientno.18: urve tting ondailyenergy use. . . .109

5.10 O-peak/on-peak option lient no.5: outputs of the BAGHEERA model, TMB loadestimations on weekdays . . . .110

5.11 O-peak/ on-peak option lient no.5 : omparison of TMB weekend's and weekday'sloadestimation. . . .111

6.1 Overviewofthe nonparametrimodel . . . .116

6.2 Statistial testsproedure. . . .117

6.3 Data diagram: historial data,1st-yeardata, and2nd-yeardata. . . .120

6.4 O-peak/on-peak optionlientno.5: statistialtestsresultof thermosensi- tive hek . . . .121

6.5 O-peak/on-peak optionlient no.5: CUSUM hartofdaily average power .121 6.6 O-peak/on-peak option lient no.5: separation result of one year'spower databyCUSUMalgorithm . . . .122

6.7 O-peak/on-peak optionlient no.5: weekdayminimumpowerestimations .122 6.8 O-peak/on-peak option lient no.5: statistial tests result for the data oherene hek . . . .123

6.9 O-peak/on-peakoptionlientno.5: ross-validation resultonthesmooth- ingparameter seletion of the kernel estimation . . . .124

6.10 NW,LL,and LL2 regressors,indiating therelationshipbetween thevaria-

tionof temperature and thelient's dailypower onsumption . . . .124

6.11 O-peak/on-peakoption lientno.5: presentation ofunertainty ofa sample125

6.12 O-peak/on-peak option lient no.5: maximumpowerestimation of week-

dayloads. . . .125

6.13 SumSquareErrors(SSE)softheBAGHEERAestimator,NW,LL,andLL2

estimatorson the test data . . . .126

6.14 Studyases and senariosin thevalidation study. . . .127

6.15 Studyase no.1, senario1: o-peak/on-peakoption lients, omparison of

SSEs of BAGHEERA, NW, LL and LL2 estimators on the days below 0

degreeduring the seondyear . . . .128

6.16 Studyase no.1, senario2: o-peak/on-peakoption lients, omparison of

SSEsofBAGHEERA,NW,LLandLL2estimators ontheo-peakhoursof

the days below0 degreeduring the seondyear. . . .128

6.17 Studyase no.2, senario1: o-peak/on-peakoption lients, omparison of

SSEs of BAGHEERA, NW, LL and LL2 estimators on the 30 oldestdays

ofthe seond-yeardata . . . .129

6.18 Studyase no.2, senario2: o-peak/on-peakoption lients, omparison of

SSEsofBAGHEERA,NW,LLandLL2estimators ontheo-peakhoursof

the 30oldest days oftheseond-yeardata . . . .129

6.19 10%hourly power exess probability threshold and median value for every

time step. . . .132

6.20 Summary of the upper-bound omparison of the real measurements, the

BAGHEERA model,and nonparametri models . . . .133

6.21 Power onsumption oflient no.22 during two years (July01, 2004

∼

^June

30,2006) . . . .134

6.22 Power onsumption oflient no.17 during two years (July01, 2004

∼

^June

30,2006) . . . .135

6.23 30-minute timestep standarddeviation(sd) oflientNo.17 . . . .135

E.1 Relation entre les modèles de harge préditifs, l'estimateur d'état, et les

fontionsavanées du réseau . . . .171

E.2 Résumédes méthodesde hargepréditives endeux dimensions. . . .176

E.3 Courbedehargeettempératurejournalièrependant

414

^{jours(du9/9/2009}

au 27/10/2010) du poste HTA/BT CE_MOU (onneté prinipalement à

deslientsrésidentiels) . . . .179

E.4 Courbedehargejournalièrependant

414

^{jours(du9/9/2009au}27/10/2010) du poste HTA/BT VI_LOG (onneté aux lients mixtes tertiaires et in-

dustriels). . . .179

E.5 Courbedehargejournalièrependant

414

^{jours(du9/9/2009au}27/10/2010) duposteHTA/BTCE_FRO (onneté àunseul lient industriel) . . . .180

E.6 Etapes pour onstruire le modèle série hronologique pour la prévision de

harge . . . .183

E.7 Proéduredu lassement par laprojetion orthogonale deGram-Shmidt . .189

E.8 Proédurede séletion duréseau de neurones . . . .190

E.9 La prise desdéisions dansleréseau de distribution . . . .194

E.10Client no.5 option heure reuse/pleine: ajustement de ourbe sur l'énergie

journalièrependantlesheurespleines. L'indieHPsignieHeurePleine

etl'indie HCsignie HeureCreuse. . . .196

E.11Client no.18 option de base: ajustement de ourbe surl'énergiejournalière. 196

E.12Clientno.5 option heurereuse/pleine: TMB estimationsde lahargepen-

dant lesjours ouvrables . . . .197

E.13La proéduredu modèle nonparamétrique . . . .199

2.1 Dierent time horizon loadforeasts . . . 15

2.2 Summaryof loadforeasting approahes andtheir features . . . 39

2.3 Sevensubstationlients'ompositionsandorrelationoeientswithtem-

peratures. . . 42

3.1 Foreasting resultomparison between the naive model and thetimeseries

modelon theSubstation VI_LOG data . . . 59

3.2 Foreasting resultomparison between the naive model and thetimeseries

modelon theMVfeeder CLdata . . . 60

3.3 Performane omparison among Time Series (TS) models with foreasting

temperature, atual temperature, andnaive model. . . 64

4.1 9variables forthe average powerneural network model . . . 80

4.2 19variables for intradaypowervariation neural network model . . . 81

4.3 SubstationCE_MOU,foreastingresults: omparisonamongthenaivemodel,

time seriesmodel andNN models . . . 84

4.4 Substation CE_FRO, foreasting results: omparison between the naive

modeland the neuralnetworkmodel . . . 84

4.5 Summary of omparison aspets between neural network models and time

seriesmodels for the short-termload foreasting appliation . . . 85

A.1 MV/LVsubstations,foreastingresults: omparisonbetweenthenaivemodel

andtheomplete TimeSeries (TS) modelof one-day-aheadforeasts. . . .155

A.2 MV/LVsubstations,foreastingresults: omparisonbetweenthenaivemodel

andtheomplete TimeSeries (TS) modelof two-day-aheadforeasts. . . .155

A.3 MV feeders, foreasting results: omparison between the naive model and

the ompleteTime Series(TS) modelof one-day-aheadforeasts.. . . .156

A.4 MV feeders, foreasting results: omparison between the naive model and

the ompleteTime Series(TS) modelof two-day-aheadforeasts. . . .156

D.1 6variables forthedailyaveragepowermodeland19 variables fortheintra-

daypowervariationmodel . . . .161

D.2 6variables forthedailyaveragepowermodeland23 variables fortheintra-

daypowervariationmodel . . . .162

D.3 6variables forthedailyaveragepowermodeland40 variables fortheintra-

daypowervariationmodel . . . .163

D.4 10 variables for the daily average power model and 37 variables for the

intradaypower variation model . . . .164

D.5 10 variables for the daily average power model and 37 variables for the

intraday powervariationmodel . . . .165

D.6 24 variables for the daily average power model and 32 variables for the

intraday powervariationmodel. . . .166

D.7 Substation CE_FRO:14variablesforthedailyaveragepowermodeland28

variables forthe intradaypowervariation model. . . .168

E.1 Diérentshorizonsde temps pour laprévisionde harge . . . .174

E.2 Résumé desmodèles de harge préditifsetleurs aratéristiques . . . .177

E.3 Résumédelaomparaisonentrelemodèleduréseaudeneuronesetlemodèle

de lasériehronologiquepourla prévisionde harge ourtterme . . . .192

Ahieving myPhD degreehassetamilestone inmy life. The thesisdefensehasdrawnan

end to my best and worst moments during the three years that I have spent in G2elab.

People thathelpedmewill alwaysremaindear to mefor myfuturelife journey.

Above all, I would like to thank the reviewers and ommittee members of my thesis.

A very big thank to Pr. Carlo Alberto Nui and Pr. Corinne Alonso for their timeand

energy to examine mydissertation and for their valuable opinions. Theirenouragements

and appreiations give me strength and ondene inmyfuture work. Thanks also go to

Pr. DidierMayerforhis interests and insightfulommentsaboutmywork. Itwasagreat

honor for me to have Pr. Nouredine Hadjsaid as the president of the ommittee, and I

aknowledgehim for that.

I'malsogratefultotherepresentativesoftheindustrialpartnersoftheompanythatI

workwith: Mr. OliverDevauxfromEDFandMr. AlainGlatignyfromShneider Eletri.

Ithankthemforthisinterestingsubjetthattheysetupandpertinentommentsregarding

theindustrialappliations ofmymodels.

I owe my sinere gratitude to myprinipal advisor, Pr. Yvon Bésanger. I would like

to thank him for his open-mind regarding ollaborations, for his support and trust, and

for hispatiene inguidane. Ithank him for always being there for measa teammate at

diulttimes thatwe enountered throughpubliations, and administrations.

IwouldliketoextendmygratitudetoDr. FrédériWurtzforhistrustandappreiation

for mywork,for hiswarmlyweloming meinto thelaboratory.

I would not forget to grant my gratitude to Pr. Gérard Dreyfus, Pr. Jean-Louis

Laoume and Pr. Daniel Baudois for their sienti guidane. I highly respet their

passion and rigorousness for the researh. I thank them to aept to oer me tehnial

advieswithout reserve.

I want to expressmy gratitudeto Mr. ChristopheKeiny, Mr. Guillaume Antoineand

Miss Letiia De-Alvaro from EDF for their energy devoting to my thesis projet. They

have been supportive industrial advisers to keep me on trak with the industrial needs,

and inthe meantimegive megreatfreedom to develop independent solutions.

I also would like to thank Mr. Frédéri Gorgette from ERDF, my supervisor of the

traineeship, for oeringmesuh agreat opportunity to pursuemyPhD.

Mydeepest gratitude reserves to myfamily and myfriends. Even though none ofmy

family member ouldattend mythesisdefense,their love and arearealways around me.

I want to thank myfriendsinG2elab fortheir tolerane andunonditional support tome

during those years. I have nevermet somany great people during so short period of my

life. I willtreasure our friendshipsfor alifelong time.

Youare responsible for what you have tamed. - The littleprine

To them,Idediatethis work.

ADA AdvanedDistribution Automation

ANN Artiial Neuronal Network

AI ArtiialIntelligene

AR AutoRegressive

ARMA AutoRegressive Moving Average

ARIMA AutoRegressive IntegratedMoving Average. Equation2.5

ARMAX AutoRegressive Moving AveragewitheXogenous inputs

ARIMAX AutoRegressive IntegratedMoving Average witheXogenous inputs

ACF AutoCorrelationFuntion. Equation2.6

AFSA Artiial FishSwarmAlgorithm

ANOVA ANalyse OfVAriane

ADF AugmentedDikey-Fullertest

AMR Automati MeterReading

CV Cross-Validation. Equation6.10

CDF Cumulated Distribution Funtion. Equation3.13

CRLP Class Representative Load Pattern

CUSUM CUmulative SUM.Equation6.3

DSO Distribution SystemOperator

DMS Distribution Management System

DG Distributed Generators

DWT DisreteWavelet Transform. Equation2.17

DFT DisreteFourier Transform. Equation3.6

DLE Distribution Load Estimation

ERDF Eletriité RéseauDistribution Frane

EMS Energy Management System

FL FuzzyLogi

FCM Fuzzy C-Means

GDP Gross DomestiProdut

GA Geneti Algorithm

GEV GeneralizedExtreme Value

GPD Generalized Pareto Distribution

HV/MV High Voltage/MediumVoltage

HV High Voltage

HW Holt-Winters

IA Immune Algorithm

ISODATA IterativeSelf-Organizing DATA-analysis tehnique algorithm

KNN K-Nearest Neighbor(s)

KPSS Kwiatkowski-Phillips-Shmidt-Shin tests

KDE KernelDensity Estimation. Equation 6.1

LV Low Voltage

LFC Load FrequenyControl

LTLF Long-Term Load Foreast

LOO Leave-One-Out. Equation4.6

LL LoalLinear. Equation 6.9

LL2 AdaptedLoalLinear

MV Medium Voltage

MV/LV Medium Voltage/ Low Voltage

MTLF Medium-Term Load Foreast

MAPE Mean AbsolutePerentage Error. Equation2.32

MA Moving Average

MLE Maximum LikelihoodEstimation

MLP Multi LayerPereptron

MAE Mean AbsoluteError. Equation2.33

MSE Mean Square Error

NN Neuronal Network

NARMA Nonlinear AutoRegressive Moving Average

NW Nadaraya-Watson. Equation 6.6

OLS Ordinary LeastSquare

PDF ProbabilityDensity Funtion

PARMA Periodi AutoRegressiveMoving Average

PACF Partial AutoCorrelation Funtion

PSO Partile SwarmOptimization

PRESS PreditedREsidualSumof Squares. Equation 4.6

PNN ProbabilityNeural Network

RNN Reurrent Neural Network

RBF Radial BasisFuntion

RBFN RadialBasis Funtion Networks

RLP Representative Load Pattern

SE StateEstimator

STLF Short-Term Load Foreast

SOM Self-Organizing Maps

SLP Single LayerPereptron

SVM SupportVetor Mahine. Equation2.27

SVR SupportVetor Regression. Equation2.27

SCADA Supervisory Control And DataAquisition

SSR SumofSquare Residuals

SSE SumSquare Error

TLP Typial Load Prole

THI Temperature-Humidity Index

TMB Minimum Temperature Base

VVC VoltVAR Control

VLOO VirtualLeave-One-Out

VSTLF VeryShort-Term LoadForeast

WCI Wind ChillIndex

WNN Wavelet Neuronal Network. Equation 2.18

WLSE Weighted LeastSquaresEstimation

i.i.d. independent and identiallydistributed

x

^{Inuenevariablevetoror variableto bedetermined}

X _i

^{Sampled values,} measurements

X

^{Observatonmatrix,whose element}

x ij

^{isthe measuredvalueof variable}

j

^inexample

i y _t

^{Load (power)measured at time}

t

y

^Loadvetor

y _i

^{Sampled loadvalue}

ǫ _t

^{Model'snoiseat time}

t

e

^{Dierenebetween outputofthe modelandmeasured value}

γ _y ( t, t − τ )

Autoovariane funtion of

y

^{proessat thetime}

t

^and

t − τ E (⋅)

^{Expeted value operator}

{ P _i , y _i }

^{Historial data}inputs/outputspair, learningset or trainingset,

i = 1, ⋯ , N f t

^{Trendmodelvalueat time}

t

S _t

^{Cyli modelvalueat time}

t

D _α , α = 1, ⋯ , κ − 1

^{Dummyvariables,where}

κ

^{isthenumber of dierent ategories}

γ _α , α = 1, ⋯ , κ − 1

^{Dummyregressionoeients}

T _t

^{Temperature at time}

t W t

^{Detrendedseries}

p ( ǫ )

Probability densityfuntion oftherandom variable

ǫ F ǫ ( x )

^Cumulative distributionfuntion oftherandom variable

ǫ

P

^{Vetor variables}

{ p _j , j = 0, ⋯ , R }

^{of neural networks, where}

R

^{is the total number of}

inputvariables

Ω i

^{Vetorof the parameters (orweights)}

{ ω _ij , j = 0, ⋯ , R }

^{ofhidden neuron}

i

Ω

^{Setof the parameters of theneuralnetwork model}

ω

^{Vetor ofweightsof thelinear}ombination, between thehidden layerand outputlayer of theneural networkmodel

C

^Vetor

{ c _i ( P, Ω i ) , i = 1, ⋯ , M }

^{oftheoutputsofhiddenneurons,where}

M

^isthenumber

of hiddenneurons

r 0

^{Thethreshold rankof the orthogonalforward regression}

r _probe

^{Therank ofa probevariable}

ξ _i

^{Thei-th andidate variablevetor}

f ( P _i , Ω )

^{Output of the neural network with respet to the variable vetor}

P _i

^{and the}

parameters

Ω

f ^{− i} ( P i ,Ω )

^{Output of the neural network model when example}

i

^{is withdrawn from the}

training set

n _p

^Numberof realizations ofthe probe variable

n rp

^{Number of} realizations of the random probe whose rank is smaller than or equal to rank

r

δ

^{Riskhosenbythe designerto ontrol the numberof inputs}

h _ii

^{Leverage, i-th diagonal element ofthehat matrix}

H

p

^{Numberofsetof parametersof theneural networkmodel,whihisequal to}

( R + 1 ) M + ( M + 1 )

E _LOO

Leave-one-out sore

E _p

Approximationof the leave-one-out sore

Z

^{Jaobian matrix ofthe neural network model}

E _yr

^{Yearlyenergy onsumption}

E

0

Non-heatingdailyenergy onsumption

s

^Temperaturesensibility,indiating theamountofenergyonsumed(kWh)bydereasing 1

o

Ctemperature

E _n

^{Annualenergy onsumption adjusted tothenormal limationdition}

P ( t )

^{Estimated meanpower attime t}

σ ( t )

^{Estimated standard deviation at hour t}

ν ( t )

^{Estimated marginat time t}

a ( t )

^{Common groupoeient for the BAGHEERA model onverting non heating daily}

energy into non heating powerat time t

b ( t )

^{CommongroupoeientfortheBAGHEERAmodelonvertingheatingdailyenergy}

into heating powerat timet

E _d

^{Daily energy onsumption}

E _i

^{Meter reordingenergy onsumption during}

n _i

^days

Dd _i

^{Degree days duringa period of}

n _i

^days

Dd

365

Yearlydegree days inthenormal limati ondition

T d

^Dailyaverage temperature

T _{N h}

^Nonheatingtemperature,atemperaturethresholdbelowwhihtheonsumptionrises dueto the eletrial heaters

ˆ

g h ( x )

^{Kerneldensityestimator ofvariable}

x

^{,withsmoothing parameter}

h h

^{Smoothingparameter}

K ( µ )

^{Normalkernel funtionof variable}

µ γ

^Exess probability oftheload estimationmodel

h _cv

^{Optimal smoothing parameterdened byCV tehnique}

y T M B

^_

i

^{Estimated powerat TMBondition}

f ˆ _h ^′ (⋅)

Kernel-type estimator withitsoptimal smoothingparameter

h ^′

P _threshold

^{Estimated threshold power}

models in the smart grid ontext

Contents

1.1 Bakground: smartgrid and smart meters for load modeling . 2

1.2 Motivation and objetives . . . 3

1.2.a Fornetwork operationneed . . . 4

1.2.b Fornetwork planningneed . . . 5

1.3 Contributions of the thesis . . . 6

1.4 Sope and organization of the dissertation . . . 7

Abstrat

Ground-breakingevolutionshavebeenbroughttotraditionaleletrialdistributiongrids

by the onept of smart grids. The smart meter system, as one of the most impor-

tant infrastrutures in the smart grids, gives us detailed information on eletriity

onsumptionofanindividual ustomer. In thisontext, weaimatdesigning foreast-

ingmodelsandestimationmodels basedonthese informationfor needsindistribution

network operation andnetwork planning. The ontributions, aquik overview of the

sope, andthe organizationof this dissertationarealso presentedin thishapter.

1.1 Bakground: smart grid and smart meters for load mod-

eling

The smart-grid onept ombines advaned ommuniation tehnologies with traditional

eletrial distribution grids in order to improve the transpareny and the ontrollability

of distributiongrids. Faing several ground-breaking evolutions inthe eletriity systems,

suh as the large penetrations of the renewable power generation, the rapid load growth

due to plug-in eletri vehiles, to name a ouple, numerous advaned algorithms appear

in this irumstane to enhane the stabilityand the eieny of the system. These Ad-

vaned Distribution Automation (ADA) funtions inlude Volt VAR Control (VVC) [1℄,

self healing, and diret load ontrol [2℄ (to name a few). The ADA funtions are alu-

lated in real-time or in ahead of time in order to help making deisions. Generally, the

monitoring and the ontrol proess ofdistribution networksareperformedat theMedium

Voltage (MV)level.

Oneofthesmart-gridgoalsisto makedistribution systemseonomiallyeientwith

reliableenergysuppliesandlessosts. Distribution networkplanninginvolvesdevelopinga

sheduleoffutureadditionsthatensurethequalityofenergydeliveryaswell asthelowest

possibleost. Ontheonehand,the eletriityinfrastruture mustmeettheneedsof peak

loads. On the other hand, over-dimensioned systems an be very expensive. Thus, reli-

ableloadestimation models arerequiredto tightendistribution marginsand optimize the

planning investmentbyperformingdistributionnetworkalulations, i.e.,arryingout the

powerow alulationinritialsituations soasto identify poor eletriitysupply zones.

Nevertheless,the omplexityinthe problemis relatedto theunertaintyand randomness

inthelients' eletriityonsumptions.

Intheurrentstate,thesarityofmeasurementsonthedistributionsystemintrodues

bottleneks inarrying out the ADA funtions aswell asthenetwork optimization alu-

lations. Theavailable measurementsindistribution networksaremainly ontheseondary

of soure substations. It is eonomially non-feasible to implement eletri meters in all

738 000

^{Medium Voltage/ Low Voltage (MV/LV)} substations. Today, for the operation need, applying very approximate probabilisti models with50% of preision seriously af-

fets the eieny of the ADA funtions, resulting dubious analysis results. In order to

omply with the planning need, the atual model applied by the Frenh eletriity om-

pany, termedBAGHEERA, dependsmainly on thelient's individual information, whih

beomes less and less available. Thus, a new model must be designed at the request of

replaing theBAGHEERA model.

Starting from 2010, the Eletriité Réseau Distribution Frane (ERDF) (Frenh Dis-

tribution System Operator (DSO)) launhed the Linky (baptized name for the smart

meter inFrane) projet, whih aimsat installing

35 000 000

^{smartmeters inFrane. On}

the one hand, end users will pay eletriity bills based on their real onsumptions rather

than on the estimated ones as inthe today's ase inFrane. Onthe other hand, thanks

to these measurements, distribution network operators an have a better vision of the

urrent situation on networks. Atually, there are no available measurements on MV/LV

substationsonthe Frenhdistribution networks. Intheexperimental phaseoftheLinky

projet, the onsumption information of eah individual is sampled on a 30-minute basis

andtransferredoneadaytotheorrespondentdataenter. However,asdataaregathered

inpakagesandsentwithaertainfrequeny[3℄,somedelayisfoundinthemeasurements.

Therefore,usingtheaurateinformationprovidedbythesmartmeterstodevelopload

models isthe silverbulletthatmakeskeysmart-grid appliationsfeasible.

1.2 Motivation and objetives

The supervision of the power and voltage dispathing of the networks is a ritial task

in distribution exploitation. It guarantees an eonomial optimum and a dynami sta-

bility of the networks. Unlike transmission networks, on whih abundant measurements

exist,distributionnetworkshavemuhlessmeasurements. Asamatteroffat, beause of

theomplex struture and a great number of nodes (MV/LV substations) indistribution

networks, it iseonomially impossible to install meters ina great quantity on these sub-

stationsindistributionnetworks. Thus,thedistribution systemisonsideredasblind or

nonobservable. Onesolutionto improve the observability of distributionnetworksis

to introdue loadmodels inorder toreplae the measurements.

In termsofloads indistribution networks, we distinguishtwo types:

ˆ MVlients diretlyonneted to MVnetworks

ˆ Numerous Low Voltage (LV) lients onneted to MV networks through the publi

MV/LV substations

12

32

42 567

89 _A 868B _A 8 89 _C 868B _C 8 89 _D 868B _D 8

89 _E 868B _E 8

FFF

Figure1.1: Availablemeasurements(markedinred)[4℄intheFrenhdistributionnetworks.

∣ ⋅ ∣

^{representsthenorm notation,equivalent tothe magnitude.}

Currently,the measurements inthe Frenh distribution networksare(gure 1.1):

ˆ The ative and the reative power on the seondary High Voltage/Medium Voltage

(HV/MV)substations

ˆ Themean voltage value onhead of every MVfeeder sampledevery 10 minutes

ˆ The magnitudeof the urrent on head ofeveryMV feeder

ˆ The ative andthe reative powerof some MVlients

OntheLV lients' side,the only available dataarelimited to thesubsribed power in

thesupplyontrat and billing information ofthelients onneted tothepubli MV/LV

substations.

With the new available individual onsumption data olleted by smart meters, the

objetive of the researh program presented in this thesis is to build new load models

for the need in operation and in planning in distribution networks. This ontext makes

possible the design of aurate models for the distribution network planning, monitoring

and ontrol,inabsene oftheostly measuring equipments indistribution networks.

1.2.a For network operation need

For the sake of ontrol and onguration in distribution systems, the evolution of the

MV/LV substation load needs to be known. Mainly, we an point out three dierent

reasonsdesribedasfollows:

ˆ During a failure: in order to eiently restore eletriity in regions where a fault

ours,loadsinthe aetedregionsshould be knowninthefollowing threeminutes.

ˆ During network maintenane: the variation of the onsumption needs to be known

to restorethepowersupply. Generally,atwo-dayperiodisonsidered bytheFrenh

eletriitydistributorERDFasanormalrepairing time. Inthisase,atwo-dayload

foreastwithits standard error isneeded.

ˆ As inputs for the SE: the SE [5℄ is the ore funtion of any energy management

system. Itaimsat estimatingthenetwork variables,suhasthevoltage magnitudes

and angles. Figure 1.2 shows the shemati of the relationship among foreasting

models,SE,andADAfuntions. Theforeasting modelsaswellasthenetworkdata

are onsidered as inputs for the SE. The network data [5℄ inludes theinformation

aboutthenetworktopology,lineresistane,reatane, tapsetting,andlineharging,

et. The output of the SE will lead the Distribution Management System (DMS)

ontrol sheduling blok to perform onerned ADA funtions for operational dei-

sions. These deisions enable the monitoring and ontrol of various devies in the

networkssuhasapaitor banks,Distributed Generators(DG), on-load tap hang-

ingtransformers,and swithes/breakers, et.

The idea is then to design foreasting models for MV/LV substations relying on the

aggregated smartmetering dataforthe nexttwo days.

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Figure1.2: Relationshipamongforeasting models, SE,andADA funtions

1.2.b For network planning need

Designing a reliable distribution network is hallenging sine it needs to guarantee a sta-

ble and ontinuous power supply to the ustomers. As a matter of fat: a utility must

maintainthe voltage delivered toeah ustomer withina narrow range entered withinthe

voltages that the eletri equipment is designed totolerate [6℄. In theEuropean eletriity

regulation, for the LV networks, a

10%

out-of-range voltage is aeptable. Beyond this range, the ustomeris dened asapoorlysuppliedustomer.

For the sake of planning, network alulations are performed under extreme situa-

tions in order to handle worst ase senarios [7, 8℄. More speially, these alulations

are arriedout when either of these two ases ours: maximum demand withminimum

generation, and maximum generation with minimum demand [9℄. With the arrival of a

onsiderable portion of DGs into the networks, the later ase an be expeted. Beause

ofthe ustomers' various behaviors,ina samegeographizone, peak demandsof dierent

ustomers seldom happen at the same moment. Therefore, estimation of ustomer daily

loadpattern ateveryhour isrequired. Unertaintyoftheloadestimationalsoneedstobe

onsidered [10℄. Generally, for the voltage-drop alulation, the exess probability, whih

denes the threshold power bounds, is xed to 10% [11℄. Consequently, in the network

planning, a lient's total supply demand inludes the lient's daily load pattern and his

10%exess probabilityunertainty.

Moreover,inthe distributionnetwork planningproess,alistofstandardsandriteria

for equipments, suh asdistribution lines and MV/LV transformers,to namea ouple, is

alsodened. Reliableloadmodelsarealsorequiredinthefollowingases inordertoarry

out distribution network alulations:

ˆ Distribution line losses

ˆ Currents inlinesegments

ˆ Networkvoltage-drops

ˆ MV/LVtransformers: two-hourequivalentpower 1

,voltage-drops,andeletriallosses

Therefore,the objetive isto dene an individualustomer's maximumand minimum

loadlimits ofa yearwith10% exessprobability.

1.3 Contributions of the thesis

Themajorpurposesofthisdissertationaretwofold: designingnewloadforeastingmodels

for thenetwork operation and load estimation models for thenetwork planning in distri-

bution networks. Theontributions of thethesisan be summarizedasfollows:

ˆ Load foreast is an extensively investigated subjet on the transmission level [12,

13, 14, 15,16,17, 18,17,19, 20℄. However on thedistribution level, withthe same

harateristi onsumption data (several dozen kW), to the best of our knowledge,

few workshave been done.

We an think of three plausible reasons explaining this fat: rst, more attention

has been paid to thetransmission level, asthe transmission grid extents on longer

distanes and overs larger territories. The transmission grid, involving huge osts,

is thebakbone of thepowersystems. Seond, the highervoltage levelonsumption

has a more regular load urve pattern, whih makes it easier to foreast. Third,

there were no available measurements on the MV/LV substations relying on whih

theforeasting models an be designed and validated.

In this researh projet, two models based on time series and neural networks have

been proposed,for thenetwork operation need.

ˆ The dierent load types (residential, ommerial, and industrial) are examined in

this researh,and their dierent properties arepointedout.

1

Deneatransformer'sapaity

The two methods are designed and evaluated on real measurements olleted from

theFrenhdistributiongridsintheframeworkoftheLinky projet. Referene ase

isestablishedinorderto beompared to the twoproposed models. Advantagesand

drawbaksofthetwomethods aredrawnthroughtheomparison. Thetwomethods

arealternative and,at the same time, ompliment to eahother to setthepreision

limit dueto the intrinsi harateristis ofthesubstation loaddata.

ˆ Timeseriesmethodpresentedinthisdissertationisanoriginalwork,wherenumerous

statistialtoolsareintegratedinforthepursuing ofpreision. Residualofthemodel

islooked through indetailsto ensure themodel'swell being.

ˆ Neural network method, on the other hand, is inspired by the seletion proedure

proposedbyGérardDreyfus[21℄,arenownedexpertintheneuralnetworkmodeling.

WefousontheNeuronalNetwork(NN)modeldesign,whihhasbeenfullyexploited

for the rsttimeintheshort-term loadforeast.

ˆ Until theimplementationofthesmartmeters, usuallytherewerenoavailablehistor-

ialloaddatabesidesthedemand surveydataonalimitednumberof lients. Inthe

loadmodeling eld,most of theworksonerningthedistributionnetwork planning

aimatestimatingthepeakdemandforagroupofustomersduringthepeakdemand

of the system, namely the oinident peak demand [6℄. For this purpose, some re-

searhesbasedonend-usemethod[9,22℄deomposetheloadmodeloftheresidential

ustomerintoapplianeelementaryunits. Othersfousonthelassiationmethod,

sorting ustomersinto dierent ategories, and on the representation eah ategory

witha Typial Load Prole (TLP). In thesmart metering ontext, we are therst

to propose the onept of individual data-driven load model for ustomers, for the

network planning need.

ˆ Tobuildanindividualestimationmodel,therelationshipbetweentheeletriityon-

sumptionandthetemperatureisdeduedbynonparametriestimators. Themethod

isappliedtorealonsumptiondataofindividualustomersinFrane. Performaneis

omparedtotheurrentloadmodel(termedBAGHEERA)oftheeletriityompany

EDFthrough dierent validationstudies.

1.4 Sope and organization of the dissertation

Thedissertation is organizedasfollows:

ˆ Chapter1statesthatthe smartgrid andthesmartmetersareinrapid development

to improve theeieny andthe ontrollability ofdistribution networks. Therevo-

lutionaryhangesindistributionnetwork systemsurgetheaurate loadforeasting

models. Reordingindividualonsumptioninformation,thesmartmetersenablethe

buildingofthesemodels. ThethesisisenouragedbytheLinkyprojetlaunhedby

theFrenheletriitydistributorERDF,aimingatinstalling

35 000 000

^smartmeters

inFrane. Twomainobjetivesareevokedinthesmartmeteringontext: short-term

loadforeastingmodels forthenetwork operation and theestimation modelsfor the

network planning. Reasonsfor thedevelopment ofthese two objetivesaredelared.

Contributions ofthe thesis arehighlighted.

The rest of the dissertation is divided into two parts, dealing with two distint ob-

jetives. Part A takles the foreasting load models for the operation need, and inludes

hapters 2,3and 4.

ˆ Chapter 2 gives a review of the load foreasting methods in literatures and set up

basi framework for the performane evaluation. Load foreasts are stratied into

dierentobjetivesaordingtotheirleadtimesale. Dierentobjetivesaredevoted

to dierent appliations. More input information is needed for a longer lead time

foreast. Foreastingmethodsaredividedinto twoategories: thelassialapproah

and the artiial intelligent approah. Hybrid models that possess the advantages

of both ategories gain more and more popularity in the appliations. Data used

inour study arethoroughly analyzed, suggestinginuene fatorsto our short-term

load foreasting models. We argue for our hoies of timeseries and neuralnetwork

methods. Performane riteria anda referenemodel(termednaive model) arealso

established in this hapter, building a solidframework base for the presentation of

theapplied methods inthe nexttwo hapters.

ˆ Chapter 3 presents the short-term load foreasting model based on the time series

method. The foreasting proedure is detailed. The additive time series model

ontains three omponents: a trend, a yli and a random error. The rst two

omponents aredeterministi, and are designed into models respetively. Thetrend

modelistemperature-dependent, linear,anddummyvariablesintegrated,indiating

day types. Cyli model is omposed by the Fourier omponents, whose frequen-

ies are found by a smoothed periodogram. Numerous statistial tools are applied

pursuing a better preision: sliding windowstrategy isadopted sothatthemodelis

updatedduringeahforeastingperiod;ANalyseOfVAriane(ANOVA)nullitytest

is applied to estimatethe signiane ofvariables. Availabledataaredivided into a

learning set and a test set. Important parameters of the model are dened thanks

to thelearning set. Whereasthetest set isreservedfor the performane evaluation.

Residual is examined, making sure the well t of the models. Weather unertainty

impaton the preisionof theforeasting modelisdisussed intheendof thehap-

ter. We onluded thatevenwith the weather unertainty,our proposed timeseries

modelstill outperforms thenaive model.

ˆ Chapter 4 introdues the neural network model from the artiial intelligent ap-

proah family. In our study, we fous on the design of the neural network model,

hoosingtheoptimalmodelthathasthebestahievablepreditiveability. Ageneral

onept of the mahine learning tehnique is stated, and diulties suh asnding

therelevant variablesand thebias-variane dilemma,areexplained. Theorthogonal

forward regression and the Virtual Leave-One-Out (VLOO) tehnique areproposed

as solutions to these diulties. Experiments on the same data show that thepro-

posed methodology behaves better than the time series model in term of auray.

Aomparison indiverspropertiesismadebetween thetwomodelsintheend ofthis

hapter.

Part B introdues the load estimation problem for the planning need, and proposes

solutions. It ontains hapters 5 and 6.

ˆ Chapter 5 fouses on the load researh projets in distribution networks. Load re-

searh projets aimat providinghourlyloadestimationmodels for individuallient.

Three steps, i.e., tehnial analysis, eonomial analysis, and nal deision, for the

deision makings in distribution network planning are presented. The outputs of

the load researh projets ontribute to the tehnial analysis, devoting to nding

solutions in network planning. The mehanism of the aggregation of loads, the o-

inident load, is explained. Common methods ofnding TLP,whih represents the

dailyloadpattern of a ertaingroup of lients, arepresented. Load models usedby

eletrial unities in Finland, Denmark, Norway, and Taiwan aredesribed. Finally,

the omponents ofthe BAGHEERA modelapplied bytheFrenh DSOare detailed

andthe method isdemonstrated withreal measurements.

ˆ Chapter6proposesanovelapproahfortheindividualloadestimationintheontext

of smart meters. With the abundant individual onsumption information, in our

opinion,the loadmodelis readyto beindividualized rather thanestimated through

theTLPs. Thus, inthis hapter, the individual loadestimation modelbasedon the

nonparametriestimators isput forward. Numerous statistialtools,suh asbinary

hypothesis tests, kernel densityestimation, CUmulative SUM (CUSUM) algorithm,

andCross-Validation(CV)tehnique,areintegrated intheproposedmethod. Three

kernel regressors, i.e., Nadaraya-Watson (NW), Loal Linear (LL), and Adapted

Loal Linear (LL2) are applied to dedue the relationship between the load and

thetemperature variations. Dierent appliation ases aordingto thequalityand

quantityofthedataaresuggested. Themethodisillustratedwithrealmeasurements

andompared withtheBAGHEERAmodel. Thevalidityofthemethodisexamined

withextensive examples. In the end ofthehapter, adisussion onthedenition of

theunertaintyboundof theestimationmodelisarriedout.

ˆ Chapter7onludesthedissertationandproposesperspetivesforthefutureresearh

interests.

Short-term load foreasting models

for monitoring and state estimator

framework

Contents

2.1 Literature review . . . 14

2.1.a Foreastingleadtimesandinuene fators . . . 14

2.1.b Foreastingmethods . . . 16

2.1.b-i Classialapproah. . . 18

2.1.b-ii Artiialintelligentapproah . . . 25

2.1.b-iii Hybridmodels . . . 35

2.1. Literaturereviewonlusionsandperspetives . . . 37

2.2 Data desription. . . 40

2.2.a MV/LVsubstation . . . 40

2.2.a-i Temperatureinuene . . . 41

2.2.a-ii Daytypeinuene . . . 42

2.2.a-iii Timeinuene . . . 42

2.2.b MVfeeder. . . 45

2.3 Choies of Time series and NN methods. . . 45

2.4 Performane riteriaand referene ase. . . 46

2.4.a Performaneriteria: MAPEandMAE . . . 46

2.4.b Referenease: thenaivemodel. . . 47

2.5 Conlusion . . . 47

Abstrat

Load foreast plays an important role in deision makings in power systems. This

hapter begins with the review of load foreasting models in literatures. The seond

partof the hapterontributes toaframework onsisting ofdata desription,method

seletion,performaneriteria,andrefereneaseintrodutions. Inthereviewingpart,

we lassify a wide range of approahes of load foreast into two ategories: lassial

approah,andartiialintelligentapproah. Methodologiesineahategoryarebriey

presented. Theiradvantages,disadvantages,appliations andpertinentresearhworks

arealsodeveloped. Popularhybridmodelsombiningtwoormoredierentapproahes

arealso involved. In the framework part, datausedfor the design andthe evaluation

of our methodologies are analyzed. Certain behavioral omponents in the data are

pointedout. The hoies ofthe methodologies basedon the timeseriesandtheneural

networksareargued. Thesetwomethodologies aregoingtobedetailedinthe following

twohapters. Performane riteria and referene asearestated soas tolay agood

foundation forthe presentation of the modelsin the nexttwohapters.

2.1 Literature review

The quality of the deision making in eletri power systems strongly depends on the

auray of the power load preditions. Various deisions require reliable and aurate

loadforeasting models withdierent time-salesaswell asondierent hierarhial levels

innetwork systems [23℄.

A wide range of approahes have been proposed to the load foreasting problems. In

thissetion,weaimatpresentingbrieythedierentapproahesfoundinliteratures,their

speiities,appliations and tehniquesapplied to loadforeast.

Theorganization of the setion isasfollows: rst,we start byintroduingdenitions,

appliations and inuene fators of dierent lead time load foreasts. Then, a two di-

mensional digestinlead timeand involtage hierarhysales summarizes load foreasting

methods,followedbythedesriptive presentation ofeverymethod. Related worksarealso

depited. Finally,we onlude the literature reviewinatable.

Notethatfor the sake oflarityandease ofunderstanding, mathematial notations in

the referened works and internal reports have been adapted in order to keep oherene

through the entire dissertation.

2.1.a Foreasting lead times and inuene fators

Dierent foreasting lead times result into dierent foreasting models as well as their

inputvariables. Numerousfators,suhasweatheronditions,seasonaleets,andsoial,

eonomi,demographifatorsexplainthevariationsintheload[23℄. Table2.1summarizes

theappliationsandinuene fatorsfor dierent timehorizon foreasting models[23,24,

18℄.

Notiethat more input variables areinluded when thetime horizon beomeslonger.

ForaVSTLF,univariate(onlythehistorialpowersamplesareonsideredasinputs)mod-

elsan oersatisfatoryresults. TheseVSTLFsoftenpartiipateto improvetheeieny

and reliabilityofthe real-timeeletrial systems. For longerlead timeforeast,multivari-

atemodelswithexogenousvariablesarefavored. TheSTLFneedsmainlythreeategories

of inputs: weather, alendar, and historial variables [25℄. Dueto some measurement de-

lays, or theomputational time for the exeution of theADAfuntions, the STLFs often

replae VSTLFs to fulllneedsin network operations. STLF foreasts also help reduing

equipment failures and system blakouts by indiating the operational margins in power

systems. TheMTLFmodelshelpmakingnanialdeisions,suhasevaluationoftheprie

of energy produts and investment interests. In suh ases, the foreasting models need

additional inputs assoial and eonomial fators. The LTLF,onerning energy system

apitalexpendituresandmoreimportanteonomiinvestments, needstotakeintoaount

more soio-eonomi fators,and sometimes even their futureevolutions.

The herein desription is in a general way, as in setion 2.2.a, we will talk about an

industrialMV/LVsubstationloadthatisindependentto weatheronditions. Thus,what-

evertheforeasting leadtimeis, for this loadexample,weather variableis not onsidered

asan inuene fator.

Asdesribed in the table 2.1, for our appliation in network operations, espeially to

ooperatewiththeADAfuntions,wefousontheSTLF. Weather,alendarandhistorial

datainputs arethe most onerned inuene fators.

Table 2.1: Dierent timehorizon loadforeasts

Timehorizon Appliations Inuenefators

Very Short-Term Load

Foreast (VSTLF)

(1Min

∼

^1h)

ADA funtionsinDMS,Load

Frequeny Control (LFC) in

Energy Management System

(EMS)

Historial onsumptions

Short-Term Load Fore-

ast (STLF) (1h

∼

¹

week)

Operation (ADA funtions),

estimation of load ows, rep-

resentation ofsavingpotential

for eonomiand seure oper-

ationof powersystems

Historial onsumptions, al-

endar fators (day type and

houroftheday),weatheron-

ditions (

∗

⁾

Medium-Term Load

Foreast (MTLF) (1

week

∼

^{1 year)}

Negotiation of eletriityon-

trats, sheduling of fuelsup-

plies and maintenane opera-

tion

(

∗

^{) +} population, eonomi fators, et(

◇

⁾

Long-Term Load Fore-

ast (LTLF) (1 year

∼

severalyears)

Capital expenditures and

planning operations

(

◇

^{) + more} information suh as: population growth, Gross

Domesti Produt (GDP)

(

∗

^{) and (}

◇

^{) represent} respetively inuene fatorsfor short-term and medium-term fore- asts.

For a weather sensitive load, inludingtheredible foreasting weather information as

input is reommended as itan improve theperformane of the foreasting model. Tem-

perature and humidity are the most frequently used load preditors. Composite weather

variables suh asTemperature-Humidity Index (THI),Wind Chill Index(WCI) [24℄, and

smoothed weather variables [26℄ are often adopted. THI and WCI indiate respetively

thedisomfortausedbysummer heatandwinterwind hill. Thesmoothedweathervari-

able represents the eets of hanges in weather aumulated over the time. In pratie,

regardingSTLF,weather foreasting dataareapplied to alulate theperformaneof the

model [27℄. However, for the most of the time, in the onstrution phase of the model,

thepreditedweatherforeastisnot available. Inthisase, most authorsintheloadfore-

astingeldrunsimulationswiththerealizedweather data[28℄. Oneshould bearinmind

thatusingforeastingweatherinformationwillsurelydereasethemodel'soverallpreision

[26,29℄. Therefore,someauthors[30℄proposedomittingimpreise weatherinformation as

aonservativesolution, sine itwouldbringlargevarianeto themodel. Apromising way

to handle the unertainty in weather variables is the weather ensemble preditions that

generatethe loadforeastsinaprobabilistiform[29℄. Inhapter3,wewill re-disussand

showempirial evideneaddressing to thisissue.

The alendar inputs inlude the time of the year, the day of the week, the hour of

the day as well as day types (working days, weekends or national holidays). There are

importantdierenesinloadbetween weekdays andweekends. Weekendsandholidaysare

oftenmorediulttoforeastthanworkingdaysduetotheirrelativeinfrequentourrene

and thelients' irregular behaviors. Someauthors workon thelassiation methods [19℄

inorder to ndor even reate similar days [31℄for these anomalous dayforeasts.

Historialdatainputsarealsoveryimportant totheSTLF,fromwhihtheseasonality

information an beextrated [14℄.

2.1.b Foreasting methods

This subsetiongives anoverviewof various approahes for loadforeasts. Manyof them

aredevelopedforSTLF onthe HighVoltage(HV)level,althoughMVandLVlevelsbegan

to attrat more attention with the expansion of the smart grids during the past years.

Figure 2.1 gives a two dimensional digest on the methods and the models in the load

foreasting eldboth inthe leadtimeand thevoltage hierarhial sales.

Mainly,twolasses ofapproahes anbedistinguished [14,23℄: lassialapproah and

ArtiialIntelligene(AI) approah. Classialapproahrequiresanexpliitmathematial

modelwhihinterpretstherelationshipbetween loadanditsinuenefators. Thisfamily

inludes regressionmodel, timeseries method, similardayapproah, end-use method and

eonometri approah. AI approah, on the other hand, extrating non linear relation-

ships between input fators and load hasbeome very popular nowadays. This family of

algorithms inludesArtiial Neuronal Network (ANN),fuzzylogi, and expertsystems.

Inthesequel,we introdue these dierent approahes.

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Figure 2.1: Summary of load foreasting methods in two dimensions: time horizon and

voltagehierarhy. HV:HighVoltage,MV:MediumVoltageandLV:LowVoltage. Numbers

appear inthe gureorrespond tothe relatedworks.

a

a

(1):[13,14℄(2):[13,15,14℄(3):[16℄(4):[17,18,17℄(5):[24℄(6):[19,20℄(7):[32,33,34℄(8):[35,36℄(9):[31℄

(10):[37,38℄(11):[39℄(12):[22℄(13):[40℄(14):[41℄

b

Univariatetimeseriesmodelreferstothemodelwithonlyoneobservationseries,i.e.,loaddata.

c

Multivariatetimeseriesmodelorrespondstothemodelontainingboththeexogenousvariablesandthe

2.1.b-i Classial approah

Regression model. Regression is one of the most widely used statistial tehniques.

Eletri load foreasting regression methods are usually used to express the relationship

between loadonsumption and external fators[24,42℄:

y i = a i x i + e i

^(2.1)

where

y i

^{is the i-th load sample,}

x i

^{is the inuene variable vetor} orrespondent to the i-th load sample,

a _i

^{is the transposed regression oeient vetor, and}

e _i

^{is a Gaussian}

error.

The advantages of regression methods are relatively easy implementation and inter-

pretation for the relationship between input and outputvariables. Another advantage of

the method is that it is easy to ompute thepredition interval through estimation error

of the model. The disadvantage of regression methods is the need to identify a orret

form inluding eetive inputs and output. This is hard due to the omplex non-linear

relationship [23℄.

C.L.Horetal. [43℄developedseveralmultipleregressionmodelsinorporatingweather-

relatedandsoio-eonomivariablesontheloaddemandforEnglandandWales. Monthly

data from 1989 to 1995 are usedfor theoeient estimation of the model and monthly

data from 1996 to 2003 are used to evaluate the auray of theforeasting model. The

non-linearrelationshipbetweenweather-relatedfators(meanmonthlytemperaturevalue)

and load suggests introduing other weather omposite variables, suh asHeating Degree

Days (HDD),Cooling Degree Days(CDD),and EnthalpyLatent Days(ELD).The soio-

eonomi variable GDP has evidently an impat on the trend. One of their regression

modelis set up as:

E ˆ 1 = ( E ˆ A + α 7

^GDP

) F _adj ( y )

^{, where}

E ˆ 1

^{is the predited eletriity de-}

mand,

E ˆ _A = α 0 + α 1

^CDD

+ α 2

^HDD

+ α 3

^ELD

+ α 4 V _w + α 5 M _s + α 6 M _r

^{,whih represents the}

weather-related model.

V _w

^{stands for the mean monthly wind speed,}

M _s

^{stands for the}

mean monthly sunshine hours, and

M r

^{stands for the monthly rainfall.}

α n , n = 0, ⋯ , 7

^are

onstant oeients.

F _adj ( y )

^{is the adjustment fator for eah year. The Mean Abso-}

lute Perentage Error (MAPE) of the model, whih represents theaverage portion of the

absolute foreasting errorsto the realforeasting values,wasaround 2%.

A. Bruhns et al. [17℄designed a non-linear regression model for MTLF. Thishourly

loadpreditionmodeltermedEventail hasbeenappliedbytheFrenheletriityompany

EDF sine 2001. They deomposite the load

P _i

^{into three omponents:}

P _i = P hc _i + P c _i + e _i

^{, where}

P c _i

^and

P hc _i

^are respetively the weather-dependent and the weather- independent parts,

e i

^{isa Gaussian error. The}weather-dependent partis ttedbyanon- linear model of the observed temperature, the exponential smoothing temperature, and

theloud over. Two thresholds for heating andooling temperatures arealso adopted in

ordertoopewiththenon-linearity. Theexponentialsmoothingontemperaturereetsthe

inertiaoftemperatureinsidebuildingsto theoutsidetemperature variation. Theweather-

independentpartintegratestrends,day,week,yearperiods,anddaytypeinformation. The

dummyvariables are usedto indiate daytypes and four termsof Fourier series areused

to model the seasonality pattern. Despite of the omputational diulty in estimation

dueto thetemperaturesmoothingparameters,thresholds,andstrongnon-linearities,they

delared that with the known weather data, a MAPE of around 2% for one-year-ahead

foreast anda MAPEof 1.5% for one-day-ahead foreasthave been ahieved.