Load models for operation and planning of electricity distribution networks with smart metering data

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Ni Ding

To cite this version:

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Spé ialité: Génie Éle trique

Arrêtéministériel: 7 Aut 2006

Présentée par

Ni DING

Thèse dirigée par Yvon BÉSANGERet

odirigée par Frédéri WURTZ

préparée ausein du

Laboratoire G2ELAB

dans l'É ole Do torale: EEATS

Load models for operation and planning of

ele tri ity distribution networks with smart

metering data

Thèse soutenue publiquementle 30 Novembre 2012,

devant lejury omposé de:

Pr. Nouredine Hadjsaid

GrenobleINP, Président

Pr. Carlo Alberto Nu i

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

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A knowledgments xiii

Notations xix

1 General introdu tion: the new problemati of load models

in the smart grid ontext 1

1.1 Ba kground: smartgrid and smart meters for load modeling . . 2

1.2 Motivation and obje tives . . . 3

1.2.a Fornetworkoperationneed. . . 4

1.2.b Fornetworkplanningneed . . . 5

1.3 Contributions of the thesis . . . 6

1.4 S ope and organization of the dissertation . . . 7

A Short-term load fore asting models for monitoring and state es-timator 11 2 Load fore astingte hniques andshort-term modelframework 13 2.1 Literature review . . . 14

2.1.a Fore astingleadtimesandinuen e fa tors. . . 14

2.1.b Fore astingmethods . . . 16

2.1.b-i Classi alapproa h . . . 18

2.1.b-ii Arti ialintelligentapproa h . . . 25

2.1.b-iii Hybridmodels . . . 35

2.1. Literaturereview on lusionsandperspe tives . . . 37

2.2 Data des ription . . . 40

2.2.a MV/LVsubstation . . . 40

2.2.a-i Temperatureinuen e . . . 41

2.2.a-ii Daytypeinuen e . . . 42

2.2.a-iii Timeinuen e . . . 42

2.2.b MVfeeder . . . 45

2.3 Choi es of Time series and NN methods . . . 45

2.4 Performan e riteria and referen e ase . . . 46

2.4.a Performan e riteria: MAPEandMAE . . . 46

2.4.b Referen e ase: thenaivemodel . . . 47

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3 Time series model 49

3.1 Additive time series model and pro edure overview . . . 50

3.2 Statisti al tools . . . 51

3.2.a DummyVariableRegression . . . 51

3.2.b TrendComponentEstimation . . . 52

3.2. Cy li ComponentEstimation . . . 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 CompleteFore astingModel . . . 55

3.3 Appli ation 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 Independen e . . . 61

3.4 Weather un ertainty . . . 62

3.5 Con lusion . . . 64

4 Neural network model 67 4.1 Ma hine learning te hnique . . . 68

4.2 Multi Layer Per eptrons and trainingpro ess . . . 69

4.3 Model design. . . 71

4.3.a Variablesele tion . . . 71

4.3.b Modelsele tion . . . 73

4.3.b-i Modelsele tionmethodology . . . 73

4.3.b-ii Assessmentofthegeneralizationabilityofthemodels . . . 74

4.4 Numeri al illustration . . . 76

4.4.a Framework . . . 76

4.4.b Modeldesign: anillustrativeexample . . . 77

4.4.b-i Variablesele tionexample. . . 77

4.4.b-ii Sele tingthebest modelforagiven omplexity . . . 81

4.4.b-iii Complexitysele tionexample. . . 81

4.4. Results . . . 83

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

4.6 Con lusion and perspe tive . . . 86

B Load estimation models for distribution network planning 89 5 Loadresear hproje tsindistributionnetworks: stateofthe art 91 5.1 De ision making in distribution network planning . . . 92

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5.1.b Typi alLoadProle(TLP) . . . 95

5.2 Load resear h proje ts in different ountries . . . 96

5.2.a FinlandDSOmodel . . . 97

5.2.b DenmarkDongEnergy . . . 98

5.2. NorwaySINTEFEnergyResear h . . . 99

5.2.d Taipowersystem. . . 99

5.3 Fren h load resear h proje t . . . .100

5.3.a Datades ription. . . .102

5.3.b EDFBAGHEERA model. . . .103

5.3.b-i TMB temperatureandbasi model. . . .104

5.3.b-ii Common oe ientestimation . . . .105

5.3.b-iii Spe i parameterestimation . . . .105

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

5.4 Con lusion . . . .111

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

6.1.a Statisti altests . . . .116

6.1.b Kerneldensityestimation. . . .117

6.1. CUSUMalgorithm . . . .117

6.1.d Kernelregression . . . .118

6.1.e Smoothingparametersele tion: ross-validationte hnique. . . .119

6.2 Computational example . . . .120

6.2.a Illustrativeexampleresults . . . .121

6.2.b ComparisonwiththeBAGHEERAmodel. . . .124

6.3 Validation study . . . .127

6.4 Dis ussion . . . .129

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

6.4.b Upperboundin thenonparametri models . . . .131

6.4. Validationtrialontheupper-bound estimation . . . .132

6.5 Con lusion and perspe tive . . . .137

7 General on lusion and perspe tive 139 7.1 Con lusion . . . .139

7.2 Perspe tive . . . .140

Bibliographie 154

Appendi es 155

A Time series model's result summary 155

B Binary hypothesis test 157

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D Comparisonresultsof naivemodel, timeseriesmodeland

neu-ralnetwork model 161

E Résumé français 169

E.1 Introdu tion générale: la nouvelle problématique du modèle

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

E.1.a Réseauintelligentet ompteurs intelligentspourlesmodèlesde harge . . .169

E.1.b Obje tifset plandurésuméfrançais . . . .170

E.1. Contributiondethèse . . . .172

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

E.2.a Méthodesdelaprévisionde hargedanslalittérature . . . .174

E.2.b Des riptiondedonnées . . . .178

E.2. Choixdesméthodes: série hronologiqueet réseaudeneurones . . . .180

E.2.d Critèresdeperforman eet modèlederéféren e. . . .181

E.2.e Modèlesérie hronologique . . . .182

E.2.f Modèleréseaudeneurones . . . .187

E.2.f-i Con eptiondumodèle . . . .188

E.2.f-ii Comparaisonglobaleave lemodèledesérie hronologique. . . .191

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

E.3.a ModèleBAGHEERA . . . .195

E.3.b Modèlenonparamétrique. . . .198

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1.1 Availablemeasurements intheFren h distribution networks . . . 3

1.2 Relationshipamongfore asting models,SE, andADA fun tions. . . 5

2.1 Summaryof loadfore asting methods intwo dimensions . . . 17

2.2 Singleper eptronstru ture . . . 27

2.3 One-hidden-layer network stru ture . . . 27

2.4 Supervised learningpro edure . . . 28

2.5 Re urrent neural network stru ture . . . 29

2.6 FuzzyLogi pro ess . . . 34

2.7 Fuzzylogi : inputvariables membership fun tion . . . 35

2.8 Fuzzylogi : outputvariablesmembership fun tion. . . 35

2.9 Daily average load and temperature data through

414

days (from Sept. 9, 2009 to O t. 27,2010)ofsubstation CE_MOU (mainly residential) . . . 40

2.10 Dailyaverage loadthrough

414

days (from Sept. 9,2009 to O t. 27,2010) ofsubstation VI_LOG (mixedservi ese tor andindustrial) . . . 41

2.11 Dailyaverage loadthrough

414

days (from Sept. 9,2009 to O t. 27,2010) ofsubstation CE_FRO (an industrial lient) . . . 41

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

2.13 Similarity index al ulatedbased onall days of substationCE_MOU . . . . 44

2.14 Similarityindexwithoutweekendsandpubli holidaysofsubstationCE_MOU 44 2.15 MVfeeders and position of onne ted MV/LVsubstations . . . 45

3.1 Stepsof the designed time seriesfore asting method . . . 51

3.2 Trainingset andtest setperiodsof theavailable data. . . 55

3.3 A weekly onsumption pattern (O tober 5,2009 to O tober11, 2009) of a mixedindustrialand servi ese torsubstation VI_LOG. . . 56

3.4 SubstationVI_LOG,MAE riteria al ulatedonthetrainingset(117days) fordierent slidingwindow sizes(weeks). . . 56

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

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

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

3.9 Substation VI_LOG,densityfun tion plotand umulative densityfun tion plotof the residual. . . 61

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3.11 Histogram of the Gaussian distributed temperature un ertainty adding to

thea tual temperature . . . 63

3.12 Three-day fore asting temperatures ompared to thea tual temperatures . . 64

4.1 Orthogonal forward rankingpro ess. . . 73

4.2 Neural network sele tion pro edure . . . 74

4.3 Separation of the load urve into the daily averagepowerand theintraday power variation . . . 77

4.4 Generation of se ondary 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 Modelsele tion for theintradaypowervariationmodel . . . 82

4.7 Neural network omplexitysele tion strategieswithVLOOs oreand lever-age distribution . . . 82

5.1 Network de ision makingpro edure . . . 93

5.2 Example of oin iden e fa tor al ulation . . . 94

5.3 Distribution Load Estimation (DLE)pro ess . . . 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 option lient no.5 . . . .103

5.6 Two-year(July01,2004

∼

June 30,2006)dailyaverageloadsofbasi option 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-peak dailyenergy use . . . .108

5.9 Basi option 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 nonparametri model . . . .116

6.2 Statisti al testspro edure. . . .117

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

6.4 O-peak/on-peak option lientno.5: statisti altestsresultof thermosensi-tive he k . . . .121

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

6.7 O-peak/on-peak option lient no.5: weekdayminimumpower estimations .122 6.8 O-peak/on-peak option lient no.5: statisti al tests result for the data oheren e he k . . . .123

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6.10 NW,LL,and LL2 regressors,indi ating therelationshipbetween the

varia-tionof temperature and the lient's dailypower onsumption . . . .124

6.11 O-peak/on-peakoption lientno.5: presentation ofun ertainty 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 Study ases and s enariosin thevalidation study. . . .127

6.15 Study ase no.1, s enario1: o-peak/on-peakoption lients, omparison of

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

degreeduring the se ondyear . . . .128

SSEsofBAGHEERA,NW,LLandLL2estimators ontheo-peakhoursof

the days below0 degreeduring these ondyear . . . .128

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

ofthe se ond-yeardata . . . .129

SSEsofBAGHEERA,NW,LLandLL2estimators ontheo-peakhoursof

the 30 oldest days ofthese ond-yeardata . . . .129

6.19 10%hourly power ex ess 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 of lient no.22 during two years (July01, 2004

∼

June 30,2006) . . . .134

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

∼

June 30,2006) . . . .135

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

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

fon tionsavan ées du réseau . . . .171

E.2 Résumédes méthodesde hargeprédi tives endeux dimensions. . . .176

E.3 Courbede hargeettempératurejournalièrependant

414

jours(du9/9/2009 au 27/10/2010) du poste HTA/BT CE_MOU ( onne té prin ipalement à

des lientsrésidentiels) . . . .179

E.4 Courbede hargejournalièrependant

414

jours(du9/9/2009au27/10/2010) du poste HTA/BT VI_LOG ( onne té aux lients mixtes tertiaires et

in-dustriels). . . .179

E.5 Courbede hargejournalièrependant

414

jours(du9/9/2009au27/10/2010) duposteHTA/BTCE_FRO ( onne té àunseul lient industriel) . . . .180

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

harge . . . .183

E.7 Pro éduredu lassement par laproje tion orthogonale deGram-S hmidt . .189

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E.9 La prise desdé isions dansleréseau de distribution . . . .194

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

journalièrependantlesheurespleines. L'indi eHPsignieHeurePleine

etl'indi e HCsignie HeureCreuse. . . .196

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

E.12Clientno.5 option heure reuse/pleine: TMB estimationsde la harge

pen-dant lesjours ouvrables . . . .197

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2.1 Dierent time horizon loadfore asts . . . 15

2.2 Summaryof loadfore asting approa hes andtheir features . . . 39

2.3 Sevensubstation lients' ompositionsand orrelation oe ientswith

tem-peratures. . . 42

3.1 Fore asting result omparison between the naive model and thetimeseries

modelon the Substation VI_LOG data . . . 59

3.2 Fore asting result omparison between the naive model and thetimeseries

modelon the MVfeeder CLdata . . . 60

3.3 Performan e omparison among Time Series (TS) models with fore asting

temperature, a tual 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,fore astingresults: omparisonamongthenaivemodel,

time seriesmodel andNN models . . . 84

4.4 Substation CE_FRO, fore asting results: omparison between the naive

modeland theneuralnetworkmodel . . . 84

4.5 Summary of omparison aspe ts between neural network models and time

seriesmodels for the short-termload fore asting appli ation . . . 85

A.1 MV/LVsubstations,fore astingresults: omparisonbetweenthenaivemodel

andthe omplete TimeSeries (TS) modelof one-day-aheadfore asts. . . .155

A.2 MV/LVsubstations,fore astingresults: omparisonbetweenthenaivemodel

andthe omplete TimeSeries (TS) modelof two-day-aheadfore asts. . . .155

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

the ompleteTime Series(TS) modelof one-day-ahead fore asts.. . . .156

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

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

D.1 6variables forthedailyaveragepowermodeland19 variables forthe

intra-daypowervariationmodel . . . .161

D.2 6variables forthe dailyaveragepowermodeland23 variables forthe

D.3 6variables forthe dailyaveragepowermodeland40 variables forthe

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

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intraday powervariationmodel . . . .165

intraday powervariationmodel. . . .166

D.7 Substation CE_FRO:14variablesforthedailyaveragepowermodeland28

variables forthe intradaypower variation model. . . .168

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

E.2 Résumé desmodèles de harge prédi tifsetleurs ara téristiques . . . .177

E.3 Résumédela omparaisonentrelemodèleduréseaudeneuronesetlemodèle

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A hieving 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 Nu i and Pr. Corinne Alonso for their timeand

energy to examine mydissertation and for their valuable opinions. Theiren ouragements

and appre iations give me strength and onden e inmyfuture work. Thanks also go to

Pr. DidierMayerforhis interests and insightful ommentsaboutmywork. Itwasagreat

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

a knowledgehim for that.

I'malsogratefultotherepresentativesoftheindustrialpartnersofthe ompanythatI

workwith: Mr. OliverDevauxfromEDFandMr. AlainGlatignyfromS hneider Ele tri .

Ithankthemforthisinterestingsubje tthattheysetupandpertinent ommentsregarding

theindustrialappli ations ofmymodels.

I owe my sin ere gratitude to myprin ipal advisor, Pr. Yvon Bésanger. I would like

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

for hispatien e inguidan e. Ithank him for always being there for measa teammate at

di ulttimes thatwe en ountered throughpubli ations, and administrations.

IwouldliketoextendmygratitudetoDr. Frédéri Wurtzforhistrustandappre iation

for mywork,for hiswarmlywel oming meinto thelaboratory.

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

La oume and Pr. Daniel Baudois for their s ienti guidan e. I highly respe t their

passion and rigorousness for the resear h. I thank them to a ept to oer me te hni al

advi eswithout reserve.

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

Miss Leti ia De-Alvaro from EDF for their energy devoting to my thesis proje t. They

have been supportive industrial advisers to keep me on tra k 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

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Mydeepest gratitude reserves to myfamily and my friends. Even though none ofmy

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

I want to thank myfriendsinG2elab fortheir toleran e andun onditional 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 forwhat you have tamed. - The littleprin e

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ADA Advan edDistribution Automation

ANN Arti ial Neuronal Network

AI Arti ialIntelligen e

AR AutoRegressive

ARMA AutoRegressive Moving Average

ARIMA AutoRegressive IntegratedMoving Average. Equation2.5

ARMAX AutoRegressive Moving AveragewitheXogenous inputs

ARIMAX AutoRegressive Integrated Moving Average witheXogenous inputs

ACF AutoCorrelationFun tion. Equation2.6

AFSA Arti ial FishSwarmAlgorithm

ANOVA ANalyse OfVArian e

ADF AugmentedDi key-Fullertest

AMR Automati MeterReading

CV Cross-Validation. Equation6.10

CDF Cumulated Distribution Fun tion. Equation3.13

CRLP Class Representative Load Pattern

CUSUM CUmulative SUM.Equation6.3

DSO Distribution SystemOperator

DMS Distribution Management System

DG Distributed Generators

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DFT Dis reteFourier Transform. Equation3.6

DLE Distribution Load Estimation

ERDF Ele tri ité RéseauDistribution Fran e

EMS Energy Management System

FL FuzzyLogi

FCM Fuzzy C-Means

GDP Gross Domesti Produ t

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 te hnique algorithm

KNN K-Nearest Neighbor(s)

KPSS Kwiatkowski-Phillips-S hmidt-Shin tests

KDE KernelDensity Estimation. Equation 6.1

LV Low Voltage

LFC Load Frequen yControl

LTLF Long-Term Load Fore ast

LOO Leave-One-Out. Equation4.6

LL Lo alLinear. Equation 6.9

LL2 AdaptedLo alLinear

MV Medium Voltage

MV/LV Medium Voltage/ Low Voltage

MTLF Medium-Term Load Fore ast

MAPE Mean AbsolutePer entage Error. Equation2.32

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MLE Maximum LikelihoodEstimation

MLP Multi LayerPer eptron

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 Fun tion

PARMA Periodi AutoRegressiveMoving Average

PACF Partial AutoCorrelation Fun tion

PSO Parti le SwarmOptimization

PRESS Predi tedREsidualSumof Squares. Equation 4.6

PNN ProbabilityNeural Network

RNN Re urrent Neural Network

RBF Radial BasisFun tion

RBFN RadialBasis Fun tion Networks

RLP Representative Load Pattern

SE StateEstimator

STLF Short-Term Load Fore ast

SOM Self-Organizing Maps

SLP Single LayerPer eptron

SVM SupportVe tor Ma hine. Equation2.27

SVR SupportVe tor Regression. Equation2.27

SCADA Supervisory Control And DataA quisition

SSR SumofSquare Residuals

SSE SumSquare Error

TLP Typi al Load Prole

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TMB Minimum Temperature Base

VVC VoltVAR Control

VLOO VirtualLeave-One-Out

VSTLF VeryShort-Term LoadFore ast

WCI Wind ChillIndex

WNN Wavelet Neuronal Network. Equation 2.18

WLSE Weighted LeastSquaresEstimation

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x

Inuen evariableve toror 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

Loadve tor

y

i

Sampled loadvalue

ǫ

t

Model'snoiseat time

t

e

Dieren ebetween outputofthe modelandmeasured value

γ

y

(t, t − τ)

Auto ovarian e fun tion of

y

pro essat thetime

t

and

t

− τ

E

_(⋅)

Expe ted value operator

{P

i

, y

i

}

Histori al datainputs/outputspair, learningset or trainingset,

i

= 1,⋯,N

f

t

Trendmodelvalueat time

t

S

t

Cy li modelvalueat time

t

D

α

, α

= 1,⋯,κ − 1

Dummyvariables,where

κ

isthenumberof dierent ategories

γ

α

, α

= 1,⋯,κ − 1

Dummyregression oe ients

T

t

Temperature at time

t

W

t

Detrendedseries

p

_(ǫ)

Probability densityfun tion oftherandom variable

ǫ

F

ǫ

(x)

Cumulative distributionfun tion ofthe random variable

ǫ

P

Ve tor variables

{p

j

, j

= 0,⋯,R}

of neural networks, where

R

is the total number of inputvariables

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Ω

Setof theparameters of theneuralnetwork model

ω

Ve tor ofweightsof the linear ombination, between thehidden layerand outputlayer of theneural networkmodel

C

Ve tor

{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 variableve tor

f

_(P

i

, Ω

)

Output of the neural network with respe t to the variable ve tor

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

Risk hosenbythedesignerto ontrol thenumberof inputs

h

ii

Leverage, i-th diagonal element ofthe hat matrix

H

p

Numberofsetof parametersof theneural networkmodel,whi hisequal to

(R + 1)M +

(M + 1)

E

LOO

Leave-one-out s ore

E

p

Approximationof the leave-one-out s ore

Z

Ja obian matrix ofthe neural network model

E

yr

Yearlyenergy onsumption

E

0

Non-heatingdailyenergy onsumption

s

Temperaturesensibility,indi ating theamountofenergy onsumed(kWh)byde reasing 1

o

Ctemperature

E

n

Annualenergy onsumption adjusted tothe normal limati ondition

P

_(t)

Estimated meanpower attime t

σ

_(t)

Estimated standard deviation at hour t

ν

_(t)

Estimated marginat timet

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b

_(t)

Commongroup oe ientfortheBAGHEERAmodel onvertingheatingdailyenergy into heating powerat time t

E

d

Daily energy onsumption

E

i

Meter re ordingenergy onsumption during

n

i

days

Dd

i

Degree days duringa period of

n

i

days

Dd

365

Yearlydegree days inthe normal limati ondition

T

d

Dailyaverage temperature

T

N h

Nonheatingtemperature,atemperaturethresholdbelowwhi hthe onsumptionrises due tothe ele tri al heaters

ˆ

g

h

(x)

Kerneldensityestimator ofvariable

x

,withsmoothing parameter

h

Smoothingparameter

K

_(µ)

Normalkernel fun tionof variable

µ

γ

Ex ess probability oftheload estimationmodel

h

cv

Optimal smoothing parameterdened byCV te hnique

y

T M B

_

i

Estimated powerat TMB ondition

ˆ

f

h

′

(⋅)

Kernel-type estimator withitsoptimal smoothingparameter

h

′

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models in the smart grid ontext

Contents

1.1 Ba kground: smartgrid and smart meters for load modeling . 2

1.2 Motivation and obje tives . . . 3

1.2.a Fornetworkoperationneed . . . 4

1.2.b Fornetworkplanningneed . . . 5

1.3 Contributions of the thesis . . . 6

1.4 S ope and organization of the dissertation . . . 7

Abstra t

Ground-breakingevolutionshavebeenbroughttotraditionalele tri aldistributiongrids

by the on ept of smart grids. The smart meter system, as one of the most

impor-tant infrastru tures in the smart grids, gives us detailed information on ele tri ity

onsumptionofanindividual ustomer. In this ontext, weaimatdesigning

fore ast-ingmodelsandestimationmodels basedonthese informationfor needsindistribution

network operation andnetwork planning. The ontributions, aqui k overview of the

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1.1 Ba kground: smart grid and smart meters for load

mod-eling

The smart-grid on ept ombines advan ed ommuni ation te hnologies with traditional

ele tri al distribution grids in order to improve the transparen y and the ontrollability

of distributiongrids. Fa ing several ground-breaking evolutions inthe ele tri ity systems,

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

due to plug-in ele tri vehi les, to name a ouple, numerous advan ed algorithms appear

in this ir umstan e to enhan e the stabilityand thee ien y of the system. These

Ad-van ed Distribution Automation (ADA) fun tions in lude Volt VAR Control (VVC) [1℄, self healing, and dire t load ontrol [2℄ (to name a few). The ADA fun tions are al u-lated in real-time or in ahead of time in order to help making de isions. Generally, the

monitoring and the ontrol pro ess ofdistribution networksareperformedat theMedium

Voltage (MV)level.

Oneofthesmart-gridgoalsisto makedistribution systemse onomi allye ientwith

reliableenergysuppliesandless osts. Distribution networkplanninginvolvesdevelopinga

s heduleoffutureadditionsthatensurethe qualityofenergydeliveryaswell asthelowest

possible ost. Ontheonehand,the ele tri ityinfrastru ture mustmeettheneedsof peak

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

reli-ableloadestimation models arerequiredto tightendistribution marginsand optimize the

planning investmentbyperformingdistributionnetwork al ulations, i.e., arryingout the

powerow al ulationin riti alsituations soasto identify poor ele tri itysupply zones.

Nevertheless,the omplexityinthe problemis relatedto theun ertaintyand randomness

inthe lients' ele tri ity onsumptions.

Inthe urrentstate,thes ar ityofmeasurementsonthedistributionsystemintrodu es

bottlene ks in arrying out theADA fun tions aswell asthenetwork optimization

al u-lations. Theavailable measurementsindistribution networksaremainly onthese ondary

of sour e substations. It is e onomi ally non-feasible to implement ele tri meters in all

738 000

Medium Voltage/ Low Voltage (MV/LV) substations. Today, for the operation need, applying very approximate probabilisti models with50% of pre ision seriously

af-fe ts the e ien y of the ADA fun tions, resulting dubious analysis results. In order to

omply with the planning need, the a tual model applied by the Fren h ele tri ity

om-pany, termedBAGHEERA, dependsmainly on the lient's individual information, whi h

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

repla ing theBAGHEERA model.

Starting from 2010, the Ele tri ité Réseau Distribution Fran e (ERDF) (Fren h

Dis-tribution System Operator (DSO)) laun hed the Linky (baptized name for the smart

meter inFran e) proje t, whi h aimsat installing

35 000 000

smart meters inFran e. On the one hand, end users will pay ele tri ity bills based on their real onsumptions rather

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

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

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substationsonthe Fren hdistribution networks. Intheexperimental phaseoftheLinky

proje t, the onsumption information of ea h individual is sampled on a 30-minute basis

andtransferredon eadaytothe orrespondentdata enter. However,asdataaregathered

inpa kagesandsentwitha ertainfrequen y[3℄,somedelayisfoundinthemeasurements.

Therefore,usingthea urateinformationprovidedbythesmartmeterstodevelopload

models isthe silverbulletthatmakeskeysmart-grid appli ationsfeasible.

1.2 Motivation and obje tives

The supervision of the power and voltage dispat hing of the networks is a riti al task

in distribution exploitation. It guarantees an e onomi al optimum and a dynami

sta-bility of the networks. Unlike transmission networks, on whi h abundant measurements

exist,distributionnetworkshavemu hlessmeasurements. Asamatteroffa t, be ause of

the omplex stru ture and a great number of nodes (MV/LV substations) indistribution

networks, itis e onomi ally impossible to install meters ina great quantity on these

sub-stationsindistributionnetworks. Thus,thedistribution systemis onsideredasblind or

nonobservable. Onesolutionto improve the observability of distributionnetworksis

to introdu e loadmodels inorder torepla e themeasurements.

In termsofloads indistribution networks, we distinguishtwo types:

MV lients dire tly onne ted toMV networks

Numerous Low Voltage (LV) lients onne ted to MV networks through the publi

MV/LV substations

HV

MV

LV

P,Q

|U

₁

|,|I

₁

|

|U

₂

|,|I

₂

|

|U

3 |,|I

3 |

|U

n

|,|I

n

|

...

Figure1.1: Availablemeasurements(markedinred)[4℄intheFren hdistributionnetworks.

∣ ⋅ ∣

representsthe norm notation,equivalent tothe magnitude.

Currently,the measurements intheFren h distribution networksare(gure 1.1):

The a tive and the rea tive power on the se ondary High Voltage/Medium Voltage

(HV/MV)substations

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The magnitudeof the urrent on head ofeveryMV feeder

The a tive andthe rea tive powerof some MV lients

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

the supply ontra t and billing information ofthe lients onne ted tothepubli MV/LV

substations.

With the new available individual onsumption data olle ted by smart meters, the

obje tive of the resear h 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 a urate models for the distribution network planning, monitoring

and ontrol,inabsen e ofthe ostly 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

reasonsdes ribedasfollows:

During a failure: in order to e iently restore ele tri ity in regions where a fault

o urs,loadsintheae tedregionsshould be knowninthefollowingthree minutes.

During network maintenan e: the variation of the onsumption needs to be known

to restorethepowersupply. Generally,atwo-dayperiodis onsidered bytheFren h

ele tri itydistributorERDFasanormalrepairing time. Inthis ase,atwo-dayload

fore astwithits standard error isneeded.

As inputs for the SE: the SE [5℄ is the ore fun tion of any energy management system. Itaimsat estimatingthenetwork variables,su hasthevoltage magnitudes

and angles. Figure 1.2 shows the s hemati of the relationship among fore asting

models,SE,andADAfun tions. Thefore asting modelsaswellasthenetworkdata

are onsidered as inputs for the SE. The network data [5℄ in ludes theinformation aboutthenetworktopology,lineresistan e,rea tan e, tapsetting, andline harging,

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

ontrol s heduling blo k to perform on erned ADA fun tions for operational

de i-sions. These de isions enable the monitoring and ontrol of various devi es in the

networkssu has apa itor banks,Distributed Generators(DG), on-load tap

hang-ingtransformers,and swit hes/breakers, et .

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

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Linky

MV/LV Substation

Forecasting models

MV/LV Substation

Distributed Generation (DG)

Capacitor banks

HV/MV Substation

State estimator

Advanced Distribution Automation (ADA)

functions (VVC, self-healing...)

Optimized network reliability

Optimized network securities

Optimal economic benefit

Distribution Management System (DMS)

Figure1.2: Relationshipamongfore asting models, SE,andADA fun tions

1.2.b For network planning need

Designing a reliable distribution network is hallenging sin e it needs to guarantee a

sta-ble and ontinuous power supply to the ustomers. As a matter of fa t: a utility must

maintainthe voltage delivered toea h ustomer withina narrow range entered withinthe

voltages that the ele tri equipment is designed totolerate [6℄. In theEuropean ele tri ity regulation, for the LV networks, a

10%

out-of-range voltage is a eptable. Beyond this range, the ustomeris dened asapoorlysupplied ustomer.

For the sake of planning, network al ulations are performed under extreme

situa-tions in order to handle worst ase s enarios [7, 8℄. More spe i ally, these al ulations are arriedout when either of these two ases o urs: 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 expe ted. Be ause

ofthe ustomers' various behaviors,ina samegeographi zone, peak demandsof dierent

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loadpattern ateveryhour isrequired. Un ertaintyoftheloadestimationalsoneedstobe

onsidered [10℄. Generally, for the voltage-drop al ulation, the ex ess probability, whi h denes the threshold power bounds, is xed to 10% [11℄. Consequently, in the network planning, a lient's total supply demand in ludes the lient's daily load pattern and his

10%ex ess probabilityun ertainty.

Moreover,inthe distributionnetwork planningpro ess,alistofstandardsand riteria

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

alsodened. Reliableloadmodelsarealsorequiredinthefollowing ases inorderto arry

out distribution network al ulations:

Distribution line losses

Currents inlinesegments

Networkvoltage-drops

MV/LVtransformers: two-hourequivalentpower 1

,voltage-drops,andele tri allosses

Therefore,the obje tive isto dene an individual ustomer's maximumand minimum

loadlimits ofa yearwith10% ex essprobability.

1.3 Contributions of the thesis

Themajorpurposesofthisdissertationaretwofold: designingnewloadfore astingmodels

for thenetwork operation and load estimation models for thenetwork planning in

distri-bution networks. The ontributions of thethesis an be summarizedasfollows:

Load fore ast is an extensively investigated subje t on the transmission level [12,

13, 14, 15,16,17, 18,17,19, 20℄. However on the distribution level, withthe same hara teristi onsumption data (several dozen kW), to the best of our knowledge,

few workshave been done.

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

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

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

is theba kbone of the powersystems. Se ond, thehighervoltage level onsumption

has a more regular load urve pattern, whi h makes it easier to fore ast. Third,

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

thefore asting models an be designed and validated.

In this resear h proje t, two models based on time series and neural networks have

been proposed,for thenetwork operation need.

The dierent load types (residential, ommer ial, and industrial) are examined in

this resear h,and their dierent properties arepointedout.

1

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The two methods are designed and evaluated on real measurements olle ted from

theFren hdistributiongridsintheframeworkoftheLinky proje t. Referen e ase

isestablishedinorderto be ompared to the twoproposed models. Advantagesand

drawba ksofthe twomethods aredrawnthroughthe omparison. Thetwomethods

arealternative and,at thesame time, ompliment to ea hother to setthepre ision

limit dueto theintrinsi hara teristi s ofthesubstation loaddata.

Timeseriesmethodpresentedinthisdissertationisanoriginalwork,wherenumerous

statisti altoolsareintegratedinforthepursuing ofpre ision. Residualofthemodel

islooked through indetailsto ensure the model'swell being.

Neural network method, on the other hand, is inspired by the sele tion pro edure

proposedbyGérardDreyfus[21℄,arenownedexpertintheneuralnetworkmodeling. Wefo usontheNeuronalNetwork(NN)modeldesign,whi hhasbeenfullyexploited

for the rsttime inthe short-term loadfore ast.

Until theimplementationofthesmartmeters, usuallytherewerenoavailable

histor-i alloaddatabesidesthedemand surveydataonalimitednumberof lients. Inthe

loadmodeling eld,most of theworks on erningthedistributionnetwork planning

aimatestimatingthepeakdemandforagroupof ustomersduringthepeakdemand

of the system, namely the oin ident peak demand [6℄. For this purpose, some re-sear hesbasedonend-usemethod[9,22℄de omposetheloadmodeloftheresidential ustomerintoapplian eelementaryunits. Othersfo usonthe lassi ationmethod,

sorting ustomersinto dierent ategories, and on the representation ea h ategory

witha Typi al Load Prole (TLP). In the smart metering ontext, we are therst

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

network planning need.

Tobuildanindividualestimationmodel,therelationshipbetweentheele tri ity

on-sumptionandthetemperatureisdedu edbynonparametri estimators. Themethod

isappliedtoreal onsumptiondataofindividual ustomersinFran e. Performan eis

omparedtothe urrentloadmodel(termedBAGHEERA)oftheele tri ity ompany

EDFthrough dierent validationstudies.

1.4 S ope and organization of the dissertation

Thedissertation is organizedasfollows:

Chapter1statesthatthe smartgrid andthe smartmetersareinrapid development

to improve the e ien y andthe ontrollabilityof distribution networks. The

revo-lutionary hangesindistributionnetwork systemsurgethea urate loadfore asting

models. Re ordingindividual onsumptioninformation,thesmartmetersenablethe

buildingofthesemodels. Thethesisisen ouragedbytheLinkyproje tlaun hedby

theFren hele tri itydistributorERDF,aimingatinstalling

35 000 000

smartmeters inFran e. Twomainobje tivesareevokedinthesmartmetering ontext: short-term

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network planning. Reasonsfor thedevelopment ofthese two obje tivesarede lared.

Contributions ofthe thesis arehighlighted.

The rest of the dissertation is divided into two parts, dealing with two distin t

ob-je tives. Part A ta kles the fore asting load models for the operation need, and in ludes

hapters 2,3and 4.

Chapter 2 gives a review of the load fore asting methods in literatures and set up

basi framework for the performan e evaluation. Load fore asts are stratied into

dierentobje tivesa ordingtotheirleadtimes ale. Dierentobje tivesaredevoted

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

fore ast. Fore astingmethodsaredividedinto two ategories: the lassi alapproa h

and the arti ial intelligent approa h. Hybrid models that possess the advantages

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

inour study arethoroughly analyzed, suggestinginuen e fa torsto our short-term

load fore asting models. We argue for our hoi es of timeseries and neuralnetwork

methods. Performan e riteria anda referen emodel(termednaive model) arealso

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

theapplied methods inthe nexttwo hapters.

Chapter 3 presents the short-term load fore asting model based on the time series

method. The fore asting pro edure is detailed. The additive time series model

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

omponents aredeterministi , and are designed into models respe tively. Thetrend

modelistemperature-dependent, linear,anddummyvariablesintegrated,indi ating

day types. Cy li model is omposed by the Fourier omponents, whose

frequen- ies are found by a smoothed periodogram. Numerous statisti al tools are applied

pursuing a better pre ision: sliding windowstrategy isadopted sothatthemodelis

updatedduringea hfore astingperiod;ANalyseOfVArian e(ANOVA)nullitytest

is applied to estimatethesigni an e ofvariables. Availabledataaredivided into a

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

to thelearning set. Whereasthe test set isreservedfor the performan e evaluation.

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

impa ton the pre isionof thefore asting modelisdis ussed intheendof the

hap-ter. We on luded thatevenwith theweather un ertainty,our proposed timeseries

modelstill outperforms thenaive model.

Chapter 4 introdu es the neural network model from the arti ial intelligent

ap-proa h family. In our study, we fo us on the design of the neural network model,

hoosingtheoptimalmodelthathasthebesta hievablepredi tiveability. Ageneral

on ept of the ma hine learning te hnique is stated, and di ulties su h asnding

therelevant variablesand thebias-varian e dilemma,areexplained. Theorthogonal

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

as solutions to these di ulties. Experiments on the same data show that the

pro-posed methodology behaves better than the time series model in term of a ura y.

A omparison indiverspropertiesismadebetween thetwomodelsintheend ofthis

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

solutions. It ontains hapters 5 and 6.

Chapter 5 fo uses on the load resear h proje ts in distribution networks. Load

re-sear h proje ts aimat providinghourlyloadestimationmodels for individual lient.

Three steps, i.e., te hni al analysis, e onomi al analysis, and nal de ision, for the

de ision makings in distribution network planning are presented. The outputs of

the load resear h proje ts ontribute to the te hni al analysis, devoting to nding

solutions in network planning. The me hanism of the aggregation of loads, the

o-in ident load, is explained. Common methods ofnding TLP,whi h represents the

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

ele tri al unities in Finland, Denmark, Norway, and Taiwan aredes ribed. Finally,

the omponents ofthe BAGHEERA modelapplied bytheFren h DSOare detailed

andthe method isdemonstrated withreal measurements.

Chapter6proposesanovelapproa hfortheindividualloadestimationinthe ontext

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

opinion,the loadmodelis readyto beindividualized rather thanestimated through

the TLPs. Thus, inthis hapter, theindividual loadestimation modelbasedon the

nonparametri estimators isput forward. Numerous statisti altools,su h asbinary

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

andCross-Validation(CV)te hnique,areintegrated intheproposedmethod. Three

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

Lo al Linear (LL2) are applied to dedu e the relationship between the load and

the temperature variations. Dierent appli ation ases a ording to thequalityand

quantityofthedataaresuggested. Themethodisillustratedwithrealmeasurements

and ompared withtheBAGHEERAmodel. Thevalidityofthemethodisexamined

withextensive examples. In the end ofthe hapter, adis ussion onthedenition of

the un ertaintyboundof theestimationmodelis arriedout.

Chapter7 on ludesthedissertationandproposesperspe tivesforthefutureresear h

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Short-term load fore asting models

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(36)

framework

Contents

2.1 Literature review . . . 14

2.1.a Fore astingleadtimesandinuen e fa tors . . . 14

2.1.b Fore astingmethods . . . 16

2.1.b-i Classi alapproa h. . . 18

2.1.b-ii Arti ialintelligentapproa h . . . 25

2.1.b-iii Hybridmodels . . . 35

2.1. Literaturereview on lusionsandperspe tives . . . 37

2.2 Data des ription. . . 40

2.2.a MV/LVsubstation . . . 40

2.2.a-i Temperatureinuen e . . . 41

2.2.a-ii Daytypeinuen e . . . 42

2.2.a-iii Timeinuen e . . . 42

2.2.b MVfeeder. . . 45

2.3 Choi es of Time series and NN methods. . . 45

2.4 Performan e riteria and referen e ase. . . 46

2.4.a Performan e riteria: MAPEandMAE . . . 46

2.4.b Referen e ase: thenaivemodel. . . 47

2.5 Con lusion . . . 47

Abstra t

Load fore ast plays an important role in de ision makings in power systems. This

hapter begins with the review of load fore asting models in literatures. The se ond

partof the hapter ontributes toaframework onsisting ofdata des ription,method

sele tion,performan e riteria,andreferen e aseintrodu tions. Inthereviewingpart,

we lassify a wide range of approa hes of load fore ast into two ategories: lassi al

approa h,andarti ialintelligentapproa h. Methodologiesinea h ategoryarebriey

presented. Theiradvantages,disadvantages,appli ations andpertinentresear hworks

arealsodeveloped. Popularhybridmodels ombiningtwoormoredierentapproa hes

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 hoi es ofthe methodologies basedon the timeseriesandtheneural

networksareargued. Thesetwomethodologies aregoingtobedetailedinthe following

two hapters. Performan e riteria and referen e asearestated soas tolay agood

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2.1 Literature review

The quality of the de ision making in ele tri power systems strongly depends on the

a ura y of the power load predi tions. Various de isions require reliable and a urate

loadfore asting models withdierent time-s alesaswell asondierent hierar hi al levels

innetwork systems [23℄.

A wide range of approa hes have been proposed to the load fore asting problems. In

thisse tion,weaimatpresentingbrieythedierentapproa hesfoundinliteratures,their

spe i ities,appli ations and te hniquesapplied to loadfore ast.

Theorganization of the se tion isasfollows: rst,we start byintrodu ingdenitions,

appli ations and inuen e fa tors of dierent lead time load fore asts. Then, a two

di-mensional digestinlead timeand involtage hierar hy s alessummarizes load fore asting

methods,followedbythe des riptive presentation ofeverymethod. Related worksarealso

depi ted. Finally,we on lude theliterature reviewinatable.

Notethatfor the sake of larityandease ofunderstanding, mathemati al notations in

the referen ed works and internal reports have been adapted in order to keep oheren e

through theentiredissertation.

2.1.a Fore asting lead times and inuen e fa tors

Dierent fore asting lead times result into dierent fore asting models as well as their

inputvariables. Numerousfa tors,su hasweather onditions,seasonalee ts,andso ial,

e onomi ,demographi fa torsexplainthevariationsintheload[23℄. Table2.1summarizes theappli ationsandinuen e fa torsfor dierent timehorizon fore asting models[23,24,

18℄.

Noti ethat more input variables arein luded when thetime horizon be omeslonger.

ForaVSTLF,univariate(onlythehistori alpowersamplesare onsideredasinputs)

mod-els an oersatisfa toryresults. TheseVSTLFsoftenparti ipateto improvethee ien y

and reliabilityofthe real-timeele tri al systems. For longerlead timefore ast,

multivari-atemodelswithexogenousvariablesarefavored. TheSTLF needsmainlythree ategories

of inputs: weather, alendar, and histori al variables [25℄. Dueto some measurement de-lays, or the omputational timefor the exe ution of theADAfun tions, the STLFs often

repla e VSTLFs to fulllneedsin network operations. STLF fore asts also help redu ing

equipment failures and system bla kouts by indi ating the operational margins in power

systems. TheMTLFmodelshelpmakingnan ialde isions,su hasevaluationofthepri e

of energy produ ts and investment interests. In su h ases, the fore asting models need

additional inputs asso ial and e onomi al fa tors. The LTLF, on erning energy system

apitalexpendituresandmoreimportante onomi investments, needstotakeintoa ount

more so io-e onomi fa tors,and sometimes even their futureevolutions.

The herein des ription is in a general way, as in se tion 2.2.a, we will talk about an

industrialMV/LVsubstationloadthatisindependentto weather onditions. Thus,

what-everthefore asting leadtime is, for this loadexample,weather variableis not onsidered

asan inuen e fa tor.

Asdes ribed in the table 2.1, for our appli ation in network operations, espe ially to

ooperatewiththeADAfun tions,wefo usontheSTLF. Weather, alendarandhistori al

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Table 2.1: Dierent timehorizon loadfore asts

Timehorizon Appli ations Inuen efa tors

Very Short-Term Load

Fore ast (VSTLF)

(1Min

∼

1h)

ADA fun tionsinDMS,Load

Frequen y Control (LFC) in

Energy Management System

(EMS)

Histori al onsumptions

Short-Term Load

Fore- ast (STLF) (1h

∼

1 week)

Operation (ADA fun tions),

estimation of load ows,

rep-resentation ofsavingpotential

for e onomi and se ure

oper-ationof powersystems

Histori al onsumptions,

al-endar fa tors (day type and

houroftheday),weather

on-ditions (

∗

)

Medium-Term Load

Fore ast (MTLF) (1

week

∼

1 year)

Negotiation of ele tri ity

on-tra ts, s heduling of fuel

sup-plies and maintenan e

opera-tion

(

∗

) + population, e onomi fa tors, et (

◇

)

Long-Term Load

Fore- ast (LTLF) (1 year

∼

severalyears)

Capital expenditures and

planning operations

(

◇

) + more information su h as: population growth, Gross

Domesti Produ t(GDP)

(

∗

) and (

◇

) represent respe tively inuen e fa torsfor short-term and medium-term fore- asts.

For a weather sensitive load, in ludingthe redible fore asting weather information as

input is re ommended as it an improve the performan e of the fore asting model. T

em-perature and humidity are the most frequently used load predi tors. Composite weather

variables su h asTemperature-Humidity Index (THI),Wind Chill Index(WCI) [24℄, and smoothed weather variables [26℄ are often adopted. THI and WCI indi ate respe tively thedis omfort ausedbysummerheatandwinterwind hill. Thesmoothedweather

vari-able represents the ee ts of hanges in weather a umulated over the time. In pra ti e,

regardingSTLF,weather fore asting data areapplied to al ulate theperforman eof the

model [27℄. However, for the most of the time, in the onstru tion phase of the model, thepredi tedweatherfore astisnot available. Inthis ase, most authorsintheload

fore- astingeldrunsimulationswiththe realizedweather data[28℄. Oneshould bearinmind thatusingfore astingweatherinformationwillsurelyde reasethemodel'soverallpre ision

[26,29℄. Therefore,someauthors[30℄proposedomittingimpre ise weatherinformation as a onservativesolution, sin e itwouldbringlargevarian eto themodel. Apromising way

to handle the un ertainty in weather variables is the weather ensemble predi tions that

generatetheloadfore astsinaprobabilisti form[29℄. In hapter3,wewillre-dis ussand showempiri al eviden eaddressing to thisissue.

The alendar inputs in lude 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

(39)

oftenmoredi ulttofore astthanworkingdaysduetotheirrelativeinfrequento urren e

and the lients' irregular behaviors. Someauthors workon the lassi ation methods [19℄ inorder to ndor even reate similar days [31℄for these anomalous dayfore asts.

Histori aldatainputsarealsoveryimportant totheSTLF,fromwhi htheseasonality

information an beextra ted [14℄.

2.1.b Fore asting methods

This subse tiongives anoverviewof various approa hes for loadfore asts. Manyof them

aredevelopedforSTLF onthe HighVoltage(HV)level,althoughMVandLVlevelsbegan

to attra t 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

fore asting eldboth intheleadtimeand thevoltage hierar hi al s ales.

Mainly,two lasses ofapproa hes anbedistinguished [14,23℄: lassi alapproa h and Arti ialIntelligen e(AI) approa h. Classi alapproa hrequiresanexpli itmathemati al

modelwhi hinterpretstherelationshipbetween loadanditsinuen efa tors. Thisfamily

in ludes regressionmodel, timeseries method, similardayapproa h, end-use method and

e onometri approa h. AI approa h, on the other hand, extra ting non linear

relation-ships between input fa tors and load hasbe ome very popular nowadays. This family of

algorithms in ludesArti ial Neuronal Network (ANN),fuzzylogi , and expertsystems.

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Very short-term

Short-term

Medium-term Long-term

H

V

M

V

L

V

ANN

(12)

End use method

(13)

ANN (14)

(MAPE 4.9-7.74%

depending on the

forecast season)

ANN (11)

(Inputs: 1. Historical load data

2. Estimated load pattern)

C

lassification method

(Client typical pattern)

+ANN (15)

SVM

(8)

Similar days+NN correction model

(9)

Expert system

(10)

FL or Fuzzy Neural Networks

(FNN) (7)

ANN

(6)

Regression method

(4)

Multivariable time series

ARIMAX (3)

Univariable time series:

(1) Exponential smoothing

(2)Box-Jenkins (AR, ARMA,

ARIMA)

Econometric approach

(5)

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

voltagehierar hy. HV:HighVoltage,MV:MediumVoltageandLV:LowVoltage. Numbers

appearinthe gure orrespond 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

(41)

2.1.b-i Classi al approa h

Regression model. Regression is one of the most widely used statisti al te hniques.

Ele tri load fore asting regression methods are usually used to express the relationship

between load onsumption and external fa tors[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 inuen e variable ve tor orrespondent to the i-th load sample,

a

i

is the transposed regression oe ient ve tor, 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 thepredi tion interval through estimation error

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

form in luding ee tive inputs and output. This is hard due to the omplex non-linear

relationship [23℄.

C.L.Horetal. [43℄developedseveralmultipleregressionmodelsin orporating weather-relatedandso io-e onomi variablesontheloaddemandforEnglandandWales. Monthly

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

data from 1996 to 2003 are used to evaluate the a ura y of thefore asting model. The

non-linearrelationshipbetweenweather-relatedfa tors(meanmonthlytemperaturevalue)

and load suggests introdu ing other weather omposite variables, su h asHeating Degree

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

so io-e onomi variable GDP has evidently an impa t on the trend. One of their regression

modelis set up as:

E

ˆ

1 = ( ˆ

E

A

+ α

7

GDP

)F

adj

(y)

, where

E

ˆ

1

is the predi ted ele tri ity de-mand,

ˆ

E

A

= α

0 + α

1

CDD

+ α

2

HDD

+ α

3

ELD

+ α

4 V

w

+ α

5 M

s

+ α

6 M

r

,whi h 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 themonthly rainfall.

α

n

, n

= 0,⋯,7

are onstant oe ients.

F

adj

(y)

is the adjustment fa tor for ea h year. The Mean Abso-lute Per entage Error (MAPE) of themodel, whi h represents theaverage portion of the

absolute fore asting errorsto therealfore asting values,wasaround 2%.

A. Bruhns et al. [17℄designed a non-linear regression model for MTLF. This hourly loadpredi tionmodeltermedEventail hasbeenappliedbytheFren hele tri ity ompany

EDF sin e 2001. They de omposite the load

P

i

into three omponents:

P

i

= Phc

i

+

P c

i

+ e

i

, where

P c

i

and

P hc

i

are respe tively the weather-dependent and the weather-independent parts,

e

i

isa Gaussian error. Theweather-dependent partis ttedbya non-linear model of the observed temperature, the exponential smoothing temperature, and

the loud over. Two thresholds for heating and ooling temperatures arealso adopted in

orderto opewiththenon-linearity. Theexponentialsmoothingontemperatureree tsthe

inertiaoftemperatureinsidebuildingsto theoutsidetemperature variation. The

weather-independentpartintegratestrends,day,week,yearperiods,anddaytypeinformation. The

dummyvariables are usedto indi ate daytypes and four termsof Fourier series areused

to model the seasonality pattern. Despite of the omputational di ulty in estimation

dueto thetemperaturesmoothingparameters,thresholds,andstrongnon-linearities,they

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

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W. Charytoniuk et al. [26℄ introdu ed a nonparametri regression model for STLF. They onsidered load as a weighted average of past loads. The spe i weights are

de-ned by amultivariate kernel and its smoothing parameters. The optimal values ofthese

smoothing parameters are al ulated using CV te hnique. A onditional expe tation of

theload is built based on thelo al neighborhood loads

P

i

:

P

ˆ

(x) =

∑

n

i

=1

{P

i

∏

r

j

=1

K

(

xj −xji

hj

)}

∑

n

i

=1

{∏

r

j

=1

K

(

xj −xji

hj

)}

,

where

h

1 ,

⋯, h

r

aresmoothingparametersand

K

(µ)

isanormalkernel.

j

denotesthej-th inuen e variable in the exogenous variable ve tor

x

and

i

denotes the i-th observation sample. They have obtained with a urate temperature values, up to one-week-ahead, a

MAPE of2.78% ompared to an ANNmodel of2.64%. Theyarguedthateven theerrors

areslightly higherthan theANN,the errorsobtained bytheregressionmodelhave better

properties ompared to those oftheANN model.

Time series method. Timeseries methodisalinearmodelbasedontheassumption

that there existsan internal stru ture within data. This stru ture onsists of

auto orre-lation, trend and periodi variations. Time series methods dete t and explore these

rela-tionshipsbetweenthe urrent loadvalue,histori aldataandsometimes exogenousfa tors.

A distin tive property oftime series models is to onsidertime asone of theexplanatory

variables. As a linear model, time series method is suitable for VSTLF and STLF and

it is able to provide the predi tion interval. Whereas for MTLF and LTLF, these

inter-nalrelationships are no longer linear and themodel be omes ompli ated. Thus, itis no

longer e ient to use a linear timeseries model for the MTLF or the LTLF appli ation.

Inparti ular, Box-Jenkinsmodels andexponential smoothing modelsarethemost widely

usedtime series methods.

1. Box-Jenkins models [44℄in lude AutoRegressive (AR), Moving Average (MA), Au-toRegressive Moving Average (ARMA), AutoRegressive Integrated Moving A

ver-age (ARIMA), Periodi AutoRegressive Moving Average (PARMA), and

AutoRe-gressive Moving Average with eXogenous inputs (ARMAX). They are adapted for