Maintenance scheduling in the electricity industry

181 Pages·2017·3.12 MB·English

by  Aurelien Froger

Thèse de Doctorat
Aurélien F
ROGER
Mémoire présenté en vue de l’obtention du
gradedeDocteurdel’Université d’Angers
sous le sceau de l’Université Bretagne Loire
Écoledoctorale: Sciencesettechnologiesdel’information,etmathématiques
Discipline: Informatiqueetapplications,sectionCNU27,61
Unitéderecherche: LaboratoireAngevindeRechercheenIngénieriedesSystèmes(LARIS)
Soutenuele14décembre2016
Maintenance scheduling in the electricity
industry: a particular focus on a problem rising
in the onshore wind industry
JURY
Rapporteurs: M.JacquesCARLIER,Professeurdesuniversités,UniversitédeTechnologiedeCompiègne
M.ChristianARTIGUES,Directeurderecherche,LAAS-CNRS
Examinateurs: M.Jean-CharlesBILLAUT,Professeurdesuniversités,ÉcolePolytechniquedel’UniversitédeTours
M.DavidRIVREAU,Professeur,InstitutdeMathématiquesAppliquéesd’Angers
Invité: M.MichelGENDREAU,Professeurtitulaire,ÉcolePolytechniquedeMontréal
Directeurdethèse: M.ÉricPINSON,Professeur,InstitutdeMathématiquesAppliquéesd’Angers
Co-encadrantsdethèse: M.JorgeE.MENDOZA,Maîtredeconférences,ÉcolePolytechniquedel’UniversitédeTours
M.Louis-MartinROUSSEAU,Professeurtitulaire,ÉcolePolytechniquedeMontréal

Acknowledgments
Thisthesishasbecomerealitywiththekindsupportofmanyindividuals.
The path I was following some years ago was definitely not leading me pursuing PhD studies.
Therefore,IwouldliketoparticularlythankProfessorsEricPinsonandJorgeE.Mendozaforhaving
believedinmewhenIcamebackformymaster’sdegree,andforhavingconvincedmethatIcould
becomearesearcher. IamgratefultothemformakingmepassionateforOperationsResearch.
Iwouldlikenowtoexpressmygratitudetomygroupofadvisors. Withouttheirprecioussupport
theconductedresearchwouldnothavebeenpossible. Iamsincerelygratefultothemforputtingtheir
trust in me during the 3 years of this thesis when it came to define the main research orientations. I
thank Eric for all his invaluable comments on my work. The many discussions and debates we had
havebeenveryinstructive. IthankJorgeforhisencouragementandhisvaluableadviceonbothmy
research and my career. I am also very thankful for the help he provides me, all along this thesis,
to improve my writing skills in English. I also thank Professors Michel Gendreau and Louis Martin
Rousseau who provided me with the opportunity to spend one year and a half at Polytechnique
Montreal. Ithasbeenanexceptionalexperiencetoworkwiththem.
I thank very sincerely Pr. Jacques Carlier and Christian Artigues for having accepted to be "rap-
porteur"ofmythesis. IalsothankPr. Jean-CharlesBillautandDavidRivreauforhavingacceptedto
bepartofthejury.
I also wish to express my gratitude to the WPred team (Christophe, Thomas, Hugo, Jérôme,
François) for this enriching collaboration. I am very thankful to them for having taken the time to
explain me their work with the wind industry and having kindly accepted me as a member of the
team. Ihavegreatlyappreciatedthisexperiencethathasenabledthisworktobereallyconnectedto
whatishappeningontheground. Thiscollaborationhasbeenpossiblethankstothegrantprogram
of the Natural Sciences and Engineering Research Council of Canada – this support is gratefully
acknowledged. IwouldalsoliketoacknowledgethefinancialsupportfromAngersLoireMetropole.
I also thank Julien, Maria, Vinicius, Selene, Philippe, Diego, Shohre, Andrea, Slavic, Maëlle,
Ragheb, Pirmin, and all my fellow labmates in CIRRELT for the stimulating discussions and also
allthefunwehavehad. Thankyouforhavingcreatedanenjoyableenvironmentduringmystayin
Montreal.
Finally,Ithankmyparentsfortheirunanimoussupportofmychoices,whatevertheywere.
3

Contents
Introduction 9
Listofpublications 17
I Context,literature,andtechnicalbackground 19
1 Maintenanceschedulingintheelectricityindustry: aliteraturereview 21
1.1 Theenergyindustry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Maintenanceintheelectricityindustry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.1 Maintenanceschedulingofgeneratingunits . . . . . . . . . . . . . . . . . . . . 24
1.2.2 Transmissionmaintenanceschedulingandnetworkconsiderations . . . . . . . 28
1.2.3 Managementofuncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.2.4 Fuelmanagementandmaintenancescheduling . . . . . . . . . . . . . . . . . . 30
1.2.5 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.2.6 Electricitygeneratingtechnologies . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3 Solutionmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.1 Mathematicalprogrammingapproaches . . . . . . . . . . . . . . . . . . . . . . 32
1.3.2 Heuristicsandmetaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3.3 Constraintprogramming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.3.4 Gametheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.4 Conclusionandperspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.5 Classificationofthebibliographicalreferences . . . . . . . . . . . . . . . . . . . . . . . 37
2 Technicalbackground 41
2.1 ConstraintprogrammingvsLinearprogramming . . . . . . . . . . . . . . . . . . . . . 41
2.2 LargeNeighborhoodSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3 Bendersdecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Dantzig-Wolfedecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Robustoptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
II Awindturbinemaintenanceschedulingproblemintheonshorewindindustry 57
3 Problemdescription 61
3.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Problemstatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 Complexity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Instancegeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5
6 CONTENTS
4 Formalization 69
4.1 NaturalILPformulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 CompactILPformulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.1 Baselineformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.2 Alternativeformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.3 Breakingsymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Computationalexperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 Aconstraintprogramming-basedlargeneighborhoodsearchtosolvethedeterministicprob-
lem 79
5.1 Constraintprogrammingformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Aconstraintprogramming-basedlargeneighborhoodapproach . . . . . . . . . . . . . 81
5.2.1 Destroyoperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.2 Repairoperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.3 Acceptancecriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3 Computationalexperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 CPformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 CPLNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.5 IndustrialprototypeforWPred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 Abranch-and-checkapproachtosolvethedeterministicproblem 95
6.1 Problemdecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2 Cutgenerationprocedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Bendersfeasibilitycuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.2 Maximumcardinalityb-matchingcuts. . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.3 Maximum-weightcliquecuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.4 Illustrativeexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 Thealgorithm: generalstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 Computationalexperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4.1 Resultsoftheexactapproaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.4.2 Acooperativeapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.6 Complement: sub-problemandcomplexity . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.6.1 EquivalencetotheL-coloringproblem. . . . . . . . . . . . . . . . . . . . . . . . 115
6.6.2 Specialcasesofpolynomialcomplexity . . . . . . . . . . . . . . . . . . . . . . . 116
7 Maximizingavailabilityvsmaximizingrevenue: ashortcomparativestudy 119
8 Arobustapproachtotacklethestochasticproblem 123
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2 Additionalelementsintheproblemdefinition . . . . . . . . . . . . . . . . . . . . . . . 124
8.3 Definitionoftheuncertaintyconsideredintheproblem . . . . . . . . . . . . . . . . . . 125
8.3.1 Non-correlateduncertaintyset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.3.2 Correlateduncertaintyset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8.4 Robustcounterpartoftheproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.5 Solutionmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
8.5.1 Problemreformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8.5.2 Generalschemeofthesolutionmethod . . . . . . . . . . . . . . . . . . . . . . . 131
8.5.3 Alternativerobustapproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8.6 Computationalexperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8.6.1 Baselinerobustapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.6.2 Alternativerobustapproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
CONTENTS 7
8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.8 Complement: combiningcolumngenerationwiththedecomposition . . . . . . . . . . 141
Generalconclusionandperspectives 145
A Notations 159
B Instancegeneration 163
C Detailedcomputationalresults 169
C.1 CPformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
C.2 CPLNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
C.3 Branch-and-check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Introduction
This thesis discusses the optimization of maintenance scheduling in the electricity industry and
particularly focuses on a problem rising in the onshore wind industry. This introductory chapter
aimstomakethereaderunderstandthepositioning,themotivation,andtherelevanceofthiswork.
Nowadays,theelectricityindustryexperiencesmajorchallengesandiscurrentlyinatransitional
phaseinvariousrespects. Theopeningoftheelectricitymarkettocompetition,followingthedereg-
ulation of the sector, has notably triggered fundamental changes. Electricity prices are no longer
essentially regulated by the government (hence the terms deregulation and liberalization), but they
aresubjecttomarketinteractions. Giventhesuccessofthissystemintheaeronauticsandtelephone
industries, this reform is promoted as a benefit for the sector. It is intended to favor innovation,
to lower prices, and to lead to better services. But the fact is that the transition from the original
monopoly (state) system is a slow and lengthy process. Indeed, this new system introduces new
actors and redefines the role or activities of the existing ones in such a way that this raises new is-
sues, especially on the organization and the regulation of the market. Along with this change, the
sectorissteadilygrowing. Withtheincreasingworldpopulation, thedevelopmentofcountries, the
overallneedsforenergyservicesfortheworldispredictedtobemultipliedby3.2between2000and
2100 (European Commission, 2011). If we exclusively focus on the electricity industry, the demand
ispredictedtoincreaseatarateof2%peryearuntil2035(EuropeanCommission,2011). Inamarket
driven economy, electric companies are turned towards cost-management and profitability. There-
fore,inthisgrowthcontext,theytendtopledgeformoreand/orreliableelectricitytomaintaintheir
positiononthemarketortogainmarketshare. Predominantly,companiesinthesectorconsistently
aimtobeabletomeetthedemandtheycommittedtoproducewithahighdegreeofreliabilitywhile
being cost-effective for suppliers. As a long-term development strategy, they may also choose to
built more generating units or to increase the capacity of those existing if the return on investments
isworthit. Thedifferentelectricitygeneratingtechnologiesthenpresentvariousinvestmentsoptions
tothosecompanies.
As it is widely known, electricity can be produced from fuel (e.g., oil, gasoline, uranium, gas,
coal, wood) or natural forces (e.g., sun, wind, water, biomass, geothermal). The costs incurred in
producingelectricityandtherevenuegeneratedfromitssalevarydependingonthegeneratingtech-
nologies. Take the example of nuclear power plants; the construction costs excesses by far the fuel
(uranium and heavy water), operating and maintenance costs (even if these latter costs are signifi-
cant). Onthecontrary,fossilfuelpowerplants(coal,oilornaturalgas)arelessexpensivetobuild,but
thefuelcostsaremoreimportantandsubjecttorisingorvolatility. Similartonuclearplants,hydro-
electricpowerstationshavemuchhigherfixedcoststhanfossilfueltechnologiesbut,onceinstalled,
tendtorequirelessmaintenanceandlastmuchlongerthantheirnuclearandfossil-fuelcounterpart.
The remarkable advantage of hydroelectricity is the elimination of fuel costs. The same holds for
wind farms and photovoltaic (PV) power stations for which the costs are essentially composed of
the building costs and some maintenance costs. Nonetheless, for the amount of electricity they can
generate, renewable energy technologies are quite often more expensive. One should not ignored
that the renewable sources of power are usually located in the desert, the mountains, or off-shore,
that is far away from the location of the large proportion of the demand. New transmission lines
are therefore required to connect to the existing network, and these building costs are significant.
However,inthepastdecade,theinvestmentandexploitationcostsofrenewableenergytechnologies
have already drastically reduced to make them competitive alternatives, especially if we also take
9
10 INTRODUCTION
intoaccounttaxbreaksandincentivesthathavebeensetupinmanycountries. Nonetheless,perfor-
mance and efficiency of electricity generating technologies still remain the most critical point when
speaking about profitability. If one looks at the availability factor (AF) of generating units, renew-
able energy sounds attractive. Indeed, while gas, coal, and nuclear plants carry AF over 80%, often
around90%,windfarmsAFtop95%,PVpowerplantsAFreachover98%,andhydropowerplants
AFstaysabove90%everysummer(butfellaslowas75%infallandspring). However,highAFdoes
nottranslateintoafullcapacitypowergeneration. Forinstance,itisnotalwayspossibletoreleaseall
thewaterneededtoreachthemaximumpower. Inthesameway,inthemiddleofthenight,during
cloudy days, or during winter, an available PV power plant will not generate any output or a very
small one. Similarly, a wind farm will not generate power if the wind speed is too low. In order to
assess the effectiveness of the electricity generating technologies, the most relevant criterion is the
capacity factor (CF). Figures are then clearly different. Nuclear plants have a CF usually between
80% and 90% , gas and coal plants around 50-60%, biomass around 80%, geothermal around 60%,
hydro power plants around 40% and wind farms around 25-30%, while PV power stations barely
reach 15-20%1. However, the choice of an electricity generating technology over another cannot be
madesolelybasedonthisfactor.
Takingalookattheevolutionoftheelectricityproductionperfueltypefrom2005to2015forthe
countriespartoftheOrganizationforEconomicCo-operationandDevelopment(OECD)andforthe
particular case of France (see Figure 1), we observe that the share of renewable energy sources has
significantly increased, whereas the share of combustible fuels (coal, gas) and nuclear have slightly
reducedinthepastdecade. AlthoughCFfiguresandtheprofit-drivennatureofcompaniesraisele-
gitimatequestionsaboutrenewableenergysources(aspointedoutabove),theunprecedentedboom
experienced by renewable energy is in fact explained by the increasing development of policies to
reduce (if not cut) greenhouse gas emissions. Driven by climate change mitigation and adaptation
measures (e.g., the tax incentives previously mentioned), the renewable energy sector is called to
keep growing as producing low-carbon power or carbon-free electricity becomes the priority. The
Paris Agreement – resulting from the 2015 United Nations Climate Change Conference (COP21) –
is in this respect a clear evidence supporting this claim. Nuclear and/or natural gas power stations
(called to replace coal power plants since they produce twice less CO emissions) are then usually
2
predictedtocompensatetheintermittencyofrenewableenergyaslongasenergystoragedevicesare
not fully developed and applicable on a wide scale. It is therefore clear that the transition to a low
carbon society by 2050 has already a significant impact on the electricity industry, and this impact
willcontinuetogrow.
Thisbriefoverviewoftheenergysectorpointsouttheveryimportantchallengesfacednowadays
bytheelectricityindustrytoreconcilethequestofprofits–whichgrewoutwiththepolicyofopening
upcompetition–withenvironmentalsustainability.
The issue of profitability is naturally, although not exclusively, linked to the question of relia-
bility. Indeed, electrical companies aim to avoid costly unexpected breakdowns and try to mini-
mizethedowntimethatfollows. Maintenancemanagementisthereforeamajoreconomicissueasit
savessomeinvestmentcostswiththelifeextensionofthegeneratingunitsandpreventsunnecessary
downtime and excessive operational costs. Just to cite few examples, equipment maintenance man-
agement in electric power systems is concerned with decisions such as: when to stop a generation
unit for maintenance, according to what criteria, and when to re-start it again. These decisions are
taken under complex environments and constraints such as resource availability, demand satisfac-
tion, and reliability thresholds. They aim to build effective and efficient business strategies based
on revenue or profits maximization. Maintenance in the electricity industry is therefore an ongoing
challenge. For clarification purposes, maintenance represents the actions required to ensure that a
generating unit provides reliable service. Maintenance is generally split into two categories accord-
ingtothenatureoftheactions,whethertheyareproactiveorreactive. Ontheonehand,asareactive
approach,correctivemaintenanceisperformedafterabreakdowninordertorestoretheserviceability
1. U.S.EnergyInformationAdministration-Electricgeneratorcapacityfactorsvarywidelyacrosstheworld,
http://www.eia.gov/todayinenergy/detail.cfm?id=22832