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Estimation of the net charging demand from privately owned electric vehicles using Game Theory

Mishra, Dev · 2017

Abstract

Electric vehicles are growing at a significant rate in the world and that makes it essential for modern day electricity networks to be prepared for their integration. A common approach of preparing the network for any kind of demand is to be able to predict or estimate the same based on data and simulations using optimization techniques. This work was aimed at the same in two distinct parts. In the first part, game theoretic methods were tried to be applied to an existing multi agent probabilistic model estimating net demand from electric vehicle. Owing to the complexity of the undertaking, it was decided to only include a payoff based allocation of electric vehicle charging scenarios to estimate electric vehicle demand which accounted for all scenarios rather than all vehicles charging in a single scenario. In the second part, a smaller scenario of an affluent household with two electric vehicles and typical mobility pattern was formulated. Game theory solution concept of Nash Equilibrium was used to optimize the charging of both electric vehicles over a week of usage. The results from the first part, displayed an overall reduction in maximum loads while there were certain shifts in loads observed as well. As an exercise without any inherent optimization mechanism the overall results from this segment were inconclusive. The results from the second part, demonstrated needs for charging the EVs shifting to offpeak hours and charging of vehicles, a maximum of 1-2 times per week based on user range anxiety, game theoretic competition and mobility needs. Further, savings from charging at off-peak tariffs based on time of use electricity tariffs were also evaluated.

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Estimation of the net charging demand from privately owned electric vehicles using Game Theory

Author: Mishra, Dev
Publisher: Universitat Politècnica de Catalunya
Year: 2017
Source: https://upcommons.upc.edu/bitstream/2117/110800/1/Master_Thesis_Report_Dev_Mishra.pdf
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Mas e !Thesis!
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M.Sc.!Ene gy! o !Sma !Ci ies!
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Es ima ion!o ! he!ne !cha ging!demand!
om!p i a ely!owned!elec ic! ehicles!
using!Game!Theo y!
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Au ho !:!! De !Mish a!
Di ec o !:!!Robe o!Villa á ila!Robles!
Session!:!July!2017!
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Escola Tècnica Supe io
d’Enginye ia Indus ial de Ba celona
2! ! Mas e !Thesis!
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Abs ac !
Elec ic! ehicles!a e!g owing!a !a!signi ican ! a e!in! he!wo ld!and! ha !makes!i !essen ial!
o ! mode n! day! elec ici y! ne wo ks! o! be! p epa ed! o ! hei ! in eg a ion.! A! common!
app oach!o !p epa ing! he!ne wo k! o !any!kind!o !demand!is! o!be!able! o!p edic !o !
es ima e! he!same!based!on!da a!and!simula ions!using!op imiza ion! echniques.!
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This!wo k!was!aimed!a ! he!same!in! wo!dis inc !pa s.!In! he! i s !pa ,!game! heo e ic!
me hods! we e! ied! o! be! applied! o! an! exis ing! mul i! agen ! p obabilis ic! model!
es ima ing!ne !demand! om!elec ic! ehicle.!Owing! o! he!complexi y!o ! he!unde aking,!
i ! was! decided! o! only! include! a! payo ! based! alloca ion! o ! elec ic! ehicle! cha ging!
scena ios! o!es ima e!elec ic! ehicle!demand!which!accoun ed! o !all!scena ios! a he !
han!all! ehicles!cha ging!in!a!single!scena io.!In! he!second!pa ,!a!smalle !scena io!o !an!
a luen ! household! wi h! wo! elec ic! ehicles! and! ypical! mobili y! pa e n! was!
o mula ed.!Game! heo y!solu ion!concep !o !Nash!Equilib ium!was!used! o!op imize! he!
cha ging!o !bo h!elec ic! ehicles!o e !a!week!o !usage.!
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The! esul s! om! he! i s !pa ,!displayed!an!o e all! educ ion!in!maximum!loads!while!
he e!we e!ce ain!shi s!in!loads!obse ed!as!well.!As!an!exe cise!wi hou !any!inhe en !
op imiza ion!mechanism! he!o e all! esul s! om! his!segmen !we e!inconclusi e.!The!
esul s! om! he!second!pa ,!demons a ed!needs! o !cha ging! he!EVs!shi ing! o!o -
peak!hou s!and!cha ging!o ! ehicles,!a!maximum!o !1-2! imes!pe !week!based!on!use !
ange! anxie y,! game! heo e ic! compe i ion! and! mobili y! needs.! Fu he ,! sa ings! om!
cha ging!a !o -peak! a i s!based!on! ime!o !use!elec ici y! a i s!we e!also!e alua ed.!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !3!
De !Mish a!
Con en s!
ABSTRACT!______________________________________________________________________________________!2!
CONTENTS!______________________________________________________________________________________!3!
LIST!OF!FIGURES!______________________________________________________________________________!5!
LIST!OF!TABLES!________________________________________________________________________________!6!
GLOSSARY!______________________________________________________________________________________!7!
1.!PREFACE!_________________________________________________________________________________!8!
2.!INTRODUCTION!_________________________________________________________________________!9!
2.1.!In oduc ion! o!Elec ic!Vehicles!...................................................................................................!9!
2.1.1.!EV!Technology!Basics!.............................................................................................................!10!
2.1.2.!Types!o !Elec ic!Vehicles!.....................................................................................................!11!
2.1.3.!Ba e y!Technology!..................................................................................................................!13!
2.1.4.!EV!Cha ging!In as uc u e!and!Cha ging!Technologies!......................................!14!
2.1.5.!EV! egula ion!and!policy!.......................................................................................................!17!
2.1.6.!EVs!in!Spain!.................................................................................................................................!20!
2.2.!In oduc ion! o!Game!Theo y!......................................................................................................!21!
2.3.!Game!Theo y!Applica ions!in!Rela ed!Fields!.......................................................................!24!
3.!LITERATURE!REVIEW!AND!TECHNICAL!BACKGROUND!_________________________!27!
3.1.!Elec ic!Vehicles!..................................................................................................................................!27!
3.2.!Demand!Models!..................................................................................................................................!27!
3.3.!Game!Theo y!Modelling!.................................................................................................................!29!
3.4.!P oposed!Me hodology!...................................................................................................................!37!
4.!METHODOLOGY!________________________________________________________________________!39!
4.1.!Pa ! 1:! Modi ica ion! o ! exis ing! EV! demand! p edic ion! model-! All! cha ging!
s a egies!................................................................................................................................................!39!
4.2.!Pa !2:!Two!playe !game!in!a!single!household!..................................................................!41!
4.2.1.!Two!playe !household!game!scena io!desc ip ion!..................................................!42!
4.2.2.!Da a!used! o!build! he!scena io!.........................................................................................!43!
4.2.3.!Me hodology!implemen a ion!in! he!Scena io!...........................................................!44!
5.!RESULTS!AND!DISCUSSION!___________________________________________________________!46!
5.1.!Resul s!and!Discussion:!Pa !1!....................................................................................................!46!
5.2.!Resul s!&!Discussion:!Pa !2!.........................................................................................................!48!
4! ! Mas e !Thesis!
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6.!CONCLUSIONS!__________________________________________________________________________!53!
6.1.!Scope! o !Addi ional!Wo k!............................................................................................................!53!
7.!ACKNOWLEDGEMENTS!_______________________________________________________________!55!
8.!BIBLIOGRAPHY!________________________________________________________________________!56!
ANNEXURE!A:!ELECTRICITY!PRICES!_______________________________________________________!59!
ANNEXURE!B:!MATLAB!CODE!______________________________________________________________!60!
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Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !5!
De !Mish a!
Lis !o !Figu es!
Figu e!1:!Global!G ow h!o !Elec ic!Vehicle!S ock! om!2010! o!2015![2] ........................ 10!
Figu e!2:!Se ies,!Pa allel!and!Se ies-Pa allel!HEVs(a,b,c)!and!PHEVS(d,e, )![3] ............... 12!
Figu e!3:!Typical!powe ain!layou ! o !BEVs![3] ................................................................ 12!
Figu e!4:!Ba e y!Densi y!and!Cos !E olu ion![2] ................................................................ 13!
Figu e!5:!De elopmen ! imeline!o !EV!ba e y![3] .............................................................. 14!
Figu e!6:!Global!Cha ging!In as uc u e!O e iew ............................................................ 15!
Figu e!7:!CC/CV!cha ging!p o ile![6] .................................................................................... 17!
Figu e!8:!Pulse!cha ging!and!nega i e!pulse!cha ging ........................................................ 17!
Figu e!9:!Scale!o !Pu chase!incen i es! o !EVs![2] .............................................................. 19!
Figu e!10:!Summa y!o !policy!suppo !mechanisms! o !EVSE!deploymen ![2] ................ 20!
Figu e!11:!Technical!da a!(ene gy)! o !EVs!sold!in!Spain![8] ............................................. 20!
Figu e!12:!Game!Theo e ic! echniques! o !Mic o!G id!Applica ions![11] ......................... 24!
Figu e!13:!Rep esen a ion!o !Sequen ial!games![18] .......................................................... 31!
Figu e!14:!Flowcha !illus a ing!algo i hm!and!in e ac ion!o !da a ................................. 38!
Figu e!15:!O iginal!Demand!a !each!node ............................................................................ 46!
Figu e!16:!Demand!a !each!node!wi h!weigh ed!s a egies ................................................ 46!
Figu e!17:!O iginal!demand! o !e e y! ime!s ep! o !Agen !G oup!1 .................................. 47!
Figu e!18:!Modi ied!demand!wi h!weigh ed!s a egies! o !Agen !G oup!1 ....................... 47!
Figu e!19:!Fi s !Equilib ium!wi h!EV2!cha ging!on!Day!4 .................................................. 50!
Figu e!20:!Second!Equilib ium!wi h!EV1!cha ging!on!Day!5 .............................................. 51!
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6! ! Mas e !Thesis!
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Lis !o !Tables!
Table!1:!P isone 's!Dilemma!payo !ma ix ......................................................................... 30!
Table!2:!Ma ching!Pennies!payo !ma ix ............................................................................. 31!
Table!3:!Ba le!o ! he!sexes!payo !ma ix ............................................................................ 36!
Table!4:!Mixed!s a egy!Nash!Equilib ium:!Ba le!o ! he!Sexes .......................................... 37!
Table!5:!Household!Loads!conside ed! o !Load!P o ile ...................................................... 43!
Table!6:!EV!Cha ac e is ics .................................................................................................... 43!
Table!7:!Mobili y!Da a ............................................................................................................ 44!
Table!8:!Pe cen age!o !agen s!cha ging!in!a!scena io ......................................................... 48!
Table!9:!Typical!Payo !ma ix!as!ob ained! o !Cha ge/Cha ge!equilib ium!scena io ..... 49!
Table!10:!Sa ings! om!game! heo e ic!elec ic! ehicle!cha ging!using!o -peak! a i s .. 52!
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Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !7!
De !Mish a!
Glossa y!
AC!–!Al e na ing!Cu en !!
BEV!–!Ba e y!Elec ic!Vehicle!!
DC!–!Di ec !Cu en !
EV!–!Elec ic!Vehicle!
EVSE!–!Elec ic!Vehicle!Supply!Equipmen !
ICE!–!In e nal!Combus ion!Engine!
IEEE!–!Ins i u e!o !Elec ical!and!Elec onics!Enginee s!
IESD!–!I e a ed!Elimina ion!o !S ic ly!Domina ed!S a egies!
HEV!–!Hyb id!Elec ic!Vehicles!
PHEV!–!Plug-in!Hyb id!Vehicles!
PPF!–!P obabilis ic!Powe !Flow!
SOC!–!S a e!o !Cha ge!
SAE!–!Socie y!o !Au omo i e!Enginee s!
TOU!–!Time-o -use!
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8! ! Mas e !Thesis!
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1. P e ace!
This!p ojec !came!abou !as!a!mas e ! hesis!based!on!a ailable!posi ions!a !CITCEA-!UPC!
o !mas e ! hesis!s uden s!in! he! ield!o !elec ic! ehicles.!A!need!was! el ! o!p edic ! he!
ne ! demand! om! Elec ic! Vehicles! (EV)! as! he! same! can! help! he! g id! p epa e! o !
scena ios!in!which!elec ic! ehicles!a e! he!no m!and!wide!scale!EV!pene a ion!can! hus!
be! acili a ed.!P e ious!a emp s!had!been!made! o!es ima e! he!ne !load! om!p i a ely!
owned!EVs!and! he!mo i a ion!behind!unde aking! his!s udy!is! o!see!i ! he!applica ion!
o !a!new!app oach!namely!game! heo e ic!me hods!can!be e !help!in!simula ing! he!load!
om!EVs!and!p esen ! esul s!which!a e!close ! o! he!ac ual!da a.!I !was!decided! o!u ilize!
da a! and! algo i hms! om! [1]! o! un! simula ions! and! compa e! esul s! o! ob ain! an!
unde s anding!as! o!which!me hod!is!be e !sui ed!and!deli e s! esul s!close ! o! eal!li e!
scena ios.!While! ha !does! o m!a!pa !o ! his!wo k,! he!comple e!implemen a ion!o ! he!
es ima ion! o ! he! elec ic! ehicle! demand! using! he! p e ious! wo k! by! applying! game!
heo y! o! he!agen !based!p obabilis ic!model,!could!no !be!possible!due! o! easons!o !
complexi y.!!
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Fu he !discussions!wi h! he!supe iso ! esul ed!in! he!p ojec !e ol ing! o!a! wo-s ep!
unde aking.!In! he! i s !s ep,!i !was!decided! ha ! he!model! om![1]!would!be!modi ied!
o!accoun ! o !all!kinds!o !cha ging!s a egies!simul aneously.!In! he!second!s ep,!i !was!
decided! o! o mula e!a!household!scena io!comp ising!o ! wo!EVs!and!using!game! heo y!
o!p edic ! he!schedule!and!demand!o !elec ic! ehicle!cha ging.!
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Topics!which!we e!s udied!as!pa !o ! his!endea o ! o!apply!game! heo e ic!me hods! o!
elec ic! ehicle! cha ging!include,! ypes! o ! games,! game! heo y! logic! and! algo i hms,!
solu ion!concep s!including!Nash!equilib ium,!pa e o!op imali y!amongs !o he .!I !will!be!
a emp ed! o!use!Nash!equilib ium!as! he!solu ion!concep s! o!iden i y!op imal!s a egies!
which!sui !all!playe s!in! he!gi en!scena io.!
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Ini ial!s udies!du ing! he!in e nship!ca ied!ou !p e iously!in ol ed! esea ch!on!elec ic!
ehicles!and!game! heo y! o!build!a! ounda ion! o ! he!mas e ! hesis.!This! esea ch!is!
p esen ed!in!pa ! o!gi e! he! eade !an!unde s anding!and!backg ound!on! he!necessa y!
echnical!aspec s!o ! his!wo k.!
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Thus,! in! o ali y,! his! mas e ! hesis! wo k! b ings! oge he ! elec ic! ehicle! echnology,!
demand!modeling!and!game! heo y!unde !a!single!umb ella! o!ob ain!use ul!insigh !in!
his!domain.!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !9!
De !Mish a!
2. In oduc ion!
A ! he!ou se !o ! his!p ojec !i !was!decided! o!a emp ! o!u ilize!game! heo y! o!model! he!
ne !elec ic! ehicle!cha ging!demand! om!p i a ely!owned!EVs.!In! he! echnical!sec ion!
o ! his! epo ,!we!will!a ! i s !go! h ough! he!basics!o !elec ic! ehicle! echnology,! he!s a e!
o !a !o ! he! echnology!and!in as uc u e!pe aining! o!EVs,!iden i y!all! he!s ake!holde s!
in! he!EV!scena io!and!look!a ! egula ions!and!ini ia i es!in!di e en !coun ies! ega ding!
EVs.!The ea e ,!we!will!p oceed! o!su ey! echnical!aspec s!which!a e!in ol ed!in! his!
s udy! and! a e! necessa y! o! o mula e! he! algo i hms! o ! his! wo k.! This! will! include!
de ails!on! he!elec ic! ehicles!used,! esea ch!on!demand!models,!applica ions!o !game!
heo e ic!concep s!in! he!elec ic!powe !sec o !and!mo e!speci ically! o!elec ic! ehicles!
and! hei ! cha ging! and! game! heo e ic! modeling! concep s.! Pos ! his! we! p esen !an!
app oach! o!c ea e!models!and!simula ions!based!on!ou !lea ning!and!a ailable!da a.!Fi s !
up,!in! he!nex !sec ions!we!go! h ough! he!basics!o !elec ic! ehicle! echnology.!
2.1. In oduc ion! o!Elec ic!Vehicles!
An!elec ic! ehicle!is!an!au omobile!which!uses!elec ic!mo o s!o ! ac ion!mo o s! o !
p opulsion!o ! he! ehicle.!EVs! echnically!include!bo h! ail!and! oad! anspo ,!su ace!
and!unde wa e ! essels!as!well!as!ai ! anspo !mediums!bu ! o ! his! epo ! he! e m!
elec ic! ehicle!o !EV!will! e e ! o!jus ! oad! anspo .!The!elec i ica ion!o !all!modes!o !
anspo a ion!is!one!o ! he!key!app oaches! o! ackle! he!issue!o !clima e!change.!The!
con inual!adop ion! o !EVs!in o! ma ke s!wo ldwide! in ol es!mul iple! aspec s!b inging!
oge he !impac s!on! he!powe !g id,!de elopmen !o !powe ain,!ba e y!and!cha ging!
echnologies,!as!well!as!policy!and! egula ion!in!di e en !pa !o ! he!globe.!In! his!sec ion,!
we!will!look!a ! hese!mul iple!aspec s!in!de ail!and!unde s and! he!cu en !s a e!o !a ai s!
in! hese!aspec s.!!
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The! ocus! on! EV! de elopmen ! has! been! on! powe ains,! ba e ies! and! cha ging!
equipmen ! o ! elec ic! ehicle! supply! equipmen ! (EVSE).! In! o de ! o! mee ! a ious!
equi emen s! o ! he! au omobile! indus y! such! as! uel! economy,! di e en ! powe ain!
se ups! a e! ied! o ! hyb id! ehicles! such! as! se ies,! pa allel! and! se ies-pa allel!
con igu a ions.!Ad ances!ha e!also!been!made!on! he!elec ic!mo o !used! o!d i e! he!
ehicle!o ! o!suppo !ope a ions.!All! hese!de elopmen s!ha e! esul ed!in! ehicles!wi h!
be e ! uel!economy!and!highe !e iciency.!Ba e y! echnology!meanwhile,!has!e ol ed!
om!lead!acid! o!nickel!based!and!now! o!li hium!ion!based!ba e ies!in!a!ques ! o!de elop!
ba e ies! which! ha e! highe ! ene gy! densi y! and! highe !powe ! densi y! along! wi h!
p ope ies!o !being!ligh weigh !and!du able.!Simila ly,!cha ging!s a ions!ha e!p og essed!
om!slow!cha ge s! o! as !cha ge s! o!add ess! he!limi a ion!o !low! ange!on!EVs.!All!
hese!de elopmen s!in!EV! echnology!ha e! esul ed!in!a! as e !adop ion!o !EVs!globally,!
mo e!so!in!de eloped!na ions!and!na ions!which!a e!leading! he!way!in!implemen a ion!
o ! EVs.! This! can! be! seen! in! Fig.! 1! om! he! Global! EV! Ou look! 2016! epo ! by! he!
16! ! Mas e !Thesis!
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boa d! cha ging! powe ! supply.! The! high! cha ging! powe ! o ! he! Tesla! supe cha ge !
ne wo k!allows!a!cha ge!o !up! o!100%!SOC!in!75!minu es.!
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O he !common!cha ging!s a ions!include! he!CHAdeMO!s anda d!which!is!a!le el!3!DC!
as !cha ging!s a ion!which!was!de eloped!by! he!CHAdeMO!Associa ion! o med!by! he!
Tokyo!Elec ic!Powe !Company,!Nissan,!Mi subishi!and!Fuji!Hea y!Indus ies.!These!a e!
p ima ily! u ilized!by! Japanese! ca s! such! as! he! Nissan! Lea ! and! Mi subishi! i-MiEV.!
Cu en ly! he!CHAdeMO!cha ge s!ha e!a!max!powe !ou pu !o !50!kW.!
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The! SAE! de eloped! i s! own! le el! 3! DC! as ! cha ge ! e med! he! SAE! Combo! Cha ging!
Sys em!(CCS)!which!is! he!p e e ed! ype! o !Ge man!and!US!au omobile!manu ac u e s.!
The!BMW!i3!and!VW!e-Gol !use! hese! ype!o !cha ge !connec ions.!The!CCS!allows! o !
slow!and! as !cha ging! om!a!single!cha ging!inle !as!opposed! o! he!CHAdeMO!which!
equi ed!sepa a e!inle s! o !slow!and! as !cha ging.!The!cu en !max!powe !ou pu !le el!
o !SAE!CCS!cha ge s!is!also!50!kW.!
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Be o e!mo ing!on! o! he!nex !sec ion,!we!b ie ly!look!a ! he!di e en ! echniques! ha !can!
be!used! o!cha ge!an!EV!ba e y.!These!a e!impo an !as! hey!can!help!unde s and! he!
load!p o ile!o e ! he!en i e!cha ge!du a ion!o !an!EV.!
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The e!a e!se e al!cha ging!me hods! ha !can!be!used! o!cha ge! he!ba e y!o !an!EV.!Some!
cha ging! echniques! s udied! in! he! academia! and! used! con en ionally! a e! cons an !
cu en ! (CC),! cons an ! ol age! (CV),! cons an ! powe ! (CP),! ape ! cha ging! and! ickle!
cha ging![5].!Addi ionally,!ad anced!cha ging! echniques!include!combina ion!o !one!o !
mo e!o ! he!abo e!me hods! esul ing!in! echniques!such!as!cons an !cu en /cons an !
ol age!(CC/CV).!Some!o he !ad anced! echniques!include!Pulse-cha ging!and!nega i e!
pulse-cha ging!which!a e!conside ed!good!modes!o !ope a ion! o ! as !cha ging!o !EV!
ba e ies![5].!
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CC!uses!cons an !cha ging!cu en ! low! o! he!ba e y! ill! he!ba e y!a ains!a!ce ain!
ol age!le el!whe e!as!CV!applies!a!cons an ! ol age!ac oss! he!ba e y! e minals!while!
cons an ly!adap ing! he!cha ging!cu en ! ill!i ! alls! o!almos !ze o[6]!.!CP!as! he!name!
sugges s!uses!cons an !powe !while! ape !cha ging!is!done! ia!an!un egula ed!cons an !
ol age!sou ce!and! he e!is!no!con ol!o e ! he!d op!o !cha ging!cu en !as!cell! ol age!o !
he! cha ge!builds! up[6].! This! can! end! o! damage! he! ba e y! in! case! an! o e cha ge!
happens.! T ickle! cha ging! uses! small! cu en s! o! accoun ! o ! ba e y! sel -discha ge.!
CC/CV! cha ging! is! he! p e e ed! mode! o ! ope a ion! o ! as ! cha ging! o ! li hium-ion!
ba e ies.!This!kind!o !cha ging!uses!cons an !cu en !up! o!a!ce ain!p ede ined! ol age!
o ! he!ba e y!pos !which!i !swi ches! o!cons an ! ol age.!So.!while!majo i y!o ! he!cha ge!
is!done!a !cons an !cu en ,! he! emaining! ime!cons an ! ol age!is!used!wi h! educed!

Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !17!
De !Mish a!
cha ging!cu en ! o! op-o ! he!ba e y.!The!CC/CV!cha ge!p o ile!is!illus a ed!in! he!Fig!
8.!
!
Figu e'7:'CC/CV'cha ging'p o ile'[6]'
Pulse-cha ging!p o ile!uses!a!pulse!based!cha ge!cu en ! o!cha ge! he!EV!ba e y.!This!
u ilizes! a! sho ! es ! pe iod! be ween! pulses! which! can! help! s abilize! ba e y! chemical!
ac ions![5].!This! es !pe iod!is!supposed! o!allow! he!chemical!p ocesses!in! he!ba e y! o!
keep!up!wi h! he!cha ging!p ocess! he eby!a oiding!gas! o ma ion!a ! he!elec odes[6].!
Nega i e!pulse!cha ging! ollows!an!opposi e!p o ile! o!pulse!cha ging!in!addi ion! o! he!
pulse!cha ging!p o ile!by!applying!a!sho !discha ge!pulse!du ing! he! es !pe iod!o ! he!
pulse!cha ging!p o ile.!This!is!done! o!depola ize! he!ba e y! hus!clea ing!gas!bubbles!
which! migh ! ha e! o med! on! he! elec ode! du ing! pulse-cha ging[5].! This! kind! o !
cha ging!is!said! o!imp o e! he!e iciency!o ! he!o e all!cha ging!p ocess!and!p olong!
ba e y!li e.!Fig!9.!o e s!demons a es!pulse!and!nega i e!pulse!cha ging! echniques.!
!
!
Figu e'8:'Pulse'cha ging'and'nega i e'pulse'cha ging'
2.1.5. EV! egula ion!and!policy!
!
An!EV!o e s!much!lowe ! unning!cos s!when!compa ed! o! adi ional!ICE.!I !is!es ima ed!
in! he!Global!EV!Ou look!2016![2]! ha !a!100!km! ip!in!an!EV!would!cos !abou !1/4 h! o!
1/5 h!o ! he!cos !o !using!an!ICE!powe ed! ehicle.!!O e !a!pe iod!o ! i e!yea s,!i ! hese!
sa ings!a e!agg ega ed,! uel!sa ings!exceeding!USD!3000!may!be!achie ed.!E en!in! he!
ligh !o !such!sa ings! he e!a e!po en ial!obs acles!in! he!way!o !wide!scale!EV!deploymen !
18! ! Mas e !Thesis!
! ! De !Mish a
! !
including!bu !no !limi ed! o!high!cos !o !ba e y! echnology,!access! o!EV!in as uc u e,!
ins alla ion!and!cos s!o !such!in as uc u e!as!well!as!gene al!awa eness!and!in e es !in!
his!kind!o ! echnology.!Howe e ,! he!iden i ied!bene i s!in! e ms!o !pollu ion! educ ion,!
highe !in eg a ion!o ! enewables,!clima e!change!mi iga ion!as!well!as! educed!cos !o ! he!
echnology! o e ! he! pas ! decade! igge ! suppo ! mechanisms! based! on! policy! and!
egula ion! o! inc ease! he! pene a ion! o ! EVs! while! o e coming! he! a o emen ioned!
obs acles.!In! his!sec ion,!we!will!go!o e !some!o ! hese!policy!suppo !mechanisms.!!
!
These!policy!suppo !mechanisms!can!b oadly!be!classi ied!in o!3!ca ego ies![2]:!
!
• Regula o y!measu es:!These!include! egula ions!on! ehicle!emissions! egula ions!
and! uel!economy! equi emen s!and!homologa ion,!which!may!include!c edi s!in!
a o !o !elec ic! ehicles!!
• Financial!Le e s:!These!include!di e en ia ed! ehicle! axa ion!which!maybe!based!
on! uel!economy!o !g eenhouse!gas(GHG)!emissions!pe !kilome e !!
• O he !measu es:!These!can!include!wai e s!on!pa king! ees!and! olls,!as!well!as!
li ing!o !access! es ic ions!(e.g.!access! o!EVs! on!bus,! axi! o !high-occupancy!
ehicle![HOV]!lanes).!
In! he! ollowing!sec ions,!we!will!look!a !some!examples!o !EV!pu chase!incen i es,!EV!
use!and!ci cula ion!incen i es,!li ing!o !access! es ic ions!and!emission!s anda ds!and!
examine!how!di e en !policies!a e!aimed!a !inc easing! he!adop ion!o !EVs.!
EV'Pu chase' Incen i es:! As!men ioned!in! [7],! pu chase!incen i es! a e!one!o ! he! mos !
mo i a ing!o !incen i es! o!p oduce!a!shi ! o !consume s! om!con en ional!ICE!based!
ehicles! o!EVs.!In!2013,!F ance!s a ed!o e ing!pu chase!incen i es!o !EUR!6300! o !
BEVs!(de ined!as!emi ing!less! han!20!g ams!o !CO2!pe !kilome e !and!EUR!1000! o !
PHEVs!(de ined!as!emi ing!be ween!20!g am!CO2/km!and!60!g am!CO2/km).!Since!2016!
he!Ne he lands,!exemp !ca s!emi ing!ze o!CO2!a ! he! ailpipe! om! egis a ion! ax.!Fo !
o he ! ehicles!and!EVs,! hey!implemen ed!a!sec ionalized! axa ion!scheme!wi h! i e!le els!
o !CO2!emissions!while!p og essi ely!inc easing! axa ion!pe !g am!CO2/km.!Fo !example,!
PHEVs!which!quali y! o ! he! i s !le el!(below!80!g!CO2/km)!pay!EUR!6!pe !g am!CO2/km.!
Compa ed! o! adi ional!ICE!based! ehicles! his!o e !a!signi ican ! eba e! o!BEVs!and!
PHEVs,!as! ehicles!wi h!ICE!ha e!emissions! a ings!abo e!106!g!CO2/km.!In!Sweden,!
ehicles!wi h!emissions!le els!lowe ! han!50!g am!CO2/km!a e!g an ed!40000!k ono !as!
eba e.! Fig! 10.! demons a es! he! scale! o ! mone a y! incen i es! o e ed! in! di e en !
coun ies! o !di e en ! ypes!o !EVs.!
!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !19!
De !Mish a!
!
Figu e'9:'Scale'o 'Pu chase'incen i es' o 'EVs'[2]'
EV'Use'and'Ci cula ion'Incen i es:!Le !us!now!look!a !some!examples!o !incen i es!based!
on! he! use! and! ci cula ion! o ! EVs.! BEVs! and! PHEVs! in! Ge many! a e! exemp ! om!
ci cula ion! ax! o !a!pe iod!o ! en!yea s! om! he!da e!o ! hei ! i s ! egis a ion.!In! he!
Ne he lands,! ze o-emission! ca s! do! no ! ha e! o! pay! any! oad! axes.! Japan! has!
implemen ed!exemp ions! om!annual! onnage! ax!and! educ ions! o !au omobile! ax! o !
EVs.!In!Sweden,!EVs!a e!exemp ! om! oad! ax!based!on!CO2!emissions.!
!
Access' Res ic ions' Wai e :! Some! examples! o ! his! a e! access! o! EVs! o! bus! lanes! in!
On a io,!in!HOV!lanes!in!Spain,!and!also!in!some!ci ies!in!F ance,! he!Uni ed!Kingdom!and!
No way.! In! China,! he e! ha e! been! ials! wi h! es ic ing! license! pla es! and! gi ing!
p e e en ial!allo men ! o!EVs.!
!
Emissions:! The! deploymen ! o ! EVs! is! a o ed! by! inc easingly! s ingen ! uel! economy!
equi emen s! and! ailpipe! ca bon! dioxide! (CO2)! emission! s anda ds! as! well! on! he!
emission!o !o he !local!pollu an s.!BEVs!which!ha e!ze o! ailpipe!emissions!and! e y!good!
ene gy! e iciency,! and! PHEVs! which! ha e! educed! emissions,! bene i ! om! hese!
egula ions!in!a!big!way.!In! e ms!o !clima e!change!mi iga ion,!EVs!can!deli e !only!i !
he e!a e!ne !CO2!emissions!when!conside ing! he!elec ici y!gene a ion!used! o!cha ge!
he! ehicle!which!is!challenge! o !coun ies!which!a e!p ima ily!dependen !on! ossil! uel!
based!ene gy!sou ces! o ! hei !elec ici y!p oduc ion.!
!
20! ! Mas e !Thesis!
! ! De !Mish a
! !
!
!
Figu e'10:'Summa y'o 'policy'suppo 'mechanisms' o 'EVSE'deploymen '[2]'
2.1.6. EVs!in!Spain!
!
The! ollowing! able!shows! he!EVs!and!lis !ou ! hei !ene gy! ela ed! echnical!pa ame e s.!
I !is! o!be!no ed! ha !au onomy!he e! e e s! o! he! ange!o ! he!lis ed! ehicles!and!has!no!
e e ence! o!au onomous!elec ic! ehicles.!
!
!
Figu e'11:'Technical'da a'(ene gy)' o 'EVs'sold'in'Spain'[8]'
Acco ding! o! he!Global!EV!Ou look!2016,!Spain!has!an!EV!s ock!o !6000! ehicles!as!o !
2015,!wi h!a!2020! a ge !o !200,000!EVs.!O ! he!cu en !6000!EV!s ock,!a ound!4500!a e!
BEVs! and! 1500! a e! PHEVs.! Le ! us! now! look! a ! some! incen i es! and! policy! ela ed!
in o ma ion.! Spain’s! na ional! go e nmen ! o mula ed! he! “In eg al! Plan! o ! he!
P omo ion! o ! Elec ic! Vehicles”,! which! comp ised! o ! he! “In eg a ed! S a egy! o ! EVs!
2010–2014”!ini ia i e!in!Spain! ha !included! he! a ge !o !1!million!hyb id!and!elec ic!
ehicles!on! oad!in!Spain!by! he!yea !2014![9].!The! ollowing!sec ion!summa izes!some!
o ! he!p o isions!unde ! his!ini ia i e! o!p omo e!EVs.!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !21!
De !Mish a!
!
Acco ding! o![10],! he!maximum!limi ! o ! o al!amoun !o !mone a y!g an s! o ! ehicles!
ha !a e!d i en!by!ba e ies!which!may!be! ully!o !pa ially!cha ged!by!elec ici y! om!
he!g id!and!whose!maximum!p ice!does!no !exceed!32,000!eu os,!is!speci ied!as! ollows:!
!
- 2,700!eu os! o ! ehicles!wi h! ange!no !exceeding!40!km!and!bu !g ea e ! han!15!km.!
- 3,700!eu os! o ! ehicles!wi h! ange!g ea e ! han!40!km!and!less! han!o !equal! o!90!
km.!
- 5,500!eu os! o ! ehicles!wi h! ange!o !mo e! han!90!km.!
I !is! o!be!no ed! ha ! ange!abo e!means!elec ic! ange!i ! he! ehicle!is!a!hyb id.!
!
In! he! case! o ! cha ging! poin s! o ! elec ic! ehicles! in! publicly! accessible! a eas,! he!
maximum!amoun !o !aid!can!be!40%!o ! he! o al!eligible!cos !wi h! he! ollowing!limi s!in!
place:!
!
- 15,000!eu os!pe !quick! echa ge!poin !ins alled.!
- 2,000!eu os!pe !semi- as ! e ueling!poin !ins alled.!
A e !a!b ie !o e iew!o !elec ic! ehicle! echnology!and!some!insigh s!on! egula ion!and!
policy,!as!well!as!looking!a ! he!EV!scene!in!Spain,!we!will!now!explo e! he! ield!o !Game!
Theo y,! he!basic!concep s!and!i s!applicabili y! o! he!pu pose!o !ou !s udies.!
2.2. In oduc ion! o!Game!Theo y!
Game! heo y!p o ides!ma hema ical! amewo ks! o!analyze!si ua ions!o !‘con lic !and!
coope a ion’!(as!desc ibed!by!Roge !B.!Mye son!in!his!publica ion!Game'Theo y:'Analysis'
o ' Con lic )' be ween! playe s! who! can! ope a e! on! s a egies! which! may! o ! may! no !
in luence! he!s a egies!o !o he !playe s.!I !is!essen ial! o!no e!he e! ha ! he! e ms!‘playe s’!
and! ‘s a egies’! a e! used! in! his! ega d! o! indica e! a! model! o ! a! scena io! and! no !
ec ea ional!o !spo s!ac i i ies.!
!
Game! heo y! o e ! he! yea s! has! seen! se e al! classi ica ions:! co-ope a i e! and! non-
coope a i e;!symme ical!and!asymme ical;!ze o-sum!and!non-ze o-sum;! o!name!a! ew.!
Fo ! he!pu poses!o ! his!s udy! he!classi ica ion!o !impo ance!is!co-ope a i e!and!non-
co-ope a i e! game! heo y.! As! men ioned! in![11],! Non-coope a i e! game! heo y! is! o !
impo ance! o!analyze! he!s a egic!decision!making!p ocesses!o !independen !playe s!
who! ha e! con lic ing! in e es s! o e ! he! esul ! o ! a! decision! making! p ocess! which! is!
in luenced! by! hei ! ac ions.! I ! is! o! be! no ed! ha ! he! e m! non-coope a i e! does! no !
essen ially!imply! ha ! he!playe s!do!no !co-ope a e,!bu !i !means! ha ,!any!co-ope a ion!
is!obse ed!a ises! om!sel -in e es !wi hou !any!co-o dina ion!and!communica ion!o !
s a egies! be ween! di e en ! playe s.! Thus,! i ! can! be! said! ha ! non-coope a i e! game!
heo y!may!be!used! o!model!a!dis ibu ed!p ocess! o!op imize!an!o e all!goal!which!is!a!

22! ! Mas e !Thesis!
! ! De !Mish a
! !
esul !o !playe ! decisions!wi hou ! any!communica ion!and!co-o dina ion!be ween! he!
s a egies!o !indi idual!playe s.!
!
Co-ope a i e!game! heo y!on! he!o he !hand!conside !incen i es! o !indi idual!playe s! o!
collabo a e.!The e!a e! wo!majo ! ame! wo ks!which! o m!co-ope a i e!game! heo y:!
Nash!ba gaining!and!coali ional!game! heo y.!Nash!ba gaining!employs!ag eemen !based!
on! e ms!and!condi ions!be ween!indi idual!playe s!while!coali ional!game! heo y! akes!
in o!accoun ! o ma ion!o !g oups!o !coali ions.!
!
Le !us!now!p oceed! o!look!a !some!o ! he!ma hema ical!basics!o !Game!Theo y.!To! ollow!
a!consis ency!o !no a ion!and! ep esen a ion!we!will!be! ollowing! he!s yle! om![12]!in!
o de ! o!ha e!a!cohe en !p esen a ion!o ! he!concep s.!
!
[12]!desc ibes!s a egic!games!as!a!model!o !in e ac ing!decision!make s.!I ! u he !goes!
on! o!de ine!s a egic!games!as!one!which!consis s! he! ollowing:!
!
-!a!se !o !playe s!
-!a!se !o !ac ions! o !each!indi idual!playe !
-!a!p e e ence!p o ile!o e ! he!se !o !ac ion!p o iles!
!
A!se !A!is!assumed! o!be!consis ing!o !all! he!ac ions! ha ,!unde !ce ain!condi ions,!a e!
a ailable! o!a!playe .!In!any!speci ic!condi ion! he!playe !is! aced!wi h!a!subse !o !A!and!
chooses!a!single!elemen ! he ein.!The!nex !elemen !which!cons i u es!a!s a egic!game!
model!is! he!no ion!o ! he!playe !p e e ences.!Playe !p e e ences!a e! ep esen ed!in! he!
o m!o !payo ! unc ions!which!associa es!a!numbe ! o! he!ou come!o !each!ac ion!in!a!
way!such! ha ! ac ions!wi h!highe !numbe s!a e!mo e! a o able! o! he! playe !and!a e!
hence!p e e ed.!Ma hema ically! o !any! wo!ac ions!a!and!b!in! he!ac ion!se !A,!and!u(a)!
is!said! o! ep esen ! he!payo ! unc ion,! hen!u(a)!>!u(b)!implies! ha ! he!playe !p e e s!
ac ion!a!o e !b.!I !mus !be!no ed! ha ! he!payo ! unc ion!only!con eys!o dinal!in o ma ion!
[12].!This!means! ha ! he!payo ! unc ion!can!only!sugges !i !an!ac ion!is!p e e ed!o e !
ano he !and!no ! he!in ensi y!wi h!which!i !maybe!p e e ed.!!
!
Be o e!p oceeding! u he !wi h! he!no ion!o !s a egic!games,!i !is!essen ial! o!men ion!
he e! he!concep !o ! he! heo y!o ! a ional!choice!which!as!desc ibed!in![12]!s a es! ha ! he!
ac ion! aken! by! a! decision-make ! o ! playe ! in! a! speci ic! si ua ion! is! a ! leas ! as! good,!
acco ding! o! he!playe ’s!p e e ences,!as!e e y!o he !a ailable!ac ion.!This! heo y!is! e y!
essen ial! o!de ine!why!a!playe !would!choose!a!ce ain!ac ion!in!a!ce ain!condi ion!and!
hus!enhances! he!unde s anding!o !any!si ua ion.!
!
Mo ing!on! om! he! heo y!o ! a ional!choice!we!mus !examine!wha !ac ions!will!be! aken!
by!a!playe !in!a!s a egic!game.!As! he! heo y!o ! a ional!choice!implies!a!playe !would!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !23!
De !Mish a!
choose! he!bes !a ailable!ac ion.!Howe e ,!in!a!game! he!bes !a ailable!ac ion!will!depend!
on! he!ac ions!o !o he !playe s.!Thus,!a!playe !mus ! o m!an!opinion!abou ! he!ac ions!o !
o he ! playe s! and! hen! base! his/he ! ac ion! on! he! same.! In! basic! game! heo y,!i ! is!
assumed! ha !each!playe ’s!opinion!o !o he !playe s’!ac ions!is!de i ed! om! hei !pas !
expe ience! o ! playing! he! game.! Fu he mo e,! i ! is! assumed! ha ! his! expe ience! is!
su icien ly! ex ensi e! ha ! he/she! knows! is! su e! o ! how! hei ! will! ac .! In[12],! i ! is!
sugges ed! o! iew!o ! his!scena io!in! he! ollowing!idealized!manne .!Each!playe !in! he!
game!is! aced!wi h!a!popula ion!o !di e en !playe s!who!may,!on!any!occasion,!by!means!
o ! o a ions! ake! ha !playe ’s! ole.!Fo !e e y!play!o ! he!game,!playe s!a e!picked! om!
each!popula ion! andomly.!The e o e,!each!playe !pa icipa es!in! he!game!agains !an!
e e -changing!pool!o !opponen s.!Thei !expe ience!helps! hem! o m!an!opinion!abou !a!
ypical!se !o !opponen s,!no !any!speci ic!se !o !opponen s.!Based!on! his!backg ound!we!
will!now!p oceed! o!unde s and! he!concep !o !Nash!equilib ium!which!is!an!essen ial!
concep !in!unde s anding!s a egic!games.!We!will!bo ow! he!de ini ion! om![12]!which!
s a es! ha :!
!
“A'Nash'equilib ium'is'an'ac ion'p o ile'a
∗
'wi h' he'p ope y' ha 'no'playe 'i'can'do'be e '
by'choosing'an'ac ion'di e en ' om'ai
∗
,'gi en' ha 'e e y'o he 'playe #j'adhe es' o'aj
∗
”''
!
Wha ! his!essen ially!implies!is! ha ! o !any!gi en!play!o ! he!game!in!which! he!playe s!
a e! andomly!d awn! om!a!collec ion!o !popula ions,! he!Nash!equilib ium!co esponds!
o!a!s eady!s a e.!In!simple! e ms!i !a!game!is!played!a !a!ce ain!poin !o ! ime!wi h!an!
ac ion! p o ile! co esponding! o! he! Nash! equilib ium! p o ile! a*,! hen! no! playe ! has! a!
eason! o!choose!any!ac ion!ou side! hei !componen !in!a*.!This!concep !will!be! u he !
demons a ed!as!i !will! o m! he!backbone!o ! o ming! he!solu ion!o !ou !gi en!case.!The!
discussion!on! he!same!will!be! aken!up!in!Chap e !4.!
!
The!abo e!concep !o !a!s eady!s a e!is!essen ial!in!s udying!s a egic!games!as!we!can!
apply! o! eal!li e!scena ios!whe e!ac ions!can! ollow! a ional!choice!and!i !can!be!assumed!
ha !playe s!a e!mo e!o !less!su e!o ! he!ac ions!o !o he !playe s!and!will!ac !only!in!sel -
in e es .!Tes ing!ou ! he!applicabili y!o !Nash!equilib ium!in! eal!li e!si ua ions! akes!up!a!
signi ican !pa !o !game! heo y!applied! o! eal!li e!p oblems!and! he!no ion!o !equilib ium!
has!now!been!expanded! o!di e en ! o ms!o !game.!When! he!modelling!o !elec ic! ehicle!
cha ging!demand!is!a emp ed,! his!will!also!be! aken!in o!conside a ion.!
!
In! he! ollowing!sec ion,!we!examine!some!cases!whe e!in!Game!Theo y!was!employed!in!
ela ed!domains!and!s udy!wha !app oaches!and!me hodologies!we e!used! he ein.!This!
will!be!help ul!in!iden i ying! echniques!which!can!be!use ul!in!ca ying!ou ! his!p ojec .!
!
24! ! Mas e !Thesis!
! ! De !Mish a
! !
2.3. Game!Theo y!Applica ions!in!Rela ed!Fields!
In! his!sec ion,!will!look!a !how! esea che s!and!ma hema icians!ha e! ied! o!apply!game!
heo e ic!concep s!and! o mula ions! o! he!elec ic!powe !sec o !especially!looking!a !
sma ! g ids,! decen alized! elec ici y! ma ke s! and! elec ic! ehicles! in eg a ion! and!
op imiza ions! o!unde s and!be e ! he!possibili y!and!scope!o !applying!simila !concep s!
and! o mula ions! o! de e mine! he! ne ! elec ic! ehicle! cha ging! demand! o ! p i a ely!
owned!EVs.!
!
In![11]! he!au ho s!en ision! he! u u e!sma !g id! o!be!a!scaled!up!cybe -physical!sys em!
wi h!buil !in!s a e-o - he!a !powe ,!con ol,!communica ions!and!compu ing! echnology.!
The! pape ! analyses! he! po en ial! o ! applying! game! heo e ic! solu ions! o! add ess! he!
challenge!o !in eg a ing! hese! echnologies!in o! he!Sma !G id.!The!au ho s!explo e! h ee!
eme ging! echnology!a eas!in! he!Sma !g id!namely!mic o-g id!sys ems,!demand-side!
managemen ,! and! ad anced! communica ions! sys ems! and! s udy! he! con ibu ions! o !
di e en ! ma hema ical! game! heo y! modelling! sys ems! can! ha e! in! simula ing! he!
espec i e!beha io !o ! hese! echnologies.!The!au ho s!discuss!on!how!game! heo y!can!
help!in!p ocessing!and!op imizing! he! a ious!pa ame e s!in!each!o ! hese! echnologies!
and!sugges ! u he !applica ions!o ! he!same.!!
!
!
Figu e'12:'Game'Theo e ic' echniques' o 'Mic o'G id'Applica ions'[11]!
The!main! echnical!challenges!in!each!o ! hese! echnology!a eas!a e!iden i ied!and! hen!i !
is! discussed! how! speci ic! game! heo y! app oaches! can! be! applied! o! mi iga e! hese!
challenges.!The!au ho s!also!sugges ! u u e!di ec ions,!such!as!implemen ing!mo e! obus !
and! ool! p oo ! s a egies! amongs ! o he ! measu es,! o! ensu e! ha ! he! gap! be ween!
heo e ical!simula ions!and!p ac ical!implemen a ion!o !Sma !G ids!is! educed.!This!is!
illus a ed!in! he!abo e! able! om![11]!which!delinea es! he!abo e!men ioned!analysis!
o ! he!mic o!g ids! echnology!a ea.!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !25!
De !Mish a!
!
I !is!also! no ed! ha !mos ! cu en !and!pas !wo k!is! ocused!on! s a ic!non-coope a i e!
games!and!i !is!sugges ed! ha ! hese!be!also!analyzed! om!a!dynamic!pe spec i e!as!a!lo !
o !pa ame e s! ela ed! o! he!g id!such!as!gene a ion!and!demand!a e! ime! a iable!in!
na u e.!The e!is!also!men ion!o !Bayesian!games!which!is!a! ype!o !non-coope a i e!game!
in!which!di e en !playe s!ha e! e y!limi ed!knowledge!o ! he!ac ions!and!s a egies!o !o !
o he ! playe s.! The! au ho s! say! ha ! gi en! he! la ge-scale!na u e! o ! he! g id! i ! can! be!
in e es ing! o! see! how! Bayesian! games! can! o e come! he! echnical! di icul ies! in!
es ima ing! he!exac !s a egies!o !a!la ge!numbe !o !playe s.!
!
In![6],! he!au ho s!unde ake!an!analysis!o ! he!economic!aspec s!o ! he!in eg a ion!o !EVs!
in! he!sma !g id!by!de eloping!a!mean! ield!game!model.!They!de elop!a! amewo k!
which!enabled!an!analysis!o ! he! a ia ion!o !elec ici y!p ice,!o ! he!hou ly!demand,!and!
he!possibili y!o !ene gy! ese es!in! he!Sma !G id!when!EV!owne s!choose! o!buy/sell!
ene gy!based!on! hei !sel ish!bu ! a ional!in e es s!aimed!a !maximizing! hei !bene i s!
unde ! he! es ain !o !di e en !elec ici y!p icing.!The!au ho s!go!on! o!say! ha !since! he!
numbe !o !playe s!is!la ge!and!alike,! he!p icing!policy!becomes!a!consequence!o ! he!
ac ion!o !all! he!playe s,!and! hus! he!p oblem!was! he! o mula ed!as!a!mean! ield!game!
and! he! undamen al!di e en ial!equa ions! o !which!was!sol ed! o!ob ain!conclusions.!
F om! his!pape ,!i !is!in e es ing! o!obse e! he!use!o !a!mean! ield!game!analysis.!Unlike!
adi ional!N!playe !games!whe e! he!objec i e!is! o! ollow! he!s a e!o !each!playe ,!in!a!
mean! ield!game!analysis! he!objec i e!is! o!ob ain! he!op imal!dis ibu ion! o !all!playe s!
o!be!a !a!ce ain!s a e!X!a !an!ins an !o ! ime! .!Thus,!in!such!a!case!i !allows! he!simula ion!
o! ollow! he!s a e!o !all!use s!a ! he!same! ime.!A!de ailed!desc ip ion!o ! he!no ion!o !
Nash! equilib ium! in! mean! ield! games,! which! is! e med! as! mean! ield! equilib ium! is!
ou side! o ! he! scope! o ! his! epo ,! and! he! o iginal! publica ion! ci ed! he e! should! be!
e e ed! o !de ailed!unde s anding.!Howe e ,!in!essence! he!concep !o ! he!equilib ium!
ep esen ing!a!s eady!s a e!is!simila ! o! ha !o !a!Nash!Equilib ium!as!has!been!discussed!
in! he!sec ion!explaining! he!basics!o !game! heo y.!
!
In![13],! he!au ho s! o mula e!an!ene gy!managemen !game!which!exploi s! he!po en ial!
o ! elec ic! ehicles! as! he! mos ! shi able! load! o! achie e! esiden ial! demand! side!
managemen ! in! he! u u e! sma ! gi d.! The! u ilize! game! heo y! o! come! up! wi h! an!
au onomous!ene gy!managemen !sys em! o ! esiden ial!use s!who!wan ! o!sell!ene gy!
back! o! he!g id!by!discha ging! he!ba e y!o ! hei !EVs.!In! his!case! he!playe s!o ! he!
game!a e! he! esiden ial!use s!and! hei !s a egies!a e! hei !p o iles!o !daily!usage!o ! hei !
household!appliances.!The! u he !demons a e! ha ! he!Nash!equilib ium!o ! hei !game!
heo y! implemen a ion! esul s! in! op imiza ion! o ! ene gy! cos s! e en! including! he!
dep ecia ion!cos !and!ad e se!e ec s!on! he!li e!o ! he!ba e y!as!a! esul !o ! equen !
discha ging!and!selling!ene gy!back! o! he!g id.!The!applica ion!o !game! heo y! o! hei !
ene gy!managemen !model! esul s!in! educ ion!o ! o al!ene gy!cos s!and!indi idual!u ili y!
bills.!They!do!conclude!in! he!end!by!saying! ha !conside ing! he!dep ecia ion!cos s!o ! he!
32! ! Mas e !Thesis!
! ! De !Mish a
! !
On! he! o he ! hand! i ! he! sum! 𝑢-𝑎-, 𝑎.… … , 𝑎/+44… … + 𝑢/𝑎-, 𝑎.… … , 𝑎/!is! no ! a!
cons an !o !ze o!and!is!di e en ! o !di e en !ac ion!p o iles,! he!game!is!called!a!non-ze o!
sum!game.!The!unique! ea u e!o ! hese!games!is! ha ! hey!can! ea u e!co-o dina ion!and!
co-ope a ion.!
!
S a egies!in!Games!
In!games,! he e!can!be!in!essence! wo!kinds!o !s a egies!which!playe s!can!adop !and!
hese!a e!classi ied!based!on!su e y!o !p obabili y!o ! he!playe s! aking!a!ce ain!ac ion.!
While!in!one!se !o !s a egies!each!ac ion!is! ully!ce ain,!in! he!o he !ce ain!p obabili y!
is!associa ed!wi h!each!ac ion!p o ile.!These! wo!kinds!o !s a egies!a e!Pu e!S a egy!and!
Mixed!S a egy.!
!
Pu e!s a egy!is!de ined!as!a!single!ac ion! ha !a!playe !o !agen !can! ake!in!a!game.!I !
comp ises!o !a!single!ac ion!on!pa !o !each!o ! he!agen s!o !playe s.!Each! ow!and!column!
o !a!payo !ma ix! ep esen !a!pu e!s a egy.!A!se !o !all!such!s a egies!is! e med!as!pu e!
s a egy!ac ion!p o ile.!
!
A!mixed!s a egy!is!one!which!has!a!ce ain!p obabili y!a ached! o!each!o ! he!ac ions!
ha !an!agen !can! ake.!A!mixed!s a egy!when! ep esen ed!as!𝑠+,!implies:!
!
!
𝑠+𝑎+=!p obabili y! ha !ac ion!𝑎+!will!be!played!unde !mixed!s a egy!𝑠+!
!(5)!
!
Bo h! hese!kinds!o !s a egies!will!be!be e !explained!in! he!sec ion!on!sol ing!games,!
whe e! wi h! he! help! o ! simple! games,! examples! would! be! p o ided! o ! hese! kinds! o !
s a egies.!
!
Since!a!payo !ma ix!o !game! ee! ep esen s!only!payo s!o !u ili y!ob ained! om!pu e!
s a egy! p o iles,! he e! is! need! o! in oduce! a! concep ! ega ding! he! u ili y! o ! mixed!
s a egy!p o iles.!
!
Expec ed!U ili y!
In!a!payo !ma ix,!each! ow!and!column! ep esen s!a!pu e!s a egy!and!each!cell!gi es!
he!payo ! o !a!ce ain!s a egy!based!on! he!ac ions!o !all! he!playe s.!Howe e ,!when!
he!case!is!gene alized! o!include!mixed!s a egies,!we!ha e! o!in oduce! he!concep !o !
expec ed!u ili y.!The!key!he e!is! o!calcula e! he!p obabili y!o !each!ou come!based!on! he!
s a egies!o !all!agen s!and! hen!calcula e! he!a e age!payo ! o !agen !i!weigh ed!by! he!
p obabili ies.!Fo !a!s a egy!p o ile! 𝑠-, 𝑠.… … , 𝑠/! he!expec ed!u ili y!is!
!
!
𝑢+𝑠-, 𝑠.… … , 𝑠/= 𝑢+𝑎-, 𝑎.… … , 𝑎/
:;,:<……,:=∈>
4 𝑠?𝑎?
/
?@-
!
(6)!

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This!will!be!demons a ed!nume ically!in! he!la e !pa !o ! he!nex !sec ion.!
!
Sol ing!games:!
When!we!a e!dealing!wi h!a!single!agen ! he!op imal!s a egy!can!be!based!on!maximizing!
he!payo !in! he! ield! he!decision! heo y!is!being!applied! o.!Howe e ,!wi h!mul iple!
agen s,! he!bes !s a egy!can!and!will!usually!depend!on!o he !agen s’!choices.!This!is!
sol ed!by! ying! o!iden i y!ce ain!logical!ou comes!de ined!by!di e en !game! heo y!
ex s!and!li e a u e!and!a e!called!solu ion!concep s.!
!
In! he! ollowing! sec ion,! we! will! b ie ly! go! h ough! he! mos ! impo an ! game! heo y!
solu ion!concep s!and!see!in!de ail! h ough!examples! he!solu ion!concep !we!will!be!
applying! o! he!p oblem!a !hand,! he!Nash!Equilib ium.!
!
Dominance!
A!s a egy!𝑠+!is!said! o!domina e!s a egy!𝑠+
A,!i ! he! o me !gi es! he!agen !a!be e !payo !
han! he!la e ! o !e e y!s a egy!p o ile!𝑠B+o !o he !agen .!Thus,! his!solu ion!concep !is!
based!on!I e a ed!elimina ion!o !s ic ly!domina ed!s a egies!(IESD)!o !o he !ways!o ! ind!
s a egies! domina ed! by! o he ! s a egies! as! by! he! heo y! o ! a ional! choice! and! o!
maximize!payo !no!agen !would!e e !play!a!domina ed!s a egy.!This!me hod!is!based!on!
i e a ing! epea edly! o!check!i !a!ce ain!s a egy!domina es!o he ! o !a!ce ain!agen .!
Pa e o!op imali y!
A!s a egy!p o ile!S'is!said! o!Pa e o!domina e!s a egy!p o ile!S’!i !no!agen !i!ge s!a!payo !
which!is!wo se!by!playing!wi h!p o ile!S!o e !p o ile!S’! o !all!i.!While! his!implies! ha ! he!
payo s!maybe!equal,! he e!is!an!addi ional!clause!which!s a es! ha !a !leas !one!agen !
should!ha e!a!be e !payo !wi h!s a egy!S! han!wi h!S’.!
!
The!concep !o !Pa e o!op imali y!is!based!on! he!abo e!de ini ion!o !Pa e o!dominance.!A!
s a egy! p o ile! S! is! said! o! be! Pa e o! Op imal! i ! he e! is! no! p o ile! S’! which! Pa e o!
domina es!S.!I !is!also!known! ha !e e y!game!mus !ha e!a !leas !!one!Pa e o!Op imal!
p o ile! and! he e! always! exis s! one! Pa e o! Op imal! p o ile! whe ein! all! s a egies! a e!
pu e.[18]!
Nash!equilib ium!
While! he!concep !o !Nash!Equilib ium!was!b ie ly!men ioned!in! he!in oduc ion! o!game!
heo y!in!chap e !2,!he e!we!will!del e!deepe !in o! he!concep .!I !is!essen ial! o!s a e!he e!
ha !mos !solu ion!concep s!a e!in e ela ed!in!one!way!o ! he!o he !and! his!pa icula !
solu ion!concep !was!chosen! o ! his!p ojec !as!a!Nash!equilib ium! ep esen s!a!s eady!
and!s able!s a e! o !a! gi en!sys em!whe e!no!agen ! has!an!incen i e! o!shi ! om!his!
ac ions.!As! o !a!mul i!agen !sys em!a !which! his!p ojec !was!o iginally!aimed! he!goal!is!
o! ind! he! inal!s a e!o ! he!sys em!which!is!s able! his!concep !was!chosen! o !sol ing! he!
p oblem!a !hand!using!game! heo y.!!
!
34! ! Mas e !Thesis!
! ! De !Mish a
! !
To! unde s and! he! concep ! o ! Nash! equilib ium! i ! is! essen ial! o! know! i s ! o ! bes !
esponse.! A! bes ! esponse! o ! a! gi en! playe ! is! an! ac ion! p o ile! whe e! in! he! playe !
canno !gain!mo e!u ili y!by!shi ing! o!ano he !ac ion!p o ile.!In!essence!d awing! om! he!
de ini ion!in!chap e !2,!i !can!be!said!when!each!playe !is!playing!bes ! esponses! o!o he !
playe s!bes ! esponses,! he!sys em!is!said! o!be!in!Nash!Equilib ium.!
!
Ma hema ically! his!can!be!explained!as! ollows.!Le !𝑆B+be! he!se !o !all!s a egies!wi hou !
he!s a egy!o !agen !i.!
!
𝑆B+ = 𝑠-, 𝑠.… 𝑠+B-𝑠+D- … , 𝑠/!
(7)!
!
Thus!𝑆B+!is! he!s a egy!p o ile!S'wi h! he!s a egy!o !agen !i.!Le !𝑠+!be!by!s a egy! o !agen !
i.!Then,!
!
(𝑠+, 𝑆B+) = 𝑆!
(8)!
!
Le !𝑠+
A!be! he!bes ! esponse! o!𝑆B+,! hen! o !all!s a egy!𝑠+!a ailable! o!agen !i:!
!
𝑢+𝑠+
A, 𝑆B+ 4≥ 𝑢+(𝑠, 𝑆B+)!
(9)!
!
Now!coming!back! o!Nash!Equilib ium,!a!s a egy!p o ile!𝑠 = 𝑠-, 𝑠., … … , 𝑠/!is!a!Nash!
equilib ium!i ! o !e e y!i,!𝑠+!is! he!bes ! esponse! o!𝑆B+,! ha !is!no!agen !o !playe !can!
bene i ! om!de ia ing! om!his!s a egy.!
!
A!Nash!Equilib ium!is!said! o!be!s ic !i !𝑠+!is! he!only!bes ! esponse! o!𝑆B+,! ha !is!any!
de ia ion! om! he!equilib ium!s a egy!will! esul !in! he!playe !doing!wo se.!I ! he e!a e!
mul iple!bes ! esponses! o!𝑆B+,! hen!each!o ! hem!will! o m!weak!Nash!equilib ium.!Pu e!
s a egy! nash! equilib ia! can! be! bo h! wea ! o ! s ic ! whe e! as! mixed! s a egy! nash!
equilib ia!a e!always!weak.!The! eason! o !mixed!s a egy!Nash!equilib ia!being!weak!is!
because!i ! he e!a e!mo e! han!2!pu e!s a egies! ha !a e!bes ! esponses! o!𝑆B+,! hen!any!
mix u e!o ! hem!is!also!a!bes ! esponse.!
I !a!s ic ly!dominan !s a egy!exis s! o !one!playe !in!a!game,! ha !playe !will!play! ha !
s a egy!in!each!o ! he!game's!Nash!equilib ia.!I !bo h!playe s!ha e!a!s ic ly!dominan !
s a egy,! he! game! has! only! one! unique! Nash! equilib ium.! Howe e ,! ha ! Nash!
equilib ium! is! no ! necessa ily! Pa e o! op imal,! meaning! ha ! he e! may! be! non-
equilib ium!ou comes!o ! he!game! ha !would!be!be e ! o !bo h!playe s.!!
!
Please!no e!he e,! ha !sol ing!games!is!no !being!discussed!ex ensi ely!wi h! espec ! o!
sequen ial!games,!as! o !ou !s udy! he!scena io! educes! o!mul iple!cha ge/no !cha ge!
simul aneous!games!a !e e y! ime!s ep!o ! he!day!which!is!essen ially!a!sequen ial!game.!
And! he!me hod! o!sol e!a!sequen ial!game!o en!in ol es! educing!i ! o!no mal! o m!and!
hen! p oceeding! wi h! a! solu ion! concep .! While! alking! o ! sol ing! sequen ial! games!
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wi hou !con e ing! o!no mal! o m,! wo!concep s!a e!o en!discussed!sub-game!pe ec !
equilib ium! and! backwa d! induc ion.! Subgame! pe ec ! equilib ium! deals! wi h! an!
equilib ium! si ua ion! in! a! ce ain! b anch! o ! he! game! whe e! a! ce ain! agen ! has! no!
incen i e! o! ollow!a!ce ain!pa h!based!on! he!ou comes.!Backwa d!induc ion!is!a!me hod!
o !sol ing!games!by!s a ing!a ! he!end!o ! ee!b anch! e acing!s eps! o!see! he!logical!
solu ion!o ! he!game!o en!iden i ying!subgame!equilib ia!as!well.!
!
A e ! discussing! he! abo e! s a egies,! we! will! now! p oceed! o! see! some! nume ical!
examples!whe e!i !will!be!demons a ed!on!how!Nash!Equilib ia!a e! ound!in!di e en !
cases.!Le !us! i s !look!a ! he!p isone ’s!dilemma!game! o!unde s and!sol ing! o !pu e!
s a egy!Nash!equilib ium.!
!
Le !us!se ! he!p emise!o ! he!game! i s .!The e!a e! wo!p isone s!in!police!cus ody!in! wo!
sepa a e! ooms.!Fo !each!p isone ,! he!police!a e! ying! o!ge ! hem! o! es i y!agains ! he!
o he !p isone !and!in! e u n! o ! es i ying!agains ! he!o he !p isone ,! he!p isone !who!
es i ies!will!be!o e ed!a! educed!sen ence.!The!scena io!boils!down! o! he! ac ! ha !i ! hey!
bo h! es i y!agains !each!o he !i.e.!de ec /be ay!wi h! he!o he !p isone ,! hey!bo h!ge !
sen ence!o !3!yea s!each.!I ! hey!on! he!o he !hand!bo h! e use! o! es i y!agains !each!
o he ,! he eby!coope a ing!wi h!each!o he !and! emain!silen ,! he!police!has!less!e idence!
and!can!only!pu ! hem!bo h!away! o !1!yea .!Howe e ,!i !one!be ays(de ec )!and!o he !
emains!silen (co-ope a e),! he!one!who!be ays!goes! ee!while! he!o he !is!sen enced! o!
4!yea s!o !p ison! ime.!These!jail! imes!a e! ep esen ed!as! hei !nega i es! o! o m! he!
payo !ma ix!in!Table!1!so! ha !highe !jail! ime!is!a!lowe !payo .!
!
I ! we! analyze! he! game,! le ! us! see! he! ou comes! when! playe ! 1! ei he ! de ec s! o ! co-
ope a es.!I !playe !1!co-ope a es!bu !playe !2!de ec s,!playe !1!ge s!a!jail! ime!o !4!yea s!
and!playe !2!goes! ee.!Howe e ,!i !playe !2!co-ope a es!bo h!ge !a!jail! ime! o !1!yea .!So,!
i !playe !1,!goes!wi h!co-ope a ion!i s!always!in!playe !2’s!in e es ! o!de ec .!Now,!i !playe !
1!choses! o!de ec ,!playe !2!will!s ill!p e e ! o!de ec !as!3!yea s!is!less!jail! ime! han!4.!And!
his!will!hold! ue! he!o he !way!a ound.!Thus,! he!de ec ,!de ec !s a egy!p o ile!becomes!
a!s ic !Nash!equilib ium.!He e!i !can!be!no iced! ha !de ec ion!always! esul s!in!a!be e !
ou come! and! hence! i ! is! he! dominan ! s a egy! and! co-ope a ion! is! he! domina ed!
s a egy!and!hence!can!be!elimina ed.!Any!unila e al!de ia ion! om! he!equilib ium!is!
wo se! o !each!playe !and! his!is!co e!o ! he!algo i hm!which!will!be!used! o!de e mine!
he!exis ence!o !pu e!s a egy!Nash!equilib ium!in!ou !p ojec .!
!
Le !us!now!explo e!ano he !game!called! he!Ba le!o ! he!Sexes! o!demons a e!how! o!
ind!mixed!s a egy!Nash!equilib ium.!The!p emise!o ! he!game!is!as! ollows.!A!man!and!
a!woman!in!a!couple!wan ! o!go!ou !one!e ening! o !en e ainmen !bu ! hey!ha e!no!
means!o !communica ion!and!co-o dina ion.!The!man!wan s! o!go! o!wa ch!a! igh !while!
he!woman!p e e s! o!go! o! he!balle .!Mo eo e ,! hey!bo h!p e e !being! oge he ! han!
36! ! Mas e !Thesis!
! ! De !Mish a
! !
ending!up!alone!a ! hei !p e e ed! o m!o !en e ainmen .!The!payo !ma ix! o ! his!game!
is!demons a ed!in! he! ollowing! able.!
Table'3:'Ba le'o ' he'sexes'payo 'ma ix'
Man/Woman!
Balle !
Figh !
Balle !
1,2!
0,0!
Figh !
0,0!
2,1!
!
As!can!be!obse ed! he!woman!has!a!highe !payo !o !2!o e ! he!man’s!1,!i ! hey!bo h!
a end! he!balle !while! he!man!has! he!highe !payo !i ! hey!bo h!a end! he! igh .!Incase,!
hey!a end!any! o m!o !en e ainmen !alone!bo h! ecei e!no!payo s.!I !is!easy! o!obse e!
ha !balle ,!balle !and! igh ,! igh !a e!bo h!pu e!s a egy!Nash!equilib ia!as! he e!is!no!
unila e al!de ia ion! o !ei he !playe !in!ei he !case! o!be!able! o!ob ain!a!be e !ou come.!
Le !us!now!mo e!on! o!explo e! he!me hod!o ! inding!mixed!s a egy!Nash!equilib ium.!
The!way! o!do! ha !is! o!employ!a!mixed!s a egy!algo i hm! o !each!playe .!We!begin!he e!
by!applying!i ! o !playe !1,! he!man!in! his!case.!Au oma ically!playe !2!is! he!woman.!The!
concep !is! o!equa e!expec ed!u ili ies! o !playe !2,!when!playe !2!plays!ei he !balle !o !
igh ,!based!on!wha !playe !1!plays.!As!men ioned!ea lie ! he!expec ed!u ili y!is!a! unc ion!
o ! he!playe s!mixed!s a egy!p obabili y.!Le !us!deno e! his!as! ollows:!
!
!
𝑢.H = 𝑓 𝜎-H = 𝜎-H 2 + 1 − 𝜎-H ∗ 0!
(10)!
!
𝑢.N = 𝑓 𝜎-H = 𝜎-H 0 + 1 − 𝜎-H ∗ 1!
(11)!
!
𝑢.H = 𝑢.N!
(12)!
!
The! abo e! equa ions! nume ically! illus a e! he! expec ed! u ili ies! o ! playe ! 2! playing!
balle ,!when!playe !1!plays!balle !wi h!a!p obabili y!𝜎-H.!Thus!in!eq.!10!when!playe !1!
plays!balle !wi h!a!p obabili y!𝜎-H,!playe !2!ge s!a!payo !o !2! o !playing!balle !while! he!
es !o ! he! ime!playe !1!plays! igh !wi h!a!p obabili y!1 − 𝜎-Hand! hen!playe !2! ecei es!
0!payo .!!Eq.!11!does! he!same! o !playe !2!playing! igh .!When! hese!a e!equa ed!in!eq.!
12!and!sol ed! o !𝜎-H,!we!ge !𝜎-H = 1/3.!
!
Thus!playe !1’s!mixed!s a egy!Nash!equilib ium,!is!(Balle !=1/3|Figh =2/3).!Howe e ,!
his!is!no !su icien ! ep esen a ion!and!we!need! o! ind! he!co esponding!mixed!s a egy!
o !playe !2.!On!sol ing!simila ly!as!abo e,!we!ob ain!𝜎.H = 2/3.!Thus!playe !2’s!mixed!
s a egy! componen ! o ! hese! equilib ia!is! (Balle ! =2/3|Figh =1/3).!Thus! (Balle !
=1/3|Figh =2/3,!Balle !=2/3|Figh =1/3)!is! he!mixed!s a egy!Nash!equilib ium! o ! his!
game.!
!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !37!
De !Mish a!
To! calcula e! he! payo ! o ! each! playe ! when! playing! he! abo e! mixed! s a egy! Nash!
equilib ium,!we!mul iply! he!indi idual!p obabili ies!o ! he!playe s! o !a!ce ain!ou come!
and! hen!in! u n!mul iply!wi h!each!playe s!payo !and! he!sum!o !all! hese!numbe s!is!
he!indi idual’s!playo ! o !playing! he!mixed!s a egy!equilib ium.!This!is!demons a ed!
h ough! he! able!below.!
Table'4:'Mixed's a egy'Nash'Equilib ium:'Ba le'o ' he'Sexes'
Man/Woman!
Balle !(2/3)!
Figh !(1/3)!
Balle !(1/3)!
1,!2!(2/9)!
0,!0!(1/9)!
Figh !(2/3)!
0,!0!(4/9)!
2,!1!(2/9)!
!
Thus! playe ! 1’s! u ili y! can! be! calcula ed! as! 1× .
Q+ 0× -
Q+ 2× .
Q+ 0× R
Q=S
Q=.
T.! When!
calcula ed! o !playe !2,!i !comes! o! he!same.!Thus,!i !is!in e es ing! o!no e! ha ! o !bo h!
playe ! he!pu e!s a egy!Nash!equilib ia!men ioned!ea lie !o e !highe !payo s! han! he!
mixed!s a egy!ones.!
!
A e !ha ing!co e ed! he! equi ed! opic! o !ca ying!ou !game! heo y!modeling! o !ou !
p ojec ,!we!will!now!p oceed! o!make!an!ou line!o ! he!p ocess! ollowed! o!achie e! he!
esul s.!
3.4. P oposed!Me hodology!
As!has!p e iously!been!men ioned,! he!p oposed!ou line! o ! he!p ojec !was!supposed! o!
be! based! on! he! u iliza ion! o ! he! algo i hm! in! [1]! and! he ea e ! making! he! agen s!
compe e!amongs ! hemsel es!using!game! heo y! o! o mula e!a!scena io!whe e!all! he!
cha ging! s a egies! which! we e! o mula ed! by! he! au ho ! a e! chosen! based! on!
compe i ion! and! o! check! i ! he! sys em! had! any! equilib ia.! Howe e ,! as! he! wo k!
p og essed,!due! o!lack!o !expe ise!in! he!domain!o !game! heo y!modeling!i !was!ag eed!
and! he!complexi y!o !modeling!an!ex ensi e!n!pe son!game,!i !was!decided! o!na ow! he!
scope!o ! he!p ojec .!Th ough!discussions!wi h! he!supe iso ,!i !was!concluded,! ha !in!
he!in e es !o ! ime!and!owing! o! he!lack!o !expe !guidance!on! he!subjec !ma e ,!i !was!
bes ! o! educe! he!gi en!p oblem! o!a!smalle !scope!and!apply!game! heo y! o!i ! o!be e !
unde s and! he! heo y! and! obse e! i s! pe o mance! on! a! simple! sys em! be o e!
a emp ing! o!employ!i !in!a!la ge!sys em.!Thus,! his!p ojec !was! es ic ed! o!a! wo-s ep!
unde aking;!in! he! i s !pa ,!i !was!a emp ed! o!employ!game! heo y! o!a!mul i-agen !
sys em!bu !due! o! he!complexi y!o ! he!sys em,!i !was! educed! o!a! o m!o !selec ing!
s a egies!based!on!weigh age!assigned! o!a!ce ain!s a egy! o !a!single!agen !which!in!
u n!was!based!on!a!payo !assigned.!The!second!s ep!employs!game! heo y! o!a!smalle !
scena io!a !hand!o !a!household!wi h!2!elec ic! ehicles!wi h!di e en !mobili y!pa e ns!
and! o!see!i ! hese!elec ic! ehicles!we e!made! o!compe e!using!game! heo y,!wha !kind!

38! ! Mas e !Thesis!
! ! De !Mish a
! !
o ! load! p o ile! was! o! be! obse ed! o ! he! elec ic! ehicle! cha ging.! A! low! diag am!
indica ing! he!p ocess! low! o ! he!second!pa !is!demons a ed!below:!!
!
!
Figu e'14:'Flowcha 'illus a ing'algo i hm'and'in e ac ion'o 'da a'
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !39!
De !Mish a!
4. Me hodology!
As!men ioned!in! he!p e ious!chap e ,! he!cen al! hough !behind! his!unde aking!was!
o!employ! he!exis ing!se up! om![1]!and!employ!game! heo y! o! he!selec ion!o !cha ging!
s a egies!by!use s.!In! he!simples !o ! e ms,! he!p ocedu e!will!allow! o !payo s! o!be!
associa ed!wi h!each!agen ’s!cha ging!needs!based!on! he! ime!o !day,!elec ici y!p ice!
and!cha ging!p ice! and!an!agen ! is!mo e!likely! o!cha ge!his!elec ic! ehicle! i !highe !
payo !is!associa ed!a !a!ce ain!poin !o ! ime.!He e,!i !becomes!di icul ! o!conside ! he!
in luence!o ! he! emaining!agen s!on! he!beha io !o ! he!said!agen .!I !can!be!assumed!
ha !an!agen ’s!beha io !will!be!comple ely!d i en!by!his!own!sel ish!in en !and!as! he e!
is!no! easonable!way!o ! he!agen ! o!know!o ! he!ac ions!o !o he !agen s,!he!will!ac !solely!
wi h! he!pu pose!o !maximizing!his!pay!o .!
!
While! a ! he! ou se ! i ! was! planned! o! employ! game! heo y! o! a! p e ious! wo k,! he!
complexi y!o !sol ing!mul i-agen !n!playe !games!was! ound! o!be!subs an ial!and! he!
necessa y!expe ise!in!game! heo y!modeling!was!no !a ailable!and!i !was!deemed! ha !
he! equi ed!expe ise!could!no !be!acqui ed!wi hin! he! ime! ame!o ! he!mas e ! hesis.!!
!
As!such!i !was!decided! o!unde ake! his!s udy!in! he! ollowing! wo!pa s:!
!
1. To!use! he!exis ing!wo k!and!allo !weigh age! o!di e en !cha ging!s a egies!based!
on!SOC,!p ice!o !elec ici y!and! ime!o !day!and!e alua e!how! he!load!p o ile! om!
elec ic! ehicles!would!change!as!a! esul ! ha !
!
2. To!s ay! ue! o! he!ini ial!aim!o !employing!game! heo y,!i !was!decided! o! educe!
he!p oblem! o! he!scope!o !a!single!household!and!simula e!a!game!o ! wo!playe s!
in! he!same!household-!a!scena io!was!buil !whe e!a! amily!household!had! wo!
dis inc !EVs! o !di e en !pu poses!and! hus!di e en !mobili y!pa e ns!and! hey!
would!compe e!amongs ! hemsel es! o!cha ge!o !no !cha ge!a !a!gi en! ime!in! he!
day.!The!game!could!be! ea ed!as!mul iple!simul aneous!mo e!games!a !e e y!
ime!s ep!o ! he!day!o !one!single!sequen ial!mo e!game! o!de e mine!op imum!
equilib ium!s a egy! o !each!playe .!
In! he! ollowing!sec ions,!we!will!go! h ough! he!s eps!ca ied!ou ! o!implemen ! he!abo e!
pa s.!
4.1. Pa !1:!Modi ica ion!o !exis ing!EV!demand!p edic ion!model-!
All!cha ging!s a egies!
Fo ! his! pa ! i ! is! essen ial! o! unde s and! he! me hodology! applied! in! [1].! A! de ailed!
e iew!o ! he!publica ion!in![1]!is!necessa y! o! ully!unde s and! he!app oach!applied!and!
he!s eps! aken! o!es ima e! he!elec ic! ehicle!cha ging!demand.!In! his!sec ion,!we!will!
b ie ly!go! h ough! he!app oach!and! he!modi ica ions!made! o!ob ain!a!di e en !cha ging!
40! ! Mas e !Thesis!
! ! De !Mish a
! !
demand! a ! he! 37-node! sys em! as! conside ed! in! he! o iginal! publica ion.! A! sho !
desc ip ion! o ! he! model! is! men ioned! in! Sec ion! 3.2.!He ea e ! we! will! lis ! ce ain!
necessa y! de ails! o ! he! model! which! a e! equi ed! o! unde s and! he! modi ica ions!
ca ied!ou !in! his!s udy:!
!
1. Agen ! based! modelling! de ails:! Six! g oups! o ! agen s! we e! de ined! in! his! s udy!
conside ing!mobili y!and! hei ! esidence.!Mobili y! easons!we e!based!on!pe sonal!
o ! p o essional! unc ions.! Th ee! di e en ! a eas! o ! esidence! we e! iden i ied! and!
o med! he!basis!o !s a !and!end!o ! ips!and!addi ionally!need! o !cha ging!wi hin!
he!ne wo k!being!examined.!These!6!agen !g oups!a e!enlis ed!he e:!
!
- G oup!1:!Residen s!o ! he!ne wo k!
- G oup!2:!Non-Residen s!bu !will!cha ge!once! hei ! ip!is!o e !and!will!s op!wi hin!
ne wo k!
- G oup!3:!P i a e!indi iduals! om! he!me opoli an!
- G oup!4:!P o essionals!-! esiden !o ! he!ne wo k!
- G oup!5:!P o essionals!-!non- esiden s!o ! he!ne wo k!
- G oup!6:!Me opoli an!a ea!p o essionals!
These!di e en !g oups!ha e!an!inclina ion! o!cha ge!a !di e en ! imes! o !examples!a!
esiden !o ! he!ne wo k!p e e s! o!cha ge!a ! he!comple ion!o !his! ips!whe e!as!someone!
a elling! om! u ban/me opoli an! a eas! can! cha ge! be ween! consecu i e!
displacemen s.!The!numbe !o ! hese!g oups!is!sou ced! om!open!da a!and!conside s! ha !
38%! o ! all! ehicles![19]!in! Ba celona! a e! d i en! e e y! day.! Addi ionally,! an! EV!
pene a ion! ac o !o !10%!-!40%!can!be!applied! o!e alua e!di e en ! esul s.!Fo ! he!sake!
o ! his!s udy!we!ha e!used!an!EV!pene a ion! ac o !o !10%!which!implies! ha !10%!o !all!
ehicles!being!d i en!in!Ba celona!
!
2. The! es ! ne wo k! is! a!37-node! IEEE! es ! eede ! MV! ne wo k!which! is! adap ed! o!
Ba celona!ne wo k!cha ac e is ics!o !25!kV!MV!and! he!geog aphic!dis ibu ion!is!
adap ed! o!Ba celona’s!mobili y!da a.!High,!medium!and!low!inhabi an s!pe !house!
and! ehicles!pe !inhabi an !a e!iden i ied!and!a!dis ibu ion!o !b anches!and!nodes!is!
ca ied!ou .!Mo e!de ails!on! he!same!a e!a ailable!in![1].!
!
3. The!au ho !in![1]!has!c ea ed!4!cha ging!scena ios!be ween!which!we!will!be!mixing!
in! his!s udy! o!ob ain!a!modi ied!cha ging!demand.!These!a e!desc ibed!in!b ie !he e:!
- Scena io!A-!In ensi e!Cha ge!–!Use !cha ges!as!soon!as!possible!whene e !possible!
- Scena io!B-!Plug-And-Play!–!Use !cha ges!a !home!when!SOC!is!less! han!20%!
- Scena io!C-!O -Peak!Ta i !–!Use !has!a!Time-o -Use!(TOU)! a i !specially! o !EVs!
based! on! Spanish! Regula ion! wi h! he! cheapes ! hou ! o !elec ici y! p icing!
beginning!a !1:00!AM!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !41!
De !Mish a!
- Scena io!D-!Sma !Cha ging-!Realized!by! he!agg ega o !who!manages!all!EVs! o!
consume!minimum!powe !a !a!ce ain! ans o me !
!
Based!on! his!back!g ound!we!will!now!p oceed! o!unde s and! he!modi ica ions! equi ed!
o! he!model! o!implemen !a!scena io!in!which!agen s!can!cha ge!using!all!o ! he! i s !3!
cha ging!scena ios.!
!
The!me hodology!and!s eps! ollowed!he e!we e! he! ollowing:!
!
1) Based!on! he!elec ici y! a i s!on!a!ce ain,!a!sa ings!po en ial!was!iden i ied! o !
each!agen !in!e e y!agen !g oup! o ! he!di e en !cha ging!scena ios.!
2) The! sa ings! po en ial! along! wi h! elec ic! ehicle! s a e! o ! cha ge! and! ene gy!
equi emen s! o !nex ! ip! o med! he!basis!o !allo ing!a!payo /weigh age! o!each!
agen .!
3) Based!on! he!abo e!weigh age!assigned! o! he!use ,! he!use !decides! o!cha ge!in!
scena io!A,!B!o !C!
4) These!elec ic!cha ging!demands!a e!agg ega ed!a !each!node! h oughou ! he!day!
and! he!di e ence!is!plo ed!and!in e ences!do ed! he ein.!
5) Addi ionally,!i !is!de e mined!wha !pe cen age!o !use s!in!a!speci ic!agen !g oup!
cha ge!using!a!ce ain!scena io.!
6) Ca e!is!also! aken! o! ake!in o!accoun ! ha !ce ain!use !in!an!agen !g oup!migh !no !
be!eligible! o !Scena io!B!and!C!which!a e!applicable! o !use s!who!only!cha ge!a !
home!and/o !ha e!access! o!TOU! a i s.!
- G oup!1:!Residen s!o ! he!ne wo k:!This!g oup!is!eligible! o !all! h ee!cha ging!
scena ios!conside ed!
- G oup! 2:! Non-Residen s!bu ! will! cha ge! once! hei ! ip! is! o e ! and! will! s op!
wi hin!ne wo k:!As! hese!a e!non- esiden s! hey!will!no !be!able! o!a ail!Scena io!
B!and!Scena io!C!
- G oup!3:!P i a e! om! he!me opoli an:!These!g oup!o !Agen s!a e!ou side! he!
u ban!limi s!and!hence!canno !a ail!Scena io!B!and!C!ei he .!
- G oup!4:!P o essional! esiden !o ! he!ne wo k:!This!g oup!is!eligible! o !all! h ee!
cha ging!scena ios!conside ed!
- G oup!5:!P o essional!non- esiden !o ! he!ne wo k:!As! hese!a e!non- esiden s!
hey!will!no !be!able! o!a ail!Scena io!B!and!Scena io!C!
- G oup!6:!Me opoli an!a ea!p o essionals:!This!g oup!since!ou side! he!ne wo k!
is!no !eligible! o !ei he !o ! he! h ee!cha ging!scena ios!conside ed!
4.2. Pa !2:!Two!playe !game!in!a!single!household!
In! his!pa ,!a!scena io!was!cons uc ed!conside ing!an!a luen ! amily!household!wi h!a!
single!cha ging!poin !wi h! ypical!mobili y!pa e ns!o !commu e! o!wo k,!d opping!kids!
a !school,! isi ing!supe ma ke s,!gym!and! unning!e ands.!This!was!done! o!simpli y! he!
48! ! Mas e !Thesis!
! ! De !Mish a
! !
Table'8:'Pe cen age'o 'agen s'cha ging'in'a'scena io'
!
Pe cen age!o !use !cha ging!in!each!Scena io!%!
A!
B!
C!
Agen !G oup!1!
76!
15!
9!
Agen !G oup!4!
75!
25!
0!
!
As! can! be! obse ed,! he! majo i y! o ! he! agen s! do! con inue! o! cha ge! in! he! mos !
con enien ! in ensi e! cha ge! scena io! which! allows! o ! cha ging! whene e ! possible,!
howe e !a!shi ! owa ds!scena ios!B!and!C!a e!also!in ol ed.!As! his!pa !o ! he!s udy!was!
done!by!a!simple!weigh ed!scheme!ins ead!o !a!game! heo e ic!op imiza ion!app oach!
echnique,!i !is!di icul ! o!d aw!any!s ong!conclusions! om! he!abo e! esul s.!
!
Le !us!now!explo e!in!de ail! he! esul s!ob ained! om!Pa !2!o ! his!s udy.!
5.2. Resul s!&!Discussion:!Pa !2!
In! his! sec ion,! we! will! examine! he! esul s! om! he! second! pa ! o ! he! s udy! which!
in ol es!a!specially!c ea ed!scena io!o !a!household!wi h! wo!elec ic! ehicles.!
!
As!a! i s !s ep,!we!examined! he! esul s! om! he!scena io! o !one!day! o!check!i ! he!
algo i hm!was!beha ing!as!expec ed!and!i ! he! indings!seemed!logical.!I !is!in e es ing! o!
obse e! he!equilib ia!we!ha e!ob ained!when! he!game!is!sol ed!as!simul aneous!game!
a !each! ime!s ep.!As!expec ed! he!game!shows!no!equilib ia! o ! he!ini ial!du a ions!o !
he!day!and!e en ually!when!bo h!EVs!a e!a ailable!a ! he! esidence!and! he!p ice!o !
elec ici y!is!simul aneously!low,!bo h!playe s!ha e!a!pu e!s a egy!Nash!equilib ium!wi h!
he!cha ge!s a egy!wi h!p e e ence!going! o! he!playe !wi h!lowe !SOC!and!while! he!
ehicle!wi h!p e e ence!cha ges! he e!can!be!no!game!un il! he!playe ’s!SOC! equi emen !
o !subsequen ! ips!is!me .!The ea e ,! he!second!EV!s a !cha ging!and!again! he e!is!
no!game!in ol ed! ill! he!second!EV!a ains!a!desi able!SOC.!While! his!seems!logical,! he e!
a e!o he !i e a ions! which! can!be! examined! he ein!whe e! playe ! wo!belie es!he!has!
highe !u ili y!by!cha ging!when!playe !1!is!no !a ailable! o!cha ge!e en! hough! he!p ice!
o ! elec ici y! is! highe ,! hus! essen ially! no ! compe ing! in! he! game.! This! is! based! on!
subjec i e!u ili y!gi en! o!con enience!and! ac o s!and! esul s!in!a!shi !in!equilib ium! o!
ou side!wha !is!obse ed!ea lie !in! he!o -peak!hou s.!A e !obse ing! his!on!a!singula !
day! he!game!was!expanded! o! un! o !a!week!wi h!addi ional! ips.!
!
Jus ! o!demons a e!wha !a! ypical!2x2!ma ix! o !a! ime!s ep!looks!like,!in! he! ollowing!
able!we!will!see! he! i s !equilib ium! eached!whe e!EV2!has!a!low!SOC!and!decides! o!
s a !cha ging.!!

Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !49!
De !Mish a!
Table'9:'Typical'Payo 'ma ix'as'ob ained' o 'Cha ge/Cha ge'equilib ium'scena io'
EV1/EV2!
Cha ge!
No !Cha ge!
Cha ge!
3,!6!
1,!1!
No !Cha ge!
1,!1!
1,!1!
!
In! he!abo e! able,!i !is!a!cha ge/cha ge!equilib ium!bu !in!ou !scena io!only!one!EV!can!
cha ge! a ! a! ime! and! i ! makes! sense! o! cha ge! he! one! ha ing! a! highe ! payo ! which!
inciden ally!and!because!o ! he!design!on! he!algo i hm!has!a!highe !payo !which!in! his!
case!is!EV2.!I !is!also!essen ial! o!obse e! ha ! he! esul ing!game!is!no !a!ze o-sum!game!
and! hus!is!no !pu ely!compe i i e!and! hus! he e!can!be!scope! o !co-ope a ion!and!co-
o dina ion.!
!
In! he! ollowing!sec ion,!we!will!see!how! he!load!p o ile!looks!in!compa ison! o!p ices!
and!du ing!wha ! ime! his!equilib ium!occu s!and!whe he ! he!playe !also!bene i s! om!
low! a i s!a ! ha !poin !and!how! he!p og ession!o !SOC! akes!place! hus!indica ing! ill!
wha ! ime! he! EV! cha ges.! The e! a e! e iciency! ac o s! which! a e! applied! o! he! EV!
cha ging!as!well!as! o!ba e y!deple ion! o!ensu e! ha !all!p ocesses!a e!no !occu ing!
pe ec ly!ideally!and!a e!ins ead!mo e! ealis ic.!
!
The! i s !equilib ium!is!obse ed!on!day!4,!when!EV2!has!a!highe !payo ! o!cha ge!du ing!
a!low-p ice! ime!on!day!4!o ! he!week.!This!can!be!obse ed!in!Fig.!19!whe e!a! ise!in!
household!load!is!obse ed!a ound!0900!h s.!This!is!a e !EV2!has!comple ed!i s! i s ! ip!
o !d opping! he!child en!a !school!and!is!back!a ! he!household!un il! he!nex ! ip!which!
is!scheduled! o!pick!up! he!child en! om!school.!The!game! esul s!in!EV2!cha ging!in! his!
du a ion!up! ill!a!poin !whe e! he!no mal!p ices!a e!highe ! han! he!o -peak!p ices.!This!
is!ensu ed!by!a!co ec !cons uc ion!o ! he!payo !allo ing! unc ion!in! he!code!and!is!
e i ied!by!ob aining! his! esul .!I !is!also!in e es ing! o!no e! ha ! he!game!decides!when!
he!EV!should!cha ge!based!on!i !mobili y!needs.!I !is!seen!in!Fig.!19! ha !EV2!engages!in!
cha ging! o ! he! i s ! ime!in! he!week!on!day!4!based!on! he!knowledge!o ! he!mobili y!
pa e n! o ! he! week.! Addi ional! equilib iums! wi h! EV2! ha ing! highe ! payo s! a e!
obse ed!du ing! he!weekend!depending!on! he!p ice!o !elec ici y!and!a e!con ibu ed!
o! he!mobili y!pa e n! o !weekends!being!di e en ,! ha !is! he e!a e! ewe !o !no! ips,!
he!weekend!cha ging!allows! o !cha ging!up! o!100%!SOC! o !EV2!on!day!6! hus!being!
p epa ed! o ! he!mobili y! equi emen s!o ! he!coming!week.!
50! ! Mas e !Thesis!
! ! De !Mish a
! !
!
Figu e'19:'Fi s 'Equilib ium'wi h'EV2'cha ging'on'Day'4'
Pos ! his! he!nex !equilib ium,! ha !is!obse ed!is! o !EV1!wi h!highe !u ili y!being!obse ed!
o !EV1!du ing! he!ea ly!hou s!o !day!5.!This!is!illus a ed!in!Fig.!20.!He e,!again! he!game!
decides! ha ! he! ehicle!needs! o!cha ge! aking!in o!accoun !use !p e e ences! o !SOC,!which!
is!in! u n!based!on!plans! o!use!EV1!o e ! he!weekend.!While!doing!so!i !also! akes!in o!
accoun !payo ! ela ed! o!SOC!and!elec ici y!p ices! o!cha ge! he! ehicle!in!low-p ice!hou s!
o ! he!o !peak!TOU! a i .!EV1!owing! o! he! ime!when!sys em!equilib ium!is!iden i ied!
cha ges!up! o!100!%!SOC!and!is! hus!p epa ed! o !any!weekend! ip!o !addi ional!du ies!
o e ! he!weekend.!I ’s!again!in e es ing! o!no e! ha ! he!cha ging!he e! akes!place!when! he!
ehicle!SOC!has!d opped! o!below!50%!on!day!5!o ! he!week.!A! u he !equilib ium! a o able!
o!EV1!is!obse ed!on! he! inal!day!7!du ing!o -peak!low! a i !hou s!in!case! he e!has!been!
a!weekend! ip!which!deple es! he!ba e y.!This!equilib ium!again!ensu es! ha ! he! ehicle!
has!an!SOC!o !100%!be o e! he!nex !week!commences.!I !can!be!obse ed!in! he!plo ! ha !
pos ! he!cha ging!in! he!ea ly!hou s!o !day!5! he! ehicle!con inues!wi h!i !no mal!mobili y!
pa e n! o !day!5,!and! he!same!is!seen!in! he!SOC!deple ion!obse ed!du ing! he!day!hou s.!
The!e ec !obse ed!on! he!demand!p o ile! o !cha ging!a ! he! a ed!max!high!powe ! o !EV1!
shows! ha ! he!cha ging!du a ion!is!sho !bu ! he!peak!load!is!highe !as!compa ed! o!EV1!
which!has!a!lowe !max! a ed!cha ging!powe .!This!assumes! ha !bo h! ehicles!a e!able! o!
cha ge!a ! hei !max! a ed!onboa d!cha ging!powe .''
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
0
1
2
Consump ion kWh
Load P o ile
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
0
0.05
0.1
0.15
P ice (Eu o/kWh)
P ices o No mal & O peak schemes
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
Time o day
0
50
100
SOC %
SOC
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !51!
De !Mish a!
!
Figu e'20:'Second'Equilib ium'wi h'EV1'cha ging'on'Day'5'
Some!o he !obse a ions!which! esul !in!a!close !examina ion!o ! he! esul s!a e! ha !only!
pu e! s a egy! Nash! equilib ia! a e! obse ed!and! ha ! all! equilib ia! which! a e! used! o!
e alua e! he! cha ging! demand! om! EV’s! a e! s ong! o ! s ic ! equilib ia.! Weak!
equilib iums!a e!also!obse ed!when! he e!is!no!incen i e! o !ei he ! ehicle! o!cha ge!and!
hus! he e!is!no!u ili y!assigned!a !any!ac ion!p o ile!and! hus!all!p o iles!end!up!being!
weak!equilib iums.!No!mixed!s a egy!equilib ia!a e!obse ed!and! his!a ibu ed! o! he!
ac ! ha ! he e!is!no!unce ain y!in! he!mobili y!pa e ns!o ! he!EVs.!In!case,! he e!was!a!
ac o !which!was!applied! o!assign!p obabili ies!o ! aking!ce ain! ips! o!each!EV!and!as!
a! esul ! he!SOC!a !any!poin !o ! ime!on!any!gi en!day!o ! he!week!would!be!s ochas ic,!i !
is! expec ed! ha ! in! such! case! mixed! s a egy! Nash! equilib ia! migh ! ha e! also! been!
obse ed.!As!has!been!men ioned!p e iously,! he!games!he e!non!ze o!sum!game!and!
hus!allow! o !co-o dina ion!and!co-ope a ion.!This!has!no ! ully!been!explo ed!in! his!
p ojec ,!howe e ! he e!is!scope! o!apply!co-o dina ion!and!co-ope a ion!mechanism! o!
explo e! he! indings! he ein.!
!
Be o e!p oceeding! o!conclude,!we!will!now! ake!a!quick!look!a ! he!mone a y!sa ings!
which! a! household! could! expec ! o! see! om! he! game! heo e ic! managemen ! o ! he!
elec ic! ehicles!cha ging!using!o -peak!TOU! a i !o e !no mal! a i s.!This!is!illus a ed!
in!Table!9.!!
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
0
1
2
Consump ion kWh
Load P o ile
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
0
0.05
0.1
0.15
P ice (Eu o/kWh)
P ices o No mal & O peak schemes
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
Time o day
0
50
100
SOC %
SOC
52! ! Mas e !Thesis!
! ! De !Mish a
! !
Table'10:'Sa ings' om'game' heo e ic'elec ic' ehicle'cha ging'using'o -peak' a i s'
!
Sa ing!in!Eu os!
Yea ly!Sa ings! om!EV1!
154.3!
Yea ly!Sa ings! om!EV2!
45.9!
Ne !Yea ly!Sa ings! o !household!
~!200.0!
!
Thus,!i !can!be!obse ed! ha ! h ough! he!game! heo e ic!cha ging!o ! he!elec ic! ehicles!
using!an!o -peak!TOU! a i ,!ne !yea ly!sa ing!o !almos !200!Eu os!can!be!achie ed.!While!
his!is!no !subs an ial! o !a!household,!i !does!clea ly!demons a e!how!demand! esponse!
can!ha e!a!mone a y!impac !on! he!spending!o !a!household.!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !53!
De !Mish a!
6. Conclusions
In!conclusion,! he! indings! om! his!wo k!a e!summa ized!as! ollows.!F om!including!
mul iple!cha ging!scena ios!such!as!in ensi e!cha ging,!plug!and!play,!and!o !–peak!i !is!
obse ed! ha !demand! om!elec ic! ehicles!is!modi ied.!Impo an ! ends!such!as!peaks!
being! educed!and!ce ain!amoun !o !demand!shi ing!is!obse ed!and! hus!highligh s! he!
impo ance! o ! he! ca ying! ou ! an! exe cise! as! in! pa ! one! o ! his! wo k! along! wi h! an!
op imiza ion! echnique!such! ha !s onge !conclusions!can!be!d awn! om! he!wo k!and!
be!u ilized! o!unde s and! he!impac !on! he!g id.!
!
F om!pa ! wo!o ! his!wo k,!i !is!possible! o!conclude! ha !game! heo e ic!me hods!can!be!
applied! o!op imiza ion!p oblems!in!elec ic! ehicle!cha ging!scena ios!as!well!household!
ene gy!managemen !schemes!including!demand! esponse.!The! esul s!show! ha !game!
heo y!can!be!a! e sa ile! ool! o!ensu e! ha !op imum! esul s!a e!ob ained!while! aking!
in o!accoun !p e e ences! om!agen s!o !playe s.!The! esul s!showed! ha !i !was!op imum!
o!cha ge! he! ehicles!1-2! imes!a!week,!e en!a ! imes!no !up! o!100%!SOC!while!making!
use!o !o -peak! a i s! o!gene a e!mone a y!sa ings! o ! he!household.!The! esul s!also!
demons a ed!ce ain!aspec s! om!a!game! heo e ic!poin !o ! iew.!These!in ol ed! he!
lack! o ! mixed! s a egy! Nash! Equilib ia! illus a ing! ha ! he! use ’s! ac ions! we e! ully!
de ined!and! he e!was!no!p obabili y!in ol ed!based!on!o he ! ac o s!which!could!be!used!
o!a ain!addi ional!equilib ia.!Ano he !impo an !conclusion!was! he!obse a ion,! ha !
he! game! a ! each! ime! s ep! was! a! non-ze o! sum! game! hus! demons a ing! ha ! co-
ope a ion!and!co-o dina ion!be!a! ac o !in!such!scena ios.!
6.1. Scope! o !Addi ional!Wo k!!
I !is!in e es ing! o!no e! om! he!abo e!sec ions,! ha ! he! esul s!seem! e y!logical!when!
being!p edic ed!e en!wi hou !game! heo y,!howe e ! his!s udy! ein o ces! he!logicali y!
o !concep s!in!load!managemen !such!as!demand!side!managemen !and!demand! esponse!
whe e!i !is!obse able! ha ! he! endency! o!shi ! o!o !peak!hou s! o !mone a y!bene i !is!
he!majo !obse able! end!while!conside ing! ha !i !op imizes! he!cha ging!beha io !in!
a!single!household.!!Addi ionally,!i !indica es! he!op imum!pa e n!in!which!hea y!loads!
o !elec ic! ehicles!can!be!shi ed! o!allow! o !maximizing! hei !u ili y,!while!main ain!use !
con enience.!Fu he !ex ension!o ! his!s udy!can!in ol e!ex ending! he!shi ing!o !loads!
o!all!household!appliances.!Al e na ely,! he!game! heo e ic!app oach!can!be!ex ended! o!
an!en i e!neighbo hood!o !dis ic !and! hen! he!impac !on! he!g id!can!be!obse ed!and!
po en ial! o !mechanisms!such!as!peak!shi ing!and! alley! illing!can!be!e alua ed.!Also,!
as! men ioned! owa ds! he! end! o ! he! las ! sec ion,! he e! is! scope! o! implemen ! co-
ope a ion!and!co-o dina ion!and! ha !can!be!an!in e es ing!ex ension!o ! his!wo k.!
!
Wi h! he!highe !in eg a ion!o !EVs!i !also!opens!up!oppo uni ies! o!u ilize!EVs!and!EV!
cha ging!in as uc u e!in!al e na e!ways!such!as! he!Vehicle- o-G id(V2G)!concep ! o!
supplemen ! he!g id!ene gy!and!in! u n! acili a e!highe !in eg a ion!o ! enewables.!In!

54! ! Mas e !Thesis!
! ! De !Mish a
! !
essence,! he!powe !g id!has!negligible!s o age,!as!a! esul !o !which!i !is!a!cons an !e o !
o!ma ch! ansmission!and!gene a ion! o!ma ch! he!end!use !consump ion.!This!is!usually!
achie ed!by! u ning!on/o ! acili ies!in!a!powe !plan ,!and! amping!up!and!down![29].!EVs!
as! in! he! case! o ! o he ! ehicles! a e! designed! o! deal! wi h! luc ua ions! in! powe !
equi emen !as!pe ! oad!p o ile!and!d i ing!beha io .!This!in!EVs!is!achie ed!by!hyb id!
d i e! ains,!o !ba e y! echnology!which!a e! o ms!o !ene gy!s o age!and! hus!can!p o ed!
ene gy!when! he! ehicles!a e!pa ked,!and!wi h! he! equi ed!connec ions! o! he!g id!can!
eed!powe !in o! he!g id!when! equi ed.!This!is!wha !is! e med!as! he!Vehicle- o-G id!
concep !o !V2G.!This!is!addi ionally!aided!by!d i ing!pa e ns!o !pe sonal!EVs!whe ein!i !
can!be!obse ed! ha ! hey!a e!used! o !only!5-10%!pe !cen !o !all! ime! o ! anspo a ion,!
and!90-95%! ime!a e!pa ked,!making! hem!a ailable! o !a!‘seconda y! unc ion’!such!as!
V2G![29].!Thus,!i !a!model! o !cha ging!demand!o !EVs!can!be!success ully!buil ,!i !can!be!
u he !u ilized! o!calcula e! he!po en ial!o !p i a ely!owned!EVs! o!supply!ene gy!back! o!
he! g id.! This! equi es! he! s udy! o ! addi ional! pa ame e s! and! op imiza ion! o ! hose!
pa ame e s! o!achie e!a!success ul!implemen a ion! which!is!beyond! he!scope!o ! his!
wo k.!The!concep !has!been!b ie ly!men ioned!he e!in!o de ! o!demons a e!possibili ies!
o !addi ional!wo k.!
!
Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !55!
De !Mish a!
7. Acknowledgemen s
The! ealiza ion!o ! his! hesis!has!been!a!highly! ui ul!and!cons uc i e!expe ience! o !
which!I!ha e!many!people! o! hank! o .!!
!
A !CITCEA-UPC,!a! i s ! and! o emos ! big! hank! you!goes! ou ! o! Robe o!Villa á ila! o !
i s ly!ag eeing! o!wo k!wi h!me!du ing! he!cou se!o !an!in e nship!and!mas e ! hesis!and!
his!con inued!guidance,!supe ision!and!men o ing!wi hou !which! his!wo k!would!no !
ha e!been!possible.!
!
My! hea el ! hanks! also! go! ou ! o! Pol! Oli ella-Rosell,! he! p ima y! au ho ! o ! [1],! o !
ag eeing! o!sha e!his!wo k,!da a!sou ces!and!algo i hms!wi h!me! o ! he!pu poses!o ! his!
hesis!and! o !being!a ailable! o!discuss!any!que ies!I!had!a !any!poin !o ! ime!du ing! he!
du a ion!o ! his! hesis.!
!
I!would!like! o! hank!my! ellow!Innoene gy!s uden s!and!close! iends,!Pa los!Schoinas!
and!Daniel!Kun z! o !being!a ailable! o!wo k!wi h!and!discuss! a ious!aspec s!du ing! he!
cou se!o ! his!p ojec .!
!
I!would!like! o!addi ionally! hank!e e yone!in! he!Innoene gy!CommUni y!who!a !any!
poin !discussed!wi h!me!on! opics! ela ed! o!my! hesis,!as!i !is! h ough! hese!discussions!
I!was!able! o!ga he !addi ional!insigh s!and!ideas! o!implemen !in! his! hesis!wo k.!
!
I!would!like! o! hank!my! iends!a !home!in!India!and!ab oad! o !being! he e! o !me!and!
being!a!cons an !sou ce!o !inspi a ion!and!op imism!a !all! imes.!
!
And! inally,!I!would!like! o! hank!my! amily! o ! hei !in aluable!suppo !and!guidance! o !
my!choices!and!decision!wi hou !which!I!would!no !ha e!been!able! o!ge ! his! a .!They!
ha e!always!p o ided!me!wi h!mo e! han!I!could!as! o ,!and! o ! ha !I!am! hank ul!and!
g a e ul.!
56! ! Mas e !Thesis!
! ! De !Mish a
! !
8. Bibliog aphy
[1]!P.! Oli ella-Rosell,! R.! Villa a ila-Robles,! A.! Sumpe ,! and! J.! Be gas-Jané,! “P obabilis ic!
Agen -Based! Model! o ! Elec ic! Vehicle! Cha ging! Demand! o! Analyse! he! Impac ! on!
Dis ibu ion!Ne wo ks,”!Ene gies,! ol.!8,!no.!5,!pp.!4160–4187,!May!2015.!
[2]!In e na ional!Ene gy!Agency,!“Global!EV!Ou look!2016:!Beyond!One!Million!Ca s.”!
[3]!J.!Y.!Yong,!V.!K.!Ramachanda amu hy,!K.!M.!Tan,!and!N.!Mi hulanan han,!“A! e iew!on!
he!s a e-o - he-a ! echnologies!o !elec ic! ehicle,!i s!impac s!and!p ospec s,”!Renew.'
Sus ain.'Ene gy'Re .,! ol.!49,!pp.!365–385,!Sep.!2015.!
[4]!M.! Yilmaz! and! P.! T.! K ein,! “Re iew! o ! Ba e y! Cha ge ! Topologies,! Cha ging! Powe !
Le els,!and!In as uc u e! o !Plug-In!Elec ic!and!Hyb id!Vehicles,”!IEEE'T ans.'Powe '
Elec on.,! ol.!28,!no.!5,!pp.!2151–2169,!May!2013.!
[5]!C.! H.! Dha makee hi,! N.! Mi hulanan han,!and! T.! K.! Saha,! “A! comp ehensi e! planning!
amewo k! o !elec ic! ehicle!cha ging!in as uc u e!deploymen !in! he!powe !g id!
wi h!enhanced! ol age!s abili y,”!In .'T ans.'Elec .'Ene gy'Sys .,! ol.!25,!no.!6,!pp.!1022–
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64! ! Mas e !Thesis!
! ! De !Mish a
! !
o i=1:1:288
load_p o ile(i)=load_p o ile(i)+((2.19*2)/(24*12)+0.2);
i loo (i/12)>c
c =c +1;
end
i c >=7 && c <=8
load_p o ile(i)=load_p o ile(i)+i/1000;
end
i c >=15
load_p o ile(i)=load_p o ile(i)+i/1000;
end
i c >=21 && c <23
load_p o ile(i)=load_p o ile(i)+1/12;
end
i c >=21 && c <24
load_p o ile(i)=load_p o ile(i)+3.06/12;
end
end
Func ion o Pu e S a egy Nash Equilib ium:
unc ion [EQM]=PS_NE_1W(PayO _EV1,PayO _EV2,day_week,EQM)
%EQM =[C,C C,NC NC,NC NC,C] clockwise ac oss he 2x2 g id
o i=1:1:288 %decision block e e y 5 mins
i PayO _EV2(1,1,day_week*288+i) >
PayO _EV2(1,2,day_week*288+i) && PayO _EV2(1,1,day_week*288+i) >
PayO _EV2(2,1,day_week*288+i)
i PayO _EV1(1,1,day_week*288+i) >
PayO _EV1(1,2,day_week*288+i) && PayO _EV1(1,1,day_week*288+i) >
PayO _EV1(2,1,day_week*288+i)
%i bo h abo e s a emen s become ue hen C,C is a PS_NE
EQM(day_week*288+i,1)=1;
end
elsei PayO _EV2(2,2,day_week*288+i) >
PayO _EV2(1,2,day_week*288+i) && PayO _EV2(2,2,day_week*288+i) >
PayO _EV2(2,1,day_week*288+i)
i PayO _EV1(2,2,day_week*288+i) >
PayO _EV1(1,2,day_week*288+i) && PayO _EV1(2,2,day_week*288+i) >
PayO _EV1(2,1,day_week*288+i)
%i bo h abo e s a emen s become ue hen NC, NC is a
PS_NE
EQM(day_week*288+i,3)=1;
end
elsei PayO _EV2(1,2,day_week*288+i) >
PayO _EV2(1,1,day_week*288+i) && PayO _EV2(1,2,day_week*288+i) >
PayO _EV2(2,2,day_week*288+i)
i PayO _EV1(1,2,day_week*288+i) >
PayO _EV1(1,1,day_week*288+i) && PayO _EV1(1,2,day_week*288+i) >
PayO _EV1(2,2,day_week*288+i)

Es ima ion!o ! he!ne !cha ging!demand! om!p i a ely!owned!elec ic! ehicles!using!Game!Theo y! !65!
De !Mish a!
%i bo h abo e s a emen s become ue hen C, NC is a
PS_NE
EQM(day_week*288+i,2)=1;
end
elsei PayO _EV2(2,1,day_week*288+i) >
PayO _EV2(1,1,day_week*288+i) && PayO _EV2(2,1,day_week*288+i) >
PayO _EV2(2,2,day_week*288+i)
i PayO _EV1(2,1,day_week*288+i) >
PayO _EV1(1,1,day_week*288+i) && PayO _EV1(2,1,day_week*288+i) >
PayO _EV1(2,2,day_week*288+i)
%i bo h abo e s a emen s become ue hen NC, C is a
PS_NE
EQM(day_week*288+i,4)=1;
end
end
end
end
Func ion o Mixed S a egy Nash Equilib ium:
unc ion [Pa _EV1,Pa _EV2]=MS_NE(PayO _EV1,PayO _EV2,Pa _EV1,Pa _EV2)
o i=1:1:288 %decision block e e y 5 mins
syms sig_u exp_u il_l exp_u il_
syms sig_l exp_u il_u exp_u il_d
sig_P1=0;
sig_P2=0;
%playe 1 mixed s a egy
eqn1=exp_u il_l==sig_u*PayO _EV2(1,1,i)+(1-
sig_u)*PayO _EV2(1,2,i);
eqn2=exp_u il_ ==sig_u*PayO _EV2(2,1,i)+(1-
sig_u)*PayO _EV2(2,2,i);
eqn3=exp_u il_l==exp_u il_ ;
[A,B] = equa ionsToMa ix([eqn1, eqn2, eqn3], [sig_u,
exp_u il_l, exp_u il_ ]);
sol_1 = sol e([eqn1, eqn2, eqn3], [sig_u, exp_u il_l,
exp_u il_ ]);
sig_P1(i,1)=sol_1.sig_u;
i sig_P1>0 & sig_P1<1
Pa _EV1(i,5)=sig_P1;
end
%playe 2 mixed s a egy
eqn4=exp_u il_u==sig_l*PayO _EV1(1,1,i)+(1-
sig_l)*PayO _EV1(1,2,i);
eqn5=exp_u il_d==sig_l*PayO _EV1(2,1,i)+(1-
sig_l)*PayO _EV1(2,2,i);
eqn6=exp_u il_u==exp_u il_d;
[C,D] = equa ionsToMa ix([eqn4, eqn5, eqn6], [sig_l,
exp_u il_u, exp_u il_d]);
sol_2 = sol e([eqn4, eqn5, eqn6], [sig_l, exp_u il_u,
exp_u il_d]);
66! ! Mas e !Thesis!
! ! De !Mish a
! !
sig_P2=sol_2.sig_l;
i sig_P2>0 & sig_P2<1
Pa _EV2(i,5)=sig_P2;
end
end
end