Copyright 2016 Mushfiqur R. Sarker

Transcription

1 Copyrigh 2016 Mushfiqur R. Sarker

2 Elecric Vehicles as Grid Resources Mushfiqur R. Sarker A disseraion submied in parial fulfillmen of he requiremens for he degree of Docor of Philosophy Universiy of Washingon 2016 Reading Commiee: Miguel Orega-Vazquez, Chair Daniel Kirschen Baosen Zhang Program Auhorized o Offer Degree: Elecrical Engineering

3 Universiy of Washingon Absrac Elecric Vehicles as Grid Resources Mushfiqur R. Sarker Chair of he Supervisory Commiee: Professor Miguel Orega-Vazquez Elecrical Engineering Elecric vehicles (EV) are poised as environmenally-friendly alernaives o convenional combusion vehicles because of he inernal baery which uses elecriciy for ransporaion. I is esimaed he global EV peneraion will hi upwards of 20 million on he road by Even wih his echnology available oday, consumers EV adopion is hindered due o he high upfron cos, lack of adequae charging infrasrucure, range anxiey, and slow charging imes. On he oher hand, he poenial revoluion of he ransporaion secor will bring forh economic benefis o he operaions of he power sysem. The EV baeries allow flexibiliy in he amoun of power and he specific ime of day when hey can charge and discharge. Such feaures enable he exracion of resources from hese baeries in order o benefi he power sysem and EV owner s hemselves. However, he challenge remains on how o reduce he issues of EV ownership while he power sysem exracs services from EVs ha benefi operaions. The main moivaion behind his disseraion is o develop frameworks ha ake advanage of EVs as grid resources.

4 TABLE OF CONTENTS Page Abou he Auhor Acknowledgemens Glossary Lis of Figures Lis of Tables Lis of Publicaions vi vii viii xi xv xvi Chaper 1: Inroducion Background Issues peraining o EV adopion Lieraure Survey EVs performing in grid-o-vehicle mode EVs performing in vehicle-o-grid mode EVs and household appliance managemen Aggregaed paricipaion of EVs in power markes Required infrasrucure for he roll-ou of EVs Degradaion of baeries Summary Proposed Frameworks Ouline of he disseraion Chaper 2: Opimal Coordinaion and Scheduling of Demand Response of Residenial Consumer Loads i

5 2.1 Inroducion Aggregaor as an inermediary Incenives for demand response (DR) Framework Example: consumer s response o incenives Procuremen of DR: supply-demand economic principles Aggregaor Model Re-scheduling (RS) sage opimizaion Consumer Model Consumer pre-scheduling (PS) sage model Consumer re-scheduling (RS) sage model Appliance Models Elecric vehicle (EV) Elecric waer heaer (EWH) Heaing venilaion and air condiioning (HVAC) Refrigeraor (REF) Dishwasher, washing machine, and dryer Simulaion Resuls Impac of ariffs a he PS sage Miigaing line overloads wih incenives a he RS sage Disribuion sysem avoided coss Conclusion Chaper 3: Co-opimizaion of Disribuion Transformer Aging and Energy Arbirage using Elecric Vehicles Inroducion Transformer Model Consumer Perspecive Decenralized sraegy: consumer opimizaion model Aggregaor s Perspecive Cenralized sraegy: aggregaor co-opimizaion model Simulaion Resuls Decenralized versus cenralized sraegy ii

6 3.5.2 Effec on he ransformer life expecancy Tradeoff beween arbirage and ransformer damage Deermining he opimal replacemen ransformer raing Maximum poenial revenue of he aggregaor Conclusion Chaper 4: Opimal Paricipaion of an Elecric Vehicle Aggregaor in Day-Ahead Energy and Reserve Markes Inroducon Power sysem eniies Elecric vehicle s perspecive Aggregaor s perspecive Sysem operaor s perspecive Aggregaor Opimizaion Model Marke paricipaion Opimizaion model Simulaion Resuls Esimaion of he probabiliy of accepance/deploymen Cos/Benefi analysis wih varying baery price Offering sraegy of he aggregaor in he DA Sysem operaor s perspecive Conclusion Chaper 5: Opimal Marke Paricipaion of Aggregaed Elecric Vehicle Charging Saions Considering Uncerainy Inroducion Framework EVCS perspecive ESS Opimizaion Model Day-ahead model Demand uncerainy Marke price uncerainy Baery degradaion managemen iii

7 5.3.5 Complee DA model Case Sudy Opimal combinaion of sochasic scenarios and RO parameers Baery degradaion effecs Day-ahead schedules Yearly cos/benefi analysis Conclusion Chaper 6: Opimal Operaion and Services Scheduling for an Elecric Vehicle Baery Swapping Saion Inroducion Business Case Operaions Cusomer perspecive Power sysem benefis Opimizaion Model Assumpions Day-ahead model Demand uncerainy wih invenory robus opimizaion Price uncerainy wih muli-band robus opimizaion Baery degradaion coss Complee day-ahead model Case Sudy Small baery sock wih a single baery ype Large baery sock wih wo baery ypes Conclusion Chaper 7: Opimal Energy Sorage Managemen Sysem: Trade-off beween Grid Economics and Healh Inroducion Daa Analyics of Li-Ion Baeries Variable C-rae degradaion mechanism Variable efficiency mechanism Energy Sorage Opimizaion iv

8 7.3.1 Sandard model Variable C-rae degradaion Variable efficiency Case Sudy ES sysem operaions Conclusion Chaper 8: Conclusion Beneficiaries of he developed frameworks Suggesions for fuure work for oher researchers Appendix A: Mixed-Ineger Linear Programming (MILP) A.1 General Algebraic Modeling Sysem (GAMS) Appendix B: Linearizaion Techniques B.1 Special Ordered Ses of Type 2 (SOS2) B.2 Muliplicaion of coninous and binary variables Bibliography v

9 VITA Mushfiqur Sarker was born in Dhaka, Bangladesh in 1990 and has resided in Corvallis, Oregon, Unied Saes for he majoriy of his life. He received his BSc in Elecrical Engineering from Oregon Sae Universiy in Corvallis, Oregon on June 2012, wih an emphasis in Power Sysems. In Sepember 2012, he joined he Universiy of Washingon in Seale, Washingon, Unied Saes o pursue a PhD. He was awarded he Universiy of Washingon Clean Energy Insiue s Graduae Fellowship ( ) and also he Clean Energy Insiues Exploraion Gran ( ). In addiion, he received he Vikram Jandhyala and Suja Vaidyanahan Endowed Innovaion Award from he Universiy of Washingon. vi

10 ACKNOWLEDGMENTS This disseraion was financially suppored by he U.S. Naional Science Foundaion (Gran No ) and he Universiy of Washingon s Clean Energy Insiue. My umos graiude goes o my professor, Miguel A. Orega-Vazquez, for providing excellen guidance. His professionalism and commimen is a rai I will coninue o uphold in my career. I am also hankful o Professor Daniel S. Kirschen for providing excellen advice along he way. In addiion, hanks o all my colleagues a he Universiy of Washingon s MOVES and REAL research groups ha has assised me hroughou my PhD. Mos of all, his would no have been possible wihou he uncondiional suppor hroughou he years from my parens and my broher. They augh me wih hardwork I can achieve whaever I desire, a eaching I will coninue o follow in he years o come. In addiion, he consan encouragemen, suppor, and care I have received from my wife has allowed me o obain my PhD successfully. vii

11 ACRONYMS B2B: Baery-o-Baery B2G: Baery-o-Grid B2S: Baery-o-Saion BSS: Baery Swapping Saion CAISO: California Independen Sysem Operaor CDF: Cumulaive Disribuion Funcion DA: Day-ahead DR: Demand Response DSM: Demand Side Managemen DSO: Disribuion Sysem Operaor DW: Dishwasher EMS: Energy Managemen Sysem EMCHG: Energy Marke Charge EMDSG: Energy Marke Discharge ESOC: Energy Sae-of-Charge ES: Energy Sorage EPA: Environmenal Proecion Agency viii

12 EV: EV EVCS: Elecric Vehicle Charging Saions EWH: Elecric Waer Heaer G2B: Grid-o-Baery G2V: Grid-o-Vehicle HVAC: Heaing, venilaion, and air condiioning ICE: Inernal Combusion Engine LI-ION: Lihium-ion MILP: Mixed Ineger Linear Program MC: Mone Carlo NHTS: Naional Household Travel Survey PEV: PEV PJM: Pennsylvania-New Jersey-Maryland PQP: Price-Quaniy-Probabiliy PS: Pre-scheduling PV: Phoovolaics REF: Refrigeraor REGUP: Regulaion Up REGDN: Regulaion Down RES: Renewable Energy Resources ix

13 RO: Robus Opimizaion RS: Re-scheduling RT: Real-ime RTP: Real-Time Pricing SO: Sysem Operaor STOPCHG: Sop Charge STOPDSG: Sop Discharge SOS2: Special Ordered Ses of Type 2 TOU: Time-of-Use UC: Uni commimen V2G: Vehicle-o-Grid V2H: Vehicle-o-Home WM: Washing machine x

14 LIST OF FIGURES Figure Number Page 1.1 Comparison beween he cos of ravelling 27 miles for an average compac vehicle and an EV. Assumes a 27 miles per gallon gasoline vehicle (average compac fuel efficiency) and an EV efficiency of 0.34 kwh/mile (Nissan Leaf). Daa obained from [1] Theoreical example of he increase of EV demand on he base load wih coordinaed verse uncoordinaed G2V charging Price ariff srucures Ineracions beween he aggregaor and consumers Rolling window horizon Example of a single consumer s response o incenives β i a = Non-overload case in (a) and he overload case in (b) EV discharge power in V2H and V2G for (a) RTP and (b) ToU ariff Toal demand profile in PS wih one EV per household on (a) ToU wih EMS, and (b) RTP wih EMS (a) 30%, (b) 60%, (c) 100% peneraion showing demand in PS (black), and afer incenives are used in RS (red) (a) Damage cos for overloaded periods under RTP and (b) frequency of incenives paid Wihsand ime for 30%, 60%, and 100% EV peneraion in (a), (c), and (e), respecively. PV invesmen for 30%, 60%, and 100% EV peneraion in (b), (d), and (f), respecively Opimal consumer paricipaion in DR unil incenives are required Loss-of-life as a funcion of he loading on he ransformer for = 15 min. Noe ha he y-axis is logarihmic Revenue/paymens by he aggregaor from/o he consumer and DSO PDFs of he arrival ime o he home and deparure ime from he home (a), and rip ravel ime (b) xi

15 3.4 Dumb charging a 100%(6) EV peneraion, base load, and ransformer raing shown in (a), and he real-ime elecriciy ariff shown in (b) Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih only G2V enabled Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih V2G enabled Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih V2H enabled Transformer life expecancy in he dumb, cenralized, and decenralized sraegies under G2V (a), V2H (b), and V2G (c) operaions Toal EV discharge in (a) and arbirage daily profi/loss in (b) for differen sraegies and modes of operaion (V2G, V2H) Daily ransformer damage cos for he cenralized (a) and decenralized sraegy (b) wih varying EV peneraion Perpeual replacemen cos of ransformers in decenralized in (a) and cenralized in (b) for G2V, V2G, and V2H operaions. Noe ha resuls are shown for he 100% (6) EV peneraion case and he y-axis cos scales Decision ree for regulaion marke ineracions Acual revenues and coss when paricipaing in ancillary markes, where (a) is he case wih no penalies and (b) includes penalies Capaciy price and oal acceped capaciy quaniy complemenary CDF s shown in (a) and (b), respecively. In (c), he price-quaniy-probabiliy (PQP) curve is shown which is derived from he curves in (a) and (b) CDF of he oal profi obained by he aggregaor wih varying probabiliies. The baery cos is 250 $/kwh for all rials Iemized breakdown of he expeced revenue in (a) and coss in (b) wih varying baery cos. The expeced oal profis are shown in (c) (a) DA and RT energy price, (b) REGDN and REGUP capaciy prices, and (c) iemized breakdown of capaciy, energy, and esoc in he DA Offered, acceped, and acually deployed quaniy for (a) up reserves and (b) down reserves Aggregaor s ineracion wih he EVCSs, elecriciy marke, and power sysem. 99 xii

16 5.2 Day-ahead forecas of aggregaed EVCS demand a he workplace locaion (a), commercial locaion (b), and he oal sum of he wo (c). The inervals 50%, 90%, and 100% are shown o represen he spread of he daa. For example, 50% of he EVCS demand lies wihin he specified range Day-ahead marke price wih deviaion band for uncerainy Normalized cos CDFs for combinaions of sochasic scenarios and price robusness parameer Normalized average cos as a funcion of he number of sochasic scenarios Toal daily energy scheduled in he deerminisic case(a) and wih uncerainy managemen considered (b), as a funcion of varying ESS prices. Noe in (b) he average B2S is shown since i is a funcion of scenario s DA marke buying and selling sraegy in he deerminisic case DA marke buying and selling sraegy when uncerainy managemen is considered. Noe ha he average B2S is used in p buy wih ESS since i is dependen on he scenario se BSS ineracions wih cusomers, marke, and he power sysem Piecewise discoun funcion. The values in ( ) are used in he case sudies in Secion IV DA price deviaions wih muliple bands Disribuion of demand a BSS in (a), and uncerainy bounds in (b) Impac on B2G and B2B as baery capaciy cos decreases (a) Effec on baery shorage, discouns, and ne energy purchased, and (b) effec on B2G, G2B, and B2B services. B2G and B2B are referred o he lef-side-axis and G2B o he righ-side-axis Effec of price uncerainy on he energy injeced in B2G (a) and B2B (b) in p.u. (i.e. normalized over kwh) CDF for combinaion of robusness parameers for price and demand Probabiliy of resuling in he highes overall profi for all combinaions of θ 10% and θ 15% G2B and B2G (a), and B2B (b) services in he deerminisic case G2B and B2G (a), and B2B (b) services in he uncerainy case SoH measuremens of a Samsung INR18650 Li-ion baery cell a various C- raes xiii

17 7.2 The charge and discharge volage deviaion ( V) shown in (a) and (b), respecively, for a single cell Li-ion baery. The charging and power losses are shown in (c) and (d), respecively, for an ES sysem wih 200 kwh capaciy Piecewise approximaion of he SoH degradaion as a funcion of C-raes he ES sysem charges or discharges a in period RTP ariffs based on ime of he year and weaher, i.e. normal or high emperaures, obained from [2] Typical base demand in he winer, spring, summer, and fall seasons shown in (a), and power oupu of PV (p.u.) shown in in (b) ES sysem s DA power schedule in (a) and (b) for he case where variable C-rae and efficiency mechanisms are ignored and considered, respecively Yearly profi poenial of he ES sysem in (a) and yearly energy discharged in (b) while he ES price is varied xiv

18 LIST OF TABLES Table Number Page 1.1 Efficiency daa of common PHEV and EVs [3] Available EV charging levels [4] Typical household loads caegorized ino fully deferrable, deferrable bu noninerrupable, and non-defferable Decenralized o Cenralized Annualized Benefis Sysem Operaor s Coss Compuaional Times (seconds) Yearly Cos/Benefi Analysis xv

19 LIST OF PUBLICATIONS Journal Publicaions 1. Sarker, M. R.; Murbach, M. D.; Schwarz, D. T., Orega-Vazquez, M. A., Opimal Energy Sorage Managemen Sysem: Trade-off beween Grid Economics and Healh, in IEEE Transacions on Smar Grid, o be submied Augus Sarker, M. R.; Pandzic, H.; Sun, K., Orega-Vazquez, M. A., Opimal Marke Paricipaion of Aggregaed Elecric Vehicle Charging Saions Considering Uncerainy, in IEEE Transacions on Smar Grid, o be submied Augus Conreras Ocaña, J. E.; Sarker, M. R.; Orega-Vazquez, M. A., Decenralized Coordinaion of a Building Manager and an Elecric Vehicle Aggregaor, in IEEE Transacions on Smar Grid, Revise and resubmi July Olsen, D. J.; Sarker, M. R.; Orega-Vazquez, M. A., Opimal Peneraion of Home Energy Managemen Sysems in Disribuion Neworks Considering Transformer Aging, in IEEE Transacions on Smar Grid, Revise and resubmi June Sarker, M. R.; Olsen, D. J.; Orega-Vazquez, M. A., Co-Opimizaion of Disribuion Transformer Aging and Energy Arbirage Using Elecric Vehicles, in IEEE Transacions on Smar Grid, March 2016, Early Access. Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= xvi

20 6. Sarker, M. R.; Dvorkin, Y.; Orega-Vazquez, M.A., Opimal Paricipaion of an Elecric Vehicle Aggregaor in Day-Ahead Energy and Reserve Markes, IEEE Transacions on Power Sysems, November 2015, Early Access. Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= Sarker, M. R.; Orega-Vazquez, M.A.; Kirschen, D.S., Opimal Coordinaion and Scheduling of Demand Response via Moneary Incenives, IEEE Transacions on Smar Grid, vol. 6, no. 3, pp , May 2015 Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= Sarker, M. R.; Pandzic, H.; Orega-Vazquez, M.A., Opimal Operaion and Services Scheduling for an Elecric Vehicle Baery Swapping Saion, IEEE Transacions on Power Sysems, vol. 30, no. 2, pp , March 2015 Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= Conference Publicaions 1. Sarker, M. R.; Orega-Vazquez, M.A., Opimal Invesmen Sraegy in Phoovolaics and Energy Sorage for Commercial Buildings, in 2015 IEEE Power & Energy Sociey General Meeing, pp. 1-5, July Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= Sun, K.; Sarker, M. R.; Orega-Vazquez, M.A., Saisical Characerizaion of Elecric Vehicle Charging in Differen Locaions of he Grid, in 2015 IEEE Power & Energy Sociey General Meeing, pp. 1-5, July 2015 xvii

21 Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= Sarker, M. R.; Pandzic, H.; Orega-Vazquez, M. A., Elecric Vehicle Baery Swapping Saion: Business Case and Opimizaion Model, 2013 Inernaional Conference on Conneced Vehicles & Expo, Las Vegas, NV, USA, 2-6 Dec Link: ieeexplore.ieee.org/xpl/aricledeails.jsp?arnumber= xviii

22 1 Chaper 1 INTRODUCTION 1.1 Background The global rend is aiming owards he ransiion of he ransporaion secor from inernal combusion engine (ICE) vehicles, which use gasoline for moion, o elecric vehicles (EVs), which use elecriciy for moion. Such a push for he elecrificaion of he ranspor secor is occurring due o he effecs of climae change since ICE vehicles emi carbon dioxide emissions ino he amosphere. The Environmenal Proecion Agency (EPA) esimaed of he oal emissions in 2013, ransporaion was responsible for 27% wih elecriciy a 31% and indusry a 21% [5]. Wih elecrificaion, emissions can be reduced since a mix of renewable resources, e.g. wind and phoovolaics (PVs), and convenional generaion, e.g. coal, can be used o supply he energy needs of EVs. For such a scenario o occur, however, he EV peneraion mus increase. The global Elecric Vehicle Iniiaive esimaed he global EV peneraion in 2015 o be 665,000, which is more han a hree-fold increase from 2013 [6]. The elecrificaion is led by he Unied Saes a 39%, Japan a 16%, and China wih 12% of he oal EV populaion in 2015 [6]. This increase is in par due o he benefis EVs provide o consumers, which include lower day-o-day operaing coss (see Figure 1.1) and less emissions resuling in being environmenally conscience, along wih he social benefis of EVs being a sand-ou echnology. From he viewpoin of he power grid, he curren and increasing populaion of EVs brings forh boh benefis and challenges. The baeries inside EVs are no only beneficial for ransporaion purposes bu also o provide grid-relaed services [7, 8, 9, 10]. EVs are poised o effecively provide energy arbirage [8, 9, 10], volage regulaion [11], frequency regulaion [12, 13, 14, 15, 16], and backup

23 2 Figure 1.1: Comparison beween he cos of ravelling 27 miles for an average compac vehicle and an EV. Assumes a 27 miles per gallon gasoline vehicle (average compac fuel efficiency) and an EV efficiency of 0.34 kwh/mile (Nissan Leaf). Daa obained from [1]. power due o he on-demand charging and discharging capabiliies, known as grid-o-vehicle (G2V) and vehicle-o-grid (V2G) [17, 18], respecively. These modes can be conrolled by an energy managemen sysem (EMS) ha seeks o mee cerain objecives while considering he characerisics and behavior of he EVs. While EVs are seen as power grid resources, hey also inroduce challenges because of he addiional elecriciy consumpion required o mee ransporaion needs. This enails, in some cases, revamping of he power grid asses [8, 19], e.g. lines and ransformers, or even addiional generaion in order o accommodae he power needs. However, by managing he charging schedule of EVs, he curren grid can accommodae a large peneraion of EVs [7]. The benefis EVs provide o sociey far ouweigh he challenges, if properly managed. However, heir are several issues hindering he widespread adopion of EVs by consumers. The objecive of he following subsecion is o presen and discuss he issues relaed o EVs. 1.2 Issues peraining o EV adopion Even hough he adopion of EVs is increasing year-over-year [6], he rae is sill small compared o he immense vehicle populaion in he world. This is he case because of issues

24 3 Type All Elecric Range All Gasoline Range Toal Nissan Leaf EV BMW i3 EV Tesla Model S EV Toyoa Prius PHEV Chevrole Vol PHEV Table 1.1: Efficiency daa of common PHEV and EVs [3] peraining o range anxiey, slow charging imes, lack of infrasrucure, and upfron coss. Range Anxiey The noorious range anxiey has roubled curren and poenial EV owners [9, 20, 21]. Range anxiey is when he driver of an EV worries he baery will run ou of energy before he desinaion or a charging saion is reached. Majoriy of EVs are equipped wih Lihiumion (Li-ion) chemisry-based baeries due o heir high energy densiy [22, 23]. However, hese baeries have a shorer comparable all elecric range o heir equivalen ICE vehicles. EVs can be characerized ino wo subgroups, which are plug-in elecric vehicles (PEVs) and plug-in hybrid elecric vehicles (PHEVs) [4]. The PHEVs use a combinaion of an elecric baery and combusion engine for moion, whereas he PEVs are based on a pure elecric baery [4]. In general, PEVs have a larger capaciy elecric baery han PHEVs. Table 1.1 shows efficiency daa of common PHEV and PEVs [3]. As shown, he Tesla Model S has he larges all elecric range a 265 miles as compared o he Nissan Leaf, a 75 miles. On he oher hand, plug-in hybrid elecric vehicles such as he Toyoa Prius and Chevrole Vol use a combinaion of an elecric baery along wih a combusion vehicle for ransporaion and hus he oal range is much higher. In addiion, he issue of range anxiey is non-eviden in PHEVs because a any given ime, he consumers can approach a gasoline saion o replenish heir reservoir. Range anxiey can be miigaed by eiher improving baery echnology so he all elecric range is increased, and/or by insalling adequae EV infrasrucures. While research is

25 4 Requiremens Raing Typical Time Typical Cos AC Level I 120 vols/12 amps 1.6 kw < 17 hrs - AC Level II 240 vols/16 amps 3.3kW < 7 hrs $1,354 [27] DC Fas Charging 480 vols/125 amps 60 kw < 30 mins $10,000 [28] Table 1.2: Available EV charging levels [4] ongoing on he former, he laer is a mus for widespread EV adopion. Lack of Public Infrasrucure In mos counries, he infrasrucure for ICE vehicles, i.e. gasoline saions, is welldeveloped. However, such canno be said for EVs. In he Unied Saes alone, heir are 121,000 gasoline saions [24] as compared o he 12,922 EV charging saions (see [25] for a deailed map of EV saions) as of Innovaive companies such as ChargePoin [26] are developing neworks of public charging saions and is based on a pay-as-you-go and subscripion model. From an invesor s poin-of-view, however, hey may no inves in EV infrasrucure because he curren populaion of EVs may no be sufficien o generae revenue o offse he insallaion coss. A he same ime, here is a lack in EV peneraion because owners do no see sufficien public infrasrucures o jusify he purchase. Furhermore, charging saions may sill employ slow charging equipmen which does no benefi EV owners. Thus, more innovaive approaches of public charging need o be deployed in order o decrease wai-ime for EV charging. Slow Charging Times Unlike ICE vehicles which only require a few minues o fill up heir gasoline reservoir, EVs mus plug-in o an elecric source o be charged [7]. Such charging can ake approximaely minues o many hours depending on he vehicle and ype of infrasrucure, e.g. residenial charging can ake upwards of 7 hours 1. Currenly, for direc charging here are 1 Calculaions are based on characerisics of a Nissan Leaf EV wih a 24 kwh baery [29].

26 5 hree levels available, Level I, Level II, and Level III (DC Fas Charging) which are summarized in Table 1.2 [4]. In Table 1.2, Level I is when he vehicle plugs direcly ino a sandard power oule. The majoriy of EVs in he marke come pre-packaged wih Level I cordse which on one side conains he sandard SAE J1772 plug [4, 30] and on he oher side is a sandard household plug. These household oules are readily available in all locaions (i.e. residenial, workplace, and commercial), however, he radeoff is he large ime requiremens. On he oher hand, Level II requires insallaion of specialized chargers, e.g. [31], along wih poenial infrasrucure upgrades. Lasly, DC fas charging, i.e. Level III, is a specialized insallaion usually in public areas, e.g. Tesla supercharging saions [32], and hey resul in he fases charging in less han 30 minues 2 [1]. However, hey require specialized cordses o aach o EVs [4] and large invesmens in he equipmen. Upfron Coss Mos EVs, e.g. Nissan Leaf, Tesla Moors, among ohers, use Lihium-ion(Li-ion) baery chemisry. From 2012 o 2015, he price of Li-ion baeries has decreased from approximaely 500 o 300 $/kwh showing he benefi of economies of scale and innovaion in he field [33]. However, for a ypical EV (e.g. Nissan Leaf) ha houses a 24 kwh baery he cos of he baery was $12000 in 2012 o $7200 in Therefore, for a Nissan Leaf [29] priced a $29,000 reail, he cos of he baery ranged from approximaely 41% o 25% of he oal reail price from 2012 o 2015, respecively. This is a significan reason as o why EVs are priced much higher han heir radiional ICE counerpars as of However, he price per kwh baery is rapidly decreasing wih ime [34]. For example, he bes-in-class players, e.g. Panasonic, are expeced o have Li-ion prices a approximaely 170 $/kwh by 2025 [35]. This is a posiive sign for he adven of EVs. In addiion o such cos decreases, he upfron cos of EVs can be furher offse by exploiing he flexibiliy of EVs as grid resources and in reurn generae revenue or minimize he oal cos of energy consumpion.

27 6 The objecive of he nex secion is o presen a general overview of he soluions developed o ackle hese issues relaed o EVs from a power sysem poin-of-view. 1.3 Lieraure Survey In he early 1980s, i was firs discovered load managemen sraegies mus be in place o handle he adven of EVs [36]. Over he years, he concep of EVs being used as a variable energy sorage device ha can charge, i.e. G2V mode, and discharge, i.e. V2G mode [37, 38, 39], on-demand was inroduced and developed. Such conceps opened up research and indusry secors o he capabiliies of he EV baeries. However, hese capabiliies can only be harnessed if EVs are equipped wih bidirecional chargers and such research has been summarized in [39, 40]. From he poin of view of he power sysem, inensive research has been underaken o sudy he benefis of hese EV modes of operaion, e.g. see [41], o provide disribuion grid services, e.g. mainaining grid limis, by performing in G2V and V2G mode, or globally providing services in he wholesale elecriciy markes, i.e. regulaion and energy markes. The focus of his survey is on he works relaed o he use of EV baeries as grid resources. Previous works have aemped o exrac grid services from EVs in cenralized verses decenralized sraegies. Because wholesale elecriciy markes are no designed o manage large numbers of small consumers, profi-seeking eniies, e.g. aggregaors, are expeced o emerge and serve as coordinaors beween hese consumers and he wholesale markes [7]. On he oher hand, a he disribuion level, consumers may op o perform under an aggregaor where he eniy akes conrol of he EV operaions, or in a decenralized manner where he consumers manage he operaions of heir EV wih he use of an EMS. The paricipaion in any services or a combinaion hereof in a decenralized or cenralized manner can provide a recurring income which may make he vehicles an affordable alernaive. The following subsecions will focus on he curren works sudying EVs a he differen levels of he power grid, i.e. disribuion and ransmission, providing various ypes of grid services.

28 7 Consumpion Base Load Uncoordinaed G2V Coordinaed G2V Time (h) Figure 1.2: Theoreical example of he increase of EV demand on he base load wih coordinaed verse uncoordinaed G2V charging EVs performing in grid-o-vehicle mode Demand Response (DR) is a G2V service ha boh EV owners and he power grid can reap benefis from, if and only if properly implemened. EVs can perform DR by shifing heir charging in G2V mode o anoher period in ime o mee cerain objecives, e.g. o lower coss or o mee grid objecives, or by modulaing heir charging power. In general, research has shown majoriy of EVs end o arrive a heir final desinaion, i.e. home, a some poin in he afernoon (e.g hrs), and hus will begin charging immediaely if coordinaion echniques are no in place [42]. An example of G2V is shown in Figure 1.2 where if EVs are uncoordinaed hen he he base load will increase during he peak-hours of he day, as opposed o he coordinaed case where charging occurs in he nighime hours, i.e valley-filling. Such uncoordinaed operaions may cause sress o he local disribuion grid by overloading asses, e.g. ransformers and lines, and increases he oal sysem coss since peaking power plans mus come online o mee he increased power needs [7]. Several works have proposed mehods o manage EV charging in order o mee cerain oucomes and hese are summarized below: EVs can miigae renewable energy uncerainy, e.g. wind [43, 44, 45, 46] and PVs [47, 48].

29 8 EVs can mainain a consan consumpion profile, i.e. valley-filling [49, 50, 51], in order o reduce peaks and increase asse uilizaion. EVs can manage disribuion sysem limis [11, 52, 53, 54, 55, 56] o ensure hey are no violaed. The subsequen discussions will explore he works for each of he siuaions where an EV can provide DR EVs and renewable energy resources Renewable energy resources (RESs), e.g. wind, exhibi uncerainies and variabiliy in ime and power oupu. If hese issues are no compensaed, hen a any given ime heir may be an excess or defici of power on he sysem. The effec of hese uncerainies and variabiliies can be minimized wih he use of EVs and soluions have been developed in works [43, 44, 45, 46]. Specifically in [43, 44, 45], opimal algorihms are developed for managing he EVs while considering he wind as an inpu. However, hese approaches ignore he sysem-wide operaing coss of inegraing wind and EV resources, which he approach in [46] considers. In he realm of RESs, PVs are also an uncerain resource ha can cause significan issues a he disribuion level, such as volage deviaions [47]. For example, cloud coverage can cause PVs o decrease from a high oupu of power o close o zero oupu in a small amoun of ime. Such issues can also be managed wih EVs and opimal frameworks were developed in works [47, 48] EVs performing demand response and managemen of grid limis Anoher echnique o manage EV charging is o mainain a consan demand profile, or also known as valley-filling shown in Figure 1.2. The work in [49] developed a conrol algorihm using non-cooperaive games o shif EV consumpion o nighime hours in an aemp o keep he charging consan over many hours. The algorihm in [49] can perform in a decenralized manner where minimal communicaions is required o reach he global

30 9 opimum. Similar o [49], he work in [50] develops an opimizaion model and considers explicily he EV owners convenience. Anoher work [51] bridges he communicaion barrier beween he power uiliy and EVs using a conrol signal o reach he same valley-filling oucome. Oher echniques aemp o use EVs o ensure proper grid limi mainenance such as power losses [52], nodal volage deviaions [11, 53], and ransformer capaciy limis [54, 56, 57, 58, 55]. As for power losses, he work in [52] developed an opimizaion algorihm o shif charging o minimize disribuion sysem power losses in a cenralized manner. On he oher hand, volage deviaions are more eviden in disribuion grids because of he laeral design of he sysem as compared he neworked ransmission grid [59, 60]. In [11, 53], opimal algorihms were developed o schedule EVs in a cenralized way ha mainains volages wihin defined bounds. As for ransformer capaciy violaions, i is expeced ha EVs will ypically be conneced o chargers locaed in residenial homes, which are conneced o local pole-op disribuion ransformers. Wih he increased EV load, such ransformers will be more likely o experience capaciy overloads resuling in acceleraed aging (or also known as loss-of-life) as assesed in [61, 62]. To miigae such adverse effec of overloads, operaing models are developed ha caer EV charging behavior in [54, 56, 57] and appliance behavior in [58] o he dynamics of he ransformer. All of hese algorihms ha use EV load managemen o benefi he power grid, i.e. [11, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58], do no consider he impac of heir approaches o he economics of EV owners. Essenially, he elecriciy ariff consumers are subjec o from heir power uiliy company is ignored and hus he algorihms force charging behaviors ha may no be in he bes ineres for he consumers. On he oher hand, he power indusry is slowly ransiioning consumers, albei mosly he commercial ones (see Duke Power [63] and Souhern California Edison [2]), o ime-varying elecriciy ariffs since i moivaes demand response (DR) naurally. However, pilo projecs such as he Pacific Norhwes Smar Grid Demonsraion Projecs [64] have discovered ha even residenial consumers find benefis in such arriffs, e.g. real-ime pricing (RTP) and ime-ofuse (ToU). Examples of hese ariffs along wih he convenional fla ariff is shown in Figure

31 10 Tariff ($/MWh) RTP ToU FLAT Time (h) Figure 1.3: Price ariff srucures 1.3. If EV owners are under RTP (or even oher less ime-varying srucure such as ToU) in he near fuure and such algorihms are implemened, hey will be worse off economically and will op o perform heir own decenralized managemen o reduce elecriciy bills, hus leading o poenial damage o he grid. This is he case because each of he algorihms aemp o mee some sysem need by exploiing he EV baeries. However, if EV baeries are used as grid resources hen hey mus be compensaed for heir services economically. As a soluion, incenive mechanisms mus be in place o compensae consumers for assising he sysem s well-being. The work in [65] aemps o develop a mechanism of giving coupon incenives on op of fla price ariffs, however, by using fla ariffs EVs canno provide services economically due o he lack of change in prices EVs performing in vehicle-o-grid mode Time varying-ariff srucures enable V2G o be economic for EV owners, if proper echniques are implemened. Energy arbirage wih EV baeries is a echnique ha explois he difference in prices during he day o obain furher revenue for he owners. For example, an EV can charge in he nighime periods of he day in G2V mode when elecriciy prices are low and hen discharge in V2G mode in he evening hours of he day when prices are high. Several works developed operaing models of arbirage in he local disribuion grid under ime-varying ariffs [10, 18, 66, 67, 68]. The underlying goal of hese models was o

32 11 use V2G o increase revenue for consumers, as opposed o sole G2V operaions. However, because V2G requires addiional charging o sore energy in he baeries o be discharged laer, he EV baeries will undergo life cycle degradaion (see [10, 69]) in addiion o he expeced degradaion for ransporaion energy needs. Thus, models for V2G applicaions mus consider he cos of degrading he baery verses he revenue colleced from performing arbirage or oher such services ha require discharging acions [10]. Unlike [18, 66, 67, 68], he work in [10] developed an opimal framework considering such degradaion rade-offs for arbirage. From[10], i was concluded he poenial cos savings o consumers is decreased as a funcion of he EV baery coss. Thus, addiional sreams of revenue mus be inroduced in order o assis he widespread adopion of EVs and one such approach is o combine he managemen of EVs wih household appliances, which do no experience degradaion similar o baeries EVs and household appliance managemen Consumers can, as an ensemble, manage EV arbirage wih scheduling of household appliances such as elecric waer heaers (EWH) [70], heaing, venilaion, and air condiioning (HVAC) [71], refrigeraors (REF) [72], among ohers. Table 1.3 shows ypical appliances found in residenial home organized ino hree caegories: fully-deferrable, deferrable bu non-inerrupable, and non-deferrable. Loads such as EWHs, HVACs, and REFs are hermosaically-conrolled and hus have ineria which can be sored for a period of ime. For example, a smar EMS can pre-schedule he EWH o urn ON during he nighime hours when prices are low in order o pre-hea waer for he consumers when hey wake up. This way appliances can be predicive in order o lower he elecriciy bill of consumers. This ype of smar home conrol has been he focus of much research and indusry producs. The research works in [73, 74, 70, 75, 76, 71, 72] developed frameworks o schedule household appliances. Specifically in [73, 74], opimal scheduling models are developed for arbirary appliances ha have pre-deermined energy requiremens bu accuracy is reduced because hermal ineria is no considered. The approach in [75] developed an opimal conrol

33 12 Deferrable Fully Non-Inerrupable Non-Deferrable EV EWH HVAC REF Washing machine Dishwasher Dryer Lighs TV Table 1.3: Typical household loads caegorized ino fully deferrable, deferrable bu noninerrupable, and non-defferable. algorihm and[76] developed a heurisic algorihm, however, boh considered pre-deermined emperaure hresholds of appliances, i.e. if he hreshold is reached, appliance mus urn ON or OFF. Accurae models of hermal inerial response of appliances were considered in [70, 71, 72] for cerain appliances and hen embedded ino conrol algorihms. A common shorcominginallofheseworks[73,74,70,75,76,71,72]isinhedevelopmen ofacomplee household EMS ha considers he opimal scheduling of all appliances(e.g. hermosaicallyconrolled loads, loads such as washing machines, and especially EVs) as an ensemble wih he goal o minimize elecriciy coss for consumers. A he indusry-level, companies are researching and developing innovaive echnologies for appliance managemen. A he forefron is he Nes Thermosa which is capable of scheduling HVAC s by learning he consumers day-o-day behavior [77]. This is seen as a rerofi o he curren hermosa in he household. On he oher hand, smar appliances are being developed, e.g. EWHs [78], which include learning algorihms and bi-direcional

34 13 communicaion. Ohers are developing digial plaforms, e.g. [79, 80], where consumers can visualize and conrol heir energy consumpion in real-ime. Even hough he benefis of reduced elecriciy bills, insigh ino appliance consumpion, and real-ime conrol are viable wih a complee smar home, pracically i may be expensive [81]. For example, in he case of an EWH, he smar appliance counerpar has a 50% increase in is price as compared o he convenional appliance [78]. However, he innovaive players in his indusry are reducing coss quickly o make i affordable for he average consumer. As an alernaive, however, furher revenue can be colleced from jus he EVs if consumers paricipae in more services Aggregaed paricipaion of EVs in power markes WhilemanagingappliancesisoneopionooffsehecosofEVs, anoheropionisoexrac addiional services from EVs insead of solely relying on G2V and/or V2G a he disribuion level. Due o he fas response of EV baeries [17], hey are poised o provide energy and/or ancillary services a he ransmission level, hrough he wholesale power markes. Specifically, EVs do no have sarup or shudown coss compared o convenional generaion and hus he provision of ancillary services (i.e. in he regulaion marke) from EVs leads o lower sysem coss [13]. However, due o he capaciy resricions se forh by wholesale power markes, e.g. 1 MW minimum capaciy in Pennsylvania-Jersey-Maryland (PJM) [82] and 0.1 MW in California Independen Sysem Operaor (CAISO) marke [83], hierarchical agens mus aggregae a large flee of EVs. An EV owner may be moivaed o paricipae under an aggregaor because hey receive addiional compensaion, and do no need o manage he day-o-day operaions. The laer moivaion is only viable if he aggregaor provides guaranees each vehicle will receive heir energy needs for ransporaion. Research has been conduced on he business and operaing models of aggregaors for marke paricipaion [84, 13, 16, 85, 86, 87, 14, 88]. The approaches can be characerized ino wo sraegies, where he firs includes separae paricipaion in he energy marke [84] and regulaion marke [13, 16], or he second considering a combined paricipaion sraegy in boh markes

35 14 [85, 86, 87, 14, 88]. The separae paricipaion in markes poses concerns. The firs prioriy of EV owners is o receive heir energy needs for ransporaion. However, he ancillary markes have limied capaciy requiremens pre-defined by he power sysem operaor (SO) and hus bids/offers by aggregaors can be rejeced if no compeiive. Therefore, relying on such markes for ransporaion needs may resul in a lack of energy for EV owners. While he energy marke is also compeiive in naure in erms of bidding/offering, any paricipan may purchase elecriciy a he marke clearing price in any given period (i.e. a price-aker) [89]. On he oher hand, approaches ha only consider he energy marke paricipaion are foregoing poenial revenue from he regulaion marke, as was done in [84]. As a soluion, approaches in [85, 86, 87, 14, 88] co-opimize he paricipaing in boh markes simulaneously o deermine offering/bidding sraegies. In [85] and [87], he core assumpion is ha he aggregaor paricipaes in ancillary markes on privileged erms, i.e. aggregaor s offers ino he marke are always acceped and is revenue is fixed a a cerain percenage of is capaciy being deployed in he real-ime, e.g. 10%. However, in pracice he aggregaor s revenue depends on he oucome of a compeiive marke process [90]. Furhermore, in [86], he aggregaor is assumed o submi quaniy-only zero-price bids (e.g. 10 MW a 0 $/MW represening price-aker bids) ino boh markes, hus assuming he ancillary service offers will be acceped. This assumpion, however, may reduce he revenue if he acual accepance is no as anicipaed by he aggregaor. A common shorcoming in [84, 13, 16, 85, 86, 87, 14, 88] is he use of simplified marke clearing procedures of he SO, which has an impac on he poenial revenues obained by he aggregaor in a real-life deploymen. Addiionally, he approaches do no consider he effec and compensaion of EV baery cycling degradaion, which if considered would aler he paricipaion sraegy in each marke for he aggregaor. A complee model mus sudy he economic rade-offs of boh markes in a realisic marke environmen while considering degradaion.

36 Required infrasrucure for he roll-ou of EVs In summary, he aforemenioned approaches provide revenue sreams for residenial consumers ha can offse he large upfron cos of owning an EV. The consumers will essenially have a choice of eiher paricipaing in services via an aggregaor, or individually, which has limied opions (i.e. energy arbirage) because individual marke paricipaion is no viable. As a profi-seeking business eniy, he aggregaor may need o provide addiional compensaion or producs (e.g. insallaion of a free EMS in homes) o enice a large enough flee of consumers loads, e.g. EVs and poenially oher loads such as EWHs, for a viable business. While EVs will spend mos of heir ime parked a heir residenial homes and can provide services as discussed, oher imes will be spen a he workplace or commercial locaions [42, 91]. I has been shown ha wih public (i.e. workplace and/or commercial) EVCS infrasrucure in place, 1 in 73 people would drive an EV, as opposed o he naional average of 1 in 1400 in he US [92]. Therefore, adequae EV charging infrasrucure is needed o ease range anxiey. Such charging infrasrucure may be in he form of parking los equipped wih chargers [93] or charging saions sraegically placed in a ciy [94, 95]. To properly allocae infrasrucure, he raffic roues of EVs along wih power grid limiaions mus be considered as was done in [93]. In [95], he allocaion opimizaion considered he disance beween each charging saion insallaion in order o ensure he daily journey needs of EVs are me. However, once allocaion of infrasracure is performed, operaing procedures mus be developed EV charging saions (EVCS) The public infrasrucure ha is poised o provide such needs are public AC and/or DC, i.e. fas charging, elecric vehicle charging saions (EVCS) insalled a commercial and workplace locaions [96]. A ypical charging saion can provide EVs power ranging from 1.6 o 7.2 kw (Level 1-2 proocols) and up o 120 kw of power using DC Level 3 proocol [96]. Several works have developed operaing operaing procedures for hese saions o inerac

37 16 wih each individual EV cusomer, such as done in [97, 98, 99], or wih he power grid, such as in [93, 100, 101, 102, 103, 104]. Specifically, [93] developed a wo-sage framework, where in he firs-sage he profis from an ensemble of charging saions paricipaing in energy and reserve markes is considered. On he oher hand, [100] considered in he real-ime, he scheduling of boh he charging saions and commercial buildings. Such an approach ensured he coordinaed charging is economically jusified for boh EVs and buildings ha hos he saions. The approaches in [93, 100] scheduled EVs solely considering he impac o he power grid, however, he work in [101] explored he viewpoin of EV owners as well. Furhermore, [101] showed alernaive approaches, e.g. [93, 100], ha manage EV charging o mainain he grid may conradic EV owners requiremens. Opimal sizing and operaion of an ESS for charging saions is sudied in [102] such ha energy procuremen and ESS operaional coss are minimized. A rule-based conrol algorihm was developed in [103] ha roues power beween he saion, grid, ESS, and phoovolaics. In [104], a scheme is developed ha allocaes power from he grid plus ESS o a nework of charging saions and also roues EV cusomers. In addiion, he EVCSs have no only been considered in heory. Commercial businesses have developed around his concep o ake advanage of he growing EV peneraion. This secor includes eniies ha insall, e.g. General Elecric [105], among ohers, and hose ha boh insall and manage EVCSs, e.g. ChargePoin [26], Tesla Moors [32], among ohers. For eniies ha manage EVCSs, heir revenue sreams are based on he money colleced from each EVs charging needs, and for he case of Tesla Moors, heir charging nework is free o use for heir EV models. In general, EVCS are seen as large invesmens because of he required equipmen, poenial grid rerofis, and licensing permi coss. These coss can be offse if saions operaed similar o an aggregaor and hus managed he charging and discharging as ensembles o paricipae in wholesale markes, or simply exploi reail ariffs provided from heir power uiliy (e.g. RTP or ToU).

38 Alernaive o EV charging saions While adequae infrasrucure will aid in he widespread adopion of EVs, i is also crucial o deploy he ype of infrasrucure ha will ease he ensions of owning an EV. The issue of slow charging will sill be eviden wih public EVCSs since hey will end o use Level II charging, see Table 1.2. A soluion o his is fas charging saions using Level III echnology, however, hen he issue of fas degradaion of he baery comes ino play. An alernaive soluion presened by he indusry and research communiy is baery swapping saions (BSSs). These saions resemble radiional gasoline saions, where a consumer arrives a hesaionandaswapisperformedofheirdepleedbaerywihafullychargedonehahe BSS keeps in sock [106, 107, 108]. Real-life applicaions have shown his operaion can be performed even quicker han filling a gasoline ank [109]. Several pioneering research works have developed operaing (e.g. [110, 111, 112]) and business models (e.g. [106, 107, 108]) for BSSs. In [110], he opimal locaions where BSS can be insalled and operaed in disribuion sysems are deermined. In his model, he ype of load, he required reinforcemens o he disribuion sysem, and reliabiliy of he sysem are explicily considered. However, he EV model uses a heurisic approach o deermine charging/discharging schedules. An economic dispach model ha uses BSS o manage wind power inermiency is developed in [112]. In [111], he number of baeries o be purchased along wih heir charging schedules are deermined using a basic dynamic programming framework. However, he number of baeries purchased depends on he scheduling model of he EV baeries which, in such an approach, is simplified o a wide exen. A common shorcoming of all he BSS works is he ineracion wih he elecriciy markes which can generae addiional revenue, since in essence he BSS can operae similar o an EV aggregaor. The business aspec of he BSS has also been he subjec of research. The idea of a subscripion pricing srucure, along wih he required infrasrucure cos, is presened in [107]. The associaed risks, classificaion of invesmens, and poenial services ha could

39 18 be sold by he BSS are invesigaed in [106]. The deailed cos analysis required for he sarup of a BSS is performed in [108]. However, hese models are simplified since hey do no consider he ineracions beween he BSS and he power sysem. The BSS business and operaing models have no only been reaed in heory. Commercial businesses have developed around he BSS concep o ake advanage of he exising EV populaions. For example, he company Beer Place in 2012 insalled muliple saions ha handle specific ype of EVs [113]. In 2013, Tesla Moors inroduced baery swapping echnology for heir EVs and in lae 2014, deployed heir firs pilo saion in California [109]. Also, several uiliies in China insalled BSSs for heir EV populaion in 2013 [114]. However, he profis in such acual BSSs are enirely dependen on he fees charged for baery swapping, and ignore he exra revenue ha could be colleced by paricipaing in he energy and ancillary services markes. Alogeher, a complee operaing and business model of a BSS mus consider he ineracions wih EV owners and he wholesale elecriciy markes o maximize is revenue poenial Degradaion of baeries EVs are equipped wih baeries, which in mos cases are Li-ion based chemisries. Baery energy sorage (ES) sysems, such as available in EVs, are highly beneficial if exploied for power grid services. However, by doing such exploiaion, hey undergo adverse degradaion effecs ha mus also be aken ino consideraion. In mos cases, however, research has been segregaed ino works on chemical properies, e.g. [115, 116, 117, 118, 119] of Li-ion baeries o hose who develop models for heir exploiaion, e.g. [8, 9, 10, 120]. Some pioneering works exis on bridging he gap beween baery chemisry mechanisms and grid economics [10, 121, 122]. In [121], baery ES is explored in he conex of a microgrid considering boh cycle-life degradaion and power losses due o he charging/discharging. Addiionally, he radeoff beween charge opimizaion and baery degradaion were explored in [10, 122] for EV Li-ion baeries. The work in [10] developed an operaing model considering an economic indice for cycle-life degradaion agains power grid revenues. Such

40 19 an approach enables eniis, e.g. aggregaors, o reimburse cusomers for exploiaion of heir baeries for grid services. Wihou such mechanisms in place, EV owners are unlike o paricipae since heir baeries are being degraded. The baery ES sysems are reaed as asses o sakeholders. Therefore, o economically exploi such sysems, he economic cos of degrading he baeries mus be aken ino consideraion in he day-o-day operaing frameworks Summary This survey presened he landscape of EV developmens in he research communiy and indusry. I can be seen EVs are poised as excellen resources for grid services. They can be managed eiher solely by he owner or a hierarchical eniy, such as an aggregaor. They can provide services when charging a home, workplace, or commercial locaion. For he widespread adopion of EVs, furher research is required o exrac services from EVs o generae more revenue for owners. In addiion, he issues of slow charging imes and range anxiey, can be managed by insalling proper EV infrasrucures ha can provide services o he grid and hus generae profis. The nex secion discusses he proposed frameworks developed in his disseraion o ackle such issues. 1.4 Proposed Frameworks In his disseraion, six frameworks are developed ha overcome issues wih EVs: range anxiey, slow charging imes, lack of public infrasrucure, and EV coss. In he firs proposed framework, he focus is on exracing services from a residenial household o aid he power grid in miigaing disribuion line overloads. Each consumer is equipped wih an EMS ha opimizes he operaion of appliances, including EVs, in order o minimize he elecriciy coss. However, if all consumers selfishly opimize heir own benefis agains an elecriciy ariff, e.g. RTP, hen heir will be syncing of power consumpion. This will lead o overloads in he disribuion power grid. Therefore, a hierarchical aggregaor can provide moneary incenives o consumers in order o moivae demand response shifing

41 20 from overloaded periods o normal periods. The aggregaor performs is own opimizaion o maximize profis while deermining he leas-cos allocaion of consumer demand response. Overall, his framework allows he consumers o obain addiional revenue by using heir conrollable loads o ake advanage of energy arbirage and he poenial incenives from he aggregaor. Essenially, hese addiional revenues can provide a jusificaion for offseing he coss o own EVs. In addiion, i develops a business model of an aggregaor o ake par in he day-o-day operaions of coordinaing a large ensemble of consumers. Sarker, M. R.; Orega-Vazquez, M.A.; Kirschen, D.S., Opimal Coordinaion and Scheduling of Demand Response via Moneary Incenives, IEEE Transacions on Smar Grid, vol. 6, no. 3, pp , May 2015 In he second proposed framework, he aggregaor model is furher developed o manage he effec EV charging/discharging on disribuion ransformers. Majoriy of EVs are expeced o be plugged-in and charging a residenial homes. Such residenial homes are conneced o pole-op disribuion ransformers, which will overload wih he addiion of EV loads. As a consequence, ransformers will experience acceleraed aging and hus loss-of-life will occur. An aggregaor framework is developed ha co-opimizes EV charging/discharging behavior and ransformer aging in order o deermine an opimal radeoff beween EV arbirage revenue and ransformer aging coss. This framework can be seen as an exension of he firs proposed framework based on moneary incenives, since he aggregaor mus compensae EVs in order o manage heir emporal charging behavior and his resuls in addiional reducion of coss. This framework is based on he following work: Sarker, M. R.; Olsen, D. J.; Orega-Vazquez, M. A., Co-Opimizaion of Disribuion Transformer Aging and Energy Arbirage Using Elecric Vehicles, in IEEE Transacions on Smar Grid, March 2016, Early Access. In he hird proposed framework, he aggregaor model is furher developed o ake advanage of he wholesale markes, including energy and secondary regulaion. EV baeries

42 21 can be used o exrac boh energy and regulaion services o he grid. However, hese services can only be provided if hey are economically jusified agains he cos of degrading he baery by addiional charging/discharging beyond ransporaion needs. Therefore, a model is developed where an aggregaor manages a large flee of EVs o deermine is bidding and offering schedule in he power markes, while considering he economics of providing such services. The EV owners obain addiional revenue from allowing an aggregaor o use he vehicle o paricipae in boh markes. Wih his framework along wih he incenive framework, he revenue colleced by EV owners will help offse EV coss and essenially increase he adopion. This framework is based on he following work: Sarker, M. R.; Dvorkin, Y.; Orega-Vazquez, M.A., Opimal Paricipaion of an Elecric Vehicle Aggregaor in Day-Ahead Energy and Reserve Markes, IEEE Transacions on Power Sysems, November 2015, Early Access. The previous hree frameworks explored aggregaor business models for he residenial secor, i.e. consumers. In he fourh proposed framework, a differen business model for an aggregaor is explored where i manages elecric vehicle charging saions as ensembles. In addiion o residenial charging, EVs are also expeced o obain energy from charging saions insalled in commercial and workplace locaions. This will require infrasrucure in he form of charging saions. The infrasrucures energy needs will be procured hrough a power uiliy, which may no have he capaciy o provide such volaile and highpower needs on-demand and canno provide energy a he minimal cos. As a soluion, an aggregaor can manage an ensemble of charging saions in order o paricipae in wholesale elecriciy markes o reduce energy porecuremen coss. The benefis of his framework is hreefold: 1) he saions can focus on heir business model of providing services o EV cusomers insead of aemping o minimizing energy coss, and 2) he charging saions do no need o change heir business procedures o conform o he aggregaor s framework. This framework is based on he following work:

43 22 Sarker, M. R.; Pandzic, H.; Sun, K., Orega-Vazquez, M. A., Opimal Marke Paricipaion of Aggregaed Elecric Vehicle Charging Saions Considering Uncerainy, in IEEE Transacions on Smar Grid, o be submied Augus 2016 In he fifh proposed framework, he issue of EV infrasrucure is ackled. An operaing and business model is developed for a BSS. This BSS resembles a radiional gasoline saion, where consumers arrive a he saion wih heir depleed baeries and receive a fully charged baery in reurn. The BSS has a sock of EV baeries which mus be scheduled o be ready for incoming cusomers ha require a swap. The oucome of he operaing model is a bidding and offering sraegy o paricipae in he wholesale energy marke in order o generae revenue. The deploymen of BSSs can reduce issues of range anxiey and slow charging imes, since consumer s can do a swap wih a fully charged baery. Overall, his proposed BSS framework is a viable alernaive o charging for EV owners and also inroduces a business eniy in he power sysem ha exracs services from EV baeries. This framework is based on he following work: Sarker, M. R.; Pandzic, H.; Orega-Vazquez, M.A., Opimal Operaion and Services Scheduling for an Elecric Vehicle Baery Swapping Saion, IEEE Transacions on Power Sysems, vol. 30, no. 2, pp , March 2015 In all of hese frameworks, he common elemen is baery energy sorage sysems, eiher mobile such as equipped in EVs or saionary. Improved operaing models of such energy sorage sysems can lead o addiional revenue generaion or even exended cycle-life. The research on such sysems, however, has ypically been segregaed ino focus on he chemisry and maerial properies and focus on he grid inegraion, operaion, and economic performance (such as done in he previous frameworks). This gap is noorious in boh he research communiy and in commercial usage of baeries; especially for grid applicaions where he day-ahead marke-based decision-making ools use simplified models ha limi he operaions of he baery because he baeries cycle-life degradaion and charging/discharging

44 23 efficiencies are no properly characerized. The sixh proposed framework proposes a daadriven mehodology o characerize energy sorage sysems embedded ino a decision-making opimizaion model. Such daa-driven approaches enable he major baery characerisics along wih grid economics o be co-opimized as a mixed ineger linear program, which benefis from low compuaional burden and opimaliy. This proposed framework improves he operaions of energy sorage sysems for addiional revenue generaion for boh EVs and saionary applicaions. This framework is based on he following work: Sarker, M. R.; Murbach, M. D.; Schwarz, D. T., Orega-Vazquez, M. A., Opimal Energy Sorage Managemen Sysem: Trade-off beween Grid Economics and Healh, in IEEE Transacions on Smar Grid, o be submied Augus 2016 In general, hese approaches arge several problems, such as offseing he upfron coss of owning an EV, slow charging imes, public infrasrucure, and range anxiey. By providing soluions o hese issues, i may assis he increased adopion of EVs. In addiion, from a business sandpoin, he proposed frameworks inroduce new players in he marke, e.g. an aggregaor, whose roles are o essenially manage he day-o-day operaions of large flees of conrollable loads, e.g. EVs. These frameworks are organized and presened as described in he following subsecion. 1.5 Ouline of he disseraion Chaper 2: Opimal Coordinaion and Scheduling of Demand Response of Residenial Consumer Loads In Chaper 2, he firs proposed framework is developed and resuls are shared. The mixed-ineger linear program (MILP) is developed for boh he consumer and he aggregaor. The consumer aemps o minimize coss, while he aggregaor aemps o maximize profi. The framework includes wo sages, where in he firs, he consumers provide heir opimal schedule of loads, and if overloads are presen, he aggregaor iniiaes he second

45 24 sage where incenives are used. Resuls are shown on he effeciveness of incenives o miigae overloads on disribuion feeder lines. Chaper 3: Co-opimizaion of Disribuion Transformer Aging and Energy Arbirage using Elecric Vehicles In Chaper 3, he second proposed framework is developed. An opimizaion model is developed for an aggregaor co-opimizing he radeoff beween EV charging/discharging behavior and disribuion ransformer aging. Resuls are presened on he model s effeciveness in managing many EVs conneced o a disribuion ransformer, while in some cases even increasing he poenial lifeime. Chaper 4: Opimal Paricipaion of an Elecric Vehicle Aggregaor in Day- Ahead Energy and Reserve Markes In Chaper 4, he hird proposed framework is developed. The opimizaion problem is developed for an aggregaor managing a large flee of EVs. The model considers he power marke srucures for he energy and regulaion marke. The model is flexible o be applied o any marke. The model considers he rade-off of paricipaing in he energy verses he regulaion marke, while considering baery degradaion. Resuls are presened on he revenue poenial for he aggregaor. Chaper 5: Opimal Marke Paricipaion of Aggregaed Elecric Vehicle Charging Saions Considering Uncerainy In Chaper 5, a framework is developed for an aggregaor o manage an ensemble of elecric vehicle charging saions. The framework includes he business case for he aggregaor along wih he day-o-day bidding/offering model in he wholesale elecriciy markes. Resuls are shown on he revenue poenial of he aggregaor along wih he benefis of managing uncerainy in he elecriciy marke prices and he aggregaed charging saion demand, which are boh highly volaile.

46 25 Chaper 6: Opimal Operaion and Services Scheduling for an Elecric Vehicle Baery Swapping Saion In Chaper 6, a framework is developed for he BSS. The framework includes he business case for he BSS along wih he day-o-day operaing model. The discussions include he benefis of he BSS o consumers and he power sysem. Resuls are shown on he revenue poenial of he BSS along wih he benefis of managing uncerainy in he elecriciy marke prices and consumer swapping demand. Chaper 7: Opimal Energy Sorage Managemen Sysem: Trade-off beween Grid Economics and Healh In Chaper 7, a daa-driven mehodology and opimizaion model is developed for exploiing baery-based energy sorage sysems a high power (high C-rae) oupus while characerizing he effec on degradaion and efficiencies. Resuls are shown on he poenial revenue benefis wih such a model. Chaper 8: Conclusion In Chaper 8, conclusions are provided for his disseraion.

47 26 Chaper 2 OPTIMAL COORDINATION AND SCHEDULING OF DEMAND RESPONSE OF RESIDENTIAL CONSUMER LOADS 2.1 Inroducion In his chaper, he moivaion is o exploi he flexibiliy of conrollable loads (e.g. see Table 1.3) for DR and in reduce elecriciy bills of consumers [8]. To provide DR, however, consumers mus be equipped wih an EMS which schedules conrollable loads while communicaing wih grid eniies. An EMS s objecive is o minimize he elecriciy bill of consumers by scheduling loads, which include hermal loads such as an EWH, HVAC, REF, and non-hermal loads such as washing machines (WM), dishwashers (DW), and EVs, as an ensemble. However, he savings are highly dependen on he elecriciy ariff and examples of fla, ToU, and RTP are shown in Figure 1.3. The EMS can exploi elecriciy ariffs by opimizing he conrollable loads o be scheduled o urn ON during he low-price periods of he day. However, if he EMS of each individual consumer were o schedule agains RTP ariff hen he majoriy of loads would acivae a he lowes priced periods of he day. As a soluion, a hierarchical aggregaor provides moneary incenives o invoke DR such ha overloads are miigaed. As for he conribuions, he developed framework uses a combinaion of RTP and incenives o minimize he cos of elecriciy for consumers while miigaing overloads on disribuion sysem lines. A decenralized approach is applied wih price-based signals sen downsream o consumers by a hierarchical agen, e.g. an aggregaor, and demand-based signals from EMS sen upsream o he aggregaor. As response o he RTP, consumers are hen able o deermine heir base consumpion profiles a he Pre-Scheduling (PS) sage and

48 27 adjus heir demand a he Re-Scheduling (RS) sage in response o addiional signals, i.e. incenives, sen by he aggregaor. The aggregaor mus provide hese incenives and a he same ime paricipae in he elecriciy markes o obain is profis. In he followings secions, he aggregaor s role and operaions are discussed followed by he consumers. 2.2 Aggregaor as an inermediary Wih he RTP ariff srucure, consumers can now schedule loads considering he acions a he wholesale elecriciy markes. However, because elecriciy markes are no designed o manage large numbers of small consumers, profi-seeking eniies called aggregaors are expeced o emerge and serve as inermediaries beween hese small consumers and he wholesale markes [7, 17, 18]. The aggregaor s role is o communicae wih he EMSs o provide real-ime updaes of he elecriciy ariff and in reurn receive opimized load schedules. While consumers will save on heir elecriciy bill by allowing heir EMS schedule loads under a specific ariff provided by he aggregaor, he disribuion power grid, e.g. disribuion feeders, could experience excessive loads ha may lead o damage. This is he case because each EMS aemps o minimize he oal elecriciy cos incurred by he consumer on a day-o-day basis. This resuls in many consumers loads o be scheduled a he lowespriced hours of he day (e.g. a 0300 hours under RTP in Figure 1.3), resuling in a sacking effec. For example, all EVs under a disribuion feeder will end o schedule charging a he lowes priced period Aggregaor s role The aggregaor supplies is consumers via disribuion neworks which usually have a radial opology [59]. The funcions of an aggregaor can be performed by a uiliy company ha owns and operaes he disribuion nework or by a separae commercial eniy. If he aggregaor is he Disribuion Sysem Operaor (DSO), i incurs all he coss associaed

49 28 wih he use or abuse of he sysem. On he oher hand, if i rades as a separae commercial eniy, i mus compensae he DSO for all he coss resuling from is ransacions wih consumers. These coss include he cos of repairing he damage caused by hermal overloads on sysem componens. However insead of incurring hese coss, he aggregaor can reward responsive consumers ha shif heir load away from he overloaded periods wih moneary incenives. 2.3 Incenives for demand response (DR) Incenives provided by he aggregaor ac as a mechanism o invoke DR in consumers in order o keep he disribuion sysem wihin is operaing limis. To achieve his, he aggregaor offers ime-dependen economic incenives β,i, where is an index o he se of ime periods T and i is an index o he se of incenives I. These incenives are offered o all consumers as an adjusmen on op of he elecriciy prices a ime period. Consumers are free o accep or rejec he incenives ha hey are offered. However, if a consumer responds posiively and is chosen by he aggregaor, hen an agreemen beween he paries is creaed. The consumer hen modifies is demand and receives he corresponding reward. For fairness, all consumers mus be allowed o respond and he incenives mus be non-discriminaory. As an example, consider wo consumers where consumer 1 is more flexible han consumer 2. Boh consumers will receive he same se of incenive parameers, which are[1, 5] $/MWh. Consumer 1 s demand decrease o hese incenives is [2, 3] kwh and consumer 2 s decrease is [1, 2] kwh. Since he aggregaor s objecive is o procure DR a he leas-cos, i will herefore use consumer 1 s service. Such analysis of DR procuremen is performed by he aggregaor s profi maximizaion model. The nex subsecions discuss he framework in which he consumers minimize heir cos of elecriciy procuremen, while he aggregaor aemps o maximize is profis and mainain he grid limis.

50 29 Sar = 0 Aggregaor in PS (a) Forecas price Consumer in PS (b) Min cos ( ) yes = T? no Aggregaor in RS (c) Deermine incenives (f ) Max profi ( ) = + 1 Consumer in RS (d) Min cos ( ) (e) Creae incenive demand profiles Figure 2.1: Ineracions beween he aggregaor and consumers 2.4 Framework The framework developed for he opimal coordinaion and scheduling of DR of residenial consumers is shown in Figure 2.1. The figure shows he ineracions of he consumer and he aggregaor a boh, he PS and RS sages. A he PSsage, heaggregaorforecasshe nex-day wholesale prices λ h anddeermines he base case demand profile of is consumers. This profile akes ino accoun he consumers response o he ime varying prices of elecrical energy bu no he addiional incenives used o deal wih he consrains imposed by he disribuion nework. The PS sage has a ime-

51 30 Figure 2.2: Rolling window horizon horizon of 24 hours, divided ino minue inervals ( ). In he PS sage, he reail ariff a period sen by he aggregaor o all is consumers akes he form of Equaion (2.1) below: π h = λ h +λ u +λ p h (2.1) Whereλ h ishewholesaleenergyprice, λ u ishedisribuionsysemusageprice, andλ p h is he aggregaor s profi margin. In response o hese prices, he auomaed energy managers of he consumers opimize heir anicipaed load usage and submi heir pre-scheduled demand profile o he aggregaor. The aggregaor combines he profiles Dh,f,c PS of all he consumers c locaed a disribuion node f. Poenial overloads in he sysem are hen idenified using hese aggregaed PS profiles. If overloads are expeced, hen he RS sage is required. The RS sage considers a rolling window from h = [, T + 1] [73], as illusraed in Figure 2.2. For example, a period = 10 he opimizaion would occur from h = [10,96+101] = [10,105]. In each rolling window, incenives are issued only for he curren period of he horizon, hus allowing he aggregaor and he consumers o be proacive and o maximize heir respecive benefis. This is he case because he aggregaor has he mos accurae knowledge of he consumer demand when opimizing a period as opposed o he fuure periods where hey may change heir consumpion, e.g. lae arrival of he EV. The aggregaor sends o he consumers he ime-varying prices π h and he incenive se β,i. Consumers calculae wha heir opimally adjused demand profile Dh,f,c,i RS would be for each β,i. This profile represens each consumer s abiliy o respond o a given incenive over he rolling window. The consumer performs heir opimizaion for he number of incenives he aggregaor chooses o offer, e.g. I = 6 requires 6 independen opimizaions from he consumers. Using hese individual profiles he aggregaor selecs wihin he pre-defined se

52 31 he opimal β,i for each consumer ha will mee is adjused demand wihou violaing nework limis. The aggregaor performs is opimizaion only once in each ime period. The RS sage hus yields an agreemen on price and quaniies beween each consumer and he aggregaor. The quaniies agreed wih each consumer are such ha violaions of sysem operaing limis are miigaed. From he aggregaor s perspecive, he prices include he DR incenives needed o achieve his goal and a he same ime, hey reflec each consumer s opimal balance beween comfor and cos. This approach is a non-ieraive decenralized algorihm, which has a guaraneed soluion if consumers are paricipaing in DR. By avoiding ieraions, he communicaion beween he aggregaor and consumers is minimal and poenial nonconvergen processes are avoided Example: consumer s response o incenives The consumers response o an incenive a period shifs he energy from his period o laer periods. This is known as he rebound effec. Figure 2.3 shows a consumer s response o incenives a period = 6, in which he conrollable loads shifs o periods = 8 and 9. Figure 2.3 also shows ha differen incenives, e.g. β 1 and β 2, yield a differen profile Dh,f,c,i RS, which he aggregaor considers when miigaing overloads. However, he incenives he aggregaor needs o offer a he RS sage in order o moivae consumers o shif heir demand and miigae all he overloads mus be based on sound economic principles, i.e. supply and demand curves [89]. 2.5 Procuremen of DR: supply-demand economic principles The procuremen of DR by he aggregaor are base on supply-demand principles. Since he aggregaor requires DR, i can be seen as he demand-side. Whereas, he consumers provide DR and hus are he supply side. The crossing of he supply and demand curves equaes o he equilibrium price a which he DR is priced a. A heoreical diagram of his is depiced infigure2.4. Figure2.4illusraes howhesupply andhedemand arebalancedonaspecific

53 32 Power (kw) β 0 =0 β 1 β 2 Base loads Incenives offered Demand rebound Conrollable loads Time (h) Figure 2.3: Example of a single consumer s response o incenives β i a = 6. Figure 2.4: Non-overload case in (a) and he overload case in (b). disribuion feeder a a paricular period. I also shows he process he aggregaor performs in is opimizaion o deermine which consumer s offers are acceped and he amoun of DR. For simpliciy in Figure 2.4, he ime index has been dropped from he incenives β i and he real-ime prices π h. The abiliy of each consumer o supply DR is calculaed by aking he difference beween D PS h,f,c and DRS h,f,c,i. These values are hen aggregaed o obain he cumulaive sepwise curve (dashed line in Figure 2.4) represening he DR supply curve. The sepwise price funcion in Figure 2.4 is he sum of he reail RTP π, which is fixed from he PS sage, and he incenives β i for each sep. Each sep in his curve represens he oal demand response offered by he consumers o a specific incenive, which he aggregaor can use o miigae overloads, if economical. If,

54 33 based on he consumer demand profiles a he PS sage, he aggregaor deermines ha he feeder will be overloaded, i calculaes is demand response requiremen (DRR). The DRR hus represens he reducion in consumer demand required o bring he flow on he feeder wihin is line capaciy (LC) limi. Figure 2.4a shows a case where he aggregaor s DRR = 0 because he LC limi is no violaed. There is hus no need for he aggregaor o offer any incenive, and he profiles agreed upon a he PS sage a price π are used wih no gain or loss in revenue. In he case shown in Figure 4b, he consumers response o reail price π resuls in he LC limi being violaed. The aggregaor herefore needs a DRR > 0 and consumer demand reducion is required. Wih he sepwise funcion, he aggregaor may accep offers a differen β i values for each consumer depending on heir DR amoun and locaion in he nework. The aggregaor opimally deermines he required incenive β i needed o obain his DRR. The acceped consumers hen receive π upd = π + β i for he demand reducion, where π was already agreed upon in he PS sage and is reimbursed and an addiional β i is given for he reducion. The oal amoun ha he aggregaor has o pay o he consumers o avoid an overload is shown in gray in Figure 2.4b. There may be cases where a large incenive is required o obain consumer response. In some exreme cases, he DRR of he aggregaor and he cusomers supply may no inersec. In he former case, he aggregaor incurs a very large cos o obain DR from he consumers while in he laer, i incurs damage coss o he disribuion sysem asses. Regular occurrence of such cases provide a basis for invesmen in upgrading he disribuion nework so ha i can handle he increased demand. The following subsecions explain he opimizaion model of he aggregaor ha incorporaes he discussed heories.

55 Aggregaor Model Re-scheduling (RS) sage opimizaion The aggregaor s RS opimizaion deermines which consumers need o be incenivized o remove overloads semming from he PS sage schedule. Mahemaically, his RS opimizaion is formulaed as follows: T + 1 max h= (f B) (c C) (i I) (π h +β,i )(D RS h,f,c,i DPS h,f,c ) η f,c,i T + 1 h= λ h p marke h (2.2) The firs erm in he objecive funcion (2.2) represens he amoun colleced (if posiive) or paid (if negaive) by he aggregaor. If he firs erm is negaive, i indicaes ha a paymen was made o consumers a period because incenives were needed. On he oher hand, if he erm is posiive he demand is reduced a period, bu a rebound is expeced in subsequen periods and will resul in revenue for he aggregaor (see Figure 2.3). Changes in demand beween he RS and he PS are calculaed using he binary variable n f,c,i {0,1}. This binary variable deermines he opimal incenive demand profile D RS h,f,c,i o be agreed uponwiheachconsumer. β,i dependsonwhichdemandresponseprofileischosen. However, β,i is only given for he curren period of he horizon. Therefore, β h,i = 0 for h >. The las erm represens he profi or loss resuling from purchasing or selling elecriciy p marke h in he wholesale elecriciy marke. The opimizaion is subjec o he energy balance consrain (2.3) which deermines he amoun of energy o be purchased or sold in he wholesale elecriciy marke and includes he nework losses. p marke h = (Dh,f,c,i RS DPS (f B) (c C) (i I) h,f,c ) η f,c,i + (f,g) B R fg l h,f,g h [, T + 1] (2.3) In he power balance consrain, however, he aggregaor mus choose a single RS profile o be used for each consumer. This is managed in consrain (2.4) as shown below. n f,c,i = 1 f B,c C (2.4) (i I)

56 35 In he nex se of consrains, he power flows in he disribuion nework are modelled [60]. Consrain (2.5) ensures he disribuion lines are operaing wihin heir limis. This consrain, however, is non-linear and is linearized via he special-ordered-ses-of-ype 2 (SOS2) echnique [123], furher discussed in Appendix B.1. l h,f,g (pflow h,f,g )2 +(q flow h,f,g )2 e h,f h [, T + 1],(f,g) B (2.5) The nex wo consrains (2.6 and 2.7) calculae he real and reacive power flows in each disribuion line. The real and reacive power, p flow h,f,g and qflow h,f,g, have a power facor of κ and are used o calculae he curren l h,f,g and he volage e h,f, aking he resisance R f,g and reacance X f,g of each line ino accoun. p flow h,f,g = (j B) q flow h,f,g = (j B) p flow h,g,j +R f,gl h,f,g +κ (c C) (i I) q flow h,g,j +X f,g l h,f,g +(1 κ) D RS h,g,c,i n g,c,i (c C) (i I) D RS h,g,c,in g,c,i h [, T + 1],(f,g) B (2.6) h [, T + 1],(f,g) B (2.7) Each disribuion node has an associaed volage which depends on he real and reacive power flow. This is calculaed by consrain (2.8), as shown below. e h,f e h,g = 2 ( R f,g p flow h,f,g +X f,g q flow h,f,g) ( R 2 f,g +Q 2 f,g) lh,f,g h [, T + 1],(f,g) B (2.8) In addiion, o ensure he disribuion grid is operaing wihin limis, he volage and curren mus be bounded. This is done wih equaion (2.9) for he volage a each node and wih equaion (2.10) for he curren hrough each line. e f e h,f ē f h [, T + 1],f B (2.9) 0 l h,f,g LC f,g R 2 f,g +Q2 f,g h [, T + 1],(f,g) B (2.10)

57 Consumer Model Consumers EMS incorporaes a cos-minimizaion model ha incorporaes specific needs of each load in he home, e.g. comfor requiremens, and EV availabiliy. Apar from he conrollable loads, he house also has non-conrollable, e.g. lighing, which are consumer conrolled and modelled as fixed demands. Table 1.3 shows he appliance loads considered in his framework. The objecive of he consumer is o minimize he oal cos and i has wo sages, he PS and RS sage Consumer pre-scheduling (PS) sage model The consumer s PS opimizaion akes place afer he forecased reail prices τ h from he aggregaor are sen o he consumers and is used o deermine he appliance schedule for he nex day, which runs from h = 1 o h = T. The objecive funcion (2.11) seeks o minimize he oal energy coss and shown below: min + (h T) π h P base h (a A) P a δ a,h AL a + (v V ) (p chg v,h ηdsg v p dsg The objecive funcion of he consumer is subjec o he following consrains: v,h ) (2.11) 0 δ a,h AL a h T,a A (2.12) δ a,h P a + (p chg v,h AL +ηdsg v p dsg v,h ) Pmains h T (2.13) a (a A) (v V ) In equaions (2.11) and (2.13), P a is he maximum power consumpion of appliance a in he se of appliances A, p chg v,h and pdsg v,h se of EVs V of each household, and P base h are he charge/discharge powers of EV v in he is he oal base load power, e.g. lighing. The appliances have an ineger number of operaing saes AL a, which allow he appliances o be used in a deraed manner (e.g. a 50% raher han 100% of raing). The ineger decision variable δ a,h for each appliance mus remain a or below he number of operaing saes AL a as shown in consrain (2.12). Consrain (2.13) ensures ha he household power limi

58 37 P mains is no violaed. This model is subjec o he appliance consrains presened in laer subsecions. The RS sage model is similar o he PS sage model and is discussed in he following secion Consumer re-scheduling (RS) sage model A he RS sage, consumers can make adjusmens o heir PS profile for h = [, T + 1] in response o he incenives provided by he aggregaor. Equaion (2.14) implemens hese adjusmens, where p and p represen increase and decrease in he power consumed by each load. The increase and decrease adjusmen in power depend on he PS sage load profiles U PS and are calculaed in consrain (2.16) for he appliances and consrain (2.17) for he EVs. The loads inerruped due o acceped incenives mus be enabled in a fuure period o mainain comfor requiremens. This is also considered in consrains (2.16) and (2.17). T + 1 min (π h +β,i ) (p a,h p a,h )+ (p v,h p v,h ) (2.14) subjec o: h= (a A) (v V ) Consrains (2.12) and (2.13) (2.15) P a δ a,h AL a p a,h +p a,h = UPS a,h a A,h T (2.16) (p chg v,h ηdsg v p dsg v,h ) p v,h +p v,h = UPS v,h v V,h T (2.17) This model is also subjec o appliance consrains presened in he nex subsecions. 2.8 Appliance Models Elecric vehicle (EV) The EVs are modeled as sorage devices ha can charge heir baeries from he grid in G2V mode, injec power o he household in Vehicle-o-Home (V2H) mode, or injec power back

59 38 o he grid in V2G mode. In order o know when an EV can perform hese funcions, is availabiliy α v,h mus be declared upfron as well as is rip schedule S v,h. As EVs charge and discharge, he baeries energy-sae-of-charge (esoc) varies. The esoc indicaes he amoun of energy presen a a given ime h in he baery. Equaion (2.18) calculaes he esoc in he baery a each ime period h which is a funcion of is sae-of-chargeinhepreviousperiod, hecharge/dischargepowersp chg v,h andpdsg v,h, hecharging efficiency η chg v, and he oal energy required for moion ξ v soc EV v,h = soc EV v,h 1 +p chg v,h ηchg v p dsg v,h ξ v S v,h h S v,h h T,v V (2.18) The esoc, soc EV v,h, also mus be wihin is maximum o avoid he risk of seing he baery on fire, and a minimum o avoid rapid degradaion, as shown below: soc EV v,h socev v,h socev v,h h T,v V (2.19) Furhermore,consrains(2.20)and(2.21)limihepowerac max v wih he EV availabiliy α v,h. for charging/discharging 0 p chg v,h α v,h c max v h T,v V (2.20) 0 p dsg v,h α v,h c max v h T,v V (2.21) Elecric waer heaer (EWH) Each consumer s EMS predics he need for ho waer H h (gal) for he nex day based on hisorical average usage. The model considers he hea rae Q, hermal resisance R, and hea capaciy C of EWHs. Consrain (2.22) deermines he waer emperaure φ waer h ( C) wih he saus of he appliance δ a,h. Consrain (2.23) calculaes he emperaure in he EWH ank, where G (gal) is he ank capaciy and φ ou h is he oudoor ambien emperaure. Consrain (2.24)

60 39 ensures he waer emperaure remains wihin bounds. ( = φ ank h φ ank h + δ ewh,h φ waer h φ ank h = φwaer h + δ ewh,h QR AL ewh (G H h ) φ ou h H h G QR φ waer h 1 AL ewh ) e RC h T (2.22) h T (2.23) φ waer φ waer h φ waer h T (2.24) Heaing venilaion and air condiioning (HVAC) The HVAC sysem uses he hermal mass inside he house o pre-hea or pre-cool during low-price periods, while keeping he emperaure wihin accepable bounds φ room and φ room se by he consumer as shown in (2.25). Consrain (2.26) updaes he room emperaure where Q, R, and C are he hermal parameers of he house. While he definiion of Q, R, and C for he HVAC and EWH is he same, he parameer values are differen. φ room h = φ ou h + δ ( hvac,h QR φ ou h + δ ) hvac,h QR φ room h 1 e RC h T (2.25) AL hvac AL hvac φ room φ room h φ room h T (2.26) Refrigeraor (REF) Shifing refrigeraion load in ime provides minimal discomfor o consumers if he emperaure inside he refrigeraor remains wihin bounds as shown in (2.28). Consrain (2.27) calculaes he emperaure φ ref h, where ψ = e TI TM, TI is he hermal insulaion, TM is he hermal mass, η ref is he efficiency, and P comp is he compressor power. φ ref h = ψ ( ) φ ref h 1 φ room h +φ room h δ ref,h (1 ψ) ηref P comp AL ref TI h T (2.27) φ ref φ ref h φref h T (2.28) Dishwasher, washing machine, and dryer These ypes of loads are in he caegory of non-inerrupible and deferrable loads. Consrain (2.29) ensures ha heir operaion is wihin he ime range specified by he consumer TR d,h,

61 40 where d is he index of he subse of he appliance se A. Consrain (2.30) ensures ha operaion is no inerruped once i has begun. Consrain (2.31) ensures he operaion of he appliance is equal o is cycle ime CT d. +H d z=+1 (h T) δ d,h TR d,h h T,d A (2.29) δ d,z CT d (δ d,h+1 δ d,h ) h T,d A (2.30) δ d,h = CT d d A (2.31) 2.9 Simulaion Resuls 100 consumers wih varying EV driving paerns were simulaed using he 2009 NHTS daa [124]. Each consumer has all he appliances described above and one EV. Typical curves for marke prices λ h and oudoor emperaures are based on PJM daa [125], for every Thursday during January-March Thursday was chosen in order o show he impac on a ypical weekday. The reail RTP π h was calculaed using equaion (1), where λ u = 20 $/MWh and he profi margin λ p h = 0.1 λ h. 50 consumers were placed on each of he las wo nodes of he IEEE 4-node disribuion nework [126]. Each consumer is allocaed 15 kw as is mains power limi. The line limis of he disribuion sysem were reduced and only one phase of he nework was considered. Since all he power flows hrough he subsaion feeder o reach he consumers, his line will overload if he EV peneraion increases. The feeder line capaciy LC was se a 600 kva. The nominal esoc of he EV baeries is 24 kwh. The esoc, however, can range only beween a minimum of 15% and a maximum of 95% of he nominal esoc [127]. The charging and discharging power is 3.3 kw, he iniial esoc of he EVs are randomized, and he round rip charging/discharging efficiency is assumed o be 90% [85]. The hermal parameers and emperaure bounds of he appliances were randomized and each appliance was given wo levels of operaion (50% and 100%). The EWH, HVAC, and REF power are uniformly randomized beween [ ], [ ], and [ ] kw, respecively. Consumers have

62 41 EV discharge (kw) V2H V2G τ h Time (h) (a) Price ($/MWh) EV discharge (kw) V2H V2G τ h Time (h) (b) Figure 2.5: EV discharge power in V2H and V2G for (a) RTP and (b) ToU ariff. Price ($/MWh) randomized dishwasher, washing machine, and dryer schedules each wih a raing of 1.0 kw. The base load varies wihin he range [50 200] W and is randomized for each consumer. The EWH waer usage was forecased as explained in [128] considering he number of members in he household and heir age. The power facor is 0.9. The approach described in [129] is used o calculae he hermal overloads if he line capaciy limi is violaed, which hen is used o obain he percenage loss of ensile-srengh, W,f,g [130]. In general, lines require repair when heir ensile-srengh drops below 85% of he nominal [131]. The value of he line mainenance cos LMC f,g is assumed o be $100,000 [59]. Based on his observaion, equaion (2.32) defines he poenial damage cos DC,f,g as a percenage of LMC f,g if incenives are no used: DC,f,g = LMC f,g W,f,g (2.32) Wih hese case sudy parameers, several simulaions were performed and heir resuls are discussed below Impac of ariffs a he PS sage Tariffs influence how each consumer s EMS schedules loads. Fla, ToU, and RTP ariffs are considered o invesigae he consumers response o each and o deermine which would

63 42 Apparen Power (kva) Apparen Power (kva) fǫb cǫc DPS π hfc h LC fg Time (h) (a) Time (h) (b) Price ($/MWh) Price ($/MWh) Figure 2.6: Toal demand profile in PS wih one EV per household on (a) ToU wih EMS, and (b) RTP wih EMS. require incenives o avoid overloads. The EV peneraion is assumed o be 100%. Figures 2.5a and 2.5b show V2H and V2G power under RTP and ToU, respecively. Buying excess energy o discharge and sell laer in V2G/V2H mode does no make sense under a fla ariff because prices are he same during all periods. The EVs enable consumers o sell excess energy in V2G afer supplying household loads in V2H. The RTP schedules a larger porion of discharge power in V2G mode as compared o V2H, hus selling energy o he aggregaor. WihToU(off-peak: 0000o0715,2145o2400hoursa54.1 $/MWhandpeak: 0730o2130 hours a 65.1 $/MWh), he majoriy of he discharge is in V2H mode. The oal discharge under RTP and ToU are and kwh, respecively. The RTP incorporaes muliple low and high price periods where he EMS can exploi EVs, whereas ToU has limied price blocks. The RTP ariff hus provides larger benefis wih regards o he EVs. Figure 2.6 shows he consumers EMS response o ToU and RTP. Here again, consumers have no incenive o schedule heir loads under a fla ariff. This resuls in a larger demand

64 43 during peak-hours. In addiion, he consumers response o a fla ariff is he wors-case scenario. Wih a fla ariff of 59.6 $/MWh (average of he reail RTP π h ), he oal PS sage energy coss for all consumers is $271.5 wih a line damage cos of $ Wih he ToU ariff, he energy cos decreases o $169.0 wih a line damage cos of $ However, under he RTP ariff, he energy cos is $150.4 wih he smalles line damage cos of $ The RTP ariff provides he mos benefis o consumers and he aggregaor, because he former pays he leas for energy and he laer incurs he leas damage cos for overloads. However, he RTP case in Figure 2.6b exceeds he line limis hus requires he use of incenives in order o avoid he damage coss Miigaing line overloads wih incenives a he RS sage Figure 2.7 illusraes he benefis of using incenives a he RS sage o remove overloads under RTP for differen levels of EV peneraion. Consumers are assumed o have an EMS ha can receive and ac on he basis of RTPs and incenives. The se of incenives offered o consumers consiss of [0,1,2,5,10,30] $/MWh. Figure 2.7 shows he incenives he aggregaor offers o he consumers are sufficien o reduce he demand below LC a each period. The rebound effec causes he demand o increase a laer periods o ensure he desired level of comfor is mainained. Wih lower EV peneraions, e.g. 30% in Figure 2.7a, enough capaciy is available during off-peak periods o handle his rebound wihou adverse effecs. As EV peneraion increases, more cosly incenives are required o miigae overloads. For example, in he case of 100% EV peneraion in Figure 2.7c, he available capaciy is small and he amoun of overload is large. When he iniial incenives are given, he poenial overloads are miigaed bu creae new overloads during subsequen periods. To correc hese new overloads, he aggregaor has o offer furher incenives. For insance, he incenive given a 0230 in Figure 2.7c eliminaes an overload bu his shifs he demand o a laer period causing a new overload and he need for more cosly incenives. Figure 2.8a shows he poenial damage cos under he RTP ariff if incenives are no

65 44 Apparen Power (kva) Apparen Power (kva) Apparen Power (kva) fǫb cǫc DPS hfc fǫb cǫc iǫi DRS hfci n fci LC fg Time (h) (a) Time (h) (b) Time (h) (c) Figure 2.7: (a) 30%, (b) 60%, (c) 100% peneraion showing demand in PS (black), and afer incenives are used in RS (red). offered. In Fig 2.8a, a 100% EV peneraion, he line overloads are high resuling in high poenial damage coss compared o he 30% and 60% peneraion levels. If here are no overloads, hen he damage cos is zero as is he case for hour 16:00 wih peneraions of 30% and 60% EVs. As an alernaive o paying he damage coss, he aggregaor can reward consumers wih incenives. The oal incenive cos a 30%, 60%, and 100% EV peneraion from Figure 2.7 are $0.39, $0.71, and $0.85, respecively. If he aggregaor does no use incenives o moivae consumers o shif heir energy consumpion, hen he incurred

66 45 Damage cos (DCfg), $ % EV 60% EV 100% EV Frequency of DRIs % EV 60% EV 100% EV 0 02:15 02:30 15:45 16:00 Overloaded periods (a) Incenives (β i ) (b) Figure 2.8: (a) Damage cos for overloaded periods under RTP and(b) frequency of incenives paid. poenial damage coss are much higher han he oal rewards given o consumers. However, in he long run since incenives decrease aggregaor profis and increase operaing coss, he reail price of energy will increase for consumers. The aggregaor mus also analyze wheher he se of incenives ha i offers o he consumers are effecive in moivaing DR. Figure 2.8b shows ha, a larger EV peneraion levels (e.g. 100%), incenives are no only more frequen bu also larger (e.g. 30 $/MWh). Dealing wih larger overloads requires he paricipaion of less flexible consumers, who demand larger incenives. From Figure 2.8b, i can be seen ha large incenives are infrequenly given o consumers. However, if given frequenly, i indicaes inflexible consumers which eiher have limied ineres in paricipaing in DR or have sric comfor requiremens. If his case persiss over ime, he disribuion sysem may require reinforcemen due o a lack of DR a an economic value o he aggregaor. On he oher hand, he high frequency of smaller incenives, e.g. 1 $/MWh, shown in Figure 7b shows ha consumers are paricipaing a an economic value o he aggregaor. Over ime as he aggregaor learns abou is consumer-base, i will deermine a igher range of incenives ha yields enough response o remove he overloads a each period.

67 46 The proposed approach can also be implemened for infrequen siuaions, e.g. sporing evens, when a large flee of EVs may require energy for ransporaion. The only requiremen will be a managemen eniy, e.g. sadium, capable of providing heir consumpion and DR schedule o he aggregaor o use in miigaing overloads. In addiion, anoher exreme case includes when he number of EVs increases for a emporary period of ime, e.g. visiors from neighboring areas. Even hough he curren area, for example, may have a low EV peneraion (30%), he visiing EVs resemble he impac on he demand a 60% or even poenially higher levels, which as shown in Figure 2.8 can be managed effecively Disribuion sysem avoided coss Consumers paricipaion in DR requires invesmens in smar-grid echnologies. This secion examines how much invesmen is jusified and deermines he poin where he rae of DR paricipaion becomes oo high and causes overloads during periods of low prices. I is assumed DR paricipans have an EMS capable of receiving RTPs and incenives. The ensile-srengh loss W,f,g of he feeder is deermined for he wors-case demand scenario where all consumers respond o a fla ariff on a daily basis. The number of days needed o reduce he ensile srengh o he minimum of 85% is hen calculaed. If demand is shifed from peak price hours o off-peak hours using DR, here will be fewer overloads and he number of days before he line mus be replaced will increase. Presen-Value (PV) analysis is performed o deermine he curren invesmens in order o delay or avoid repair coss. In he analysis, one p.u. cos is accrued by he aggregaor a a fuure day when he srengh of he line reaches 85% due o overloads. An ineres rae of 5% compounded monhly is used in he PV analysis [131]. Figures 2.9a, 2.9c and 2.9e show he effec of 30%, 60%, and 100% EV peneraions on he number of days during which he feeder line can wihsand increased loading unil i mus be replaced. The presen values of invesmens are shown in Figures 2.9b, 2.9d and 2.9f for hese same EV peneraions. For example, a 0% consumer paricipaion in DR and 30% EV peneraion (Figure 2.9a), overloads could be wihsood for 600 days. This line will herefore have o be replaced afer

68 47 Wihsand ime (days) G2V G2V/V2H G2V/V2H/V2G 1 0% 5% 10% Consumer paricipaion in DR wih 30% EVs (a) Presen value (p.u.) % 5% 10% Consumer paricipaion in DR wih 30% EVs (b) Wihsand ime (days) % 5% 10% Consumer paricipaion in DR wih 60% EVs (c) Presen value (p.u.) % 5% 10% Consumer paricipaion in DR wih 60% EVs (d) Wihsand ime (days) % 5% 10% 20% Consumer paricipaion in DR wih 100% EVs (e) Presen value (p.u.) % 5% 10% 20% Consumer paricipaion in DR wih 100% EVs (f) Figure 2.9: Wihsand ime for 30%, 60%, and 100% EV peneraion in (a), (c), and (e), respecively. PV invesmen for 30%, 60%, and 100% EV peneraion in (b), (d), and (f), respecively. 600 days a a cos of 1 p.u. However, 1 p.u. in 600 days is equivalen o a PV of 0.93 as shown in Figure 2.9b. This amoun can be invesed in consumer paricipaion o avoid he lump-sum cos of replacing he line. The wors-case siuaion includes consumers charging heir EVs as soon as hey arrive in heir homes, which is represened by 0% consumer paricipaion in DR. As he EV peneraion increases a his DR paricipaion level, he wihsand ime of he feeder decreases due o non-opimal charging, as shown in Figures 2.9a, 2.9c, and 2.9e. Lower wihsand

69 48 Opimal consumer paricipaion (%) G2V G2V/V2H G2V/V2H/V2G % 60% 100% EV peneraion (%) 30 Figure 2.10: Opimal consumer paricipaion in DR unil incenives are required. imes jusify larger invesmens in DR. As he paricipaion in DR increases (e.g. from 0% o 10%), he wihsand ime of he feeder increases and he jusifiable presen value of invesmens decreases. This occurs because more consumers are shifing heir consumpion from high-price o low-price hours, hus miigaing he overloads. Figure 2.9 also shows how limiing he EV modes of operaion affecs he amoun of invesmens ha can be jusified. In G2V, EVs are limied o charging only. In G2V/V2H, EVs can discharge and supply loads in he home. In G2V/V2H/V2G, any excess energy afer supplying loads can be sold back o he sysem. V2H and V2G aid he sysem by decreasing he amoun of power flowing hrough he feeder. Comparing G2V and G2V/V2H modes in Figure 2.9 shows V2H resuls in only a sligh increase in wihsand ime and decrease in jusifiable invesmens. This is he case because V2H occurs during high-price periods. However, RTP ariff decreases consumpion during hese high-price periods and limis he power ha could be injeced in V2H. On he oher hand, G2V/V2H/V2G modes creae larger benefis. Wih V2G, EVs discharge during high-price periods and he power is used o supply oher consumers in he sysem, including hose ha are no paricipaing in DR. The G2V/V2H/V2G mode hus resul in he larges wihsand imes and he leas jusifiable invesmens for all EV peneraion levels. Figure 2.10 shows ha all EV peneraion levels have an opimal DR paricipaion level. Lower values of opimal DR paricipaion are beneficial because hey require smaller invesmens. The G2V/V2H/V2G mode requires he leas consumer paricipaion because of he

70 49 benefi of V2G. Since he demand is shifed o lower price hours, an increase in consumer paricipaion in DR above he opimal level may cause overloads and require incenives Conclusion This chaper presens a mehodology o exploi flexibiliy of household appliances and EVs o manage he operaion of he disribuion grid. In he approach, an aggregaing eniy seeks o maximize profis, while consumers seek o minimize coss of purchasing elecriciy under ime-varying ariffs. In addiion o day-ahead ariffs, he aggregaing eniy offers incenives o relieve overloads in he sysem. Enabling he demand-side o paricipae in daily operaions has several advanages, no only in avoiding overloads in he operaing ime frame, bu also in he long run by avoiding or deferring invesmens in he grid. The use of incenives in his framework is no purely limied o mainaining disribuion line limis. Oher applicaions are: Volage sabiliy- EVs can moderae heir charging/discharging o mainain he volage a a node. Frequency regulaion - similar o volage sabiliy, EVs can receive frequency signals and modulae charging accordingly. Wholesale Power Markes - an aggregaor can conrol he charging/discharge of EVs o obain revenue from wholesale markes and a porion of his revenue can be passed on o consumers. Damage miigaion- EVs can moderae heir charging/discharging o minimize damage o asses, e.g. disribuion ransformers. In he nex chaper, a framework is developed in which an aggregaor manages charging/discharging of EVs conneced o disribuion ransformers o ensure he loss-of-life of he ransformer is minimized, while a he same ime, he EVs arbirage revenue is maximized. The nex chaper s framework, where EVs should be rewarded for heir paricipaion, is an ideal applicaion for he incenive mechanism developed in his chaper.

71 50 Chaper 3 CO-OPTIMIZATION OF DISTRIBUTION TRANSFORMER AGING AND ENERGY ARBITRAGE USING ELECTRIC VEHICLES 3.1 Inroducion In Chaper 2, a framework was developed on how an aggregaor can incenivize consumers o shif heir power consumpion in ime o mainain he power grid. Such a framework can also be applied o conrolling EV charging and discharging o mainain grid asses, e.g. pole-op disribuion ransformers. The adven of EVs will bring forh increases in power ransmied over he disribuion power grid. Since i is expeced for consumers o mosly charge EVs a heir homes [42], he major impac will be on he local pole-op disribuion ransformers. This impac would ranslae ino acceleraed aging of he ransformers [132] and earlier replacemen o accommodae he addiional power peaks required by he EVs load. This chaper proposes a cenralized sraegy of co-opimizing ransformer loss-of-life wih EV charging and discharging in order o minimize he oal cos of operaions. The consumers allow a managemen eniy, e.g. an aggregaor, o perform he scheduling of heir EVs. The managemen eniy seeks o minimize he energy procuremen coss of is consumers by aking advanage of heir price ariff o schedule charging (G2V) and energy arbirage (V2G or V2H), and o minimize he ransformer damage due o EV charging, while ensuring ha EVs receive heir required energy for ransporaion. Wih his, he aggregaor obains revenue from he ransformer owner for mainaining lifeime, and some porion of his revenue mus be given o consumers for heir services. Through compensaion, all paries can benefi financially. Furhermore, a ransformer life expecancy analysis is performed for sraegies

72 51 in which consumers independenly manage heir EVs (i.e. decenralized) and in which a managemen aggregaor akes conrol (i.e. cenralized). The major conribuions of his work are as follows: Cenralized co-opimizaion model of ransformer aging and energy arbirage of EVs. Analysis of he use of EVs in G2V, V2H, and V2G o maximize he lifeime of he ransformer under various levels of EV peneraion. Mehodology o analyze he coss/benefis of a ransiion from decenralized o cenralized operaional sraegy for EV charging. 3.2 Transformer Model The aging of ransformers is dependen upon hermal effecs from loading. The IEEE sandard C [132] proposes a model for esimaing he various ransformer emperaures, which are correlaed wih is aging facor and LoL. In order o esimae he ransformer windings hoes-spo emperaure (HST), he following equaion is used: θ HST = θ A + θ TO + θ HST T (3.1) θ TO where θ HST is he windings hoes-spo emperaure, θ A is he ambien emperaure, is he op-oil rise over he ambien emperaure, and θ HST is he winding HST rise over he op oil emperaure, all for ime period in he se of all ime periods T. From (3.1), he value θ TO is calculaed by: θ TO =( θ TO,U θ 1 TO )(1 eτ TO )+ θ 1 TO T (3.2) 1 Alernaive approaches such as geneic algorihms [133] and mehods based on experimenal ess [57] can also be used o esimae he ransformer life.

73 52 where θ TO,U is he ulimae op-oil rise over he ambien emperaure, is he ime inerval, and τ TO is he op-oil ime consan. In (3.2), he θ TO in he previous period. The erm θ HST in (3.1) is calculaed wih Equaion (3.3), where θ HST,U is dependen on he sae is he ulimae op-oil rise over he ambien emperaure, and τ w is he windings ime consan. Noe ha as in equaion (3.2), he erm θ HST is also dependen on is previous sae. θ HST =( θ HST,U θ HST 1 )(1 e τ w )+ θ HST 1 T (3.3) are shown in (3.4) and (3.5), respecively. The equaions ha calculae θ TO,U and θ HST,U θ TO,U = θ TO,R ( ) k 2 n R+1 T (3.4) R+1 θ HST,U = θ HST,R k 2 m T (3.5) where θ TO,R is he op-oil rise over ambien a he raed load, θ HST,R is he hoesspo rise over op-oil a he raed load, k is he raio of he load on he ransformer o is nameplae raing, R is he raio beween he losses a raed load and a no load, and m and n are he cooling parameers of he ransformer. The raio k is defined as: where TX load k = TXload T (3.6) TX raing is he load on he ransformer in a cerain period and TX raing is he nameplae raing. I can be seen ha as he load raio k increases, he ransformer emperaures vary based on Equaions (3.1) o (3.5). Equaion (3.7) relaes he acceleraed aging facor, F AA, o he winding hoes-spo emperaure, θ HST. The erm F AA F AA ( = exp ) θ HST +273 T (3.7) is he acceleraed aging facor a a given emperaure θ HST. If F AA > 1 hen he ransformer is experiencing acceleraed aging. Wih his facor, he LoL of he

74 Loss of Life (LoL) (log, %) F AA = 241 F AA = 5 F AA = 1 F AA = Raio of load o raing, k Figure 3.1: Loss-of-life as a funcion of he loading on he ransformer for = 15 min. Noe ha he y-axis is logarihmic. ransformer can be deermined as shown in Equaion (3.8) below: LoL = FAA β T (3.8) where β is he normal insulaion life of he ransformer. Noe ha according o IEEE sandard, a ypical ransformer mus have a minimum normal insulaion life (β) of 180,000 hours (20.5 years) [132]. Wih equaions (3.1)-(3.8), he aging of he ransformer can be esimaed aking ino consideraion loading, emperaure, and characerisic parameers. For example, if a ransformer wih parameers: m = 0.8, n = 0.9, R = 6, θ TO,R = 56 C, θ HST,R = 80 C, τ TO = 90 min, τ w = 7 min; is loaded a 90%, where θ A = 24 C, θ TO 1 = 25 C, and θ HST 1 = 20 C, for a of 15 minues, he ransformer would lose 75.5 minues of is insulaion life. As shown, high loadings lead o acceleraed aging of he ransformer. The effec of k on he LoL is shown in Fig In addiion, he aging facor F AA shown for cerain k raios. The loading on he ransformer increases exponenially he aging facor and hus he LoL a high loadings. This hermal-based ransformer model can be embedded ino an opimizaion framework. is

75 Consumer Perspecive Consumers are assumed o reside in a household conneced o he disribuion sysem and o purchase heir elecriciy under a variable elecriciy ariff π. Therefore i is expeced ha he consumers will srive o minimize heir elecriciy coss, by opimizing heir consumpion under ariff π. In general, consumers are no responsible for day-o-day wear and ear of disribuion sysem asses, especially local pole-op ransformers. In some insances, consumers pay a fixed cos per monh for he usage of he disribuion sysem [134]. The disribuion sysem operaor (DSO), which in many cases is he same eniy as he power uiliy company, has he responsibiliy of insalling and mainaining disribuion asses in order o provide elecriciy o is consumer-base. Since he consumers are no responsible for he day-o-day damage of he ransformer hey are conneced o, heir opimizaion problem only considers he managemen of heir asses (i.e. EVs). The consumers can manage heir own EV charging and discharging by insalling an energy managemen sysem or smar charger in heir home [7, 10]. Such a managemen sysem can consider he elecriciy ariff, ravel schedule of he EV, and oher facors o procure energy a he leas cos on behalf of he consumer. In addiion, he managemen sysem may be able o ake advanage of he EV baery o perform energy arbirage (e.g. V2G or V2H) if i provides furher cos savings. In general, his mehod is independen from he perspecive of he power uiliy and does no require he use of a managemen eniy Decenralized sraegy: consumer opimizaion model The consumer s goal is o minimize is elecriciy coss, herefore he objecive funcion can be wrien as: min π T Where π is he elecriciy ariff, η dsg v v V ( p chg,v η dsg v ) p dsg,v (3.9) is he discharging efficiency for EV v in he se of

76 55 EVs V, and p chg,v and p dsg,v are he charging and discharging powers, respecively. The objecive funcion (3.9) is subjec o several consrains. In consrain (3.10), he energysae-of-chargeisafuncionofisprevioussae, chargingefficiency η chg v, power obained from he grid p chg,v and injeced o he grid p dsg,v, oal energy required for ransporaion ξ v, and he moion schedule S,v {0,1}. The parameer ξ v is calculaed based on he expeced oal miles ha he EV v will ravel and hen muliplied by a conversion facor (kwh/miles) o obain he oal energy needs. The parameer S,v = 1 if he EV is in moion in period, oherwise S,v = 0. Furhermore in (3.10), he energy for moion a period is calculaed as S ξ,v v ( T) S,v. For example, if an EV consumes 5 kwh for is rip and ravels for a oal of 5 ime periods, hen he EV consumes 1 kwh every ime period. The acions of charging and discharging he EV, however, needs o be wihin he maximum power Pv max. Also, he EV can only charge or discharge if i is available and conneced o he household circuis. This availabiliy is deermined by he parameer α,v {0,1}, as shown in consrains (3.11) and (3.12). Noe ha α,v = 1 before deparure from he home and also afer arrival from a rip back o he home, oherwise α,v = 0. Also, in all ime periods, he sae-of-charge mus be wihin he minimum and maximum bounds as shown in consrain (3.13). Consrain (3.14) ensures he oal energy conen of he baery a he end of he opimizaion horizon is he same as i was a he beginning of he day. Lasly, consrain (3.15) ensures he oal load including he base consumpion P base he household s power limi P limi. is bounded by soc,v = soc 1,v +η chg v p chg,v p dsg,v ξ v S,v ( T) S,v T,v V (3.10) 0 p chg,v α,v P max v T,v V (3.11) 0 p dsg,v α,v P max v T,v V (3.12) soc min v soc,v soc max v T,v V (3.13) soc = T,v = soc ini v v V (3.14) P limi P base +p chg,v p dsg,v P limi (3.15)

77 Aggregaor s Perspecive Consumers EV self-opimizaions could resul in increased damage o he disribuion poleop ransformer o which hey are conneced. The owner of he ransformer, i.e. uiliy or DSO,willincurhesecossinwopars: 1)alossofhecurrenlyinsalledransformer, and2) required invesmen of a ransformer of larger capaciy ransformer in order o accommodae increased EV loading. To reduce hese coss, he owner of he ransformer (e.g. DSO), or separae managemen eniy (e.g. aggregaor), can conrol he charging/discharging of EVs in a cenralized fashion. The ransfer of money beween he DSO, aggregaor, consumers, and he uiliy can be seen in Fig If he aggregaor is separae from he ransformer owner, he owner should pay he aggregaor a porion r manage of he savings r save i obains from no needing o frequenly replace ransformers. On he oher hand, if he ransformer owner is acing as he aggregaor, hen he savings are direcly capured. In addiion, he consumers pay heir energy bill r energy o he uiliy company. Inhiswork, amodelisdevelopedforheaggregaorwhichfocusesonlyonheconsumers, heir EVs, and he ransformer. In his cenralized sraegy, he consumers allow he aggregaor o conrol heir EVs. The aggregaor co-opimizes he ransformer damage cos and cos of energy (including any arbirage profis) o deermine he charging/discharging profiles wih he lowes oal cos of operaions. In reurn, he consumers receive compensaion c pay from he aggregaor o offse heir increased energy cos (compared o he decenralized case), r energy. All paries benefi if r save > r manage > c pay > r energy Cenralized sraegy: aggregaor co-opimizaion model The aggregaor objecive funcion is defined as: min TX cos T LOL + T v V π ( p chg,v η dsg v ) p dsg,v (3.16)

78 57 Figure 3.2: Revenue/paymens by he aggregaor from/o he consumer and DSO subjec o: Consrains (3.1) (3.5), (3.7), (3.8), and(3.10) (3.15) (3.17) TX k + k base + ( ) (v V ) p chg,v p dsg,v = T (3.18) TX raing θ HST θ HST T (3.19) In(3.16),heLoL ismulipliedbyheoalransformercostx cos oobainhedamage cos o he ransformer. The ransformer cos is defined as TX cos = TX raing TX price, where TX raing is he nameplae raing and he TX price is he price per kva. For insance, for a ransformer ha coss $ (i.e. a ransformer wih a raing of 25 kva priced a $/kva [135]) ha is loaded a 90%, wih he parameers as specified in Secion 3.2, he damage cos is hen $0.03. Noe ha he second erm in (3.16) is idenical o he consumers decenralized objecive funcion (3.9), because now he aggregaor is responsible for managing EV energy procuremen coss. The consumers are hands-off in he managemen of heir EVs wih he guaranee hey will receive heir energy needs for ransporaion and revenue for assising he grid. The operaor s objecive funcion is subjec o he ransformer model equaions (3.1)- (3.5), (3.7), (3.8), and he EV consrains (3.10)-(3.15). An addiional consrain deermines he absolue loading of he ransformer while considering he base consumer load TX base and

79 Arrival Deparure Trip ime PDF 0.1 PDF Time (h) (a) Trip ime (h) (b) Figure 3.3: PDFs of he arrival ime o he home and deparure ime from he home (a), and rip ravel ime (b). he ne EV power consumpion, which is (3.18). Noe ha TX base is he sum of he base load of all consumers in each period, i.e. P base = TX base. Also, in (3.18) he oal load could be negaive and his makes he loading raio k, negaive. To avoid his, wo non-negaive variables, k + and k are inroduced in (3.18) and k = k + +k. Such a formulaion models he absolue value of he loading raio. Furhermore, in (3.19) he ho-spo emperaure θ HST is bounded by he maximum emperaure θ HST and he oil [132]. o avoid gassing in he solid insulaion Wih he ransformer equaions in he opimizaion, he model becomes non-linear. Transformer equaions (3.4), (3.5), and (3.7) are linearized using SOS2 [123], as discussed in Appendix B Simulaion Resuls The proposed sraegies are applied o a pole-op ransformer wih a raing of 25 kva, servicing 6 residenial consumers wih an individual household limi of 15 kw [136, 8]. Each consumers consumpion profile was obained from a daabase of empirical daa from he region of Ausin, Texas and San Diego, California [137], and scaled so ha he peak loading (wihou EVs) is similar o loadings in a ypical suburban feeder, as described in [138].

80 59 30 Dumb Charging Base Load TX raing 210 Apparen Power (kva) Tariff ($/MWh) Time (h) (a) Time (h) (b) Figure 3.4: Dumb charging a 100% (6) EV peneraion, base load, and ransformer raing shown in (a), and he real-ime elecriciy ariff shown in (b). The 2009 Naional Household Travel Survey (NHTS) daa [124] is used o deermine he characerisics of EVs and generae dumb-charging profiles. Wih such daa, represenaive profiles were creaed by using K-means clusering [139]. Fig. 3.4a shows he base load and dumb charging load for 100% EV peneraion, and Fig. 3.4b shows he real-ime price ariff, (i.e. average price of 92.1 $/MWh wih a range from 37.6 o $/MWh and he median price of 92 $/MWh), obained from [2]. Using he NHTS daase [124], probabiliy disribuion funcions (PDF) were creaed for he deparure ime from he home, arrival ime o he home, and rip ravel ime. The PDFs are shown in Fig. 3.3 and were used o generae he characerisics of he EVs. The EVs are available for charging and discharging during he period before hey depar and he period afer hey arrive home again. For he EV characerisics, he charging/discharging power rae is se a 3.3 kw and he energy capaciy of EV baeries is 24 kwh, as in [8]. The sae-of-charge, however, can only range from a minimum of 15% and a maximum of 95% of he oal capaciy because of safey and elecrochemical consrains on he baery [127]. The round-rip efficiency is se o 90% [8] and he iniial energy sae-of-charge is uniformly randomized beween 15% and 60% of soc max v. A conversion facor of 0.33 kwh/mile [42] was used o conver he oal

81 60 Apparen Power (kva) Toal load TX raing F AA Time (h) (a) F AA Apparen Power (kva) Time (h) (b) Figure 3.5: Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih only G2V enabled F AA miles ravelled, obained from NHTS [124], o he oal energy required for moion ξ v. Hisorical daa of ambien emperaures from July 2014 was obained from San Diego, California [140]. The ambien emperaures were in he range [18.9, 25.6] C wih an average emperaure of 21.7 C. The iniial ransformer emperaures are se by performing he opimizaion and using he end-of-day emperaure resuls. The maximum ho-spo emperaure is 140 C as discussed in [132]. The ransformer parameers are as described in Secion 3.2 and in [141]. The cos of he ransformer replacemen is $/kva, which considers he fixed and variable coss in a consolidaed per-uni of kva erm, as discussed in [135]. The oucome of he cenralized opimizaion is he opimized EVs charging/discharging profiles and associaed ransformer impacs (e.g. aging, LoL, and damage cos) and arbirage benefis. By conras, he decenralized opimizaion ignores he ransformer damage. Therefore, a pos-process calculaion of he ransformer damage is performed using he oal load profile obained from he opimizaion in order o be able o compare agains he cenralized opimizaion.

82 61 Apparen Power (kva) Toal load TX raing F AA Time (h) (a) F AA Apparen Power (kva) Time (h) (b) Figure 3.6: Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih V2G enabled F AA Decenralized versus cenralized sraegy In he decenralized case, he consumers opimize he charging/discharging of heir EVs and in he cenralized case, he aggregaor opimizes all EVs as an ensemble. Boh models were simulaed for 100% EV peneraion o show he oal load and he aging effec on he ransformer (F AA ). The oal load hrough he ransformer including EVs, he ransformer raing, and he associaed aging acceleraion facor F AA are shown in Fig. 3.5(a) for he decenralized case and in Fig. 3.5(b) for he cenralized case, boh while allowing only G2V (i.e. EVs only charge o mee heir energy needs for ransporaion). By comparing Fig. 3.5(a) and Fig. 3.5(b),icanbeseenhaheloadingonheransformerhashigherpeaksinhedecenralized case because each consumer aemps o minimize only heir cos of operaion independenly. Such acions resul in he syncing of power consumpion during he low-priced periods of he day (e.g hours). On he oher hand, in he cenralized case he aggregaor opimizes he EVs while also considering he ransformer LoL. Therefore, he charging of he EVs is spread ou during he low-price periods. This minimizes he peak power consumpion during he nighime and consequenly reduces he oal F AA. However, he cos of energy

83 62 Apparen Power (kva) Toal load TX raing F AA Time (h) (a) F AA Apparen Power (kva) Time (h) (b) Figure 3.7: Loading on he ransformer and aging facor for he decenralized case in (a) and cenralized case in (b) wih V2H enabled F AA is increased as a radeoff for improving he ransformer lifeime. The aggregaor will need o compensae he consumer for such a radeoff. Some EVs have he capabiliy o discharge heir baeries o supply energy direcly o he grid in V2G mode. Similar o Fig. 3.5, Fig. 3.6 shows he decenralized case in (a) and he cenralized case in (b) wih V2G enabled. In he decenralized case in Fig. 3.6(a), he EVs charge in excess of ransporaion needs during he low-price periods (e.g o 0800) in order o discharge during he high-price periods. The discharge leads o he oal load on he ransformer o be negaive during 1500 o 1800 hours because all EVs are offseing he base loads and hen supplying energy back o he grid. To perform V2G, however, excessive charging occurs resuling in a large increase in he oal aging facor F AA, ulimaely reducing he lifeime of he ransformer. On he oher hand, wih cenralized managemen as shown in Fig. 3.6(b), he aggregaor keeps he loading on he ransformer relaively consan during he nighime periods. This resuls in a lower oal aging facor F AA. Again, o achieve he low aging facor he aggregaor mus reduce energy arbirage and consumers mus be compensaed. The las mode in which an EV can perform is in V2H. Tha is, EVs can discharge heir

84 63 baeries o offse he base loads of he consumer, bu canno expor power o he grid. Fig. 3.7 shows he oal load and aging facor for he decenralized and cenralized case in (a) and (b), respecively. The V2H operaion is similar o V2G, excep ha he oal F AA is lower in boh he decenralized and cenralized operaions. This is he case because in V2H, EVs are consrained o discharge only up o he magniude needed o offse base loads, while in V2G mode he EVs have more freedom o ake advanage of arbirage. Essenially, V2G does no reduce ransformer damage as much as V2H because he high-price periods (in which he consumer would prefer o discharge) may no correlae wih he high base load periods (in which he oal F AA can be mos effecively reduced). Regardless of he sraegy, V2H provides slighly lower aging effec o he ransformers as compared o V2G, bu does no capure he maximum benefis from energy arbirage. The cenralized sraegy is superior in keeping he oal F AA low, whereas he decenralized sraegy maximizes he benefis from charging/discharging of he EVs under real-ime pricing. Mos consumers would prefer o perform under he decenralized sraegy unless he aggregaor can provide he necessary incenives for a hand-over of conrol of he EVs Effec on he ransformer life expecancy The cenralized and decenralized sraegies are run for EV peneraions from 0 o 6 (i.e. 0% o 100% EV peneraion) for a 24-hour period in order o see he effec on he ransformer life and he associaed ransformer damage cos. The damage o he ransformer is assumed o occur on a daily basis and by using he following equaion an approximae value for he ransformer life expecancy in years is obained: TX life = ( T) LoL (3.20) Fig. 3.8 shows he life expecancy for he dumb (i.e. unopimized), cenralized, and decenralized charging cases for G2V in (a), V2G in (b), and V2H in (c). Noe ha he G2V case wih dumb charging is shown in Fig. 3.4(a), where he EVs charge immediaely when hey arrive home wihou any sor of managemen. Wih zero EV peneraion (i.e.

85 64 Transformer life (yr) G2V Transformer life (yr) V2H EV Peneraion EV Peneraion EV Peneraion (a) (b) (c) Dumb Cenralized Decenralized Transformer life (yr) V2G Figure 3.8: Transformer life expecancy in he dumb, cenralized, and decenralized sraegies under G2V (a), V2H (b), and V2G (c) operaions. base load shown in Fig. 3.4(a)), he ypical life expecancy as saed in he IEEE sandard C57.91 of 20.5 years is susained [132]. This can be seen in all subplos in Fig. 3.8 a 0 EV peneraion. From Fig. 3.8a i can be seen ha as he EV peneraion increases, he life expecancy under he dumb charging sraegy decreases significanly. This is expeced since he EVs are adding heir charging power ono he peak base load as shown in Fig. 3.4(a) in red. In he decenralized case considering only G2V, he expecancy is closely mainained a he ypical 20.5 years up o 50% EV peneraion (3 EVs). However, wih furher increase in EV peneraion, he ransformer life decreases drasically. This is he case because each consumer is self-opimizing heir benefis and hus a large peak is creaed in he low-price periods (see Fig. 3.5(a)). In he cenralized case wih G2V (Fig. 3.8(a)), he life expecancy remains near he ypical value, even under high EV peneraion. For example, a a peneraion of 6 EVs, he life only decreases o years. The life expecancy wih V2H enabled is shown in Fig. 3.8(b). Since V2H discharging offses he base loads, he ransformer life expecancy is increased from he ypical life for low EV peneraions under boh sraegies. This is beneficial because he ransformer owner

86 65 obains increased lifeime of heir sunk-cos asse. However, wih higher EV peneraion in he decenralized case (e.g. greaer han 3 EVs), he life is significanly decreased because of he excessive charging during he low-price periods (see Fig. 3.7(a)). Wih cenralized charginga100%evpeneraion, helifeis11.8years. ThisshowshabyenablingV2H,he ransformer owner experiences a decrease of 5.65 years of ransformer lifeime, because EVs will increase heir charging in order o offse house loads during peak price hours. Under V2H, he aggregaor receives addiional ransformer life and consumers receive arbirage benefis. Wih V2G enabled, as shown in Fig. 3.8(c), neiher sraegy experiences an increase in lifeime as high as ha in V2H. This effec occurs because V2G akes full advanage of he price difference in he elecriciy ariff and herefore obains larger amouns of energy during he nighime period as compared o V2H. In he cenralized case under 100% EV peneraion, he lifeime is years. Therefore, V2G is no beneficial in erms of minimizing he damage cos of he ransformer as compared o V2H. However, i does provide he larges arbirage benefis o he consumers, and has he lowes overall operaional cos. In Fig. 3.8(b) and Fig. 3.8(c) i can be seen ha for some peneraion levels, he lifeime of he ransformer is more han doubled. This is echnically feasible in erms of he elecrical and hermal characerisics of he ransformer. However, oher exernal facors, e.g. sorms, corrosion, ec., may be a limiing facor on his exended lifeime. An analysis of hese facors is ouside he scope of his work. Wih he iniial inroducion of EVs, he mos probable operaing mode is G2V, hen V2H, and finally V2G. This is he case because V2H/V2G require bidirecional chargers in he EVs and V2G requires bidirecional power flow in he grids as well [40]. A high peneraions of EVs, he ransformer will experience a relaively small decrease in lifeime if and only if he sysem is cenrally managed under all modes of operaions. The ransformer owner, however, mus provide he proper incenives o a managemen aggregaor for performing his cenralized sraegy. A he same ime, he aggregaor mus provide he proper incenives o consumers for paricipaion in such a sraegy. If he ransformer owner ops o forgo cen-

87 66 Toal EV discharge (kwh) Cenralized V2G Decenralized V2G Cenralized V2H Decenralized V2H EV Peneraion (a) Arbirage Daily Profi ($) EV Peneraion (b) Figure 3.9: Toal EV discharge in (a) and arbirage daily profi/loss in (b) for differen sraegies and modes of operaion (V2G, V2H). ralized managemen, hen each consumer will perform heir decenralized opimizaion and he owner mus replace he ransformer frequenly or insall a larger capaciy ransformer Tradeoff beween arbirage and ransformer damage The noion ha here is a radeoff beween obaining he maximum benefis of arbirage and he minimum ransformer damage cos is eviden in he cenralized sraegy. On he oher hand, he decenralized sraegy favors maximum arbirage benefis and ignores he ransformer. I is of imporance o analyze hese aspecs. Fig. 3.9 shows he oal discharge energy ha is supplied by he EVs and he overall profi/loss for V2G and V2H modes. Noe ha overall profi is defined as he oal discharge revenue minus oal cos of charging energy (including ransporaion needs) for he EV. In addiion, Fig shows he daily ransformer damage cos for boh sraegies wih varying EV peneraion. The oal energy discharged by EV baeries is always higher in he decenralized case as compared o he cenralized case, as is shown in Fig. 3.9a. Consequenly, he arbirage profis are also higher in he decenralized case, as shown in Fig. 3.9b. This is expeced because in his sraegy, consumers ake advanage of arbirage o is fulles poenial ignoring he ransformer s damage. Wih low EV peneraions (i.e. less han 4 EVs), he cenralized and

88 67 Daily TX damage Cos ($) Cenralized under RTP G2V V2G V2H EV Peneraion (a) Daily TX damage Cos ($) Decenralized under RTP G2V V2G V2H EV Peneraion (b) Figure 3.10: Daily ransformer damage cos for he cenralized (a) and decenralized sraegy (b) wih varying EV peneraion. decenralized sraegies have negligible difference in he oal EV discharge and arbirage profis. This is he case because he aggregaor can use he few EVs conneced o he ransformer o caer a charging/discharge profile ha boh reaps arbirage benefis and reduces he damage cos as shown in Fig. 3.10(a) for V2G and V2H. In addiion, he EVs abiliy o discharge during he peak hours acually reduces he overall damage cos compared o G2V mode (see Fig. 3.10(a)). However, as he EV peneraion grows in he cenralized sraegy, he addiional charging of he EVs sars o increase he ransformer damage and herefore he cenralized sraegy begins o limi arbirage aciviies, as shown in Fig. 3.10)(a). This discharge limiing ulimaely reduces he oal arbirage profis as a radeoff for mainaining he ransformer life. Under 100% EV peneraion, he oal daily arbirage profis in V2G mode in he decenralized and cenralized case are $5.73 and $3.94, respecively. In addiion, he life expecancies of he ransformer for he decenralized and cenralized sraegies are 0.10 years and 10.6 years, respecively. For a loss of $1.79 of arbirage profi, he cenralized case can provide an increase of wo orders of magniude in he ransformer life expecancy. The ransformer owner and he aggregaor can perform such analyses o effecively deermine he radeoffs

89 Decenralized 6000 Cenralized Cos ($) Cos ($) Transformer Raing (kva) Transformer Raing (kva) (a) (b) G2V V2H V2G Opimal raing Figure 3.11: Perpeual replacemen cos of ransformers in decenralized in (a) and cenralized in (b) for G2V, V2G, and V2H operaions. Noe ha resuls are shown for he 100% (6) EV peneraion case and he y-axis cos scales and benefis of boh sraegies Deermining he opimal replacemen ransformer raing Once he 25 kva ransformer reaches is end-of-life, he ransformer owner mus decide he capaciy raing of he replacemen ransformer. To do so, an opimizaion is performed over a se of replacemen ransformer raings S = {25,30,35,40,45,50} kva. The presen cos of perpeual replacemens [142] is calculaed using a 5% annual ineres rae [143]. This approach balances he replacemen ransformer cos and he replacemen frequency. The resuls are shown in Fig Fig. 3.11(a) shows he decenralized sraegy and Fig. 3.11(b) shows he cenralized sraegy under G2V, V2G, and V2H operaions for he 6 EV case. By considering he already-esablished loadings on he ransformer (shown in Fig ) and by varying he ransformer raing, i can be seen ha he presen cos of perpeual replacemens in he decenralized sraegy is much higher han in he cenralized sraegy, due o he lack of coordinaion beween consumers. In addiion, he opimal ransformer raing ha minimizes his cos is 35 kva in he cenralized sraegy regardless of he mode

90 69 # of Invesmen deferral Consumer arbirage Max. poenial EVs benefi ($) benefi ($) profi ($) G2V V2H V2G , , , , , , , 422 Table 3.1: Decenralized o Cenralized Annualized Benefis of operaions, whereas in he decenralized sraegy, he opimal raing varies from 35 o 45 kva, wih V2G requiring he larges capaciy Maximum poenial revenue of he aggregaor For he aggregaor o develop a business case, i mus quanify is poenial profi from a decenralized o cenralized ransiion. I is shown in Fig. 9b ha he consumers obain greaer arbirage benefi in he decenralized sraegy compared o he cenralized sraegy. On he oher hand, he ransformer owner obains he benefi of increased ransformer lifeime under a cenralized sraegy compared o a decenralized one. The aggregaor can negoiae o obain a share of he ransformer lifeime benefi, and a porion of ha mus be provided o consumers o compensae for heir lower arbirage revenue. The cos of he opimally-sized ransformer replacemen (as described in Secion 3.5.4) is discouned based on he lifeime of he 25 kva ransformer (see Fig. 3.8) and a 5% ineres rae. For example, if he 25 kva ransformer reaches is end-of-life in 10 years,

91 70 hen a replacemen ransformer mus be insalled and is presen cos is 61% of he fuure cos. The presen cos in he cenralized sraegy is subraced from he cos in decenralized sraegy o obain he invesmen deferral benefi for ransiioning o a cenralized sraegy. This represens he ransformer owner s benefi, of which he aggregaor can negoiae is share. On he oher hand, he aggregaor mus quanify he benefi (in acualiy, he cos) for consumers of a ransiion o a cenralized sraegy. This is calculaed by aking he difference beween he annual arbirage revenue in he cenralized and decenralized sraegies. Table 3.1 shows hese benefis in he firs and second column for he differen modes of operaion(i.e. G2V, V2H, and V2G) and EV peneraions. The las column is he maximum profi he aggregaor can obain, which is he sum of he invesmen deferral benefi and he consumer arbirage benefi (loss). The invesmen deferral benefis are annualized by represening he one-ime ransformer replacemen cos wih he equivalen-annual-annuiy approach, as described in [142]. From Table 3.1, he benefi seen by he ransformer owner is highes in V2G mode under 100% EV peneraion. This is because in he decenralized sraegy, he consumers have he maximum flexibiliy o use heir EVs for arbirage, which is exremely damaging o he ransformer. In conras, a cenralized sraegy avoids much of his damage. Therefore, he aggregaor has a srong case o negoiae a conrac wih he ransformer owner. However, wih low EV peneraions (e.g. 1-4), he annualized deferral benefi is much smaller. In his case, he aggregaor may no have a srong business case when considering he cos o equip and conrol hese EVs. The consumer arbirage benefi (shown in he second column) is negaive in all cases. This is expeced because in he decenralized sraegy consumers are able o generae more revenue from energy arbirage (see Fig. 3.9(b)). Thus, consumers mus be compensaed for heir loss in revenue by he aggregaor, oherwise hey would no be willing o hand over conrol of heir EVs. The maximum poenial revenue (las column) shows he amoun of money available for he aggregaor s business case. A porion of his money should be

92 71 given o consumers for allowing he conrol of heir EVs for he aggregaor s benefi, and he ransformer owner will likely wan o reain some of he invesmen deferral benefi. Using an analysis such as he one shown in Table 3.1, an aggregaor can negoiae conracs wih boh he ransformer asse owner and consumers in which all he eniies profi. 3.6 Conclusion A cenralized model is developed in his chaper which co-opimizes he ransformer loss-oflife (LoL) wih elecric vehicle (EV) charging and discharging for arbirage, while ensuring he EVs obain heir energy needs for ransporaion. Such a model can be implemened by he ransformer asse owner, e.g. disribuion sysem operaor, or a separae hierarchical eniy. The model considers he ransformer s hermal emperaures, acceleraed aging facor, and LoL. For comparison, a decenralized model is also presened which could be implemened by consumers energy managemen sysems or smar chargers in heir homes. In he decenralized approach, he consumers are no responsible for ransformer damage and hus opimize heir EV charging/discharging only for arbirage. Resuls show ha in he cenralized sraegy he ransformer life decreases under high peneraions of EVs when charging only. In he decenralized sraegy, he ransformer mus be fully replaced under similarly high peneraions afer fracions of is expeced lifeime. Furhermore, when he EV peneraion is moderae, he ransformer life is increased beyond is expeced lifeime when performing in vehicle-o-home (V2H) and vehicle-o-grid (V2G) modes under boh sraegies. This is he case because he EVs discharge heir baery and decrease he ne load experienced by he ransformer during peak hours, when ransformer damage is greaes. In he decenralized sraegy, he EV consumers receive addiional revenue for performing energy arbirage, as compared o he cenralized sraegy (V2G mode a a high EV peneraion). The cenralized aggregaor essenially limis energy arbirage in order o mainain or even increase he lifeime of he ransformer. However, he decrease in arbirage benefi is more han offse by he ransformer invesmen deferral benefi, creaing a siuaion where

93 72 a managemen aggregaor can reduce he coss of he consumers and he ransformer owner simulaneously, and sill have a viable business case. Alhough he benefis of cenralized EV charging managemen have been demonsraed in his chaper, he DSO would have o inves in communicaions and conrol infrasrucure in order o implemen such a sraegy, and hus would have o weigh heir poenial coss and benefis o ensure such a venure is profiable. The proposed model and resuls ha can be obained wih i will: inform DSOs of he poenial impac EVs may have on heir disribuion ransformer asses quanify he marke poenial for new businesses, i.e. aggregaors, o emerge and manage EVs In he nex chaper, a framework is developed considering an aggregaor s paricipaion in he wholesale power markes. Such a framework allows for furher revenue generaion by he aggregaor which can hen be used o reward EV owners for heir paricipaion.

94 73 Chaper 4 OPTIMAL PARTICIPATION OF AN ELECTRIC VEHICLE AGGREGATOR IN DAY-AHEAD ENERGY AND RESERVE MARKETS 4.1 Inroducon EVs are poised as effecive paricipans in boh he energy and reserve markes. In he energy markes, hey can shif consumpion in ime o exploi he low and high prices of he day. On he oher hand in he reserve markes where capaciy mus be on sand-by in he DA and hen deployed in he RT based on he need of he sysem, EV baeries can reac quickly o provide such services. The combined paricipaion in hese markes increases he revenue poenial of EV owners. However, he aggregaor exploiing EVs mus consider he radeoff beween he cos of degrading he baeries verses revenue poenial from he markes and hus make an opimal economic decision. In his chaper, a framework is proposed o assess he aggregaor s capabiliies o provide energy and differen reserve services in a realisic marke environmen [120]. The aggregaor paricipaes in he energy marke as a price-aker, and is offers o he ancillary services marke are opimized aking ino accoun boh i) he probabiliy of accepance and ii) he probabiliy of deploymen in he marke environmen. The former represens he expeced probabiliy of he aggregaor s offers being acceped in he DA ancillary marke, hus receiving he revenues a he marke capaciy price for is bid, and he laer is he probabiliy he acceped offer o be deployed in he RT, hus receiving he revenues for he deployed energy a he RT energy price. The conribuions of his framework are as follows: An opimal sraegy for boh energy and reserve markes considering heir radeoffs

95 74 and effec on EV baery degradaion. Realisic approach o paricipaing in he volunary reserve markes wih price-quaniy offers ha are jusified. Assessing he expeced profi he EV aggregaor can collec by paricipaing in he energy and regulaion marke. 4.2 Power sysem eniies Elecric vehicle s perspecive EV owners can allow he aggregaor o manage heir EVs scheduling by charging energy in G2V mode and discharging energy in V2G mode, as long as hese prioriies are fulfilled: 1. Energy requiremens for ransporaion are no comprised, 2. Moneary benefis are provided for paricipaion, and 3. Compensaion is provided for he aggregaor s addiional usage of EV baeries. For he aggregaor o properly schedule EVs, each EV mus inform heir availabiliy α,v {1,0} (1 if available o charge/discharge, and 0 oherwise) a each ime period for each vehicle v. During he availabiliy periods (α,v = 1), he EVs mus obain heir energy for moion ξ v and charge any addiional energy ha he aggregaor schedules o provide services o he power grid. In essence, he process from he EVs perspecive should be well-inegraed and auomaed wih minimal owner paricipaion Aggregaor s perspecive The goal of he he aggregaor is o exploi is EV flee o maximize profis. The profis are he difference beween he revenues for providing services o he sysem and he coss of services provision. The coss of providing hese services are a funcion of he incurred baery degradaion ha mus be reimbursed o EV owners. In order for he services from

96 75 EVs o be economically viable, he revenues mus ouweigh he cos compensaion for he degradaion of EV baeries. If his is no he case, hen using EV baeries beyond supplying heir moion needs does no make economic sense. The aggregaor paricipaes in wo markes: day-ahead energy and day-ahead regulaion. However, in he regulaion marke i submis separae up and down offers. The aggregaor can submi compeiive offers in order o provide a share of he regulaion services, because he SO fulfills is regulaion requiremen by selecing he leas priced offers. The markes i paricipaes in and he revenue srucure is described below: Day-ahead Energy Marke: aggregaor is a price-aker in his marke and hus canno influence is oucome. I forecass marke prices and schedules EVs accordingly o maximize profi. Day-ahead Up Regulaion Marke: aggregaor can influence he price, i.e. pricemaker, in his marke. The revenues are obained in he DA in he form of a capaciy paymen for being on-sand by and an addiional deploymen paymen in RT if called o deploy he energy. Day-ahead Down Regulaion Marke: similar o he up regulaion marke, he DA capaciy paymen is obained for sand-by, however, no deploymen paymen is given since oherwise he EVs receive a double benefi of free energy and revenue. Considering hese opporuniies, he aggregaor can make opimal decisions on he paricipaion in each individual marke Probabiliy of accepance and deploymen In order o srucure a compeiive bid pair(i.e. price and quaniy) in he regulaion marke, he aggregaor mus use he probabiliy of accepance (π a ) and probabiliy of deploymen (π d ). π a represens he aggregaor s assumpion on he likelihood of is capaciy offers p cap o be acceped p accep in he DA regulaion marke, i.e. Prob(p cap 0) π a. Similarly,

97 76 Figure 4.1: Decision ree for regulaion marke ineracions π d represens he assumed likelihood of he acceped offers p accep o be deployed in realime, i.e. Prob(0 p depl p accep ) π d, where p depl is he expeced power deploymen. The sysem operaor canno call upon he aggregaor o deploy more han he DA acceped capaciy. Since he aggregaor is no aware wha fracion of p accep he SO can call upon in he RT, i needs o schedule he purchase of he shorage p shor in he RT energy marke, where p shor = p accep p depl. This shorage power has an associaed probabiliy Prob(p shor = p accep p depl 0) = 1 π d = π shor and hus allows a risk-averse decision o be made by he aggregaor. Figure 4.1 shows he probabiliy-based decision ree considered by he aggregaor in is DA model. In branch (I), he DA capaciy offer is acceped wih a probabiliy π a. Afer he offer is acceped, i may be deployed by he SO up o p accep, i.e. 0 p depl p accep. This occurs wih probabiliy π d as shown in branch (II). The aggregaor also needs o consider if he acual deploymen required by he SO is larger han expeced p depl, and hus i considers he cos of he shorage p shor. An ideal case wihou penalies is shown in Figure 4.2a where he aggregaor obains he DA capaciy price λ cap for he acceped capaciy p accep and he expeced RT energy price λ RT for he deploymen p depl. In branch (V), he aggregaor expecs is DA offer o be acceped wih probabiliy π a bu

98 77 no deployed by he SO in he RT. In his case, i canno ake advanage of he addiional revenue for deploymen, however, i does no have he risk of being unable o deploy if called upon by he SO. I receives only he DA acceped offer imes he capaciy price λ cap. In branch (IV), he offer is acceped and he full acceped capaciy is expeced o be deployed. This occurs wihou he aggregaor assuming any expeced energy shorage in he DA because i is able o use is available EV flee. The aggregaor obains benefis from boh he DA capaciy and RT marke revenue sreams. This is summarized in Figure 4.2a when p depl = p accep. Figure 4.2b summarizes branch (III) which includes penalies. In branch (III), he aggregaor considers some porion is full capaciy offer o be acceped and some fracion ha o be deployed beyond he expeced p depl. This occurs because he aggregaor s decisions in he DA are based on esimaes of is EV flee availabiliy in he RT. Therefore, i has he risk of over-offering in he ancillary marke, which if acceped, i may no be able o deploy due o a lack of capaciy. Thus, i needs o consider he possibiliy he acual deploymen requiremen in RT p ac o be larger han is expecaion p depl. In Figure 4.2b, he aggregaor receives he DA capaciy revenue. As for RT revenue, he SO requesed p ac which he aggregaor is unable o provide. Therefore, i receives he RT price for p depl and mus purchase he acual shorage, p ac p depl, a λ RT. However, in he DA, he aggregaor already considers he possibiliy of shorage (p shor ) and hus he decisions are hedged agains. These cases are incorporaed ino he DA opimizaion o deermine he opimal offering schedule for regulaion services. The differen cases shown in Figure 4.1 are consruced by deermining heir corresponding probabiliy of accepance for regulaion up π a and down φ a, as well as he probabiliy of deploymen for regulaion up π d and down φ d Deermining marke prices for energy and regulaion The aggregaor obains he prices for he reserve and energy markes when hese markes clear. In he reserve marke, he clearing process requires a quaniy-price offer from he aggregaor, which mus be compeiive due o a limied capaciy requiremen in hese markes.

99 78 Figure 4.2: Acual revenues and coss when paricipaing in ancillary markes, where (a) is he case wih no penalies and (b) includes penalies. Therefore, he aggregaor needs a mehod o esimae hese prices in order o opimally bid ino hese markes. By using hisorical daa, price-quaniy-probabiliy (PQP) curves, as shown in Figure 4.3, can be incorporaed ino he model. Figure 4.3a represens he complemenary CDF of prices, Figure 4.3b represens he complenary cumulaive disribuion funcion (CDF) of quaniy, and Figure 4.3c shows he PQP curve which is derived from he curves in Figure 4.3a and Figure 4.3b. In order o creae hese funcions, hisorical daa mus be obained from markes for regulaion prices, energy prices, and capaciy acceped and deployed. The process o obain he PQP curve shown in Figure 4.3c is consruced following hese seps: i) Firs, he complemenary CDF, i.e. 1-CDF, is calculaed for prices (see Figure 4.3a) and quaniy (see Figure 4.3b), individually. ii) Nex, hese separae curves are hen combined as shown in Figure 3c, where he x-axis is he quaniy and he y-axis maps he prices. Each corresponding sep in he PQP curve represens a probabiliy π, which has a corresponding marke price o be used in he aggregaor s opimizaion model. This process is applied o he reserve prices agains he oal acceped quaniies for regulaion up and down wih heir respeced probabiliy of accepances (i.e. π a, φ a ), and also o he real-ime energy price agains he regulaion deployed in he RT wih he probabiliy of deploymens (i.e. π d, φ d ). The probabiliies are sored in descending order: π 1 > π 2 > > π B where

100 79 Figure 4.3: Capaciy price and oal acceped capaciy quaniy complemenary CDF s shown in(a) and(b), respecively. In(c), he price-quaniy-probabiliy(pqp) curve is shown which is derived from he curves in (a) and (b). B is he se of segmens wih index b. For example, he firs wo corresponding seps in Figure 4.3c labeled π 1 and π 2 can ake on he values of 100% and 90%, respecively. As he price-quaniy pair increases, he likelihood decreases Sysem operaor s perspecive In he presened model, i is assumed he sysem operaor clears a simulaneous energy and reserve pool-based marke wih uni commimen (UC) in order o deermine he schedule and power oupu of generaors. A generic wo-sage marke srucure of a DA and RT planning is implemened in his work. These marke srucures are common in Unied Saes elecriciy markes, e.g. PJM [82] and ERCOT [144]. However, he marke design used in his work is generic o be compaible wih oher marke-based power sysems [89]. Such

101 80 co-opimizaion of energy and reserve 1 markes yields subsanial cos savings for he SO [147, 148], and incenivizes he SO o enable paricipaion of all eligible energy and reserve providers, including EV aggregaors. The energy price is a by-produc of he clearing process, as well as he leas-cos allocaion of regulaion up/down, resuling in regulaion prices [149]. When an imbalance maerializes as a lack of generaion o mee he demand, hen regulaion up is required o accommodae such imbalance. On he oher hand, if he imbalance maerializes as an excess of generaion o mee he demand, hen regulaion down is required. In he DA, he sysem operaor enforces a pre-esablished requiremen of regulaion up and down for each hourly period of he opimizaion horizon, which in his work is deermined by he 3+5 rule [150]. This crierion ensures he hourly reserve requiremens are se o 3% of he hourly load and 5% of he hourly available renewable energy capaciy. Therefore, his rule accouns for all sub-hourly balancing needs of he SO o miigae he impac of wind power and load forecas errors [151]. The SO hen opimally deermines in a leas-cos manner which marke paricipan s offers o accep o mee he requiremen. If a paricipan s offer is acceped, i receives he marke clearing price for he specific service i provides (i.e. capaciy price for being on sandby). If a paricipan s acceped capaciy is called upon for deploymen in RT, hen hey mus provide he energy and hen receive he RT price for energy deployed. If hey are unable o provide he energy, hey may purchase i in he RT energy marke. In his work, he UC model is implemened as explained in [149]. 4.3 Aggregaor Opimizaion Model Marke paricipaion The aggregaor paricipaes in he DA energy and regulaion marke. In he energy marke, he aggregaor is a price-aker, hus submiing quaniy-only zero-price bids. On he oher hand, he regulaion marke has pre-defined requiremens. 1 Throughou his chaper, regulaion is assumed o be a join reserve produc, i.e. i combines he secondary and eriary regulaion inerval, as explained in [145] and [146].

102 81 From he aggregaor s perspecive, heir are several acions ha can be exploied from EVs. These include: Energy Marke Charge (EMCHG): Schedule EVs o charge energy from he DA energy marke hus receiving he DA energy revenue. Energy Marke Discharge (EMDSG): Schedule EVs o discharge energy o he DA energy marke hus receiving he DA energy revenue. Regulaion Up (REGUP): Schedule EVs o discharge energy o he grid and receive he capaciy revenue for being on-sandby and he RT energy revenue for deploying he capaciy if required. Regulaion Down (REGN): Schedule EVs o charge energy o he grid and receive he capaciy revenue for being on-sandby. No RT deploymen compensaion colleced because EVs will hen obain wo benefis of free energy. Sop Charging (STOPCHG): Par of he REGUP produc which can only occur if a subse of he EV flee is already scheduled o charge energy from he energy marke and are inerruped volunarily. Sop Discharge (STOPDSG): Similar o STOPCHG bu bundled wih he REGDN produc. Also can be only scheduled if he EV flee is already scheduled o discharge in he energy marke. The scheduling of charging and discharging in he energy, regulaion up, and regulaion down marke are considered by he opimizaion model as described in he following subsecion Opimizaion model The aggregaor seeks o maximize is profis. The objecive funcion of he aggregaor is: max r em +r cap +r depl c regup c regdn c deg (4.1)

103 82 where r em is DA energy marke revenue, r cap is he DA regulaion marke revenue for capaciy, r depl is he expeced revenue for deploymen in real-ime, and in erms of coss, c regup is he cos for regulaion up service, c regdn is he cos for regulaion down service, and c deg are he baery degradaion coss ha mus be compensaed o consumers. The DA energy marke revenue r em is given as: r em = ( T) (v V ) ( λ DA ηv dsg p emdsg,v ) p emchg,v (4.2) p emdsg,v where λ DA and p emchg,v is he DA energy marke price, η dsg v is he baery discharge efficiency, and are he discharge and charging powers specifically argeed for he energy marke, respecively. The revenue r cap is obained from he DA regulaion marke as: where λ up,b r cap = and λdn,b ( T) (b B) [( w up,b λup,b ) πa p up + ( ] w,b dn λdn,b ) φa p dn (4.3) are he DA regulaion up and down capaciy prices, respecively, obained from he CDF curves. The binary variable w up,b {1,0} acivaes only one segmen of he capaciy price CDF curves asafuncion of he probabiliy π a. Similar raionaleapplies for w dn,b as a funcion of probabiliy φa. The revenue erm, akes ino accoun he likelihood of capaciy offers o be acceped and is represened by branch (I) in Figure 4.1. The power p up and p dn are he regulaion up and down capaciy offers o he marke. This revenue sream only considers he capaciy revenue, however, if he capaciy is deployed by he SO, addiional revenue for deploymen r depl should be accouned a RT prices: r depl = π a π d η dsg ( T) (v V )(b B) ( v up ) (,b λrt,b e regup,v ) +e sopdsg,v where λ RT,b is he RT energy price obained from he CDF curve, e regup,v energydeploymen forregulaionupservice, ande sopdsg,v (4.4) is he expeced is he energy in regulaion up service ha is only poenially scheduled in he same period in which energy marke discharging (EMDSG) is scheduled. Each segmen of he real-ime energy price CDF curve has a binary variable v up,b {1,0}. This variable deermines which paricular segmen b is acive, and

104 83 i is a funcion of he probabiliy π d. Therefore, r depl represens he revenue ha may be obained from deploymen in he RT marke and represens he case in branch III (Figure 4.1). This, however, assumes he aggregaor would deploy a fracion of is capaciy offer and ignores he risk of being deployed more han i anicipaed. In order o accoun for his oucome, equaion (4.5) is he cos c regup for regulaion up service: c regup = π a π d (1 π d ) ( T) (b B) ( v up )(,b λrt,b p up π a π d p up ) (4.5) where hedifference beween hecapaciyoffersp up andheexpeced deploymen π a π b p up deermines he amoun of shorage ha may need o be purchased in he RT energy marke. This siuaion can occur wih a condiional probabiliy produc of π a π d (1 π d ), where 1 π d = π shor, which is represened by branch (IV) (Figure 4.1). This case covers he penaly for being unable o deploy in he RT. Similar raionale applies for regulaion down service as shown below: c regdn = φ a φ d (1 φ d ) ( T) (b B) ( )( ) v dn,b λrt,b p dn φ a φ d p dn (4.6) Since he aggregaor is no he owner of he EV baeries, i mus compensae EV owners for degrading heir baeries. In his work, i is assumed he degradaion characerisic is sensiive o he number of cycles and insensiive o he deph-of-discharge, as explained in [10]. The degradaion cos is: c deg = Cv ba m v ( T) 100 (v V ) ) +p emchg,v ξ v + BC v ( p emdsg,v In (4.7), BC v is he baery energy capaciy, C ba v ( T) ( π a e regup,v BC v +φ a e regdn,v ) (4.7) is he baery cos, ξ v is he oal energy for moion, and m v is he linear approximaed slope of he baery life as a funcion of he number of cycles [10]. The value of m v is esimaed from manufacurer daashees [10]. In (4.7), he aggregaor mus compensae EVs for discharging in V2G mode for energy marke arbirage as deermined by he erm p emdsg,v. On he oher hand, for energy obained

105 84 for charging from he energy marke, i only needs o compensae addiional energy on op of he moion needs as deermined by subracing ξ v. For he regulaion services, only he componens ofhe service ha degrade he baery areincluded, i.e. e regup,v ande regdn,v. This is he case because sop charge and sop discharge acions do no degrade he baery, insead hey only inerrup he acions of he EVs in he period. The objecive funcion in(4.1) is subjec o several consrains. The firs se of consrains (4.8) and (4.9) calculae he capaciy offer for regulaion up and down, respecively. In hese consrains, he sum of he energy for each service calculaed from each EV mus equal he oal regulaion offer. Furhermore, hese consrains relae he offered capaciy in he DA regulaion marke o he expeced deploymen in he RT. The capaciy offer is muliplied by he probabiliy π d for regulaion up in (4.8) and φ d for regulaion down in (4.9), o ge RT deploymen. p up π d = (v V ) p dn φ d = (v V ) ( e regup,v ( e regdn,v ) +e sopchg,v ) +e sopdsg,v T (4.8) T (4.9) Consrains (4.10) o (4.15) deermine he energy sae-of-charge (esoc) soc,v of each EVandheenergyofeachproducofferedinhemarke. In(4.10),heeSOCisdependen on he previous sae, power obained from he energy marke p emchg,v and injeced o he energy marke p emdsg,v, moion needs, and moion schedule S,v. Noe ha his same consrain allows arbirage in he energy marke. However, before arbirage can be scheduled, he moion needs mus be fulfilled which are obained from he energy marke, because unlike he regulaion marke, his marke is open o all paricipans wihou any prese SO requiremens. This is managed in consrain (4.11). If addiional capaciy is available in he baeries, hey can be scheduled o provide regulaion down/up service as shown in consrains (4.12)-(4.13). A all ime periods, he esoc mus be wihin he defined minimum and maximum bounds as shown in consrain (4.14). Consrain (4.15) ensures he oal energy a he end of he opimizaion horizon is he same as i was a he beginning of he day. This ensures he

106 85 aggregaor reurns he EV baeries o heir iniial sae. soc,v = soc 1,v +η chg soc,v ξ v 0 e regdn,v 0 e regup,v SoC min v S,v ( T) S,v +e sopdsg,v +e sopchg,v v p emchg,v p emdsg S,v,v ξ v ( T) S,v T,v V (4.10) T,v V (4.11) SoC max v +soc,v T,v V (4.12) soc,v SoC min v T,v V (4.13) soc,v SoC max v T,v V (4.14) soc = T,v = SoC ini v v V (4.15) Consrains (4.16) o (4.20) deermine how much energy and a which periods regulaion and energy marke services can be provided. In (4.16) and (4.17), an individual EV can perform charging or discharging if i is available, such ha α,v = 1. An EV a a specific periodcaneiherchargeforheenergyorheregulaiondownmarke asshowninconsrain (4.16), or i can discharge for he energy or regulaion up marke as shown in consrain(4.17). This is managed in such consrains by he auxiliary binary variable z,v and he maximum power P max v ha an EV can provide. If an EV is scheduled o discharge in he energy marke, he aggregaor may decide o inerrup his discharging by scheduling regulaion as shown in consrain (4.18). The same raionale applies for consrain (4.19) o inerrup energy marke charging. Since he aggregaor mus mee each EV s moion requiremens, i can only inerrup charging ha is in addiion o energy obained for moion as shown in consrain (4.20). 0 p emchg,v +e regdn,v α,v (Pv max )(1 z,v ) T,v V (4.16) 0 p emdsg,v +e regup,v α,v (Pv max )z,v T,v V (4.17) 0 e sopdsg,v 0 e sopchg,v ( T) e sopchg,v p emdsg,v T,v V (4.18) p emchg,v T,v V (4.19) ( ) ξ v v V (4.20) ( T) p emchg,v

107 86 The las se of consrains for he aggregaor are relaed o he regulaion and energy marke PQP curves as shown in Figure 4.3. In consrain (4.21), binary variable w up,b acive a one specific segmen b when parameer PQP up b will be equals π a. This raionale applies o consrains (4.21) o (4.24). By deciding which segmen of he CDF curves is acive, a corresponding marke price can be used in equaion (4.1). (b B) w up,b PQPup b = π a T (4.21) (b B) (b B) (b B) v up,b PQPRT b = π d T (4.22) w dn,b PQPdn b = φ a T (4.23) v dn,b PQPRT b = φ d T (4.24) Noe ha consrains(4.3)-(4.6) include muliplicaion of binary and coninuous variables, which are linearized as discussed in [123]. The linearizaion is furher explained in Appendix B.1. A discussion on he sofware and echniques used o solve his model is presened in Appendix A. 4.4 Simulaion Resuls The proposed approach is applied o a flee of 1000 EVs managed by an aggregaor. The driving paerns are obained from he 2009 NHTS [124]. The capaciy of he EV baeries is 24 kwh [9], however he esoc can only range beween a minimum of 15% and a maximum of 95% of he capaciy due o elecrochemical consrains on he baery [127]. Boh he charging and discharging power rae was 3.3 kw, he iniial esoc was randomized, and he round rip charging/discharging efficiency was se o 90% [85]. The degradaion cos was accouned for using equaion (4.7) wih he cos per EV baery se o [ ] $/kwh and wih corresponding slopes m v = [ ] [9]. The lower

108 87 slope is he approximaion of 2012 echnology and he higher slope represens echnological improvemen in he baery cycle-life o hree imes he curren value [9, 34]. Hisorical daa was obained from he ERCOT marke for capaciy and energy prices along wih heir corresponding marke clearing power quaniies from [152]. The daa was used o creae he price-quaniy-probabiliy curves as shown in Figure 4.3 for regulaion up and down, and he RT markes. Each curve has 10 seps wih descending probabiliy from 100% o 0% wih uniform incremens and he curves were creaed for each hour of he operaing day, i.e. 24 hours. For simpliciy, i is assumed he probabiliies of accepance for regulaion up/down follow π a = φ a and for deploymen π d = φ d. The day-ahead energy marke prices were obained o creae a ypical represenaive curve using k-means clusering [139]. In order o model he SO, UC was performed on a modified IEEE RTS-96 wih 96 generaors, an aggregaor, and wind resources [149]. For simpliciy, he regulaion up/down offers of he generaors are 10% of heir energy offers. The sofwares and echniques used o solve he model are discussed in Appendix A Esimaion of he probabiliy of accepance/deploymen The aggregaor esimaes he probabiliy of accepance and deploymen o maximize is revenue for offer accepance in he DA and capaciy deploymen in he RT, while compensaing EV owners for degradaion. In order o deermine he bes esimaion of such probabiliies, Mone Carlo (MC) simulaions are performed. The process is as follows. Firs, he aggregaor performs is opimizaion and he offers/bids for he DA energy and regulaion marke are submied o he SO. Nex, he operaor performs UC in he DA o deermine he energy price and which offers are acceped for he provision of down and up regulaion, resuling in capaciy prices. Afer ha, he aggregaor is noified wheher is offers were acceped, however, i remains unaware if i will be requesed o deploy is capaciy in he RT. Finally, o validae if he aggregaor is able o deploy in he RT wih maximum profis, MC simulaions are performed. Each rial of he MC consiss of a randomly generaed wind and demand realizaion using he sampling process discussed in [153]. The number of MC rials

109 CDF Toal profi (p.u.,$) π a = 0.1,π d = 0.8 π a = 0.4,π d = 0.3 π a = 0.7,π d = 0.3 π a = 0.8,π d = 0.3 π a = 0.9,π d = 0.3 π a = 1.0,π d = 0.3 π a = 0.8,π d = 0.5 π a = 0.9,π d = 0.8 π a = 1.0,π d = 0.8 Figure 4.4: CDF of he oal profi obained by he aggregaor wih varying probabiliies. The baery cos is 250 $/kwh for all rials. is se o max (1000,N MC ), where N MC is he number of MC rials required o ensure a 95% confidence inerval of an error less han 1% [154]. The oal profis of he aggregaor from all rials are used o creae a CDF curve for each combinaion of probabiliy of deploymen and accepance. The resuls are shown in Figure 4.4. Noe ha all poenial combinaions of he probabiliies in he range of [0,1] wih sep-size of 0.1 were solved bu only a subse is shown for clariy. Figure 4.4 shows he CDF where he righ-mos curves indicae larger profis obained by he aggregaor. When π a is low and π d is relaively high, e.g. π a = 0.1 and π d = 0.8, he majoriy of he profis are obained from energy arbirage, hus all rials resul in he same profis (i.e. sraigh line). This occurs because he probabiliy of accepance π a is oo low o yield any acceped offers in he regulaion marke and resuls in no deploymens. On he oher hand, if π d = 0.3 and π a is varied (doed cases in Figure 4.4), he oal profis decrease because hese combinaions resul in higher penaly coss, calculaed in (4.5)-(4.6), if he aggregaor is unable o deploy is capaciy offers. As a resul, less overall capaciy is offered o he regulaion marke o minimize such coss.

110 89 Furher shown in Figure 4.4, if π d is increased from 0.5 o 0.8, e.g. solid line cases, he oal profis are subsanially increased, because he aggregaor will now be deployed in he RT wih a higher probabiliy and so i increases is DA capaciy offers. However, less energy is scheduled o be supplied ino he energy marke so ha i may be insead offered o he regulaion marke. Such a radeoff maerializes because he poenial revenue obained in he regulaion marke is greaer han he energy marke. Moreover in Figure 4.4, he profis decrease when π a > 0.9 and π d > 0.8, because a his poin he aggregaor is over-offering ino he regulaion marke and hus when asked o deploy in he RT, i fails o fulfill he requiremens due o a lack of energy capaciy. This resuls in addiional coss since i mus compensae he imbalance hrough he RT marke. The combinaion of π a = 0.9 and π d = 0.8 yields he larges profis for he aggregaor and is used in subsequen analysis Cos/Benefi analysis wih varying baery price Using he bes combinaion of probabiliies (π a = 0.9 and π d = 0.8), he iemized coss and revenues are analyzed wih varying baery coss. The aggregaor mus compensae EVs for he charging and discharging of heir baeries for is own moneary benefi. The aggregaor, however, mus deermine how o cycle is flee of EVs o decide he quaniy o provide in energy, and up/down regulaion markes o maximize profi. By varying he baery coss from 550 o 250 $/kwh, accouning for he expeced advancemen of baery echnologies [34], he iemized expeced revenue and coss are shown in Figure 4.5a and Figure 4.5b, respecively, and he expeced oal profis in Figure 4.5c. A higher baery coss (e.g. 550 and 450 $/kwh), he energy marke provides he larges revenue opporuniies (Figure 4.5a). On he oher hand, he paricipaion of he aggregaor in he regulaion marke is kep o a minimum due o he effec of he degradaion coss and he poenial inabiliy o deploy in he RT. As he baery cos decreases o 350 $/kwh, he paricipaion in he regulaion marke leads o larger revenues (Figure 4.5a), bu a he same ime he aggregaor is unable o deploy some of ha capaciy in he RT resuling in

111 90 Expeced revenue ($) Energy arbirage DA capaciy RT excercise Baery cos, Cv ba ($/kwh) (a) Expeced cos ($) Degradaion: Energy Degradaion: REG REG penaly Baery cos, Cv ba ($/kwh) (b) 500 Expeced oal profi ($) Baery cos, Cv ba (c) 350 ($/kwh) 250 Figure 4.5: Iemized breakdown of he expeced revenue in (a) and coss in (b) wih varying baery cos. The expeced oal profis are shown in (c). penaly coss, as shown in Figure 4.5b. If he baery cos decreases o 250 $/kwh, he aggregaor now decreases is paricipaion in he energy marke o increase paricipaion in he regulaion marke. This shif is explained by lower degradaion cos which resuls in increased revenues from boh DA capaciy and RT exercise paymens as shown in Figure 4.5a. Also shown in Figure 4.5a is he RT exercise revenue which is only obained because he SO requesed he aggregaor o deploy a porion of is capaciy in he RT. The aggregaor incurs coss which are in he form degradaion, because of deploymen in he RT, and penalies because of he inabiliy o supply he requiremens by he SO. The laer occurs because he aggregaor esimaes is expeced capaciy offer and deploymen using he probabiliies π a and π d. For example, in a cerain period, he aggregaor may offer

112 91 ino he marke a quaniy of 2 MW, however, due o is expecaion of his full quaniy o be acceped in he compeiive marke, i schedules he EV flee s charging/discharging for a quaniy less han 2 MW depending on he values of π a and π d. Therefore, he difference beween he offered quaniy, which he SO can eiher accep fully or a porion hereof, and he acual scheduled quaniy demonsraes he aggressiveness of he aggregaor s marke paricipaion. The aggregaor runs he risk of over-offering ino he marke, which i may be unable o deploy and hus mus purchase he imbalance in he RT. Figure 4.5c shows he oal expeced profis which indicaes ha for higher coss, he profis are much lower han wih lower cos baeries. Overall, when he cos is more han 350 $/kwh, energy marke arbirage is advanageous and as echnology improves resuling in lower coss, e.g. 250 $/kwh, providing regulaion services becomes more profiable. However, noe ha he aggregaor is profiable a all levels of baery coss, which shows poenial as a commercial business paricipaing in boh markes simulaneously Offering sraegy of he aggregaor in he DA Using he bes combinaion of probabiliies (π a = 0.9 and π d = 0.8), Figure 4.6 shows he aggregaor s DA offering sraegy o obain he revenue/coss, shown in Figure 4.5, when he baery cos is 250 $/kwh. Figure 4.6a shows he DA and RT energy price. The RT price is obained from he PQP curves from he process in Figure 4.3. Figure 4.6b shows he down/up capaciy prices and Figure 4.6c shows he iemized quaniies of all services and he oal sysem esoc. From Figure 4.6b, he down reserve prices are higher during he early hours of he day as compared o he laer hours. This is beneficial o he aggregaor because EVs are more likely o be plugged-in during he nighime hours and hus can provide such services. On he oher hand, up reserve prices have wo disinc peaks a 0800 and 1900 hours and he aggregaor can provide such services around hese peaks. Figure 4.6c shows he iemized breakdown of all poenial services he aggregaor can provide o he DA energy and reserve markes. The aggregaor charges is flee from he energy marke (EMCHG) o mee ransporaion needs of EV owners. Alhough he down

113 92 Energy price ($/MWh) Day-ahead ( b λda,b ) Real-ime ( b vup,b λrt,b ) Capaciy price ($/MW) Down ( b wdn,b λdn Up ( b vup,b λup,b ),b ) Day ahead offers (kw) Time (h) Time (h) (a) (b) EMCHG REGDN STOPDSG EMDSG REGUP STOPCHG esoc Time (h) (c) Figure 4.6: (a) DA and RT energy price, (b) REGDN and REGUP capaciy prices, and (c) iemized breakdown of capaciy, energy, and esoc in he DA Day ahead oal esoc (p.u., kwh) reserve prices are cheaper han he DA energy prices, he aggregaor schedules a majoriy of he regulaion down (REGDN) beween hours 0100 o 0800 so i may use ha o provide arbirage services laer during he course of he day. Therefore, procuring ransporaion needsfromheenergymarke(emchg)decreasesherisksbecauseifhesodoesnoaccep he down regulaion offers, i is sill able o mee he EV needs. In addiion, down regulaion services are no eniled o he exercise revenue because oherwise he aggregaor would receive double benefi of energy ha can be used for ransporaion and a he same ime being paid for i. As a radeoff, by scheduling down regulaion, he aggregaor is decreasing

114 Power (MW) Power (MW) Offer Accep Deploy Toal up regulaion (a) 0 Offer Accep Deploy Toal down regulaion (b) Figure 4.7: Offered, acceped, and acually deployed quaniy for (a) up reserves and (b) down reserves. he poenial charging from he energy marke (EMCHG), which could be scheduled o discharge back ino he grid when profiable. On he oher hand, wih regulaion up, he aggregaor may poenially obain wo sources of revenue, DA capaciy and RT exercise. Therefore, regulaion up provision is scheduled in every period of he operaing day and he aggregaor is essenially performing arbirage beween wo markes. I charges is EV flee wih energy (EMCHG) and a large porion of i is supplied as regulaion up (REGUP and STOPCHG) and a smaller porion discharged back ino he energy marke (EMDSG). As a benefi, if he up regulaion offers are acceped bu only a porion is requesed o be deployed, he aggregaor essenially acquires wo benefis: 1. he energy sored in he flee of EVs can be used in fuure exploiaions, and 2. no discharging compensaion is required since no deploymen maerialized. Degradaion has a major effec on he benefis ha he aggregaor may aain from providing energy arbirage and regulaion. However, for regulaion, he aggregaor can essenially schedule for up/down regulaion in he DA o obain he capaciy revenue for being on-sandby and have a chance ha i will no be deployed in he RT. This is he bes case for he aggregaor, since i is virually using is EVs wihou causing any degradaion, hence no compensaion o he EV owners. This effec can be seen in Figure 6c wih he large

115 94 amoun of up regulaion offers, because he aggregaor is aware only a porion of hese will be acceped and even smaller porion will be acually deployed in he RT. The oal offered, acceped, and deployed quaniies for up and down reserves are shown Figure 4.7a and Figure 4.7b, respecively. The deployed values are based on he resuls of he MC simulaions performed in Figure 4.4. For deploymen, he solid bar represens he average quaniy for all rials and he confidence inerval (red) for one sandard deviaion, hus showing he variabiliy. In Figure 4.7a, 47.8 MW over he course of he day was offered as up regulaion, of which 40.7 MW (85.1%) was acceped by he SO, and of ha 8 MW (27.2%)onaverage wasdeployed wihasandarddeviaion of4.9mw(16.7%). Onheoher hand, down regulaion yielded a oal offering quaniy of 2.2 MW, of which 1.1 MW (51%) was acceped, and 0.4 MW (37.9%) wih a deviaion of 0.24 MW (22.1%) was deployed in he RT. The aggregaor favors up regulaion because i allows boh he capaciy and exercise revenues o be obained. Major reasons for lower quaniies of down regulaion is caused by he aggregaor s commimen o procuring energy for ransporaion, which limis he EV flees capaciy for addiional charging for down regulaion, and also because only he capaciy revenue can be obained. On he oher hand, STOPDSG porion of down regulaion can only be acivaed if energy marke discharging (EMDSG) occurs. However, because REGUP services are profiable, his limis EMDSG from occurring ofen and so STOPDSG is limied. For purposes of simpliciy, i was assumed he probabiliies of accepance and deploymen were equal, i.e. π a = φ a and π d = φ d. Differen values, however, can be chosen for he down regulaion which beer resemble he oucome of Figure 4.7b. A he same ime, his also shows he SO requires less down regulaion Sysem operaor s perspecive Table 4.1 uses he MC rials o show he SO s expeced operaing cos, sandard deviaion of cos, and he sarupcos of commiing addiional unis in he RT, which is compared o he cos of DA commimens. The base case in Table 4.1 presens he coss in he power sysem wihou he aggregaor. Nex, he case when he aggregaor paricipaes in energy markes

116 95 Base Energy Marke Regulaion and Energy Marke RT Toal coss (10 6 $) Sandard deviaion of coss ($) 32,755 32,690 32,282 Sar-up coss ($) 4,521 4,490 3,940 DA Sar-up coss ($) 163, , ,020 Table 4.1: Sysem Operaor s Coss only and finally, he case when aggregaor parakes in boh markes. From Table 4.1, he SO s expeced coss in he RT are reduced when he aggregaor provides services o he grid. Also, he sarup coss in he DA and RT decrease. Even hough he oal quaniaive cos savings seem low, e.g. 0.08% when he aggregaor paricipaes in energy marke and 0.12% when performing in boh markes he qualiaive benefis are of imporance [155], and hese would be mirrored as large amouns of money over an operaing year. The decrease in he sar-up coss shows ha less cycling of convenional generaion occurs in boh he DA and RT [156]. Especially in he RT, he lower sar-up coss indicae he SO requires less fas-saring unis o be on sand-by in he case of deviaions. This follows because he aggregaor obains energy when here is an abundance and less need for deploymen, and hen supplies i when here is a need, hus making i a viable alernaive o convenional generaion for reserve provision. As compared o he convenional generaion, he aggregaor has essenially no sarup coss and also has lower operaing coss, which only include he compensaion of he baery degradaion o he EVs owners. 4.5 Conclusion EV aggregaors are he required mediaors beween large flees of EVs and he SO. This chaper proposed a framework o deermine he opimal bidding/offering sraegy in he energy and regulaion reserve markes, which maximizes he aggregaor s profis while observing he

117 96 incurred loss of uiliy for he EV baeries. In addiion, he aggregaor akes ino accoun is expeced probabiliy of accepances and deploymens for up and down regulaion. EVs can provide a new sream of services o he power sysem, however in order o incenivize he EVs paricipaion in energy and reserve markes, a fair compensaion mechanism mus in place such as discussed in Chaper 2. Resuls show he aggregaor benefis from he reserve marke more han he energy marke for wo main reasons: 1) i collecs capaciy revenue for providing regulaion, which does no incur degradaion, and 2) i gains addiional revenue if required o deploy in he real-ime. When he baery coss are high, mos of he revenue is obained from he energy marke, however, wih low baery coss mos of he revenues come from regulaion reserve provision. This is because as he baery coss decrease, he provision of regulaing reserve would resul ino wo sreams of revenue: capaciy and deploymen. The provision of hese services from EVs is also beneficial o he SO, since i would reduce he oal operaing coss of he sysem. By combining he works in Chaper 2, 3, and 4, a complee business and operaing framework can be incorporaed by an aggregaor. This complee framework considers he mehodology o conrol consumer loads, e.g. EWHs, HVAC, EVs, among ohers, manage he grid limis, e.g. lines, ransformer aging, and he bidding/offering sraegy in he wholesale markes o generae revenue. Such frameworks open business opporuniies for new players o ener he marke.

118 97 Chaper 5 OPTIMAL MARKET PARTICIPATION OF AGGREGATED ELECTRIC VEHICLE CHARGING STATIONS CONSIDERING UNCERTAINTY 5.1 Inroducion In Chapers 2-4, he focus was on an aggregaor managing residenial cusomers equipped wih EVs and oher loads in order o provide benefis, i.e. addiional revenue, lower operaing coss, among ohers. However, an aggregaor is capable of no only managing ensembles of loads bu also a flee of elecric vehicle charging saions (EVCS), which is he focus of his chaper. As he EV peneraion grows high-capaciy charging infrasrucure is required o provide energy needs for ransporaion. The infrasrucures energy needs will be procured hrough a power uiliy, which may no have he capaciy o provide such volaile and high-power needs on-demand and a he same ime a he minimal cos. As a soluion, he saions can resor o he day-ahead (DA) elecriciy markes, where hey may obain heir energy needs a lower coss and ensure qualiy-of-service for heir EV cusomers. To paricipae in DA markes, marke operaors se forh minimum capaciy requiremens, e.g. 0.5 MW in CAISO [157] and 0.1 MW in ERCOT [158]. However, a single saion will no be able o mee hese minimum capaciy requiremens. On op of his, i would be exremely difficul o predic is daily load curve. Thus, a cenralized aggregaor can aggregae he power requiremens of an ensemble of EVCS in order o effecively paricipae in he DA marke and reduce he elecriciy procuremen coss. To furher reduce he coss, he aggregaor can perform energy arbirage wih an energy sorage sysem (ESS) i manages in conjuncion wih he charging saion ensemble.

119 98 The work in his chaper proposes a framework for an aggregaor o manage an ensemble of EVCSs o bid/offer ino he wholesale elecriciy marke wih he primary goal of minimizing operaing coss. The aggregaor, o furher reduce is coss, is equipped wih an ESS ha acs as a buffer which can provide flexibiliy o he marke bids/offers, while considering he effec of baery degradaion due o cycling. The aggregaor DA opimizaion model incorporaes uncerainy managemen of marke prices, using robus opimizaion (RO), and of EVCS power demand, using sochasic opimizaion. For cos-effecive operaion, he aggregaor mus effecively manage uncerainy while considering he rade-off beween poenial cos reducion compared o degradaion of is ESS. The main conribuions of his work are: Aggregaor DA opimizaion model managing aggregaed power needs of EVCSs while considering demand and marke price uncerainy. Complee ESS model ha supplies energy o he grid or o he EVCSs, if economically profiable, while considering degradaion coss. Realisic framework of an aggregaor exploiing is ESS, power sysem marke, and EVCSs. 5.2 Framework Aggregaor is a profi-seeking business eniy who acs as a mediaor beween he EVCSs and he wholesale elecriciy markes and conains an ESS. Fig. 5.1 shows is ineracions wih he differen eniies: ensemble of EVCSs, power sysem, and elecriciy markes. The aggregaor coordinaes wih each EVCS under is jurisdicion o obain heir charging demand requiremens for he nex day. The demand of each EVCS is hen used o obain he aggregaed demand. The aggregaor performs a DA opimizaion o schedule is operaion a he leas-cos, while exploiing is ESS asse. The ESS charges from he grid in grid-o-baery (G2B) mode when he price of elecriciy is low. During he periods of high elecriciy prices i can eiher supply he saions in baery-o-saion (B2S) mode or injec energy back ino

120 99 Aggregaed EVCS Aggregaor wih Energy Sorage Sysem Elecriciy Marke E V C S E V C S Demand Transacions E V E V C S C S B2S E V E V C S C S G2B B2G G2S Informaion flow Energy flow Power Sysem Figure 5.1: Aggregaor s ineracion wih he EVCSs, elecriciy marke, and power sysem. he grid in baery-o-grid (B2G) mode. If he aggregaor is unable o supply all of he energy needs from he ESS in B2S mode, i resors o obain he power direcly from he grid in grid-o-saion (G2S) mode. The aggregaor s opimizaion deermines he marke bids (G2B and G2S services) and offers (B2G services) as a price-aker in he DA wholesale markes EVCS perspecive Wihou he inervenion of an aggregaor, each individual EVCS resors o purchasing elecriciy direcly from heir local power uiliy company. From a business perspecive, he average cos of reail energy is higher han in he wholesale elecriciy markes [159]. Each individual EVCS, however, may no mee he minimum energy requiremens o paricipae in a wholesale marke, and a he same ime, heir primary objecive is o provide charging services o heir EV cusomers. On he oher hand, he purpose of he aggregaor is o opimize is marke performance and provide service o he individual EVCSs. Therefore, he aggregaor should be reimbursed for is services by he EVCSs. However, his mehodology is no in he scope of his work.

121 100 Wihin his framework, he EVCS are assumed o have in place an inernal day-o-day operaion for managing each individual EV cusomer. An ineresed reader is advised o refer o [97, 98, 99] for such mehodologies. In his framework, each EVCS mus provide is load curve for he following day. Noe ha inernally, each EVCS may accommodae any pricing srucure o expense individual EV charging and he resuling forecased demand would be a by-produc of ha. Such communicaion hides proprieary informaion, for example, he number of EVs arriving a he saions, power requiremens of EVs, ype of charging proocols used, among ohers. The major benefi is ha an EVCS is no required o change heir inernal business/operaing procedures o conform o he aggregaor s framework ESS The ESS, which is owned by he aggregaor, is beneficial when scheduling energy in he DA. Wihou he ESS, he aggregaor has no oher opion bu o blindly follow he aggregaed demand curve. Wih he ESS a he disposal, however, i can charge and sore energy which iseiher usedosupply EVCSsinB2SmodeorreurnohegridinB2Gmode, ifeconomical. These operaions by he ESS, however, cause baery degradaion [10] and for hem o be viable, he poenial cos savings incurred mus be higher han he cos of degradaion. The following secion discusses he mahemaical formulaion of he opimizaion model considering he ineracions of he aggregaor shown in Fig Opimizaion Model Day-ahead model In he DA model, an opimal charging/discharging schedule is deermined for he EVCS o maximize is profi. The EVCS deermines he amoun of energy o sell p sell and buy p buy fromhegridomee heaggregaedevcs demandd. Theobjecive funcionisformulaed

122 101 as follows: min T λ (p buy p sell ) (5.1) where p buy = p G2B + p G2S and p sell = p B2G η wihin he se of ime periods T wih index. The aggregaor sells energy (p sell ) by scheduling is ESS o perform in B2G mode, i.e. p B2G, while considering baery discharge efficiency η. On he oher hand, he aggregaor purchases energy from he marke (p buy ) o boh charge he ESS (p G2B ) and direcly supply he power consumpion requiremens of EVCSs (p G2S ). The buying and selling of energy is priced a he DA marke prices λ wih a imesep of. The objecive funcion (5.1) is subjec o several consrains. The firs se of consrains (5.2) and (5.3) deermine he energy sae-of-charge (SoC) of he ESS. In (5.2), he SoC is dependen on is previous sae, he charging power p G2B, he discharging power p B2G, and he amoun of power discharged from he baery o supply he saions p B2S. Consrain (5.3) ensures he SoC does no violae is prese minimum and maximum limis, and a he same ime is below is raed capaciy BC ES. soc = soc 1 + ( p G2B η p B2G ) p B2S T (5.2) 0 SoC soc SoC BC ES T (5.3) The aggregaor obains forecass of he power consumpion from each EVCS d which is hen summed o obain D, i.e. D = d. This hen mus be me from a combinaion of he ESS discharging in B2S mode, p B2S is managed by consrain (5.4)., or direcly from he grid in G2S mode, p G2S. This p B2S η +p G2S = D T (5.4) The se of consrains (5.5)-(5.7) ensures he differen services provided by he ESS are wihinheir minimum andmaximum power limis, P max. A hesameime, hese consrains also disallow B2S o occur simulaneously wih B2G and G2B, where x {0,1} is an auxiliary binary variable. For example, if x = 1 hen B2S is allowed whereas B2G and G2B

123 102 are disallowed. This is implemened o ensure he ESS sysem performs only charging or discharging, and no boh simulaneously, which is physically no viable. 0 p B2S P max x T (5.5) 0 p B2G P max (1 x ) T (5.6) 0 p G2B P max (1 x ) T (5.7) The las consrain (5.8) ensures he oal energy in he ESS a he beginning of he opimizaion horizon is replenished by he end, i.e. = T. soc = T = SoC ini (5.8) Demand uncerainy The aggregaor obains demand requiremens of each EVCS for he nex operaing day, which ishen aggregaedino D. However, each EVCSs demand is prone o uncerainy hus rendering D o be uncerain. This is he case because he demand is based on predicable, ye uncerain arrival, deparure, and charging imes of EVs a EVCSs. Thus, he aggregaor mus ake ino consideraion he effec of such demand uncerainy on is decision-making process for wholesale marke paricipaion. To hedge agains his uncerainy, he echnique of sochasic opimizaion[160] is implemened. This echnique akes advanage of he known probabiliy disribuions of he uncerain parameers (i.e. D ). Wih his, insead of using a singleaggregaeddemandscenariod inheopimizaion, nowaseofscenarioss wihindex s is considered, i.e. D s,. In addiion, each demand scenario D s, has an expeced probabiliy π s o maerialize in he real-ime (RT). Wih his approach, he aggregaor obains he DA bidding/offering schedule ha is opimal wih respec o all he demand scenarios insead of only of hem paricularly. The mahemaical formulaion of he aggregaor s DA sochasic opimizaion is as follows:

124 103 min T λ (p buy p sell )+ s S s S π s λ p s, T π s λ p + s, (5.9) T subjec o: soc s, = soc 1 + ( p G2B η p B2G ) p B2S s, s S, T (5.10) 0 SoC soc s, SoC BC ES s S, T (5.11) p B2S s, +p G2S +p s, p+ s, = D s, s S, T (5.12) 0 p s, p B2S s, +p G2S s S, T (5.13) 0 p + s, pb2s s, +p G2S s S, T (5.14) 0 p B2S s, P max x s S, T (5.15) soc s,= T = SoC ini s S (5.16) Consrains (5.6),(5.7) (5.17) The objecive funcion (5.9) has wo addiional erms as compared o (5.1). The expeced cos of purchasing addiional energy in he RT marke in scenario s is deermined based on he power shorage p s, and he buying price λ. Similarly, he expeced revenue from selling surplus energy in he RT marke in scenario s is deermined based on he excess power p + s, and selling price λ. Boh of hese wo erms conain probabiliy π s represening he chance of he demand scenario s o maerialize in he RT. The objecive funcion is subjec o he consrains similar o (5.2)-(5.8), however, wih he addiion of sochasic scenario index s. The decision variables ha include index s are soc s, and p B2S s,, as hey are wai-and-see decisions wihin he sochasic framework [160], and are deermined afer he demand maerializes in he RT [160]. On he oher hand, he variables represening G2B (p G2B ), B2G (p B2G ), and G2S (p G2S ) are here-and-now decisions, i.e. hey have he same value regardless on he scenario. The bidding/offering decisions ino

125 104 he markes, i.e. G2B, B2G, and G2S, are based on he weighed average values over all scenarios. Slack variables p s,,p + s, capure he shorage/excess a each scenario. The final energy balance is expeced o be obained from he RT marke. On he oher hand, B2S is he operaion of he ESS o supply he EVCSs, which does no require ineracion wih markes and can be conrolled by he aggregaor as demand maerializes in he RT Marke price uncerainy The aggregaor, using is ESS, explois elecriciy marke prices λ by purchasing energy p buy when prices are low and selling energy p sell when prices are high. To paricipae in he DA marke, however, he aggregaor forecass marke prices which are uncerain. Such price uncerainies may cause he aggregaor o incur moneary losses. For example, wih forecased prices λ, he aggregaor s opimizaion will schedule and consequenly bid ino he DA marke for large amouns of energy o be procured during he low-price periods. Afer he DA marke clears, however, he realizaion of specific prices may be higher han forecased, and hus may leave he aggregaor wih high moneary losses. To hedge agains such uncerainy in he DA, he RO echnique is implemened [161]. RO is an uncerainy modeling approach suiable for siuaions where he range of he uncerainy (e.g. range of elecriciy prices) is known and no necessarily he disribuion. Deviaions of he marke prices are modelled wihin he range [ ] λ min,λ max, where λ max λ min = + λ and λ is he highes expeced price deviaion in period. To conrol he level of proecion agains uncerainy, parameer Γ is varied from [0,J], where [J = λ > 0]. Wih Γ = 0, no price deviaions are considered and he soluion is equivalen o he deerminisic case, i.e. no consideraion of uncerainy. On he oher hand, if Γ = J he soluion is he mos conservaive since price deviaions a all ime periods are considered, i.e. prices a all ime periods are equal o λ max. This soluion is equivalen o he RO model proposed by [162]. However, he implemened RO procedure is based on [161] and i allows choosing any Γ from range [0, J], hus fine-uning he level of conservaism.

126 105 The RO-based DA model is formulaed as follows: min T λ min (p buy p sell )+Γ RO z RO + y RO (5.18) subjec o: Consrains (5.2) (5.7) (5.19) ) z RO +y RO λ (p G2B T (5.20) +p G2S y RO 0 T (5.21) z RO 0 T (5.22) In comparison o he deerminisic DA objecive funcion (5.1), he exended objecive funcion (5.18) includes wo addiional erms conaining variables z RO and y RO used o accoun for he known price bounds and parameer Γ. This objecive is subjec o he original consrains (5.2)-(5.7) along wih consrains (5.20)-(5.22). Consrain (5.20) deermines he wors se of ime periods in which price deviaions could maerialize when ineracing wih he marke in G2B and/or G2S. RO variables z RO and y RO are posiive, which is imposed in consrains (5.21)-(5.22). The ineresed reader is encouraged o refer o [161] for deails on how o obain he robus counerpar Baery degradaion managemen As he baery cells wihin he ESS charge and discharge, hey lose a fracion of heir capaciy, which is ofen referred o as baery degradaion [10]. The aggregaor incurs all coss relaed o he ESS and hus mus consider coss of degradaion in is DA opimizaion. Degradaion managemen deermines he opimal rade-off beween revenue colleced from services, i.e. B2G and B2S, and he cos of cycling he baery. Wihou degradaion managemen, he ESS would be exploied o obain he maximum revenue, however, i would experience excessive degradaion ha is no economically jusified.

127 106 The formulaion of he aggregaor model ha considers baery degradaion is as follows: min λ (p buy p sell )+ m T socdeg C ES BC ES (5.23) 100 BC ES T subjec o Consrain (5.2) (5.7) (5.24) soc deg soc 1 soc T (5.25) soc deg 0 T (5.26) The second erm in objecive funcion (5.23) represens he degradaion coss, where C ES is he $/kwh price of he ESS, which includes he balance-of-sysem coss, e.g. baery and labor [163]. In addiion, soc deg deermines he amoun of energy discharged from he baery in period and m is a linear approximaion of he baery life as a funcion of he number of cycles. Parameer m can be esimaed based on daashees of baery manufacurers [164]. The objecive funcion is subjec o consrains (5.2)-(5.7) and (5.25)-(5.26). In (5.25), he consrain models max{0,soc 1 soc }, where he amoun of energy discharged from periods 1 o is deermined. I is assumed he same energy discharged was charged ino he baery in previous ime periods in order o complee one full cycle of degradaion [10]. Consrain (5.26) imposes non-negaiviy on soc deg Complee DA model The complee aggregaor s DA model ha includes EVCSs demand uncerainy, marke price uncerainy, and ESS degradaion coss is formulaed as follows: min T λ (p buy p sell ) + π s λ p s, π s λ p + s, s S T s S T +Γ RO z RO + y RO + m 100 T socdeg BC ES C ES BC ES (5.27)

128 107 Power (kw) Power (kw) Time (h) (a) % 90% 100% Power (kw) Time (h) (b) Time (h) (c) Figure 5.2: Day-ahead forecas of aggregaed EVCS demand a he workplace locaion (a), commercial locaion (b), and he oal sum of he wo (c). The inervals 50%, 90%, and 100% are shown o represen he spread of he daa. For example, 50% of he EVCS demand lies wihin he specified range. The objecive funcion (5.27) is subjec o consrains (5.6), (5.7), (5.10)-(5.16), (5.20)- (5.22), and (5.25)-(5.26). Noe in (5.25)-(5.26), he sochasic index s is included ino he SoC, similar o (5.10)-(5.11). 5.4 Case Sudy The proposed approach is applied o aggregaed EVCS demand D obained by implemening he mehodology oulined in [42] using he vehicle daa from he Naional Household Travel Survey (NHTS) [124]. A oal of 5,000 EVs were racked over 1000 days o obain daily charging consumpion profiles in he workplace and commercial (e.g. shopping and resaurans) locaions equipped wih EVCS. The EVCSs are assumed o be fas charging saions (FCS) using Level 3 charging proocol a 40 kw power raing [96]. Fig. 5.2 shows

129 108 Prices ($/MWh) λ min λ max,10% Time (h) Figure 5.3: Day-ahead marke price wih deviaion band for uncerainy he aggregaed EVCS charging profiles a workplace (a), commercial (b), and he oal of he wo locaions (c). In Fig. 5.2(a)-(c), he ligh grey area represens he 50% band (i.e of he sandard deviaion from he mean consumpion), he red is he 90% band (i.e of he sandard deviaion from he mean), and he dark grey is he 100% band, which represens he minimum/maximum of he daa. One housand EVCS charging demand profiles are reduced o a se of scenarios wih heir respecive probabiliies π s using he K-medoids scenario reducion echnique [165]. The capaciy of he ESS is 1 MWh, however, he available SoC ranges from 15% o 95% of he raed capaciy due o consrains on he baeries [127]. The charging and discharging power raings are 500 kw, while he charging/discharging efficiencies are 95%. The iniial ( = 0) SoC of he ESS is randomized. The ESS price is se o 300 $/kwh unless oherwise specified. To represen a ypical weekday DA marke prices, he ERCOT hisorical daa in he period January-March 2016 is used [166]. A ypical price curve ha bes characerizes he daa se is obained using he K-medoids approach [165], and is shown in Fig. 5.3 as λ min. The upper bound prices λ max used in RO are proporional o λ min. To discourage scheduling of bids/offer in he RT markes under he sochasic opimizaion framework, he buying λ andselling λ pricesareassumed obewice andhalf hedaypical pricesλ min, respecively.

130 109 CDF S = 1, Γ = 0 S = 1, Γ = 36 S = 5, Γ = 48 S = 5, Γ = 60 S = 10, Γ = 72 S = 10, Γ = 96 S = 25, Γ = 72 S = 50, Γ = Cos (p.u) Figure 5.4: Normalized cos CDFs for combinaions of sochasic scenarios and price robusness parameer Opimal combinaion of sochasic scenarios and RO parameers To minimize is operaing cos, he aggregaor mus deermine is opimal bidding/offering sraegy in he DA marke. To do so, he uncerainy of energy prices and EVCS demand mus be esimaed using he RO parameer, Γ, and he number of scenarios S in sochasic opimizaion, respecively. To deermine he bes combinaion of parameers ha yield he minimal operaing cos, Mone Carlo (MC) simulaions are performed [154]. The DA schedules are obained for all discree RO parameers in Γ = [0, T ], and sochasic scenarios, S = [1,5,10,25,50,100]. For each combinaion of S and Γ yielding a DA schedule, MC rials were performed o deermine he acual cos of operaion as he uncerainy maerializes. The number of MC rials are se o min{1000,n MC }, where N MC is he number of rials required o obain a 95% confidence of an error less han 1% [154]. In he MC simulaions, 32 price and 32 EVCS demand profiles are used oalling 1024 MC rials. Fig. 5.4 shows he normalized CDF of he aggregaor operaing cos for differen combinaions of Γ and S. Cos of each MC rial is normalized agains he mean cos of he deerminisic MC rial, i.e. S = 1 and Γ = 0. In oher words, normalizaion occurs agains cos realizaions when uncerainy is no aken ino consideraion. While all combinaion of

131 110 S and Γ are considered, Fig. 5.4 shows only selec combinaions for clariy. From Fig. 5.4, he CDF curves o he lef of he deerminisic curve yield he lowes operaing cos over all MC rials. In all combinaions where S > 1 and Γ > 0, he aggregaor sees cos savings. However, if only a single scenario, i.e. S = 1, is considered wih Γ > 0, specifically he case shown in Fig. 5.4 where S = 1,Γ = 36, he coss are higher han in he deerminisic case. This is caused by he RO, where i increases B2S and decreases B2G energy o proec agains unforeseen price deviaions ha may maerialize wihin he bounds shown in Fig Thus, i is more favorable o offse he demand needs of he EVCSs using he ESS o discharge in B2S, compared o selling energy back o he grid in B2G mode. Since B2S is highly-favored wih respec o he se wih a single scenario, i.e. S = 1, he operaing cos is increased because once he demand maerializes, he single demand scenario canno capure he volaile demand variaions hus requiring addiional energy purchases. On he oher hand, he cases wih S > 1,Γ > 0 ouperform he deerminisic case. This shows ha boh he demand and price uncerainy should be properly characerized in order o obain he minimum operaing cos. In addiion, from Fig. 5.4, some combinaions ouperform ohers, e.g. S = 10,Γ = 72 and S = 25,Γ = 72. Thus, he price uncerainy parameer Γ = 72 yields he lowes cos. The major difference, however, beween hese wo cases are he number of considered scenarios, i.e. 10 compared o 25 scenarios. In erms of compuaional complexiy of sochasic opimizaion, larger number of scenarios requires addiional compuaional ime o obain he opimal soluion [160]. Thus, i is imporan o analyze he sauraion poin a which higher number of scenarios does no yield subsanial cos savings. This is sudied in Fig. 5.5, where he average normalized coss over all MC rials are shown agains he number of sochasic scenarios S for differen values of Γ. In addiion, he compuaion imes for Γ = 72 over a selec number of sochasic scenarios are shown in Table 5.1. As expeced, he average cos experiences a significan decrease from a single scenario o five scenarios. If Γ = 72, here are clear cos savings beween 10 and 25 scenarios (Fig. 5.4). However, he compuaional ime increases from 34.3 o 806 seconds.

132 111 Cos (p.u) Γ = 0 Γ = 36 Γ = Sochasic scenarios, S Figure 5.5: Normalized average cos as a funcion of he number of sochasic scenarios. Table 5.1: Compuaional Times (seconds) Sochasic Scenarios, S Γ = This increase in compuaional ime sill keeps he problem racable for marke operaions. On he oher hand, moving from 25 o 50 scenarios, he cos savings is minimal bu he compuaional ime increases drasically o 4486 seconds. The combinaion of he number of scenarios, S = 25, and he RO parameer, Γ = 72, yields a balance beween he leas operaing cos over all MC rials and compuaional burden. This combinaion is used hroughou he remainder of he es case Baery degradaion effecs As he ESS is used, i experiences cycle-life degradaion which can be ranslaed ino cos, as shown in equaion (5.23). The ES price, normalized on a per-kwh basis, is varied from 800 $/kwh o 300 $/kwh o sudy he effec on he aggregaor s G2B, B2S, and B2G acions. The degradaion model, as shown in (5.23), is linear and represened by slopes m = [0.0017, ]. The lower slope is he approximaion of he curren echnology [164], and he higher slope indicaes echnological life cycle improvemen. The aggregaor s daily oal energy scheduled as a funcion of he ESS price is shown

133 112 Energy (kwh) p G2B p B2S p B2G Baery price, C ES ($/kwh) (a) Energy (kwh) p G2B ( ) p B2S / S,s p B2G Baery price, C ES ($/kwh) (b) Figure 5.6: Toal daily energy scheduled in he deerminisic case (a) and wih uncerainy managemen considered (b), as a funcion of varying ESS prices. Noe in (b) he average B2S is shown since i is a funcion of scenario s. in Fig. 5.6 for G2B, B2S, and B2G services. Fig. 5.6(a) shows he deerminisic case, i.e. S = 1,Γ = 0, whereas Fig. 5.6(b) considers uncerainy wih he bes esimaes. In boh cases, as he ESS price decreases, he amoun of energy scheduled for all operaing modes monoonically increases because he poenial revenue ouweighs he degradaion coss. As for he specific modes, selling energy back o he grid in B2G mode is highly unfavorable when uncerainy is considered. For B2G o occur profiably, he aggregaor mus purchase energy in he low-price periods o charge he ESS (G2B) so i can sell back o he grid by discharging in he high-price periods. However, he uncerainy in marke prices renders he poenial arbirage revenue o be lower han expeced and hus as a resul, less B2G is scheduled. However, if he price of he ESS is low enough, i.e. less han 400 $/kwh, B2G is sporadically scheduled because he poenial grid revenue obained for such services ouweighs he degradaion coss, as shown in Fig. 5.6(b). On he oher hand, when considering uncerainy managemen in Fig. 5.6(b), he aggregaor decreases B2G and increases B2S for all baery prices. This happens because by scheduling B2S, he aggregaor offses he need o purchase energy from he grid (G2S) exacly in periods when he EVCSs require i. Insead, he aggregaor uses he energy purchased during low-price periods and sored in he ESS o discharge and supply he EVCS

134 113 Power (kw) p buy wihou ESS p buy wih ESS p sell λ min Time (h) Prices ($/MWh) Figure 5.7: DA marke buying and selling sraegy in he deerminisic case. (B2S). The aggregaor uses he ESS as a mehod o reduce moneary risks in he elecriciy markes Day-ahead schedules The aggregaor deermines is bidding/offering schedule in he DA as shown in Fig. 5.7 for he deerminisic case, and in Fig. 5.8 for he case considering uncerainy wih he bes esimaes. The ne power purchases p buy wih and wihou he ESS, he power sold p sell, and DA marke prices are shown in he figures. The ne purchases wih he ESS is equivalen o p buy = p G2S + p G2B ( ) s S pb2s,s / S, whereas wihou he ESS i is equivalen o p buy han p buy = p G2S. Also, p sell = p B2G in boh cases. If any period, he p buy wih ESS is greaer wihou ESS, hen he ESS is performing in G2B and hus addiional purchases are made. On he oher hand, if he opposie is rue (less han), hen B2S is occurring which reduces purchases in he marke (i.e. offses G2S). In he deerminisic case ( S = 1,Γ = 0), he aggregaor explois he low-price periods (03:00 o 04:30, and 14:15 o 15:45) by scheduling purchases in he form of G2B (p buy ESSinredislargerinheseperiods). Duringhehigh-priceperiods(07:15o08:45, and19:30 o 21:00), he aggregaor discharges he ESS o obain revenue from he marke (p buy ESS in red is lower in hese periods). The discharging, however, is spli beween B2G (p sell ) wih kwh and B2S wih 1074 kwh oal. The oal B2S energy is higher han B2G wih wih

135 114 Power (kw) p buy wihou ESS p buy wih ESS p sell λ min Time (h) Prices ($/MWh) Figure 5.8: DA marke buying and selling sraegy when uncerainy managemen is considered. Noe ha he average B2S is used in p buy scenario se. wih ESS since i is dependen on he because he demand needs of he EVCS, as shown in Fig. 5.2(c), correlae wih he high-price regions. Thus, i is economical o discharge, while incurring degradaion coss, o supply he EVCSs in B2S and offse purchases direcly from he marke in G2S. Furhermore, B2G is only exploied when he poenial revenue ha can be obained by selling in he marke ouweighs boh he degradaion cos and he poenial benefi of performing in B2S mode o offse G2S. This effec can be seen in Fig. 5.7 where B2G (p sell ) is scheduled o be sold during he high-price periods bu no during he peaks, because i is more economical o perform B2S due o correlaion wih EVCS demand. In Fig. 5.8, he DA schedule is shown considering he bes esimaes of uncerainy managemen, i.e. S = 25,Γ = 72. As compared o he deerminisic case, G2B is spanned acrossmoreimeperiods(i.e. p buy wih ESS is larger). This occurs because he RO echnique makes he aggregaor hedge agains he wors-case of unforeseen increase in marke prices. As an example, in Fig. 5.7, he lowes-price period is 03:15 hours, and he maximum power of 500 kw is scheduled by he aggregaor. However, poenial uncerainy exiss in he esimae of he marke price, and hus he aggregaor is risk-averse by scheduling 212 kw in ha ime period as shown in Fig When considering uncerainy (Fig. 5.8), he aggregaor does no schedule any B2G

136 115 (p sell = 0 in all periods). Insead, i increases he average B2S o 2161 kwh compared o he 1074 kwh in he deerminisic case in Fig An example of his can be seen from periods 18:00 o 23:30, where B2S is performed consisenly (p buy wih ESS is lower). This occurs because in he wors-case he marke prices may be higher han expeced, and hus here migh be an adverse effec on he overall cos caused by excessive purchasing in G2S mode from he marke. In addiion, since he aggregaor also considers muliple scenarios of demand ha may maerialize, he B2S is scheduled as an average response across all scenarios, as opposed o only a single scenario. Therefore, B2S is no only increased significanly, bu also spread across muliple ime periods ha correlae wih he EVCS demand (see Fig. 5.2(c)) o offse G2S purchases Yearly cos/benefi analysis The aggregaor mus obain a moneary benefi when paricipaing in he grid markes and scheduling he ESS. A yearly cos/benefi analysis is performed for wo cases: 1) day-ahead marke (DAM) case where he aggregaor schedules he aggregaed EVCSs wihou he ESS, and 2) DAM including he ESS. The resuls are summarized in Table 5.2. In he firs case (1), he aggregaor manages he EVCSs and paricipaes in he DAM, which incurs a cos of $311,092 which is solely based on purchases from he marke in G2S mode. Furhermore, if he aggregaor uses an ESS in conjuncion wih he marke scheduling, i obains revenue benefis of $47,321 by performing in B2S/B2G mode. However, his inroduces addiional coss relaed o purchasing energy in he markes in G2B mode and he respecive degradaion coss when charging/discharging as shown in Table 5.2. By implemening an ESS, he oal coss are reduced from he DAM case by 5.31%. I is imporan o emphasize ha he ESS insallaion cos, cos of marke paricipaion, bidirecional meering cos, or any oher auxiliary coss ha arise in he cases are no considered. Therefore, he presened comparison of yearly revenue should be used as a basis for a deailed cos/benefi analysis.

137 116 Table 5.2: Yearly Cos/Benefi Analysis Coss ($) Benefi ($) Toal ($) G2S G2B ES deg. B2S/B2G 1) DAM 311, ,092 2) DAM + ESS 311,092 27,185 3,627 47, , Conclusion This chaper developed a framework for an aggregaor o manage an ensemble of elecric vehicle charging saions o paricipae in he day-ahead elecriciy marke o minimize energy procuremen coss. To furher reduce coss, he aggregaor explois is energy sorage sysem o charge during he low-price periods in G2B mode, and hen o discharge and eiher supply he saions direcly in B2S mode or o injec power o he grid in B2G mode. However, since he charging/discharging of he ESS causes degradaion, his effec is ranslaed ino an economic index and aken ino consideraion. To manage uncerainy, a sochasic and robus opimizaion approach are employed for he charging saion power needs and marke prices, respecively. The employmen of robus opimizaion for marke price uncerainy allows fine-uning he conservaiveness of he soluion by varying he parameer Γ. On he oher hand, weighed sochasic scenarios capure he expeced cos of operaions over demand scenarios ha are esimaed probabilisically. The benefi of his framework is wofold. Firs, he volaile and high-power needs of he charging saions are now procured in he day-ahead marke, and second, he charging saions can now focus on heir primary role o provide services o elecric vehicle cusomers as opposed o aemping o reduce energy procuremen coss. Resuls show ha he aggregaor provides exensive benefis o he charging saions by managing heir energy procuremen from he wholesale marke. The cos savings, however, are only experienced if uncerainy is properly characerized. The oal cos savings are 5.31% if boh DA marke paricipaion and uncerainy managemen is implemened wih

138 117 an ESS, as compared o ignoring he ESS. While i is expeced ha charging saions will provide he necessary infrasrucure for EVs, oher infrasrucures are needed ha provide on-demand service for EVs. The concep of baery swapping saions have been discussed in he lieraure and also in commercial applicaions. The nex chaper develops a business and operaing framework for such swapping saions.

139 118 Chaper 6 OPTIMAL OPERATION AND SERVICES SCHEDULING FOR AN ELECTRIC VEHICLE BATTERY SWAPPING STATION 6.1 Inroducion The frameworks in Chaper 2, 3, and 4 are mehods ha ackle EV issues of upfron coss by providing sreams of revenue o owners. However, he issues of range anxiey, slow charging imes, and lack of public infrasrucure canno be solved direcly by exracing services from EVs. Baery swapping saions (BSS) are poised as effecive means of eliminaing hese issues [9]. Since he BSS is a new player ha aggregaes and operaes a large number of EV baeries in is sock, i can direcly paricipae in he wholesale power markes wihou he need of a mediaor, e.g. aggregagor. As an objecive, he BSS seeks o maximize is profis, by paricipaing in markes and providing services, such as demand response, energy sorage, and reserves. The soring capabiliies of he BSS are scheduled based on ime-varying elecriciy prices, e.g. RTP. The BSS maximizes is profis by exploiing he low-price periods of he day o purchase elecriciy and charge baeries in Grid-o-Baery mode (G2B), and sell during he high-price periods by discharging baeries o he grid in Baery-o-Grid mode (B2G). Addiionally, BSS can perform Baery-o-Baery (B2B) services in order o charge cerain baeries using he energy sored in oher baeries. The BSS mimics a radiional gasoline saion in is operaions. Consumer s arrive a he BSS wih depleed baeries and he baeries are swapped wih fully-charged ones. Such swapping relieves he sress of range anxiey and slow charging imes of EV owners. In addiion, he BSS would lease he baeries o EV owners and hus reduce he overall operaing cos in mainaining he baery. The moivaion behind his chaper is o presen

140 119 Cusomers Baery Swapping Saion Elecriciy Marke Fees B2B Transacions Services B2G G2B Power Sysem Figure 6.1: BSS ineracions wih cusomers, marke, and he power sysem. a complee BSS framework ha benefis he BSS iself, EV consumers, and he power grid. The main conribuions of his chaper are: A realisic framework of a BSS in he DA scheduling process in order o ake advanage of G2B and B2G services. Complee BSS operaing model including baery degradaion, marke price uncerainy, and baery demand uncerainy. The impac of each feaure is individually analyzed. The model explois he abiliy o ransfer energy among baeries in B2B mode, if here is an economic benefi. 6.2 Business Case Operaions The operaion of he BSS is shown in Figure 6.1 [167]. The BSS s goal is o supply he baery demand while maximizing is profis. The BSS requires a sock of baeries wih differen capaciies o serve is cusomers. I is assumed he baeries are owned by he BSS and leased o he cusomers. The cusomers benefi from his arrangemen since all he coss relaed o he baeries, including degradaion and mainenance, are accrued by he BSS. The cusomer is no concerned wih he baery lifeime nor wih he way in which he