Spatiotemporal Arbitrage of Large-Scale Portable Energy Storage for Grid Congestion Relief

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1 Spaioemporal Arbirage of Large-Scale orable Energy Sorage for Grid Congesion Relief Guannan He 1, Da Zang 2, Xidong i 1, Qixin Cen 3, Soummya Kar 1, and Jay Wiacre 1 1. Carnegie Mellon Universiy; 2. Massacuses Insiue of Tecnology; 3. Tsingua Universiy guannan@andrew.cmu.edu, zangda@mi.edu, xpi@andrew.cmu.edu, qxcen@singua.edu.cn, soummyak@andrew.cmu.edu, wiacre@andrew.cmu.edu Absrac Energy sorage as grea poenial in grid congesion relief. By making large-scale energy sorage porable roug rucking, is capabiliy o address grid congesion can be grealy enanced. Tis paper explores a business model of large-scale porable energy sorage for spaioemporal arbirage over nodes wi congesion. We propose a spaioemporal arbirage model o deermine e opimal operaion and ransporaion scedules of porable sorage. To validae e business model, we simulae e scedules of a Tesla Semi full of Tesla owerpack doing arbirage over wo nodes in California wi local ransmission congesion. Te resuls indicae a e conribuions of porable sorage o congesion relief are muc greaer an a of saionary sorage, and a rucking sorage can bring ne profi in energy arbirage applicaions. Index Terms orable energy sorage, spaioemporal arbirage, sorage rucking, ransmission congesion relief I. INTRODUCTION Te increasing deploymen of energy sorage as driven e sorage cos down due o economies of scale [1],[2], wic in urn encourages more deploymen. Tere are various sorage applicaions including energy arbirage [3], reserve [4], frequency regulaion [5],[6], renewable inegraion [7], volage suppor [8], ec. Sorage can also provide muliple services a e same ime [4],[9],[1]. Grid congesion as always been a major concern in power sysem [1]. Besides ransmission capaciy expansion, energy sorage provides anoer feasible soluion o e congesion problem. Te poenial use of baery sorage o increase ransmission capabiliy in ermal-limied ransmission lines is invesigaed in [11]. In [7], a meod o coordinae energy sorage and wind power plan is proposed o avoid wind curailmen due o ransmission congesion and is applied o e grid in norern Cile. In [12], a power flow model for e acific Norwes area is buil o idenify ransmission line congesion and analyze e poenial conribuions of energy sorage in cerain locaions o reducing e congesion. In [13], ransmission congesion relief is designed as an ancillary service, and financial compensaion is provided o incenivize e conribuion of privaely-owned sorage o congesion relief. Te concep financial sorage rig is proposed in [14] by developing e analogy beween energy sorage and ransmission line. In [1], a mulisage model is proposed o coordinae sorage in ransmission-level congesion relief and disribuion-level cos minimizaion. Tese sudies explore e use of sorage in grid congesion relief, aloug ey all consider saionary energy sorage only. Te capabiliy of energy sorage o relieve congesion is limied by is capaciy. Wen e sorage is full or empy afer a cycle, i can no longer make any conribuion. However, if a sorage device is porable and can be ranspored beween nodes wi congesion, i can make muc greaer conribuions o congesion relief compared o a saionary sorage device a e same size, especially in cases were e congesion is local (e wo nodes conneced by congesed line are close o eac oer geograpically) as e ravel ime can be very sor. Regarding energy sorage ransporaion for congesion relief, disribued elecric veicle carging conrol is sudied in [15],[16], and veicle-o-grid applicaion of railway sysem is sudied in [17],[18]. In ese sudies, ere is no acive conrol of e veicle locaion for grid congesion relief, and grid congesion relief is jus a side benefi. No large-scale sorage ransporaion for grid applicaion as been sudied so far. In is paper, we explore a business model of large-scale porable sorage, wic consiss of ruck, energy sorage, and power elecronics. In is business model, e ruck is loaded wi sorage and inverers and ravels beween nodes wi congesion, wic is named as spaioemporal arbirage. We propose a spaioemporal arbirage model a deermines e opimal operaion and ransporaion scedules of porable sorage. In e case sudy, we apply e spaioemporal arbirage model o simulae e scedules of a ruck of porable sorage using Tesla Semi and owerpack over wo nodes (3 miles away) wi local congesion in California. By comparing e life-cycle revenue of porable sorage versus saionary sorage, we find a rucking sorage can no only grealy increase e conribuion of sorage o congesion relief bu also bring ne arbirage profi o sorage owner. Te prase spaioemporal arbirage is also used in [19] bu as a oally differen meaning; e spaial decision in [19] is sorage siing, wic occurs a e long-erm planning sage,

2 Number of Hours wi rice Difference >$5/MW wile e spaial decision in is paper is sorage ransporaion, wic occurs in real-ime operaion sage. Te res of e paper is srucured as follows: e grid congesion in California is discussed in Secion II; e concep of porable energy sorage is inroduced in Secion III; e spaioemporal arbirage model is inroduced in Secion IV; Secion V presens a case sudy; Secion VI concludes e paper. II. LOCAL GRID CONGESTION IN CALIFORNIA Local ransmission congesions ave been observed in California recenly. Tere are significan differences in e locaional marginal prices (LM) beween some nodes wi very sor geograpical disance, and some occur very frequenly. Fig. 1 presens e frequency of price difference beween wo nodes around San Marcos a are only 3 miles away (5-mile drive) from Ocober 217 o Sepember 218. Over e 1-year period, ere are over 5 ours wen e price difference is greaer an $5/MW for is pair of nodes. Figure. 1. Frequency of price difference beween wo nodes around San Marcos (California, US) from Ocober 217 o Sepember 218. Node ID: NCMETER_1_N1 and SNTAMRA_1_N San Diego San Marcos Figure. 2. Monly disribuions of e number of ours wen e price difference is greaer an $5/MW for wo nodes around San Marcos, CA (Node ID: NCMETER_1_N1 and SNTAMRA_1_N5) and wo nodes around San Diego, CA (Node ID: CHCARITA_1_N12 and FRIARS_1_N9). Is ere similar emporal paern for congesions beween differen pairs of nodes? No obvious paern from Fig. 2, wic presens e monly disribuions of e number of ours wen e price difference is greaer an $5/MW for wo pairs of nodes in California, one around San Marcos, and e oer around San Diego (15 miles away). Tere are several mons TABLE I BASIC ARAMETERS OF LARGE-SCALE ORTABLE ENERGY STORAGE USING TESLA SEMI AND OWERACK Tesla Semi payload a Energy densiy of Tesla owerpack wi inverer b Toal energy capaciy per ruck wen bo pairs of nodes ave comparaively ig frequency of significan price difference, for example, April, May, and Augus in 218. However, ere are also mons wen one pair as comparaively ig frequency wile e oer does no, for example, November 217 and February 218. Te correlaion coefficien beween e wo frequency series in Fig. 2 is.34, wic indicaes only weak dependency for e congesions. Te absence of uniform congesion paern may favor e porable sorage opion as e sorage can be sared among differen pairs of nodes o make more conribuions o e sysem and earn more profis. For ransmission lines wi infrequen congesion, expanding ransmission capaciy is also less favorable an porable sorage, because e invesmen efficiency is low for e new ransmission capaciy wi low uilizaion rae. In conras, wen ere is no congesion a one locaion, porable sorage can provide oer services and serve oer locaions. III. ORTABLE ENERGY STORAGE 35 onne 13 kg/kw 2.7 MW Capial cos of Tesla Semi a $15, Energy consumpion rae of Tesla Semi a Energy consumpion per uni delivered energy for 5-mile roundrip Labor cos per uni delivered energy for 5-mile roundrip a Source: ps:// b Source: ps:// <2 kw/mile.7% $3/MW To address ransmission congesion, a ypical soluion is o expand ransmission line capaciy. However, consrucing new ransmission line is expensive and ime-consuming. Insead, ere may be anoer feasible opion, wic is o use porable large-scale energy sorage o ranspor energy. Te basic concep is o load ig-energy-densiy energy sorage (liiumion baeries for example) and inverers on rucks o mobilize energy sorage. Te rucks ravel beween subsaions wi significan price difference, discarging a e ig-price node and carging a e low-price node, wic we name as spaioemporal arbirage. Considering bo environmenal benefi and fuel economy, we invesigae e case of using Tesla Semi, an elecric ruck model, o ruck Tesla owerpack. Te parameers of Tesla Semi and owerpack are lised in Table I. Based on e payload of Tesla Semi and e energy densiy of Tesla owerpack, we esimae a one ruck can accommodae approximaely 2.7 MW baeries wi inverers, a a oal cos of $2 million. Truck cos accouns for approximaely 8% of e oal capial cos.

3 As for variable operaional cos, e energy consumpion is minimal for sor rips beween nodes a are geograpically close, wic accouns for less an 1% of e energy capaciy of a ruck for 5-mile roundrip. Te labor cos is a considerable cos a $3/MW, considering a $2/our wage for ruck driver and an average speed a 25 miles/our. IV. SATIOTEMORAL ARBITRAGE MODEL In is secion, on op of emporal arbirage, we develop a spaioemporal arbirage model for porable energy sorage o imize arbirage profi beween wo nodes subjec o operaion and ransporaion consrains. A. Objecive funcion Te objecive of e spaioemporal arbirage dispac model is o imize e oal marke revenue of e porable sorage beween wo nodes ( R ) minus e ransporaion cos ( r d C ) and minus e degradaion cos ( C ), as (1). Te ime orizon of eac dispac decision is ypically a day, represened by, and is e day index. Te decision variables are e dis discarging and carging scedules of e sorage, and ca n,, and ransporaion scedules. is e ime index, and is e dispac ime scale, wic ypically ranges from 5 minues o 1 our. r d dis ca n,, n,, n, Y = R C C () Te marke revenue of sorage is expressed as (2), were n, is e forecased LM a node n and ime ; and n A and n denoe e wo nodes a e sorage ravels beween. B () R = ( ) dis ca n, n, n, [, + ] n{ na, nb} Te main ransporaion cos is e labor cos, wic is assumed o be proporional o e oal ravel ime during day, as (3), were c r denoes e ransporaion cos per uni ime, and is a -1 variable a denoes weer e sorage in ravel a ime. r C = c () r [, + ] Te degradaion cos is an opporuniy cos a reflecs e loss of fuure profi opporuniy due o curren sorage usage[9]. Te sorage degradaion can be divided ino wo caegories according o dependen facors [2],[21]: 1) cycling degradaion a mainly depends on e amoun of energy rougpu e sorage as processed, as e firs expression in (4); and 2) calendar degradaion a mainly depends on sae of carge (SOC), emperaure, and e leng of ime e sorage as experienced [2],[22],[23]. If e average SOC and emperaure are assumed o be consan, e calendar degradaion during a cerain period of ime can also be regarded d as consan, denoed by q in (4). c is e uni degradaion cos, named as e marginal cos of usage, o be deermined by e fuure profiabiliy roug life-cycle operaion simulaions [9]. Typically, e iger e fuure poenial profi, e greaer e marginal cos of usage. d d dis ca C = c ( n, + n, ) + q () [, + ] B. Sorage operaion consrains Te energy consrains of sorage are formulaed as (5) and (6). Te energy level of sorage a ime, E, is a funcion of e energy level a ime 1, E 1, and e carging/discarging scedules a ime, as (5), were is e self-discarge rae, and is e carge/discarge efficiency. Te energy level of sorage canno exceed is capaciy, as (6), were E is e energy capaciy of e sorage. ca dis ( ) E = (1 ) E + / 1 n, n, n{ na, nb} [, + ] E E [, ] () + () Te power oupus consrains are expressed as (7), were is e power capaciy of e sorage, and n, is a -1 variable a denoes weer e sorage is a node n and a ime (1 indicaes presen and indicaes absen). We name as e locaion indicaor. Tis indicaor couples e n, operaion and ransporaion consrains in is model., n { n, n }, [, + ] () dis ca n, n, n, A B C. Sorage ransporaion consrains Te sorage can only be presen a one node a one ime, wic is formulaed as (8). n, is a -1 variable a denoes weer e sorage is raveling o node n a ime, wile is a -1 variable a denoes weer e sorage is n, raveling from node n a ime. n, 1 [, + ] () nn Te ravelling saus of sorage is modelled in (9) o (12), were n, is a -1 variable a denoes weer e sorage is raveling o node n a ime ; n, is a -1 variable a denoes weer e sorage is raveling from node n a ime ; and n, is an -1 auxiliary variable. {, }, [, ] n, n, = n, n, 1 n na nb + ()

4 ower Oupu (MW) rice ($/MW) n{ na, nb} ( n, n, ) + 1 [, + ] () ( ) n, n, = 1 [, + ] () n{ na, nb} 2.7 MW TABLE II MODEL ARAMETERS E 2.7 MW c r 95% $4/rip T 12 mins q 1.5 MW n{ na, nb} ( n, n, ) + 1 [, + ] () Te ravel ime consrain is formulaed as (13), were T is e required driving and insallaion ime for e sorage o leave from one node and be prepared o operae a e oer node, wic may vary across ime considering raffic congesion. 1 T [, + ] () V. CASE STUDY In is secion, we presen a case sudy for a ruck of porable sorage raveling beween e pair of nodes around San Marcos menioned in Secion II. We opimize e operaion and ransporaion sraegies of a ruck of porable sorage raed a 2.7 MW/2.7 MW doing spaioemporal arbirage beween wo nodes around San Marcos using model (1) o (13) for eac day from Ocober 217 o Sepember 218. Te ime scale is se o 15 minues. Te sorage is assumed o be a price-aker, wic means a e oupus of e sorage as no impac on e prices of e nodes. Te real day-aead energy prices are aken as e price forecass. Te carge/discarge efficiency is assumed o be 95%, wic represens a round-rip efficiency of 9%. Te self-discarge rae is assumed o be. For 5-mile single rip, given a $2 ourly wage for ruck driver and a 25 miles/our average speed, e ravel ime is 12 minues, and e labor cos is $4. Te end of life of elecrocemical energy sorage is ypically defined as wen e remaining capaciy decreases o 8% or 7% of e original capaciy [2],[21]. In is paper, e sorage uilizaion and degradaion are measured by energy rougpu (carging plus discarging) in megawa ours in is paper. Te cycle life of liium-ion baery is assumed o be 3 cycles, wic is equivalen o 16.2 GW. Te calendar degradaion rae for liium-ion baery is assumed o be 1% capaciy loss/year, wic is equivalen o approximaely 1.5 MW energy rougpu per day (assuming e sorage life ends wen e capaciy as decreased o 7% of e iniial). Te opimal marginal cos of usage for porable sorage is $25/MW in is case, wile $14/MW for saionary sorage, wic are deermined using an ineremporal operaional decision framework [9]. Te discoun rae is assumed o be 7%. Fig. 3 presens e opimal operaion scedules of e porable sorage and LM profiles of e wo nodes in a sample day. Te broken lines represen e LMs of e wo nodes, respecively. From Hour 8 o Hour 21, ere are remarkable price differences beween e wo nodes, wic indicae congesions, wi Node 1 being e ig-price node and Node 2 being e low-price node. Aloug e real cause of congesion is unknown, i is reasonable o speculae a ere is over-abundan solar generaion a Node 2 according o e price profile. To exploi e price differences, e sorage ravels beween e wo nodes o discarge and sell energy a Node 1 (blue bars) and o carge and buy energy a Node 2 (orange bars). In Fig. 3, eac ime e bar color canges, e sorage makes a rip from one node o e oer, and we can see e sorage makes 5 round-rips in e sample day. Te ravelling capabiliy provides e porable sorage muc more profi opporuniies compared o saionary sorage, because e porable sorage can profi from bo price differences beween differen nodes and beween differen ours wiin one node, wile e saionary sorage can only profi from e price difference wiin one node. As seen from Fig. 3, e porable sorage conducs 4 profiable cycles over e day, wile for saionary sorage i is only profiable o run 1-2 cycles during e peak and valley ours. Te congesion beween e wo nodes can be relived as e sorage brings over 9 MW energy in oal from Node 2 o Node 1 over e day ower Oupu a Node 1 ower Oupu a Node 2 LM of Node 1 LM of Node Time (Hour) Figure. 3. Opimal operaion scedules for a ruck of porable sorage doing spaioemporal arbirage beween wo nodes around San Marcos and e LM profiles of e wo nodes in a sample day (April 17, 218). Figure. 4. Daily ravel ime for a ruck of porable sorage doing spaioemporal arbirage beween wo nodes around San Marcos from Ocober 217 o Sepember 218. Fig. 4 presens e daily ravel ime for e porable sorage over a year. Te oal ravel ime is 181 ours over one year,

5 TABLE III COMARISON BETWEEN ORTABLE STORAGE AND STATIONARY STORAGE wic is approximaely.5 our per day. Te resuls indicae a ere are inensive ravels during some periods of ime, wic coincides wi e monly price difference disribuion in Fig. 2. In ose days wiou significan price difference beween ese wo nodes, e sorage can serve oer pairs of nodes wi congesion in e neigborood. Table III compares e revenues beween a ruck of porable sorage doing spaioemporal arbirage beween e wo nodes around San Marcos and a saionary sorage of e same size doing arbirage a Node 2. By rucking, e sorage revenue in e firs year is increased by $44,, and e oal life-cycle sorage revenue is increased by $24,, wic is greaer an $15,, e cos of a Tesla Semi. Tis implies a for a saionary sorage providing peak saving or renewable inegraion, wic is similar o energy arbirage, i could be profiable for sorage owner o make e sorage porable roug rucking. VI. CONCLUSIONS Tis paper explores a new business model for energy sorage, in wic energy sorage is loaded on ruck and doing spaioemporal arbirage beween nodes wi congesion. We develop an opimizaion model for spaioemporal arbirage of porable sorage and apply e model o simulae e operaion and ransporaion of a ruck of Tesla Semi loaded wi Tesla owerpack over wo nodes in California. Te resuls indicae a sorage owner can earn ne profis from convering saionary sorage o porable sorage in energy arbirage applicaion, and e ransmission congesion can be relieved a e same ime. Te spaioemporal arbirage model can be exended o muliple applicaions (suc as frequency regulaion, volage suppor, ec.), muliple nodes, and muliple rucks, wic is one of our ongoing work. One poenial issue is a weer e sorage can be assumed as price-aker or ow o compensae e sorage if i fully resolves e congesion and eliminaes e price difference. Some ecnical issues suc as safey and ermal conrol may also need aenion in pracice. ACKNOWLEDGEMENT Tis work was parially suppored by e US Deparmen of Energy under Gran DEEE7165. REFERENCES orable sorage Saionary sorage Firs-year revenue $98, $55, Toal life-cycle revenue $548, $38, Exra life-cycle revenue of porable sorage $24, Trucking cos $15, [1] N. Kiner, F. Lill, and D. M. Kammen, Energy sorage deploymen and innovaion for e clean energy ransiion, Na. Energy, vol. 2, no. 9, 217. [2] O. Scmid e al., Te fuure cos of elecrical energy sorage based on experience raes, Na. Energy, vol. 2, no. 8, 217. [3] D. Krisnamury e al., Energy Sorage Arbirage Under Day- Aead and Real-Time rice Uncerainy, IEEE Trans. ower Sys., vol. 33, no. 1, pp , 218. [4] A. Sepan e al., Limiing e public cos of saionary baery deploymen by combining applicaions, Na. Energy, vol. 1, no. 7, 216. [5] G. He e al., Opimal Bidding Sraegy of Baery Sorage in ower Markes Considering erformance-based Regulaion and Baery Cycle Life, IEEE Trans. Smar Grid, vol. 7, no. 5, pp , 216. [6] G. He e al., Cooperaion of Wind ower and Baery Sorage o rovide Frequency Regulaion in ower Markes, IEEE Trans. ower Sys., vol. 32, no. 5, pp , 217. [7] L. S. Vargas, G. Busos-Turu, and F. Larrain, Wind ower Curailmen and Energy Sorage in Transmission Congesion Managemen Considering ower lans Ramp Raes, IEEE Trans. ower Sys., vol. 3, no. 5, pp , 215. [8] M. Baramipana e al., A Decenralized Adapive Model-Based Real-Time Conrol for Acive Disribuion Neworks Using Baery Energy Sorage Sysems, IEEE Trans. Smar Grid, vol. 9, no. 4, pp , 218. [9] G. He e al., An ineremporal decision framework for elecrocemical energy sorage managemen, Na. Energy, vol. 3, no. 5, pp , 218. [1] R. T. Ellio e al., Saring Energy Sorage Beween Transmission and Disribuion, IEEE Trans. ower Sys., pp. 1-1, 218. [11] A. D. Del Rosso, and S. W. Eckroad, Energy Sorage for Relief of Transmission Congesion, IEEE Trans. Smar Grid, vol. 5, no. 2, pp , 214. [12] S. Jiajia e al., "Opimal placemen of energy sorage and demand response in e acific Norwes." pp [13] H. Kani, M. R. Dadas Zade, and A. H. Hajimiraga, Transmission Congesion Relief Using rivaely Owned Large- Scale Energy Sorage Sysems in a Compeiive Elecriciy Marke, IEEE Trans. ower Sys., vol. 31, no. 2, pp , 216. [14] J. A. Taylor, Financial Sorage Rigs, IEEE Trans. ower Sys., vol. 3, no. 2, pp , 215. [15] C. Sao e al., arial Decomposiion for Disribued Elecric Veicle Carging Conrol Considering Elecric ower Grid Congesion, IEEE Trans. Smar Grid, vol. 8, no. 1, pp , 217. [16] M. Alizade e al., Opimal ricing o Manage Elecric Veicles in Coupled ower and Transporaion Neworks, IEEE Transacions on Conrol of Nework Sysems, vol. 4, no. 4, pp , 217. [17] Y. Sun e al., Baery-Based Energy Sorage Transporaion for Enancing ower Sysem Economics and Securiy, IEEE Trans. Smar Grid, vol. 6, no. 5, pp , 215. [18] Y. Sun e al., Socasic Sceduling of Baery-Based Energy Sorage Transporaion Sysem Wi e eneraion of Wind ower, IEEE Trans. Susain. Energy, vol. 8, no. 1, pp , 217. [19] Y. Dvorkin e al., Ensuring rofiabiliy of Energy Sorage, IEEE Trans. ower Sys., vol. 32, no. 1, pp , 217. [2] M. Ecker e al., Calendar and cycle life sudy of li(nimnco)o 2- based 1865 liium-ion baeries, J. ower Sources, vol. 248, pp , 214. [21] B. Xu e al., Modeling of Liium-Ion Baery Degradaion for Cell Life Assessmen, IEEE Trans. Smar Grid, vol. 9, no. 2, pp , 218. [22] S. Grolleau e al., Calendar aging of commercial grapie/lifepo 4 cell - predicing capaciy fade under ime dependen sorage condiions, J. ower Sources, vol. 255, pp , 214. [23]. Keil e al., Calendar aging of liium-ion baeries i. Impac of e grapie anode on capaciy fade, J. Elecrocem. Soc., vol. 163, no. 9, pp. A1872-A188, 216.

BELECTRIC: Enhanced Frequency Control Capability

BELECTRIC: Enhanced Frequency Conrol Capabiliy Tim Müller, CTO 28/03/2018 0 Company profile Yearly oal revenue of 550M EUR 84 MW / 95 MWh energy sorage sysems insalled or under consrucion Over 120 paens