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Analyzing the Potential Economic Value of Energy Storage
Monica Giulietti,* Luigi Grossi,** Elisa Trujillo Baute,*** and Michael Waterson**** ൺൻඌඍඋൺർඍ
This paper examines the commercial opportunities for electrical energy storage, taking market prices as given and determining the extent to which a strategy of arbitrage across the day, buying at the lowest price times at night and selling at the highest price times during the early evening, and relying on price forecasts one GD\DKHDGJHQHUDWHVSUR¿WVLQWKH%ULWLVKFRQWH[W7KHSDSHUVHWVRXWWKHSRWHQWLDO problems as the market moves to absorb increasing amounts of wind, then char-acterises the nature of prices, which reveals the importance of a strategy in which power is absorbed into store for a relatively few hours of the day and discharged RYHUDUHODWLYHO\IHZKRXUV,WDUJXHVWKDWDGGLWLRQDOLQFHQWLYHVPD\QHHGWREHSXW into place in order to render storage over relatively longer periods more attractive DQGWRGHOLYHUEURDGHUVRFLDOEHQH¿WVZKLFKDUHXQOLNHO\WREHJHQHUDWHGDQGFDS-WXUHGDVDUHVXOWRISXUHO\FRPPHUFLDOFRQVLGHUDWLRQV
Keywords: Arbitrage; electricity markets; energy storage; market clearing; price IRUHFDVWLQJ
KWWSVGRLRUJ6,PJLX 1. INTRODUCTION
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The process of substituting renewable generating sources for fossil fuels in order to reduce FDUERQHPLVVLRQVKDVOHGWRQHZDQGVXEVWDQWLDOFKDOOHQJHVWRWKHHOHFWULFDOV\VWHPVRIDOOFRXQWULHV &RUUHVSRQGLQJDXWKRU6FKRRORI%XVLQHVVDQG(FRQRPLFV/RXJKERURXJK8QLYHUVLW\/(788.(PDLO 0*LXOLHWWL#OERURDFXN 'HSDUWPHQWRI(FRQRPLFV8QLYHUVLW\RI9HURQD9HURQD,WDO\(PDLO/XLJL*URVVL#XQLYULW: 8QLYHUVLW\RI%DUFHORQDDQG&KDLURI(QHUJ\6XVWDLQDELOLW\%DUFHORQD,QVWLWXWHRI(FRQRPLFV%DUFHORQD 6SDLQ(PDLO(OLVD7UXMLOOR#XEHGX 'HSDUWPHQWRI(FRQRPLFV8QLYHUVLW\RI:DUZLFN&RYHQWU\&9$/8.(PDLO0LFKDHOZDWHUVRQ#ZDUZLFN DFXN:
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they are of vital importance to the maintenance of readily available electricity supply which is a FRUQHUVWRQHRIHFRQRPLFDFWLYLW\DVZHNQRZLW0RVWUHQHZDEOHUHVRXUFHVIRUH[DPSOHZLQGDQG VRODUSRZHUDUHLQWHUPLWWHQWUDWKHUWKDQ¿UPDQGDUHQRWELGGDEOHLQUHVSRQVHWRSULFH(QKDQFHG LQWHUFRQQHFWLRQSURYLGHVDSDUWLDOVROXWLRQDVGRGHPDQGPDQDJHPHQWDQGVWRUDJH7KHWUDGLWLRQDO PHWKRGRIVWRUDJHLVYLDSXPSHGK\GURIDFLOLWLHVEXWWKHVHUHTXLUHJHRORJLFDOIHDWXUHVWKDWDUHQRW HDVLO\UHSOLFDWHG7KXVDOWHUQDWLYHDSSURDFKHVWKDWDUHVFDODEOHLQYROYLQJFRPSUHVVHGDLUKHDWRU EDWWHU\VWRUDJHKDYHEHHQUDLVHGDVSRVVLEOHVROXWLRQV 7KHPDLQSXUSRVHRIRXUSDSHULVWRH[DPLQHZKHWKHUWKHUHDUHVX൶FLHQWHFRQRPLFLQFHQ-WLYHVLQSODFHIRUVXFKVWRUDJHWRRSHUDWHSUR¿WDEO\E\H[SORLWLQJLQWUDGD\DUELWUDJHRSSRUWXQLWLHV LQWKH%ULWLVKZKROHVDOHPDUNHW*LYHQWKHUHODWLYHO\VPDOOVL]HRIH[LVWLQJVWRUDJHIDFLOLWLHVLQ*UHDW %ULWDLQFRPSDUHGWRWKHVL]HRIWKHHOHFWULFLW\V\VWHPLWZRXOGEHXQUHDOLVWLFWRSUHVXPHWKDWVWRUDJH IDFLOLWLHVFXUUHQWO\RSHUDWLQJLQWKHZKROHVDOHPDUNHWZRXOGEHDEOHWRD൵HFWWKHPDUNHWSULFHPXFK VHH5HQHZDEOH(QHUJ\$VVRFLDWLRQ)RUWKLVUHDVRQWKHSDSHUIRFXVHVRQWKHLGHQWL¿FDWLRQ RIDQRSWLPDOLQWUDGD\VWUDWHJ\IRURSHUDWLQJDSULFHWDNLQJVWRUDJHIDFLOLW\ 6HYHUDOFRQWULEXWLRQVLQWKHOLWHUDWXUHRQHQHUJ\WHFKQRORJLHVKDYHFRQVLGHUHGWKHLVVXH of energy storage within a broadly economic framework, commonly with a particular institutional EDFNJURXQGLQPLQG([DPSOHVZKLFKUHO\RQDQH[SOLFLWO\HFRQRPLFIUDPHZRUNLQFOXGH:DODZDONDU HWDO6LRVKDQVLHWDO6LRVKDQVL&DUVRQDQG1RYDQDQG%UDGEXU\HW DOZKRDWWHPSWWRDVVHVVSULYDWHDQGVRFLDOEHQH¿WVIURPVWRUDJHLQWKH86FRQWH[WZKLOH =D¿UDNLVHWDOLQYHVWLJDWHDUELWUDJHRSSRUWXQLWLHVLQ(XURSHDQPDUNHWV7KHVHSDSHUVDGGUHVV a range of issues, but one of the key aims is to analyse the impact of storage on prices; another is to HYDOXDWHWKHSUR¿WDELOLW\RIVWRUDJH5HFHQWFRQWULEXWLRQVZKLFKKDYHIRFXVVHGRQWKHSUR¿WDELOLW\RI ODUJH±VFDOHVWRUDJHIDFLOLWLHVLQFOXGH%DUEU\HWDO&UXLVHHWDODQG1DVURODKSRXUHW DO7KHVHVWXGLHVLQYHVWLJDWHWKHVWUDWHJLFFKRLFHVDYDLODEOHWRVWRUDJHRSHUDWRUVZKRDUHDEOH WRD൵HFWWKHZKROHVDOHPDUNHWSULFHDVDUHVXOWRIWKHODUJHVL]HRIWKHLUIDFLOLWLHV2XUZRUNIRFXVHV instead on price-taking facilities, a more realistic assumption in countries where storage activities DUHDWDUHODWLYHO\HDUO\VWDJHRIGHYHORSPHQWDQGVXEMHFWWRUHJXODWRU\XQFHUWDLQW\DVLQWKH8.
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Analyzing the Potential Economic Value of Energy Storage
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same time, some of the balancing activities potentially undertaken by storage facilities represent a form of business stealing as they would replace activities previously undertaken, and rents previ-RXVO\FDSWXUHGE\KLJKFRVWSHDNLQJSODQWV
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2. THE REQUIREMENT FOR STORAGE
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Demand management, for example through real-time pricing, has potential, but naturally cannot tackle the problem that consumers want the lights on when it is dark, more than when the VXQLVVKLQLQJDQGJHQHUDWLQJVRODUHOHFWULFLW\'HPDQGPDQDJHPHQWVKDGHVLQWRVWRUDJHEHFDXVH
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Analyzing the Potential Economic Value of Energy Storage
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The Energy Journal RIDUELWUDJHRQSULFHVGXHWRGL൵HULQJPDUJLQDOJHQHUDWLRQDQGORDGEDODQFHVEHWZHHQ%ULWDLQDQG LWVQHDUFRQWLQHQWQHLJKERXUV7KDWLVWRWKHH[WHQWWRZKLFKGL൵HUHQWLQÀXHQFHVSOD\DSDUWLQGH-WHUPLQLQJSULFHVZLWKLQ%ULWDLQDQGLWVFRQQHFWHGFRXQWULHVWKHLQWHUFRQQHFWRUZLOORSHUDWHWRPRYH HOHFWULFLW\IURPWKHORZHUSULFHGFRXQWU\WRWKHKLJKHUSULFHG2IFRXUVHWKHVHLQWHUFRQQHFWRUVH[-SHULHQFHOLQHORVVHVDQGDOVRFRQYHUVLRQORVVHVVLQFHWKHUHLVDGRXEOHFRQYHUVLRQIURPSKDVH$& WR'&WRIDFLOLWDWHXQGHUVHD+9'&FDEOHWUDQVPLVVLRQDQGEDFNDJDLQDWWKHRWKHUHQG+RZHYHU LQWRWDOVXFKORVVHVDPRXQWSUREDEO\WROHVVWKDQRIWKHSRZHUWUDQVPLWWHG The total capacity
RIWKH)UHQFK'XWFK1RUZHJLDQDQG%HOJLDQH[LVWLQJDQGSODQQHGLQWHUFRQQHFWRUVLVDURXQG*: 7KHUHIRUHHYHQLIDOODUHRSHUDWLQJDWIXOOSRWHQWLDOLQWR%ULWDLQWKH\DUHRQO\VX൶FLHQWWRWDFNOH FXUUHQWZLQGÀXFWXDWLRQVDQGDUHVRPHORQJZD\VKRUWRIEHLQJDEOHWRKDQGOHZLQGÀXFWXDWLRQV RQFHPHDQZLQGJHQHUDWLRQJHWVWRDURXQGRIWRWDOSRZHUJHQHUDWHG $WWKHVDPHWLPHWKHVWRUDJHUHTXLUHPHQWVLQDFRPSOHWHO\UHQHZDEOHV\VWHPRIRSHUDWLRQ DUHXQIHDVLEO\ODUJHIRUFRPPHUFLDORSHUDWLRQ7KLVLVZHOOLOOXVWUDWHGWKURXJKDUHFHQWSDSHU(VWH-EDQHWDODOWKRXJKWKLVLVQRWWKHSRLQWWKHSDSHUPDNHV,WFDOFXODWHVWKHUHTXLUHGPDJQLWXGH RIVWRUDJHLQDUHQHZDEOHV\VWHPLQ-DSDQZLWKVRODUDWRIWKHWRWDOFDSDFLW\DV7:K 0RUHRYHUDVLVFOHDUIURP)LJXUHLQ(VWHEDQHWDO¶VDUWLFOHIRUPXFKRIWKHWLPHWKLVVWRUDJH would be barely used; there is a long and almost continuous withdrawal from store in the period IURP-XO\WR6HSWHPEHU
Commercial stores of natural gas are able to operate on the basis of an annual withdrawal and charge cycle, but most of the variance in gas prices comes over the long term in an annual cycle, ZKHUHDVLQHOHFWULFLW\LWFRPHVRYHUH[WUHPHO\VKRUWLQWHUYDOVFRPPRQO\DGD\DVZHVKRZEHORZ 7KXVWKHUHDUHWZRGUDPDWLFGL൵HUHQFHVLQVWRUDJHDVEHWZHHQJDVDQGHOHFWULFLW\RQHEHLQJWKH QDWXUHRISULFHPRYHPHQWVRYHUWLPHWKHRWKHUWKHSK\VLFDOVSDFHUHTXLUHGIRUVWRUDJH5RXJKD GHSOHWHGJDV¿HOGLQWKH1RUWK6HDWKDWFRPSULVHV%ULWDLQ¶VPDLQVWRUHRIQDWXUDOJDVFRLQFLGHQWDOO\ KROGVXSWR7:KRIVWRUHGJDVZKLFKZRXOGDPRXQWWROHVVWKDQKDOIWKDWLQWHUPVRIJHQHUDWHG electrical power, but the energy content of compressed natural gas per cubic metre is much higher than in electricity storage media such as compressed air, so if used for compressed air storage it ZRXOGQRWDPRXQWWRDQ\ZKHUHQHDUWKHHTXLYDOHQWDPRXQWRIHOHFWULFLW\
,WLVOLNHO\WKDWERWKLQWHUFRQQHFWLRQDQGVWRUDJHZLOOFRH[LVWDVZHPRYHWRDVLJQL¿FDQWO\ less biddable system of generation, because solar power does not work in the evening in winter ZKHQGHPDQGLVKLJKHVWDQGZLQGSRZHULVLQKHUHQWO\LQWHUPLWWHQW0RUHRYHUPRWLYDWLQJDVWRUHWR RSHUDWHPD\EHDPRUHVWUDLJKWIRUZDUGPHDQVRIPRYLQJVXSSO\DQGGHPDQGLQWREDODQFH
3. ARBITRAGE AS THE FOCUS OF COMMERCIAL STORAGE
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Analyzing the Potential Economic Value of Energy Storage
PDUJLQDOIXHOWHFKQRORJ\IRUJHQHUDWLQJDWSHDNKDVUHODWLYHO\KLJKPDUJLQDOFRVW7KLVSURYLGHVDQ RSSRUWXQLW\IRUHOHFWULFLW\VWRUDJHWRDFWDVDUELWUDJHEHWZHHQWKHVHSHULRGV2IFRXUVHVLQFHVWRUDJH LVOHVVWKDQH൶FLHQWWKHYDULDWLRQEHWZHHQSHULRGVQHHGVWREHODUJHHQRXJKWKDWLWPRUHWKDQ FRYHUVWKHORVVHVHQJHQGHUHGE\VWRULQJZKLFKYDU\ZLWKWKHVWRUDJHWHFKQRORJ\:KDWVFRSHLV there for arbitrage earnings to encourage operation of storage?
+HUHZHZRUNZLWK$3;PLGSULFHVRUPDUNHWLQGH[GDWDSULFHVREWDLQHGIURP(OH[RQ10 RYHUWKHIRXU\HDUSHULRG-DQXDU\WR'HFHPEHUWRSURYLGHDQVZHUV7KHVHSULFHVDUHXVHG E\(OH[RQWRFDOFXODWHWKHUHYHUVHSULFHIRUHDFKVHWWOHPHQWSHULRGDQGµUHÀHFWWKHSULFHRIZKROHVDOH HOHFWULFLW\LQWKHVKRUWWHUPPDUNHW¶KWWSVZZZHOH[RQSRUWDOFRXNDUWLFOHYLHZ"FDFKHEXVW V-EZQGF\7KH\DUHFDOFXODWHGDVDZHLJKWHGDYHUDJHSULFHIRUDOOTXDOLI\LQJFRQWUDFWV11 )LJXUHLOOXVWUDWHVWKHSDWWHUQRIKDOIKRXUO\PDUNHWSULFHVRYHUWKHWKUHHPRQWKSHULRG IURP-DQXDU\WR0DUFK7KHJUDSKVKRZVWZRWKLQJVFOHDUO\)LUVWZKROHVDOHSULFHVÀXFWXDWH DJRRGGHDOIURPMXVWXQGHU SHU0:KWRZHOODERYHWKHKLJKHVWUHWDLOSULFH6HFRQGWKHXQGHU-O\LQJSDWWHUQLVGLXUQDO7KLVVHFRQGSRLQWLVGHPRQVWUDWHGPRUHFOHDUO\WRJHWKHUZLWKDWKLUGPRUH VXEWOHSRLQWLQ)LJXUHZKLFKWDNHVDZHHN0RQGD\WR6XQGD\IURPWKHVHGDWDDQGH[DPLQHVLW LQPRUHGHWDLO+HUHZHVHHWKDWZLWKLQHDFKGD\LWLVRQO\DFRPSDUDWLYHO\IHZKRXUVIRUZKLFKWKH SULFHLVYHU\KLJKWKLVQRUPDOO\KDSSHQVDURXQGSPLQWKHHYHQLQJ7KHH൵HFWLVVOLJKWO\ORZHUHG DWWKHZHHNHQG7KHORZHVWSULFHVRFFXUDWGHDGRIQLJKWEHWZHHQDURXQGDQGDP%HWZHHQ (OH[RQLVWKHEDODQFLQJDQGVHWWOHPHQWFRGHFRPSDQ\ZKLFKPDQDJHVHOHFWULFLW\WUDGLQJDUUDQJHPHQWVLQ(QJODQG DQG:DOHVKWWSVZZZHOH[RQFRXN µ$TXDOLI\LQJFRQWUDFWPD\WDNHWKHIRUPRIDQ\RIWKH«UHOHYDQW(3(;3URGXFWVVSHFL¿FDOO\WUDGHGRQRUDIWHU WKHWKLUGFDOHQGDUGD\SULRUWR*DWH&ORVXUHIRUWKHUHOHYDQW6HWWOHPHQW3HULRG¶VHH0DUNHW,QGH['H¿QLWLRQ6WDWHPHQWYHU-VLRQ$SSHQGL[KWWSVZZZHOH[RQFRXNZSFRQWHQWXSORDGV0,'6BYSGI :HFKRVHDWKUHHPRQWKSHULRGVLPSO\WRIDFLOLWDWHWKHJUDSKLFDOSUHVHQWDWLRQRIWKHIHDWXUHV Figure 2: First three months of 2014
The Energy Journal 1RYHPEHUDQG1RYHPEHUWKHDYHUDJHSHDNSULFHZDV SHU0:KWKHDYHUDJHR൵ SHDNSULFHZDV SHU0:K7KLVLQÀXHQFHVWKHZKROHVWUDWHJ\WKDWDQDUELWUDJLQJVWRUHZRXOG QHHGWRIROORZ ,QRUGHUWRPDNHPRQH\VLPSO\EX\LQJR൵SHDNDQGVHOOLQJSHDNDVWRUHZRXOGQHHGWR EHDWOHDVWH൶FLHQW(DUO\H[SHULPHQWVRYHUDSHULRGRIVHYHUDO\HDUVWKDWZHKDYHSHUIRUPHG LQYROYLQJDULVNIUHHVWUDWHJ\RIEX\LQJR൵SHDNRUEDVHORDGDQGVHOOLQJDWSHDNLQDIRUZDUGPDU-NHWGD\ZHHNPRQWKDKHDGLVXQOLNHO\WRH[SRVHVX൶FLHQWJDSVLQSULFHVWKH³SDUNVSUHDG´IRU DUELWUDJHWREHIHDVLEOHIRUDVWRUHZKLFKLVVD\H൶FLHQW7KHUHDUHRFFDVLRQVZKHUHWKHJDSLV ODUJHHQRXJKEXWWKH\VHOGRPRFFXU*LXOLHWWL*URVVLDQG:DWHUVRQ +RZHYHUDVFDQEHVHHQIRUWKHH[DPSOHGD\LQ)LJXUH0RQGD\WK-DQXDU\ within the day there are certainly peak times when the price is over twice as much as it is in dead RIQLJKWVRFOHDUO\WKHUHLVSRWHQWLDOIRUSUR¿WDEOHGLXUQDODUELWUDJH7KXVDPRUHVXEWOHSXUFKDVH and sale strategy needs to be undertaken, in which particular periods showing the lowest prices and SDUWLFXODUSHULRGVVKRZLQJWKHKLJKHVWSULFHVZLWKLQWKHSHDNDQGR൵SHDNSHULRGVDUHXVHG7KLV OHDGVLQWXUQWRWZRFRQVLGHUDWLRQV7KH¿UVWLVWKHDSSURSULDWHUDWLRRIVWRUHVL]HWRSXPSVL]HZKLFK ZLOOLWVHOIEHGHSHQGHQWXSRQWKHURXQGWULSH൶FLHQF\7KHVHFRQGLVWKHGHYHORSPHQWRIDVWUDWHJ\ that is able to look ahead in a relatively sophisticated manner to decide on when to take in and when WRUHOHDVHHQHUJ\IURPWKHVWRUH)ODWOH\HWDOH[DPLQHWKHQDWXUHRIVXFKDQRSWLPDOVWUDWHJ\ JLYHQWKHSDUDPHWHUVRIWKHVWRUHIRFXVLQJRQWKHORRNDKHDGWLPHLQYROYHG
5HWXUQLQJWRFRQVLGHUDWLRQRIGLXUQDOVWRUDJHFOHDUO\LWLVLQDSSURSULDWHWRKDYHDVWRUHFD-pable of carrying a large amount of energy if the purpose is to charge and discharge over relatively IHZSHULRGV,IWKHVWRUHKDVSXPSVFDSDEOHRI¿OOLQJWKHVWRUHZLWKDSRZHUUDWLQJRIP0:DQGWKH
:HGH¿QHDVDµSDUNVSUHDG¶WKHSUR¿WDELOLW\LQSHUFHQWDJHWHUPVRIVWRULQJSRZHUSXUFKDVHGDWDJLYHQGDWHWDQG VROGRQWKHVDPHGDWHYLDDFRQWUDFWVLJQHGDWWLPHWIRUGHOLYHU\DWWLPHW1Future price (t, t + N) – day-ahead price (t)/
day-ahead price (t).
Analyzing the Potential Economic Value of Energy Storage RSHUDWRUHQYLVDJHVWKHVWRUH¿OOLQJRYHUDPD[LPXPSHULRGRIWKUHHKRXUVDQGGLVFKDUJLQJRYHUQR JUHDWHUDSHULRGWKHQWKHVL]HRIWKHVWRUHQHHGEHQRODUJHUWKDQP0:K 7KHUHDUHWZRPDLQGLPHQVLRQVLQÀXHQFLQJWKHVWRUDJHIDFLOLW\7KH¿UVWLVREYLRXVO\WKH URXQGWULSH൶FLHQF\RIWKHVWRUHH[SUHVVHGDVSRZHUWKDWFDQEHVROGLQWRWKHPDUNHWGLYLGHGE\ SRZHUWDNHQIURPWKHPDUNHW7KHVHFRQGOHVVREYLRXVLVWKHVL]HRIWKHVWRUHUHODWLYHWRWKHVL]HRI WKHPD[LPXPRXWSXW+RZHYHUWKHRSWLPDOVL]HRIVWRUHJLYHQSXPSUDWLQJLVLQIDFWHQGRJHQRXV EHFDXVHLWLVLQÀXHQFHGE\WKHH൶FLHQF\UDWLQJRIWKHVWRUH7KHPRUHH൶FLHQWWKHVWRUHWKHORQJHU LVWKHUDQJHRIWLPHRYHUZKLFKHQHUJ\FDQSUR¿WDEO\EHGLVFKDUJHGDWSHDNDQGFKDUJHGR൵SHDN 7KXVJLYHQPDUNHWSULFHVWKHUHDUHWZRGHWHUPLQDQWVRIWKHSUR¿WDELOLW\RIWKHVWRUHWXUQDURXQG H൶FLHQF\DQGWKHQXPEHURISHULRGVRILQWDNHDQGRXWSXWDQGWRJHWKHUWKHVHLPSDFWRQRSWLPDO VWRUH VL]H :KLOH D UDQJH RI H൶FLHQF\ UDWLQJ DQG SXPS UDWLQJV DUH WHFKQLFDOO\ FRPSDWLEOH ZLWK VWRUHVRIGL൵HUHQWVL]HVWKHGHWHUPLQDWLRQRIWKHRSWLPDOVL]HRIDVWRUHZLOOGHSHQGRQLWVDELOLW\WR at least recover the short term variable costs associated with the store operation, which in turn de-SHQGVFULWLFDOO\RQWKHGLXUQDOGL൵HUHQFHLQZKROHVDOHSULFHVDOORZLQJWKHVWRUHWRH[SORLWDUELWUDJH RSSRUWXQLWLHV :HKDYHVHHQWKDWWKHUHDUHRQO\DIHZSHULRGVLQZKLFKGDLO\SULFHVDUHDWWKHLUSHDN7KLV OLPLWVWKHQDWXUHRIVWRUDJHZKLFKHDUQVUHYHQXHWKURXJKDUELWUDJH0RUHRYHUWKHUHDUHRQO\VPDOO VHWVRIFRQVHFXWLYHWLPHVIRUZKLFKSULFHVDUHYHU\KLJKDWSHDNFRPSDUHGZLWKSULFHVDWR൵SHDN 7KHUHIRUHLQRUGHUWRDVVHVVWKHSRWHQWLDOSUR¿WDELOLW\RIDVWRUDJHSODQWRSHUDWLQJRQDGDLO\EDVLV by exploiting arbitrage opportunities in the balancing market, we performed a series of simulations DLPHGDWLGHQWLI\LQJWKHRSWLPDOQXPEHURISHULRGVPHDVXUHGDVKDOIKRXUVWRUHÀHFWWKHELGGLQJ IUHTXHQF\LQZKROHVDOHPDUNHWVZKHQWKHVWRUHVKRXOGRSHUDWHLQRUGHUWRPD[LPLVHSUR¿WVWKURXJK
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110 / The Energy Journal
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6XSSRVHWKHSODQWKDVH൶FLHQF\UDWHRXWSXWHQHUJ\WRLQSXWHQHUJ\RIș ,QDGGLWLRQ the plant has input costs of xSHU0:KDQGH[SRUWFRVWVRIySHU0:K6RLWKDVUXQQLQJFRVWVRI>
1T x y]SHU0:KRIHOHFWULFDOHQHUJ\SURGXFHG6XSSRVHWKDWWKHSODQWLVHLWKHUFKDUJLQJDWWKHIXOOUDWHRUGLVFKDUJLQJDWWKHIXOOUDWHRU LVGRLQJQRWKLQJDQGWKDWWKHUHLVQROHDNDJH,WKDVDQLQSXWSXPSLQJFDSDELOLW\RIĮ/ș0:DQGDQ export pumping capacity of Į0:
Therefore, if it operates by inputting for IJVHWWOHPHQWSHULRGVXVXDOO\KDOIKRXUV in a day,
and exporting for the same period of time, it will input a total of WĮș0:KDQGH[SRUWDWRWDORIWĮ 0:K,QRUGHUWRGRWKLVWKHSODQW¶VVL]HZRUNLQJFDSDFLW\ZLOOQHHGWREHWD T/ A0:K,WLV DVVXPHGWKDWWKHVL]HRIWKHSODQWLVVPDOOHQRXJKWKDWLWGRHVQRWLQÀXHQFHPDUNHWSULFHV :KDWGHWHUPLQHVWKHRSWLPDOYDOXHIRUIJ",WZLOOQRWEHZRUWKZKLOHRSHUDWLQJWKHSODQWLI WKHFRVWVH[FHHGWKHEHQH¿WV7KHEHQH¿WVFDQEHUHSUHVHQWHGDVWKHGL൵HUHQFHEHWZHHQWKHSULFHSHU 0:KRIWKHLQSXWHOHFWULFLW\DQGWKHH൶FLHQF\ZHLJKWHGSULFHSHU0:KRIWKHH[SRUWRIHOHFWULFLW\ 7KDWLVLQSURGXFLQJ0:KRIHOHFWULFLW\H[SRUWWKHEHQH¿WZLOOEH>py
Tpx@7KLVZLOO change every period, but the approach that recommends itself is to start with the lowest period for the input price pxand the highest price export period pyand then to move to the next lowest input SULFHDQGWKHQH[WKLJKHVWH[SRUWSULFHDQGVRRQ7KHKDOIKRXUVHWWOHPHQWSHULRGVDUHGLYLGHGLQ ³SHDN´DQG³R൵SHDN´SHULRGV%HFDXVHLQSHDNKRXUVSULFHVDUHXVXDOO\KLJKHUWKDQLQR൵SHDN KRXUVZHFKDUJHWKHSODQWGXULQJR൵SHDNSHULRGVDQGGLVFKDUJHGXULQJSHDNKRXUV7KHQDOOSRVVL-EOHFRPELQDWLRQVRISHDNDQGR൵SHDNSHULRGVDUHDQDO\VHG,QSURGXFLQJAXQLWVRIRXWSXW0:K E\SXPSLQJDVDVVXPHGWKHEHQH¿WVZLOOEH 1 1 W T W ¦
ª¬ º¼ d d yt xt t A p p where d ytp and pdxt are the export and import price, respectively, at day d
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1 T ª¬ º¼ A x y 6XEWUDFWLQJIURPH[SHULPHQWLQJZLWKGL൵HUHQWYDOXHVRIIJVWDUWLQJZLWKPRYLQJWRHWF results in an optimum number of periods, where each period at least adds something in terms of PDUJLQDOQHWEHQH¿W1RWLFHWKDWRQO\WKHEHQH¿WVVLGHLQFRUSRUDWHVIJ2QFHWKHRSWLPDOIJ is found, we get an expression in terms of A7KLVLV
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D h d d d D D h d d D MP I SDP I 6WRFKDVWLFSURFHGXUHWR¿QGWKHRSWLPDOIJ ,QDGGLWLRQWRWKHDQDO\WLFDODSSURDFKWRWKHVHDUFKIRUWKHRSWLPDOIJdiscussed abovewe DOVRLPSOHPHQWHGDVWRFKDVWLFDSSURDFK7KHPDLQGL൵HUHQFHIURPWKHDQDO\WLFDOSURFHGXUHLVWKDW one-day-ahead forecasts of half-hourly prices are obtained through an estimated time series model EDVHGRQDUROOLQJZLQGRZSURFHGXUHIRUHDFKGD\RI,QSDUWLFXODUGDWDIURPWKHEHJLQQLQJ7KHVL]HRIWKHUROOLQJZLQGRZLVNHSWFRQVWDQWE\DGGLQJDQHZREVHUYDWLRQWRWKHRULJLQDOVHULHVRIGD\VDQGUHPRY-LQJWKHROGHVWREVHUYDWLRQDWHDFKVXFFHVVLYHVWDJH
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RIWRWKHHQGRIZHUHXVHGWRHVWLPDWH6(7$5PRGHOV with daily dummy variables
IRUHDFKRIWKHVHWWOHPHQWSHULRGV 7ZRGL൵HUHQW6(7$5PRGHOVKDYHEHHQFRQVLGHUHGDFODVVLFDOHVWLPDWRUYHUVLRQEDVHG RQUHFXUVLYH2/6DQGDQRXWOLHUUREXVWYHUVLRQEDVHGRQDSRO\QRPLDOZHLJKWLQJIXQFWLRQ*URVVL DQG1DQ 2QFHWKHSUHGLFWHGSULFHYDOXHVDUHREWDLQHGWKHRSWLPDOEX\VHOOVWUDWHJ\LVGHFLGHGHDFK GD\XVLQJWKHSULFHIRUHFDVWVIRUWKHQH[WGD\)RULQVWDQFHRQZHREWDLQWKHIRUHFDVW SULFHVIRUHDFKVHWWOHPHQWSHULRGRIDQGDVVXPLQJIJ ZHGHFLGHWKHRSWLPDOEX\VHOO VWUDWHJ\EX\LQJDWWKHPLQLPXPIRUHFDVWSULFHDQGVHOOLQJDWWKHPD[LPXPIRUHFDVWSULFH2IFRXUVH when IJ!PD[LPXPDQGPLQLPXPDUHFRPSXWHGDVDYHUDJHYDOXHVZLWKLQWKHSHULRGGH¿QHGE\IJ 3.2 Simulation results 7KHSURFHGXUHVGHVFULEHGLQVHFWLRQKDYHEHHQDSSOLHGWR¿QGWKHRSWLPDOIJunder three UHDOLVWLFYDOXHVRIWKHH൶FLHQF\UDWHIRUVWRUDJHWHFKQRORJLHVș7KH¿UVWVWDJHZDV LPSOHPHQWHGWRGH¿QHWKHRSWLPDOEX\VHOOVWUDWHJ\RSWLPDOSHULRGWREX\R൵SHDNDQGWRVHOODW SHDNWLPHXVLQJSULFHGDWDIRUWKHSHULRG±ZKLOHLQWKHVHFRQGVWDJHLWZDVDSSOLHGWR SULFHGDWDIRUWKHZKROH\HDU2XUVLPXODWLRQUHVXOWVDUHJHQHUDWHGRQWKHEDVLVRIWHFKQLFDO SDUDPHWHUVW\SLFDOO\DVVRFLDWHGZLWK&RPSUHVVHG$LU(QHUJ\6WRUDJH&$(6WHFKQRORJ\ +HUHLWLVWDNHQDVJLYHQWKDWWKHSODQWKDVEHHQFRQVWUXFWHGVRWKHPDMRUSDUWRIWKHRSHU-DWLQJFRVWVWKHFRVWVZHWDNHLQWRDFFRXQWDUHWKRVHLQYROYLQJFKDUJLQJDQGGLVFKDUJLQJWKHSODQW 7KHFRVWVRISXPSLQJDQGWXUELQLQJIRUDFRPSUHVVHGDLUHQHUJ\VWRUDJHSODQWDUHJLYHQE\/XQG DV¼SHU0:KDQG¼SHU0:KUHVSHFWLYHO\:HWUDQVODWHWKHVHYDOXHVLQWR 0:K DWDQH[FKDQJHUDWHRI¼SHU (QHUJ\LQSXWLVDVVXPHGWREHSXUFKDVHGVSRWDWPLGPDUNHW (OH[RQSULFHVDQGVROGDOVRDWWKHVHSULFHVREWDLQLQJZKHQVDOHVWDNHSODFH7KHSODQWRSHUDWHVIRUD QXPEHURISHULRGV¿OOLQJGHSHQGHQWRQVL]HRISXPSUHODWLYHWRFDSDFLW\DQGWKHVDPHQXPEHURI SHULRGVGLVFKDUJLQJODWHULQWKHGD\RURQWKHQH[WGD\,QRXUVLPXODWLRQVof the scenario analysis we DVVXPHRSHUDWLQJZLWKDVWDQGDUGFRPSUHVVHGDLUVWRUDJHSODQWZLWKDVWRUDJHFDSDFLW\RI0:K DQGDSXPSVL]HRI0: This means that the average charging/discharging time is one hour,
thus we have to exclude combinations of charge/discharge with less than one hour interval between WKHP )XUWKHUPRUH WKH SULFH YDULHV LQ WKH WZR VHWWOHPHQW SHULRGV XVHG IRU FKDUJLQJGLVFKDUJLQJ SURFHGXUHWKXVZHKDYHWRWDNHWKHDYHUDJHSULFHRIWZRFRQWLJXRXVSHULRGV
Assessing an arbitrage procedure usually implies the computation of risk measures which PXVWEHXVHGWRFRUUHFWO\HYDOXDWHWKHUHWXUQRIWKHLQYHVWPHQW9DWDQLHWDO1DVURODKSRXUHW DO)RUWKLVUHDVRQLQWKHIROORZLQJ¿JXUHVWKH6KDUSH5DWLR $YHUDJH3UR¿W6WDQGDUG'H-YLDWLRQRI3UR¿WVZLOOEHVKRZQDORQJVLGHWKHDYHUDJHSUR¿WV7KHFDOFXODWHGLQGH[HVZHUHREWDLQHG LQVWDJHWZRRIWKHSURFHGXUHIRUGL൵HUHQWYDOXHVRIșH൶FLHQF\UDWH and IJQXPEHURISHULRGVRI RSHUDWLRQXVLQJWKHDULWKPHWLFPHDQDVWKHVXPPDU\LQGH[WRGHWHUPLQHWKHRSWLPDOVWUDWHJ\LQWKH ¿UVWVWDJHRIWKHSURFHGXUH
The optimal value of IJ was also determined in stage two by considering only positive prof-LWVDQGWKHSURSRUWLRQRISRVLWLYHSUR¿WVDFURVVDOOYDOXHVRIIJ:KHQGL൵HUHQWVXPPDU\LQGH[HVZHUH used in the analysis they generated similar optimal values of IJWRWKHRQHVUHSRUWHGLQWKH¿JXUHV
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main summary index. 2XUVLPXODWLRQVVHHNWRPD[LPLVHDYHUDJHSUR¿WVUDWKHUWKDQWKHPD[LPL]D-WLRQRIWKHWRWDOSUR¿WRQDGDLO\EDVLVEHFDXVHWKLVVWUDWHJ\ZRXOGUHTXLUHDFRQVWDQWUHDGMXVWPHQW of operations in response to observed prices which is limited by the technical characteristics of the &$(6SODQW
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7KHUHIRUHFRPELQLQJDQDYHUDJHSUR¿WLQGH[ZLWKDULVNPHDVXUHLQGH[HQDEOHVWRFOHDUO\ identify the optimal value of IJ,QZHHNGD\VRIVXPPHUWKHULVNPHDVXUHIROORZVDWUDMHFWRU\ YHU\VLPLODUWRWKHDYHUDJHSUR¿WWKXVWKHSORWRIWKH6KDUSH5DWLR)LJXUHULJKWSDQHOFRQ¿UPV WKHUHVXOWVGLVSOD\HGLQWKHOHIWSDQHORIWKHVDPH¿JXUH
The results based on the stochastic approach, which rely on one-day-ahead price forecasts, are perfectly comparable with the analytical procedure because the selected optimal strategy is al-ZD\VZLWKLQRQHGD\
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Analyzing the Potential Economic Value of Energy Storage
2QFHSUHGLFWHGYDOXHVDUHREWDLQHGWKHRSWLPDOEX\VHOOVWUDWHJ\LVGHFLGHGHDFKGD\XVLQJ WKHIRUHFDVWHGSULFHVRIQH[WGD\)RULQVWDQFHDWWLPHT the forecasted prices for each settlement period of time T + 1 are available and, assuming IJ WKHRSWLPDOEX\VHOOVWUDWHJ\LVWREX\DWWKH minimum forecasted price and sell at the maximum forecasted price within day T 2IFRXUVH when IJ!PD[LPXPDQGPLQLPXPDUHFRPSXWHGDVDYHUDJHYDOXHVLQWKHSHULRGGH¿QHGE\IJ
To give an idea of the main results obtained using the stochastic approach, the average SUR¿WVDQGWKH6KDUSH5DWLRVDUHUHSRUWHGLQ)LJXUHXVLQJDUREXVW6(7$5PRGHOIRUWKH ZKROH\HDU &RPSDUHGWRWKHUHVXOWVRIWKHDQDO\WLFDODSSURDFKLOOXVWUDWHGLQ)LJXUHZH¿QGWKDWW FRXOGDOVREHFRQVLGHUHGDVWKHRSWLPDOYDOXHLQRUGHUWRPD[LPLVHDYHUDJHSUR¿WV0RUHRYHUWKH DYHUDJHSUR¿WVREWDLQHGZLWKWKHVWRFKDVWLFDSSURDFKIRUYDOXHVRIIJless thanDUHKLJKHUWKDQWKRVH REWDLQHGXVLQJWKHDQDO\WLFDODSSURDFK/RRNLQJDWWKH6KDUSH5DWLR)LJXUHULJKWSDQHOWKHWUD-MHFWRULHVDUHYHU\VLPLODUWRWKRVHREVHUYHGLQ)LJXUHDWOHDVWIRUWKHKLJKHVWOHYHORIH൶FLHQF\WKH OLQHLVYHU\ÀDWIRUORZYDOXHVRIIJ and the best performance is even compatible with IJ
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The Energy Journal
the results for weekdays in winter are virtually unchanged, while for weekdays in summer the op-timal value of IJLQFUHDVHVWRIRUDOOOHYHOVRIH൶FLHQF\DOWKRXJKZLWKVLPLODUHVWLPDWHGDYHUDJH SUR¿WVIRUWKHIRUHFDVWSHULRGDVLOOXVWUDWHGLQ)LJXUHOHIWSDQHO:KHQWKH6KDUSH5DWLRLVFRQ-VLGHUHG)LJXUHULJKWSDQHOWKHRSWLPDOYDOXHRIIJLVZKHQWKHH൶FLHQF\LVZKLOHLWLVVWLOO IRUORZHUH൶FLHQF\OHYHOV ,QVXPPDU\WKHUHVXOWVRIRXUVLPXODWLRQVLQGLFDWHWKDWDYHUDJHSULYDWHSUR¿WVFDQEHSRVL-WLYHIRUDVX൶FLHQWO\H൶FLHQWVWRUHDQGFDQEHPD[LPLVHGE\FKDUJLQJDQGGLVFKDUJLQJHQHUJ\RYHU DUHODWLYHO\OLPLWHGQXPEHURISHULRGV7KHFRPSXWDWLRQRIULVNPHDVXUHVFRPELQHGZLWKWKHDYHUDJH SUR¿WVOHDGVWRFRQFOXVLRQVZKLFKLQVRPHFDVHVFRXOGGL൵HUIURPWKRVHREWDLQHGZKHQMXVWUHO\LQJ RQSXUHSUR¿WV2XUUHVXOWVDOVRLQGLFDWHWKDWGL൵HUHQWVWUDWHJLHVPLJKWQHHGWREHHPSOR\HGLQRUGHU WRPD[LPLVHSUR¿WVGHSHQGLQJRQZKHWKHUWKHVWRUHRSHUDWHVGXULQJZHHNGD\VRUZHHNHQGVDQG GXULQJGL൵HUHQWVHDVRQV
4. FORESEEABLE CHANGES IN THE PRICE STRUCTURE
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