Working Paper Modeling storage and demand management in electricity distribution grids

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1 ecostor Der Ope-Access-Publikatiosserver der ZBW Leibiz-Iformatioszetrum Wirthaft The Ope Access Publicatio Server of the ZBW Leibiz Iformatio Cetre for Ecoomics Schroeder, Adreas; Siegmeier, Ja; Creuse Murk Workig Paper Modelig storage ad demad maagemet i electricity distributio grids Diussio papers // Germa Istitute for Ecoomic Research, No Provided i Cooperatio with: Germa Istitute for Ecoomic Research (DIW Berli) Suggested Citatio: Schroeder, Adreas; Siegmeier, Ja; Creuse Murk (2011) : Modelig storage ad demad maagemet i electricity distributio grids, Diussio papers // Germa Istitute for Ecoomic Research, No This Versio is available at: Nutzugsbediguge: Die ZBW räumt Ihe als Nutzeri/Nutzer das uetgeltliche, räumlich ubehräkte ud zeitlich auf die Dauer des Schutzrechts behräkte eifache Recht ei das ausgewählte Werk im Rahme der uter achzulesede vollstädige Nutzugsbediguge zu vervielfältige mit dee die Nutzeri/der Nutzer sich durch die erste Nutzug eiverstade erklärt. Terms of use: The ZBW grats you, the user, the o-exclusive right to use the selected work free of charge, territorially urestricted ad withi the time limit of the term of the property rights accordig to the terms specified at By the first use of the selected work the user agrees ad declares to comply with these terms of use. zbw Leibiz-Iformatioszetrum Wirthaft Leibiz Iformatio Cetre for Ecoomics

2 Deuthes Istitut für Wirthaftsforhug Diussio Papers 1110 Adreas Schroeder Ja Siegmeier Murk Creuse Modelig Storage ad Demad Maagemet i Electricity Distributio Grids Berli March 2011

3 Opiios expressed i this paper are those of the author(s) ad do ot ecessarily reflect views of the istitute. IMPRESSUM DIW Berli 2011 DIW Berli Germa Istitute for Ecoomic Research Mohrestr Berli Tel. +49 (30) Fax +49 (30) ISSN prit editio ISSN electroic editio Papers ca be dowloaded free of charge from the DIW Berli website: Diussio Papers of DIW Berli are idexed i RePEc ad SSRN:

4 Modelig Storage ad Demad Maagemet i Electricity Distributio Grids Adreas Schroeder a, Ja Siegmeier b, Murk Creuse b Abstract: Storage devices ad demad cotrol may costitute beeficial tools to optimize electricity geeratio with a large share of itermittet resources through iter-temporal substitutio of load. We quatify the related cost reductios i a simulatio model of a simplified stylized medium-voltage grid (10kV) uder ucertai demad ad wid output. Beders Decompositio Method is applied to create a two-stage stochastic program. The model iforms a optimal ivestmet sizig decisio as regards specific 'smart grid' applicatios such as storage facilities ad meters eablig load cotrol. Model results idicate that cetral storage facilities are a more promisig optio for geeratio cost reductios as compared to demad maagemet. Grid extesios are ot appropriate i ay of our earios. A sesitivity aalysis is applied with respect to the market peetratio of ucoordiated Plug-I Electric Vehicles which are foud to strogly ecourage ivestmet ito load cotrol equipmet for `smart` chargig ad slightly improve the case for cetral storage devices. Keywords: Storage, demad maageme stochastic optimizatio Beders Decompositio JEL: Q40, Q41 a Correspodig author. Germa Istitute for Ecoomic Research, Mohrestr. 58, Berli Germay. ahroeder@diw.de, Tel.: , Fax: b Berli Uiversity of Techology, Strasse des 17. Jui 135, Berli Germay Ackowledgemet: The correspodig author was fuded by the Graduate Ceter of the Germa Istitute for Ecoomic Research. We are grateful to Christia vo Hirhhause ad Wolf-Peter Schill for their fruitful commets.

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6 1. Itroductio Sice electricity demad ad the availability of output from Reewable Eergy Sources (RES) are itermittet by ature, system operators have to resort to relatively costly measures such as reserve eergy to maitai system stability. I the comig decade, back-up capacities are set to become more relevat with icreasig shares of RES peetratio. I this cotex storage devices serve to store excessive electricity geeratio ad feed-i missig eergy i times of eed. A alterative cocept of better aligig demad ad supply of electricity through two-way digital commuicatio techology is commoly referred to as 'smart meterig'. Measures to maage demad with the help of smart meters iclude demad respose ad direct load cotrol. Our work emphasises the latter. The purpose of this paper is to demostrate how stochastic optimizatio ad Beders decompositio method ca be sesibly applied to aalyze ad compare ivestmet optios i a power distributio system settig. We rutiize load cotrol ad storage facilities as potetial optios targetig at electricity geeratio cost reductios. With this commo purpose, direct load cotrol ad cetralised storage are two competig or possibly complemetary solutios from the perspective of a power distributio system operator. Besides, we test whether covetioal grid reiforcemets could alleviate the eed for storage ad load cotrol. The idea is that storage ad DSM may be used to avoid capacity shortages. If so, avoided shortage adds value to storage or DSM devices because of capacity upgrade deferral (Pudjiato et al., 2006). There exists a broad rage of literature dealig with storage sizig decisios. Some of these studies perform umerical optimizatios i a determiistic settig (Diaf et al., 2007; Aru et al., 2008). Applicatios of stochastic patters of geeratio ad demad ca be foud i Ekre et al. (2009), Ekre a Ekre (2009, 2010) ad Ta et al. (2010). Ta et al. (2010) preset a stochastic optimizatio model of battery sizig for demad maagemet with emphasis o outage probabilities which is ot dealt with i this paper. Roy et al. (2010) apply stochastic wid geeratio patters to a wid-battery system sizig model with determiistic demad. IEA (2010) do likewise with Plug-i Electric Vehicles (EV) as storage facilities. Cocerig demad-side maagemet (DSM), we foud o research publicatios to focus o ivestmet decisios ito DSM appliaces from the perspective of a distributio system operator. Mafre et al. (2011) focus o distributed geeratio plaig but abstract from ay ivestmet aalysis. Ki Lee et al. (2007) assess ivestmet ito demad maagemet systems for heatig i a atioal case study for Korea. Neea ad Hemphill (2008) ivestigate ivestmet from a societal perspective while Strbac (2008) ad Electricity Joural (2008) foud that ivestmet ito DSM appliaces might ot be all that profitable i geeral. We ited to further ivestigate this claim i our aalysis. Our cotributio is uique i so far as o study has explicitly compared the cost savig potetial of storage ad DSM i a comprehesive model icludig grid represetatio edogeous ivestmet ad factors of ucertaity. No study kow to the authors has combied a costbeefit aalysis of 'smart' techologies with a distributio etwork represetatio ad cosideratios of stochastic demad ad productio. Whilst a 11kV distributio etwork represetatio i combiatio with a beefit aalysis for storage ad demad respose measures ca be foud i Wade et al. (2010), the preset work complemets Wade et al. s aalysis by addig edogeeity to the ivestmet ito storage devices ad DSM appliaces as well as 1

7 ucertaity of demad ad wid geeratio. Furthermore, oe of our cotributios to the research area cosists i the applicatio of Beders Decompositio Method to the stochastic program. Decompositio methods have bee applied to umerous Operatios Research topics i the eergy sector, such as uit-commitmet (Nikam, 2009). To our kowledge, though, there exists o applicatio to evaluatig storage ad DSM ifrastructure ivestmet as doe i this work. The article is divided ito a deriptive par icludig the methodology ad model deriptio a explaatio of parameters ad earios applied. Subsequetly, results are outlied, diussed ad fial coclusios are draw. 2. Model Deriptio We apply a basic direct curret (DC) flow model adapted to a situatio with DSM ad storage techologies i a stylized 10 kv medium-voltage grid represetative for Germay. The model is desiged as liear program uder a cost miimizatio regime with hourly time resolutio of two exemplary holidays (witer/summer). A vertically itegrated system operator is cosidered as the cost miimizig aget. As explicated before, the aim of the operator is to reduce geeratio cost by performig load maagemet through storage ad DSM. He ca decide o whether to ivest ito storage ad DSM techology ad o how to operate it. We assume a perfectly ielastic, hece vertical demad fuctio. This is a suitable approach here, sice we focus o the producer side. There is o demad respose. Still, the operator is able to shift the vertical demad curve left ad rightwards through direct load cotrol. Thus, our extesive-form costmiimisatio objective reads as follows. mi cap max DSM _ iv }{ S }{ DSM t, } { SIN t, }{ G s, t, }{ SOUT t, }{ Δ t, } SC N T = 1= 1 t= 1 prob N cs Gs, t +,, = s s 1 cap max [ DSM _ INV dsm _ c + S s _ c] The aget miimizes geeratio cost c s G s, of each techology s as well as ivestmet cost of DSM DSM_INV dsm_c ad storage S capmax s_c. Besides geeratio ad ivestme he ca maipulate storage i- ad outflow (SIN ad SOUT ), shed or iduce cosumptio (DSM ) ad trasfer electricity from oe ode to aother ( ), subject to costraits detailed below. Sets, parameters ad variables are further specified i Table 1. Set Deriptio Uit Rage I Node - N={0,...,5} T time period (summer / witer) H T={1,...,24} S geeratio techology - 9 L Lie - 4 lies SC Sceario - 50 earios Variable Deriptio Uit Rage DSM demad-side-maagemet kwh Free SIN storage iflow kwh Positive SOUT storage outflow kwh Positive G s,, Geeratio kwh Positive DSM INV DSM ivestmet Cosumer capmax S storage capacity ivestmet kwh Positive 2

8 Δ phase agle differece (choose Δ 1 =0) - free Parameter Deriptio Uit Rage Q Total demad icludig DSM ad storage kwh Positive q ref Demad kwh Positive prob probability of eario SC % c s variable geeratio cost (acc. to merit EUR/kWh dsm c DSM ivestmet cost EUR/kWh Positive s c storage ivestmet cost EUR/kWh Positive Η storage efficiecy (zero leakage from % 75 posmax dsm positive load shift capacity kwh cf. Aex egmax dsm egative load shift capacity kwh cf. Aex lf l, electricity flow kw max see lf l B l, etwork sueptace matrix 1/Ω see x H l, weighted etwork matrix 1/Ω see x l l, icidece matrix 1 0 or 1 max lf l maximal capacity for lie flow kw 1850 slack slack variable (with slack 1 =1) 1 0 or 1 X reactace of lie 1/Ohm Table 1: Sets, variables ad parameters used. O the demad side, cosumers are aggregated at each of the 10kV/0.4kV sub-statio odes. Thus, a diural patter of cosumer demad (without DSM ad storage), deoted by q ref 0, ca be approximated usig stadard averaged load profiles weighted by the umber of customers at the respective ode. Puttig demad, supply ad etwork flows together, the eergy balace costrait per ode reads: 1) total demad 2) Eergy balace : Q s G = q ref s, + DSM + SOUT + SIN Q m, b m, Δ m, = 0 ( ) This icorporates the simultaeity of geeratio ad cosumptio as well as the first Kirchhoff rule. The cosumer demad q ref is supplemeted by cotributios from DSM ad chargig of a battery to yield total demad Q, as specified i equatio 1. O the supply side, we cosider a setup where each geeratio techology s S at time t T ad ode N cotributes a amout g s, to total electricity geeratio at margial uit cost c s, up to its capacity limit G max s, which is exogeous ad time-depedet. ( s, t ) max 3) Geeratio limit : g s, t Gs, 0, A umber of grid-related costraits are icluded to study the grid impact of storage ad DSM operatio. The topology of a lossless DC etwork with L lies is deribed by the L x N etwork adjacecy matrix l where l l, = 1 meas that lie l L starts at ode while l l,m = -1 meas that it eds at ode m. Weightig each lie with the iverse of its reactace x l, we obtai the matrix h (equ. 4.1) ad thus the etwork sueptace matrix B (equ. 4.2). If the phase agle of 3

9 ode at time t is deoted by Δ t, the flow alog lie l at time t is give by equatio 4.3, where the sig of lf l,t depeds o the directio of the flow. Sice Δ is defied relative to a referece bus, slackess coditios slack Δ, = 0 hold, ad we choose slack 1 = 1 (that is, Δ 1, = 0) to set ode 1 as the referece ode (equ. 4.5). Equatio 4.4 represets the physical costraits of the lies (i a DC etwork, oly the thermal limit is relevat). 4.1) weighted etw. matrix : 4.2) Network sueptace : 4.3) lie flow : 4.4) lie flow limits : 4.5) flow covetio : lf h b l, m l, lf slack = max l 1 = l x = lf Δ l h l l, l, l, h l,, Δ lf l, t max l l, m, = 0 ( ), ( ) ( l, ) ( l, ) slack 1 = 1 The secod set of costraits relates to DSM. Whe direct load cotrol is made possible, electricity cosumptio may be shifted to earlier or later stages if exact timig is ot crucial. This is doe by the system operator with the aim of savig cost. The optio for DSM is reflected i a additioal cotributio to total demad, DSM. Reducig ad icreasig demad is possible up to limits dsm eg,max ad dsm pos,max, respectively (equ. 5.1). Note that both parameters are defied as positive umbers while cotributios have to balace to zero over time (equ. 5.2). Likewise, storage facilities i the distributio etwork ca take up a positive charge SIN at time covert it (with some loss η) ad subsequetly provide positive amouts SOUT, where the overall balace is also govered by capacity costraits (equ. 6.2) as well as iput ad output kw power costraits, which are set equal to kwh capacity costraits for reasos of simplicity (equ. 6.3). Note that we set eergy capacity equal to power limit ad that there is o cotiuatio value of left-over storage sice the storage device is empty at the last time period (equ. 6.1). 5.1) DSM limits : 5.2) cost. total demad : 6.1) storage balace : 6.2) Storage capacity limits : 6.3) Storage power limits : 7) o - egativity : ( ) T ( SIN η SOUT ) = 0 ( ) t = 1 G S d t T t = 1 τ = 1 s, DSM SOUT cap max eg,max t DSM _ INV DSM τ, SOUT 0, = 0 t 1 τ = 1 SOUT SIN 0 τ,, 0, η 0, S cap max SIN t, τ = 1 SIN SIN 0 DSM τ, d SOUT, 0 ( s, ) ( s, ) η t 1 τ = 1 pos,max t DSM _ INV τ, S cap,max ( ) 0 ( ) The problem is formulated as two-stage stochastic optimizatio program, with iitial ivestmet at the first stage ad operative optimizatios at the secod stage, cf. Figure 1. We apply Beders Decompositio Method (Birge ad Louveaux, 1997) with coflictig variables beig iitial ivestmet levels ito storage ad DSM. The first-stage (master) ad the secod-stage (recursive sub-problem) are successively solved i loops util covergece of the upper ad lower level objective is reached. I our case, the sub-problem objective represets the upper boud as a restrictio of the iitial problem ad the master problem yields a lower boud as a relaxatio of the iitial problem. The solutio algorithm stops if the differece betwee the miimum upper boud ad the curret lower boud is less or equal to a very small umber. Otherwise the 4

10 algorithm cotiues. Beders optimality cuts are added to the problem set of costraits after each iteratio. Moreover, feasibility cuts esure that ifeasibilities i the sub-problem due to misallocatios i the master problem are ruled ou cf. Figure 1. The Beders approach reduces computatio effort as compared to solvig the extesive form expected-value-problem. The relaxed master problem objective fuctio ow reads: mi = + α max N cap max [ DSM _ INV + ] { }{ } dsm _ c S s _ c cap DSM _ INV S 1 Here, α is the objective value of the sub-problem. The recursive sub-problem objective fuctio becomes: mi { }{ }{ }{ }{ } prob cs DSM SIN G SOUT Δ t, t, s, t, t, t, = 1= 1 t= 1 SC N T s s G s, The executio of the preseted model requires the creatio of appropriate earios regardig the stochastic parameters determiig demad ad wid productio. A radom samplig method is utilized for the simulatio of realizatios, cf. Figure 1. Radom samplig techiques are popular i risk aalysis ad have bee used i previous research o electricity topics (Ta et al., 2010, Roy et al., 2010). We obtai a rage of demad ad wid profiles ad assig a uiform probability distributio to the occurrece of each eario. Subsequetly, we implemet a umerical optimizatio model i the software package Geeral Algebraic Modelig System (GAMS). Figure 1: Algorithm used for solvig the two-stage problem. (Source: Ow illustratio) 4. Iput Parameters 4.1 Demad I our stylized system, demad occurs at demad odes which are coected to idividual households ad commercial uits. Specific demad profiles are deoted q ref. Demad is treated stochastically uder the assumptio of zero correlatio betwee wid availability ad demad. Simulated demad values (cf. Figure 2) are draw from a ormal probability distributio with time-varyig mea ad stadard deviatio. Stadard deviatios of demad variability are based o empirical demad realizatios at the EEX wholesale itraday market (2010). Derivig medium-voltage demad variability from wholesale market demad fluctuatios is reasoable for model systems with aggregatio of a high umber of cosumers. Note that the more cosumers are aggregated, the less volatile is eergy cosumptio (cf. Wide ad Wäckelgard, 2010). The model icorporates electricity cosumptio of EV ito the stochastic referece demad q ref. A load patter is assumed with 8 hours home chargig time at a rate of 1.6 kw, cf. 5

11 Figure kW is a relatively slow, usually referred to as Level 1 chargig. A 12.8 kwh charge per ight correspods to a ca. 100 km rage. Note that EV are ot equivalet to storage facilities i our model. This implies we do ot cosider ay vehicle-to-grid techology. Ucotrolled EV solely behave as a additioal cosumer whose load ca be curtailed ad shifted if DSM appliaces are istalled. Chargig behaviour is uder full cotrol of the system operator if the EV is coected to a smart meter. Differet peetratio rates of EV are tested from zero to 10%, that is zero to 10% of the cosumers ow a EV. Figure 2: Covergece of sample demad mea with a icreasig amout of earios. (Source: Ow productio) Figure 3: Determiistic stadard load profile with corridor for upper ad lower bouds of the DSM potetial o a witer holiday. Additioally, the graph plots oe EV chargig profile. (Sources: Ow productio based o BDEW (2010), Grei et al. (2009), Stadler (2008)) We assume 360 cosumers per 10kV-0.4kV trasformer. Each cosumer uit is equivalet to a 1.99-perso household, a represetative mix for Germay (Progos et al., 2010). The share of commerce ad households is 21% ad 79% i the model. We abstract from the idustrial sector i our model because by law - idustrial cosumers are already equipped with appliaces for DSM whe yearly cosumptio exceeds 100,000 kwh. 4.2 Load cotrol Ivestmets i load cotrol ifrastructure for DSM have the beefit of allowig iter-temporal shifts of electricity demad. This may yield peak load reductios ad imply ifrastructure reiforcemet deferral. However, we disregard that the istallatio of DSM appliaces could yield overall demad reductios. We do this ot oly because projectios of demad reductio through DSM devices appear to be fairly ucertai ad cosumer-specific, ragig betwee zero ad 20% (Moura ad Almeidaa, 2010 versus Papagiais et al., 2008, EcoFys, 2009). Our focus lies o direct load cotrol exerted by the system operator. Demad respose measures ad related cosumptio savigs drive by cosumer behaviour are beyod the ope of this operator s cost-miimizatio model. Oce appliaces for DSM are rolled ou there is a certai time-depedet limit o the load shiftig potetial. Positive ad egative shifts are possible ad their potetial is asymmetric. D eg,max t represets the amout of eergy that ca be saved at each time by shiftig load away to aother period of the day. Accordigly, the D pos,max t curve shows the potetial load that ca be added at each time. The potetial to icrease eergy load at each time, D pos,max t, is geerally larger tha D eg,max t. The DSM potetial for average households ad commerce is calculated usig umbers from a study report for the city of Maheim, Germay, (Grei et al., 2009) ad 6

12 triagulated with Stadler (2008). EV availability is added to the DSM potetial. The resultig potetial ca be observed for each time slice i Figure 3 ad Figure 8. Figure 3 plots a average load profile for a household with the corridor of maximum ad miimum load whe DSM appliaces are istalled. The total cost of equipmet for DSM curretly figures i betwee 160 ad 350 EUR per istalled system (EcoFys, 2009). We refer to the Advaced Meterig System (AMM), which icludes two-way commuicatio via a itegrated router gateway per house. This system eables timeof-use pricig ad direct load cotrol up to the capacities detailed i Figure 8. The cost figure icludes ivestmet ito hardware such as meter, gateway, router ad its iitial istallatio. I order to calculate lifetime cos we apply a 6.5% aual diout rate with a lifetime of 16 years (EcoFys, 2009). 4.3 Storage The model cosiders ivestmet ito a cetral large-ale statioary battery with edogeous capacity ad coversio efficiecy factor 75%. We focus o batteries istead of mechaical coversio systems (pumped hydro, compressed air storage) for batteries require little up-frot istallatio cost. To accout for differet battery techologies, we vary the cost iput data. Approximated cost data of equipmet ad istallatio is compiled i Table 2 for referece. I our cost cosideratios, we assume a life-time of 3,000 cycles at 80% depth of diharge with oe cycle beig completed every three days, hece a life-time of ca. 12 years. To facilitate tractability ad icrease computatio speed, the three dimesioig vectors of a storage uit capacity i kwh, charge rate ad diharge rate i kw - are all set equal i this aalysis. We believe this assumptio to be justifiable i a settig with hourly time resolutio where rampig costraits ad thus power limits are of secodary importace i cotrast to capacity limits. I the real world, actual batteries ofte feature power limits eve higher tha eergy capacity limit. This holds true otably for storage devices that serve as reserve for capacity markets. Coversio Storage type EUR/kWh EUR/kW Cycles (100%) Efficiecy Mechaical Supercapacitor 3,800-4, , , % Flywheels 1,000-3, ,000-60, % Pumped Hydro ,000-50, % Compressed Air ,000-20, % Electrochemical Nickel-metal hydride , % Nickel-Cadmium ,000-3, % Sodium-Sulfur ,000-3, % Lithium-Io ,000-6, % Vaadium Redox-Flow 100-1, ,000-3, % Zic-Bromie > 2, % Lead Acid , % Table 2: Curret storage ivestmet cost data compiled from various sources. Mechaical bulk storage icluded for referece but ot cosidered i our calculatios. (Sources: EcoFys (2009), Schoeug ad Eyer (2008), ad Electricity Storage Associatio (2011)) 4.4 Grid Ivestmet decisios relatig to DSM ad storage should ideally cosider grid ifrastructure costraits because load shiftig may serve as a mea to avoid capacity shortage ad system outage probability. This ca be otably relevat i grids with relatively disadvatageous topology (series coectio). Pudjiato et al. (2006) explicitly take ito accout this delayig capacity replacemet value of DSM devices whe appraisig the worthiess of DSM. I the 7

13 absece of real-world data of medium-voltage grids, we decide to simulate a stylized cofiguratio with characteristics that approximate realistic grids, cf. Figure 4 (Fletcher ad Struz, 2007). The grid represetatio used i this study cosists of five odes, oe of them the grid supply poit (GSP) ad additioally demad odes with 10kV/400V trasformers. The odes are coected i lie so as to simulate a worst-case topology, cf. Figure 4. The aalysis restrais to the 10kV-level of a stylized distributio etwork. A applicatio of the preseted DC flow model to a 400V level is delicate for the DC load model does ot iclude reactive power. At 400V level, voltage drop limits ad reactive power are of high relevace. Large-ale geeratio icludig wid turbies ad pump storage are assumed to be coected at the 10kV level, whilst DG ad EV are part of the uderlyig 400V grid. 10kV overhead lies have a lateral surface of 70mm 2 with associated capacity of 185 Ampere. I a 10 kv DC settig this results i a maximum capacity limit of 1,850 kw. A typical reactace of the 10kV etwork is aroud 0.4 Ohm/km (Pudjiato et al., 2006; Fletcher ad Struz, 2007). Upgrade costs of overhead circuits i a comparable 11 kv grid lie at 3,102 /MW/km (Pudjiato et al., 2006). We assume all lies to be 2 km log ad lie flows do ot icur trasmissio losses. Figure 4: Stylized 5-ode distributio grid cofiguratio i series coectio. (Source: ow illustratio). 4.5 Geeratio Nie techologies are part of the geeratio mix i this work: Six techologies hydro, uclear, ligite, hard coal, gas ad biomass have flexible geeratio capacities with full availability ad flexibility at ay time (up to a techical factor, e.g. due to maiteace requiremets, take from Progos et al. (2010)). Three techologies have varyig availability. Small-ale heat-cotrolled CHP diural patters follow a approximatio i Pudjiato et al. (2006) for both witer ad summer ad they are weighted by a seasoal factor based o data i Bruegräber et al. (1996) to accout for higher heatig demad (ad thus more electricity supply) durig witer. Likewise, photovoltaic power (PV) exposes differet daily profiles by seaso adapted to a Norther Germa locatio (Solar-Wetter, 2010). Ivestmet decisios ito storage ad DSM cosider a log time frame ad cofrot with ucertaity about the future geeratio techology mix. Whilst a ivestmet appraisal should cosider today s ivestmet cos geeratio cost reductios accrue i the ucertai future ad should therefore be estimated accordigly. A sophisticated dyamic ivestmet model could explicitly model the evolutio of the geeratio park over time. Such log-term approach is beyod the ope of this paper, though. We believe the year 2020 to be a reasoable represetative average year regardig the peetratio of reewable eergy resources over the life-time of a storage or DSM ivestmet these days. Therefore, a hypothetical geeratio limit 8

14 of each geeratio techology is derived from a forecast for the year 2020 give i Progos et al. (2010). We ale dow the available istalled capacity i Germay so that the six base load techologies match the maximum demad i our model etwork. This esures eough power is available at all times, eve if the fluctuatig sources are ot available. Additioally, the three itermittet techologies are each aled by a idividual factor so that the total amout of diural maximum eergy productio matches the projectios for 2020 i Progos et al. (2010). Fially, we assume that geeratio capacities are distributed differetly betwee the odes of our small etwork while the bulk of power will be available via the grid supply poi some of the CHP, PV ad biomass capacity is located at the demad odes. These assumptios are summarized i the parameters G max s, specifyig the maximum available power from each geeratio techology per time slot ad per ode. Icremetal geeratio cost is illustrated i Table 3. The figures are idepedet from the utilizatio rate of a geeratio techology. Type istalled capacity (Germay 2020) [GW] electricity geeratio (Germay 2020) [TWh] capacity utilizatio (where relevat) techical availability (where relevat) istalled capacity [kw] (i model) available eergy, per day [kwh] (i model) Source Progos et al. (2010) Progos et al. (2010) Available eergy (per day, aggregated over all odes) demad peak [kw] Techology Wid PV CHP Biomass hydro uclear ligite coal gas Total timedepededepededepedet time- time- Flexible flexible Flexible flexible Flexible flexible Calculatio Progos et al. (2010) Calculatio Calculatio % 10.6% 57.1% 88% 90% 93% 86% 84% 84% Techology Wid PV Hydro CHP uclear ligite coal Gas biomass Margial cost [EUR/kWh] Table 3: Available capacity ad projectios of margial geeratio cost icl. carbo cost i (Sources: Based o Progos et al. (2010)) Special attetio is give to geeratio data of wid power which is treated as stochastic parameter. I order to calculate power desity - the distributio of wid eergy at differet average wid speeds - the power of wid speeds is multiplied with the probability of each wid speed, draw from a Weibull probability distributio with shape parameter 2 (typical for Cetral Europe) ad a ale parameter which varies by time-of-day (Ekre et al., 2009; Roy et al., 2010) ad which is calibrated to match a typical o-shore locatio i Norther Germay. A radom sample of wid speeds is created i accordace with the iverse Weibull distributio with w, the wid speed i m/s, x, a uiform radom umber betwee 0 ad 1, a ale ad a shape parameter: W = ale [- l(1- x) ] Kowig that eergy potetial per secod (the power) varies i proportio to the cube of the wid speed (i m/s) it is the possible to calculate actual wid eergy productio i kwh. The umber of wid rotors ad their coversio efficiecy were calibrated so as to match a share of wid eergy i total productio coform to projectios i Progos et al. (2010). Cut-i rated ad cut-out wid speeds are assumed to figure at 2.8 m/s ad 16.5 m/s respectively whilst rated wid speed eds at 7 m/s, cf. Figure 5 (Roy et al., 2010). 1 shape 9

15 Figure 5: Frequecy of wid speeds with average wid speed 5.22 m/s at specified cut-i ad cut-out rates. (Source: Ow productio based o Roy et al. (2010)) 5. Results The liear problem is implemeted i GAMS, usig the solver CPLEX 9.0 with stadard optios. Our 1.3 GHz CPU machie executes the stochastic liear program for oe exemplary day i betwee 2 ad 8 miutes time, depedig o cost parameter values. Up to 20 iteratios are eeded. The determiistic model is solved withi a few secods time. As show i Figure 6, we fid storage devices to pay off at ivestmet cost below 900 EUR/kWh of capacity. For istace, if costs amout to 300 EUR/kWh, storage devices are profitable up to a size of roughly 0.5 MWh capacity (ad MW power limit) i the framework of our model, depedig o the degree of EV peetratio. That correspods to ca. oe fourth of istalled geeratio capacity (2.075 MW) ad oe half of peak demad (ca MW) i the system. I total, we fid that less tha 1 % of aggregated electricity cosumptio is stored i most earios, cf. Figure 7. A higher umber of EV, hece additioal load, further improves the case for storage devices. Give these umbers, it ca be cocluded that eve relatively expesive techologies such as Nickel-Cadmium ad Nickel-metal hydride batteries seem to be profitable i medium-voltage grids of our type. I cotras super-capacitors ad flywheels eed to severely cut their cost i order to become competitive. Curret ivestmet cost lies betwee 2,000 ad 4,000 EUR/kWh. Figure 6: Ivestmet ito storage ad DSM uder varyig ivestmet cost ad peetratio degree of electric vehicles. The dotted lie correspods to results of the determiistic model. Curves are iterpolated from several mode rus. (Source: Ow productio) 10

16 Appliaces for DSM prove hardly profitable i the determiistic model settig, which echoes a fidig of Strbac (2008) ad Electricity Joural (2008). Likewise, the stochastic model predicts DSM to be little beeficial i the absece of EV. Oly if all-iclusive ivestmet costs boil dow to 200 EUR per cosumer, ivestmet ito load cotrol techology may become beeficial. Note that curret costs for AMM systems lie at 260 EUR i average ad projectios for 2020 figure at aroud 160 EUR miimum (EcoFys, 2009). The break-eve poit (tolerace threshold) for ivestmet ito DSM icreases to 700 EUR whe 10% of cosumers ow electric vehicles. Such strog shift clearly outlies that a high umber of EV iduces ivestmet ito load cotrol equipmet. Whe i competitio to each other at curret cos ivestmet ito storage devices is thus clearly favored to DSM systems. This effect is miimal or partly reversed whe EV peetratio is high. Obviously, storage devices offer more flexibility to load shiftig tha does DSM. Figure 7: Storage operatio DSM operatio ad lie flows i the course of a day i two earios. Summed over all odes, there are 117 kwh storage capacity (left graph) ad 1118 of the 1440 cosumers have DSM appliaces istalled (right graph). (Source: Ow productio) The grid capacity is sufficiet for a securely fuctioig system i all earios. Eve with high peetratio of EV, grid capacity costitutes o severe shortage sice lie flows do ot exceed 60% of thermal capacity limits at ay time slice ad ay eario, cf. Figure 7 (total limit 1850 kw). Moreover, alterative grid cofiguratios such as a meshed grid would rather improve the situatio. We coclude o grid reiforcemets are required at 10 kv level. This does ot mea grid extesios are ot eeded at 400 V low-voltage level. I order to udertake studies at 400 V level, a AC etwork model would be appropriate. Such model would icorporate reactive power ad voltage drops which are of high relevace i low-voltage grids. Figure 7 icely illustrates how lie flows arrowly coicide with storage use idicatig that lie flows are to a great extet drive by storage operatios. We expected ivestmet ito storage ad DSM to decrease the capacity utilizatio rate implyig a drop i outage probabilities. While it is hard to assig a moetary value to drops i outage probabilities, it could the at least be stated that this percetage costitutes a further positive value of storage ad DSM ivestmets. Iterestigly, though, we fid that the itroductio of storage devices could ehace lie flows at certai momets, cf. Figure 7. This implies a stroger capacity use rate tha i the absece of storage. Sice storage devices are located at demad odes, their demad for electricity sometimes passes from the grid supply poit to the demad odes ad thereby icreases grid capacity use. This happes otably i peak periods, i.e. midday. Accordigly, we coclude that storage devices ca occasioally deteriorate ad sometimes improve grid system reliability. All i all, o clear picture arises. The same holds true i the case of DSM operatios. This result may have emerged because we iclude o pealty factor for the capacity use rate i the cost fuctio. 11

17 A sesitivity study regardig the presece of EV i the year 2020 is illustrated i Figure 6. This is doe to address the questio of how EV modify the value of storage ad load cotrol. Obviously, a high umber of vehicle chargig augmets demad ad ucertaity ad therefore stregthes the case for storage devices ad DSM. If 10 % of the cosumers ow ad drive EV, ivestmet ito DSM appliaces is likely to rise by more tha 50 % as compared to a world i absece of EV. All i all, results suggest that EV strogly iduce ivestmet ito load cotrol facilities. This result pretty much reflects the trivial fact that most EV are curretly sold to home owers who also iclude smart meterig systems. A potetial alterative to smart EV home chargig solutios could have bee to istall cetral storage devices ad let EV owers charge wheever they like (so-called dumb chargig). However, the value of storage icreases oly slightly i the EV eario. This result idicates that istallig DSM appliaces for EV owers to allow for smart chargig is a much better solutio tha istallig cetral storage surrogates. 6. Diussio What is the poit of usig a stochastic model? Results of the determiistic model idicate a tedecy to uder-ivestmet as compared to the stochastic model s outcome. Figure 6 idicates that determiistic ivestmet levels (dotted lie) ca be up to 50% lower tha i the stochastic model (cotiuous lies) for storage. For both, storage ad DSM, ivestmet levels are cosistetly higher i the stochastic model. We estimate the value of the stochastic solutio (VSS) to figure at aroud 0.5% to 5% of total system costs, idicatig a gai i efficiecy whe usig the stochastic model as opposed to the determiistic model. The VSS allows us to obtai the goodess of the expected solutio value whe the expected values are replaced by the radom values for the iput variables. We coclude that the cost of disregardig ucertaity lies at aroud 0.5% to 5% of total geeratio costs. O the other had, the executio time of the stochastic model with a sample of 50 draws is roughly 15 times higher tha the determiistic model. Computatio times largely vary depedig o the cost iput data, though. All i all, we deem the stochastic model to be superior for it provides efficiecy gais at reasoable additioal CPU effort. The determiistic model appears to iduce wrog log-term ivestmet decisios. The extesive form stochastic model solves i about the same time as the Beders decompositio model. If we were to exted the model so as to dimiish stylizatio we would expect the Beders model computatio time to improve i compariso to the extesive form. Our cojecture is supported by studies such as Nikam et al. (2009). As a matter of fac Beders decompositio is most suitable for outsized problems characterized by a capacious set of variables, odes ad parameters. I these coditios it may be valuable to isolate a group of decisio variables ad ivestigate the problem partially with Beders method. The decompositio model preseted here shall costitute a basis for further models of larger size. 7. Coclusios We have preseted a DC load flow model applied to ivestmet i storage ad DSM facilities i a stylized medium-voltage grid. The model icorporates ucertaity i demad ad wid output ad uses Beders Decompositio to distiguish the ivestmet choices from operative optimizatios. 12

18 The model results idicate that grid reiforcemets at 10 kv level are ot ecessary i ay eario. Capacity utilizatio rates do ot hit the 60% boud which implies there is little harm to system stability. Results suggest that storage devices are beeficial at capacity cost of up to 900 EUR/kWh i the stipulated coditios. This implies that relatively expesive storage techologies such as Nickel- Cadmium ad Nickel-metal hydride storage should be profitable at curret cost. Flywheels ad large-ale capacitors are little competitive uless curret cost is cut by factor four miimum. DSM proves hardly beeficial i ay eario, especially ot i the determiistic model. Ivestmet is beeficial up to a all-iclusive cost of ca. 200 EUR per cosumer. This breakeve poit (tolerace threshold) boosts whe cosumers ow EV, implyig that EV strogly ecourage ivestmet ito load cotrol systems. The fidig reflects the actual fact that most EV are sold alog with smart meterig systems. As a logical cosequece, we idetify that ivestmet ito storage is likely to crowd out ivestmet ito DSM appliaces i our model settig. Sice both optios are direct alteratives for eergy maageme we predict smart meters to be of little ecoomic value to the system operator i the absece of EV. Uless govermets strogly ecourage DSM through obligatios (beyod curret obligatios) ad fiacial icetives or the promotio of EV, we believe that storage facilities are the better optio for a vertically itegrated distributio system operator facig the coditios of this model. We aimed at modelig coditios that would be represetative for a sectio of a stylized distributio system i Germay. It could be show that the stochastic model produces more efficiet solutios compared to its determiistic couterpart. The cost of disregardig ucertaity lies at 0.5-5% of total geeratio cost. Our aalysis demostrates that a stochastic treatmet of wid ad demad patters sigificatly augmets the case for the use of storage. The break-eve poit for ivestmet decisios ito storage icreases from 350 to 900 EUR/kWh whe ucertaity of wid ad demad are take ito accout. Hece, the determiistic model leads to cosiderable uderivestmet ito storage. All i all, the results are highly sesitive to the assumed ivestmet cost for storage ad load maagemet devices. EV are aother cause for variatios, ye to a lesser extet. There are a umber of caveats to our aalysis which costitute areas for improvemet. Eergy savig through demad respose is etirely factored out. Our model may therefore uderestimate the value of DSM to a mior extet. Furthermore, the ivestmet cost for batteries is calculated o a diural basis with a fixed umber of cycles per day. Fixig the cycles is a ecessary step to obtai a exogeous cost figure but somewhat arguable sice the cycles are edogeously determied i the model. Aother drawback of our model is that some potetial busiess cases of batteries ad DSM are ot icluded. Besides peak load reductios ad etwork reiforcemet deferral, Wade et al. (2010) poit to other beefits of usig storage devices. For istace, balacig markets as potetial busiess field for batteries are ot icluded i the preset model. If balacig markets were to be cosidered, a hourly time resolutio may ot be optimal. Other shortcomigs are the stylized grid cofiguratio ad the absece of rampig costraits for storage, which ca be icluded i a further model of larger size. 13

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