A Storage Pricing Mechanism for Learning Agents in Masdar City Smart Grid

Transcription

1 A Storage Prcng Mechansm for Learnng Agents n Masdar Cty Smart Grd Fatmah Ishowo-Oloko, Perukrshnen Vytelngum 2, Nck Jennngs 2, Iyad Rahwan,3 Masdar Insttute of Scence & Technology, UAE Unversty of Southampton, UK 3 Massachusetts Insttute of Technology, USA ABSTRACT Masdar Cty n the Unted Arab Emrates s desgned to be the frst modern cty powered solely by renewable energy. However, the stochastc nature of renewable energy generators has remaned a major challenge n ther sole and largescale deployment. Tradtonal approaches couple large-scale storage systems to renewable generators to mtgate the ntermttency n ther supply pattern. More recent approaches also study how emergng technologes such as electrc vehcles and mcro-batteres can be used as consumer-sde storage. Future smart grds are however lkely to contan both large and mcro batteres and t s unclear how both technologes wll work together. Hence n ths paper, we present a novel model of jont-storage management that allows both renewable energy supplers and consumers to coordnate n a decentralzed manner by gradually adoptng storage abltes. For ths model, we present a dynamc storage-prcng mechansm that makes use of the storage nformaton from the renewable suppler to generate daly, real-tme electrcty prces whch are communcated to the consumers. We emprcally evaluate the system and show that, when all homes are equpped wth storage devces, the suppler can sgnfcantly mprove the effcency of the system by up to 23%, whle the consumer reduces ts costs by up to 35%. Categores and Subject Descrptors I.2. [Artfcal Intellgence]: Dstrbuted Artfcal Intellgence Multagent systems General Terms Economcs,Expermentaton Keywords Energy and emssons, Smulaton. INTRODUCTION The growng threat of clmate change and the depleton of non-renewable energy sources have led to the growth of sustanable development. In partcular, sustanable urban development has been advocated as one of the factors n changng the way we use and produce energy. For example, urban plannng n the future would not only nvolve desgnng buldngs that mnmze n-house energy use, t would also have to consder the effects of dstrbuted energy resources lke wnd turbnes and solar panels on land-use patterns. Furthermore, these technologes wll have to be economcally feasble, for them to be adopted on a wde scale and non-ntrusve, n order not to detract from the lvng experence. Thus, future ctes would have to be desgned n ways that are sustanable, attractve and commercally vable. Masdar Cty s bult to be a poneer model for such future ctes. Masdar cty s currently fully powered by onste renewable energy. Ths ncludes a MW roof-top, solar photovoltac plant and a MW photovoltac farm coverng 22 hectares of land. However, as the cty grows, ts energy demands wll ncrease beyond what can be provded on-ste. As such, the remanng demand wll need to be sourced from outsde the cty. Lkely off-ste sources nclude the MW Concentrated Solar Power (CSP) plant and the MW wnd farm to be bult n the western regon and the sland respectvely. Gven the above features of the Masdar cty grd and nherent ntermttency of renewable energy generators, there arses the challenge of balancng supply and demand on a constant bass. Prevously, conventonal energy supplers ensured the matchng of supply and demand by mantanng a generaton capacty that was always much hgher than demand. As such, ths resulted n excess generaton capacty durng off-peak hours. Wth renewable generaton, mantanng excess capacty does not solve the problem as excess capacty s stll subject to ntermttency and cannot be dspatched at wll. Therefore, t becomes crucal for renewable energy supplers to aval themselves of emergng technologes to encourage ther consumers demand to respond to ther partcular generaton pattern. Demand response have typcally nvolved the use of drect load control strateges by the consumer or the utlty [8, 3]. Whle these strateges have been effectve n nfluencng demand, they are hghly dependent on the actve partcpaton or nformaton revelaton of the consumers. However, actve partcpaton of the consumer s not guaranteed just as consumers mght also be reluctant n revealng ther true preferences to the utlty to avod explotaton. Renewable energy generators thus requre a dynamc control sgnal that s lnked to the varablty n ther generaton patterns and an enablng technology to dampen(supply power durng defcts and store power durng excesses) ts volatlty. To address these challenges, electrcty storage devces n the form of large utlty-scale batteres and small domestc (household) batteres have been proposed for use wth renewable energy generators. These storage devces could act as shock-absorbers to the system by provdng energy when needed and thereby ncreasng the relablty and ef-

2 fcency of energy supply. Moreover, they reduce the need to over-buld capacty and thus ensurng a hgher return on nvestment n renewable generaton technologes. In ths paper, we propose the use of both utlty-scale and domestc batteres to form a decentralzed energy storagesoluton that can be coupled wth sole, large-scale renewable generators n sustanable ctes. Gven the decentralzed nature of the domestc storage and the dfferent consumpton patterns of houses, each storage unt s best represented as an autonomous agent that ams to maxmze ts own preferences. In partcular, wth the advent of smart meters, t s possble to envsage that software agents could be nstalled on meters to optmze the energy consumpton of houses. Now, ths storage-soluton could also be wdely appled for other smart grds as t makes a case for decentralzng storage. Clusters of houses wth smlar consumpton patterns could be grouped together and provded wth medum scale storage devces. On the polcy sde, amongst the key goals of the Abu Dhab Economc Vson 3 are sustanable development and economc dversfcaton by the year 3. Thus, the government s commtted to ncreasng the penetraton of renewable energy as well as provdng a conducve regulatory envronment. For ths, we provde a novel mechansm by whch renewable generators can determne the best prce sgnal to send to ther consumers gvng ther partcular seasonal and daly patterns. Ths dynamc prcng mechansm mproves the system effcency and consumer savngs by up to 23% and 35% respectvely. Thus, t outperforms the exstng fxed prce mechansm and further promotes the ntegraton of renewable energy generators nto the wder Electrcty Grd. Ths s the frst paper that addresses the novel challenge of jont-storage management wth the use of a multagent system framework. We thus demonstrate that multagent system paradgm can provde fully sustanable ctes (and others) wth solutons that help wth the sole and/or largescale deployment of renewable energy generators. It s mportant to note that whle ths research has been carred usng smulatons, t s close to actual deployment as Masdar Cty s currently testng a fleet of Mtsubshu -MEVs 2 electrc vehcles for use n the cty. Thus, ths paper contrbutes to the state of art n the followng ways:. We present the frst smart grd framework whch combnes both centralzed utlty-sde storage and dstrbuted consumer-sde storage. 2. We develop novel algorthms and a prcng mechansm to enable both the renewable energy suppler and the consumers to optmze generaton and storage decsons takng nto account the ntermttency of renewable energy. 3. We emprcally evaluate our approach and show that our mechansm(compared to the exstng prcng mechansm of Masdar Cty) results n up to 23% mprovement n effcency for the suppler and up to 35% savngs for the consumer agents. 2. MODEL DESCRIPTION 2 In ths secton, we present the models of the energy requrements of Masdar Cty. The cty s desgned to be powered solely by renewable energy wth a resdental populaton of about,. Thus, the grd conssts of renewable generators and batteres (at the supply end) and homes wth electrcal applances and mcro-batteres or electrc vehcles (at the consumer end). In the followng sectons, we detal each element of our system by provdng specfc models of Masdar energy suppler (wnd and solar power generaton usng real data) and homes (each represented by ts agent) whch may possess electrcty storage capacty (ether batteres or electrc vehcles). In our models, we consder fxed tme ntervals consstng of sngle days, each dvded nto a set of half-hourlyntervals I=, 2,..., 48 suchthateach partcpant needs to decde ts behavor (typcally a day ahead) for each nterval. 2. The Renewable Suppler The wnd speed data at an elevaton of m was obtaned from Masdar Cty Meteorologcal staton for the perod of August 8 to June 9. As the speed of wnd vares wth heght, the data was projected to the wnd turbne 3 hub heght (84m). The projecton was done usng the power law equaton [3] shown below: v h = v r ( ) n h () r where v h s the wnd speed at hub heght, v r s the wnd speed at readng heght, h s the hub heght, r s the readng heght whch n our case was m hgh and n s the powerlaw exponent (roughly about.429 for open land [4]) We modeled the stochastc process of the wnd speed wth the Webull probablty dstrbuton [4] gven by equaton 2. ( s )( vh ) [ z exp ( vh ) s ] p(v h ) = (2) z z z where v h s the wnd speed at hub heght, s s the scale parameter and z s the shape factor. The parameters of the dstrbuton (s, z) were estmated usng the Maxmum Lkelhood (ML) method. The estmated parameters are [4.88, 2.32].The power curve of the wnd turbne was approxmated by a fve-orders polynomal functon [4] (as the best ft for the curvewas foundat that order) gven n equaton 3. The power outputs of the wnd turbne at recorded speeds for each tme nterval I = {,2,3...48} were thus obtaned. o wt (v h ) = o wt max, v h v h max (.24v 5 h +.88v 4 h 53.33v 3 h v 2 h v h ), v h mn < v h < v h max, v h v h mn (3) Where o wt (v h ) s the power output of wnd turbne for a gven mean wnd speed v h, o wt max s the rated power output of the wnd turbne, vmn h denotes the cut-n wnd speed of the wnd turbne and vmax h s the cut-off wnd speed of the wnd turbne. For the solar generator, the tme data seres of the power output from a test PV panel located at Masdar Cty PV contest ste was used. The output was recorded every 5 3

3 PV Output (kw) Tme (Mnutes) Fgure : PV panel output for all days n the month mnutes (288 readngs per day) for the perod of August 8 to June 9. Fgure shows the PV output for all days n the month of June 9. The average of the sx readngs n each half-hour readngs was then obtaned for each tme nterval I. The utlty-scale storage was modeled based on the Sodum Sulphur (NaS) deep-cycle batteres produced by NGK 4. Our choce was based on ther hgh power, energy densty and capacty whch makes them sutable for utlty scale storage. They also have a hgh effcency and vrtually no self dscharge. Each generator and battery model has an assocated daly cost c g for g G = {b,pv,wt}. Ths ncludes fxed costs (captal,nstallaton) and annual costs (operatons and mantenance (O&M)). We derve the levelzed daly costs by summng all ncurred costs and dvdng by the expected lfetme n days. The approxmate values for all costs were obtaned from the manufacturers at the World Future Energy Summt whch took place n Abu Dhab The Capacty Plannng Problem Wemodel oursuppleras bengrequredtosatsfy all ofts consumers demand, solely from the energy produced from ts renewable generators. To do ths, the suppler needs to determne the optmal capacty confguraton for the generators and batteres to be nstalled. A number of potental ways of fndng the optmal desgn has been proposed n the lterature. Ths ncludes analytcal approaches as n ([2] and [5]), smulaton approaches ([5] and [6]) and optmzaton ([], [4] and [7]). A key challenge here s for the renewable suppler to be able to compete favorably n the wder electrcty market to promote the adopton of renewable energy. Thus, t needs to ensure that t mnmzes the amount of optmal capacty to nstall n order to provde ts consumers wth compettve electrcty prces. Other optons are to desgn sutable mechansms that ncentvze ts customers to respond to ts generaton patterns. Here, we present a cost optmzaton model and further optons such as the use of a prcng mechansm and learnng mechansm are shown n next secton. The optmzaton model fnds the number of wnd turbnes and PV panels that need to be nstalled and also specfes the amount of power to ether charge nto the battery or dscharge from t for each tme perod(.e. the storage profle ofthebattery). Now, thepossble poweroutputofeachwnd turbne (Equaton 3) durng tme nterval s constraned by the maxmum output power gven by: o wt o wt max (4) Also, the output of each PV panel durng tme nterval s constraned by the watt-peak ratng of the panel: o pv o pv max (5) where o pv max s the rated maxmum output (n Watt-peak) of the PV panel. Each battery has a capacty constrant whch lmts the amount of power flow nto and out of t at each tme nterval. The power flow of the battery can be calculated as the dfference between stored energes of two consecutve ntervals. As there are two possble power modes, chargng and dschargng, we defne when the battery s chargng.e. e b < e b + ( ) p ch = e b + e b / (6) And when t s dschargng e b > e b +: ( ) p dch = η e b e b + / (7) where p ch s the power nput to the battery at tme, p dch s the power output from the battery at tme, e b s the energy stored n the battery at tme, η s the dschargng effcency of the battery and s the length of a tme nterval (whch s 3 mnutes n our model). The power output of each battery durng tme nterval s also constraned by the maxmum chargng and dschargng rates: p ch < p ch max (8) p dch < p dch max (9) Lastly, for a sustanable cty, total power output from renewable generators and batteres should exactly satsfy the total load demand D A at all tme ntervals. Ths supplydemand matchng equaton for nterval can be expressed as: Q +P dch = D A +P ch () Here Q represents the total output from both wnd turbnes and PV panels, P ch s the power nput to all batteres, P dch s the power output from all batteres and D A s the total demand from consumer agents. Equaton s the objectve functon whch completes the capacty determnaton model for Masdar Cty Grd. 2.3 The Home Agents Here we descrbe our agent model of the consumer, whch s bult upon the recent model for homes equpped wth smart meters by Vytelngum et al [7]. Specfcally, we defne the set of consumer agents as A and each agent a A has a load (consumpton) profle C a I defned as the actual amount of electrcty used (consumed) by agent a for tme nterval durng each day. In our model we assume that ths load profle s fxed: an agent wants to use certan amounts of electrcty at certan tmes of the day and would rather not change ts behavor nor reveal ts preferences to ts suppler. Thus, we do not attempt to change

4 the consumpton profle of agents rather by gvng the agent storage ablty, the tme when electrcty s demanded can be decoupled from the tme when the electrcty s actually consumed. Thus, we defne the demand profle D a I as the amount of electrcty demanded (purchased) by the agent from the energy suppler for tme nterval durng each day. Furthermore, each agent a A may also have some storage avalable to t, wth capacty q a, daly costs c a and effcency η a. 3. THE STORAGE PRICING MECHANISM In ths secton, a storage prcng mechansm (SPM) s proposed to help the renewable energy suppler maxmze the effcency of ts system gven the ntermttency problem of renewable generaton. The mechansm uses the avalablty of real-tme storage nformaton (measured n kwh and representng the amount of electrc energy stored n the batteres) that s known to the suppler. Ths nformaton nvolves no extra communcaton overhead as the state of ts batteres are easly known to the suppler. For every tme nterval, the suppler (n our case study Masdar Cty) generates electrcty from both ts wnd turbnes and photovoltac panels. The amount generated s used to satsfy the demand of ts consumers. Whatever s n excess of demand s then stored n the batteres. Thus the amount of electrc charge n the batteres captures the amount of renewable generaton that s avalable but not beng demanded by the consumers. So ths storage nformaton embodes two sgnals:. It nforms the suppler of the specfc perods when generaton exceeds (or lags) demand. 2. It quantfes energy generaton.e. t tells the suppler how much the excess or defct s. Usng ths nformaton, the suppler can then determne when to decrease ts electrcty prce to encourage more demand and also by how much t should decrease the prce n order to sgnal to the consumers by how much they should also ncrease ther consumpton and vce versa. Therefore, our mechansm uses the correlaton between the amount of charge (or dscharge) and the excess (or defct) generaton. As opposed to [6] where the aggregate consumpton of the homes s dvded nto two n terms of the amount satsfed by the suppler and the amount sourced from the grd, the suppler here dentfes two dfferent tme perods. The frst perod bat I are tmes when the aggregate demand of the homes exceeds generaton such that D A > Q and the second perod I when the demand D A Q. Durngperod bat I, the demandnexcess ofgeneraton s suppled from the batteres and thus the suppler ncurs a storage cost ǫ (/kwh). Ths storage cost s measured n ($/kwh) and represents the cost n dollars per klowatt-hour of energy delvered from the batteres to the homes. More formally, from the optmal confguraton derved from the soluton to equaton, we defne the ǫ at each nterval as I Pch ǫ = c b n b () where c b s the levelzed daly cost of each battery, n b s the optmal number of batteres nstalled and P dch s the power output from all batteres at tme. The ntuton behnd ths s that dvdng the cost of the batteres by the amount of useful charge that s obtaned from them gves the margnal cost of usng batteres. So the suppler offers the consumer the ncentve of savngs n lne wth how much t saves when t avods usng storage by reducng the prce by ǫ or t charges them the margnal cost t ncurs by havng to supply ther demand from batteres. Thus, we provde retal rates for dfferent perods of tme as follows:. For the tmes bat I, the electrcty s prced based on the retal prce of electrcty p retal. 2. Forall othertmes I,.e., thetmeperodswhenthe amount demanded can be drectly satsfed by the suppler from ts generaton Q at thattme, theelectrcty s prced at ǫ less than the retal prce of electrcty.e. p retal - ǫ. By the above, the suppler ncentvzes ts consumers to use the green energy t produces drectly rather than havng to store t and later provdng t to them from storage. It s mportant to note that our storage prcng mechansm does not just shft storage from supplers to the consumers. Rather the prcng mechansm can stll be used successfully to ncentvze consumers wthout storage or wth other forms of demand management systems (such as load control programs). Also, our prcng mechansm dffers from the tradtonal tme-varyng mechansms because we do not am to smooth out peaks. Rather we encourage peak consumpton perods as long as such perods are hghly correlated wth perods of peak renewable generaton. 4. THE AGENTS ADAPTIVE RESPONSE Gven the above dynamc prcng mechansm, a self-nterested agent (wth storage ablty) that s nterested n mnmzng ts cost responds by adaptng ts storage profle n lne wth changes n daly electrcty prces. In more detal, our model adopts the day-ahead best-response adaptve strategy for agents by [7]. As opposed to ther model however, the agent does not need to predct the next day s prce for each tme slot as ths s gven by the suppler on a dayahead bass. Rather, t calculates the storage profle for day (t + ) based on the publshed market prces t receves on day (t). As the storage profle depends largely on the storage capacty, the agent also has to decde how much storage capacty t should have. Thus, the agent needs to frst learn ts optmal storage capacty as a best-response to changng electrcty prces and then optmze ts storage profle based on the determned storage capacty. The Wdrow Hoff Learnng mechansm used by [7] s based on a two-pass approach. In the frst pass, the agent computes the optmal storage capacty ξ a (maxmum energy stored daly) requred for t to mnmze ts cost by makng capacty q a, a decson varable n the optmzaton functon (Equaton 2). The agent also obtans the storage profle, b a = b ch,a forthatday 6 bymnmzngthesamefuncton. Then n the second pass, the agent gradually adapts both ts capacty and profle. ( ) arg mn (p b ch,a b a +C a I ) +c a b ch,a (2) 6 We used IBM ILOG CPLEX 2.2 to mplement and solve the optmzaton problem

5 Constrant : dscharge effcency I bdch,a = η a I bch,a Constrant 2: rated maxmum chargng capacty b ch,a b ch,a max, I Constrant 3: rated maxmum dschargng capacty Amount (kw) Supply and Demand Profles on Day wthout SPM Supply Profle on Day Demand Profle on Day max, I Constrant 4: energy that can be stored at a tme nterval q a b ch,a + ( j= j ) b ch,a j, I Constrant 5: energy that can be used at a tme nterval ( η a b ch,a + ( j= Constrant 6: no-resellng allowed j C a bdch,a, I )) b ch,a j, I In more detal, constrant expresses the fact that the amount of energy that can be dscharged from the battery s lmted by the effcency of the battery. Constrant 2 and 3 ensures that the amount of energy that can be charged or dscharged n any tme slot s always less than the rated maxmum charge and dscharge capacty of the battery. Constrant 4 and 5 captures the fact that the state of the battery n any tme slot depends on the prevous cycles of charge and dscharge. Fnally, the last constrant mples that the amount dscharged should be at most the electrcty consumpton at that tme nterval. Ths means that the agent cannot dscharge from ts battery for the purpose of sellng back to the grd. Startng from day (t = ) where the storage capacty q a () =, the agent gradually adapts ts storage capacty towards the optmal capacty ξ a obtaned from solvng the cost mnmzaton functon usng Equaton 3 q a (t+) = q a (t) +α ( ξ a q a ) (t) (3) where α s the learnng rate of the storage capacty q a of agent a. In the second pass, the agent computes the optmal storage profle requred for t to mnmze ts cost whle fxng ts capacty at q(t+). a The objectve functon of the optmzaton problem thus becomes: arg mn b a I ( p b ch,a +C a ) +c a q a (t+) (4) and a new optmal storage profle (b a, ) s obtaned. Next, the agent adapts ts daly storage profle towards the optmal profle (b a, as below: b a (t+) = b a (t) +β ( b a, b a (t)) I (5) where b a, s the optmal storage profle subject to a fxed storage capacty of q a (t+) and β s the learnng rate of the storage profle. In the next secton, we evaluate our storage prcng mechansm for dfferent proportons of the populaton wth storage devces and for dfferent learnng rates of consumer agents Tme n Half Hour Intervals Fgure 2: Supply Profle compared wth Aggregate Demand Profle on Day wthout the SPM 5. EMPIRICAL ANALYSIS Ths secton presents an emprcal evaluaton of the SPM appled to the Masdar Cty Model of a renewable energy suppler and a group of consumers. The am s to show that the proposed mechansm ncreases the system effcency and effectvely ncentvzes consumers to respond to renewable generaton patterns. We do ths by showng how the demand profle responds to the supply profle thereby resultng n less storage capacty on the part of the suppler. Next, we demonstrate how the consumers beneft as they gradually adopt storage. We evaluate ths beneft by varyng the proporton of consumers havng storage and by varyng the learnng rate at whch they adapt ther storage capactes and profles. 5. Expermental Setup The retal prce of electrcty was set at.4$/kwh whch s the current fxed-prce of electrcty n Abu Dhab where Masdar Cty s located. Our SPM then computes the devaton (equaton ) from the retal prce based on the state of the utlty batteres to generate the real-tme prces for the consumers. Each smulaton was run for days consstng of 48 half-hourly perods. Runnng the smulaton for a longer number of days dd not offer changes to the system as t converges after days. The smulaton was run for varyng proportons of the populaton wth storage and wth varyng learnng rates. The results were collected and presented n the followng sectons. 5.2 Effect of SPM on Consumers Demand Gven that the man am of the paper was to ncentvze consumers to respond to renewable generaton patterns, the frst result we present s the change n the demand profles of the consumers wth storage ablty. We show that n the system wth storage prcng mechansm, the consumers (wth storage) demand profles gradually begn to follow the supply profle untl convergence s reached. Fgures below show the change n demand patterns for % of the populaton wth storage devces and wth learnng rates (α, β) of.5. The optmal storage populaton and learnng rates used here are based on the results of the other experments presented later n Sectons 5.5 and 5.6. As can be seen from Fgure 2, the demand profle (wthout SPM) on day of the smulaton shows large devatons from the supply profle. Specfcally, whle the demand profle peaks n the evenng when the consumers are at home

6 Amount (kw) Supply and Demand Profles on Day wth SPM 7 Supply Profle on Day 6 Demand Profle on Day Tme n Half Hour Intervals System Effcency Optmal System Effcency System Effcency wth SPM Fgure 3: Supply Profle compared wth Aggregate Demand Profle after the smulaton has been run wth SPM for days Aggregate Demand Profle Convergng to the Supply Profle Smulaton Length n Days Fgure 5: Storage effcency of the system wth SPM. At the start of smulaton, the system s only 74.4% effcent Amount (kw) Learnng Rate of Agents = Tme Interval (3 mnutes) 8 6 Smulaton Length n Days Fgure 4: Aggregate Demand Profle of Consumers Changng n response to Renewable Generaton Pattern and usng a lot of electrcty, the supply profle dps n the evenng due to the absence of solar rradaton. When the smulaton s run wthout SPM for days, the demand profle stays the same as there s no ncentve for the consumers to change ther profles. However, when the smulaton s run wth SPM, the demand profle begns to algn tself wth the supply profle (Fgure 4) untl there s a near perfect algnment at day as seen n Fgure 3. Ths result shows that the behavor of a self-nterested consumer agent wth storage capablty n the presence of SPM s to optmze ts cost by changng ts demand profle to algn wth the supply profle. By so dong, the agent fulflls ts electrcty demand at mnmum cost. Ths n turn leads to greater system effcency as the percentage of renewable energy that s used drectly by the consumers ncrease. 5.3 Effect of SPM on System Effcency Gven that the SPM helps to acheve demand response as shown n the prevous experment, we now analyze quanttatvely how the effcency of the system mproves. We measure theeffcency of the system as the rato of theamount of electrcty that s demanded mmedately by the consumers and the total amount of electrcty suppled. We benchmark the SPM aganst an optmal system where there s no storage takng place and all the energy produced by the suppler s mmedately demanded by the consumers. Such a system wll have an effcency of % whch s the maxmum effcency attanable. From Fgure 5, we see that the system s only 74.4% effcent wth the current fxed prcng mechansm. Ths translates to about a quarter of the energy produced by the suppler s beng stored. Wth the use of our storage-prcng mechansm however, the effcency of the system gradually ncreases and approaches the optmal effcency. The effcency converges at about 97.4% wth the Daly Average Savngs Percentage of Populaton wth Storage Fgure 6: Average savngs on electrcty cost for consumers wth storage and wth electrcty prces determned by SPM for dfferent proportons of the populaton wth storage. whole populaton adoptng ther mcro-storage wth a learnng rate of.5. We show n secton 5.5 that the effcency of the system stll ncreases even wth smaller proportons of the populaton adoptng mcro-storage. 5.4 Effect of SPM on Consumers Electrcty Cost In ths secton, we evaluate the effect on the electrcty bll of consumers gven a fxed prcng mechansm versus the storage prcng mechansm. Specfcally, we consder the cases where the cost of usng utlty storage s prced va a fxed prcng mechansm versus va our storage prcng mechansm. The queston we wsh to answer here s: should the suppler adopt utlty storage alone and charge the consumers for ts use or the should consumers adopt mcrostorage (dstrbuted on the grd) and pay the cost of ther ndvdual storage. We know that f the utlty alone adopts storage, all consumers pay a fxed prce of electrcty whch comprses of the retal cost of producng electrcty and the margnal cost of storage. Ths fxed cost s ndependent of the consumers demand profles and the generator s supply pattern. An ndvdual consumer cannot reduce ts costs n any way (gven a fxed prce of electrcty) ether through the use of storage or through load control. For the second scenaro however, we see n Fgure 6 an ncrease n savngs for consumers as an ncreasng proporton of the populaton adopt storage. Ths s because an ncrease n populaton of

7 System Effcency System Effcency vs Storage Populaton.65 POP. POP.75.6 POP.5.55 POP.25 POP Smulaton Length n Days Fgure 7: System effcency for dfferent populatons of consumer wth storage and wth electrcty prces System Effcency.9.8 System Effcency vs Learnng Rates of Agents.7 LR. LR.5.6 LR. LR.5.5 LR. LR.5 LR Smulaton Length n Days Fgure 8: System effcency for dfferent learnng rates of consumer agents and wth electrcty prces determned by SPM Daly Average Savngs Consumers Savngs vs Learnng Rate Learnng Rate of Agents Fgure 9: Average savngs on electrcty cost for consumers wth storage and wth electrcty prces determned by SPM for dfferent learnng rates 5.6 Effect of Learnng Rate on Consumers Benefts Smlar to the experment above, here we analyze the effect of the learnng rate on the benefts to consumers. The effect of storage populaton sze on consumer savngs has been prevously analyzed. We see from Fgure 9 that as the learnng rate of agents ncreases, the average savngs also ncreases untl t peaks at a learnng rate of.5. Thereafter, the savngs only decrease wth ncreasng learnng rate. Ths result s consstent wth the results obtaned for the system effcency wth varyng learnng rate n Secton 5.5 above. Thus, the maxmum savngs to the consumers and also to the suppler s acheved when the consumer agents are learnng to adapt ther storage at a learnng rate of.5. mcro-storage means there s more collectve response to the supply patterns. 5.5 Effect of Consumers Learnng Rate and Storage Populaton on System Effcency Here, we analyze the senstvty of the system effcency (the rato of the amount of electrcty that s demanded mmedately by the consumers and the total amount of electrcty suppled) to the storage populaton and learnng rates of the agents. Fgure 7 shows that the smaller the storage populaton, the less effcent the system. Ths s to be expected as a smaller storage populaton means that fewer consumer agents are able to respond to the storage prcng mechansm. Thus, the suppler stll has to use utlty-storage to meet the demands of consumers wthout storage. In fact, we see that when there s no storage n the system, the system effcency remans constant at 74.4%. As the storage populaton begns to ncrease, the effcency of the system ncreases untl t converges at 97.4%. Thus, the system s most effcent when all the consumers have storage and are able to optmze ther demand profles n response to the storage prcng mechansm. Next, we show the senstvty to the learnng mechansm. When the consumer agents are learnng at hgher rates (α =.25,.2 e.t.c.), the system effcency mproves faster ntally but then t converges to a lower equlbrum value. As we reduce the learnng rate, the convergence s steeper, smoother and results n a hgher equlbrum value. From Fgure 8, we see that the system acheves the best possble effcency at a learnng rate of RELATED WORK The use of large-scale storage systems wth renewable generators has been extensvely studed n the lterature. There s however no known publshed work on the couplng of both utlty-scale storage and mcro-storage. Smlarly, a number of prcng ncentves have been proposed n the lterature to help acheve demand response and feld trals have been carred out to evaluate the effectveness of these mechansms. For example, Calforna s utltes [2, 9] conducted the Statewde Prcng Plot to evaluate the effect of Tme-Of- Use mechansm (ths mechansm dvdes the day nto slots wth fxed prces) and showed an estmated reducton n peak perod energy use of 5.9% durng the summer months. Furthermore, Xcel Energy [, ] also conducted a plot program that tested the effectveness of Crtcal Peak Prcng mechansm (ths dentfes some exceptonal days wth very hgh demand) gven an enablng technology wth partcpants achevng reductons of about 44.8%. Yet another prcng mechansm, Peak-Tme Rebate (PTR) was evaluated by Wolak [8]. In ths, partcpants receved a rebate of.35$/kwh for reductons relatve to ther typcal peak perod consumpton on non-ptr days. Partcpants however have the potental to game the system (as dscovered by [8]) by ncreasng ther electrcty use durng the perod n whch baselnes are establshed. Whle the aforementoned prcng mechansms have the ablty to effect a reducton n peak demand, they usually nvolve actve partcpaton on the part of the consumers. Also, these mechansms often just shft the peak demand to other tmes that have been

8 deemed to be off-peak. We beleve that gven the varablty n the renewable energy generaton, there s a need to synchronze and nfluence exactly where the shfted peak goes to n order to ensure system stablty. In general, none of these prcng mechansms deal specfcally wth the varablty of supply when renewable energy generators are nvolved. In ths regard, we note the recent work by Ramchurn et al [6] where they present a carbon prcng mechansm that s desgned specfcally for a renewable energy suppler that s operatng n the electrcty market. Ths paper s nspred by ther work, but dffers n that we look at the ssue of a renewable energy suppler that has storage capablty. Also, our work s targeted at the Masdar Cty model of a totally self-sustaned cty. Ths mples that, unlke ther work, the suppler does not have the ablty to meet the demand that exceeds ts supply from the external electrcty grd. 7. CONCLUSION In ths paper, we presented a multagent framework for jont-storage management and a prcng mechansm, SPM, for renewable energy supplers and consumers wth storage devces. We smulated the performance of the mechansm based on the Masdar Cty model and evaluated t n terms of the system effcency and consumer benefts. The results showed that unlke the fxed prcng mechansm (currently n use n UAE) whch acheves a system effcency of 74%, the storage prcng mechansm acheved a system effcency of up to 97.4% wth all consumers havng storage devces and smart meters nstalled n ther homes. Moreover, the consumers wth storage devces were able to make an average savngs on ther electrcty blls of 35% when all the consumers are equpped wth storage devces. Due to lack of avalablty of hgh-resoluton household data n the UAE, we utlzed tme-shfted UK data. 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