Effect of Price Responsive Demand on the Operation of Microgrids

Transcription

1 Effect of Price Reponive Demand on the Operation of Microrid Felipe Ramo Univerity of Waterloo Waterloo, Canada Claudio Cañizare Univerity of Waterloo Waterloo, Canada Kankar Bhattacharya Univerity of Waterloo Waterloo, Canada Abtract In thi paper, a demand elaticity model i developed and teted for the dipatch of microrid. The price obtained from dipatchin the network in a bae-cae cenario i ued a input to a demand elaticity model; thi demand model i then ued to determine the price-reponive demand for the next iteration, aumin that the load chedule i defined a day ahead. Uin thi cheme, trend for demand, hourly price, and total operation cot for a microrid can be obtained, to tudy the impact of demand repone on unit commitment. Thi way, for a microrid, the effect on the chedulin of dieel enerator and enery torae ytem can be analyzed with repect to price-elatic load. The reult for a benchmark microrid how that the propoed 24-hour model eventually convere to a teady tate, with price and cot at their lowet value for different cenario. Moreover, it i confirmed that elatic demand in a microrid reduce electricity price variability and mitiate the need for torae in the preence of hih penetration of renewable enery. Keyword Microrid dipatch, demand repone, DSM, enery torae, demand elaticity, optimization. Indexe Nomenclature d Directly controllable load. Generator unit. i, j Sytem bue. Storae device. t, k Time tep. Variable δ i,t P DCd,t P DS d,t P G,t P S,t ρ i,t Voltae anle at bu i, time t [rad]. Enery curtailed or hifted of load d at time t [kwh]. Enery hifted of load d to time t [kwh]. Enery enerated by unit at time t [kwh]. Enery aborbed or delivered by torae device at time t [kwh]. Electricity price at bu i, time t [$/kwh]. Thi work wa funded by the NSERC Strateic Network on Smart Microrid NSMG-Net, Canada. Paper ubmitted to Power Sytem Computation Conference, Auut 18-22, 214, Wroclaw, Poland, oranized by Power Sytem Computation Conference and Wroclaw Univerity of Technoloy. S OC,t State of chare at torae device, time t [kw]. U G,t Start-up deciion for unit at time t. V G,t Shutdown deciion for unit at time t. W c,t Binary deciion on charin at time t. W d,t Binary deciion on dichare at time t. W Dd,t Binary curtailment deciion of d at time t. W G,t ON/OFF tatu of enerator at time t. Parameter a Fixed cot of enerator [$]. α i Share of elatic demand from total demand at bu i [%]. B i, j Suceptance of line i and j [pu]. b Variable cot of enerator [$/kwh]. C min, C Minimum and imum torae chare level [kwh]. C d Cot of controllable load d [$/kwh]. C Cot of torae per operation [$]. E i Croed-time elaticity matrix at bu i. ε it,k Elaticity element t, k of matrix E i. η c Input efficiency of torae device [%]. η d Output efficiency of torae device [%]. G Time for which mut be ON at tart to atify MUT. L Time for which mut be OFF at tart to atify MDT. M Contant for enforcin bindin condition on. MDT, MUT Minimum down and up time of unit. P i,t Initial demand at bu i [kw]. P DGi,t Renewable enery injected at bu i at time t [kwh]. P D d Maximum power hifted or curtailed for load d [kw]. P Di,t Demand at bu i at time t [kwh]. min P G, P G Minimum and imum power limit of enerator [kw]. P line i, j Limit of the line between i and j [kw]. P S min, P S Minimum and imum capability of converter [kw].

2 Ramp down limit of [kw]. Ramp up Ramp up limit of [kw]. ρ i Reference electricity price at bu i [$/kwh]. S DC Shutdown cot of enerator [$]. S UC Start-up cot of enerator [$]. W Statu of enerator at t=. Ramp down I. Introduction With the evolution of mart rid and ditributed enery reource DER, the concept of demand repone DR ha ained more inificance. It i expected that appliance and load in eneral would have the capability of reactin to external inal, uch a price and direct chedulin command. DR would alo provide variou ytem upport ervice uch a operational reerve, frequency repone, and/or conetion manaement [1]. Mot of the practical DR example are aociated with proram etablihed by overnment or utilitie, which eek to reduce peak load or rearrane demand profile. In the cae of voluntary proram, cutomer may receive a financial incentive by adherin to a proram and modifyin their demand profile. Similarly, time-baed rate try to way enery conumption toward a point of mutual convenience for both cutomer and utilitie. Thi i achieved by offerin lower electricity price at low demand period, while charin hiher price when the ytem i treed or more expenive eneratin unit are in operation. DR proram may be claified a indirect or direct, dependin on whether demand alteration i a choice of cutomer or a utility deciion, repectively. An example of indirect DR i the time-of-ue TOU pricin cheme [2], which encourae load hiftin and curtailment by mean of different price level durin the day. Another indirect proram i the real-time-pricin RTP cheme, which repreent the actual hort-term condition of the ytem [3], thu promotin price-reponive behavior from the cutomer. Amon the direct proram worth mentionin are the direct load control DLC and the interruptible load manaement proram, which pay an incentive to cutomer [4], allowin the utility to directly control a portion of the load. One of the mot important apect of aein the effect of demand reponivene i how to model both DR and the ytem. In [5], an elaticity of electricity data collection i preented, claifyin between hort and lon term elaticitie, and provin real value etimated for reidential and indutrial demand price elaticity from different publihed tudie. A tatitical method for etimatin cutomer repone to pricin inal i developed in [6], which i then ued for calculatin an optimal RTP cheme that improve the ocial welfare; from thi work, a parallel between DLC proram and intantaneou demand elaticity effect can be derived. In [7], a data minin method i propoed to tudy reponivene and create a demand control cheme via pricin inal to control reidential heatin ytem device; a real cae tudy applie the control cheme, reducin peak conumption in up to 11%. DR tudie for an iolated ytem with renewable enery ource RES are conducted in [8] by uin two approache for load hiftin, i.e., direct control and cutomer demand elaticity, howin that with DR le unit are committed due to a lower impact of wind variation, thu reducin cot. The work in [9] how how oliopoly market efficiency i increaed when it demand i elatic, noticin that there i reduction in the urplu of producer and conumer. A tudy of the effect of elaticity from the plannin perpective coniderin operational contraint i conducted in [1] and, by includin DR in the hort-term optimization model, the work conclude that more RES can be connected with more reponive demand. A unit commitment UC method with DR i propoed in [11], which tudie economic and environmental impact, analyzin different DR proram and DLC in order to create a DR proram priority lit for independent ytem operator. So far, mot of the work that ha been done reardin DR analyi only examine it in an ex-pot bai, not properly coniderin the ide effect of intellient device and central controller. In addition, only a few tudie conider DER, DLC, and ESS, all common component to be found in a microrid. Moreover, the tudie performed o far only apply the reponivene to one day ahead, not takin into account the fact that utained reponivene may produce an evolutionary repone in demand. Thi reult in a method that i not accurate for etimatin the application and effect of DR in mart rid and microrid. Therefore, the methodoloy propoed in thi work intend to characterize the poible effect that DR may have over a microrid. To thi end, a 24-hour cro-time elaticity model i developed, baed on the behavior that load enery manaement ytem EMS, uch a [12], would have over the network. Thu, a implified verion of the full extent reidential model in [12] i ued to obtain a 24-hour elatic model with cro time dependence. Thi repreentation of EMS allow for a uitable analyi of the impact of uch load control ytem on the rid/microrid. In order to develop a imulation platform for the tudy of DR effect on dipatch and vice vera, the mixed inteer linear model from [13] i ued a a bae to develop a model uitable for microrid. Alon with the aforementioned UC model, ESS and DLC are included in the propoed martmicrorid model. RES in thi model are jut conidered a a neative load component added to the enery balance equation. The ret of the paper i tructured a follow: Demand price-reponivene and a ecurity-contrained UC model uitable for microrid are dicued in Section II, toether with a propoed procedure for tudyin demand reponivene in microrid. A novel method for etimatin demand elaticity parametrization i preented in Section III. In Section IV, a benchmark microrid and the reult of applyin the propoed model to thi ytem are preented and dicued. Finally, Section V hihliht the mot important concluion and propoe ome future work reardin price reponivene tudie in microrid. II. A. Price Elaticity of Demand Mathematical Modelin The followin cro-time elaticity matrix E i i propoed in [14] and it i ued in thi work to repreent load DR:

3 ε i1,1 ε i1,24 E i =..... ε i24,1 ε i24,24 The diaonal element of E i, iven by ε it,t, repreent elf-elaticity, i.e., the load i elaticity at time t with repect to price chane at time t. Similarly, non-diaonal element ε it,k repreent the elaticity of load i at time t with repect to price variation at time k. Note that ε it,k and ε k,t do not repreent the ame, therefore they are not required to have the ame value. The eneral expreion propoed here for etimatin demand baed on 1 i: P Di,t = P i,t 1+α i k 1 ρi,k ε it,k 1 ρ 2 i Thi equation decribe demand a a combination of elatic and inelatic demand. Reponivene i modeled by the total contribution of percentae chane in price throuhout the whole period, which i then multiplied by the bae load and it percentae modifierα i. It i important to note that the reult of thi elatic term can be poitive, zero, or neative, a it repreent the total contribution from all price variation for the demand at time t. In order to properly repreent DR, diaonal elementε it,t are poitive, while non-diaonal elementε it,k are neative or zero. In thi way, demand variation at hour t i inverely proportional to price variation at t, meanin that a price hiher than expected at t would tranlate into demand reduction at that hour. On the other hand, demand variation at t caued by price variation at k may only be poitive when the price difference at time k i not neative. The latter reflect that at a price exceedin the referenceρ i at time k would encourae an increment of conumption at any other hour, in order to reduce the demand at k load hiftin. In Section III, the etimation of the elaticity parameter to repreent load EMS i dicued in ome detail. B. Operational Model for Microrid The objective function for the problem i the minimization of the total cot of operation a follow: Cot= a W G,t + b P G,t + S UC U G,t +S DC V G,t +,t + C Wc,t + W d,t + C d P DCd,t,t The firt term in 3 denote the operational cot of dipatchable enerator, includin fixed cot when dipatched, variable cot of power output, and tartup and hutdown cot. The econd term in thi equation repreent the cot of operatin an ESS, while the lat term repreent the cot of uin DLC proram on cutomer load. d,t 3 1 Demand Supply Balance: The nodal enery balance in the ytem, includin all the ditributed component in the microrid, i repreented by: P DGi,t P Di,t + P S,t + PDCd,t P DS d,t + i d i 4 + P G,t = B i, j δ j,t δ i,t i RES in thi model are repreented a no cot neative load. 2 Feeder Limit Contraint: The power tranferred from bu i to j i contrained by line limit, which i iven by: j B i, j δi,t δ j,t P line i, j 5 3 Power Generation Limit: For dipatchable enerator, the upper and lower operation limit are iven a follow: W G,t P G min P G,t W G,t P G 6 4 Startup and Shutdown Coordination: The link between tartup and hutdown deciion, and the tranition in enerator tate from one hour to the next one are iven by: U G,t V G,t = W G,t W G,t Spinnin Reerve: For reulation purpoe, 1% pinnin reerve are aumed a follow: 1.1 P Di,t WG,t P G 8 i 6 Ramp Up and Ramp Down Contraint: Thee contraint enure that the inter-hour chane for the dipatchable unit atify neceary rampin limit. P G,t P G,t 1 Ramp up P G,t 1 P G,t Ramp down 9a 9b 7 Minimum Up and Down Time: The followin et of equation account for the minimum up time of dipatchable enerator. 24 t+mut 1 G k=1 1 WG,k = 1a W G,k MUT WG,t W G,t 1 WG,t W G,t 1 WG,k t= G + 1,...,25 MUT t=26 MUT,...,24 1b 1c In 1a, the down time condition for the firt G time tep i enforced, preventin the enerator from huttin down if it wa ON durin the lat tep of the previou iteration. Equation 1b force the enerator to be ON at leat MUT tep if it i witched on. Finally, 1c provide the condition that

4 enure that if a enerator i tarted up within the lat MUT time tep, it will tay ON until the end of the optimization time frame. Analoouly to the expreion 1a-1c, minimum down time are decribed by the followin expreion: 24 t+mdt 1 L k=1 W G,k = WG,k 1 MDT WG,t W G,t 1 t=l + 1,...,25 MDT WG,k 1+ W G,t 1 W G,t t=26 MDT,...,24 11a 11b 11c Equation 11a enforce the down time condition for the firt L time tep, preventin the enerator from tartin if it wa OFF at k=. Equation 11b force the enerator to be OFF at leat MDT tep, and 1c enure that if a enerator i hutdown within the final MDT tep, it will tay OFF until the lat period. 8 Enery Storae Sytem: The equation to repreent ESS in the model are the followin: P S,t η d C min S OC,t C 12 P S,t η c M W d,t S OC,t+1 S OC,t S OC,t+1 S OC,t P S,t η c +M W d,t M Wc,t W d,t + 1 S OC,t+1 S OC,t S OC,t+1 S OC,t P S,t η d 13a 13b 14a + M Wc,t W d,t b Here, 12 repreent the limit in torae capacity level S OC,t baed on the model hown in [15]. Expreion 13a and 13b repreent the enery balance of the torae device while charin, coniderin the charin efficiency η c. Equation 14a and 14b take care of the dicharin proce, alo coniderin the operation efficiency η d. It i important to notice that, in order to keep the model linear, the balance equation have been linearized by uin the bi M method for alternative et of contraint [16], and thu the bindin contraint are elected accordinly. The minimum and imum capability of ESS enery injection or aborption i modeled a: P S min P S,t P S 15 Finally, coordination of chare/dichare deciion variable i achieved by, W d,t + W c,t 1 17 which conider that the ESS cannot chare and dichare at the ame time. 9 Direct Controllable Load: Utility controllable load are modeled a follow, Type d P DCd,t = P DS d,t 18 t P DCd,t W Dd,t P D d P DS d,t 1 W Dd,t PD d t 19a 19b where 18 repreent the two type of controllable load: Type d = 1 for hiftable load, and Type d = for curtailable load. Thi equation allow to yntheize both clae of DLC, and i a variation from the contant enery model propoed in [17]; in the cae of load hiftin, thi uarantee that demand that i to be curtailed i reallocated to time where no curtailment i needed. Expreion 19a and 19b limit the amount of enery directly controlled, dependin on whether the load hed command W Dd,t i in place or not. With all thee equation, the traditional ecurity contraint UC model i modified to repreent a microrid appropriately. In the next ection, a eneral iterative procedure for tudyin the inter-relationhip between price and demand reponivene i preented, alon with the propoed methodoloy for etimatin indirect DR from mart load. C. Iterative Procedure In contrat to what the literature propoe, it i not abolutely correct to aume that demand reponivene only affect the final demand once. A DR i applied to conecutive day, mart device or enitive cutomer will learn from pat behavior and adapt to the price reultin from their reponivene. Thi chane the procedure to a more iterative one that take into account thi two-way influence between demand and price. Thu, a hown in Fi. 1, the operation of the propoed model i to obtain nodal price from ytem imulation, tartin with the oriinal value or the forecat for ytem demand. Then, by uin thee price vector a the input for a demand elaticity model, the demand for the next iteration i obtained. III. Load Model Etimation The value of the expected priceρ i in 2 i aumed to be contant durin the whole time frame 24 hour in thi cae, a in [1]. By makin thi aumption, it i enured that if the price were all the ame, there would be no price The charin and dicharin limit coniderin the battery SOC and the imum and minimum torae capacity are modeled a: S OC,t C η c P S,t 16a P S,t S OC,t C min η d 16b P d Fi. 1. Security Contrained Unit Commitment Œ k Demand Elaticity Model Iterative procedure for dipatch and demand correction. P d k+1

5 Fi. 2. Hitorical Enery Price Uniform Probability Ditribution Etimation Daily Random Enery Price Set é Ü Demand elaticity model etimation. Enery Manaement Sytem Minimum Square Error Optimization variation, tranlatin into no demand variation. Additionally, the expected price hould be uch that way demand profile toward a contant value, areein with [7], where the control objective i to reach a flat demand profile. In order to conider thee two aumption, the final value for expected cutomer price in 2 hould be defined by the weihted averae of price at each node, a hown below: ρ i = ' Ü t P Di,t ρ i,t t P Di,t 2 For modelin DR meaure, it ha been mentioned in the literature that the main component that are repreented in DR are water heater a well a air conditionin, heat and ventilation. However, the propoed model can be extended for more complex demand control device. Thu, after implementin a model of the load EMS, it repone baed on the hitorical data for RTP price in a certain rid can be aeed. Uniform probability ditribution for price at each hour were conidered to determine the impact of varyin price on uch load demand; the rane of thee ditribution are uch that comprie the imum and minimum price at each hour, after eliminatin the outlier. Once the ditribution i parametrized, everal daily price et 24 hour price vector are enerated and recorded; for each of thee vector, the behavior of the load i obtained. Finally, in the data eneration tep, each price i compared to the reference priceρ i, and each demand vector i compared to the bae load; in thi manner, a et of chane in price and their correpondin demand variation are created. After the aforementioned data eneration procee, the parameter for the E i matrix are obtained. A minimum quared error optimization model i ued for etimatin thee parameter baed on the difference between the etimated demand from 2 and the actual demand of the load with EMS. Thi minimization i ubjected to the fact that diaonal element of matrix E i are expected to be neative while the ret are poitive, properly characterizin DR a explained in Section I. The procedure i illutrated in Fi. 2. IV. A. Tet Microrid Decription Simulation and Reult The tet microrid ued for the tudie i a modified verion of the CIGRE-IEEE ditributed enery ource MV benchmark network propoed in [18]. In thi work, the modified ytem i a 13-bu network, by joinin toether Bue, 1 and 12 in the oriinal ytem, and replacin the HVDC link with an Bu 4 Bu 5 Bu 11 Bu 2 Bu 8 31 kw Utility Bu 1 Bu 3 Bu 9 5 kw Bu 7 Bu 6 Bu 1 Bu 12 Bu 13 5 kw Dipatchable Generator H2 Ion Battery Electrolyer Wind Turbine PV Panel Fi. 3. Microrid tet ytem baed on the CIGRE-IEEE DER benchmark MV network [18]. AC feeder a een in Fi. 3. The modified microrid conider 1,71 kw of renewable DER, 1,339 kwh of ESS intalled capacity, and 5,81 kw in dipatchable thermal capacity. Amon the dipatchable thermal eneration, the enerator at Bu 1 i aumed to be the main microrid ource. The quadratic cot of thi lare enerator 5, kw i here modeled a a 5 tep piece-wie linear enerator in order to maintain the model linear. In term of direct controllable load, a value correpondin to 7% of the lowet hourly demand for each bu i aumed to be available for curtailment, and 15% for hiftin, at any time at each of the load bue. Thee value were choen o that only a mall percentae of the load i aumed to be controllable, in order to conider a realitic cenario. Since DLC ha a major impact on the cutomer comfort, the cot of load hiftin i aumed to be $2/kWh, wherea curtailment cot i aumed to be $2/kWh, which compared to the marinal price for the microrid without DR, thee cot are about 8 time and 8 time hiher, repectively. In thi fahion, direct control only occur when the microrid load cannot be upplied from the iven ource without load reduction. Finally, the cot C of operatin the ESS wa etimated by coniderin 2 operatin cycle per day, an annual rate of return of 8%, an invetment cot of $1,2/kWh, and a lifepan of 3, cycle, a per [19]. Uin thee value for calculatin a daily annuity, the reultin averae ESS operatin cot i 54 /kwh. B. Elaticity Etimation Reult After applyin the procedure indicated in Section III for RTP value in Ontario, Canada, durin ummer, the reultin E i matrix for the EMS propoed in [12] i hown in Table

6 TABLE I. Demand elaticity matrix etimated for the load EMS in [12] I. A explained in previou ection, thee parameter value were obtained by uin the hitorical hourly Ontario enery price HOEP data available at [2], and a reultin tochatic model of hourly pricin. Thi table how that elf elaticitie at 2 AM and 7 AM are at leat 2 or 3 time hiher than the averae elf-elaticity; additionally, from 3 AM to 6 AM, and then from 1 AM to 5 PM, elf elaticitie are around the averae, while at every other hour thee are low. On the other hand, for cro-time elaticitie, variation in demand are directly proportional to the variation in price. Therefore, iven the price, demand i expected to increae at niht and decreae durin the day. It i worth mentionin that the hiher cro-elaticitie are located alon the matrix diaonal, meanin that there i a troner hiftin capability between cloe hour than there i between ditant hour. Another interetin obervation i that, for the iven load EMS, own elaticity value reach value of -8.9, and are hiher than 1 for cro elaticity, which mean that uch EMS technoloie are capable of increain demand elaticity up to 2 time more than the common DR proram, baed on the elaticitie reported in [5]. C. Benchmark Microrid Reult In the bae cae, Fi. 4 diplay how the forecated demand evolve, fillin up low demand hour by hiftin peak in demand to the valley. Since the load model ued conider thermal load, the net value of demand variation i not zero due to thermal inertia, thu increain demand at the beinnin of the 24 hour period and reducin conumption toward the end of the day. Thi i the ame behavior exhibited by the load EMS in [12], where the chedulin i done in a day-ahead bai, reultin in pre-climatizin the buildin in the mornin to meet the contraint durin day time. When comparin Fi. 4 and Fi. 5, one can oberve how the demand and price increae durin the niht, a expected. It can alo be noticed that the mornin peak i extended for an hour. Note a well that the total ytem operatin cot for the microrid decreae a the the demand evolve toward a fixed profile. When coniderin the operation under treful condition, the chane in demand are far more dratic, Pd [kw] Fi. 4. Hour Price [$/kwh],35,3,25,2,15,1,5 Fi. 5. Effect of DR on total demand for an iolated microrid. Hour Effect of DR on pricin inal for an iolated microrid. becaue both the bae load and hourly price variability are reater. Fiure 6 depict the evolution of net load in the microrid howin it converence to a fixed profile, which i between the initial and firt iteration load profile. Thi can alo be een in Fi. 7 for price correction. Under treful condition, the ESS operation occur more often than for the initial load profile, a hown in Fi. 8. The reaon for thi i that the ytem feeder are aturated at the initial loadin condition, and after coniderin reponivene, thi problem i motly mitiated. Thi fiure alo how how, after DR activation, the ESS mainly conume enery from the rid, a to enure the proper uae of the available enery durin period of hih RES eneration. It i interetin to note that in the cae preented here, there wa no need for DLC uae, a the price-elatic load and ESS were ufficient to keep the eneration-demand balance.

7 Pd[kW] Hour Fi. 6. Effect of DR on total demand for an iolated microrid under hih demand and hih content of non-dipatchable RES. Price [$/kwh],4,35,3,25,2,15,1,5 Hour Fi. 7. Effect of DR on pricin inal for an iolated microrid under hih demand and hih content of non-dipatchable RES. P[kWh] Hour Fi. 8. Effect of DR on ESS operation for an iolated microrid under hih demand and hih content of non-dipatchable RES. V. Concluion A new model for tudyin the effect of load price-elaticity in market price and dipatch ha been developed. It ha been hown here, a in previou paper, that price-elatic load may preent advere effect on the rid, uch a the cae of low price, tranlatin into hih demand peak. Hence, DR i demontrated to not alway be a beneficial a ome report claim, epecially when elatic demand become a inificant part of the total ytem load. Due to the effect of EMS in intellient load, demand will be reduced at peak-price, reultin in increae peak power durin low-price time, with thi phenomenon bein more pronounced a the load elaticity increae. In the particular cae of microrid, multi-period price-reponive load were hown to have imilar behavior a ESS, oothin ytem variability while minimizin total operatin cot. It wa demontrated that there can be a prioritization of DR over ESS, dependin on whether the price difference durin the day are reater than ESS operatin cot or not. However, in the cae when there i no other way to meet the demand balance at a certain hour, the prioritization proce i nullified. Reference [1] Staff Report, FERC, Aement of demand repone & advanced meterin, 28, [Online]. [2] J. Sheen, C. Chen, and J. Yan, Time-of-ue pricin for load manaement proram in Taiwan Power Company, IEEE Tranaction on Power Sytem, vol. 9, no. 1, pp , [3] F. Schweppe, R. Tabor, J. Kirtley, H. Outhred, F. Pickel, and A. Cox, Homeotatic utility control, IEEE Tranaction on Power Apparatu and Sytem, vol. PAS-99, no. 3, pp , 198. [4] K. Bhattacharya, M. Bollen, and J. Daalder, Real time optimal interruptible tariff mechanim incorporatin utility-cutomer interaction, IEEE Tranaction on Power Sytem, vol. 15, no. 2, pp. 7 76, 2. [5] M. G. Lijeen, The real-time price elaticity of electricity, Enery Economic, vol. 29, no. 2, pp , 27. [6] R. Yu, W. Yan, and S. Rahardja, A tatitical demand-price model with it application in optimal real-time price, IEEE Tranaction on Smart Grid, vol. 3, no. 4, pp , 212. [7] O. Corradi, H. Ochenfeld, H. Maden, and P. Pinon, Controllin electricity conumption by forecatin it repone to varyin price, IEEE Tranaction on Power Sytem, vol. 28, no. 1, pp , 213. [8] K. Dietrich, J. Latorre, L. Olmo, and A. Ramo, Demand repone in an iolated ytem with hih wind interation, IEEE Tranaction on Power Sytem, vol. 27, no. 1, pp. 2 29, 212. [9] E. Bompard, Y. Ma, R. Napoli, and G. Abrate, The demand elaticity impact on the trateic biddin behavior of the electricity producer, IEEE Tranaction on Power Sytem, vol. 22, no. 1, pp , 27. [1] C. De Jonhe, B. Hobb, and R. Belman, Optimal eneration mix with hort-term demand repone and wind penetration, IEEE Tranaction on Power Sytem, vol. 27, no. 2, pp , 212. [11] A. Abdollahi, M. Mohaddam, M. Rahidinejad, and M. Sheikh-El- Elami, Invetiation of economic and environmental-driven demand repone meaure incorporatin UC, IEEE Tranaction on Smart Grid, vol. 3, no. 1, pp , 212. [12] M. Bozchalui, S. Hahmi, H. Haen, C. Cañizare, and K. Bhattacharya, Optimal operation of reidential enery hub in mart rid, IEEE Tranaction on Smart Grid, vol. 3, no. 4, pp , 212. [13] M. Carrión and J. Arroyo, A computationally efficient mixed-inteer linear formulation for the thermal unit commitment problem, IEEE Tranaction on Power Sytem, vol. 21, no. 3, pp , 26. [14] A. David, Load forecatin under pot pricin, IEE Proceedin C; Generation, Tranmiion and Ditribution, vol. 135, no. 5, pp , [15] R. Dufo-López, J. Bernal-Autín, and J. Contrera, Optimization of control trateie for tand-alone renewable enery ytem with hydroen torae, Renewable Enery, vol. 32, no. 7, pp , 27. [16] E. Catillo, A. J. Conejo, P. Pedreal, R. García, and N. Aluacil, Buildin and Solvin Mathematical Prorammin Model in Enineerin and Science. Wiley, 22. [17] R. Palma-Behnke, J. Cerda, L. Vara, and A. Jofre, A ditribution company enery acquiition market model with interation of ditributed eneration and load curtailment option, IEEE Tranaction on Power Sytem, vol. 2, no. 4, pp , 25. [18] K. Rudion, A. Orth, Z. Styczynki, and K. Strunz, Dein of benchmark of medium voltae ditribution network for invetiation of DG interation, in IEEE Power Enineerin Society General Meetin, 26, pp [19] K. Divya and J. Øteraard, Battery enery torae technoloy for power ytem-an overview, Electric Power Sytem Reearch, vol. 79, no. 4, pp , 29. [2] Ontario IESO, Hourly ontario enery price, 212, [Online].