Towards the Interactve Effects of Demand Response Partcpaton on Electrcty Spot Market Prce Saeed Mohajeryam, Mlad Doostan, Seyedmahd Moghadas Energy Producton and Infrastructure Center (EPIC) Electrcal and Computer Engneerng Department Unversty of North Carolna at Charlotte Charlotte, NC, USA Emal:{smohajer,mdoostan,smoghada}@uncc.edu Peter Schwarz Belk College of Busness Unversty of North Carolna at Charlotte Charlotte, NC, USA Emal: pschwarz@uncc.edu Abstract The electrcty market s threatened by supply scarcty, whch may lead to very sharp prce spkes n the spot market. On the other hand, demand-sde s actvtes could effectvely mtgate the supply scarcty and absorb most of these shocks and therefore smooth out the prce volatlty. In ths paper, the postve effects of employng demand response programs on the spot market prce are nvestgated. A demand-prce elastcty based model s used to smulate the customer reacton functon n the presence of a real tme prcng. The demand acheve by DR program s used to adjust the spot market prce by usng a prce regresson model. SAS software s used to run the multple lnear regresson model and MATLAB s used to smulate the demand response model. The approach s appled on one week data n summer 14 of Connectcut n New England ISO. It could be concluded from the results of ths study that applyng DR program smooths out most of the prce spkes n the electrcty spot market and consderably reduces the customers electrcty cost. Keywords demand response, electrcty spot market prce, electrcty market, real tme prcng, prce elastcty of demand I. INTRODUCTION The market for electrcty are progressvely developng over numerous years of competton and reorganzaton. Nevertheless, there are stll several areas n the ndustry that are kept shelded from the advancement n the market, whch one of them s demand-sde. As a matter of fact, ths area s underdeveloped due to the detachment from market prce fluctuatons as the regulatory bodes attempted to gve mmunty to retal customers vulnerable to such fluctuatons. For nstance, durng and 1, Calforna experenced a major power crss under the restructured wholesale market. Although numerous factors could be lsted as reasons to create ths crss, most people agree that the lack of demand response exacerbated the stuaton[1]. However, studes over the recent years show that demand response (DR) programs could create an envronment n whch customers could engage n the process of optmzated decson makng. Consequently, t can change the customers consumpton pattern n response to the prce sgnals provded by the wholesale market. These programs can create numerous practcal possbltes for the power system operators and utltes to make an mprovement n both economc and techncal ndces of ther system. As a matter of fact, power system operators can compensate lack of ther supply durng the peak tme wth DR resources. It s estmated that the capacty to meet demand durng the top 1 peak hours accounts for 1-% of electrcty cost annually []. On the other hand, utltes can also beneft from DR by takng advantages of lower prces offered by such resources compared to electrcty spot market. DR programs are generally could be separated nto two man categores: ncentve-based programs (IBP) and tmebased rate (TBR) programs. As shown n Fg. 1, each category s composed of several programs. The authors n [3-4] elaborated these programs n detal. For many years, utltes have offered IBPs to to large ndustral and commercal customers. As an example, ERCOT offers emergency nterruptble load program to ts large customers. Moreover, Southern Calforna Edson (SCE) has offered a varety of DR programs such as automated demand response (Auto-DR), permanent load shftng (PLS) and scheduled load reducton programs (SLRP) to ts large customers [5]. On the other hand, TBR programs are typcally neglected by utltes due to the lack of proper nfrastructure, techncal complcaton and hghly captal ntensve nfrastructure. However, over the last decade, the US government and ts energy sector, due to envronmental challenges of the tradtonal electrcty generaton, attempted to adopte a supportve approach n order to provde the necessary nfrastructure for DR and energy effcency programs. These programs are mostly TBR programs. Another mpact factor that helps to launch TBR programs more convenently s the penetraton of advanced smart meters. Advanced meterng penetraton, based on 1 FERC survey, has reached to a consderable level of 8.7 percent n the US [6]. Advanced meterng s regarded by many as a cornerstone of the TBR programs. Furthermore, many utltes have recently launched plot programs to evaluate the feasblty and techncal challenges of TBR programs n the new envronment [7-11]. Although based on the prevous dscusson, the fnancal support s more avalable n order to buld the necessary nfrastructure for the TBR programs, these program face many obstacles n the mplementaton stage. One of the most major ssues that utltes face wth regard to the desgn of the programs s fndng the proper model to explan the customer s reacton to the ncentves provded by each program. As a matter of fact, the utltes cannot employ the proper proft maxmzng strateges n the absence of a relable model. Therefore, many of the programs mght not even ntated or f they do, they mght be doomed to falure. Moreover, the wrong models mght leads to proposng the wrong ncentve payments. The mproper ncentve payment can dscourage the
partcpaton n the program. Therefore, to overcome ths problem, dfferent models are proposed to explan the customer s reacton functon. Authors n [1-14] employ demand-prce elastcty concept to model the effects of mplementng demand response programs on customer s reacton. In fact, demand-prce elastcty s a concept borrowed from the consumer theory n mcroeconomcs whch reflects the relatve change n the demand wth respect to the relatve change n the prce [15-16]. The approach utlzed n [17] models the customer s reacton functon wth lnear optmzaton technque assumng the customers have access to the real-tme electrcty prces. In ths model, the objectve functon s maxmzng the utlty and mnmzng the cost of electrcty consumpton. A statstcal method ntroduced n [18] uses the demandprce elastcty to explan the customer reacton functon n the drect load control (DLC) program. Moreover, the authors n [19] apples self-organzng maps and statstcal Ward s lnkage to classfy electrcty market prces nto dfferent clusters. It also uses a non-parametrc curve estmaton approach to explore the underlyng structure n dfferent clusters whch leads to extracton of the proper customer s reacton to the dfferent prces. Furthermore, the authors n [] developed a method based on consumers theory n mcroeconomcs to ncorporate the customers wllngness to shft consumpton cross-perods based on the pertnent rates. In addton to the aforementoned models, several forecastng based approaches are proposed to explan the customer s reacton functon. These approaches whch use expost and ex-ante data are beng used to forecast the short-term and long-term customer s reacton functon. Authors n [1] report the current practce at Pacfc Gas and Electrc (PG&E) company. ex-ante and ex-post reports are used to develop ndvdual customer regresson models. In order to develop a robust model, all the nterdependences of weather, calendar days, etc are added to the regresson model. The utlzed models need substantal amount of hstorcal data and proper control groups. In ths paper, the effect of demand response on the spot market prce s examned. The objectve s to nvestgate the mpact of DR on the prce volatlty by proposng an algorthm whch feeds the outcome of DR model nto the spot market and explore the postve mpact of demand response. It wll be shown how the full partcpaton of the demand sde under real tme prcng can decrease the wholesale prce and ts fluctuatons n the market. In order to carry out such task, the customer s reacton functon model and day-ahead load forecastng are requred. In ths paper, customer s reacton model s taken from []; also, for the forecastng part, multple lnear regresson model (MLR) s used. Two man classes of load and prce forecastng are prevalent n the lterature. One assumes that merely the avalablty of the hstorcal data of the desred varable s suffcent for forecast purposes, whle the other reles on addtonal dfferent parameters lke weather, pressure, humdty, seasonalty, etc to do the forecastng. ARIMA models whch belong to the former class are popular n short term load and prce forecastng [3-4]. The latter class whch uses MLR models are sutable for short, medum and long term forecastng. Both classes could be enhanced by dfferent ntellgent technques such as Artfcal Neural Network (ANN), Fuzzy logc and Wavelet [5-8]. [9] analyzes the applcaton of aforementoned load forecastng classes n the presence of DR programs n detal. Even though, numerous models are proposed for prce forecastng, there s not any sngle model that works for all the stuatons; consequently, the utltes use multple models n parallel to create scenaro based forecasts. The organzaton of ths paper s as follows. Frst, a full descrpton of the demand response model used n ths paper s presented n secton II. Multple lnear regresson model s elaborated n Secton III. Secton IV explans the mplementaton of the proposed algorthm. Then the results for the case study as well as dscusson of the results are provded n secton V. Secton VI closes the paper wth drawng concluson from the provded dscusson and results. II. DEMAND RESPONSE MODEL In order to descrbe the employed demand response model n ths paper, t s necessary to understand the concept of demandprce elastcty. The demand for almost all goods and servces rses as the prce decreases. Based on dmnshng margnal return law, ths change n the demand s not lnear [15]. In order to quantfy the aforesad change n the demand, the concept of demand-prce elastcty has to be utlzed. Indeed, the nonlnear demand curve could be lnearzed around a gven pont. Then the change n the demand relatve to the change n prce could be measured whch s known as demand-prce elastcty. (1) represents the demand-prce elastcty functon mathematcally. P d E = (1) d p Fg. 1. Categores of the demand response programs Where E s the prce elastcty, p and d are prce and demand, P and d are ntal prce and demand respectvely. Prce elastcty has two components: self-elastcty and cross-elastcty. In other words, between two competng
commodtes, the percent change of demand wth respect to the percent change n ts own prce s self-elastcty, whereas the percent change of demand wth respect to the percent change n the prce of the other commodty s cross-elastcty. As t was mentoned, the demand response model n ths paper s defned based on the elastcty. To acheve ths target demand response model for 4 hours, frst t s requred that the model for one hour to be extracted and then expanded to 4 hours. In what follows, ths procedure s descrbed. A. Demand-prce elastcty model for one hour Suppose the customer s beneft for the -th hour s as follows: Bd ( ) = Ud ( ) d. p () Where Ud ( ( )) s customer s utlty n -th hour. Ths functon could be formulated wth the Taylor serous expanson accourdng to [9]. U( d ( )) Ud ( ( )) = Ud ( ( )) + d ( ) + (3) 1 U( d ( )) ( d ( )) d Where d s the customer demand change from d (the ntal demand) to d (optmum pont). The customer beneft can take dfferent unts; however, n ths paper, for the smplcty, t s assumed that ths beneft s n terms of dollar. Moreover, accordng to the classc economcs, t s assumed that every ndvdual optmzes her beneft. To obtan the optmum pont, the dervatve of the beneft functon wth respect to the demand must be zero. Bd ( ( )) Ud ( ( )) = p ( ) = (4) Therefore, Ud ( ( )) = p ( ) (5) Hence, accordng to (5), n the optmum pont, the margnal utlty s equal to the prce of the electrcty. Assumng that the ntal demand before mplementng the DR program s n optmum pont, (6) and (7) should hold. B U( d ( )) = p = (6) U( d ( )) = p (7) By usng (5) and the defnton of the prce elastcty of demand (1), (8) s obtaned. Ud ( ( )) p 1 p = = d d E d (8) Pluggng (7) and (8) nto the Taylor seres expanson of utlty functon (3) gves, Ud ( ) = Ud ( ) + p. d + (9) 1 1 p...( d ( )) E d (9) could be rewrtten and expanded as follows: d Ud ( ( )) = Ud ( ( )) + p. d ( )[1 + ] (1) E d Expandng d = d d and then pluggng (1) nto (5) yelds (11) and (1), p p d d = [1 + ] (11) E d p p p d d = + (1) E d Therefore, the customer s demand can be represented as follows: E ( p p) d ( ) = d( ) 1 (13) + p B. Demand-prce elastcty model for 4 hours To provde a model for 4 hours, both self- and crosselastcty have to be taken nto the consderaton. The crosselastcty between hours and j s defned as: P( j) E (, j) =, j (14) d p( j) The demand response model for 4 hours of a day could be obtaned by combnng self- and cross-elastcty of demand as follows: d d = d + E ( p p) + (15) p d 4 E (, j) ( p(j) p(j)), = 1,,..., 4 j = 1 p (j) j The varaton n the demand n (15) stems from two sources, one source s the self-elastcty whch s reflected by the frst and second terms and the other source s cross-elastcty whch s reflected by the thrd term. The obtaned relaton n (15) s employed n ths paper for demand response modelng part. III. MULTIPLE LINEAR REGRESSION MODEL As t was mentoned, to perform our proposed algorthm, the day-ahead prce forecastng s necessary. An MLR model s used n ths paper to carry out ths task. Ths model s a lnear model of demand, weather, tme of day, week and season. In addton to the day-ahead prce forecastng, ths model could be utlzed to update the spot market prces whch s a part of our algorthm. Indeed, MLR functon s able to model the dependent varable (prce) as a lnear functon of the ndependent varables, ndependent dummy varables and nteracton varables. The abundance of sample data can make the MLR model a very powerful tool.
Moreover, ths model could be enhanced by addng dfferent lag orders of the varables or dfferent functonal forms of the weather parameters; nevertheless, these extra varables are avoded n ths paper for smplcty. Indeed, the accuracy of MLR model s enough for the purposes of ths paper. The model used for the forecastng purpose s as follows: 4 P( ) = α + αk. hk( ) + α5. d( ) + α6. T( ) + α7. W( ) + (16) k = 1 H Sat Sun ( ) + ( ) + ( ) + ( ) α8. M α9. D α3. D α31. D Where α k s the coeffcent of the ndependent varables, h k s hours of the day, T() s the temperature at tme, W() s the dew pont at tme, M() s the month at tme, D H () s a bnary varable whch ndcates the holday at tme, D Sat () and D Sun () are a bnary varables whch ndcate the Saturdar and Sunday, respectvely, at tme. IV. IMPLEMENTATION Before explanng the mplementaton of the proposed algorthm, t s necessary to make several assumptons for ths study. These assumptons are lsted as follows. The utlty s an ndependent non-proft agent that functons as an ntermedary lnk between the customers and the wholesale market and purchases the electrcty on behalf of the customers. However, n practce, the utlty and the customers are two separate enttes and have dfferent proft functons. The spot market s the man market and the utltes purchase ther whole demand n ths market. However, n practce, the day-ahead market s the man market and the spot market s the real tme market where the partcpants use t to meet ther oblgatons n an emergency case. Real tme prcng s appled to DR model. Indeed, to ncent the customers to change ther consumpton pattern, real tme prcng s the best possble choce. To justfy the aforementoned assumptons, several reasons could be provded. Frst, although consderng the utlty proft s more realstc, t makes the problem extremely complcated whle does not provde any relevant outcome for ths study. Second, the prce volatlty manly exsts n spot market where the lmtaton of supply leads to sharp prce spkes whch s the man focus of ths study. However, n the day-ahead market, due to the more avalablty of supply, such sharp spkes are nonexstent. Indeed, by consderng the spot market as the man market, t s expected to observe more pronounced results. Fnally, the customers typcally pay flat rate for electrcty. However, n ths paper, the real tme prcng s selected to be appled to DR model as t would be the best ncentve for the users to shft loads at dfferent tmes. By consderng the aforementoned assumptons, the proposed algorthm for the evaluaton of the mpact of DR on spot market prces s llustrated n Fg.. The procedure s as follows. Frst, the hstorcal data ncludng the nformaton about prce, demand, weather, tme of day, week and season are loaded nto the SAS software. Then the algorthm contnues wth developng a smple basc regresson model. Snce addng too many varables to the regresson model may lead to the reducton of effcency and accuracy, t s necessary to select the most effcent varables. Therefore, a smple basc model s used at the begnnng and the Modfy the model NO START Load the hstorcal data Develop a smple multvarable regresson model Perform the n-sample analyss Perform the out-of-sample analyss Is FERMS acceptable? YES Use the real-tme prces and compute the new demand based on DR model Use the regresson model to compute the new wholesale electrcty prces END Fg.. flowchart llustratng the mplementaton process TABLE I: SELF AND CROSS ELASTICITIES Peak Off-Peak Low Peak -.1.16.1 Off-Peak.16 -.1.1 Low.1.1 -.1 others varables are added later on one at a tme to evaluate whether or not t mproves the out-of-sample forecastng error root mean square (FERMS). If the overall FERMS s acceptable, then the day-ahead prce forecastng could be performed. The resultant data could be fed nto the selected DR model n a software. In ths paper MATLAB s employed for ths purpose. DR model whch uses the day-ahead forecasted prces as a real tme prcng produces a new demand. For mplementng the DR model, the self- and cross- elastcty values of table I have been used [3-31]. Then
by usng the regresson model and applyng new demand, the updated prces could be acheved. V. CASE STUDY TABLE II: MULTIVARIALBE REGRESSION MODEL ** 1% SIGNIFICANT LEVEL, * 5% SIGNIFICANT LEVEL, + 1% SIGNIFICANT LEVEL Varable Parameter Estmate t-value Intercept -18.3786-1.81** Demand.483.66** Temperature.6756.63** Humdty -1.3893-7.** Month 9.66399 8.41** holday 7.3457 1.17 Saturday 9.345 3.53** Sunday 11.8146 4.33** hour1 15.866.65** hour 4.733 3.99** hour3 7.61 4.55** hour4 8.7496 4.64** hour5 8.4 4.67** hour6 4.956 4.** hour7 11.63418 1.93 + hour8.969. hour9-1.4514 -.5* hour1-3.1766-3.79** hour11-9.87756-4.8** hour1-3.459-5.14** hour13-34.8398-5.43** hour14-9.8674-4.57** hour15-35.55-5.3** hour16-8.775-4.34** hour17-3.7377-3.5** hour18-35.94987-5.45** hour19-45.16361-6.97** hour -39.38583-6.1** hour1-35.5788-5.67** hour -9.1475-4.73** hour3-15.38141 -.56* A. Descrpton The proposed approach s examned on the reported hourly data of New England ISO [3]. Ths ISO provdes the zonal nformaton for all ts servng areas ncludng the day-ahead prce, load forecastng, real locatonal margnal prce (LMP), load, Dry Bulb temperature and Dew Pont. For ths study, the data of summer 14 n Connectcut s used. The study has been done for one week (August 18th to 4th). Moreover, n ths case study, t s assumed that the customers had pad a flat rate of 3$/MWh for ths week before DR program. After DR program, the utlty charges the wholesale market LMP for each hour. B. Results and dscusson After applyng the proposed approach to the selected data and several teratons, varables n table II are selected as the most effcent varables for the forecastng purposes. Table II lsts the varables, ther parameter estmates (coeffcents) and ther t-value. Fg. 3. forecasted prce vs. real prce Fg. 4. Demand before and after DR program Fg. 5. spot market prce before and after DR program TABLE III: SUMMARY OF THE EFFECT OF DR ON THE SPOT MARKET PRICE Change n Energy -1358 MWh -.3 % Change n Cost -4,674,396 $ -6.3 % The parameter estmate could be nterpreted as the change n the predcted value of the dependent varable (prce) for one unt ncrease n the ndependent varable. Also, t-value s defned as a rato of the departure of an estmated parameter from ts notonal value and ts standard error. In table II, wth 31 degrees of freedom (number of varables and ntercept), t- values between 1.3 and 1.69 are sgnfcant wth 1% error. t- values between 1.69 and.45 are sgnfcant wth 5% error and t-values over.45 are sgnfcant wth 1% error. Therefore, from table II, t s understood that almost all of the varables are
sgnfcant wth 1% error. However, the selecton of some varables wth lower level of sgnfcance s necessary n terms of mprovng the out-of-sample analyss and FERMS. By usng the coeffcents of table II and comparng the results wth the real tme LMP, the forecastng error root mean square (FERMS) of electrcty prce for ths case study s computed as 11% whch s an acceptable error for volatle varable lke electrcty prce. Fg. 3 llustrates the forecastng prces and real tme LMP. The acheved forecasted prces are fed nto the selected DR model to produce the new demand. Fg. 4 shows the demand before and after applyng the demand response model. Fnally, the new demand s fed nto the regresson model to produce new prces. Fg. 5 shows the wholesale electrcty prce before and after applyng the DR model. As t s shown, the prce spkes are declned consderably. Based on the demand and prce before and after applyng DR model, the total pertnent cost of electrcty could be computed. Accordng to the calculaton, t s observed that the total demand s reduced by.3% and the total cost of electrcty for ths week s reduced by 6.3%. Table III summarzes the change n the wholesale electrcty cost. 6.3% change n the total cost stems from two major sources. Frst,.3% change n the total demand; second, a consderable shft of demand from expensve peak tme to lessexpensve off-peak perod of tme due to customer s exposure to the real tme prcng as dscussed earler. VI. CONCLUSION Ths paper studed the effect of demand response programs on the electrcty spot market prce. Demand response model was used to account for the customer reacton functon facng the real tme prcng. MLR model was employed to perform the prce forecastng n day-ahead market. Then, an algorthm comprsed of MLR and DR model was ntroduced to feed the outcome of DR model nto the spot market and explore the mpact of demand response program. 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