Modeling the Effects of Probabilistic Participation of Domestic and Industrial Customers in the Time-of-Use Pricing and Interruptible Load Programs

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1 International Journal of Science an ngineering Investigations vol. 6, issue 68, September 217 ISSN: Moeling the ffects of Probabilistic Participation of Domestic an Inustrial Customers in the Time-of-Use Pricing an Interruptible Loa Programs Mahi Samai 1, Mohamma smaeili Ra 2 1,2 Department of lectrical ngineering, Hakim Sabzevari University, Iran ( 1 ma.samai@hsu.ac.ir, 2 mohamma.es5153@gmail.com) Abstract-Nowaays, eman response programs have gaine importance ue to their purpose of improving the operation of power systems. Deman response programs are ivie into two main categories of incentive-base an price-base programs. The purpose of this paper is to moel an analyze two practical an substantial eman response programs that correspon to the two types of customers in the istribution system. In this regar, the interruptible loa program is intene for the inustrial customers an the time-of-use () pricing program is intene for the omestic customers. The interruptible loa program is a rewar-base program specific to peak hours; while the time-of-use pricing program is base on three price tariffs throughout the ay. An efficient moel base on the information of customer price elasticity is use to analyze the customers response. Moreover, the level of customers participation is taken into account in each program using two parameters; an the effects of their probabilistic participation are evaluate in three ifferent simulation cases. In orer to analyze the propose metho, a case stuy is consiere an the evaluation inices of the loa curve are calculate an analyze after executing the programs. The simulation results clearly inicate the efficiency of the propose metho. Keywors- Deman Response, Interruptible Loa, Time-of- Use Pricing, Loa Factor, Price lasticity : nergy changes (kwh) : Price changes (rial) nm:, Time perios : lasticity ( i, i ) : Self elasticity ( i, j ) : Cross elasticity SYMBOLS omestic : Initial omestic loa inustrial : Initial inustrial loa : Share of omestic loas from the total loa total : Total initial loa r : Loa consumption after the execution of each DR program : Participation factor of the omestic customer in the program IL : Participation factor of the inustrial customer in the IL program after _ DR : Total loa consumption after the execution of the two DR programs () i : Spot electricity price (rial/kwh) () i : Initial electricity price (rial/kwh) : Weight factor for rewar an penalty Ai (): The value of rewar (rial/kwh) pen () i : The value of penalty (rial/kwh) LF : Loa factor T : Stuie time perio I. INTRODUCTION Deman response program provies the basis of the customers active presence in improving the performance of the power system operation. These programs can provie the eman reuction require by the system in a relatively short time perio in critical conitions. Accoring to the efinition presente by the Feeral nergy Regulatory Commission (FRC) of the Unite States, eman response is the ability of the inustrial, commercial an resiential customers to improve the consumption pattern of electric energy in orer to achieve aequate prices an enhance system reliability. In other wors, eman response can be efine as the changes mae by customers in power consumption from their normal consumption pattern in response to the changes mae in the price of power over time [1]. In general, eman response occurs in one of two ways base on the state of the consumers participation: Price-base eman response programs Incentive-base eman response programs Fig. 1 plots the types of programs in each category. 89

2 Figure 2. The time-of-use () pricing program The operator gains benefit through the reuction of the peak loa an thus the heavy cost of prouction, an the guarantee reliability of the system. Moreover, the consumer gains benefit through the reuction of power consumption costs an especially the incentives offere by the inepenent system operator. In the following, some articles on the subject of eman response are briefly reviewe. In the references [3,4] have stuie the economic moel of the eman response program with the price sensitivity factors an the customer utility function. They have also moele an evaluate the program. Reference [5] has stuie responsive loas on the basis of price elasticity in orer to improve the reliability, reuce power fluctuations, reuce the cost an improve the loa curve. Figure 1. The categorization of eman response programs A. Time-of-Use () Pricing Progarm In program, the selling price of electric energy in each perio is epenent on the cost of prouction in that perio. Therefore, the prices are low in low-loa hours, meium in meium-loa hours, an high at the time of peak. xecuting this program leas the customers (specifically those who can transfer their loa) to aapt their consumption to the price an transfer the loa from peak hours to some other time, reucing the system s peak loa as a result. Accoring to Fig. 2, this tariff can be implemente in ifferent times of the ay, ifferent ays of the week, or ifferent ays of the year [2]. B. The Interruptible/Curtailable (I/C) Loa Program In this program, the consumer makes a contract with the power company, stating that they woul reuce or cut their consumption in case of accients. In this program, the customers are reware for reucing their consumption at the time of accient, an penalize if they on t o so [1]. Reference [2] has efine, categorize, implemente the costs an expresse the potential benefits of eman response. They have also simulate the eman response effect using a case stuy. xecuting the DR program has resulte in the improvement of reliability an the reuction of costs an power fluctuations. Reference [6] has propose an economic moel for eman response. This moel is base on price elasticity an etermines the amount of customer consumption to gain the maximum benefit in a 24-hour perio after participation in the DR program. It also prioritizes DR programs base on criteria such as improving the loa factor, reucing the peak, reucing the peak an off-peak interval an satisfying the customers. An analytic hierarchy process has been use in orer to choose the most effective DR program. Reference [7] has focuse on interruptible loas an capacity market programs which are incentive-base. In this article, penalties are set for customers participating in the interruptible/curtailable loa program if they on t reuce the loa. Then, the effect of the program on the loa curve is evaluate. The obtaine results inicate the effect of these programs on the loa shape an surface, customer utility an energy consumption reuction. Reference [8] has stuie responsive loas on the basis of price elasticity. Reference [9] has stuie the nonlinear economic moel of the eman response program which is base on the price elasticity of eman an the customer utility function in orer to extract ifferent mathematical moels for the program. International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September 217 9

3 The goal of this paper, is to stuy the economic moel of eman response programs using the price sensitivity factors of eman an the possible participation of omestic an inustrial customers, with regars to the moeling of the timeof-use () pricing an the interruptible/curtailable (I/C) programs. In section II, the economic moel of the propose metho is extracte an moele using the price sensitivity factors of eman an the utility function. Section III examines the loa curve of the stuie system an the effect of the fixe an possible participations of omestic an inustrial customers on the an I/C programs. After that, the simulation results are presente an analyze. Finally, the conclusions are articulate. II. TH CONOMIC MODL OF TH DMAND RSPONS PROGRAM Deman response programs are esigne to increase the customers sensitivity to market price changes. The sensitivity of the consumption amount to price is calle the price elasticity of eman, which is efine by the following matrix: n i ij i m m1 mj mn m For example, m an n are equivalent to 24 for one ay; so the elasticity matrix woul be a 2424 matrix. When the price of electric energy varies in ifferent perios, the loa (or eman) emonstrates two types of responses: a) Loas those are not able to transfer between ifferent perios an can only be on or off (such as lighting loas). This type of eman response to price is calle single-perio responsiveness an is evaluate through self-elasticity (the iagonal elements of the elasticity matrix). This factor is always negative; because as the price rises, the eman lowers in the same perio. b) Loas those are able to transfer between ifferent perios; which means that the consumption can transfer from peak hours to meium-loa or low-loa hours (such as air conitioning loas, electric water heater loas, etc.). This type of eman response to price is calle multiple-perio responsiveness an is evaluate through cross elasticity (the non-iagonal elements of the elasticity matrix). This factor is always positive; because as the price rises in a specific perio, the eman increases in other perios. In the following, the mathematical moels of the time-ofuse pricing an the interruptible/curtailable loa programs are presente an escribe using self an cross elasticities. In (2) an (3), it is assume that the omestic customers constitute a percentage of the total loa, an the inustrial customers make up the rest. The amounts of customer consumption after the execution of the an I/C programs (1) are obtaine from (4) an (5) respectively. In (5), is the weight factor of the rewar an penalty (accoring to customer welfare), which is use to increase the maximum benefit of the customers an the istribution company. r. omestic total (1 ). inustrial total omestic [ ( i) ( i)] 1 ( i, i ). ( i ) omestic.. 24 [ ( j) ( j)] ( i, j ). j 1 ( j ) j i i= 1,2,...,24 r inustrial inustrial.. IL i= 1,2,...,24 [ ( i) ( i) ( A( i) pen( i))] 1 ( i, i). IL () i 24 j j 1 i [ ( j) ( j) ( A( j) pen( j))] ( i, j). IL ( j) (2), (3) quation (6) an (7), it is assume that a percentage of the customers in each of the omestic an inustrial sections participate in the eman response program. The total loa consumption after the execution of the two programs is calculate through (8). (1 ) (6) omestic omestic omestic r (1 ) (7) inustrial inustrial inustrial IL r after _ DR omestic inustrial (8) In the following, the propose moels are execute on Iran s peak loa curve an the results are evaluate an analyze in terms of peak loa reuction, loa factor, percentage of the fixe an possible participation of customers, etc. A. Loa Factor In orer to evaluate the ifferent cases of DR programs an compare the response of the omestic an inustrial customers, the evaluation inex of loa factor (LF) is calculate for each case. Accoring to the efinition of evaluation inices, loa factor is the average loa to maximum loa ratio in a time perio; which is given by (9): (4) (5) International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September

4 1 24 LF T after _ DR ( ( t)) t 1 after _ DR max ( t) III. SIMULATION RSULTS A loa curve similar to the one in the reference [6] is use in orer to stuy an test the an I/C eman response programs. Accoring to Fig. 3, the three tariffs of the use program are as follows: low-loa from 1: to 9:, meium-loa from 1: to 19: an peak loa from 2: to 24:. Moreover, the amount of customer consumption after the execution of the I/C program can be calculate through (5). In this program, the customer s response epens on the price of power, the incentives an the penalty. Therefore, the eman can be obtaine in every perio by changing the price of power, the incentives an the penalty in each of the eman response programs. The tariff prices an the amount of rewar an penalty are in accorance with the reference [7]. (9) the results obtaine by the execution of the propose moel are analyze. In these simulations, the amounts of the omestic an inustrial loas are each assume to constitute 5% of the total loa of the system. The initial calculations inicate a loa factor of 83.36%, a valley-to-peak istance of 111 MW an a peak loa of 331 MW for the initial loa curve (). A. Analyzing Fixe Participation in The an I/C Programs Fig. 4 an Fig. 5 illustrate the initial loa curve an the obtaine loa curve after the execution of each of the an interruptible loa programs. Figure 4. ffect of the program on the initial loa Figure 3. Loa curve use in the simulations Accoring to the reference [7], the self an cross elasticities for the program are plotte in table I. However, the self an cross elasticities of the I/C program are consiere to be 2% higher than the program, ue to the ifference between the responses of omestic an inustrial customers. Figure 5. ffect of the I/C program on the initial loa TABL I. SLF AND CROSS LASTICITIS Low loa Meium loa Peak loa Low loa Meium loa Peak loa First, it is assume that 15% of the total omestic loas are participating in the program; while 5% of the total inustrial loas are participating in the I/C program. Then, participation in the programs is consiere to be probable; an After the execution of the program accoring to Fig. 4, the peak power consumption eman has ecrease from 331 MW to 334 MW in comparison with the initial case; an the loa factor has increase from 83.36% to 87.28% in comparison with the initial case. Moreover, Fig. 5 inicates that the peak power consumption eman has ecrease from 331 MW to 3217 MW after the execution of the I/C program; an the loa factor has increase from 83.36% to 84.36%. Fig. 6 illustrates the initial loa curve an the loa curve obtaine after the simultaneous execution of the an I/C programs. International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September

5 Loa Factor Loa Factor Power Consumption (MW) Fig. 8 an Fig. 9 illustrate the participation level/ peak power consumption an the participation level/ loa factor iagrams. Figure 6. The effect of an I/C programs execution After the simultaneous execution of the an I/C programs accoring to Fig. 6, the peak power consumption eman has ecrease from 331 MW to 357 MW in comparison with the initial case; an the loa factor has increase from 83.36% to 9.58%. Therefore, the simultaneous execution of the an I/C programs results in the maximum power eman reuction with respect to the peak ay. B. Analyzing Possible Participation in Deman Response Programs In the simulations conucte in this section, 3% of the total loa is consiere to be omestic, an the remaining 7% is consiere to be inustrial. 1) Possible Participation in The Program In this case, the percentage of participation in the interruptible loa program is consiere to be fixe an equivalent to 5%; however, the percentage of participation in the program is assume to have ranom values with a normal istribution aroun an average of 15%. The simulations are execute for 5 ranom samples an the results are presente an analyze in the following. Fig. 7 plots the values obtaine for the loa factor inex for all the implemente ranom samples. Accoring to the results, the average value is an the variance is.269. Participation in the Program Figure 8. Peak consumption as a function of possible participation in the program Participation in the Program Figure 9. Loa factor versus participation level in the program Accoring to Fig. 8, the amount of power consumption rises with the increase of participation in the program. In aition, Fig. 9 inicates that the loa factor inex also improves significantly with the increase of participation. 2) Possible Participation in The Interruptible Loa Program In this case, the percentage of participation in the program is consiere to be fixe an equivalent to 15%; however, the percentage of participation in the interruptible loa program is assume to have ranom values with a normal istribution aroun an average of 5%. The simulations are execute for 5 ranom samples an the results are presente an analyze in the following. Fig. 1 plots the changes of the loa factor for the ranom samples. Accoring to the results, the average value is an the variance is.73. Ranom Sample Figure 7. Loa factor for probabilistic participation in program International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September

6 Loa Factor Power Consumption (MW) Power Consumption (MW) Loa Factor Loa Factor Ranom Sample Figure 1. Loa factor for participation level in the IL program the loa factor inex falls. This is ue to the limite hours of eman response in the interruptible loa programs (high-loa hours only) an the nonlinear equation of the loa factor. 3) Combine Possible Participation in an Interruptible Deman Response Programs In this case, the percentages of participation in the interruptible loa an programs are assume to have ranom values with normal istributions aroun the average values of 5% an 15%, respectively. The simulations are execute for 5 ranom samples an the results are presente an analyze in the following. Fig. 13 plots the loa factor inex for the ranom samples. Accoring to the results, the average value is an the variance is.432. Fig. 11 an Fig. 12 illustrate the participation level/ peak power consumption an the participation level/ loa factor iagrams. Ranom Sample Figure 13. Loa factor in combine participation in the an IL programs Figure 11. Peak versus participation level in the IL program Fig. 14 an Fig. 15 illustrate the three-imensional iagrams regaring the level of participation in each program, the peak power consumption an the loa factor inex. It is evient that the loa factor improves significantly by consiering a combine possible participation in the an interruptible loa programs. Figure 12. Loa factor versus participation level in the IL program Participation in the Program It is evient that the amount of power consumption rises with the increase of participation in the IL program; however, Figure 14. Peak power consumption as a function of combine participation in the an IL programs International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September

7 Power Consumption (MW) fairly inicate the importance of the level of customer participation an the type of the execute program on the evaluation inices of the system. Figure 15. Loa factor as a function of combine participation in the an IL Programs IV. Participation in the Program CONCLUSION With the evelopment of smart gris an the application of eman response programs, the behavior of customers in power consumption changes has gaine importance. Deman response can have a significant role in the utilization of the power gri. In this paper, a moel is presente for eman response programs by taking into account the price elasticity matrix. Meanwhile, the effect of the fixe an possible participations of the omestic an inustrial customers is investigate on two types of eman response programs in orer to reuce the loa in peak hours an improve the loa factor of the system. The programs use in the paper are the an I/C programs which are intene for the omestic an inustrial customers respectively. The simulation results RFRNCS [1] F. Staff, Assessment of eman response an avance metering, Fe. nergy Regul. Comm. Docket AD-6-2-, 26. [2] M. H. Albai an. l-saaany, A summary of eman response in electricity markets, lectric power systems research, vol. 78, pp , 28. [3] H. A. Aalami, M. P. Moghaam, an G. R. Yousefi, valuating the execution of the country s program an proposing an optimal program using the DR moel, The 24th International Power Conference, 29. [4] S. M. Mirzaei, S. Haaipoor, Investigating loa response programs for Isfahan Power Distribution Company, CIRD Regional Conference, Tehran, Iran, January 13th & 14th, 213. [5] M. J. Iza Khasti, R. Keipoor, an H. Iza Khasti, The optimal programming of power loa response base on the economic moeling of the eman function with flexible elasticity in Iran, Journal of Iranian nergy conomics, 215. [6] H. A. Aalami, M. P. Moghaam, an G. R. Yousefi, Deman response moeling consiering interruptible/curtailable loas an capacity market programs, Appl. nergy, vol. 87, no. 1, pp , 21. [7] H. A. Aalami, M. P. Moghaam, an G. R. Yousefi, Moeling an prioritizing eman response programs in power markets, lectr. Power Syst. Res., vol. 8, no. 4, pp , 21. [8] P. T. Baboli, M. ghbal, M. P. Moghaam, an H. Aalami, Customer behavior base eman response moel, in Power an nergy Society General Meeting, 212 I, 212, pp [9] H. A. Aalami, M. P. Moghaam, an G. R. Yousefi, valuation of nonlinear moels for time-base rates eman response programs, Int. J. lectr. Power nergy Syst., vol. 65, pp , 215. International Journal of Science an ngineering Investigations, Volume 6, Issue 68, September