Incentive‐based RTP model for balanced and cost‐effective smart grid
2018; Institution of Engineering and Technology; Volume: 12; Issue: 19 Linguagem: Inglês
10.1049/iet-gtd.2018.5916
ISSN1751-8695
Autores Tópico(s)Microgrid Control and Optimization
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 19 p. 4327-4333 Research ArticleFree Access Incentive-based RTP model for balanced and cost-effective smart grid Hyesung Seok, Corresponding Author Hyesung Seok hseok@hongik.ac.kr Department of Industrial Engineering, Hongik University, 72-1 Mapo-Gu, Sangsu-Dong, Seoul, 121-791 Republic of KoreaSearch for more papers by this authorSang Phil Kim, Sang Phil Kim Department of Business Administration, Winona State University, Winona, MN, 55987 USASearch for more papers by this author Hyesung Seok, Corresponding Author Hyesung Seok hseok@hongik.ac.kr Department of Industrial Engineering, Hongik University, 72-1 Mapo-Gu, Sangsu-Dong, Seoul, 121-791 Republic of KoreaSearch for more papers by this authorSang Phil Kim, Sang Phil Kim Department of Business Administration, Winona State University, Winona, MN, 55987 USASearch for more papers by this author First published: 19 September 2018 https://doi.org/10.1049/iet-gtd.2018.5916AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The authors propose an intelligent real-time pricing (RTP)-based energy consumption scheduling model, which is especially applicable to more active and balanced demand management in a smart grid. Most previous research studies have not considered the incentive for subscribers who are more likely to move their consumption schedule to the off-peak period. Therefore, they considered the degree of the sacrifice made by each subscriber to determine an individualised price. As a result, the electricity unit price charged to each subscriber is different. An appropriate incentive coefficient is identified using a genetic algorithm and applied to the RTP model. This approach draws more active rescheduling of the energy consumption and enhances the fairness of a network. Compared with non-scheduling and day-ahead scheduling, the authors algorithm reduces the subscribers' total cost by an average of 24.9 and 15.9%, and increases the corresponding average fairness of the network by 16.7 and 5.4%, respectively. Moreover, they achieved a significant reduction in the peak-to-average-ratio. Nomenclature Notation N set of subscriber A set of schedulable appliances T set of (discrete) time slots i subscriber i ( k appliance k t time slot t operation duration of appliance k of subscriber i power usage (kW) of appliance k of subscriber i during power consumption of appliance k of subscriber i in time slot t delay cost of appliance k of subscriber i per time slot initial requested starting time of appliance k of subscriber i starting time of appliance k of subscriber i, subscriber's decision maximum allowable delay of appliance k of subscriber i total delay cost of subscriber i ap average delay cost of subscribers degree of sacrifice of subscriber i planned supply for time slot t actual consumption for time slot t wholesale price coefficient mismatch cost coefficient retail price coefficient, service provider's decision variable () set of , , where coefficient of based on , , and incentive coefficient (, decision variable of genetic algorithm (GA) wholesale price per unit electricity in time slot t additional price due to the gap between planned supply and actual consumption in time slot t comparable constant price gap in an alternate fixed rate pricing scheme individualised of subscriber i retail price of subscriber i in time slot t retail price vector of subscriber i, subscribers' total cost with an incentive mechanism subscribers' total cost without incentive mechanism Fit fitness value (objective function in the GA model) ratio of mismatch cost coefficient to wholesale price coefficient ratio of a price gap to wholesale price coefficient ratio of delay cost to average delay cost NI number of in-sample scenarios NO number of out-of-sample scenarios 1 Introduction High peak-to-average ratio (PAR) because of uncontrolled and unpredictable energy consumption has been a chronic problem in power grids. Especially during summer and winter, both residential and commercial power demands significantly increased. Several peaker plants are established and conditionally operated to avoid the blackout and cascading series of disruptions in a nation's banking, communication, traffic, and human security systems [1]. These plants are idle for most of the year and only generate electricity when necessary – when the power supply from general plants is not sufficient to cover the increasing demand. The unit price for electricity from peaker plants is relatively higher and their efficiency is very low, e.g. only 5% or less of the hours per year. In such a situation, demand management by using a smart grid can be a good solution. The smart grid consists of millions of components: meters, controllers, computers, power lines, and communication equipment [2]. Each participant of a network, such as a generator, service provider, and subscribers, has its control and communication tool called the energy management controller (EMC) and can act independently and self-interested. Smart grid makes it possible to anticipate the subscriber's consumption and the electricity unit price through real-time communication among the participants. Based on the shared information, each subscriber can decide a more cost-effective energy consumption schedule, and the service provider can choose the appropriate price to maximise his profit [3]. In this study, we have proposed an innovative distributed decision-making model for service providers and subscribers, which enhance the energy balance and effectiveness of the smart grid. Many studies on the energy distribution in a power grid have been conducted using various approaches [4–7]. However, we have proposed an innovative real-time pricing (RTP) model, which can differentiate between the ideal electricity unit prices for each subscriber. Predicted prices only based on historical price information have been firstly used [8]. However, since the consumption can be estimated in real-time due to the development of technology, the electricity unit price has been decided based on the planned supply load and actual consumption load in a lot of previous research. It means that the electricity unit price per time slot was only decided by the total amount of usage in its corresponding time slot, regardless of the subscriber's degree of sacrifice based on the shifting of consumption to off-peak hours. Hence, in our model, we have considered an incentive based on the subscriber's degree of sacrifice. Depending on it, the electricity unit price charged to the subscriber would be individually decided. This incentive-based RTP model can reduce the PAR and the cost borne by the subscribers, and increases the fairness of the network. The remainder of the paper is organised as follows. The background of the proposed study is presented in Section 2, and the mechanism of incentive-based RTP model and its detailed procedure are described in Section 3. The performance of our model is empirically demonstrated in Section 4, and the conclusion and necessary future work are discussed in Section 5. 2 Background and motivation 2.1 Centralised RTP model The day-ahead optimisation has been used in power grids to mitigate the risk of price volatility and manage the supply and demand [9]. Moreover, load forecasting has been frequently studied [10, 11]. In the case of day-ahead pricing, the electricity unit price in each time slot is set by the supply-side in a day-ahead market clearing process [12, 13]. This is a significant drawback. First, a centralised decision-making unit is hard to operate with a large number of subscribers. Second, it is risky to provide a centralised unit with a subscriber's private information. Third, it is unreasonable for each subscriber to adhere to the given consumption schedule even under unpredicted consumption/price fluctuations. 2.2 Distributed RTP model Distributed energy consumption models have been formulated to consider all aspects of the participants. Many studies have developed distributed energy consumption models by applying the concept of game theory because the interests of subscribers and service providers have naturally conflicted with each other. Some studies have found Nash equilibrium (NE) in Cournot competition among subscribers, and Stackelberg game between a service provider and its subscribers [14–16]. Atzeni et al. designed a day-ahead optimisation as a non-cooperative Nash game to consider the storage facility available at each subscriber location. They simplified the price function to obtain equilibrium. Mohsenian-Rad et al. have also proposed a distributed algorithm derived from a game-theoretic analysis; the objective function and constraints are limited to allow the determination of the NE [8]. Chen et al. have developed an innovative model based on the Stackelberg game, which focuses on the equilibrium between each subscriber and the service provider [15]. Hobbs and Pang have regarded the consumption scheduling game among subscribers as a Cournot game and proposed equilibrium of scheduling game [17]. It is difficult to find the NE in such a way because the actual electricity pricing and consumption functions are complex and non-differential/non-concave. Furthermore, the existence of a pure and unique NE is not guaranteed in most cases, and it entails a high-computational time [18]. Hence, most previous models based on the game theory have simplified the problem under specific conditions, as mentioned above, to use the explicit form of NE and analytically find the NE [8, 19]. Alternatively, a heuristic NE by using various methods such as genetic algorithm (GA), approximation, or an iterative process has been presented [18, 20, 21]. In our paper, we have developed a distributed RTP model by regarding the relationship between each subscriber and provider as an independent Stackelberg game and established a heuristic NE by using backward induction. Many previous studies have developed a Stackelberg game-based model consisting of a service provider (leader) and subscribers (followers) [15, 22–25]. In such models, a service provider decides the retail price and subscribers decide an optimal consumption schedule to minimise the total costs. However, they have not considered an incentive according to the level of sacrifice of each subscriber due to consumption rescheduling. In addition, they have simplified a model to find an analytical NE, but it is difficult to apply it to an actual case due to the lack of practicability of the approach. In addition, our model conducts an appliance-based scheduling and considers the delay cost due to the consumption rescheduling. These settings address the lack of practicability of previous studies. Most previous research studies have proposed a time-slot-based scheduling regardless of the continuous usage of specific appliances [26, 27], and the delay cost due to the consumption rescheduling has not been considered. The consumption usage is instead decided to optimise the subscriber's utility, but they have not sufficiently considered the individual energy usage demand [3]. Moreover, most previous research studies have simplified the operations of the service provider [28]. In our model, the objective function of the service provider becomes more realistic by considering the sales profit and mismatch cost. 2.3 Individualised RTP model To the best of our knowledge, an individually varying unit pricing of electricity based on the price-sensitivity/degree of sacrifice of each subscriber has not yet been studied. Usually, the electricity unit price is the same for all subscribers. With the price information, some subscribers are more likely to shift their consumption to the off-peak period; other subscribers, who are relatively price-insensitive, tend to retain their preferred consumption schedule. Hence, the utility function of each subscriber (price-sensitivity) significantly affected the result. In such a case, a price-insensitive (less degree of sacrifice) subscriber has an advantage when compared with a price-sensitive subscriber, who reschedules his/her consumption according to the price. Borenstein et al. have discussed the importance of the redistribution of electricity pricing for such low-income population, i.e. price-sensitive subscribers [29]. However, a reward/penalty mechanism has not been considered. Our incentive-based RTP model can achieve more balanced and fairer distributions of usage and cost. More details will be provided in Section 3. 3 Methodology We consider a residential power system consisting of a service provider and residential subscribers. The service provider buys electricity from the wholesale market and sells to the subscribers. The energy consumption schedule of each subscriber is decided by a controller (EMC) through communication with the service provider, who supplies electricity according to the determined schedule of the subscriber. There are n subscribers (). Each subscriber has m appliances (). We consider their energy consumption schedule during h time slots (). We have not considered the reducible energy consumption. We have referred to (1), (2), (3), and (7) in the previous RTP-based model by Chen et al. [15]. The retail price, , by a service provider is the sum of the wholesale price, , and the price gap, (8). The wholesale price influences the EMC scheduling so that the peak load is reduced while the price gap decreases. The wholesale price, , is defined as in (1) by referring to [15]. The price gap, , is designed to influence the difference between the actual demand, , and the planned supply, . Referring to [15] is designed to be proportional to , and it decreases with minus , i.e. the larger the value of minus , the lower the price gap, , so that the EMC is more willing to schedule the appliance to operate during this period, and vice versa. If an appliance requests to start at time slot , is calculated by (3). We set as in (2) and as in (3) by referring to [15] (1) (2) (3) (4) We have partially revised the price function to make it continuous and modified the method of computing the electricity unit cost per individual using (5)–(7). The electricity unit cost would vary between customers depending on the degree of shift in consumption of each subscriber, which we call the 'degree of sacrifice'. This value can be calculated by comparing the delay cost of each subscriber with the average delay cost of the subscribers using (5) and (6). An individualised retail price of each subscriber is determined based on the degree of sacrifice with coefficient (7) (5) (6) (7) (8) A decision-making model of each subscriber and provider is formulated using the Stackelberg game (Fig. 1a) [5, 22–25]. A service provider plays the role of a 'leader' and subscribers play the role of 'followers' according to the retail price determined by the service provider. The objective of the service provider is to find to maximise his profit (10). The purpose of each subscriber is to find to minimise his total cost. Our model is a distributed model; a service provider and each subscriber decide an optimal and , respectively, and update and through two-way communication. In such a Stackelberg game, we find an appropriate incentive coefficient, , to minimise the subscriber's total cost using GA (9). The detailed mechanism is described in Section 3.3. The lowest value of fit is zero, i.e. there is no improvement by incentive (9) Fig. 1Open in figure viewerPowerPoint Incentive-based RTP model (a) Stackelberg game between a subscriber and a service provider, (b) In-sample and out-of-sample analyses 3.1 Service provider's aspect The objective function of a service provider is described in (10) [15]. The service provider solves (10) and updates after receiving the request from a subscriber. The second term in (10) is the additional operation cost due to the mismatch between the planned supply and the actual consumption. This process can be solved by backward induction [15, 20]. To avoid a high-computational time, we use the set of feasible discrete , (10) 3.2 Subscriber's aspect Each subscriber solves the problem in (11) and informs the value of to the service provider [15]. Next, the service provider updates by using (10), and sends the updated price information back to the subscriber. Finally, the subscriber solves (11) again and updates accordingly (Fig. 1a) (11) 3.3 Incentive-based RTP model Our incentive-based RTP model consists of in-sample and out-of sample scenarios. In each in-sample scenario, the subscriber's initial setting is different, and the best incentive coefficient , which minimises the subscribers' total cost, i.e. maximises the fitness value (9), is obtained with GA. Then, the average of the in-sample scenarios is applied to the out-of-sample scenario to validate the average decrease in the subscribers' total cost by the incentive-based mechanism (Fig. 1b). The in-sample scenario works in chronological order. First, we consider the consumption scheduling without the incentive . For each scenario, in time slot t, if any is equal to t, the subscriber i starts the procedure. Subscriber i finds based on the current price information and consumption schedule, and (11), updates , and notifies all the values to the service provider. The service provider then updates (10) and the price information. Next, the service provider notifies the subscriber i. Based on the updated information, the subscriber i finalises , updates (11), and notifies the values to the service provider again. The service provider also finalises (10) and updates the price information. Then, the decision-making process moves to the next subscriber j whose is equal to t. If there is no subscriber with the current starting time equal to t, the algorithm moves to the time slot . The procedure is repeated until . As a result, the consumption schedules of all subscribers are determined, i.e. the NE in a Stackelberg game, and the subscribers' total cost (in case of no incentive, ) is calculated. Second, we consider the consumption scheduling with incentive . The GA searches for an appropriate value of incentive coefficient, , which makes the subscribers' total cost as low as possible under the same scenario. In other words, the GA tries to minimise its fitness value (9) by updating . When is updated, the corresponding subscribers' total cost is newly calculated and compared with the previous one. Through such a procedure, the GA continuously updates until the exit condition (stopping condition) is reached. [We used a 'GA' function in MATLAB with settings: (i) initial population is randomly created by 'gacreationuniform' function with a uniform distribution. The uniform distribution is in [0, 144] and population size is 200, (ii) crossover, selection and mutation functions are 'crossoverscattered', 'selectionstochunif', and 'mutationuniform' (mutation rate: 0.01) respectively, and (iii) exit (stopping) conditions are MaxGenerations = 50, MaxStallGenerations = 50, MaxStallTime = Inf, and TolFun = {1×10−6}. The rest of the options were set to their default values in [30]. The improvement of the performance of the GA is beyond the scope of our study.] After all the scenarios are processed in the in-sample scenario, the average value of is calculated and applied to the new scenarios in the out-of-sample analysis. Then, the average and the decrease in PAR are finally calculated. These are the effective performance indicators of our incentive mechanism. 4 Simulation results Appliances have an on-peak period from 5:00 PM to 8:00 PM. We have referred to the settings in Chen et al. [15]. We obtained of 20 in-sample scenarios through experiments and applied their average value to 100 new scenarios (Figs. 1 and 2), i.e. NI = 20, NO = 100. We compared four scheduling models: (i) non-scheduling (M1), (ii) day-ahead scheduling (M2), (iii) revised Chen's RTP model (M3), and (iv) incentive-based RTP model (M4). [The original model by Chen et al. charges a subscriber the ex-ante cost, which is assumed and used in decision-making. This charges a different electricity unit price to subscribers even in the same time slot. The revised model charges a subscriber the actual cost. In this case, the electricity unit price is common to all subscribers in the same time slot.] The number of subscribers in the simulation is 80, and each consumer has three schedulable appliances (referring to the setting in [15]). Depending on the appliance type, , , , and are given as described in Table 1. We assume that has an exponential distribution with a mean of . Since the effects of heterogeneous factors are complicated and cannot be considered in the validation of the performance of our model, we have assumed the homogeneity of subscribers only with respect to the delay cost , power usage (kW) , mean operation duration , and maximum allowable delay . [15], i.e. , , , and . Table 1. Parameter setting II Appliance type , kW , $/h , h , h 1 1.8 6 0.10 3.0 2 3.4 4 0.25 1.0 3 0.4 2 0.40 0.5 An initial requested starting time of appliance is randomly set based on the data from Chen et al. [15] by considering historical peak and off-peak periods. Each time slot is 10 min; h is 144 (24 h). Other price/cost related parameters are listed in Table 2. These data are from [15] and partially updated based on the 2015 electricity report [31]. To validate the performance of our model, 100 replications were simulated, and the average values of each measure were recorded, e.g. TC, energy consumption, and standard deviation of the subscriber's cost. The simulation experiments have been coded with MATLAB using the parameter settings shown in Tables 1 and 2. [When , the average unit delay cost is approximately four times larger than the unit wholesale cost. When , the unit mismatch cost is approximately half of the unit wholesale cost. When , the unit price gap is approximately half of the unit wholesale cost.] Table 2. Parameter setting III Parameter Value 5.6 × 10−4 1 0.5 20 Four types of scheduling models have been analysed with variable delay cost , mismatch cost (β), and price gap . These variable costs are expressed as the ratio of the wholesale price (α), as shown in Table 2. The experimental results are illustrated in Sections 4.1–4.4. 4.1 Performance of incentive-based RTP model As shown in Fig. 2, the rescheduled consumptions by M3 and M4 are more flattened than that of M1 and M2. Since M3 and M4 use the real-time consumption and price information, a rebound peak such as in the case of M2 does not occur. Instead, the consumption patterns become similar to the planned supply load. Especially, M4 has a lower standard deviation of consumption, which is an average of 28.2% in contrast to M1 (Table 3). Fig. 2Open in figure viewerPowerPoint Comparison of electricity consumption Table 3. Standard deviation of performance Model Standard deviation of consumption (within a day), kWh Standard deviation of subscriber's cost, $ M1 28.5 1.78 M2 24.3 1.57 M3 21.1 1.75 M4 20.5 1.48 Besides, M4 reduces the PAR by an average of 34.3% in contrast to M1 (PAR of M1, M2, M3, and M4 are 3.46, 3.11, 2.30, and 2.27, respectively). It seems that the different fares of each subscriber based on his (intentional) degree of sacrifice draws a more balanced and active redistribution of electricity consumption. In this way, our model can remedy the problem of high PAR in current electricity markets, thereby enhancing the efficiency and reliability of power plants. M4 significantly lessened the subscriber's load compared with other models. In contrast to M1, M2, M3, and M4 reduce the subscribers' total cost by an average of 10.6, 8.7, and 24.9%, respectively (Fig. 3). These three models reduce the wholesale price by avoiding the peak time consumption, and partially reduced the price gap cost by flattening the consumption fluctuation. M4 especially reduced the price gap cost by 71.1% when compared with that of M1. Furthermore, M4 enhances the fairness in pricing among subscribers with the smallest standard deviation of the subscriber's cost (Table 3). Therefore, our incentive-based RTP model can be preferably established in power systems because it considers the interest of the subscriber along with that of the provider. Fig. 3Open in figure viewerPowerPoint Comparison of subscribers' cost 4.2 Performance of incentive-based RTP model under variable delay cost The performance of the incentive-based RTP model is analysed to examine the sensitivity to the delay cost . The rest of the simulation parameters are the same as in Tables 1 and 2. Results of this simulation are summarised in Figs. 4–6. Fig. 4Open in figure viewerPowerPoint Comparison of subscribers' cost under variable delay cost – four bars in the same represent M1, M2, M3, and M4 Fig. 5Open in figure viewerPowerPoint Comparison of the standard deviation of consumption (thin a day) under variable (a) Delay cost , (b) Mismatch cost , and (c) Price gap – four bars in the same , , and represent M1, M2, M3, and M4 Fig. 6Open in figure viewerPowerPoint Standard deviation of subscriber's cost under (a) Delay cost , (b) Mismatch cost , and (c) Price gap – four bars in the same , , and represent M1, M2, M3, and M4 As shown in Fig. 4, the subscriber's total cost generally increased as becomes large in case of M3 and M4. This is a natural occurrence. High delay cost interrupts the consumption rescheduling; therefore, it aggravates the efficiency of energy usage and increases the subscribers' total cost. However, M4 still achieves the least subscribers' cost except under the excessive delay cost condition . Most home appliances are included in this range except for few appliances, which are restricted from being rescheduled, e.g. refrigerator and heater. The incentive mechanism by M4 enables the subscribers to reschedule their consumptions more actively and to obtain rewards from it. On the other hand, the subscribers' cost in M3 grows quickly as increases. In addition, as shown in Fig. 5a, M4 always achieves the least standard deviation of consumption with a stable pattern. It shows that our proposed model can improve the high PAR problem of power plants regardless of the different delay costs of appliances. The standard deviation of the subscriber's cost tends to increase as becomes large in the case of M3 and M4 (Fig. 6a). However, M4 results in the smallest standard deviation of the subscriber's cost, i.e. the most balanced distribution of the subscriber's cost when . Electricity storage systems will be considered in future studies to deal with the fairness of pricing offered to subscribers over a broader range of . 4.3 Performance of incentive-based RTP model under variable mismatch cost (β) It seems that there is no significant effect of mismatch cost on the performances of M3 and M4. Naturally, when is quite large , the subscribers' costs in M3 and M4 tend to increase. It is because the service provider prefers to choose higher to avoid a negative profit. M4 always outperforms other models. The subscribers' cost by M4 is on average 23.5, 13.7, and 17.8% lesser than that of M1, M2, and M3, respectively (Fig. 7). M4 also achieves the evenest distribution of consumption with the smallest standard deviation (Fig. 5b). The pricing in M4 is mostly more fair than in other models, as shown in Fig. 6b ; the only exception to this is when the mismatch cost is very excessive . It is because the service provider tends to choose a higher to deal with high-mismatch cost. Hence, the gaps between the costs of the subscribers become large under M3 and M4. Fig. 7Open in figure viewerPowerPoint Comparison of subscribers' cost under variable mismatch cost – four bars in the same represent M1, M2, M3, and M4 4.4 Performance of incentive-based RTP model under variable price gap As increases, the subscribers' cost and its standard deviation naturally increase except for M2. However, M4 prevents the subscribers' cost from quickly increasing by employing dynamic and balanced rescheduling. Therefore, M4 achieves the smallest subscribers' cost (Fig. 8). The subscribers' cost in M4 is on average, 38.7%, 35.0%, and 26.8% less than that of M1, M2, and M3, respectively. Furthermore, M4 draws the smallest deviation of consumption (Fig. 5c) and maintains a relatively small standard deviation of the subscriber's cost within a reasonable range of price gap, (Fig. 6c). Fig. 8Open in figure viewerPowerPoint Comparison of subscribers' cost under variable price gap – four bars in the same represent M1, M2, M3, and M4 In summary, our incentive-based RTP model outperforms other models by decreasing the subscribers' cost, flattening consumption fluctuation, and increasing the fairness of pricing offered to subscribers within a reasonable range of price gap. 5 Conclusion and future work In this study, we have developed an incentive-based RTP model, which draws an active and balanced rescheduling of energy consumption to achieve a more cost-effective and fairer smart grid. A numerical example shows the behaviour and performance of the incentive-based RTP model under variable conditions. As a result, our model achieves a decrease in the subscribers' total cost, consumption fluctuation, and standard deviation of the subscriber's cost under variable delay cost, mismatch cost, and price gap. These observations imply that the incentive-based RTP model can help current power systems to be more sustainable and cost-effective. Future research will be continued with more realistic assumptions and approaches: (i) the performance of the service provider will be analysed, (ii) heterogeneous characteristics of the subscribers will be considered, and (iii) other heuristic methods will be considered to find more efficiently and accurately in complicated condition. Especially in the case of (ii), the degree of flexibility of the subscribers will be classified and analysed based on two factors: (i) variable delay cost and (ii) variable maximum allowable delay . In practice, the performance of our model will vary depending on the actual distribution of the subscriber group shown in Table 4. In addition, various factors such as the supplier's price policy, subscriber's specific consumption pattern, and other external features can affect the performance and complicate the interaction between the provider and the subscriber. Table 4. Classification of heterogeneous subscribers maximum allowable delay Delay cost Low Medium High low √ √ √ medium √ √ √ high √ √ √ 6 Acknowledgments This work was supported by the National Research Foundation of Korea (NRF), with a grant funded by the Korean government (MSIT) (No. 2016R1C1B1015974). 7 References 1Varaiya, P.P., Wu, F.F., Bialek, J.W.: 'Smart operation of smart grid: risk-limiting dispatch', Proc. IEEE, 2011, 99, (1), pp. 40– 57 2Samadi, P., Mohsenian-Rad, A.H., Schober, R. et al.: 'Optimal real-time pricing algorithm based on utility maximization for smart grid'. IEEE Int. Conf. on Smart Grid Communications, Gaithersburg, MD, USA, October 2010, pp. 415– 420 3Samadi, P., Mohsenian-Rad, H., Schober, R. et al.: 'Advanced demand side management for the future smart grid using mechanism design', IEEE Trans. Smart Grid, 2012, 3, (3), pp. 1170– 1180 4Aghaei, J., Alizadeh, M.I.: 'Critical peak pricing with load control demand response program in unit commitment problem', IET Gener. Transm. Distrib., 2013, 7, (7), pp. 681– 690 5Di Silvestre, M.L., Graditi, G., Sanseverino, E.R.: 'A generalized framework for optimal sizing of distributed energy resources in micro-grids using an indicator-based swarm approach', IEEE Trans. Ind. Inf., 2014, 10, (1), pp. 152– 162 6Graditi, G., Di Silvestre, M.L., Gallea, R. et al.: 'Heuristic-based shiftable loads optimal management in smart micro-grids', IEEE Trans. Ind. Inf., 2015, 11, (1), pp. 271– 280 7Labeeuw, W., Deconinck, G.: 'Residential electrical load model based on mixture model clustering and Markov models', IEEE Trans. Ind. Inf., 2013, 9, (3), pp. 1561– 1569 8Mohsenian-Rad, A.H., Wong, V.W., Jatskevich, J. et al.: 'Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid', IEEE Trans. Smart Grid, 2010, 1, (3), pp. 320– 331 9Joe-Wong, C., Sen, S., Ha, S. et al.: 'Optimized day-ahead pricing for smart grids with device-specific scheduling flexibility', IEEE J. Sel. Areas Commun., 2012, 30, (6), pp. 1075– 1085 10Fernandes, R.A.S., da Silva, I.N., Oleskovicz, M.: 'Load profile identification interface for consumer online monitoring purposes in smart grids', IEEE Trans. Ind. Inf., 2013, 9, (3), pp. 1507– 1517 11Khosravi, A., Nahavandi, S.: 'Load forecasting using interval type-2fuzzy logic systems: optimal type reduction. IEEE Trans. Ind. Inf., 2014, 10, (2), pp. 1055– 1063 12Bompard, E., Ciwei, G., Napoli, R. et al.: 'Dynamic price forecast in a competitive electricity market', IET Gener. Transm. Distrib., 2007, 1, (5), pp. 776– 783 13Chow, J.H., De Mello, R.W., Cheung, K.W.: 'Electricity market design: an integrated approach to reliability assurance', Proc. IEEE, 2005, 93, (11), pp. 1956– 1969 14Atzeni, I., Ordóñez, L.G., Scutari, G. et al.: 'Demand-side management via distributed energy generation and storage optimization', IEEE Trans. Smart Grid, 2013, 4, (2), pp. 866– 876 15Chen, C., Kishore, S., Snyder, L.V.: 'An innovative RTP-based residential power scheduling scheme for smart grids'. Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 2011, pp. 5956– 5959 16Maharjan, S., Zhu, Q., Zhang, Y. et al.: 'Dependable demand response management in the smart grid: a Stackelberg game approach', IEEE Trans. Smart Grid, 2013, 4, (1), pp. 120– 132 17Hobbs, B.F., Pang, J.S.: 'Nash-Cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints', Oper. Res., 2007, 55, (1), pp. 113– 127 18Yang, Y., Zhang, Y., Li, F. et al.: 'Computing all Nash equilibria of multiplayer games in electricity markets by solving polynomial equations', IEEE Trans. Power Syst., 2012, 27, (1), pp. 81– 91 19Ibars, C., Navarro, M., Giupponi, L.: 'Distributed demand management in smart grid with a congestion game'. IEEE Int. Conf. on Smart grid Communications, Gaithersburg, MD, USA, October 2010, pp. 495– 500 20Fudenberg, D., Tirole, J.: ' Game theory' ( MIT Press, Cambridge, MA, USA, 1991) 21Liu, B.: 'Stackelberg-Nash equilibrium for multilevel programming with multiple followers using genetic algorithms', Comput. Math. Appl., 1998, 36, (7), pp. 79– 789 22Chen, J., Yang, B., Guan, X.: 'Optimal demand response scheduling with Stackelberg game approach under load uncertainty for smart grid'. 2012 IEEE Third Int. Conf. on Smart Grid Communications (SmartGridComm), 2012, November, pp. 546– 551 23Meng, F.L., Zeng, X.J.: 'A Stackelberg game-theoretic approach to optimal real-time pricing for the smart grid', Soft Comput., 2013, 17, (12), pp. 2365– 2380 24Tushar, W., Chai, B., Yuen, C. et al.: 'Three-party energy management with distributed energy resources in smart grid', IEEE Trans. Ind. Electron., 2015, 62, (4), pp. 2487– 2498 25Wei, W., Liu, F., Mei, S.: 'Energy pricing and dispatch for smart grid retailers under demand response and market price uncertainty', IEEE Trans. Smart Grid, 2015, 6, (3), pp. 1364– 1374 26Gatsis, N., Giannakis, G.B.: 'Cooperative multi-residence demand response scheduling'. 2011 45th Annual Conf. Information Sciences and Systems (CISS), Baltimore, MD, USA, March 2011, pp. 1– 6 27Gkatzikis, L., Koutsopoulos, I., Salonidis, T.: 'The role of aggregators in smart grid demand response markets. IEEE J. Sel. Areas Commun., 2013, 31, (7), pp. 1247– 1257 28Li, N., Chen, L., Low, S.H.: 'Optimal demand response based on utility maximization in power networks'. Power and Energy Society General Meeting, 2011, Detroit, MI, USA, July 2011, pp. 1– 8 29Borenstein, S., Jaske, M., Rosenfeld, A.: ' Dynamic pricing, advanced metering, and demand response in electricity markets' ( University of California, Berkeley, CA, USA, 2002) 30Available at https://kr.mathworks.com/help/gads/gaoptimset.html 31Available at https://www.eia.gov/electricity/monthly Volume12, Issue19October 2018Pages 4327-4333 FiguresReferencesRelatedInformation
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